isl_local_space.c

   1 /*
   2  * Copyright 2011      INRIA Saclay
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #include <isl_ctx_private.h>
  12 #include <isl_map_private.h>
  13 #include <isl_local_space_private.h>
  14 #include <isl_space_private.h>
  15 #include <isl_mat_private.h>
  16 #include <isl/seq.h>
  17
  18 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  19 {
  20         return ls ? ls->dim->ctx : NULL;
  21 }
  22
  23 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  24         __isl_take isl_mat *div)
  25 {
  26         isl_ctx *ctx;
  27         isl_local_space *ls = NULL;
  28
  29         if (!dim)
  30                 goto error;
  31
  32         ctx = isl_space_get_ctx(dim);
  33         ls = isl_calloc_type(ctx, struct isl_local_space);
  34         if (!ls)
  35                 goto error;
  36
  37         ls->ref = 1;
  38         ls->dim = dim;
  39         ls->div = div;
  40
  41         return ls;
  42 error:
  43         isl_space_free(dim);
  44         isl_local_space_free(ls);
  45         return NULL;
  46 }
  47
  48 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  49         unsigned n_div)
  50 {
  51         isl_ctx *ctx;
  52         isl_mat *div;
  53         unsigned total;
  54
  55         if (!dim)
  56                 return NULL;
  57
  58         total = isl_space_dim(dim, isl_dim_all);
  59
  60         ctx = isl_space_get_ctx(dim);
  61         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  62         return isl_local_space_alloc_div(dim, div);
  63 }
  64
  65 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  66 {
  67         return isl_local_space_alloc(dim, 0);
  68 }
  69
  70 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  71 {
  72         if (!ls)
  73                 return NULL;
  74
  75         ls->ref++;
  76         return ls;
  77 }
  78
  79 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  80 {
  81         if (!ls)
  82                 return NULL;
  83
  84         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  85                                          isl_mat_copy(ls->div));
  86
  87 }
  88
  89 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  90 {
  91         if (!ls)
  92                 return NULL;
  93
  94         if (ls->ref == 1)
  95                 return ls;
  96         ls->ref--;
  97         return isl_local_space_dup(ls);
  98 }
  99
 100 void *isl_local_space_free(__isl_take isl_local_space *ls)
 101 {
 102         if (!ls)
 103                 return NULL;
 104
 105         if (--ls->ref > 0)
 106                 return NULL;
 107
 108         isl_space_free(ls->dim);
 109         isl_mat_free(ls->div);
 110
 111         free(ls);
 112
 113         return NULL;
 114 }
 115
 116 /* Is the local space that of a set?
 117  */
 118 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 119 {
 120         return ls ? isl_space_is_set(ls->dim) : -1;
 121 }
 122
 123 /* Return true if the two local spaces are identical, with identical
 124  * expressions for the integer divisions.
 125  */
 126 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 127         __isl_keep isl_local_space *ls2)
 128 {
 129         int equal;
 130
 131         if (!ls1 || !ls2)
 132                 return -1;
 133
 134         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 135         if (equal < 0 || !equal)
 136                 return equal;
 137
 138         if (!isl_local_space_divs_known(ls1))
 139                 return 0;
 140         if (!isl_local_space_divs_known(ls2))
 141                 return 0;
 142
 143         return isl_mat_is_equal(ls1->div, ls2->div);
 144 }
 145
 146 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 147         enum isl_dim_type type)
 148 {
 149         if (!ls)
 150                 return 0;
 151         if (type == isl_dim_div)
 152                 return ls->div->n_row;
 153         if (type == isl_dim_all)
 154                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 155         return isl_space_dim(ls->dim, type);
 156 }
 157
 158 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 159         enum isl_dim_type type)
 160 {
 161         isl_space *dim;
 162
 163         if (!ls)
 164                 return 0;
 165
 166         dim = ls->dim;
 167         switch (type) {
 168         case isl_dim_cst:       return 0;
 169         case isl_dim_param:     return 1;
 170         case isl_dim_in:        return 1 + dim->nparam;
 171         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 172         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 173         default:                return 0;
 174         }
 175 }
 176
 177 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 178         enum isl_dim_type type, unsigned pos)
 179 {
 180         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 181 }
 182
 183 __isl_give isl_div *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 184         int pos)
 185 {
 186         isl_basic_map *bmap;
 187
 188         if (!ls)
 189                 return NULL;
 190
 191         if (pos < 0 || pos >= ls->div->n_row)
 192                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 193                         "index out of bounds", return NULL);
 194
 195         if (isl_int_is_zero(ls->div->row[pos][0]))
 196                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 197                         "expression of div unknown", return NULL);
 198
 199         bmap = isl_basic_map_from_local_space(isl_local_space_copy(ls));
 200         return isl_basic_map_div(bmap, pos);
 201 }
 202
 203 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 204 {
 205         if (!ls)
 206                 return NULL;
 207
 208         return isl_space_copy(ls->dim);
 209 }
 210
 211 __isl_give isl_local_space *isl_local_space_set_dim_name(
 212         __isl_take isl_local_space *ls,
 213         enum isl_dim_type type, unsigned pos, const char *s)
 214 {
 215         ls = isl_local_space_cow(ls);
 216         if (!ls)
 217                 return NULL;
 218         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 219         if (!ls->dim)
 220                 return isl_local_space_free(ls);
 221
 222         return ls;
 223 }
 224
 225 __isl_give isl_local_space *isl_local_space_reset_space(
 226         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 227 {
 228         ls = isl_local_space_cow(ls);
 229         if (!ls || !dim)
 230                 goto error;
 231
 232         isl_space_free(ls->dim);
 233         ls->dim = dim;
 234
 235         return ls;
 236 error:
 237         isl_local_space_free(ls);
 238         isl_space_free(dim);
 239         return NULL;
 240 }
 241
 242 /* Reorder the columns of the given div definitions according to the
 243  * given reordering.
 244  * The order of the divs themselves is assumed not to change.
 245  */
 246 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 247         __isl_take isl_reordering *r)
 248 {
 249         int i, j;
 250         isl_mat *mat;
 251         int extra;
 252
 253         if (!div || !r)
 254                 goto error;
 255
 256         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 257         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 258         if (!mat)
 259                 goto error;
 260
 261         for (i = 0; i < div->n_row; ++i) {
 262                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 263                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 264                 for (j = 0; j < r->len; ++j)
 265                         isl_int_set(mat->row[i][2 + r->pos[j]],
 266                                     div->row[i][2 + j]);
 267         }
 268
 269         isl_reordering_free(r);
 270         isl_mat_free(div);
 271         return mat;
 272 error:
 273         isl_reordering_free(r);
 274         isl_mat_free(div);
 275         return NULL;
 276 }
 277
 278 /* Reorder the dimensions of "ls" according to the given reordering.
 279  * The reordering r is assumed to have been extended with the local
 280  * variables, leaving them in the same order.
 281  */
 282 __isl_give isl_local_space *isl_local_space_realign(
 283         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 284 {
 285         ls = isl_local_space_cow(ls);
 286         if (!ls || !r)
 287                 goto error;
 288
 289         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 290         if (!ls->div)
 291                 goto error;
 292
 293         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 294
 295         isl_reordering_free(r);
 296         return ls;
 297 error:
 298         isl_local_space_free(ls);
 299         isl_reordering_free(r);
 300         return NULL;
 301 }
 302
 303 __isl_give isl_local_space *isl_local_space_add_div(
 304         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 305 {
 306         ls = isl_local_space_cow(ls);
 307         if (!ls || !div)
 308                 goto error;
 309
 310         if (ls->div->n_col != div->size)
 311                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 312                         "incompatible dimensions", goto error);
 313
 314         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 315         ls->div = isl_mat_add_rows(ls->div, 1);
 316         if (!ls->div)
 317                 goto error;
 318
 319         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 320         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 321
 322         isl_vec_free(div);
 323         return ls;
 324 error:
 325         isl_local_space_free(ls);
 326         isl_vec_free(div);
 327         return NULL;
 328 }
 329
 330 __isl_give isl_local_space *isl_local_space_replace_divs(
 331         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 332 {
 333         ls = isl_local_space_cow(ls);
 334
 335         if (!ls || !div)
 336                 goto error;
 337
 338         isl_mat_free(ls->div);
 339         ls->div = div;
 340         return ls;
 341 error:
 342         isl_mat_free(div);
 343         isl_local_space_free(ls);
 344         return NULL;
 345 }
 346
 347 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 348  * defined by "exp".
 349  */
 350 static void expand_row(__isl_keep isl_mat *dst, int d,
 351         __isl_keep isl_mat *src, int s, int *exp)
 352 {
 353         int i;
 354         unsigned c = src->n_col - src->n_row;
 355
 356         isl_seq_cpy(dst->row[d], src->row[s], c);
 357         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 358
 359         for (i = 0; i < s; ++i)
 360                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 361 }
 362
 363 /* Compare (known) divs.
 364  * Return non-zero if at least one of the two divs is unknown.
 365  */
 366 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
 367 {
 368         int li, lj;
 369
 370         if (isl_int_is_zero(div->row[j][0]))
 371                 return -1;
 372         if (isl_int_is_zero(div->row[i][0]))
 373                 return 1;
 374
 375         li = isl_seq_last_non_zero(div->row[i], div->n_col);
 376         lj = isl_seq_last_non_zero(div->row[j], div->n_col);
 377
 378         if (li != lj)
 379                 return li - lj;
 380
 381         return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
 382 }
 383
 384 /* Combine the two lists of divs into a single list.
 385  * For each row i in div1, exp1[i] is set to the position of the corresponding
 386  * row in the result.  Similarly for div2 and exp2.
 387  * This function guarantees
 388  *      exp1[i] >= i
 389  *      exp1[i+1] > exp1[i]
 390  * For optimal merging, the two input list should have been sorted.
 391  */
 392 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 393         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 394 {
 395         int i, j, k;
 396         isl_mat *div = NULL;
 397         unsigned d = div1->n_col - div1->n_row;
 398
 399         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 400                                 d + div1->n_row + div2->n_row);
 401         if (!div)
 402                 return NULL;
 403
 404         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 405                 int cmp;
 406
 407                 expand_row(div, k, div1, i, exp1);
 408                 expand_row(div, k + 1, div2, j, exp2);
 409
 410                 cmp = cmp_row(div, k, k + 1);
 411                 if (cmp == 0) {
 412                         exp1[i++] = k;
 413                         exp2[j++] = k;
 414                 } else if (cmp < 0) {
 415                         exp1[i++] = k;
 416                 } else {
 417                         exp2[j++] = k;
 418                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 419                 }
 420         }
 421         for (; i < div1->n_row; ++i, ++k) {
 422                 expand_row(div, k, div1, i, exp1);
 423                 exp1[i] = k;
 424         }
 425         for (; j < div2->n_row; ++j, ++k) {
 426                 expand_row(div, k, div2, j, exp2);
 427                 exp2[j] = k;
 428         }
 429
 430         div->n_row = k;
 431         div->n_col = d + k;
 432
 433         return div;
 434 }
 435
 436 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 437 {
 438         int i;
 439
 440         if (!ls)
 441                 return -1;
 442
 443         for (i = 0; i < ls->div->n_row; ++i)
 444                 if (isl_int_is_zero(ls->div->row[i][0]))
 445                         return 0;
 446
 447         return 1;
 448 }
 449
 450 __isl_give isl_local_space *isl_local_space_domain(
 451         __isl_take isl_local_space *ls)
 452 {
 453         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 454                                         0, isl_local_space_dim(ls, isl_dim_out));
 455         ls = isl_local_space_cow(ls);
 456         if (!ls)
 457                 return NULL;
 458         ls->dim = isl_space_domain(ls->dim);
 459         if (!ls->dim)
 460                 return isl_local_space_free(ls);
 461         return ls;
 462 }
 463
 464 /* Construct a local space for a map that has the given local
 465  * space as domain and that has a zero-dimensional range.
 466  */
 467 __isl_give isl_local_space *isl_local_space_from_domain(
 468         __isl_take isl_local_space *ls)
 469 {
 470         ls = isl_local_space_cow(ls);
 471         if (!ls)
 472                 return NULL;
 473         ls->dim = isl_space_from_domain(ls->dim);
 474         if (!ls->dim)
 475                 return isl_local_space_free(ls);
 476         return ls;
 477 }
 478
 479 __isl_give isl_local_space *isl_local_space_add_dims(
 480         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 481 {
 482         int pos;
 483
 484         if (!ls)
 485                 return NULL;
 486         pos = isl_local_space_dim(ls, type);
 487         return isl_local_space_insert_dims(ls, type, pos, n);
 488 }
 489
 490 /* Remove common factor of non-constant terms and denominator.
 491  */
 492 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 493 {
 494         isl_ctx *ctx = ls->div->ctx;
 495         unsigned total = ls->div->n_col - 2;
 496
 497         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 498         isl_int_gcd(ctx->normalize_gcd,
 499                     ctx->normalize_gcd, ls->div->row[div][0]);
 500         if (isl_int_is_one(ctx->normalize_gcd))
 501                 return;
 502
 503         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 504                             ctx->normalize_gcd, total);
 505         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 506                             ctx->normalize_gcd);
 507         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 508                             ctx->normalize_gcd);
 509 }
 510
 511 /* Exploit the equalities in "eq" to simplify the expressions of
 512  * the integer divisions in "ls".
 513  * The integer divisions in "ls" are assumed to appear as regular
 514  * dimensions in "eq".
 515  */
 516 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 517         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 518 {
 519         int i, j, k;
 520         unsigned total;
 521         unsigned n_div;
 522
 523         ls = isl_local_space_cow(ls);
 524         if (!ls || !eq)
 525                 goto error;
 526
 527         total = isl_space_dim(eq->dim, isl_dim_all);
 528         if (isl_local_space_dim(ls, isl_dim_all) != total)
 529                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 530                         "dimensions don't match", goto error);
 531         total++;
 532         n_div = eq->n_div;
 533         for (i = 0; i < eq->n_eq; ++i) {
 534                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 535                 if (j < 0 || j == 0 || j >= total)
 536                         continue;
 537
 538                 for (k = 0; k < ls->div->n_row; ++k) {
 539                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 540                                 continue;
 541                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 542                                         &ls->div->row[k][0]);
 543                         normalize_div(ls, k);
 544                 }
 545         }
 546
 547         isl_basic_set_free(eq);
 548         return ls;
 549 error:
 550         isl_basic_set_free(eq);
 551         isl_local_space_free(ls);
 552         return NULL;
 553 }
 554
 555 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 556         enum isl_dim_type type)
 557 {
 558         if (!ls)
 559                 return -1;
 560         return isl_space_is_named_or_nested(ls->dim, type);
 561 }
 562
 563 __isl_give isl_local_space *isl_local_space_drop_dims(
 564         __isl_take isl_local_space *ls,
 565         enum isl_dim_type type, unsigned first, unsigned n)
 566 {
 567         isl_ctx *ctx;
 568
 569         if (!ls)
 570                 return NULL;
 571         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 572                 return ls;
 573
 574         ctx = isl_local_space_get_ctx(ls);
 575         if (first + n > isl_local_space_dim(ls, type))
 576                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 577                         return isl_local_space_free(ls));
 578
 579         ls = isl_local_space_cow(ls);
 580         if (!ls)
 581                 return NULL;
 582
 583         if (type == isl_dim_div) {
 584                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 585         } else {
 586                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 587                 if (!ls->dim)
 588                         return isl_local_space_free(ls);
 589         }
 590
 591         first += 1 + isl_local_space_offset(ls, type);
 592         ls->div = isl_mat_drop_cols(ls->div, first, n);
 593         if (!ls->div)
 594                 return isl_local_space_free(ls);
 595
 596         return ls;
 597 }
 598
 599 __isl_give isl_local_space *isl_local_space_insert_dims(
 600         __isl_take isl_local_space *ls,
 601         enum isl_dim_type type, unsigned first, unsigned n)
 602 {
 603         isl_ctx *ctx;
 604
 605         if (!ls)
 606                 return NULL;
 607         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 608                 return ls;
 609
 610         ctx = isl_local_space_get_ctx(ls);
 611         if (first > isl_local_space_dim(ls, type))
 612                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 613                         return isl_local_space_free(ls));
 614
 615         ls = isl_local_space_cow(ls);
 616         if (!ls)
 617                 return NULL;
 618
 619         if (type == isl_dim_div) {
 620                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 621         } else {
 622                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 623                 if (!ls->dim)
 624                         return isl_local_space_free(ls);
 625         }
 626
 627         first += 1 + isl_local_space_offset(ls, type);
 628         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 629         if (!ls->div)
 630                 return isl_local_space_free(ls);
 631
 632         return ls;
 633 }
 634
 635 /* Check if the constraints pointed to by "constraint" is a div
 636  * constraint corresponding to div "div" in "ls".
 637  *
 638  * That is, if div = floor(f/m), then check if the constraint is
 639  *
 640  *              f - m d >= 0
 641  * or
 642  *              -(f-(m-1)) + m d >= 0
 643  */
 644 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 645         isl_int *constraint, unsigned div)
 646 {
 647         unsigned pos;
 648
 649         if (!ls)
 650                 return -1;
 651
 652         if (isl_int_is_zero(ls->div->row[div][0]))
 653                 return 0;
 654
 655         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 656
 657         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 658                 int neg;
 659                 isl_int_sub(ls->div->row[div][1],
 660                                 ls->div->row[div][1], ls->div->row[div][0]);
 661                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 662                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 663                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 664                 isl_int_add(ls->div->row[div][1],
 665                                 ls->div->row[div][1], ls->div->row[div][0]);
 666                 if (!neg)
 667                         return 0;
 668                 if (isl_seq_first_non_zero(constraint+pos+1,
 669                                             ls->div->n_row-div-1) != -1)
 670                         return 0;
 671         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 672                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 673                         return 0;
 674                 if (isl_seq_first_non_zero(constraint+pos+1,
 675                                             ls->div->n_row-div-1) != -1)
 676                         return 0;
 677         } else
 678                 return 0;
 679
 680         return 1;
 681 }
 682
 683 /*
 684  * Set active[i] to 1 if the dimension at position i is involved
 685  * in the linear expression l.
 686  */
 687 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 688 {
 689         int i, j;
 690         isl_ctx *ctx;
 691         int *active = NULL;
 692         unsigned total;
 693         unsigned offset;
 694
 695         ctx = isl_local_space_get_ctx(ls);
 696         total = isl_local_space_dim(ls, isl_dim_all);
 697         active = isl_calloc_array(ctx, int, total);
 698         if (!active)
 699                 return NULL;
 700
 701         for (i = 0; i < total; ++i)
 702                 active[i] = !isl_int_is_zero(l[i]);
 703
 704         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 705         for (i = ls->div->n_row - 1; i >= 0; --i) {
 706                 if (!active[offset + i])
 707                         continue;
 708                 for (j = 0; j < total; ++j)
 709                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 710         }
 711
 712         return active;
 713 }