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