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_aff_private.h>
  17 #include <isl/seq.h>
  18
  19 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  20 {
  21         return ls ? ls->dim->ctx : NULL;
  22 }
  23
  24 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  25         __isl_take isl_mat *div)
  26 {
  27         isl_ctx *ctx;
  28         isl_local_space *ls = NULL;
  29
  30         if (!dim)
  31                 goto error;
  32
  33         ctx = isl_space_get_ctx(dim);
  34         ls = isl_calloc_type(ctx, struct isl_local_space);
  35         if (!ls)
  36                 goto error;
  37
  38         ls->ref = 1;
  39         ls->dim = dim;
  40         ls->div = div;
  41
  42         return ls;
  43 error:
  44         isl_space_free(dim);
  45         isl_local_space_free(ls);
  46         return NULL;
  47 }
  48
  49 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  50         unsigned n_div)
  51 {
  52         isl_ctx *ctx;
  53         isl_mat *div;
  54         unsigned total;
  55
  56         if (!dim)
  57                 return NULL;
  58
  59         total = isl_space_dim(dim, isl_dim_all);
  60
  61         ctx = isl_space_get_ctx(dim);
  62         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  63         return isl_local_space_alloc_div(dim, div);
  64 }
  65
  66 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  67 {
  68         return isl_local_space_alloc(dim, 0);
  69 }
  70
  71 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  72 {
  73         if (!ls)
  74                 return NULL;
  75
  76         ls->ref++;
  77         return ls;
  78 }
  79
  80 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  81 {
  82         if (!ls)
  83                 return NULL;
  84
  85         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  86                                          isl_mat_copy(ls->div));
  87
  88 }
  89
  90 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  91 {
  92         if (!ls)
  93                 return NULL;
  94
  95         if (ls->ref == 1)
  96                 return ls;
  97         ls->ref--;
  98         return isl_local_space_dup(ls);
  99 }
 100
 101 void *isl_local_space_free(__isl_take isl_local_space *ls)
 102 {
 103         if (!ls)
 104                 return NULL;
 105
 106         if (--ls->ref > 0)
 107                 return NULL;
 108
 109         isl_space_free(ls->dim);
 110         isl_mat_free(ls->div);
 111
 112         free(ls);
 113
 114         return NULL;
 115 }
 116
 117 /* Is the local space that of a set?
 118  */
 119 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 120 {
 121         return ls ? isl_space_is_set(ls->dim) : -1;
 122 }
 123
 124 /* Return true if the two local spaces are identical, with identical
 125  * expressions for the integer divisions.
 126  */
 127 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 128         __isl_keep isl_local_space *ls2)
 129 {
 130         int equal;
 131
 132         if (!ls1 || !ls2)
 133                 return -1;
 134
 135         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 136         if (equal < 0 || !equal)
 137                 return equal;
 138
 139         if (!isl_local_space_divs_known(ls1))
 140                 return 0;
 141         if (!isl_local_space_divs_known(ls2))
 142                 return 0;
 143
 144         return isl_mat_is_equal(ls1->div, ls2->div);
 145 }
 146
 147 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 148         enum isl_dim_type type)
 149 {
 150         if (!ls)
 151                 return 0;
 152         if (type == isl_dim_div)
 153                 return ls->div->n_row;
 154         if (type == isl_dim_all)
 155                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 156         return isl_space_dim(ls->dim, type);
 157 }
 158
 159 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 160         enum isl_dim_type type)
 161 {
 162         isl_space *dim;
 163
 164         if (!ls)
 165                 return 0;
 166
 167         dim = ls->dim;
 168         switch (type) {
 169         case isl_dim_cst:       return 0;
 170         case isl_dim_param:     return 1;
 171         case isl_dim_in:        return 1 + dim->nparam;
 172         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 173         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 174         default:                return 0;
 175         }
 176 }
 177
 178 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 179         enum isl_dim_type type, unsigned pos)
 180 {
 181         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 182 }
 183
 184 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 185         int pos)
 186 {
 187         isl_aff *aff;
 188
 189         if (!ls)
 190                 return NULL;
 191
 192         if (pos < 0 || pos >= ls->div->n_row)
 193                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 194                         "index out of bounds", return NULL);
 195
 196         if (isl_int_is_zero(ls->div->row[pos][0]))
 197                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 198                         "expression of div unknown", return NULL);
 199
 200         aff = isl_aff_alloc(isl_local_space_copy(ls));
 201         if (!aff)
 202                 return NULL;
 203         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 204         return aff;
 205 }
 206
 207 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 208 {
 209         if (!ls)
 210                 return NULL;
 211
 212         return isl_space_copy(ls->dim);
 213 }
 214
 215 __isl_give isl_local_space *isl_local_space_set_dim_name(
 216         __isl_take isl_local_space *ls,
 217         enum isl_dim_type type, unsigned pos, const char *s)
 218 {
 219         ls = isl_local_space_cow(ls);
 220         if (!ls)
 221                 return NULL;
 222         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 223         if (!ls->dim)
 224                 return isl_local_space_free(ls);
 225
 226         return ls;
 227 }
 228
 229 __isl_give isl_local_space *isl_local_space_reset_space(
 230         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 231 {
 232         ls = isl_local_space_cow(ls);
 233         if (!ls || !dim)
 234                 goto error;
 235
 236         isl_space_free(ls->dim);
 237         ls->dim = dim;
 238
 239         return ls;
 240 error:
 241         isl_local_space_free(ls);
 242         isl_space_free(dim);
 243         return NULL;
 244 }
 245
 246 /* Reorder the columns of the given div definitions according to the
 247  * given reordering.
 248  * The order of the divs themselves is assumed not to change.
 249  */
 250 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 251         __isl_take isl_reordering *r)
 252 {
 253         int i, j;
 254         isl_mat *mat;
 255         int extra;
 256
 257         if (!div || !r)
 258                 goto error;
 259
 260         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 261         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 262         if (!mat)
 263                 goto error;
 264
 265         for (i = 0; i < div->n_row; ++i) {
 266                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 267                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 268                 for (j = 0; j < r->len; ++j)
 269                         isl_int_set(mat->row[i][2 + r->pos[j]],
 270                                     div->row[i][2 + j]);
 271         }
 272
 273         isl_reordering_free(r);
 274         isl_mat_free(div);
 275         return mat;
 276 error:
 277         isl_reordering_free(r);
 278         isl_mat_free(div);
 279         return NULL;
 280 }
 281
 282 /* Reorder the dimensions of "ls" according to the given reordering.
 283  * The reordering r is assumed to have been extended with the local
 284  * variables, leaving them in the same order.
 285  */
 286 __isl_give isl_local_space *isl_local_space_realign(
 287         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 288 {
 289         ls = isl_local_space_cow(ls);
 290         if (!ls || !r)
 291                 goto error;
 292
 293         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 294         if (!ls->div)
 295                 goto error;
 296
 297         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 298
 299         isl_reordering_free(r);
 300         return ls;
 301 error:
 302         isl_local_space_free(ls);
 303         isl_reordering_free(r);
 304         return NULL;
 305 }
 306
 307 __isl_give isl_local_space *isl_local_space_add_div(
 308         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 309 {
 310         ls = isl_local_space_cow(ls);
 311         if (!ls || !div)
 312                 goto error;
 313
 314         if (ls->div->n_col != div->size)
 315                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 316                         "incompatible dimensions", goto error);
 317
 318         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 319         ls->div = isl_mat_add_rows(ls->div, 1);
 320         if (!ls->div)
 321                 goto error;
 322
 323         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 324         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 325
 326         isl_vec_free(div);
 327         return ls;
 328 error:
 329         isl_local_space_free(ls);
 330         isl_vec_free(div);
 331         return NULL;
 332 }
 333
 334 __isl_give isl_local_space *isl_local_space_replace_divs(
 335         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 336 {
 337         ls = isl_local_space_cow(ls);
 338
 339         if (!ls || !div)
 340                 goto error;
 341
 342         isl_mat_free(ls->div);
 343         ls->div = div;
 344         return ls;
 345 error:
 346         isl_mat_free(div);
 347         isl_local_space_free(ls);
 348         return NULL;
 349 }
 350
 351 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 352  * defined by "exp".
 353  */
 354 static void expand_row(__isl_keep isl_mat *dst, int d,
 355         __isl_keep isl_mat *src, int s, int *exp)
 356 {
 357         int i;
 358         unsigned c = src->n_col - src->n_row;
 359
 360         isl_seq_cpy(dst->row[d], src->row[s], c);
 361         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 362
 363         for (i = 0; i < s; ++i)
 364                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 365 }
 366
 367 /* Compare (known) divs.
 368  * Return non-zero if at least one of the two divs is unknown.
 369  */
 370 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
 371 {
 372         int li, lj;
 373
 374         if (isl_int_is_zero(div->row[j][0]))
 375                 return -1;
 376         if (isl_int_is_zero(div->row[i][0]))
 377                 return 1;
 378
 379         li = isl_seq_last_non_zero(div->row[i], div->n_col);
 380         lj = isl_seq_last_non_zero(div->row[j], div->n_col);
 381
 382         if (li != lj)
 383                 return li - lj;
 384
 385         return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
 386 }
 387
 388 /* Combine the two lists of divs into a single list.
 389  * For each row i in div1, exp1[i] is set to the position of the corresponding
 390  * row in the result.  Similarly for div2 and exp2.
 391  * This function guarantees
 392  *      exp1[i] >= i
 393  *      exp1[i+1] > exp1[i]
 394  * For optimal merging, the two input list should have been sorted.
 395  */
 396 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 397         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 398 {
 399         int i, j, k;
 400         isl_mat *div = NULL;
 401         unsigned d = div1->n_col - div1->n_row;
 402
 403         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 404                                 d + div1->n_row + div2->n_row);
 405         if (!div)
 406                 return NULL;
 407
 408         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 409                 int cmp;
 410
 411                 expand_row(div, k, div1, i, exp1);
 412                 expand_row(div, k + 1, div2, j, exp2);
 413
 414                 cmp = cmp_row(div, k, k + 1);
 415                 if (cmp == 0) {
 416                         exp1[i++] = k;
 417                         exp2[j++] = k;
 418                 } else if (cmp < 0) {
 419                         exp1[i++] = k;
 420                 } else {
 421                         exp2[j++] = k;
 422                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 423                 }
 424         }
 425         for (; i < div1->n_row; ++i, ++k) {
 426                 expand_row(div, k, div1, i, exp1);
 427                 exp1[i] = k;
 428         }
 429         for (; j < div2->n_row; ++j, ++k) {
 430                 expand_row(div, k, div2, j, exp2);
 431                 exp2[j] = k;
 432         }
 433
 434         div->n_row = k;
 435         div->n_col = d + k;
 436
 437         return div;
 438 }
 439
 440 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 441 {
 442         int i;
 443
 444         if (!ls)
 445                 return -1;
 446
 447         for (i = 0; i < ls->div->n_row; ++i)
 448                 if (isl_int_is_zero(ls->div->row[i][0]))
 449                         return 0;
 450
 451         return 1;
 452 }
 453
 454 __isl_give isl_local_space *isl_local_space_domain(
 455         __isl_take isl_local_space *ls)
 456 {
 457         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 458                                         0, isl_local_space_dim(ls, isl_dim_out));
 459         ls = isl_local_space_cow(ls);
 460         if (!ls)
 461                 return NULL;
 462         ls->dim = isl_space_domain(ls->dim);
 463         if (!ls->dim)
 464                 return isl_local_space_free(ls);
 465         return ls;
 466 }
 467
 468 /* Construct a local space for a map that has the given local
 469  * space as domain and that has a zero-dimensional range.
 470  */
 471 __isl_give isl_local_space *isl_local_space_from_domain(
 472         __isl_take isl_local_space *ls)
 473 {
 474         ls = isl_local_space_cow(ls);
 475         if (!ls)
 476                 return NULL;
 477         ls->dim = isl_space_from_domain(ls->dim);
 478         if (!ls->dim)
 479                 return isl_local_space_free(ls);
 480         return ls;
 481 }
 482
 483 __isl_give isl_local_space *isl_local_space_add_dims(
 484         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 485 {
 486         int pos;
 487
 488         if (!ls)
 489                 return NULL;
 490         pos = isl_local_space_dim(ls, type);
 491         return isl_local_space_insert_dims(ls, type, pos, n);
 492 }
 493
 494 /* Remove common factor of non-constant terms and denominator.
 495  */
 496 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 497 {
 498         isl_ctx *ctx = ls->div->ctx;
 499         unsigned total = ls->div->n_col - 2;
 500
 501         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 502         isl_int_gcd(ctx->normalize_gcd,
 503                     ctx->normalize_gcd, ls->div->row[div][0]);
 504         if (isl_int_is_one(ctx->normalize_gcd))
 505                 return;
 506
 507         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 508                             ctx->normalize_gcd, total);
 509         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 510                             ctx->normalize_gcd);
 511         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 512                             ctx->normalize_gcd);
 513 }
 514
 515 /* Exploit the equalities in "eq" to simplify the expressions of
 516  * the integer divisions in "ls".
 517  * The integer divisions in "ls" are assumed to appear as regular
 518  * dimensions in "eq".
 519  */
 520 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 521         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 522 {
 523         int i, j, k;
 524         unsigned total;
 525         unsigned n_div;
 526
 527         ls = isl_local_space_cow(ls);
 528         if (!ls || !eq)
 529                 goto error;
 530
 531         total = isl_space_dim(eq->dim, isl_dim_all);
 532         if (isl_local_space_dim(ls, isl_dim_all) != total)
 533                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 534                         "dimensions don't match", goto error);
 535         total++;
 536         n_div = eq->n_div;
 537         for (i = 0; i < eq->n_eq; ++i) {
 538                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 539                 if (j < 0 || j == 0 || j >= total)
 540                         continue;
 541
 542                 for (k = 0; k < ls->div->n_row; ++k) {
 543                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 544                                 continue;
 545                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 546                                         &ls->div->row[k][0]);
 547                         normalize_div(ls, k);
 548                 }
 549         }
 550
 551         isl_basic_set_free(eq);
 552         return ls;
 553 error:
 554         isl_basic_set_free(eq);
 555         isl_local_space_free(ls);
 556         return NULL;
 557 }
 558
 559 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 560         enum isl_dim_type type)
 561 {
 562         if (!ls)
 563                 return -1;
 564         return isl_space_is_named_or_nested(ls->dim, type);
 565 }
 566
 567 __isl_give isl_local_space *isl_local_space_drop_dims(
 568         __isl_take isl_local_space *ls,
 569         enum isl_dim_type type, unsigned first, unsigned n)
 570 {
 571         isl_ctx *ctx;
 572
 573         if (!ls)
 574                 return NULL;
 575         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 576                 return ls;
 577
 578         ctx = isl_local_space_get_ctx(ls);
 579         if (first + n > isl_local_space_dim(ls, type))
 580                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 581                         return isl_local_space_free(ls));
 582
 583         ls = isl_local_space_cow(ls);
 584         if (!ls)
 585                 return NULL;
 586
 587         if (type == isl_dim_div) {
 588                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 589         } else {
 590                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 591                 if (!ls->dim)
 592                         return isl_local_space_free(ls);
 593         }
 594
 595         first += 1 + isl_local_space_offset(ls, type);
 596         ls->div = isl_mat_drop_cols(ls->div, first, n);
 597         if (!ls->div)
 598                 return isl_local_space_free(ls);
 599
 600         return ls;
 601 }
 602
 603 __isl_give isl_local_space *isl_local_space_insert_dims(
 604         __isl_take isl_local_space *ls,
 605         enum isl_dim_type type, unsigned first, unsigned n)
 606 {
 607         isl_ctx *ctx;
 608
 609         if (!ls)
 610                 return NULL;
 611         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 612                 return ls;
 613
 614         ctx = isl_local_space_get_ctx(ls);
 615         if (first > isl_local_space_dim(ls, type))
 616                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 617                         return isl_local_space_free(ls));
 618
 619         ls = isl_local_space_cow(ls);
 620         if (!ls)
 621                 return NULL;
 622
 623         if (type == isl_dim_div) {
 624                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 625         } else {
 626                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 627                 if (!ls->dim)
 628                         return isl_local_space_free(ls);
 629         }
 630
 631         first += 1 + isl_local_space_offset(ls, type);
 632         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 633         if (!ls->div)
 634                 return isl_local_space_free(ls);
 635
 636         return ls;
 637 }
 638
 639 /* Check if the constraints pointed to by "constraint" is a div
 640  * constraint corresponding to div "div" in "ls".
 641  *
 642  * That is, if div = floor(f/m), then check if the constraint is
 643  *
 644  *              f - m d >= 0
 645  * or
 646  *              -(f-(m-1)) + m d >= 0
 647  */
 648 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 649         isl_int *constraint, unsigned div)
 650 {
 651         unsigned pos;
 652
 653         if (!ls)
 654                 return -1;
 655
 656         if (isl_int_is_zero(ls->div->row[div][0]))
 657                 return 0;
 658
 659         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 660
 661         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 662                 int neg;
 663                 isl_int_sub(ls->div->row[div][1],
 664                                 ls->div->row[div][1], ls->div->row[div][0]);
 665                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 666                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 667                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 668                 isl_int_add(ls->div->row[div][1],
 669                                 ls->div->row[div][1], ls->div->row[div][0]);
 670                 if (!neg)
 671                         return 0;
 672                 if (isl_seq_first_non_zero(constraint+pos+1,
 673                                             ls->div->n_row-div-1) != -1)
 674                         return 0;
 675         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 676                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 677                         return 0;
 678                 if (isl_seq_first_non_zero(constraint+pos+1,
 679                                             ls->div->n_row-div-1) != -1)
 680                         return 0;
 681         } else
 682                 return 0;
 683
 684         return 1;
 685 }
 686
 687 /*
 688  * Set active[i] to 1 if the dimension at position i is involved
 689  * in the linear expression l.
 690  */
 691 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 692 {
 693         int i, j;
 694         isl_ctx *ctx;
 695         int *active = NULL;
 696         unsigned total;
 697         unsigned offset;
 698
 699         ctx = isl_local_space_get_ctx(ls);
 700         total = isl_local_space_dim(ls, isl_dim_all);
 701         active = isl_calloc_array(ctx, int, total);
 702         if (!active)
 703                 return NULL;
 704
 705         for (i = 0; i < total; ++i)
 706                 active[i] = !isl_int_is_zero(l[i]);
 707
 708         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 709         for (i = ls->div->n_row - 1; i >= 0; --i) {
 710                 if (!active[offset + i])
 711                         continue;
 712                 for (j = 0; j < total; ++j)
 713                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 714         }
 715
 716         return active;
 717 }