isl_local_space.c

   1 /*
   2  * Copyright 2011      INRIA Saclay
   3  * Copyright 2012-2014 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_vec_private.h>
  20 #include <isl_seq.h>
  21
  22 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  23 {
  24         return ls ? ls->dim->ctx : NULL;
  25 }
  26
  27 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  28         __isl_take isl_mat *div)
  29 {
  30         isl_ctx *ctx;
  31         isl_local_space *ls = NULL;
  32
  33         if (!dim || !div)
  34                 goto error;
  35
  36         ctx = isl_space_get_ctx(dim);
  37         ls = isl_calloc_type(ctx, struct isl_local_space);
  38         if (!ls)
  39                 goto error;
  40
  41         ls->ref = 1;
  42         ls->dim = dim;
  43         ls->div = div;
  44
  45         return ls;
  46 error:
  47         isl_mat_free(div);
  48         isl_space_free(dim);
  49         isl_local_space_free(ls);
  50         return NULL;
  51 }
  52
  53 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  54         unsigned n_div)
  55 {
  56         isl_ctx *ctx;
  57         isl_mat *div;
  58         unsigned total;
  59
  60         if (!dim)
  61                 return NULL;
  62
  63         total = isl_space_dim(dim, isl_dim_all);
  64
  65         ctx = isl_space_get_ctx(dim);
  66         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  67         return isl_local_space_alloc_div(dim, div);
  68 }
  69
  70 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  71 {
  72         return isl_local_space_alloc(dim, 0);
  73 }
  74
  75 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  76 {
  77         if (!ls)
  78                 return NULL;
  79
  80         ls->ref++;
  81         return ls;
  82 }
  83
  84 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  85 {
  86         if (!ls)
  87                 return NULL;
  88
  89         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  90                                          isl_mat_copy(ls->div));
  91
  92 }
  93
  94 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  95 {
  96         if (!ls)
  97                 return NULL;
  98
  99         if (ls->ref == 1)
 100                 return ls;
 101         ls->ref--;
 102         return isl_local_space_dup(ls);
 103 }
 104
 105 __isl_null isl_local_space *isl_local_space_free(
 106         __isl_take isl_local_space *ls)
 107 {
 108         if (!ls)
 109                 return NULL;
 110
 111         if (--ls->ref > 0)
 112                 return NULL;
 113
 114         isl_space_free(ls->dim);
 115         isl_mat_free(ls->div);
 116
 117         free(ls);
 118
 119         return NULL;
 120 }
 121
 122 /* Is the local space that of a set?
 123  */
 124 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 125 {
 126         return ls ? isl_space_is_set(ls->dim) : -1;
 127 }
 128
 129 /* Return true if the two local spaces are identical, with identical
 130  * expressions for the integer divisions.
 131  */
 132 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 133         __isl_keep isl_local_space *ls2)
 134 {
 135         int equal;
 136
 137         if (!ls1 || !ls2)
 138                 return -1;
 139
 140         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 141         if (equal < 0 || !equal)
 142                 return equal;
 143
 144         if (!isl_local_space_divs_known(ls1))
 145                 return 0;
 146         if (!isl_local_space_divs_known(ls2))
 147                 return 0;
 148
 149         return isl_mat_is_equal(ls1->div, ls2->div);
 150 }
 151
 152 /* Compare two isl_local_spaces.
 153  *
 154  * Return -1 if "ls1" is "smaller" than "ls2", 1 if "ls1" is "greater"
 155  * than "ls2" and 0 if they are equal.
 156  *
 157  * The order is fairly arbitrary.  We do "prefer" divs that only involve
 158  * earlier dimensions in the sense that we consider local spaces where
 159  * the first differing div involves earlier dimensions to be smaller.
 160  */
 161 int isl_local_space_cmp(__isl_keep isl_local_space *ls1,
 162         __isl_keep isl_local_space *ls2)
 163 {
 164         int i;
 165         int cmp;
 166         int known1, known2;
 167         int last1, last2;
 168         int n_col;
 169
 170         if (ls1 == ls2)
 171                 return 0;
 172         if (!ls1)
 173                 return -1;
 174         if (!ls2)
 175                 return 1;
 176
 177         cmp = isl_space_cmp(ls1->dim, ls2->dim);
 178         if (cmp != 0)
 179                 return cmp;
 180
 181         if (ls1->div->n_row != ls2->div->n_row)
 182                 return ls1->div->n_row - ls2->div->n_row;
 183
 184         n_col = isl_mat_cols(ls1->div);
 185         for (i = 0; i < ls1->div->n_row; ++i) {
 186                 known1 = isl_local_space_div_is_known(ls1, i);
 187                 known2 = isl_local_space_div_is_known(ls2, i);
 188                 if (!known1 && !known2)
 189                         continue;
 190                 if (!known1)
 191                         return 1;
 192                 if (!known2)
 193                         return -1;
 194                 last1 = isl_seq_last_non_zero(ls1->div->row[i] + 1, n_col - 1);
 195                 last2 = isl_seq_last_non_zero(ls2->div->row[i] + 1, n_col - 1);
 196                 if (last1 != last2)
 197                         return last1 - last2;
 198                 cmp = isl_seq_cmp(ls1->div->row[i], ls2->div->row[i], n_col);
 199                 if (cmp != 0)
 200                         return cmp;
 201         }
 202
 203         return 0;
 204 }
 205
 206 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 207         enum isl_dim_type type)
 208 {
 209         if (!ls)
 210                 return 0;
 211         if (type == isl_dim_div)
 212                 return ls->div->n_row;
 213         if (type == isl_dim_all)
 214                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 215         return isl_space_dim(ls->dim, type);
 216 }
 217
 218 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 219         enum isl_dim_type type)
 220 {
 221         isl_space *dim;
 222
 223         if (!ls)
 224                 return 0;
 225
 226         dim = ls->dim;
 227         switch (type) {
 228         case isl_dim_cst:       return 0;
 229         case isl_dim_param:     return 1;
 230         case isl_dim_in:        return 1 + dim->nparam;
 231         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 232         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 233         default:                return 0;
 234         }
 235 }
 236
 237 /* Does the given dimension have a name?
 238  */
 239 int isl_local_space_has_dim_name(__isl_keep isl_local_space *ls,
 240         enum isl_dim_type type, unsigned pos)
 241 {
 242         return ls ? isl_space_has_dim_name(ls->dim, type, pos) : -1;
 243 }
 244
 245 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 246         enum isl_dim_type type, unsigned pos)
 247 {
 248         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 249 }
 250
 251 int isl_local_space_has_dim_id(__isl_keep isl_local_space *ls,
 252         enum isl_dim_type type, unsigned pos)
 253 {
 254         return ls ? isl_space_has_dim_id(ls->dim, type, pos) : -1;
 255 }
 256
 257 __isl_give isl_id *isl_local_space_get_dim_id(__isl_keep isl_local_space *ls,
 258         enum isl_dim_type type, unsigned pos)
 259 {
 260         return ls ? isl_space_get_dim_id(ls->dim, type, pos) : NULL;
 261 }
 262
 263 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 264         int pos)
 265 {
 266         isl_aff *aff;
 267
 268         if (!ls)
 269                 return NULL;
 270
 271         if (pos < 0 || pos >= ls->div->n_row)
 272                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 273                         "index out of bounds", return NULL);
 274
 275         if (isl_int_is_zero(ls->div->row[pos][0]))
 276                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 277                         "expression of div unknown", return NULL);
 278         if (!isl_local_space_is_set(ls))
 279                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 280                         "cannot represent divs of map spaces", return NULL);
 281
 282         aff = isl_aff_alloc(isl_local_space_copy(ls));
 283         if (!aff)
 284                 return NULL;
 285         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 286         return aff;
 287 }
 288
 289 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 290 {
 291         if (!ls)
 292                 return NULL;
 293
 294         return isl_space_copy(ls->dim);
 295 }
 296
 297 /* Replace the identifier of the tuple of type "type" by "id".
 298  */
 299 __isl_give isl_local_space *isl_local_space_set_tuple_id(
 300         __isl_take isl_local_space *ls,
 301         enum isl_dim_type type, __isl_take isl_id *id)
 302 {
 303         ls = isl_local_space_cow(ls);
 304         if (!ls)
 305                 goto error;
 306         ls->dim = isl_space_set_tuple_id(ls->dim, type, id);
 307         if (!ls->dim)
 308                 return isl_local_space_free(ls);
 309         return ls;
 310 error:
 311         isl_id_free(id);
 312         return NULL;
 313 }
 314
 315 __isl_give isl_local_space *isl_local_space_set_dim_name(
 316         __isl_take isl_local_space *ls,
 317         enum isl_dim_type type, unsigned pos, const char *s)
 318 {
 319         ls = isl_local_space_cow(ls);
 320         if (!ls)
 321                 return NULL;
 322         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 323         if (!ls->dim)
 324                 return isl_local_space_free(ls);
 325
 326         return ls;
 327 }
 328
 329 __isl_give isl_local_space *isl_local_space_set_dim_id(
 330         __isl_take isl_local_space *ls,
 331         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 332 {
 333         ls = isl_local_space_cow(ls);
 334         if (!ls)
 335                 goto error;
 336         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 337         if (!ls->dim)
 338                 return isl_local_space_free(ls);
 339
 340         return ls;
 341 error:
 342         isl_id_free(id);
 343         return NULL;
 344 }
 345
 346 __isl_give isl_local_space *isl_local_space_reset_space(
 347         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 348 {
 349         ls = isl_local_space_cow(ls);
 350         if (!ls || !dim)
 351                 goto error;
 352
 353         isl_space_free(ls->dim);
 354         ls->dim = dim;
 355
 356         return ls;
 357 error:
 358         isl_local_space_free(ls);
 359         isl_space_free(dim);
 360         return NULL;
 361 }
 362
 363 /* Reorder the columns of the given div definitions according to the
 364  * given reordering.
 365  * The order of the divs themselves is assumed not to change.
 366  */
 367 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 368         __isl_take isl_reordering *r)
 369 {
 370         int i, j;
 371         isl_mat *mat;
 372         int extra;
 373
 374         if (!div || !r)
 375                 goto error;
 376
 377         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 378         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 379         if (!mat)
 380                 goto error;
 381
 382         for (i = 0; i < div->n_row; ++i) {
 383                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 384                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 385                 for (j = 0; j < r->len; ++j)
 386                         isl_int_set(mat->row[i][2 + r->pos[j]],
 387                                     div->row[i][2 + j]);
 388         }
 389
 390         isl_reordering_free(r);
 391         isl_mat_free(div);
 392         return mat;
 393 error:
 394         isl_reordering_free(r);
 395         isl_mat_free(div);
 396         return NULL;
 397 }
 398
 399 /* Reorder the dimensions of "ls" according to the given reordering.
 400  * The reordering r is assumed to have been extended with the local
 401  * variables, leaving them in the same order.
 402  */
 403 __isl_give isl_local_space *isl_local_space_realign(
 404         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 405 {
 406         ls = isl_local_space_cow(ls);
 407         if (!ls || !r)
 408                 goto error;
 409
 410         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 411         if (!ls->div)
 412                 goto error;
 413
 414         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 415
 416         isl_reordering_free(r);
 417         return ls;
 418 error:
 419         isl_local_space_free(ls);
 420         isl_reordering_free(r);
 421         return NULL;
 422 }
 423
 424 __isl_give isl_local_space *isl_local_space_add_div(
 425         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 426 {
 427         ls = isl_local_space_cow(ls);
 428         if (!ls || !div)
 429                 goto error;
 430
 431         if (ls->div->n_col != div->size)
 432                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 433                         "incompatible dimensions", goto error);
 434
 435         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 436         ls->div = isl_mat_add_rows(ls->div, 1);
 437         if (!ls->div)
 438                 goto error;
 439
 440         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 441         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 442
 443         isl_vec_free(div);
 444         return ls;
 445 error:
 446         isl_local_space_free(ls);
 447         isl_vec_free(div);
 448         return NULL;
 449 }
 450
 451 __isl_give isl_local_space *isl_local_space_replace_divs(
 452         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 453 {
 454         ls = isl_local_space_cow(ls);
 455
 456         if (!ls || !div)
 457                 goto error;
 458
 459         isl_mat_free(ls->div);
 460         ls->div = div;
 461         return ls;
 462 error:
 463         isl_mat_free(div);
 464         isl_local_space_free(ls);
 465         return NULL;
 466 }
 467
 468 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 469  * defined by "exp".
 470  */
 471 static void expand_row(__isl_keep isl_mat *dst, int d,
 472         __isl_keep isl_mat *src, int s, int *exp)
 473 {
 474         int i;
 475         unsigned c = src->n_col - src->n_row;
 476
 477         isl_seq_cpy(dst->row[d], src->row[s], c);
 478         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 479
 480         for (i = 0; i < s; ++i)
 481                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 482 }
 483
 484 /* Compare (known) divs.
 485  * Return non-zero if at least one of the two divs is unknown.
 486  * In particular, if both divs are unknown, we respect their
 487  * current order.  Otherwise, we sort the known div after the unknown
 488  * div only if the known div depends on the unknown div.
 489  */
 490 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 491         unsigned n_row, unsigned n_col)
 492 {
 493         int li, lj;
 494         int unknown_i, unknown_j;
 495
 496         unknown_i = isl_int_is_zero(row_i[0]);
 497         unknown_j = isl_int_is_zero(row_j[0]);
 498
 499         if (unknown_i && unknown_j)
 500                 return i - j;
 501
 502         if (unknown_i)
 503                 li = n_col - n_row + i;
 504         else
 505                 li = isl_seq_last_non_zero(row_i, n_col);
 506         if (unknown_j)
 507                 lj = n_col - n_row + j;
 508         else
 509                 lj = isl_seq_last_non_zero(row_j, n_col);
 510
 511         if (li != lj)
 512                 return li - lj;
 513
 514         return isl_seq_cmp(row_i, row_j, n_col);
 515 }
 516
 517 /* Call cmp_row for divs in a matrix.
 518  */
 519 int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)
 520 {
 521         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 522 }
 523
 524 /* Call cmp_row for divs in a basic map.
 525  */
 526 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 527         unsigned total)
 528 {
 529         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 530 }
 531
 532 /* Sort the divs in "bmap".
 533  *
 534  * We first make sure divs are placed after divs on which they depend.
 535  * Then we perform a simple insertion sort based on the same ordering
 536  * that is used in isl_merge_divs.
 537  */
 538 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 539         __isl_take isl_basic_map *bmap)
 540 {
 541         int i, j;
 542         unsigned total;
 543
 544         bmap = isl_basic_map_order_divs(bmap);
 545         if (!bmap)
 546                 return NULL;
 547         if (bmap->n_div <= 1)
 548                 return bmap;
 549
 550         total = 2 + isl_basic_map_total_dim(bmap);
 551         for (i = 1; i < bmap->n_div; ++i) {
 552                 for (j = i - 1; j >= 0; --j) {
 553                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 554                                 break;
 555                         isl_basic_map_swap_div(bmap, j, j + 1);
 556                 }
 557         }
 558
 559         return bmap;
 560 }
 561
 562 /* Sort the divs in the basic maps of "map".
 563  */
 564 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 565 {
 566         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 567 }
 568
 569 /* Combine the two lists of divs into a single list.
 570  * For each row i in div1, exp1[i] is set to the position of the corresponding
 571  * row in the result.  Similarly for div2 and exp2.
 572  * This function guarantees
 573  *      exp1[i] >= i
 574  *      exp1[i+1] > exp1[i]
 575  * For optimal merging, the two input list should have been sorted.
 576  */
 577 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 578         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 579 {
 580         int i, j, k;
 581         isl_mat *div = NULL;
 582         unsigned d;
 583
 584         if (!div1 || !div2)
 585                 return NULL;
 586
 587         d = div1->n_col - div1->n_row;
 588         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 589                                 d + div1->n_row + div2->n_row);
 590         if (!div)
 591                 return NULL;
 592
 593         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 594                 int cmp;
 595
 596                 expand_row(div, k, div1, i, exp1);
 597                 expand_row(div, k + 1, div2, j, exp2);
 598
 599                 cmp = isl_mat_cmp_div(div, k, k + 1);
 600                 if (cmp == 0) {
 601                         exp1[i++] = k;
 602                         exp2[j++] = k;
 603                 } else if (cmp < 0) {
 604                         exp1[i++] = k;
 605                 } else {
 606                         exp2[j++] = k;
 607                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 608                 }
 609         }
 610         for (; i < div1->n_row; ++i, ++k) {
 611                 expand_row(div, k, div1, i, exp1);
 612                 exp1[i] = k;
 613         }
 614         for (; j < div2->n_row; ++j, ++k) {
 615                 expand_row(div, k, div2, j, exp2);
 616                 exp2[j] = k;
 617         }
 618
 619         div->n_row = k;
 620         div->n_col = d + k;
 621
 622         return div;
 623 }
 624
 625 /* Swap divs "a" and "b" in "ls".
 626  */
 627 __isl_give isl_local_space *isl_local_space_swap_div(
 628         __isl_take isl_local_space *ls, int a, int b)
 629 {
 630         int offset;
 631
 632         ls = isl_local_space_cow(ls);
 633         if (!ls)
 634                 return NULL;
 635         if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)
 636                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 637                         "index out of bounds", return isl_local_space_free(ls));
 638         offset = ls->div->n_col - ls->div->n_row;
 639         ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);
 640         ls->div = isl_mat_swap_rows(ls->div, a, b);
 641         if (!ls->div)
 642                 return isl_local_space_free(ls);
 643         return ls;
 644 }
 645
 646 /* Construct a local space that contains all the divs in either
 647  * "ls1" or "ls2".
 648  */
 649 __isl_give isl_local_space *isl_local_space_intersect(
 650         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 651 {
 652         isl_ctx *ctx;
 653         int *exp1 = NULL;
 654         int *exp2 = NULL;
 655         isl_mat *div;
 656
 657         if (!ls1 || !ls2)
 658                 goto error;
 659
 660         ctx = isl_local_space_get_ctx(ls1);
 661         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 662                 isl_die(ctx, isl_error_invalid,
 663                         "spaces should be identical", goto error);
 664
 665         if (ls2->div->n_row == 0) {
 666                 isl_local_space_free(ls2);
 667                 return ls1;
 668         }
 669
 670         if (ls1->div->n_row == 0) {
 671                 isl_local_space_free(ls1);
 672                 return ls2;
 673         }
 674
 675         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 676         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 677         if (!exp1 || !exp2)
 678                 goto error;
 679
 680         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 681         if (!div)
 682                 goto error;
 683
 684         free(exp1);
 685         free(exp2);
 686         isl_local_space_free(ls2);
 687         isl_mat_free(ls1->div);
 688         ls1->div = div;
 689
 690         return ls1;
 691 error:
 692         free(exp1);
 693         free(exp2);
 694         isl_local_space_free(ls1);
 695         isl_local_space_free(ls2);
 696         return NULL;
 697 }
 698
 699 /* Does "ls" have an explicit representation for div "div"?
 700  */
 701 int isl_local_space_div_is_known(__isl_keep isl_local_space *ls, int div)
 702 {
 703         if (!ls)
 704                 return -1;
 705         if (div < 0 || div >= ls->div->n_row)
 706                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 707                         "position out of bounds", return -1);
 708         return !isl_int_is_zero(ls->div->row[div][0]);
 709 }
 710
 711 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 712 {
 713         int i;
 714
 715         if (!ls)
 716                 return -1;
 717
 718         for (i = 0; i < ls->div->n_row; ++i)
 719                 if (isl_int_is_zero(ls->div->row[i][0]))
 720                         return 0;
 721
 722         return 1;
 723 }
 724
 725 __isl_give isl_local_space *isl_local_space_domain(
 726         __isl_take isl_local_space *ls)
 727 {
 728         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 729                                         0, isl_local_space_dim(ls, isl_dim_out));
 730         ls = isl_local_space_cow(ls);
 731         if (!ls)
 732                 return NULL;
 733         ls->dim = isl_space_domain(ls->dim);
 734         if (!ls->dim)
 735                 return isl_local_space_free(ls);
 736         return ls;
 737 }
 738
 739 __isl_give isl_local_space *isl_local_space_range(
 740         __isl_take isl_local_space *ls)
 741 {
 742         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 743                                         0, isl_local_space_dim(ls, isl_dim_in));
 744         ls = isl_local_space_cow(ls);
 745         if (!ls)
 746                 return NULL;
 747
 748         ls->dim = isl_space_range(ls->dim);
 749         if (!ls->dim)
 750                 return isl_local_space_free(ls);
 751         return ls;
 752 }
 753
 754 /* Construct a local space for a map that has the given local
 755  * space as domain and that has a zero-dimensional range.
 756  */
 757 __isl_give isl_local_space *isl_local_space_from_domain(
 758         __isl_take isl_local_space *ls)
 759 {
 760         ls = isl_local_space_cow(ls);
 761         if (!ls)
 762                 return NULL;
 763         ls->dim = isl_space_from_domain(ls->dim);
 764         if (!ls->dim)
 765                 return isl_local_space_free(ls);
 766         return ls;
 767 }
 768
 769 __isl_give isl_local_space *isl_local_space_add_dims(
 770         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 771 {
 772         int pos;
 773
 774         if (!ls)
 775                 return NULL;
 776         pos = isl_local_space_dim(ls, type);
 777         return isl_local_space_insert_dims(ls, type, pos, n);
 778 }
 779
 780 /* Remove common factor of non-constant terms and denominator.
 781  */
 782 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 783 {
 784         isl_ctx *ctx = ls->div->ctx;
 785         unsigned total = ls->div->n_col - 2;
 786
 787         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 788         isl_int_gcd(ctx->normalize_gcd,
 789                     ctx->normalize_gcd, ls->div->row[div][0]);
 790         if (isl_int_is_one(ctx->normalize_gcd))
 791                 return;
 792
 793         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 794                             ctx->normalize_gcd, total);
 795         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 796                             ctx->normalize_gcd);
 797         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 798                             ctx->normalize_gcd);
 799 }
 800
 801 /* Exploit the equalities in "eq" to simplify the expressions of
 802  * the integer divisions in "ls".
 803  * The integer divisions in "ls" are assumed to appear as regular
 804  * dimensions in "eq".
 805  */
 806 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 807         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 808 {
 809         int i, j, k;
 810         unsigned total;
 811         unsigned n_div;
 812
 813         if (!ls || !eq)
 814                 goto error;
 815
 816         total = isl_space_dim(eq->dim, isl_dim_all);
 817         if (isl_local_space_dim(ls, isl_dim_all) != total)
 818                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 819                         "spaces don't match", goto error);
 820         total++;
 821         n_div = eq->n_div;
 822         for (i = 0; i < eq->n_eq; ++i) {
 823                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 824                 if (j < 0 || j == 0 || j >= total)
 825                         continue;
 826
 827                 for (k = 0; k < ls->div->n_row; ++k) {
 828                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 829                                 continue;
 830                         ls = isl_local_space_cow(ls);
 831                         if (!ls)
 832                                 goto error;
 833                         ls->div = isl_mat_cow(ls->div);
 834                         if (!ls->div)
 835                                 goto error;
 836                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 837                                         &ls->div->row[k][0]);
 838                         normalize_div(ls, k);
 839                 }
 840         }
 841
 842         isl_basic_set_free(eq);
 843         return ls;
 844 error:
 845         isl_basic_set_free(eq);
 846         isl_local_space_free(ls);
 847         return NULL;
 848 }
 849
 850 /* Plug in the affine expressions "subs" of length "subs_len" (including
 851  * the denominator and the constant term) into the variable at position "pos"
 852  * of the "n" div expressions starting at "first".
 853  *
 854  * Let i be the dimension to replace and let "subs" be of the form
 855  *
 856  *      f/d
 857  *
 858  * Any integer division starting at "first" with a non-zero coefficient for i,
 859  *
 860  *      floor((a i + g)/m)
 861  *
 862  * is replaced by
 863  *
 864  *      floor((a f + d g)/(m d))
 865  */
 866 __isl_give isl_local_space *isl_local_space_substitute_seq(
 867         __isl_take isl_local_space *ls,
 868         enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,
 869         int first, int n)
 870 {
 871         int i;
 872         isl_int v;
 873
 874         if (n == 0)
 875                 return ls;
 876         ls = isl_local_space_cow(ls);
 877         if (!ls)
 878                 return NULL;
 879         ls->div = isl_mat_cow(ls->div);
 880         if (!ls->div)
 881                 return isl_local_space_free(ls);
 882
 883         if (first + n > ls->div->n_row)
 884                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 885                         "index out of bounds", return isl_local_space_free(ls));
 886
 887         pos += isl_local_space_offset(ls, type);
 888
 889         isl_int_init(v);
 890         for (i = first; i < ls->div->n_row; ++i) {
 891                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 892                         continue;
 893                 isl_seq_substitute(ls->div->row[i], pos, subs,
 894                         ls->div->n_col, subs_len, v);
 895                 normalize_div(ls, i);
 896         }
 897         isl_int_clear(v);
 898
 899         return ls;
 900 }
 901
 902 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 903  * of "ls".
 904  *
 905  * Let i be the dimension to replace and let "subs" be of the form
 906  *
 907  *      f/d
 908  *
 909  * Any integer division with a non-zero coefficient for i,
 910  *
 911  *      floor((a i + g)/m)
 912  *
 913  * is replaced by
 914  *
 915  *      floor((a f + d g)/(m d))
 916  */
 917 __isl_give isl_local_space *isl_local_space_substitute(
 918         __isl_take isl_local_space *ls,
 919         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 920 {
 921         ls = isl_local_space_cow(ls);
 922         if (!ls || !subs)
 923                 return isl_local_space_free(ls);
 924
 925         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 926                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 927                         "spaces don't match", return isl_local_space_free(ls));
 928         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 929                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 930                         "cannot handle divs yet",
 931                         return isl_local_space_free(ls));
 932
 933         return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
 934                                             subs->v->size, 0, ls->div->n_row);
 935 }
 936
 937 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 938         enum isl_dim_type type)
 939 {
 940         if (!ls)
 941                 return -1;
 942         return isl_space_is_named_or_nested(ls->dim, type);
 943 }
 944
 945 __isl_give isl_local_space *isl_local_space_drop_dims(
 946         __isl_take isl_local_space *ls,
 947         enum isl_dim_type type, unsigned first, unsigned n)
 948 {
 949         isl_ctx *ctx;
 950
 951         if (!ls)
 952                 return NULL;
 953         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 954                 return ls;
 955
 956         ctx = isl_local_space_get_ctx(ls);
 957         if (first + n > isl_local_space_dim(ls, type))
 958                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 959                         return isl_local_space_free(ls));
 960
 961         ls = isl_local_space_cow(ls);
 962         if (!ls)
 963                 return NULL;
 964
 965         if (type == isl_dim_div) {
 966                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 967         } else {
 968                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 969                 if (!ls->dim)
 970                         return isl_local_space_free(ls);
 971         }
 972
 973         first += 1 + isl_local_space_offset(ls, type);
 974         ls->div = isl_mat_drop_cols(ls->div, first, n);
 975         if (!ls->div)
 976                 return isl_local_space_free(ls);
 977
 978         return ls;
 979 }
 980
 981 __isl_give isl_local_space *isl_local_space_insert_dims(
 982         __isl_take isl_local_space *ls,
 983         enum isl_dim_type type, unsigned first, unsigned n)
 984 {
 985         isl_ctx *ctx;
 986
 987         if (!ls)
 988                 return NULL;
 989         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 990                 return ls;
 991
 992         ctx = isl_local_space_get_ctx(ls);
 993         if (first > isl_local_space_dim(ls, type))
 994                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 995                         return isl_local_space_free(ls));
 996
 997         ls = isl_local_space_cow(ls);
 998         if (!ls)
 999                 return NULL;
1000
1001         if (type == isl_dim_div) {
1002                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
1003         } else {
1004                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
1005                 if (!ls->dim)
1006                         return isl_local_space_free(ls);
1007         }
1008
1009         first += 1 + isl_local_space_offset(ls, type);
1010         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
1011         if (!ls->div)
1012                 return isl_local_space_free(ls);
1013
1014         return ls;
1015 }
1016
1017 /* Check if the constraints pointed to by "constraint" is a div
1018  * constraint corresponding to div "div" in "ls".
1019  *
1020  * That is, if div = floor(f/m), then check if the constraint is
1021  *
1022  *              f - m d >= 0
1023  * or
1024  *              -(f-(m-1)) + m d >= 0
1025  */
1026 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
1027         isl_int *constraint, unsigned div)
1028 {
1029         unsigned pos;
1030
1031         if (!ls)
1032                 return -1;
1033
1034         if (isl_int_is_zero(ls->div->row[div][0]))
1035                 return 0;
1036
1037         pos = isl_local_space_offset(ls, isl_dim_div) + div;
1038
1039         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
1040                 int neg;
1041                 isl_int_sub(ls->div->row[div][1],
1042                                 ls->div->row[div][1], ls->div->row[div][0]);
1043                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
1044                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
1045                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
1046                 isl_int_add(ls->div->row[div][1],
1047                                 ls->div->row[div][1], ls->div->row[div][0]);
1048                 if (!neg)
1049                         return 0;
1050                 if (isl_seq_first_non_zero(constraint+pos+1,
1051                                             ls->div->n_row-div-1) != -1)
1052                         return 0;
1053         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
1054                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
1055                         return 0;
1056                 if (isl_seq_first_non_zero(constraint+pos+1,
1057                                             ls->div->n_row-div-1) != -1)
1058                         return 0;
1059         } else
1060                 return 0;
1061
1062         return 1;
1063 }
1064
1065 /*
1066  * Set active[i] to 1 if the dimension at position i is involved
1067  * in the linear expression l.
1068  */
1069 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
1070 {
1071         int i, j;
1072         isl_ctx *ctx;
1073         int *active = NULL;
1074         unsigned total;
1075         unsigned offset;
1076
1077         ctx = isl_local_space_get_ctx(ls);
1078         total = isl_local_space_dim(ls, isl_dim_all);
1079         active = isl_calloc_array(ctx, int, total);
1080         if (total && !active)
1081                 return NULL;
1082
1083         for (i = 0; i < total; ++i)
1084                 active[i] = !isl_int_is_zero(l[i]);
1085
1086         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
1087         for (i = ls->div->n_row - 1; i >= 0; --i) {
1088                 if (!active[offset + i])
1089                         continue;
1090                 for (j = 0; j < total; ++j)
1091                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
1092         }
1093
1094         return active;
1095 }
1096
1097 /* Given a local space "ls" of a set, create a local space
1098  * for the lift of the set.  In particular, the result
1099  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1100  * range of the wrapped map.
1101  */
1102 __isl_give isl_local_space *isl_local_space_lift(
1103         __isl_take isl_local_space *ls)
1104 {
1105         ls = isl_local_space_cow(ls);
1106         if (!ls)
1107                 return NULL;
1108
1109         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
1110         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
1111         if (!ls->dim || !ls->div)
1112                 return isl_local_space_free(ls);
1113
1114         return ls;
1115 }
1116
1117 /* Construct a basic map that maps a set living in local space "ls"
1118  * to the corresponding lifted local space.
1119  */
1120 __isl_give isl_basic_map *isl_local_space_lifting(
1121         __isl_take isl_local_space *ls)
1122 {
1123         isl_basic_map *lifting;
1124         isl_basic_set *bset;
1125
1126         if (!ls)
1127                 return NULL;
1128         if (!isl_local_space_is_set(ls))
1129                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1130                         "lifting only defined on set spaces", goto error);
1131
1132         bset = isl_basic_set_from_local_space(ls);
1133         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
1134         lifting = isl_basic_map_domain_map(lifting);
1135         lifting = isl_basic_map_reverse(lifting);
1136
1137         return lifting;
1138 error:
1139         isl_local_space_free(ls);
1140         return NULL;
1141 }
1142
1143 /* Compute the preimage of "ls" under the function represented by "ma".
1144  * In other words, plug in "ma" in "ls".  The result is a local space
1145  * that is part of the domain space of "ma".
1146  *
1147  * If the divs in "ls" are represented as
1148  *
1149  *      floor((a_i(p) + b_i x + c_i(divs))/n_i)
1150  *
1151  * and ma is represented by
1152  *
1153  *      x = D(p) + F(y) + G(divs')
1154  *
1155  * then the resulting divs are
1156  *
1157  *      floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1158  *
1159  * We first copy over the divs from "ma" and then
1160  * we add the modified divs from "ls".
1161  */
1162 __isl_give isl_local_space *isl_local_space_preimage_multi_aff(
1163         __isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
1164 {
1165         int i;
1166         isl_space *space;
1167         isl_local_space *res = NULL;
1168         int n_div_ls, n_div_ma;
1169         isl_int f, c1, c2, g;
1170
1171         ma = isl_multi_aff_align_divs(ma);
1172         if (!ls || !ma)
1173                 goto error;
1174         if (!isl_space_is_range_internal(ls->dim, ma->space))
1175                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1176                         "spaces don't match", goto error);
1177
1178         n_div_ls = isl_local_space_dim(ls, isl_dim_div);
1179         n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
1180
1181         space = isl_space_domain(isl_multi_aff_get_space(ma));
1182         res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
1183         if (!res)
1184                 goto error;
1185
1186         if (n_div_ma) {
1187                 isl_mat_free(res->div);
1188                 res->div = isl_mat_copy(ma->p[0]->ls->div);
1189                 res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
1190                 res->div = isl_mat_add_rows(res->div, n_div_ls);
1191                 if (!res->div)
1192                         goto error;
1193         }
1194
1195         isl_int_init(f);
1196         isl_int_init(c1);
1197         isl_int_init(c2);
1198         isl_int_init(g);
1199
1200         for (i = 0; i < ls->div->n_row; ++i) {
1201                 if (isl_int_is_zero(ls->div->row[i][0])) {
1202                         isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
1203                         continue;
1204                 }
1205                 isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
1206                                 ma, 0, 0, n_div_ma, n_div_ls, f, c1, c2, g, 1);
1207                 normalize_div(res, n_div_ma + i);
1208         }
1209
1210         isl_int_clear(f);
1211         isl_int_clear(c1);
1212         isl_int_clear(c2);
1213         isl_int_clear(g);
1214
1215         isl_local_space_free(ls);
1216         isl_multi_aff_free(ma);
1217         return res;
1218 error:
1219         isl_local_space_free(ls);
1220         isl_multi_aff_free(ma);
1221         isl_local_space_free(res);
1222         return NULL;
1223 }
1224
1225 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "ls"
1226  * to dimensions of "dst_type" at "dst_pos".
1227  *
1228  * Moving to/from local dimensions is not allowed.
1229  * We currently assume that the dimension type changes.
1230  */
1231 __isl_give isl_local_space *isl_local_space_move_dims(
1232         __isl_take isl_local_space *ls,
1233         enum isl_dim_type dst_type, unsigned dst_pos,
1234         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1235 {
1236         unsigned g_dst_pos;
1237         unsigned g_src_pos;
1238
1239         if (!ls)
1240                 return NULL;
1241         if (n == 0 &&
1242             !isl_local_space_is_named_or_nested(ls, src_type) &&
1243             !isl_local_space_is_named_or_nested(ls, dst_type))
1244                 return ls;
1245
1246         if (src_pos + n > isl_local_space_dim(ls, src_type))
1247                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1248                         "range out of bounds", return isl_local_space_free(ls));
1249         if (dst_pos > isl_local_space_dim(ls, dst_type))
1250                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1251                         "position out of bounds",
1252                         return isl_local_space_free(ls));
1253         if (src_type == isl_dim_div)
1254                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1255                         "cannot move divs", return isl_local_space_free(ls));
1256         if (dst_type == isl_dim_div)
1257                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1258                         "cannot move to divs", return isl_local_space_free(ls));
1259         if (dst_type == src_type && dst_pos == src_pos)
1260                 return ls;
1261         if (dst_type == src_type)
1262                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
1263                         "moving dims within the same type not supported",
1264                         return isl_local_space_free(ls));
1265
1266         ls = isl_local_space_cow(ls);
1267         if (!ls)
1268                 return NULL;
1269
1270         g_src_pos = 1 + isl_local_space_offset(ls, src_type) + src_pos;
1271         g_dst_pos = 1 + isl_local_space_offset(ls, dst_type) + dst_pos;
1272         if (dst_type > src_type)
1273                 g_dst_pos -= n;
1274         ls->div = isl_mat_move_cols(ls->div, g_dst_pos, g_src_pos, n);
1275         if (!ls->div)
1276                 return isl_local_space_free(ls);
1277         ls->dim = isl_space_move_dims(ls->dim, dst_type, dst_pos,
1278                                         src_type, src_pos, n);
1279         if (!ls->dim)
1280                 return isl_local_space_free(ls);
1281
1282         return ls;
1283 }
1284
1285 /* Remove any internal structure of the domain of "ls".
1286  * If there is any such internal structure in the input,
1287  * then the name of the corresponding space is also removed.
1288  */
1289 __isl_give isl_local_space *isl_local_space_flatten_domain(
1290         __isl_take isl_local_space *ls)
1291 {
1292         if (!ls)
1293                 return NULL;
1294
1295         if (!ls->dim->nested[0])
1296                 return ls;
1297
1298         ls = isl_local_space_cow(ls);
1299         if (!ls)
1300                 return NULL;
1301
1302         ls->dim = isl_space_flatten_domain(ls->dim);
1303         if (!ls->dim)
1304                 return isl_local_space_free(ls);
1305
1306         return ls;
1307 }
1308
1309 /* Remove any internal structure of the range of "ls".
1310  * If there is any such internal structure in the input,
1311  * then the name of the corresponding space is also removed.
1312  */
1313 __isl_give isl_local_space *isl_local_space_flatten_range(
1314         __isl_take isl_local_space *ls)
1315 {
1316         if (!ls)
1317                 return NULL;
1318
1319         if (!ls->dim->nested[1])
1320                 return ls;
1321
1322         ls = isl_local_space_cow(ls);
1323         if (!ls)
1324                 return NULL;
1325
1326         ls->dim = isl_space_flatten_range(ls->dim);
1327         if (!ls->dim)
1328                 return isl_local_space_free(ls);
1329
1330         return ls;
1331 }