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         if (!isl_local_space_is_set(ls))
 223                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 224                         "cannot represent divs of map spaces", return NULL);
 225
 226         aff = isl_aff_alloc(isl_local_space_copy(ls));
 227         if (!aff)
 228                 return NULL;
 229         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 230         return aff;
 231 }
 232
 233 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 234 {
 235         if (!ls)
 236                 return NULL;
 237
 238         return isl_space_copy(ls->dim);
 239 }
 240
 241 __isl_give isl_local_space *isl_local_space_set_dim_name(
 242         __isl_take isl_local_space *ls,
 243         enum isl_dim_type type, unsigned pos, const char *s)
 244 {
 245         ls = isl_local_space_cow(ls);
 246         if (!ls)
 247                 return NULL;
 248         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 249         if (!ls->dim)
 250                 return isl_local_space_free(ls);
 251
 252         return ls;
 253 }
 254
 255 __isl_give isl_local_space *isl_local_space_set_dim_id(
 256         __isl_take isl_local_space *ls,
 257         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 258 {
 259         ls = isl_local_space_cow(ls);
 260         if (!ls)
 261                 return isl_id_free(id);
 262         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 263         if (!ls->dim)
 264                 return isl_local_space_free(ls);
 265
 266         return ls;
 267 }
 268
 269 __isl_give isl_local_space *isl_local_space_reset_space(
 270         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 271 {
 272         ls = isl_local_space_cow(ls);
 273         if (!ls || !dim)
 274                 goto error;
 275
 276         isl_space_free(ls->dim);
 277         ls->dim = dim;
 278
 279         return ls;
 280 error:
 281         isl_local_space_free(ls);
 282         isl_space_free(dim);
 283         return NULL;
 284 }
 285
 286 /* Reorder the columns of the given div definitions according to the
 287  * given reordering.
 288  * The order of the divs themselves is assumed not to change.
 289  */
 290 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 291         __isl_take isl_reordering *r)
 292 {
 293         int i, j;
 294         isl_mat *mat;
 295         int extra;
 296
 297         if (!div || !r)
 298                 goto error;
 299
 300         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 301         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 302         if (!mat)
 303                 goto error;
 304
 305         for (i = 0; i < div->n_row; ++i) {
 306                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 307                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 308                 for (j = 0; j < r->len; ++j)
 309                         isl_int_set(mat->row[i][2 + r->pos[j]],
 310                                     div->row[i][2 + j]);
 311         }
 312
 313         isl_reordering_free(r);
 314         isl_mat_free(div);
 315         return mat;
 316 error:
 317         isl_reordering_free(r);
 318         isl_mat_free(div);
 319         return NULL;
 320 }
 321
 322 /* Reorder the dimensions of "ls" according to the given reordering.
 323  * The reordering r is assumed to have been extended with the local
 324  * variables, leaving them in the same order.
 325  */
 326 __isl_give isl_local_space *isl_local_space_realign(
 327         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 328 {
 329         ls = isl_local_space_cow(ls);
 330         if (!ls || !r)
 331                 goto error;
 332
 333         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 334         if (!ls->div)
 335                 goto error;
 336
 337         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 338
 339         isl_reordering_free(r);
 340         return ls;
 341 error:
 342         isl_local_space_free(ls);
 343         isl_reordering_free(r);
 344         return NULL;
 345 }
 346
 347 __isl_give isl_local_space *isl_local_space_add_div(
 348         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 349 {
 350         ls = isl_local_space_cow(ls);
 351         if (!ls || !div)
 352                 goto error;
 353
 354         if (ls->div->n_col != div->size)
 355                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 356                         "incompatible dimensions", goto error);
 357
 358         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 359         ls->div = isl_mat_add_rows(ls->div, 1);
 360         if (!ls->div)
 361                 goto error;
 362
 363         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 364         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 365
 366         isl_vec_free(div);
 367         return ls;
 368 error:
 369         isl_local_space_free(ls);
 370         isl_vec_free(div);
 371         return NULL;
 372 }
 373
 374 __isl_give isl_local_space *isl_local_space_replace_divs(
 375         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 376 {
 377         ls = isl_local_space_cow(ls);
 378
 379         if (!ls || !div)
 380                 goto error;
 381
 382         isl_mat_free(ls->div);
 383         ls->div = div;
 384         return ls;
 385 error:
 386         isl_mat_free(div);
 387         isl_local_space_free(ls);
 388         return NULL;
 389 }
 390
 391 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 392  * defined by "exp".
 393  */
 394 static void expand_row(__isl_keep isl_mat *dst, int d,
 395         __isl_keep isl_mat *src, int s, int *exp)
 396 {
 397         int i;
 398         unsigned c = src->n_col - src->n_row;
 399
 400         isl_seq_cpy(dst->row[d], src->row[s], c);
 401         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 402
 403         for (i = 0; i < s; ++i)
 404                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 405 }
 406
 407 /* Compare (known) divs.
 408  * Return non-zero if at least one of the two divs is unknown.
 409  * In particular, if both divs are unknown, we respect their
 410  * current order.  Otherwise, we sort the known div after the unknown
 411  * div only if the known div depends on the unknown div.
 412  */
 413 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 414         unsigned n_row, unsigned n_col)
 415 {
 416         int li, lj;
 417         int unknown_i, unknown_j;
 418
 419         unknown_i = isl_int_is_zero(row_i[0]);
 420         unknown_j = isl_int_is_zero(row_j[0]);
 421
 422         if (unknown_i && unknown_j)
 423                 return i - j;
 424
 425         if (unknown_i)
 426                 li = n_col - n_row + i;
 427         else
 428                 li = isl_seq_last_non_zero(row_i, n_col);
 429         if (unknown_j)
 430                 lj = n_col - n_row + j;
 431         else
 432                 lj = isl_seq_last_non_zero(row_j, n_col);
 433
 434         if (li != lj)
 435                 return li - lj;
 436
 437         return isl_seq_cmp(row_i, row_j, n_col);
 438 }
 439
 440 /* Call cmp_row for divs in a matrix.
 441  */
 442 int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)
 443 {
 444         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 445 }
 446
 447 /* Call cmp_row for divs in a basic map.
 448  */
 449 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 450         unsigned total)
 451 {
 452         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 453 }
 454
 455 /* Sort the divs in "bmap".
 456  *
 457  * We first make sure divs are placed after divs on which they depend.
 458  * Then we perform a simple insertion sort based on the same ordering
 459  * that is used in isl_merge_divs.
 460  */
 461 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 462         __isl_take isl_basic_map *bmap)
 463 {
 464         int i, j;
 465         unsigned total;
 466
 467         bmap = isl_basic_map_order_divs(bmap);
 468         if (!bmap)
 469                 return NULL;
 470         if (bmap->n_div <= 1)
 471                 return bmap;
 472
 473         total = 2 + isl_basic_map_total_dim(bmap);
 474         for (i = 1; i < bmap->n_div; ++i) {
 475                 for (j = i - 1; j >= 0; --j) {
 476                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 477                                 break;
 478                         isl_basic_map_swap_div(bmap, j, j + 1);
 479                 }
 480         }
 481
 482         return bmap;
 483 }
 484
 485 /* Sort the divs in the basic maps of "map".
 486  */
 487 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 488 {
 489         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 490 }
 491
 492 /* Combine the two lists of divs into a single list.
 493  * For each row i in div1, exp1[i] is set to the position of the corresponding
 494  * row in the result.  Similarly for div2 and exp2.
 495  * This function guarantees
 496  *      exp1[i] >= i
 497  *      exp1[i+1] > exp1[i]
 498  * For optimal merging, the two input list should have been sorted.
 499  */
 500 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 501         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 502 {
 503         int i, j, k;
 504         isl_mat *div = NULL;
 505         unsigned d;
 506
 507         if (!div1 || !div2)
 508                 return NULL;
 509
 510         d = div1->n_col - div1->n_row;
 511         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 512                                 d + div1->n_row + div2->n_row);
 513         if (!div)
 514                 return NULL;
 515
 516         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 517                 int cmp;
 518
 519                 expand_row(div, k, div1, i, exp1);
 520                 expand_row(div, k + 1, div2, j, exp2);
 521
 522                 cmp = isl_mat_cmp_div(div, k, k + 1);
 523                 if (cmp == 0) {
 524                         exp1[i++] = k;
 525                         exp2[j++] = k;
 526                 } else if (cmp < 0) {
 527                         exp1[i++] = k;
 528                 } else {
 529                         exp2[j++] = k;
 530                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 531                 }
 532         }
 533         for (; i < div1->n_row; ++i, ++k) {
 534                 expand_row(div, k, div1, i, exp1);
 535                 exp1[i] = k;
 536         }
 537         for (; j < div2->n_row; ++j, ++k) {
 538                 expand_row(div, k, div2, j, exp2);
 539                 exp2[j] = k;
 540         }
 541
 542         div->n_row = k;
 543         div->n_col = d + k;
 544
 545         return div;
 546 }
 547
 548 /* Swap divs "a" and "b" in "ls".
 549  */
 550 __isl_give isl_local_space *isl_local_space_swap_div(
 551         __isl_take isl_local_space *ls, int a, int b)
 552 {
 553         int offset;
 554
 555         ls = isl_local_space_cow(ls);
 556         if (!ls)
 557                 return NULL;
 558         if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)
 559                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 560                         "index out of bounds", return isl_local_space_free(ls));
 561         offset = ls->div->n_col - ls->div->n_row;
 562         ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);
 563         ls->div = isl_mat_swap_rows(ls->div, a, b);
 564         if (!ls->div)
 565                 return isl_local_space_free(ls);
 566         return ls;
 567 }
 568
 569 /* Construct a local space that contains all the divs in either
 570  * "ls1" or "ls2".
 571  */
 572 __isl_give isl_local_space *isl_local_space_intersect(
 573         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 574 {
 575         isl_ctx *ctx;
 576         int *exp1 = NULL;
 577         int *exp2 = NULL;
 578         isl_mat *div;
 579
 580         if (!ls1 || !ls2)
 581                 goto error;
 582
 583         ctx = isl_local_space_get_ctx(ls1);
 584         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 585                 isl_die(ctx, isl_error_invalid,
 586                         "spaces should be identical", goto error);
 587
 588         if (ls2->div->n_row == 0) {
 589                 isl_local_space_free(ls2);
 590                 return ls1;
 591         }
 592
 593         if (ls1->div->n_row == 0) {
 594                 isl_local_space_free(ls1);
 595                 return ls2;
 596         }
 597
 598         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 599         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 600         if (!exp1 || !exp2)
 601                 goto error;
 602
 603         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 604         if (!div)
 605                 goto error;
 606
 607         free(exp1);
 608         free(exp2);
 609         isl_local_space_free(ls2);
 610         isl_mat_free(ls1->div);
 611         ls1->div = div;
 612
 613         return ls1;
 614 error:
 615         free(exp1);
 616         free(exp2);
 617         isl_local_space_free(ls1);
 618         isl_local_space_free(ls2);
 619         return NULL;
 620 }
 621
 622 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 623 {
 624         int i;
 625
 626         if (!ls)
 627                 return -1;
 628
 629         for (i = 0; i < ls->div->n_row; ++i)
 630                 if (isl_int_is_zero(ls->div->row[i][0]))
 631                         return 0;
 632
 633         return 1;
 634 }
 635
 636 __isl_give isl_local_space *isl_local_space_domain(
 637         __isl_take isl_local_space *ls)
 638 {
 639         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 640                                         0, isl_local_space_dim(ls, isl_dim_out));
 641         ls = isl_local_space_cow(ls);
 642         if (!ls)
 643                 return NULL;
 644         ls->dim = isl_space_domain(ls->dim);
 645         if (!ls->dim)
 646                 return isl_local_space_free(ls);
 647         return ls;
 648 }
 649
 650 __isl_give isl_local_space *isl_local_space_range(
 651         __isl_take isl_local_space *ls)
 652 {
 653         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 654                                         0, isl_local_space_dim(ls, isl_dim_in));
 655         ls = isl_local_space_cow(ls);
 656         if (!ls)
 657                 return NULL;
 658
 659         ls->dim = isl_space_range(ls->dim);
 660         if (!ls->dim)
 661                 return isl_local_space_free(ls);
 662         return ls;
 663 }
 664
 665 /* Construct a local space for a map that has the given local
 666  * space as domain and that has a zero-dimensional range.
 667  */
 668 __isl_give isl_local_space *isl_local_space_from_domain(
 669         __isl_take isl_local_space *ls)
 670 {
 671         ls = isl_local_space_cow(ls);
 672         if (!ls)
 673                 return NULL;
 674         ls->dim = isl_space_from_domain(ls->dim);
 675         if (!ls->dim)
 676                 return isl_local_space_free(ls);
 677         return ls;
 678 }
 679
 680 __isl_give isl_local_space *isl_local_space_add_dims(
 681         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 682 {
 683         int pos;
 684
 685         if (!ls)
 686                 return NULL;
 687         pos = isl_local_space_dim(ls, type);
 688         return isl_local_space_insert_dims(ls, type, pos, n);
 689 }
 690
 691 /* Remove common factor of non-constant terms and denominator.
 692  */
 693 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 694 {
 695         isl_ctx *ctx = ls->div->ctx;
 696         unsigned total = ls->div->n_col - 2;
 697
 698         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 699         isl_int_gcd(ctx->normalize_gcd,
 700                     ctx->normalize_gcd, ls->div->row[div][0]);
 701         if (isl_int_is_one(ctx->normalize_gcd))
 702                 return;
 703
 704         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 705                             ctx->normalize_gcd, total);
 706         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 707                             ctx->normalize_gcd);
 708         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 709                             ctx->normalize_gcd);
 710 }
 711
 712 /* Exploit the equalities in "eq" to simplify the expressions of
 713  * the integer divisions in "ls".
 714  * The integer divisions in "ls" are assumed to appear as regular
 715  * dimensions in "eq".
 716  */
 717 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 718         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 719 {
 720         int i, j, k;
 721         unsigned total;
 722         unsigned n_div;
 723
 724         ls = isl_local_space_cow(ls);
 725         if (!ls || !eq)
 726                 goto error;
 727
 728         total = isl_space_dim(eq->dim, isl_dim_all);
 729         if (isl_local_space_dim(ls, isl_dim_all) != total)
 730                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 731                         "dimensions don't match", goto error);
 732         total++;
 733         n_div = eq->n_div;
 734         for (i = 0; i < eq->n_eq; ++i) {
 735                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 736                 if (j < 0 || j == 0 || j >= total)
 737                         continue;
 738
 739                 for (k = 0; k < ls->div->n_row; ++k) {
 740                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 741                                 continue;
 742                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 743                                         &ls->div->row[k][0]);
 744                         normalize_div(ls, k);
 745                 }
 746         }
 747
 748         isl_basic_set_free(eq);
 749         return ls;
 750 error:
 751         isl_basic_set_free(eq);
 752         isl_local_space_free(ls);
 753         return NULL;
 754 }
 755
 756 /* Plug in the affine expressions "subs" of length "subs_len" (including
 757  * the denominator and the constant term) into the variable at position "pos"
 758  * of the "n" div expressions starting at "first".
 759  *
 760  * Let i be the dimension to replace and let "subs" be of the form
 761  *
 762  *      f/d
 763  *
 764  * Any integer division starting at "first" with a non-zero coefficient for i,
 765  *
 766  *      floor((a i + g)/m)
 767  *
 768  * is replaced by
 769  *
 770  *      floor((a f + d g)/(m d))
 771  */
 772 __isl_give isl_local_space *isl_local_space_substitute_seq(
 773         __isl_take isl_local_space *ls,
 774         enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,
 775         int first, int n)
 776 {
 777         int i;
 778         isl_int v;
 779
 780         if (n == 0)
 781                 return ls;
 782         ls = isl_local_space_cow(ls);
 783         if (!ls)
 784                 return NULL;
 785         ls->div = isl_mat_cow(ls->div);
 786         if (!ls->div)
 787                 return isl_local_space_free(ls);
 788
 789         if (first + n > ls->div->n_row)
 790                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 791                         "index out of bounds", return isl_local_space_free(ls));
 792
 793         pos += isl_local_space_offset(ls, type);
 794
 795         isl_int_init(v);
 796         for (i = first; i < ls->div->n_row; ++i) {
 797                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 798                         continue;
 799                 isl_seq_substitute(ls->div->row[i], pos, subs,
 800                         ls->div->n_col, subs_len, v);
 801                 normalize_div(ls, i);
 802         }
 803         isl_int_clear(v);
 804
 805         return ls;
 806 }
 807
 808 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 809  * of "ls".
 810  *
 811  * Let i be the dimension to replace and let "subs" be of the form
 812  *
 813  *      f/d
 814  *
 815  * Any integer division with a non-zero coefficient for i,
 816  *
 817  *      floor((a i + g)/m)
 818  *
 819  * is replaced by
 820  *
 821  *      floor((a f + d g)/(m d))
 822  */
 823 __isl_give isl_local_space *isl_local_space_substitute(
 824         __isl_take isl_local_space *ls,
 825         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 826 {
 827         ls = isl_local_space_cow(ls);
 828         if (!ls || !subs)
 829                 return isl_local_space_free(ls);
 830
 831         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 832                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 833                         "spaces don't match", return isl_local_space_free(ls));
 834         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 835                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 836                         "cannot handle divs yet",
 837                         return isl_local_space_free(ls));
 838
 839         return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
 840                                             subs->v->size, 0, ls->div->n_row);
 841 }
 842
 843 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 844         enum isl_dim_type type)
 845 {
 846         if (!ls)
 847                 return -1;
 848         return isl_space_is_named_or_nested(ls->dim, type);
 849 }
 850
 851 __isl_give isl_local_space *isl_local_space_drop_dims(
 852         __isl_take isl_local_space *ls,
 853         enum isl_dim_type type, unsigned first, unsigned n)
 854 {
 855         isl_ctx *ctx;
 856
 857         if (!ls)
 858                 return NULL;
 859         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 860                 return ls;
 861
 862         ctx = isl_local_space_get_ctx(ls);
 863         if (first + n > isl_local_space_dim(ls, type))
 864                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 865                         return isl_local_space_free(ls));
 866
 867         ls = isl_local_space_cow(ls);
 868         if (!ls)
 869                 return NULL;
 870
 871         if (type == isl_dim_div) {
 872                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 873         } else {
 874                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 875                 if (!ls->dim)
 876                         return isl_local_space_free(ls);
 877         }
 878
 879         first += 1 + isl_local_space_offset(ls, type);
 880         ls->div = isl_mat_drop_cols(ls->div, first, n);
 881         if (!ls->div)
 882                 return isl_local_space_free(ls);
 883
 884         return ls;
 885 }
 886
 887 __isl_give isl_local_space *isl_local_space_insert_dims(
 888         __isl_take isl_local_space *ls,
 889         enum isl_dim_type type, unsigned first, unsigned n)
 890 {
 891         isl_ctx *ctx;
 892
 893         if (!ls)
 894                 return NULL;
 895         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 896                 return ls;
 897
 898         ctx = isl_local_space_get_ctx(ls);
 899         if (first > isl_local_space_dim(ls, type))
 900                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 901                         return isl_local_space_free(ls));
 902
 903         ls = isl_local_space_cow(ls);
 904         if (!ls)
 905                 return NULL;
 906
 907         if (type == isl_dim_div) {
 908                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 909         } else {
 910                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 911                 if (!ls->dim)
 912                         return isl_local_space_free(ls);
 913         }
 914
 915         first += 1 + isl_local_space_offset(ls, type);
 916         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 917         if (!ls->div)
 918                 return isl_local_space_free(ls);
 919
 920         return ls;
 921 }
 922
 923 /* Check if the constraints pointed to by "constraint" is a div
 924  * constraint corresponding to div "div" in "ls".
 925  *
 926  * That is, if div = floor(f/m), then check if the constraint is
 927  *
 928  *              f - m d >= 0
 929  * or
 930  *              -(f-(m-1)) + m d >= 0
 931  */
 932 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 933         isl_int *constraint, unsigned div)
 934 {
 935         unsigned pos;
 936
 937         if (!ls)
 938                 return -1;
 939
 940         if (isl_int_is_zero(ls->div->row[div][0]))
 941                 return 0;
 942
 943         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 944
 945         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 946                 int neg;
 947                 isl_int_sub(ls->div->row[div][1],
 948                                 ls->div->row[div][1], ls->div->row[div][0]);
 949                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 950                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 951                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 952                 isl_int_add(ls->div->row[div][1],
 953                                 ls->div->row[div][1], ls->div->row[div][0]);
 954                 if (!neg)
 955                         return 0;
 956                 if (isl_seq_first_non_zero(constraint+pos+1,
 957                                             ls->div->n_row-div-1) != -1)
 958                         return 0;
 959         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 960                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 961                         return 0;
 962                 if (isl_seq_first_non_zero(constraint+pos+1,
 963                                             ls->div->n_row-div-1) != -1)
 964                         return 0;
 965         } else
 966                 return 0;
 967
 968         return 1;
 969 }
 970
 971 /*
 972  * Set active[i] to 1 if the dimension at position i is involved
 973  * in the linear expression l.
 974  */
 975 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 976 {
 977         int i, j;
 978         isl_ctx *ctx;
 979         int *active = NULL;
 980         unsigned total;
 981         unsigned offset;
 982
 983         ctx = isl_local_space_get_ctx(ls);
 984         total = isl_local_space_dim(ls, isl_dim_all);
 985         active = isl_calloc_array(ctx, int, total);
 986         if (!active)
 987                 return NULL;
 988
 989         for (i = 0; i < total; ++i)
 990                 active[i] = !isl_int_is_zero(l[i]);
 991
 992         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 993         for (i = ls->div->n_row - 1; i >= 0; --i) {
 994                 if (!active[offset + i])
 995                         continue;
 996                 for (j = 0; j < total; ++j)
 997                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 998         }
 999
1000         return active;
1001 }
1002
1003 /* Given a local space "ls" of a set, create a local space
1004  * for the lift of the set.  In particular, the result
1005  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1006  * range of the wrapped map.
1007  */
1008 __isl_give isl_local_space *isl_local_space_lift(
1009         __isl_take isl_local_space *ls)
1010 {
1011         ls = isl_local_space_cow(ls);
1012         if (!ls)
1013                 return NULL;
1014
1015         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
1016         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
1017         if (!ls->dim || !ls->div)
1018                 return isl_local_space_free(ls);
1019
1020         return ls;
1021 }
1022
1023 /* Construct a basic map that maps a set living in local space "ls"
1024  * to the corresponding lifted local space.
1025  */
1026 __isl_give isl_basic_map *isl_local_space_lifting(
1027         __isl_take isl_local_space *ls)
1028 {
1029         isl_basic_map *lifting;
1030         isl_basic_set *bset;
1031
1032         if (!ls)
1033                 return NULL;
1034         if (!isl_local_space_is_set(ls))
1035                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1036                         "lifting only defined on set spaces",
1037                         return isl_local_space_free(ls));
1038
1039         bset = isl_basic_set_from_local_space(ls);
1040         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
1041         lifting = isl_basic_map_domain_map(lifting);
1042         lifting = isl_basic_map_reverse(lifting);
1043
1044         return lifting;
1045 }
1046
1047 /* Compute the preimage of "ls" under the function represented by "ma".
1048  * In other words, plug in "ma" in "ls".  The result is a local space
1049  * that is part of the domain space of "ma".
1050  *
1051  * If the divs in "ls" are represented as
1052  *
1053  *      floor((a_i(p) + b_i x + c_i(divs))/n_i)
1054  *
1055  * and ma is represented by
1056  *
1057  *      x = D(p) + F(y) + G(divs')
1058  *
1059  * then the resulting divs are
1060  *
1061  *      floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1062  *
1063  * We first copy over the divs from "ma" and then
1064  * we add the modified divs from "ls".
1065  */
1066 __isl_give isl_local_space *isl_local_space_preimage_multi_aff(
1067         __isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
1068 {
1069         int i;
1070         isl_space *space;
1071         isl_local_space *res = NULL;
1072         int n_div_ls, n_div_ma;
1073         isl_int f, c1, c2, g;
1074
1075         ma = isl_multi_aff_align_divs(ma);
1076         if (!ls || !ma)
1077                 goto error;
1078         if (!isl_space_is_range_internal(ls->dim, ma->space))
1079                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1080                         "spaces don't match", goto error);
1081
1082         n_div_ls = isl_local_space_dim(ls, isl_dim_div);
1083         n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
1084
1085         space = isl_space_domain(isl_multi_aff_get_space(ma));
1086         res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
1087         if (!res)
1088                 goto error;
1089
1090         if (n_div_ma) {
1091                 isl_mat_free(res->div);
1092                 res->div = isl_mat_copy(ma->p[0]->ls->div);
1093                 res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
1094                 res->div = isl_mat_add_rows(res->div, n_div_ls);
1095                 if (!res->div)
1096                         goto error;
1097         }
1098
1099         isl_int_init(f);
1100         isl_int_init(c1);
1101         isl_int_init(c2);
1102         isl_int_init(g);
1103
1104         for (i = 0; i < ls->div->n_row; ++i) {
1105                 if (isl_int_is_zero(ls->div->row[i][0])) {
1106                         isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
1107                         continue;
1108                 }
1109                 isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
1110                                     ma, n_div_ma, n_div_ls, f, c1, c2, g, 1);
1111                 normalize_div(res, n_div_ma + i);
1112         }
1113
1114         isl_int_clear(f);
1115         isl_int_clear(c1);
1116         isl_int_clear(c2);
1117         isl_int_clear(g);
1118
1119         isl_local_space_free(ls);
1120         isl_multi_aff_free(ma);
1121         return res;
1122 error:
1123         isl_local_space_free(ls);
1124         isl_multi_aff_free(ma);
1125         isl_local_space_free(res);
1126         return NULL;
1127 }