isl_local_space.c

   1 /*
   2  * Copyright 2011      INRIA Saclay
   3  * Copyright 2012      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the GNU LGPLv2.1 license
   6  *
   7  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   8  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   9  * 91893 Orsay, France
  10  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  11  */
  12
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include <isl_local_space_private.h>
  16 #include <isl_space_private.h>
  17 #include <isl_mat_private.h>
  18 #include <isl_aff_private.h>
  19 #include <isl/seq.h>
  20
  21 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  22 {
  23         return ls ? ls->dim->ctx : NULL;
  24 }
  25
  26 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  27         __isl_take isl_mat *div)
  28 {
  29         isl_ctx *ctx;
  30         isl_local_space *ls = NULL;
  31
  32         if (!dim || !div)
  33                 goto error;
  34
  35         ctx = isl_space_get_ctx(dim);
  36         ls = isl_calloc_type(ctx, struct isl_local_space);
  37         if (!ls)
  38                 goto error;
  39
  40         ls->ref = 1;
  41         ls->dim = dim;
  42         ls->div = div;
  43
  44         return ls;
  45 error:
  46         isl_mat_free(div);
  47         isl_space_free(dim);
  48         isl_local_space_free(ls);
  49         return NULL;
  50 }
  51
  52 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  53         unsigned n_div)
  54 {
  55         isl_ctx *ctx;
  56         isl_mat *div;
  57         unsigned total;
  58
  59         if (!dim)
  60                 return NULL;
  61
  62         total = isl_space_dim(dim, isl_dim_all);
  63
  64         ctx = isl_space_get_ctx(dim);
  65         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  66         return isl_local_space_alloc_div(dim, div);
  67 }
  68
  69 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  70 {
  71         return isl_local_space_alloc(dim, 0);
  72 }
  73
  74 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  75 {
  76         if (!ls)
  77                 return NULL;
  78
  79         ls->ref++;
  80         return ls;
  81 }
  82
  83 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  84 {
  85         if (!ls)
  86                 return NULL;
  87
  88         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  89                                          isl_mat_copy(ls->div));
  90
  91 }
  92
  93 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  94 {
  95         if (!ls)
  96                 return NULL;
  97
  98         if (ls->ref == 1)
  99                 return ls;
 100         ls->ref--;
 101         return isl_local_space_dup(ls);
 102 }
 103
 104 void *isl_local_space_free(__isl_take isl_local_space *ls)
 105 {
 106         if (!ls)
 107                 return NULL;
 108
 109         if (--ls->ref > 0)
 110                 return NULL;
 111
 112         isl_space_free(ls->dim);
 113         isl_mat_free(ls->div);
 114
 115         free(ls);
 116
 117         return NULL;
 118 }
 119
 120 /* Is the local space that of a set?
 121  */
 122 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 123 {
 124         return ls ? isl_space_is_set(ls->dim) : -1;
 125 }
 126
 127 /* Return true if the two local spaces are identical, with identical
 128  * expressions for the integer divisions.
 129  */
 130 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 131         __isl_keep isl_local_space *ls2)
 132 {
 133         int equal;
 134
 135         if (!ls1 || !ls2)
 136                 return -1;
 137
 138         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 139         if (equal < 0 || !equal)
 140                 return equal;
 141
 142         if (!isl_local_space_divs_known(ls1))
 143                 return 0;
 144         if (!isl_local_space_divs_known(ls2))
 145                 return 0;
 146
 147         return isl_mat_is_equal(ls1->div, ls2->div);
 148 }
 149
 150 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 151         enum isl_dim_type type)
 152 {
 153         if (!ls)
 154                 return 0;
 155         if (type == isl_dim_div)
 156                 return ls->div->n_row;
 157         if (type == isl_dim_all)
 158                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 159         return isl_space_dim(ls->dim, type);
 160 }
 161
 162 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 163         enum isl_dim_type type)
 164 {
 165         isl_space *dim;
 166
 167         if (!ls)
 168                 return 0;
 169
 170         dim = ls->dim;
 171         switch (type) {
 172         case isl_dim_cst:       return 0;
 173         case isl_dim_param:     return 1;
 174         case isl_dim_in:        return 1 + dim->nparam;
 175         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 176         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 177         default:                return 0;
 178         }
 179 }
 180
 181 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 182         enum isl_dim_type type, unsigned pos)
 183 {
 184         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 185 }
 186
 187 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 188         int pos)
 189 {
 190         isl_aff *aff;
 191
 192         if (!ls)
 193                 return NULL;
 194
 195         if (pos < 0 || pos >= ls->div->n_row)
 196                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 197                         "index out of bounds", return NULL);
 198
 199         if (isl_int_is_zero(ls->div->row[pos][0]))
 200                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 201                         "expression of div unknown", return NULL);
 202
 203         aff = isl_aff_alloc(isl_local_space_copy(ls));
 204         if (!aff)
 205                 return NULL;
 206         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 207         return aff;
 208 }
 209
 210 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 211 {
 212         if (!ls)
 213                 return NULL;
 214
 215         return isl_space_copy(ls->dim);
 216 }
 217
 218 __isl_give isl_local_space *isl_local_space_set_dim_name(
 219         __isl_take isl_local_space *ls,
 220         enum isl_dim_type type, unsigned pos, const char *s)
 221 {
 222         ls = isl_local_space_cow(ls);
 223         if (!ls)
 224                 return NULL;
 225         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 226         if (!ls->dim)
 227                 return isl_local_space_free(ls);
 228
 229         return ls;
 230 }
 231
 232 __isl_give isl_local_space *isl_local_space_set_dim_id(
 233         __isl_take isl_local_space *ls,
 234         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 235 {
 236         ls = isl_local_space_cow(ls);
 237         if (!ls)
 238                 return isl_id_free(id);
 239         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 240         if (!ls->dim)
 241                 return isl_local_space_free(ls);
 242
 243         return ls;
 244 }
 245
 246 __isl_give isl_local_space *isl_local_space_reset_space(
 247         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 248 {
 249         ls = isl_local_space_cow(ls);
 250         if (!ls || !dim)
 251                 goto error;
 252
 253         isl_space_free(ls->dim);
 254         ls->dim = dim;
 255
 256         return ls;
 257 error:
 258         isl_local_space_free(ls);
 259         isl_space_free(dim);
 260         return NULL;
 261 }
 262
 263 /* Reorder the columns of the given div definitions according to the
 264  * given reordering.
 265  * The order of the divs themselves is assumed not to change.
 266  */
 267 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 268         __isl_take isl_reordering *r)
 269 {
 270         int i, j;
 271         isl_mat *mat;
 272         int extra;
 273
 274         if (!div || !r)
 275                 goto error;
 276
 277         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 278         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 279         if (!mat)
 280                 goto error;
 281
 282         for (i = 0; i < div->n_row; ++i) {
 283                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 284                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 285                 for (j = 0; j < r->len; ++j)
 286                         isl_int_set(mat->row[i][2 + r->pos[j]],
 287                                     div->row[i][2 + j]);
 288         }
 289
 290         isl_reordering_free(r);
 291         isl_mat_free(div);
 292         return mat;
 293 error:
 294         isl_reordering_free(r);
 295         isl_mat_free(div);
 296         return NULL;
 297 }
 298
 299 /* Reorder the dimensions of "ls" according to the given reordering.
 300  * The reordering r is assumed to have been extended with the local
 301  * variables, leaving them in the same order.
 302  */
 303 __isl_give isl_local_space *isl_local_space_realign(
 304         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 305 {
 306         ls = isl_local_space_cow(ls);
 307         if (!ls || !r)
 308                 goto error;
 309
 310         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 311         if (!ls->div)
 312                 goto error;
 313
 314         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 315
 316         isl_reordering_free(r);
 317         return ls;
 318 error:
 319         isl_local_space_free(ls);
 320         isl_reordering_free(r);
 321         return NULL;
 322 }
 323
 324 __isl_give isl_local_space *isl_local_space_add_div(
 325         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 326 {
 327         ls = isl_local_space_cow(ls);
 328         if (!ls || !div)
 329                 goto error;
 330
 331         if (ls->div->n_col != div->size)
 332                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 333                         "incompatible dimensions", goto error);
 334
 335         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 336         ls->div = isl_mat_add_rows(ls->div, 1);
 337         if (!ls->div)
 338                 goto error;
 339
 340         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 341         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 342
 343         isl_vec_free(div);
 344         return ls;
 345 error:
 346         isl_local_space_free(ls);
 347         isl_vec_free(div);
 348         return NULL;
 349 }
 350
 351 __isl_give isl_local_space *isl_local_space_replace_divs(
 352         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 353 {
 354         ls = isl_local_space_cow(ls);
 355
 356         if (!ls || !div)
 357                 goto error;
 358
 359         isl_mat_free(ls->div);
 360         ls->div = div;
 361         return ls;
 362 error:
 363         isl_mat_free(div);
 364         isl_local_space_free(ls);
 365         return NULL;
 366 }
 367
 368 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 369  * defined by "exp".
 370  */
 371 static void expand_row(__isl_keep isl_mat *dst, int d,
 372         __isl_keep isl_mat *src, int s, int *exp)
 373 {
 374         int i;
 375         unsigned c = src->n_col - src->n_row;
 376
 377         isl_seq_cpy(dst->row[d], src->row[s], c);
 378         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 379
 380         for (i = 0; i < s; ++i)
 381                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 382 }
 383
 384 /* Compare (known) divs.
 385  * Return non-zero if at least one of the two divs is unknown.
 386  * In particular, if both divs are unknown, we respect their
 387  * current order.  Otherwise, we sort the known div after the unknown
 388  * div only if the known div depends on the unknown div.
 389  */
 390 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 391         unsigned n_row, unsigned n_col)
 392 {
 393         int li, lj;
 394         int unknown_i, unknown_j;
 395
 396         unknown_i = isl_int_is_zero(row_i[0]);
 397         unknown_j = isl_int_is_zero(row_j[0]);
 398
 399         if (unknown_i && unknown_j)
 400                 return i - j;
 401
 402         if (unknown_i)
 403                 li = n_col - n_row + i;
 404         else
 405                 li = isl_seq_last_non_zero(row_i, n_col);
 406         if (unknown_j)
 407                 lj = n_col - n_row + j;
 408         else
 409                 lj = isl_seq_last_non_zero(row_j, n_col);
 410
 411         if (li != lj)
 412                 return li - lj;
 413
 414         return isl_seq_cmp(row_i, row_j, n_col);
 415 }
 416
 417 /* Call cmp_row for divs in a matrix.
 418  */
 419 static int mat_cmp_row(__isl_keep isl_mat *div, int i, int j)
 420 {
 421         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 422 }
 423
 424 /* Call cmp_row for divs in a basic map.
 425  */
 426 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 427         unsigned total)
 428 {
 429         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 430 }
 431
 432 /* Sort the divs in "bmap".
 433  *
 434  * We first make sure divs are placed after divs on which they depend.
 435  * Then we perform a simple insertion sort based on the same ordering
 436  * that is used in isl_merge_divs.
 437  */
 438 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 439         __isl_take isl_basic_map *bmap)
 440 {
 441         int i, j;
 442         unsigned total;
 443
 444         bmap = isl_basic_map_order_divs(bmap);
 445         if (!bmap)
 446                 return NULL;
 447         if (bmap->n_div <= 1)
 448                 return bmap;
 449
 450         total = 2 + isl_basic_map_total_dim(bmap);
 451         for (i = 1; i < bmap->n_div; ++i) {
 452                 for (j = i - 1; j >= 0; --j) {
 453                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 454                                 break;
 455                         isl_basic_map_swap_div(bmap, j, j + 1);
 456                 }
 457         }
 458
 459         return bmap;
 460 }
 461
 462 /* Sort the divs in the basic maps of "map".
 463  */
 464 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 465 {
 466         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 467 }
 468
 469 /* Combine the two lists of divs into a single list.
 470  * For each row i in div1, exp1[i] is set to the position of the corresponding
 471  * row in the result.  Similarly for div2 and exp2.
 472  * This function guarantees
 473  *      exp1[i] >= i
 474  *      exp1[i+1] > exp1[i]
 475  * For optimal merging, the two input list should have been sorted.
 476  */
 477 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 478         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 479 {
 480         int i, j, k;
 481         isl_mat *div = NULL;
 482         unsigned d;
 483
 484         if (!div1 || !div2)
 485                 return NULL;
 486
 487         d = div1->n_col - div1->n_row;
 488         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 489                                 d + div1->n_row + div2->n_row);
 490         if (!div)
 491                 return NULL;
 492
 493         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 494                 int cmp;
 495
 496                 expand_row(div, k, div1, i, exp1);
 497                 expand_row(div, k + 1, div2, j, exp2);
 498
 499                 cmp = mat_cmp_row(div, k, k + 1);
 500                 if (cmp == 0) {
 501                         exp1[i++] = k;
 502                         exp2[j++] = k;
 503                 } else if (cmp < 0) {
 504                         exp1[i++] = k;
 505                 } else {
 506                         exp2[j++] = k;
 507                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 508                 }
 509         }
 510         for (; i < div1->n_row; ++i, ++k) {
 511                 expand_row(div, k, div1, i, exp1);
 512                 exp1[i] = k;
 513         }
 514         for (; j < div2->n_row; ++j, ++k) {
 515                 expand_row(div, k, div2, j, exp2);
 516                 exp2[j] = k;
 517         }
 518
 519         div->n_row = k;
 520         div->n_col = d + k;
 521
 522         return div;
 523 }
 524
 525 /* Construct a local space that contains all the divs in either
 526  * "ls1" or "ls2".
 527  */
 528 __isl_give isl_local_space *isl_local_space_intersect(
 529         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 530 {
 531         isl_ctx *ctx;
 532         int *exp1 = NULL;
 533         int *exp2 = NULL;
 534         isl_mat *div;
 535
 536         if (!ls1 || !ls2)
 537                 goto error;
 538
 539         ctx = isl_local_space_get_ctx(ls1);
 540         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 541                 isl_die(ctx, isl_error_invalid,
 542                         "spaces should be identical", goto error);
 543
 544         if (ls2->div->n_row == 0) {
 545                 isl_local_space_free(ls2);
 546                 return ls1;
 547         }
 548
 549         if (ls1->div->n_row == 0) {
 550                 isl_local_space_free(ls1);
 551                 return ls2;
 552         }
 553
 554         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 555         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 556         if (!exp1 || !exp2)
 557                 goto error;
 558
 559         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 560         if (!div)
 561                 goto error;
 562
 563         free(exp1);
 564         free(exp2);
 565         isl_local_space_free(ls2);
 566         isl_mat_free(ls1->div);
 567         ls1->div = div;
 568
 569         return ls1;
 570 error:
 571         free(exp1);
 572         free(exp2);
 573         isl_local_space_free(ls1);
 574         isl_local_space_free(ls2);
 575         return NULL;
 576 }
 577
 578 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 579 {
 580         int i;
 581
 582         if (!ls)
 583                 return -1;
 584
 585         for (i = 0; i < ls->div->n_row; ++i)
 586                 if (isl_int_is_zero(ls->div->row[i][0]))
 587                         return 0;
 588
 589         return 1;
 590 }
 591
 592 __isl_give isl_local_space *isl_local_space_domain(
 593         __isl_take isl_local_space *ls)
 594 {
 595         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 596                                         0, isl_local_space_dim(ls, isl_dim_out));
 597         ls = isl_local_space_cow(ls);
 598         if (!ls)
 599                 return NULL;
 600         ls->dim = isl_space_domain(ls->dim);
 601         if (!ls->dim)
 602                 return isl_local_space_free(ls);
 603         return ls;
 604 }
 605
 606 __isl_give isl_local_space *isl_local_space_range(
 607         __isl_take isl_local_space *ls)
 608 {
 609         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 610                                         0, isl_local_space_dim(ls, isl_dim_in));
 611         ls = isl_local_space_cow(ls);
 612         if (!ls)
 613                 return NULL;
 614
 615         ls->dim = isl_space_range(ls->dim);
 616         if (!ls->dim)
 617                 return isl_local_space_free(ls);
 618         return ls;
 619 }
 620
 621 /* Construct a local space for a map that has the given local
 622  * space as domain and that has a zero-dimensional range.
 623  */
 624 __isl_give isl_local_space *isl_local_space_from_domain(
 625         __isl_take isl_local_space *ls)
 626 {
 627         ls = isl_local_space_cow(ls);
 628         if (!ls)
 629                 return NULL;
 630         ls->dim = isl_space_from_domain(ls->dim);
 631         if (!ls->dim)
 632                 return isl_local_space_free(ls);
 633         return ls;
 634 }
 635
 636 __isl_give isl_local_space *isl_local_space_add_dims(
 637         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 638 {
 639         int pos;
 640
 641         if (!ls)
 642                 return NULL;
 643         pos = isl_local_space_dim(ls, type);
 644         return isl_local_space_insert_dims(ls, type, pos, n);
 645 }
 646
 647 /* Remove common factor of non-constant terms and denominator.
 648  */
 649 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 650 {
 651         isl_ctx *ctx = ls->div->ctx;
 652         unsigned total = ls->div->n_col - 2;
 653
 654         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 655         isl_int_gcd(ctx->normalize_gcd,
 656                     ctx->normalize_gcd, ls->div->row[div][0]);
 657         if (isl_int_is_one(ctx->normalize_gcd))
 658                 return;
 659
 660         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 661                             ctx->normalize_gcd, total);
 662         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 663                             ctx->normalize_gcd);
 664         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 665                             ctx->normalize_gcd);
 666 }
 667
 668 /* Exploit the equalities in "eq" to simplify the expressions of
 669  * the integer divisions in "ls".
 670  * The integer divisions in "ls" are assumed to appear as regular
 671  * dimensions in "eq".
 672  */
 673 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 674         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 675 {
 676         int i, j, k;
 677         unsigned total;
 678         unsigned n_div;
 679
 680         ls = isl_local_space_cow(ls);
 681         if (!ls || !eq)
 682                 goto error;
 683
 684         total = isl_space_dim(eq->dim, isl_dim_all);
 685         if (isl_local_space_dim(ls, isl_dim_all) != total)
 686                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 687                         "dimensions don't match", goto error);
 688         total++;
 689         n_div = eq->n_div;
 690         for (i = 0; i < eq->n_eq; ++i) {
 691                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 692                 if (j < 0 || j == 0 || j >= total)
 693                         continue;
 694
 695                 for (k = 0; k < ls->div->n_row; ++k) {
 696                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 697                                 continue;
 698                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 699                                         &ls->div->row[k][0]);
 700                         normalize_div(ls, k);
 701                 }
 702         }
 703
 704         isl_basic_set_free(eq);
 705         return ls;
 706 error:
 707         isl_basic_set_free(eq);
 708         isl_local_space_free(ls);
 709         return NULL;
 710 }
 711
 712 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 713  * of "ls".
 714  *
 715  * Let i be the dimension to replace and let "subs" be of the form
 716  *
 717  *      f/d
 718  *
 719  * Any integer division with a non-zero coefficient for i,
 720  *
 721  *      floor((a i + g)/m)
 722  *
 723  * is replaced by
 724  *
 725  *      floor((a f + d g)/(m d))
 726  */
 727 __isl_give isl_local_space *isl_local_space_substitute(
 728         __isl_take isl_local_space *ls,
 729         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 730 {
 731         int i;
 732         isl_int v;
 733
 734         ls = isl_local_space_cow(ls);
 735         if (!ls || !subs)
 736                 return isl_local_space_free(ls);
 737
 738         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 739                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 740                         "spaces don't match", return isl_local_space_free(ls));
 741         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 742                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 743                         "cannot handle divs yet",
 744                         return isl_local_space_free(ls));
 745
 746         pos += isl_local_space_offset(ls, type);
 747
 748         isl_int_init(v);
 749         for (i = 0; i < ls->div->n_row; ++i) {
 750                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 751                         continue;
 752                 isl_int_set(v, ls->div->row[i][1 + pos]);
 753                 isl_int_set_si(ls->div->row[i][1 + pos], 0);
 754                 isl_seq_combine(ls->div->row[i] + 1,
 755                                 subs->v->el[0], ls->div->row[i] + 1,
 756                                 v, subs->v->el + 1, subs->v->size - 1);
 757                 isl_int_mul(ls->div->row[i][0],
 758                             ls->div->row[i][0], subs->v->el[0]);
 759                 normalize_div(ls, i);
 760         }
 761         isl_int_clear(v);
 762
 763         return ls;
 764 }
 765
 766 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 767         enum isl_dim_type type)
 768 {
 769         if (!ls)
 770                 return -1;
 771         return isl_space_is_named_or_nested(ls->dim, type);
 772 }
 773
 774 __isl_give isl_local_space *isl_local_space_drop_dims(
 775         __isl_take isl_local_space *ls,
 776         enum isl_dim_type type, unsigned first, unsigned n)
 777 {
 778         isl_ctx *ctx;
 779
 780         if (!ls)
 781                 return NULL;
 782         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 783                 return ls;
 784
 785         ctx = isl_local_space_get_ctx(ls);
 786         if (first + n > isl_local_space_dim(ls, type))
 787                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 788                         return isl_local_space_free(ls));
 789
 790         ls = isl_local_space_cow(ls);
 791         if (!ls)
 792                 return NULL;
 793
 794         if (type == isl_dim_div) {
 795                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 796         } else {
 797                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 798                 if (!ls->dim)
 799                         return isl_local_space_free(ls);
 800         }
 801
 802         first += 1 + isl_local_space_offset(ls, type);
 803         ls->div = isl_mat_drop_cols(ls->div, first, n);
 804         if (!ls->div)
 805                 return isl_local_space_free(ls);
 806
 807         return ls;
 808 }
 809
 810 __isl_give isl_local_space *isl_local_space_insert_dims(
 811         __isl_take isl_local_space *ls,
 812         enum isl_dim_type type, unsigned first, unsigned n)
 813 {
 814         isl_ctx *ctx;
 815
 816         if (!ls)
 817                 return NULL;
 818         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 819                 return ls;
 820
 821         ctx = isl_local_space_get_ctx(ls);
 822         if (first > isl_local_space_dim(ls, type))
 823                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 824                         return isl_local_space_free(ls));
 825
 826         ls = isl_local_space_cow(ls);
 827         if (!ls)
 828                 return NULL;
 829
 830         if (type == isl_dim_div) {
 831                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 832         } else {
 833                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 834                 if (!ls->dim)
 835                         return isl_local_space_free(ls);
 836         }
 837
 838         first += 1 + isl_local_space_offset(ls, type);
 839         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 840         if (!ls->div)
 841                 return isl_local_space_free(ls);
 842
 843         return ls;
 844 }
 845
 846 /* Check if the constraints pointed to by "constraint" is a div
 847  * constraint corresponding to div "div" in "ls".
 848  *
 849  * That is, if div = floor(f/m), then check if the constraint is
 850  *
 851  *              f - m d >= 0
 852  * or
 853  *              -(f-(m-1)) + m d >= 0
 854  */
 855 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 856         isl_int *constraint, unsigned div)
 857 {
 858         unsigned pos;
 859
 860         if (!ls)
 861                 return -1;
 862
 863         if (isl_int_is_zero(ls->div->row[div][0]))
 864                 return 0;
 865
 866         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 867
 868         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 869                 int neg;
 870                 isl_int_sub(ls->div->row[div][1],
 871                                 ls->div->row[div][1], ls->div->row[div][0]);
 872                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 873                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 874                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 875                 isl_int_add(ls->div->row[div][1],
 876                                 ls->div->row[div][1], ls->div->row[div][0]);
 877                 if (!neg)
 878                         return 0;
 879                 if (isl_seq_first_non_zero(constraint+pos+1,
 880                                             ls->div->n_row-div-1) != -1)
 881                         return 0;
 882         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 883                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 884                         return 0;
 885                 if (isl_seq_first_non_zero(constraint+pos+1,
 886                                             ls->div->n_row-div-1) != -1)
 887                         return 0;
 888         } else
 889                 return 0;
 890
 891         return 1;
 892 }
 893
 894 /*
 895  * Set active[i] to 1 if the dimension at position i is involved
 896  * in the linear expression l.
 897  */
 898 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 899 {
 900         int i, j;
 901         isl_ctx *ctx;
 902         int *active = NULL;
 903         unsigned total;
 904         unsigned offset;
 905
 906         ctx = isl_local_space_get_ctx(ls);
 907         total = isl_local_space_dim(ls, isl_dim_all);
 908         active = isl_calloc_array(ctx, int, total);
 909         if (!active)
 910                 return NULL;
 911
 912         for (i = 0; i < total; ++i)
 913                 active[i] = !isl_int_is_zero(l[i]);
 914
 915         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 916         for (i = ls->div->n_row - 1; i >= 0; --i) {
 917                 if (!active[offset + i])
 918                         continue;
 919                 for (j = 0; j < total; ++j)
 920                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 921         }
 922
 923         return active;
 924 }
 925
 926 /* Given a local space "ls" of a set, create a local space
 927  * for the lift of the set.  In particular, the result
 928  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
 929  * range of the wrapped map.
 930  */
 931 __isl_give isl_local_space *isl_local_space_lift(
 932         __isl_take isl_local_space *ls)
 933 {
 934         ls = isl_local_space_cow(ls);
 935         if (!ls)
 936                 return NULL;
 937
 938         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
 939         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
 940         if (!ls->dim || !ls->div)
 941                 return isl_local_space_free(ls);
 942
 943         return ls;
 944 }
 945
 946 /* Construct a basic map that maps a set living in local space "ls"
 947  * to the corresponding lifted local space.
 948  */
 949 __isl_give isl_basic_map *isl_local_space_lifting(
 950         __isl_take isl_local_space *ls)
 951 {
 952         isl_basic_map *lifting;
 953         isl_basic_set *bset;
 954
 955         if (!ls)
 956                 return NULL;
 957         if (!isl_local_space_is_set(ls))
 958                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 959                         "lifting only defined on set spaces",
 960                         return isl_local_space_free(ls));
 961
 962         bset = isl_basic_set_from_local_space(ls);
 963         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
 964         lifting = isl_basic_map_domain_map(lifting);
 965         lifting = isl_basic_map_reverse(lifting);
 966
 967         return lifting;
 968 }