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 /* Does the given dimension have a name?
 182  */
 183 int isl_local_space_has_dim_name(__isl_keep isl_local_space *ls,
 184         enum isl_dim_type type, unsigned pos)
 185 {
 186         return ls ? isl_space_has_dim_name(ls->dim, type, pos) : -1;
 187 }
 188
 189 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 190         enum isl_dim_type type, unsigned pos)
 191 {
 192         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 193 }
 194
 195 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 196         int pos)
 197 {
 198         isl_aff *aff;
 199
 200         if (!ls)
 201                 return NULL;
 202
 203         if (pos < 0 || pos >= ls->div->n_row)
 204                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 205                         "index out of bounds", return NULL);
 206
 207         if (isl_int_is_zero(ls->div->row[pos][0]))
 208                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 209                         "expression of div unknown", return NULL);
 210
 211         aff = isl_aff_alloc(isl_local_space_copy(ls));
 212         if (!aff)
 213                 return NULL;
 214         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 215         return aff;
 216 }
 217
 218 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 219 {
 220         if (!ls)
 221                 return NULL;
 222
 223         return isl_space_copy(ls->dim);
 224 }
 225
 226 __isl_give isl_local_space *isl_local_space_set_dim_name(
 227         __isl_take isl_local_space *ls,
 228         enum isl_dim_type type, unsigned pos, const char *s)
 229 {
 230         ls = isl_local_space_cow(ls);
 231         if (!ls)
 232                 return NULL;
 233         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 234         if (!ls->dim)
 235                 return isl_local_space_free(ls);
 236
 237         return ls;
 238 }
 239
 240 __isl_give isl_local_space *isl_local_space_set_dim_id(
 241         __isl_take isl_local_space *ls,
 242         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 243 {
 244         ls = isl_local_space_cow(ls);
 245         if (!ls)
 246                 return isl_id_free(id);
 247         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 248         if (!ls->dim)
 249                 return isl_local_space_free(ls);
 250
 251         return ls;
 252 }
 253
 254 __isl_give isl_local_space *isl_local_space_reset_space(
 255         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 256 {
 257         ls = isl_local_space_cow(ls);
 258         if (!ls || !dim)
 259                 goto error;
 260
 261         isl_space_free(ls->dim);
 262         ls->dim = dim;
 263
 264         return ls;
 265 error:
 266         isl_local_space_free(ls);
 267         isl_space_free(dim);
 268         return NULL;
 269 }
 270
 271 /* Reorder the columns of the given div definitions according to the
 272  * given reordering.
 273  * The order of the divs themselves is assumed not to change.
 274  */
 275 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 276         __isl_take isl_reordering *r)
 277 {
 278         int i, j;
 279         isl_mat *mat;
 280         int extra;
 281
 282         if (!div || !r)
 283                 goto error;
 284
 285         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 286         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 287         if (!mat)
 288                 goto error;
 289
 290         for (i = 0; i < div->n_row; ++i) {
 291                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 292                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 293                 for (j = 0; j < r->len; ++j)
 294                         isl_int_set(mat->row[i][2 + r->pos[j]],
 295                                     div->row[i][2 + j]);
 296         }
 297
 298         isl_reordering_free(r);
 299         isl_mat_free(div);
 300         return mat;
 301 error:
 302         isl_reordering_free(r);
 303         isl_mat_free(div);
 304         return NULL;
 305 }
 306
 307 /* Reorder the dimensions of "ls" according to the given reordering.
 308  * The reordering r is assumed to have been extended with the local
 309  * variables, leaving them in the same order.
 310  */
 311 __isl_give isl_local_space *isl_local_space_realign(
 312         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 313 {
 314         ls = isl_local_space_cow(ls);
 315         if (!ls || !r)
 316                 goto error;
 317
 318         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 319         if (!ls->div)
 320                 goto error;
 321
 322         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 323
 324         isl_reordering_free(r);
 325         return ls;
 326 error:
 327         isl_local_space_free(ls);
 328         isl_reordering_free(r);
 329         return NULL;
 330 }
 331
 332 __isl_give isl_local_space *isl_local_space_add_div(
 333         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 334 {
 335         ls = isl_local_space_cow(ls);
 336         if (!ls || !div)
 337                 goto error;
 338
 339         if (ls->div->n_col != div->size)
 340                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 341                         "incompatible dimensions", goto error);
 342
 343         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 344         ls->div = isl_mat_add_rows(ls->div, 1);
 345         if (!ls->div)
 346                 goto error;
 347
 348         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 349         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 350
 351         isl_vec_free(div);
 352         return ls;
 353 error:
 354         isl_local_space_free(ls);
 355         isl_vec_free(div);
 356         return NULL;
 357 }
 358
 359 __isl_give isl_local_space *isl_local_space_replace_divs(
 360         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 361 {
 362         ls = isl_local_space_cow(ls);
 363
 364         if (!ls || !div)
 365                 goto error;
 366
 367         isl_mat_free(ls->div);
 368         ls->div = div;
 369         return ls;
 370 error:
 371         isl_mat_free(div);
 372         isl_local_space_free(ls);
 373         return NULL;
 374 }
 375
 376 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 377  * defined by "exp".
 378  */
 379 static void expand_row(__isl_keep isl_mat *dst, int d,
 380         __isl_keep isl_mat *src, int s, int *exp)
 381 {
 382         int i;
 383         unsigned c = src->n_col - src->n_row;
 384
 385         isl_seq_cpy(dst->row[d], src->row[s], c);
 386         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 387
 388         for (i = 0; i < s; ++i)
 389                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 390 }
 391
 392 /* Compare (known) divs.
 393  * Return non-zero if at least one of the two divs is unknown.
 394  * In particular, if both divs are unknown, we respect their
 395  * current order.  Otherwise, we sort the known div after the unknown
 396  * div only if the known div depends on the unknown div.
 397  */
 398 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 399         unsigned n_row, unsigned n_col)
 400 {
 401         int li, lj;
 402         int unknown_i, unknown_j;
 403
 404         unknown_i = isl_int_is_zero(row_i[0]);
 405         unknown_j = isl_int_is_zero(row_j[0]);
 406
 407         if (unknown_i && unknown_j)
 408                 return i - j;
 409
 410         if (unknown_i)
 411                 li = n_col - n_row + i;
 412         else
 413                 li = isl_seq_last_non_zero(row_i, n_col);
 414         if (unknown_j)
 415                 lj = n_col - n_row + j;
 416         else
 417                 lj = isl_seq_last_non_zero(row_j, n_col);
 418
 419         if (li != lj)
 420                 return li - lj;
 421
 422         return isl_seq_cmp(row_i, row_j, n_col);
 423 }
 424
 425 /* Call cmp_row for divs in a matrix.
 426  */
 427 static int mat_cmp_row(__isl_keep isl_mat *div, int i, int j)
 428 {
 429         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 430 }
 431
 432 /* Call cmp_row for divs in a basic map.
 433  */
 434 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 435         unsigned total)
 436 {
 437         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 438 }
 439
 440 /* Sort the divs in "bmap".
 441  *
 442  * We first make sure divs are placed after divs on which they depend.
 443  * Then we perform a simple insertion sort based on the same ordering
 444  * that is used in isl_merge_divs.
 445  */
 446 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 447         __isl_take isl_basic_map *bmap)
 448 {
 449         int i, j;
 450         unsigned total;
 451
 452         bmap = isl_basic_map_order_divs(bmap);
 453         if (!bmap)
 454                 return NULL;
 455         if (bmap->n_div <= 1)
 456                 return bmap;
 457
 458         total = 2 + isl_basic_map_total_dim(bmap);
 459         for (i = 1; i < bmap->n_div; ++i) {
 460                 for (j = i - 1; j >= 0; --j) {
 461                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 462                                 break;
 463                         isl_basic_map_swap_div(bmap, j, j + 1);
 464                 }
 465         }
 466
 467         return bmap;
 468 }
 469
 470 /* Sort the divs in the basic maps of "map".
 471  */
 472 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 473 {
 474         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 475 }
 476
 477 /* Combine the two lists of divs into a single list.
 478  * For each row i in div1, exp1[i] is set to the position of the corresponding
 479  * row in the result.  Similarly for div2 and exp2.
 480  * This function guarantees
 481  *      exp1[i] >= i
 482  *      exp1[i+1] > exp1[i]
 483  * For optimal merging, the two input list should have been sorted.
 484  */
 485 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 486         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 487 {
 488         int i, j, k;
 489         isl_mat *div = NULL;
 490         unsigned d;
 491
 492         if (!div1 || !div2)
 493                 return NULL;
 494
 495         d = div1->n_col - div1->n_row;
 496         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 497                                 d + div1->n_row + div2->n_row);
 498         if (!div)
 499                 return NULL;
 500
 501         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 502                 int cmp;
 503
 504                 expand_row(div, k, div1, i, exp1);
 505                 expand_row(div, k + 1, div2, j, exp2);
 506
 507                 cmp = mat_cmp_row(div, k, k + 1);
 508                 if (cmp == 0) {
 509                         exp1[i++] = k;
 510                         exp2[j++] = k;
 511                 } else if (cmp < 0) {
 512                         exp1[i++] = k;
 513                 } else {
 514                         exp2[j++] = k;
 515                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 516                 }
 517         }
 518         for (; i < div1->n_row; ++i, ++k) {
 519                 expand_row(div, k, div1, i, exp1);
 520                 exp1[i] = k;
 521         }
 522         for (; j < div2->n_row; ++j, ++k) {
 523                 expand_row(div, k, div2, j, exp2);
 524                 exp2[j] = k;
 525         }
 526
 527         div->n_row = k;
 528         div->n_col = d + k;
 529
 530         return div;
 531 }
 532
 533 /* Construct a local space that contains all the divs in either
 534  * "ls1" or "ls2".
 535  */
 536 __isl_give isl_local_space *isl_local_space_intersect(
 537         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 538 {
 539         isl_ctx *ctx;
 540         int *exp1 = NULL;
 541         int *exp2 = NULL;
 542         isl_mat *div;
 543
 544         if (!ls1 || !ls2)
 545                 goto error;
 546
 547         ctx = isl_local_space_get_ctx(ls1);
 548         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 549                 isl_die(ctx, isl_error_invalid,
 550                         "spaces should be identical", goto error);
 551
 552         if (ls2->div->n_row == 0) {
 553                 isl_local_space_free(ls2);
 554                 return ls1;
 555         }
 556
 557         if (ls1->div->n_row == 0) {
 558                 isl_local_space_free(ls1);
 559                 return ls2;
 560         }
 561
 562         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 563         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 564         if (!exp1 || !exp2)
 565                 goto error;
 566
 567         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 568         if (!div)
 569                 goto error;
 570
 571         free(exp1);
 572         free(exp2);
 573         isl_local_space_free(ls2);
 574         isl_mat_free(ls1->div);
 575         ls1->div = div;
 576
 577         return ls1;
 578 error:
 579         free(exp1);
 580         free(exp2);
 581         isl_local_space_free(ls1);
 582         isl_local_space_free(ls2);
 583         return NULL;
 584 }
 585
 586 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 587 {
 588         int i;
 589
 590         if (!ls)
 591                 return -1;
 592
 593         for (i = 0; i < ls->div->n_row; ++i)
 594                 if (isl_int_is_zero(ls->div->row[i][0]))
 595                         return 0;
 596
 597         return 1;
 598 }
 599
 600 __isl_give isl_local_space *isl_local_space_domain(
 601         __isl_take isl_local_space *ls)
 602 {
 603         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 604                                         0, isl_local_space_dim(ls, isl_dim_out));
 605         ls = isl_local_space_cow(ls);
 606         if (!ls)
 607                 return NULL;
 608         ls->dim = isl_space_domain(ls->dim);
 609         if (!ls->dim)
 610                 return isl_local_space_free(ls);
 611         return ls;
 612 }
 613
 614 __isl_give isl_local_space *isl_local_space_range(
 615         __isl_take isl_local_space *ls)
 616 {
 617         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 618                                         0, isl_local_space_dim(ls, isl_dim_in));
 619         ls = isl_local_space_cow(ls);
 620         if (!ls)
 621                 return NULL;
 622
 623         ls->dim = isl_space_range(ls->dim);
 624         if (!ls->dim)
 625                 return isl_local_space_free(ls);
 626         return ls;
 627 }
 628
 629 /* Construct a local space for a map that has the given local
 630  * space as domain and that has a zero-dimensional range.
 631  */
 632 __isl_give isl_local_space *isl_local_space_from_domain(
 633         __isl_take isl_local_space *ls)
 634 {
 635         ls = isl_local_space_cow(ls);
 636         if (!ls)
 637                 return NULL;
 638         ls->dim = isl_space_from_domain(ls->dim);
 639         if (!ls->dim)
 640                 return isl_local_space_free(ls);
 641         return ls;
 642 }
 643
 644 __isl_give isl_local_space *isl_local_space_add_dims(
 645         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 646 {
 647         int pos;
 648
 649         if (!ls)
 650                 return NULL;
 651         pos = isl_local_space_dim(ls, type);
 652         return isl_local_space_insert_dims(ls, type, pos, n);
 653 }
 654
 655 /* Remove common factor of non-constant terms and denominator.
 656  */
 657 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 658 {
 659         isl_ctx *ctx = ls->div->ctx;
 660         unsigned total = ls->div->n_col - 2;
 661
 662         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 663         isl_int_gcd(ctx->normalize_gcd,
 664                     ctx->normalize_gcd, ls->div->row[div][0]);
 665         if (isl_int_is_one(ctx->normalize_gcd))
 666                 return;
 667
 668         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 669                             ctx->normalize_gcd, total);
 670         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 671                             ctx->normalize_gcd);
 672         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 673                             ctx->normalize_gcd);
 674 }
 675
 676 /* Exploit the equalities in "eq" to simplify the expressions of
 677  * the integer divisions in "ls".
 678  * The integer divisions in "ls" are assumed to appear as regular
 679  * dimensions in "eq".
 680  */
 681 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 682         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 683 {
 684         int i, j, k;
 685         unsigned total;
 686         unsigned n_div;
 687
 688         ls = isl_local_space_cow(ls);
 689         if (!ls || !eq)
 690                 goto error;
 691
 692         total = isl_space_dim(eq->dim, isl_dim_all);
 693         if (isl_local_space_dim(ls, isl_dim_all) != total)
 694                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 695                         "dimensions don't match", goto error);
 696         total++;
 697         n_div = eq->n_div;
 698         for (i = 0; i < eq->n_eq; ++i) {
 699                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 700                 if (j < 0 || j == 0 || j >= total)
 701                         continue;
 702
 703                 for (k = 0; k < ls->div->n_row; ++k) {
 704                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 705                                 continue;
 706                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 707                                         &ls->div->row[k][0]);
 708                         normalize_div(ls, k);
 709                 }
 710         }
 711
 712         isl_basic_set_free(eq);
 713         return ls;
 714 error:
 715         isl_basic_set_free(eq);
 716         isl_local_space_free(ls);
 717         return NULL;
 718 }
 719
 720 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 721  * of "ls".
 722  *
 723  * Let i be the dimension to replace and let "subs" be of the form
 724  *
 725  *      f/d
 726  *
 727  * Any integer division with a non-zero coefficient for i,
 728  *
 729  *      floor((a i + g)/m)
 730  *
 731  * is replaced by
 732  *
 733  *      floor((a f + d g)/(m d))
 734  */
 735 __isl_give isl_local_space *isl_local_space_substitute(
 736         __isl_take isl_local_space *ls,
 737         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 738 {
 739         int i;
 740         isl_int v;
 741
 742         ls = isl_local_space_cow(ls);
 743         if (!ls || !subs)
 744                 return isl_local_space_free(ls);
 745
 746         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 747                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 748                         "spaces don't match", return isl_local_space_free(ls));
 749         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 750                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 751                         "cannot handle divs yet",
 752                         return isl_local_space_free(ls));
 753
 754         pos += isl_local_space_offset(ls, type);
 755
 756         isl_int_init(v);
 757         for (i = 0; i < ls->div->n_row; ++i) {
 758                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 759                         continue;
 760                 isl_int_set(v, ls->div->row[i][1 + pos]);
 761                 isl_int_set_si(ls->div->row[i][1 + pos], 0);
 762                 isl_seq_combine(ls->div->row[i] + 1,
 763                                 subs->v->el[0], ls->div->row[i] + 1,
 764                                 v, subs->v->el + 1, subs->v->size - 1);
 765                 isl_int_mul(ls->div->row[i][0],
 766                             ls->div->row[i][0], subs->v->el[0]);
 767                 normalize_div(ls, i);
 768         }
 769         isl_int_clear(v);
 770
 771         return ls;
 772 }
 773
 774 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 775         enum isl_dim_type type)
 776 {
 777         if (!ls)
 778                 return -1;
 779         return isl_space_is_named_or_nested(ls->dim, type);
 780 }
 781
 782 __isl_give isl_local_space *isl_local_space_drop_dims(
 783         __isl_take isl_local_space *ls,
 784         enum isl_dim_type type, unsigned first, unsigned n)
 785 {
 786         isl_ctx *ctx;
 787
 788         if (!ls)
 789                 return NULL;
 790         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 791                 return ls;
 792
 793         ctx = isl_local_space_get_ctx(ls);
 794         if (first + n > isl_local_space_dim(ls, type))
 795                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 796                         return isl_local_space_free(ls));
 797
 798         ls = isl_local_space_cow(ls);
 799         if (!ls)
 800                 return NULL;
 801
 802         if (type == isl_dim_div) {
 803                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 804         } else {
 805                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 806                 if (!ls->dim)
 807                         return isl_local_space_free(ls);
 808         }
 809
 810         first += 1 + isl_local_space_offset(ls, type);
 811         ls->div = isl_mat_drop_cols(ls->div, first, n);
 812         if (!ls->div)
 813                 return isl_local_space_free(ls);
 814
 815         return ls;
 816 }
 817
 818 __isl_give isl_local_space *isl_local_space_insert_dims(
 819         __isl_take isl_local_space *ls,
 820         enum isl_dim_type type, unsigned first, unsigned n)
 821 {
 822         isl_ctx *ctx;
 823
 824         if (!ls)
 825                 return NULL;
 826         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 827                 return ls;
 828
 829         ctx = isl_local_space_get_ctx(ls);
 830         if (first > isl_local_space_dim(ls, type))
 831                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 832                         return isl_local_space_free(ls));
 833
 834         ls = isl_local_space_cow(ls);
 835         if (!ls)
 836                 return NULL;
 837
 838         if (type == isl_dim_div) {
 839                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 840         } else {
 841                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 842                 if (!ls->dim)
 843                         return isl_local_space_free(ls);
 844         }
 845
 846         first += 1 + isl_local_space_offset(ls, type);
 847         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 848         if (!ls->div)
 849                 return isl_local_space_free(ls);
 850
 851         return ls;
 852 }
 853
 854 /* Check if the constraints pointed to by "constraint" is a div
 855  * constraint corresponding to div "div" in "ls".
 856  *
 857  * That is, if div = floor(f/m), then check if the constraint is
 858  *
 859  *              f - m d >= 0
 860  * or
 861  *              -(f-(m-1)) + m d >= 0
 862  */
 863 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 864         isl_int *constraint, unsigned div)
 865 {
 866         unsigned pos;
 867
 868         if (!ls)
 869                 return -1;
 870
 871         if (isl_int_is_zero(ls->div->row[div][0]))
 872                 return 0;
 873
 874         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 875
 876         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 877                 int neg;
 878                 isl_int_sub(ls->div->row[div][1],
 879                                 ls->div->row[div][1], ls->div->row[div][0]);
 880                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 881                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 882                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 883                 isl_int_add(ls->div->row[div][1],
 884                                 ls->div->row[div][1], ls->div->row[div][0]);
 885                 if (!neg)
 886                         return 0;
 887                 if (isl_seq_first_non_zero(constraint+pos+1,
 888                                             ls->div->n_row-div-1) != -1)
 889                         return 0;
 890         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 891                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 892                         return 0;
 893                 if (isl_seq_first_non_zero(constraint+pos+1,
 894                                             ls->div->n_row-div-1) != -1)
 895                         return 0;
 896         } else
 897                 return 0;
 898
 899         return 1;
 900 }
 901
 902 /*
 903  * Set active[i] to 1 if the dimension at position i is involved
 904  * in the linear expression l.
 905  */
 906 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 907 {
 908         int i, j;
 909         isl_ctx *ctx;
 910         int *active = NULL;
 911         unsigned total;
 912         unsigned offset;
 913
 914         ctx = isl_local_space_get_ctx(ls);
 915         total = isl_local_space_dim(ls, isl_dim_all);
 916         active = isl_calloc_array(ctx, int, total);
 917         if (!active)
 918                 return NULL;
 919
 920         for (i = 0; i < total; ++i)
 921                 active[i] = !isl_int_is_zero(l[i]);
 922
 923         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 924         for (i = ls->div->n_row - 1; i >= 0; --i) {
 925                 if (!active[offset + i])
 926                         continue;
 927                 for (j = 0; j < total; ++j)
 928                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 929         }
 930
 931         return active;
 932 }
 933
 934 /* Given a local space "ls" of a set, create a local space
 935  * for the lift of the set.  In particular, the result
 936  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
 937  * range of the wrapped map.
 938  */
 939 __isl_give isl_local_space *isl_local_space_lift(
 940         __isl_take isl_local_space *ls)
 941 {
 942         ls = isl_local_space_cow(ls);
 943         if (!ls)
 944                 return NULL;
 945
 946         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
 947         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
 948         if (!ls->dim || !ls->div)
 949                 return isl_local_space_free(ls);
 950
 951         return ls;
 952 }
 953
 954 /* Construct a basic map that maps a set living in local space "ls"
 955  * to the corresponding lifted local space.
 956  */
 957 __isl_give isl_basic_map *isl_local_space_lifting(
 958         __isl_take isl_local_space *ls)
 959 {
 960         isl_basic_map *lifting;
 961         isl_basic_set *bset;
 962
 963         if (!ls)
 964                 return NULL;
 965         if (!isl_local_space_is_set(ls))
 966                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 967                         "lifting only defined on set spaces",
 968                         return isl_local_space_free(ls));
 969
 970         bset = isl_basic_set_from_local_space(ls);
 971         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
 972         lifting = isl_basic_map_domain_map(lifting);
 973         lifting = isl_basic_map_reverse(lifting);
 974
 975         return lifting;
 976 }