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 MIT 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 int isl_local_space_has_dim_id(__isl_keep isl_local_space *ls,
 196         enum isl_dim_type type, unsigned pos)
 197 {
 198         return ls ? isl_space_has_dim_id(ls->dim, type, pos) : -1;
 199 }
 200
 201 __isl_give isl_id *isl_local_space_get_dim_id(__isl_keep isl_local_space *ls,
 202         enum isl_dim_type type, unsigned pos)
 203 {
 204         return ls ? isl_space_get_dim_id(ls->dim, type, pos) : NULL;
 205 }
 206
 207 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 208         int pos)
 209 {
 210         isl_aff *aff;
 211
 212         if (!ls)
 213                 return NULL;
 214
 215         if (pos < 0 || pos >= ls->div->n_row)
 216                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 217                         "index out of bounds", return NULL);
 218
 219         if (isl_int_is_zero(ls->div->row[pos][0]))
 220                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 221                         "expression of div unknown", return NULL);
 222
 223         aff = isl_aff_alloc(isl_local_space_copy(ls));
 224         if (!aff)
 225                 return NULL;
 226         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 227         return aff;
 228 }
 229
 230 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 231 {
 232         if (!ls)
 233                 return NULL;
 234
 235         return isl_space_copy(ls->dim);
 236 }
 237
 238 __isl_give isl_local_space *isl_local_space_set_dim_name(
 239         __isl_take isl_local_space *ls,
 240         enum isl_dim_type type, unsigned pos, const char *s)
 241 {
 242         ls = isl_local_space_cow(ls);
 243         if (!ls)
 244                 return NULL;
 245         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 246         if (!ls->dim)
 247                 return isl_local_space_free(ls);
 248
 249         return ls;
 250 }
 251
 252 __isl_give isl_local_space *isl_local_space_set_dim_id(
 253         __isl_take isl_local_space *ls,
 254         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 255 {
 256         ls = isl_local_space_cow(ls);
 257         if (!ls)
 258                 return isl_id_free(id);
 259         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 260         if (!ls->dim)
 261                 return isl_local_space_free(ls);
 262
 263         return ls;
 264 }
 265
 266 __isl_give isl_local_space *isl_local_space_reset_space(
 267         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 268 {
 269         ls = isl_local_space_cow(ls);
 270         if (!ls || !dim)
 271                 goto error;
 272
 273         isl_space_free(ls->dim);
 274         ls->dim = dim;
 275
 276         return ls;
 277 error:
 278         isl_local_space_free(ls);
 279         isl_space_free(dim);
 280         return NULL;
 281 }
 282
 283 /* Reorder the columns of the given div definitions according to the
 284  * given reordering.
 285  * The order of the divs themselves is assumed not to change.
 286  */
 287 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 288         __isl_take isl_reordering *r)
 289 {
 290         int i, j;
 291         isl_mat *mat;
 292         int extra;
 293
 294         if (!div || !r)
 295                 goto error;
 296
 297         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 298         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 299         if (!mat)
 300                 goto error;
 301
 302         for (i = 0; i < div->n_row; ++i) {
 303                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 304                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 305                 for (j = 0; j < r->len; ++j)
 306                         isl_int_set(mat->row[i][2 + r->pos[j]],
 307                                     div->row[i][2 + j]);
 308         }
 309
 310         isl_reordering_free(r);
 311         isl_mat_free(div);
 312         return mat;
 313 error:
 314         isl_reordering_free(r);
 315         isl_mat_free(div);
 316         return NULL;
 317 }
 318
 319 /* Reorder the dimensions of "ls" according to the given reordering.
 320  * The reordering r is assumed to have been extended with the local
 321  * variables, leaving them in the same order.
 322  */
 323 __isl_give isl_local_space *isl_local_space_realign(
 324         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 325 {
 326         ls = isl_local_space_cow(ls);
 327         if (!ls || !r)
 328                 goto error;
 329
 330         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 331         if (!ls->div)
 332                 goto error;
 333
 334         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 335
 336         isl_reordering_free(r);
 337         return ls;
 338 error:
 339         isl_local_space_free(ls);
 340         isl_reordering_free(r);
 341         return NULL;
 342 }
 343
 344 __isl_give isl_local_space *isl_local_space_add_div(
 345         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 346 {
 347         ls = isl_local_space_cow(ls);
 348         if (!ls || !div)
 349                 goto error;
 350
 351         if (ls->div->n_col != div->size)
 352                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 353                         "incompatible dimensions", goto error);
 354
 355         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 356         ls->div = isl_mat_add_rows(ls->div, 1);
 357         if (!ls->div)
 358                 goto error;
 359
 360         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 361         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 362
 363         isl_vec_free(div);
 364         return ls;
 365 error:
 366         isl_local_space_free(ls);
 367         isl_vec_free(div);
 368         return NULL;
 369 }
 370
 371 __isl_give isl_local_space *isl_local_space_replace_divs(
 372         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 373 {
 374         ls = isl_local_space_cow(ls);
 375
 376         if (!ls || !div)
 377                 goto error;
 378
 379         isl_mat_free(ls->div);
 380         ls->div = div;
 381         return ls;
 382 error:
 383         isl_mat_free(div);
 384         isl_local_space_free(ls);
 385         return NULL;
 386 }
 387
 388 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 389  * defined by "exp".
 390  */
 391 static void expand_row(__isl_keep isl_mat *dst, int d,
 392         __isl_keep isl_mat *src, int s, int *exp)
 393 {
 394         int i;
 395         unsigned c = src->n_col - src->n_row;
 396
 397         isl_seq_cpy(dst->row[d], src->row[s], c);
 398         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 399
 400         for (i = 0; i < s; ++i)
 401                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 402 }
 403
 404 /* Compare (known) divs.
 405  * Return non-zero if at least one of the two divs is unknown.
 406  * In particular, if both divs are unknown, we respect their
 407  * current order.  Otherwise, we sort the known div after the unknown
 408  * div only if the known div depends on the unknown div.
 409  */
 410 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 411         unsigned n_row, unsigned n_col)
 412 {
 413         int li, lj;
 414         int unknown_i, unknown_j;
 415
 416         unknown_i = isl_int_is_zero(row_i[0]);
 417         unknown_j = isl_int_is_zero(row_j[0]);
 418
 419         if (unknown_i && unknown_j)
 420                 return i - j;
 421
 422         if (unknown_i)
 423                 li = n_col - n_row + i;
 424         else
 425                 li = isl_seq_last_non_zero(row_i, n_col);
 426         if (unknown_j)
 427                 lj = n_col - n_row + j;
 428         else
 429                 lj = isl_seq_last_non_zero(row_j, n_col);
 430
 431         if (li != lj)
 432                 return li - lj;
 433
 434         return isl_seq_cmp(row_i, row_j, n_col);
 435 }
 436
 437 /* Call cmp_row for divs in a matrix.
 438  */
 439 int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)
 440 {
 441         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 442 }
 443
 444 /* Call cmp_row for divs in a basic map.
 445  */
 446 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 447         unsigned total)
 448 {
 449         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 450 }
 451
 452 /* Sort the divs in "bmap".
 453  *
 454  * We first make sure divs are placed after divs on which they depend.
 455  * Then we perform a simple insertion sort based on the same ordering
 456  * that is used in isl_merge_divs.
 457  */
 458 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 459         __isl_take isl_basic_map *bmap)
 460 {
 461         int i, j;
 462         unsigned total;
 463
 464         bmap = isl_basic_map_order_divs(bmap);
 465         if (!bmap)
 466                 return NULL;
 467         if (bmap->n_div <= 1)
 468                 return bmap;
 469
 470         total = 2 + isl_basic_map_total_dim(bmap);
 471         for (i = 1; i < bmap->n_div; ++i) {
 472                 for (j = i - 1; j >= 0; --j) {
 473                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 474                                 break;
 475                         isl_basic_map_swap_div(bmap, j, j + 1);
 476                 }
 477         }
 478
 479         return bmap;
 480 }
 481
 482 /* Sort the divs in the basic maps of "map".
 483  */
 484 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 485 {
 486         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 487 }
 488
 489 /* Combine the two lists of divs into a single list.
 490  * For each row i in div1, exp1[i] is set to the position of the corresponding
 491  * row in the result.  Similarly for div2 and exp2.
 492  * This function guarantees
 493  *      exp1[i] >= i
 494  *      exp1[i+1] > exp1[i]
 495  * For optimal merging, the two input list should have been sorted.
 496  */
 497 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 498         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 499 {
 500         int i, j, k;
 501         isl_mat *div = NULL;
 502         unsigned d;
 503
 504         if (!div1 || !div2)
 505                 return NULL;
 506
 507         d = div1->n_col - div1->n_row;
 508         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 509                                 d + div1->n_row + div2->n_row);
 510         if (!div)
 511                 return NULL;
 512
 513         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 514                 int cmp;
 515
 516                 expand_row(div, k, div1, i, exp1);
 517                 expand_row(div, k + 1, div2, j, exp2);
 518
 519                 cmp = isl_mat_cmp_div(div, k, k + 1);
 520                 if (cmp == 0) {
 521                         exp1[i++] = k;
 522                         exp2[j++] = k;
 523                 } else if (cmp < 0) {
 524                         exp1[i++] = k;
 525                 } else {
 526                         exp2[j++] = k;
 527                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 528                 }
 529         }
 530         for (; i < div1->n_row; ++i, ++k) {
 531                 expand_row(div, k, div1, i, exp1);
 532                 exp1[i] = k;
 533         }
 534         for (; j < div2->n_row; ++j, ++k) {
 535                 expand_row(div, k, div2, j, exp2);
 536                 exp2[j] = k;
 537         }
 538
 539         div->n_row = k;
 540         div->n_col = d + k;
 541
 542         return div;
 543 }
 544
 545 /* Swap divs "a" and "b" in "ls".
 546  */
 547 __isl_give isl_local_space *isl_local_space_swap_div(
 548         __isl_take isl_local_space *ls, int a, int b)
 549 {
 550         int offset;
 551
 552         ls = isl_local_space_cow(ls);
 553         if (!ls)
 554                 return NULL;
 555         if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)
 556                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 557                         "index out of bounds", return isl_local_space_free(ls));
 558         offset = ls->div->n_col - ls->div->n_row;
 559         ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);
 560         ls->div = isl_mat_swap_rows(ls->div, a, b);
 561         if (!ls->div)
 562                 return isl_local_space_free(ls);
 563         return ls;
 564 }
 565
 566 /* Construct a local space that contains all the divs in either
 567  * "ls1" or "ls2".
 568  */
 569 __isl_give isl_local_space *isl_local_space_intersect(
 570         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 571 {
 572         isl_ctx *ctx;
 573         int *exp1 = NULL;
 574         int *exp2 = NULL;
 575         isl_mat *div;
 576
 577         if (!ls1 || !ls2)
 578                 goto error;
 579
 580         ctx = isl_local_space_get_ctx(ls1);
 581         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 582                 isl_die(ctx, isl_error_invalid,
 583                         "spaces should be identical", goto error);
 584
 585         if (ls2->div->n_row == 0) {
 586                 isl_local_space_free(ls2);
 587                 return ls1;
 588         }
 589
 590         if (ls1->div->n_row == 0) {
 591                 isl_local_space_free(ls1);
 592                 return ls2;
 593         }
 594
 595         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 596         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 597         if (!exp1 || !exp2)
 598                 goto error;
 599
 600         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 601         if (!div)
 602                 goto error;
 603
 604         free(exp1);
 605         free(exp2);
 606         isl_local_space_free(ls2);
 607         isl_mat_free(ls1->div);
 608         ls1->div = div;
 609
 610         return ls1;
 611 error:
 612         free(exp1);
 613         free(exp2);
 614         isl_local_space_free(ls1);
 615         isl_local_space_free(ls2);
 616         return NULL;
 617 }
 618
 619 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 620 {
 621         int i;
 622
 623         if (!ls)
 624                 return -1;
 625
 626         for (i = 0; i < ls->div->n_row; ++i)
 627                 if (isl_int_is_zero(ls->div->row[i][0]))
 628                         return 0;
 629
 630         return 1;
 631 }
 632
 633 __isl_give isl_local_space *isl_local_space_domain(
 634         __isl_take isl_local_space *ls)
 635 {
 636         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 637                                         0, isl_local_space_dim(ls, isl_dim_out));
 638         ls = isl_local_space_cow(ls);
 639         if (!ls)
 640                 return NULL;
 641         ls->dim = isl_space_domain(ls->dim);
 642         if (!ls->dim)
 643                 return isl_local_space_free(ls);
 644         return ls;
 645 }
 646
 647 __isl_give isl_local_space *isl_local_space_range(
 648         __isl_take isl_local_space *ls)
 649 {
 650         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 651                                         0, isl_local_space_dim(ls, isl_dim_in));
 652         ls = isl_local_space_cow(ls);
 653         if (!ls)
 654                 return NULL;
 655
 656         ls->dim = isl_space_range(ls->dim);
 657         if (!ls->dim)
 658                 return isl_local_space_free(ls);
 659         return ls;
 660 }
 661
 662 /* Construct a local space for a map that has the given local
 663  * space as domain and that has a zero-dimensional range.
 664  */
 665 __isl_give isl_local_space *isl_local_space_from_domain(
 666         __isl_take isl_local_space *ls)
 667 {
 668         ls = isl_local_space_cow(ls);
 669         if (!ls)
 670                 return NULL;
 671         ls->dim = isl_space_from_domain(ls->dim);
 672         if (!ls->dim)
 673                 return isl_local_space_free(ls);
 674         return ls;
 675 }
 676
 677 __isl_give isl_local_space *isl_local_space_add_dims(
 678         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 679 {
 680         int pos;
 681
 682         if (!ls)
 683                 return NULL;
 684         pos = isl_local_space_dim(ls, type);
 685         return isl_local_space_insert_dims(ls, type, pos, n);
 686 }
 687
 688 /* Remove common factor of non-constant terms and denominator.
 689  */
 690 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 691 {
 692         isl_ctx *ctx = ls->div->ctx;
 693         unsigned total = ls->div->n_col - 2;
 694
 695         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 696         isl_int_gcd(ctx->normalize_gcd,
 697                     ctx->normalize_gcd, ls->div->row[div][0]);
 698         if (isl_int_is_one(ctx->normalize_gcd))
 699                 return;
 700
 701         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 702                             ctx->normalize_gcd, total);
 703         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 704                             ctx->normalize_gcd);
 705         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 706                             ctx->normalize_gcd);
 707 }
 708
 709 /* Exploit the equalities in "eq" to simplify the expressions of
 710  * the integer divisions in "ls".
 711  * The integer divisions in "ls" are assumed to appear as regular
 712  * dimensions in "eq".
 713  */
 714 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 715         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 716 {
 717         int i, j, k;
 718         unsigned total;
 719         unsigned n_div;
 720
 721         ls = isl_local_space_cow(ls);
 722         if (!ls || !eq)
 723                 goto error;
 724
 725         total = isl_space_dim(eq->dim, isl_dim_all);
 726         if (isl_local_space_dim(ls, isl_dim_all) != total)
 727                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 728                         "dimensions don't match", goto error);
 729         total++;
 730         n_div = eq->n_div;
 731         for (i = 0; i < eq->n_eq; ++i) {
 732                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 733                 if (j < 0 || j == 0 || j >= total)
 734                         continue;
 735
 736                 for (k = 0; k < ls->div->n_row; ++k) {
 737                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 738                                 continue;
 739                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 740                                         &ls->div->row[k][0]);
 741                         normalize_div(ls, k);
 742                 }
 743         }
 744
 745         isl_basic_set_free(eq);
 746         return ls;
 747 error:
 748         isl_basic_set_free(eq);
 749         isl_local_space_free(ls);
 750         return NULL;
 751 }
 752
 753 /* Plug in the affine expressions "subs" of length "subs_len" (including
 754  * the denominator and the constant term) into the variable at position "pos"
 755  * of the "n" div expressions starting at "first".
 756  *
 757  * Let i be the dimension to replace and let "subs" be of the form
 758  *
 759  *      f/d
 760  *
 761  * Any integer division starting at "first" with a non-zero coefficient for i,
 762  *
 763  *      floor((a i + g)/m)
 764  *
 765  * is replaced by
 766  *
 767  *      floor((a f + d g)/(m d))
 768  */
 769 __isl_give isl_local_space *isl_local_space_substitute_seq(
 770         __isl_take isl_local_space *ls,
 771         enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,
 772         int first, int n)
 773 {
 774         int i;
 775         isl_int v;
 776
 777         if (n == 0)
 778                 return ls;
 779         ls = isl_local_space_cow(ls);
 780         if (!ls)
 781                 return NULL;
 782         ls->div = isl_mat_cow(ls->div);
 783         if (!ls->div)
 784                 return isl_local_space_free(ls);
 785
 786         if (first + n > ls->div->n_row)
 787                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 788                         "index out of bounds", return isl_local_space_free(ls));
 789
 790         pos += isl_local_space_offset(ls, type);
 791
 792         isl_int_init(v);
 793         for (i = first; i < ls->div->n_row; ++i) {
 794                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 795                         continue;
 796                 isl_seq_substitute(ls->div->row[i], pos, subs,
 797                         ls->div->n_col, subs_len, v);
 798                 normalize_div(ls, i);
 799         }
 800         isl_int_clear(v);
 801
 802         return ls;
 803 }
 804
 805 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 806  * of "ls".
 807  *
 808  * Let i be the dimension to replace and let "subs" be of the form
 809  *
 810  *      f/d
 811  *
 812  * Any integer division with a non-zero coefficient for i,
 813  *
 814  *      floor((a i + g)/m)
 815  *
 816  * is replaced by
 817  *
 818  *      floor((a f + d g)/(m d))
 819  */
 820 __isl_give isl_local_space *isl_local_space_substitute(
 821         __isl_take isl_local_space *ls,
 822         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 823 {
 824         ls = isl_local_space_cow(ls);
 825         if (!ls || !subs)
 826                 return isl_local_space_free(ls);
 827
 828         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 829                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 830                         "spaces don't match", return isl_local_space_free(ls));
 831         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 832                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 833                         "cannot handle divs yet",
 834                         return isl_local_space_free(ls));
 835
 836         return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
 837                                             subs->v->size, 0, ls->div->n_row);
 838 }
 839
 840 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 841         enum isl_dim_type type)
 842 {
 843         if (!ls)
 844                 return -1;
 845         return isl_space_is_named_or_nested(ls->dim, type);
 846 }
 847
 848 __isl_give isl_local_space *isl_local_space_drop_dims(
 849         __isl_take isl_local_space *ls,
 850         enum isl_dim_type type, unsigned first, unsigned n)
 851 {
 852         isl_ctx *ctx;
 853
 854         if (!ls)
 855                 return NULL;
 856         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 857                 return ls;
 858
 859         ctx = isl_local_space_get_ctx(ls);
 860         if (first + n > isl_local_space_dim(ls, type))
 861                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 862                         return isl_local_space_free(ls));
 863
 864         ls = isl_local_space_cow(ls);
 865         if (!ls)
 866                 return NULL;
 867
 868         if (type == isl_dim_div) {
 869                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 870         } else {
 871                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 872                 if (!ls->dim)
 873                         return isl_local_space_free(ls);
 874         }
 875
 876         first += 1 + isl_local_space_offset(ls, type);
 877         ls->div = isl_mat_drop_cols(ls->div, first, n);
 878         if (!ls->div)
 879                 return isl_local_space_free(ls);
 880
 881         return ls;
 882 }
 883
 884 __isl_give isl_local_space *isl_local_space_insert_dims(
 885         __isl_take isl_local_space *ls,
 886         enum isl_dim_type type, unsigned first, unsigned n)
 887 {
 888         isl_ctx *ctx;
 889
 890         if (!ls)
 891                 return NULL;
 892         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 893                 return ls;
 894
 895         ctx = isl_local_space_get_ctx(ls);
 896         if (first > isl_local_space_dim(ls, type))
 897                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 898                         return isl_local_space_free(ls));
 899
 900         ls = isl_local_space_cow(ls);
 901         if (!ls)
 902                 return NULL;
 903
 904         if (type == isl_dim_div) {
 905                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 906         } else {
 907                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 908                 if (!ls->dim)
 909                         return isl_local_space_free(ls);
 910         }
 911
 912         first += 1 + isl_local_space_offset(ls, type);
 913         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 914         if (!ls->div)
 915                 return isl_local_space_free(ls);
 916
 917         return ls;
 918 }
 919
 920 /* Check if the constraints pointed to by "constraint" is a div
 921  * constraint corresponding to div "div" in "ls".
 922  *
 923  * That is, if div = floor(f/m), then check if the constraint is
 924  *
 925  *              f - m d >= 0
 926  * or
 927  *              -(f-(m-1)) + m d >= 0
 928  */
 929 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 930         isl_int *constraint, unsigned div)
 931 {
 932         unsigned pos;
 933
 934         if (!ls)
 935                 return -1;
 936
 937         if (isl_int_is_zero(ls->div->row[div][0]))
 938                 return 0;
 939
 940         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 941
 942         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 943                 int neg;
 944                 isl_int_sub(ls->div->row[div][1],
 945                                 ls->div->row[div][1], ls->div->row[div][0]);
 946                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 947                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 948                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 949                 isl_int_add(ls->div->row[div][1],
 950                                 ls->div->row[div][1], ls->div->row[div][0]);
 951                 if (!neg)
 952                         return 0;
 953                 if (isl_seq_first_non_zero(constraint+pos+1,
 954                                             ls->div->n_row-div-1) != -1)
 955                         return 0;
 956         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 957                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 958                         return 0;
 959                 if (isl_seq_first_non_zero(constraint+pos+1,
 960                                             ls->div->n_row-div-1) != -1)
 961                         return 0;
 962         } else
 963                 return 0;
 964
 965         return 1;
 966 }
 967
 968 /*
 969  * Set active[i] to 1 if the dimension at position i is involved
 970  * in the linear expression l.
 971  */
 972 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 973 {
 974         int i, j;
 975         isl_ctx *ctx;
 976         int *active = NULL;
 977         unsigned total;
 978         unsigned offset;
 979
 980         ctx = isl_local_space_get_ctx(ls);
 981         total = isl_local_space_dim(ls, isl_dim_all);
 982         active = isl_calloc_array(ctx, int, total);
 983         if (!active)
 984                 return NULL;
 985
 986         for (i = 0; i < total; ++i)
 987                 active[i] = !isl_int_is_zero(l[i]);
 988
 989         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 990         for (i = ls->div->n_row - 1; i >= 0; --i) {
 991                 if (!active[offset + i])
 992                         continue;
 993                 for (j = 0; j < total; ++j)
 994                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 995         }
 996
 997         return active;
 998 }
 999
1000 /* Given a local space "ls" of a set, create a local space
1001  * for the lift of the set.  In particular, the result
1002  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1003  * range of the wrapped map.
1004  */
1005 __isl_give isl_local_space *isl_local_space_lift(
1006         __isl_take isl_local_space *ls)
1007 {
1008         ls = isl_local_space_cow(ls);
1009         if (!ls)
1010                 return NULL;
1011
1012         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
1013         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
1014         if (!ls->dim || !ls->div)
1015                 return isl_local_space_free(ls);
1016
1017         return ls;
1018 }
1019
1020 /* Construct a basic map that maps a set living in local space "ls"
1021  * to the corresponding lifted local space.
1022  */
1023 __isl_give isl_basic_map *isl_local_space_lifting(
1024         __isl_take isl_local_space *ls)
1025 {
1026         isl_basic_map *lifting;
1027         isl_basic_set *bset;
1028
1029         if (!ls)
1030                 return NULL;
1031         if (!isl_local_space_is_set(ls))
1032                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1033                         "lifting only defined on set spaces",
1034                         return isl_local_space_free(ls));
1035
1036         bset = isl_basic_set_from_local_space(ls);
1037         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
1038         lifting = isl_basic_map_domain_map(lifting);
1039         lifting = isl_basic_map_reverse(lifting);
1040
1041         return lifting;
1042 }
1043
1044 /* Compute the preimage of "ls" under the function represented by "ma".
1045  * In other words, plug in "ma" in "ls".  The result is a local space
1046  * that is part of the domain space of "ma".
1047  *
1048  * If the divs in "ls" are represented as
1049  *
1050  *      floor((a_i(p) + b_i x + c_i(divs))/n_i)
1051  *
1052  * and ma is represented by
1053  *
1054  *      x = D(p) + F(y) + G(divs')
1055  *
1056  * then the resulting divs are
1057  *
1058  *      floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1059  *
1060  * We first copy over the divs from "ma" and then
1061  * we add the modified divs from "ls".
1062  */
1063 __isl_give isl_local_space *isl_local_space_preimage_multi_aff(
1064         __isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
1065 {
1066         int i;
1067         isl_space *space;
1068         isl_local_space *res = NULL;
1069         int n_div_ls, n_div_ma;
1070         isl_int f, c1, c2, g;
1071
1072         ma = isl_multi_aff_align_divs(ma);
1073         if (!ls || !ma)
1074                 goto error;
1075         if (!isl_space_is_range_internal(ls->dim, ma->space))
1076                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1077                         "spaces don't match", goto error);
1078
1079         n_div_ls = isl_local_space_dim(ls, isl_dim_div);
1080         n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
1081
1082         space = isl_space_domain(isl_multi_aff_get_space(ma));
1083         res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
1084         if (!res)
1085                 goto error;
1086
1087         if (n_div_ma) {
1088                 isl_mat_free(res->div);
1089                 res->div = isl_mat_copy(ma->p[0]->ls->div);
1090                 res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
1091                 res->div = isl_mat_add_rows(res->div, n_div_ls);
1092                 if (!res->div)
1093                         goto error;
1094         }
1095
1096         isl_int_init(f);
1097         isl_int_init(c1);
1098         isl_int_init(c2);
1099         isl_int_init(g);
1100
1101         for (i = 0; i < ls->div->n_row; ++i) {
1102                 if (isl_int_is_zero(ls->div->row[i][0])) {
1103                         isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
1104                         continue;
1105                 }
1106                 isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
1107                                     ma, n_div_ma, n_div_ls, f, c1, c2, g, 1);
1108                 normalize_div(res, n_div_ma + i);
1109         }
1110
1111         isl_int_clear(f);
1112         isl_int_clear(c1);
1113         isl_int_clear(c2);
1114         isl_int_clear(g);
1115
1116         isl_local_space_free(ls);
1117         isl_multi_aff_free(ma);
1118         return res;
1119 error:
1120         isl_local_space_free(ls);
1121         isl_multi_aff_free(ma);
1122         isl_local_space_free(res);
1123         return NULL;
1124 }