isl_morph.c

   1 /*
   2  * Copyright 2010-2011 INRIA Saclay
   3  * Copyright 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_map_private.h>
  14 #include <isl_aff_private.h>
  15 #include <isl_morph.h>
  16 #include <isl_seq.h>
  17 #include <isl_mat_private.h>
  18 #include <isl_space_private.h>
  19 #include <isl_equalities.h>
  20
  21 isl_ctx *isl_morph_get_ctx(__isl_keep isl_morph *morph)
  22 {
  23         if (!morph)
  24                 return NULL;
  25         return isl_basic_set_get_ctx(morph->dom);
  26 }
  27
  28 __isl_give isl_morph *isl_morph_alloc(
  29         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  30         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  31 {
  32         isl_morph *morph;
  33
  34         if (!dom || !ran || !map || !inv)
  35                 goto error;
  36
  37         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  38         if (!morph)
  39                 goto error;
  40
  41         morph->ref = 1;
  42         morph->dom = dom;
  43         morph->ran = ran;
  44         morph->map = map;
  45         morph->inv = inv;
  46
  47         return morph;
  48 error:
  49         isl_basic_set_free(dom);
  50         isl_basic_set_free(ran);
  51         isl_mat_free(map);
  52         isl_mat_free(inv);
  53         return NULL;
  54 }
  55
  56 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  57 {
  58         if (!morph)
  59                 return NULL;
  60
  61         morph->ref++;
  62         return morph;
  63 }
  64
  65 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  66 {
  67         if (!morph)
  68                 return NULL;
  69
  70         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  71                 isl_basic_set_copy(morph->ran),
  72                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  73 }
  74
  75 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  76 {
  77         if (!morph)
  78                 return NULL;
  79
  80         if (morph->ref == 1)
  81                 return morph;
  82         morph->ref--;
  83         return isl_morph_dup(morph);
  84 }
  85
  86 void isl_morph_free(__isl_take isl_morph *morph)
  87 {
  88         if (!morph)
  89                 return;
  90
  91         if (--morph->ref > 0)
  92                 return;
  93
  94         isl_basic_set_free(morph->dom);
  95         isl_basic_set_free(morph->ran);
  96         isl_mat_free(morph->map);
  97         isl_mat_free(morph->inv);
  98         free(morph);
  99 }
 100
 101 /* Is "morph" an identity on the parameters?
 102  */
 103 static int identity_on_parameters(__isl_keep isl_morph *morph)
 104 {
 105         int is_identity;
 106         unsigned nparam;
 107         isl_mat *sub;
 108
 109         nparam = isl_morph_dom_dim(morph, isl_dim_param);
 110         if (nparam != isl_morph_ran_dim(morph, isl_dim_param))
 111                 return 0;
 112         if (nparam == 0)
 113                 return 1;
 114         sub = isl_mat_sub_alloc(morph->map, 0, 1 + nparam, 0, 1 + nparam);
 115         is_identity = isl_mat_is_scaled_identity(sub);
 116         isl_mat_free(sub);
 117
 118         return is_identity;
 119 }
 120
 121 /* Return an affine expression of the variables of the range of "morph"
 122  * in terms of the parameters and the variables of the domain on "morph".
 123  *
 124  * In order for the space manipulations to make sense, we require
 125  * that the parameters are not modified by "morph".
 126  */
 127 __isl_give isl_multi_aff *isl_morph_get_var_multi_aff(
 128         __isl_keep isl_morph *morph)
 129 {
 130         isl_space *dom, *ran, *space;
 131         isl_local_space *ls;
 132         isl_multi_aff *ma;
 133         unsigned nparam, nvar;
 134         int i;
 135         int is_identity;
 136
 137         if (!morph)
 138                 return NULL;
 139
 140         is_identity = identity_on_parameters(morph);
 141         if (is_identity < 0)
 142                 return NULL;
 143         if (!is_identity)
 144                 isl_die(isl_morph_get_ctx(morph), isl_error_invalid,
 145                         "cannot handle parameter compression", return NULL);
 146
 147         dom = isl_morph_get_dom_space(morph);
 148         ls = isl_local_space_from_space(isl_space_copy(dom));
 149         ran = isl_morph_get_ran_space(morph);
 150         space = isl_space_map_from_domain_and_range(dom, ran);
 151         ma = isl_multi_aff_zero(space);
 152
 153         nparam = isl_multi_aff_dim(ma, isl_dim_param);
 154         nvar = isl_multi_aff_dim(ma, isl_dim_out);
 155         for (i = 0; i < nvar; ++i) {
 156                 isl_val *val;
 157                 isl_vec *v;
 158                 isl_aff *aff;
 159
 160                 v = isl_mat_get_row(morph->map, 1 + nparam + i);
 161                 v = isl_vec_insert_els(v, 0, 1);
 162                 val = isl_mat_get_element_val(morph->map, 0, 0);
 163                 v = isl_vec_set_element_val(v, 0, val);
 164                 aff = isl_aff_alloc_vec(isl_local_space_copy(ls), v);
 165                 ma = isl_multi_aff_set_aff(ma, i, aff);
 166         }
 167
 168         isl_local_space_free(ls);
 169         return ma;
 170 }
 171
 172 /* Return the domain space of "morph".
 173  */
 174 __isl_give isl_space *isl_morph_get_dom_space(__isl_keep isl_morph *morph)
 175 {
 176         if (!morph)
 177                 return NULL;
 178
 179         return isl_basic_set_get_space(morph->dom);
 180 }
 181
 182 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
 183 {
 184         if (!morph)
 185                 return NULL;
 186
 187         return isl_space_copy(morph->ran->dim);
 188 }
 189
 190 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 191 {
 192         if (!morph)
 193                 return 0;
 194
 195         return isl_basic_set_dim(morph->dom, type);
 196 }
 197
 198 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 199 {
 200         if (!morph)
 201                 return 0;
 202
 203         return isl_basic_set_dim(morph->ran, type);
 204 }
 205
 206 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 207         enum isl_dim_type type, unsigned first, unsigned n)
 208 {
 209         unsigned dom_offset;
 210
 211         if (n == 0)
 212                 return morph;
 213
 214         morph = isl_morph_cow(morph);
 215         if (!morph)
 216                 return NULL;
 217
 218         dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
 219
 220         morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
 221
 222         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 223
 224         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 225
 226         if (morph->dom && morph->ran && morph->map && morph->inv)
 227                 return morph;
 228
 229         isl_morph_free(morph);
 230         return NULL;
 231 }
 232
 233 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 234         enum isl_dim_type type, unsigned first, unsigned n)
 235 {
 236         unsigned ran_offset;
 237
 238         if (n == 0)
 239                 return morph;
 240
 241         morph = isl_morph_cow(morph);
 242         if (!morph)
 243                 return NULL;
 244
 245         ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
 246
 247         morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
 248
 249         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 250
 251         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 252
 253         if (morph->dom && morph->ran && morph->map && morph->inv)
 254                 return morph;
 255
 256         isl_morph_free(morph);
 257         return NULL;
 258 }
 259
 260 /* Project domain of morph onto its parameter domain.
 261  */
 262 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
 263 {
 264         unsigned n;
 265
 266         morph = isl_morph_cow(morph);
 267         if (!morph)
 268                 return NULL;
 269         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 270         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 271         if (!morph)
 272                 return NULL;
 273         morph->dom = isl_basic_set_params(morph->dom);
 274         if (morph->dom)
 275                 return morph;
 276
 277         isl_morph_free(morph);
 278         return NULL;
 279 }
 280
 281 /* Project range of morph onto its parameter domain.
 282  */
 283 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 284 {
 285         unsigned n;
 286
 287         morph = isl_morph_cow(morph);
 288         if (!morph)
 289                 return NULL;
 290         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 291         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 292         if (!morph)
 293                 return NULL;
 294         morph->ran = isl_basic_set_params(morph->ran);
 295         if (morph->ran)
 296                 return morph;
 297
 298         isl_morph_free(morph);
 299         return NULL;
 300 }
 301
 302 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 303 {
 304         if (!morph)
 305                 return;
 306
 307         isl_basic_set_dump(morph->dom);
 308         isl_basic_set_dump(morph->ran);
 309         isl_mat_print_internal(morph->map, out, 4);
 310         isl_mat_print_internal(morph->inv, out, 4);
 311 }
 312
 313 void isl_morph_dump(__isl_take isl_morph *morph)
 314 {
 315         isl_morph_print_internal(morph, stderr);
 316 }
 317
 318 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 319 {
 320         isl_mat *id;
 321         isl_basic_set *universe;
 322         unsigned total;
 323
 324         if (!bset)
 325                 return NULL;
 326
 327         total = isl_basic_set_total_dim(bset);
 328         id = isl_mat_identity(bset->ctx, 1 + total);
 329         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 330
 331         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 332                 id, isl_mat_copy(id));
 333 }
 334
 335 /* Create a(n identity) morphism between empty sets of the same dimension
 336  * a "bset".
 337  */
 338 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 339 {
 340         isl_mat *id;
 341         isl_basic_set *empty;
 342         unsigned total;
 343
 344         if (!bset)
 345                 return NULL;
 346
 347         total = isl_basic_set_total_dim(bset);
 348         id = isl_mat_identity(bset->ctx, 1 + total);
 349         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 350
 351         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 352                 id, isl_mat_copy(id));
 353 }
 354
 355 /* Construct a basic set described by the "n" equalities of "bset" starting
 356  * at "first".
 357  */
 358 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 359         unsigned first, unsigned n)
 360 {
 361         int i, k;
 362         isl_basic_set *eq;
 363         unsigned total;
 364
 365         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 366
 367         total = isl_basic_set_total_dim(bset);
 368         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 369         if (!eq)
 370                 return NULL;
 371         for (i = 0; i < n; ++i) {
 372                 k = isl_basic_set_alloc_equality(eq);
 373                 if (k < 0)
 374                         goto error;
 375                 isl_seq_cpy(eq->eq[k], bset->eq[first + i], 1 + total);
 376         }
 377
 378         return eq;
 379 error:
 380         isl_basic_set_free(eq);
 381         return NULL;
 382 }
 383
 384 /* Given a basic set, exploit the equalties in the basic set to construct
 385  * a morphishm that maps the basic set to a lower-dimensional space.
 386  * Specifically, the morphism reduces the number of dimensions of type "type".
 387  *
 388  * We first select the equalities of interest, that is those that involve
 389  * variables of type "type" and no later variables.
 390  * Denote those equalities as
 391  *
 392  *              -C(p) + M x = 0
 393  *
 394  * where C(p) depends on the parameters if type == isl_dim_set and
 395  * is a constant if type == isl_dim_param.
 396  *
 397  * Use isl_mat_final_variable_compression to construct a compression
 398  *
 399  *      x = T x'
 400  *
 401  *      x' = Q x
 402  *
 403  * If T is a zero-column matrix, then the set of equality constraints
 404  * do not admit a solution.  In this case, an empty morphism is returned.
 405  *
 406  * Both matrices are extended to map the full original space to the full
 407  * compressed space.
 408  */
 409 __isl_give isl_morph *isl_basic_set_variable_compression(
 410         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 411 {
 412         unsigned otype;
 413         unsigned ntype;
 414         unsigned orest;
 415         unsigned nrest;
 416         int f_eq, n_eq;
 417         isl_space *dim;
 418         isl_mat *E, *Q, *C;
 419         isl_basic_set *dom, *ran;
 420
 421         if (!bset)
 422                 return NULL;
 423
 424         if (isl_basic_set_plain_is_empty(bset))
 425                 return isl_morph_empty(bset);
 426
 427         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 428
 429         otype = 1 + isl_space_offset(bset->dim, type);
 430         ntype = isl_basic_set_dim(bset, type);
 431         orest = otype + ntype;
 432         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 433
 434         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 435                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 436                         break;
 437         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 438                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 439                         break;
 440         if (n_eq == 0)
 441                 return isl_morph_identity(bset);
 442
 443         E = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, 0, orest);
 444         C = isl_mat_final_variable_compression(E, otype - 1, &Q);
 445         if (!Q)
 446                 C = isl_mat_free(C);
 447         if (C && C->n_col == 0) {
 448                 isl_mat_free(C);
 449                 isl_mat_free(Q);
 450                 return isl_morph_empty(bset);
 451         }
 452
 453         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 454         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 455
 456         dim = isl_space_copy(bset->dim);
 457         dim = isl_space_drop_dims(dim, type, 0, ntype);
 458         dim = isl_space_add_dims(dim, type, ntype - n_eq);
 459         ran = isl_basic_set_universe(dim);
 460         dom = copy_equalities(bset, f_eq, n_eq);
 461
 462         return isl_morph_alloc(dom, ran, Q, C);
 463 }
 464
 465 /* Construct a parameter compression for "bset".
 466  * We basically just call isl_mat_parameter_compression with the right input
 467  * and then extend the resulting matrix to include the variables.
 468  *
 469  * The implementation assumes that "bset" does not have any equalities
 470  * that only involve the parameters and that isl_basic_set_gauss has
 471  * been applied to "bset".
 472  *
 473  * Let the equalities be given as
 474  *
 475  *      B(p) + A x = 0.
 476  *
 477  * We use isl_mat_parameter_compression_ext to compute the compression
 478  *
 479  *      p = T p'.
 480  */
 481 __isl_give isl_morph *isl_basic_set_parameter_compression(
 482         __isl_keep isl_basic_set *bset)
 483 {
 484         unsigned nparam;
 485         unsigned nvar;
 486         unsigned n_div;
 487         int n_eq;
 488         isl_mat *H, *B;
 489         isl_mat *map, *inv;
 490         isl_basic_set *dom, *ran;
 491
 492         if (!bset)
 493                 return NULL;
 494
 495         if (isl_basic_set_plain_is_empty(bset))
 496                 return isl_morph_empty(bset);
 497         if (bset->n_eq == 0)
 498                 return isl_morph_identity(bset);
 499
 500         n_eq = bset->n_eq;
 501         nparam = isl_basic_set_dim(bset, isl_dim_param);
 502         nvar = isl_basic_set_dim(bset, isl_dim_set);
 503         n_div = isl_basic_set_dim(bset, isl_dim_div);
 504
 505         if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,
 506                                     nvar + n_div) == -1)
 507                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 508                         "input not allowed to have parameter equalities",
 509                         return NULL);
 510         if (n_eq > nvar + n_div)
 511                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 512                         "input not gaussed", return NULL);
 513
 514         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 515         H = isl_mat_sub_alloc6(bset->ctx, bset->eq,
 516                                 0, n_eq, 1 + nparam, nvar + n_div);
 517         inv = isl_mat_parameter_compression_ext(B, H);
 518         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 519         map = isl_mat_right_inverse(isl_mat_copy(inv));
 520
 521         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 522         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 523
 524         return isl_morph_alloc(dom, ran, map, inv);
 525 }
 526
 527 /* Add stride constraints to "bset" based on the inverse mapping
 528  * that was plugged in.  In particular, if morph maps x' to x,
 529  * the the constraints of the original input
 530  *
 531  *      A x' + b >= 0
 532  *
 533  * have been rewritten to
 534  *
 535  *      A inv x + b >= 0
 536  *
 537  * However, this substitution may loose information on the integrality of x',
 538  * so we need to impose that
 539  *
 540  *      inv x
 541  *
 542  * is integral.  If inv = B/d, this means that we need to impose that
 543  *
 544  *      B x = 0         mod d
 545  *
 546  * or
 547  *
 548  *      exists alpha in Z^m: B x = d alpha
 549  *
 550  * This function is similar to add_strides in isl_affine_hull.c
 551  */
 552 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 553         __isl_keep isl_morph *morph)
 554 {
 555         int i, div, k;
 556         isl_int gcd;
 557
 558         if (isl_int_is_one(morph->inv->row[0][0]))
 559                 return bset;
 560
 561         isl_int_init(gcd);
 562
 563         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 564                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 565                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 566                         continue;
 567                 div = isl_basic_set_alloc_div(bset);
 568                 if (div < 0)
 569                         goto error;
 570                 isl_int_set_si(bset->div[div][0], 0);
 571                 k = isl_basic_set_alloc_equality(bset);
 572                 if (k < 0)
 573                         goto error;
 574                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 575                             morph->inv->n_col);
 576                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 577                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 578                             morph->inv->row[0][0]);
 579         }
 580
 581         isl_int_clear(gcd);
 582
 583         return bset;
 584 error:
 585         isl_int_clear(gcd);
 586         isl_basic_set_free(bset);
 587         return NULL;
 588 }
 589
 590 /* Apply the morphism to the basic set.
 591  * We basically just compute the preimage of "bset" under the inverse mapping
 592  * in morph, add in stride constraints and intersect with the range
 593  * of the morphism.
 594  */
 595 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 596         __isl_take isl_basic_set *bset)
 597 {
 598         isl_basic_set *res = NULL;
 599         isl_mat *mat = NULL;
 600         int i, k;
 601         int max_stride;
 602
 603         if (!morph || !bset)
 604                 goto error;
 605
 606         isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
 607                     goto error);
 608
 609         max_stride = morph->inv->n_row - 1;
 610         if (isl_int_is_one(morph->inv->row[0][0]))
 611                 max_stride = 0;
 612         res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
 613                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 614
 615         for (i = 0; i < bset->n_div; ++i)
 616                 if (isl_basic_set_alloc_div(res) < 0)
 617                         goto error;
 618
 619         mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
 620                                         0, morph->inv->n_row);
 621         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 622         if (!mat)
 623                 goto error;
 624         for (i = 0; i < bset->n_eq; ++i) {
 625                 k = isl_basic_set_alloc_equality(res);
 626                 if (k < 0)
 627                         goto error;
 628                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 629                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 630                                 morph->inv->row[0][0], bset->n_div);
 631         }
 632         isl_mat_free(mat);
 633
 634         mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
 635                                         0, morph->inv->n_row);
 636         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 637         if (!mat)
 638                 goto error;
 639         for (i = 0; i < bset->n_ineq; ++i) {
 640                 k = isl_basic_set_alloc_inequality(res);
 641                 if (k < 0)
 642                         goto error;
 643                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 644                 isl_seq_scale(res->ineq[k] + mat->n_col,
 645                                 bset->ineq[i] + mat->n_col,
 646                                 morph->inv->row[0][0], bset->n_div);
 647         }
 648         isl_mat_free(mat);
 649
 650         mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
 651                                         1, morph->inv->n_row);
 652         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 653         if (!mat)
 654                 goto error;
 655         for (i = 0; i < bset->n_div; ++i) {
 656                 isl_int_mul(res->div[i][0],
 657                                 morph->inv->row[0][0], bset->div[i][0]);
 658                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 659                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 660                                 bset->div[i] + 1 + mat->n_col,
 661                                 morph->inv->row[0][0], bset->n_div);
 662         }
 663         isl_mat_free(mat);
 664
 665         res = add_strides(res, morph);
 666
 667         if (isl_basic_set_is_rational(bset))
 668                 res = isl_basic_set_set_rational(res);
 669
 670         res = isl_basic_set_simplify(res);
 671         res = isl_basic_set_finalize(res);
 672
 673         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 674
 675         isl_morph_free(morph);
 676         isl_basic_set_free(bset);
 677         return res;
 678 error:
 679         isl_mat_free(mat);
 680         isl_morph_free(morph);
 681         isl_basic_set_free(bset);
 682         isl_basic_set_free(res);
 683         return NULL;
 684 }
 685
 686 /* Apply the morphism to the set.
 687  */
 688 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 689         __isl_take isl_set *set)
 690 {
 691         int i;
 692
 693         if (!morph || !set)
 694                 goto error;
 695
 696         isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
 697
 698         set = isl_set_cow(set);
 699         if (!set)
 700                 goto error;
 701
 702         isl_space_free(set->dim);
 703         set->dim = isl_space_copy(morph->ran->dim);
 704         if (!set->dim)
 705                 goto error;
 706
 707         for (i = 0; i < set->n; ++i) {
 708                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 709                 if (!set->p[i])
 710                         goto error;
 711         }
 712
 713         isl_morph_free(morph);
 714
 715         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 716
 717         return set;
 718 error:
 719         isl_set_free(set);
 720         isl_morph_free(morph);
 721         return NULL;
 722 }
 723
 724 /* Construct a morphism that first does morph2 and then morph1.
 725  */
 726 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 727         __isl_take isl_morph *morph2)
 728 {
 729         isl_mat *map, *inv;
 730         isl_basic_set *dom, *ran;
 731
 732         if (!morph1 || !morph2)
 733                 goto error;
 734
 735         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 736         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 737         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 738                                   isl_basic_set_copy(morph1->dom));
 739         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 740         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 741                                   isl_basic_set_copy(morph2->ran));
 742         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 743
 744         isl_morph_free(morph1);
 745         isl_morph_free(morph2);
 746
 747         return isl_morph_alloc(dom, ran, map, inv);
 748 error:
 749         isl_morph_free(morph1);
 750         isl_morph_free(morph2);
 751         return NULL;
 752 }
 753
 754 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 755 {
 756         isl_basic_set *bset;
 757         isl_mat *mat;
 758
 759         morph = isl_morph_cow(morph);
 760         if (!morph)
 761                 return NULL;
 762
 763         bset = morph->dom;
 764         morph->dom = morph->ran;
 765         morph->ran = bset;
 766
 767         mat = morph->map;
 768         morph->map = morph->inv;
 769         morph->inv = mat;
 770
 771         return morph;
 772 }
 773
 774 /* We detect all the equalities first to avoid implicit equalties
 775  * being discovered during the computations.  In particular,
 776  * the compression on the variables could expose additional stride
 777  * constraints on the parameters.  This would result in existentially
 778  * quantified variables after applying the resulting morph, which
 779  * in turn could break invariants of the calling functions.
 780  */
 781 __isl_give isl_morph *isl_basic_set_full_compression(
 782         __isl_keep isl_basic_set *bset)
 783 {
 784         isl_morph *morph, *morph2;
 785
 786         bset = isl_basic_set_copy(bset);
 787         bset = isl_basic_set_detect_equalities(bset);
 788
 789         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 790         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 791
 792         morph2 = isl_basic_set_parameter_compression(bset);
 793         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 794
 795         morph = isl_morph_compose(morph2, morph);
 796
 797         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 798         isl_basic_set_free(bset);
 799
 800         morph = isl_morph_compose(morph2, morph);
 801
 802         return morph;
 803 }
 804
 805 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
 806         __isl_take isl_vec *vec)
 807 {
 808         if (!morph)
 809                 goto error;
 810
 811         vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
 812
 813         isl_morph_free(morph);
 814         return vec;
 815 error:
 816         isl_morph_free(morph);
 817         isl_vec_free(vec);
 818         return NULL;
 819 }