isl_morph.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #include <isl_morph.h>
  12 #include <isl_seq.h>
  13 #include <isl_map_private.h>
  14 #include <isl_dim_private.h>
  15 #include <isl_equalities.h>
  16
  17 __isl_give isl_morph *isl_morph_alloc(
  18         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  19         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  20 {
  21         isl_morph *morph;
  22
  23         if (!dom || !ran || !map || !inv)
  24                 goto error;
  25
  26         morph = isl_alloc_type(in_dim->ctx, struct isl_morph);
  27         if (!morph)
  28                 goto error;
  29
  30         morph->ref = 1;
  31         morph->dom = dom;
  32         morph->ran = ran;
  33         morph->map = map;
  34         morph->inv = inv;
  35
  36         return morph;
  37 error:
  38         isl_basic_set_free(dom);
  39         isl_basic_set_free(ran);
  40         isl_mat_free(map);
  41         isl_mat_free(inv);
  42         return NULL;
  43 }
  44
  45 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  46 {
  47         if (!morph)
  48                 return NULL;
  49
  50         morph->ref++;
  51         return morph;
  52 }
  53
  54 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  55 {
  56         if (!morph)
  57                 return NULL;
  58
  59         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  60                 isl_basic_set_copy(morph->ran),
  61                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  62 }
  63
  64 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  65 {
  66         if (!morph)
  67                 return NULL;
  68
  69         if (morph->ref == 1)
  70                 return morph;
  71         morph->ref--;
  72         return isl_morph_dup(morph);
  73 }
  74
  75 void isl_morph_free(__isl_take isl_morph *morph)
  76 {
  77         if (!morph)
  78                 return;
  79
  80         if (--morph->ref > 0)
  81                 return;
  82
  83         isl_basic_set_free(morph->dom);
  84         isl_basic_set_free(morph->ran);
  85         isl_mat_free(morph->map);
  86         isl_mat_free(morph->inv);
  87         free(morph);
  88 }
  89
  90 __isl_give isl_dim *isl_morph_get_ran_dim(__isl_keep isl_morph *morph)
  91 {
  92         if (!morph)
  93                 return NULL;
  94
  95         return isl_dim_copy(morph->ran->dim);
  96 }
  97
  98 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
  99         enum isl_dim_type type, unsigned first, unsigned n)
 100 {
 101         unsigned dom_offset;
 102
 103         if (n == 0)
 104                 return morph;
 105
 106         morph = isl_morph_cow(morph);
 107         if (!morph)
 108                 return NULL;
 109
 110         dom_offset = 1 + isl_dim_offset(morph->dom->dim, type);
 111
 112         morph->dom = isl_basic_set_remove(morph->dom, type, first, n);
 113
 114         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 115
 116         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 117
 118         if (morph->dom && morph->ran && morph->map && morph->inv)
 119                 return morph;
 120
 121         isl_morph_free(morph);
 122         return NULL;
 123 }
 124
 125 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 126         enum isl_dim_type type, unsigned first, unsigned n)
 127 {
 128         unsigned ran_offset;
 129
 130         if (n == 0)
 131                 return morph;
 132
 133         morph = isl_morph_cow(morph);
 134         if (!morph)
 135                 return NULL;
 136
 137         ran_offset = 1 + isl_dim_offset(morph->ran->dim, type);
 138
 139         morph->ran = isl_basic_set_remove(morph->ran, type, first, n);
 140
 141         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 142
 143         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 144
 145         if (morph->dom && morph->ran && morph->map && morph->inv)
 146                 return morph;
 147
 148         isl_morph_free(morph);
 149         return NULL;
 150 }
 151
 152 void isl_morph_dump(__isl_take isl_morph *morph, FILE *out)
 153 {
 154         if (!morph)
 155                 return;
 156
 157         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 158         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 159         isl_mat_dump(morph->map, out, 4);
 160         isl_mat_dump(morph->inv, out, 4);
 161 }
 162
 163 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 164 {
 165         isl_mat *id;
 166         isl_basic_set *universe;
 167         unsigned total;
 168
 169         if (!bset)
 170                 return NULL;
 171
 172         total = isl_basic_set_total_dim(bset);
 173         id = isl_mat_identity(bset->ctx, 1 + total);
 174         universe = isl_basic_set_universe(isl_dim_copy(bset->dim));
 175
 176         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 177                 id, isl_mat_copy(id));
 178 }
 179
 180 /* Create a(n identity) morphism between empty sets of the same dimension
 181  * a "bset".
 182  */
 183 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 184 {
 185         isl_mat *id;
 186         isl_basic_set *empty;
 187         unsigned total;
 188
 189         if (!bset)
 190                 return NULL;
 191
 192         total = isl_basic_set_total_dim(bset);
 193         id = isl_mat_identity(bset->ctx, 1 + total);
 194         empty = isl_basic_set_empty(isl_dim_copy(bset->dim));
 195
 196         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 197                 id, isl_mat_copy(id));
 198 }
 199
 200 /* Given a matrix that maps a (possibly) parametric domain to
 201  * a parametric domain, add in rows that map the "nparam" parameters onto
 202  * themselves.
 203  */
 204 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 205         unsigned nparam)
 206 {
 207         int i;
 208
 209         if (nparam == 0)
 210                 return mat;
 211         if (!mat)
 212                 return NULL;
 213
 214         mat = isl_mat_insert_rows(mat, 1, nparam);
 215         if (!mat)
 216                 return NULL;
 217
 218         for (i = 0; i < nparam; ++i) {
 219                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 220                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 221         }
 222
 223         return mat;
 224 }
 225
 226 /* Construct a basic set described by the "n" equalities of "bset" starting
 227  * at "first".
 228  */
 229 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 230         unsigned first, unsigned n)
 231 {
 232         int i, k;
 233         isl_basic_set *eq;
 234         unsigned total;
 235
 236         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 237
 238         total = isl_basic_set_total_dim(bset);
 239         eq = isl_basic_set_alloc_dim(isl_dim_copy(bset->dim), 0, n, 0);
 240         if (!eq)
 241                 return NULL;
 242         for (i = 0; i < n; ++i) {
 243                 k = isl_basic_set_alloc_equality(eq);
 244                 if (k < 0)
 245                         goto error;
 246                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 247         }
 248
 249         return eq;
 250 error:
 251         isl_basic_set_free(eq);
 252         return NULL;
 253 }
 254
 255 /* Given a basic set, exploit the equalties in the a basic set to construct
 256  * a morphishm that maps the basic set to a lower-dimensional space.
 257  * Specifically, the morphism reduces the number of dimensions of type "type".
 258  *
 259  * This function is a slight generalization of isl_mat_variable_compression
 260  * in that it allows the input to be parametric and that it allows for the
 261  * compression of either parameters or set variables.
 262  *
 263  * We first select the equalities of interest, that is those that involve
 264  * variables of type "type" and no later variables.
 265  * Denote those equalities as
 266  *
 267  *              -C(p) + M x = 0
 268  *
 269  * where C(p) depends on the parameters if type == isl_dim_set and
 270  * is a constant if type == isl_dim_param.
 271  *
 272  * First compute the (left) Hermite normal form of M,
 273  *
 274  *              M [U1 U2] = M U = H = [H1 0]
 275  * or
 276  *                            M = H Q = [H1 0] [Q1]
 277  *                                             [Q2]
 278  *
 279  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 280  * Define the transformed variables as
 281  *
 282  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 283  *                          [ x2' ]           [Q2]
 284  *
 285  * The equalities then become
 286  *
 287  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 288  *
 289  * If the denominator of the constant term does not divide the
 290  * the common denominator of the parametric terms, then every
 291  * integer point is mapped to a non-integer point and then the original set has no
 292  * integer solutions (since the x' are a unimodular transformation
 293  * of the x).  In this case, an empty morphism is returned.
 294  * Otherwise, the transformation is given by
 295  *
 296  *              x = U1 H1^{-1} C(p) + U2 x2'
 297  *
 298  * The inverse transformation is simply
 299  *
 300  *              x2' = Q2 x
 301  *
 302  * Both matrices are extended to map the full original space to the full
 303  * compressed space.
 304  */
 305 __isl_give isl_morph *isl_basic_set_variable_compression(
 306         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 307 {
 308         unsigned otype;
 309         unsigned ntype;
 310         unsigned orest;
 311         unsigned nrest;
 312         unsigned total;
 313         int f_eq, n_eq;
 314         isl_dim *dim;
 315         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 316         isl_basic_set *dom, *ran;
 317
 318         if (!bset)
 319                 return NULL;
 320
 321         if (isl_basic_set_fast_is_empty(bset))
 322                 return isl_morph_empty(bset);
 323
 324         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 325
 326         otype = 1 + isl_dim_offset(bset->dim, type);
 327         ntype = isl_basic_set_dim(bset, type);
 328         orest = otype + ntype;
 329         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 330
 331         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 332                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 333                         break;
 334         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 335                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 336                         break;
 337         if (n_eq == 0)
 338                 return isl_morph_identity(bset);
 339
 340         H = isl_mat_sub_alloc(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 341         H = isl_mat_left_hermite(H, 0, &U, &Q);
 342         if (!H || !U || !Q)
 343                 goto error;
 344         Q = isl_mat_drop_rows(Q, 0, n_eq);
 345         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 346         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 347         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 348         if (!C)
 349                 goto error;
 350         isl_int_set_si(C->row[0][0], 1);
 351         isl_seq_clr(C->row[0] + 1, otype - 1);
 352         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 353         H1 = isl_mat_sub_alloc(H->ctx, H->row, 0, H->n_row, 0, H->n_row);
 354         H1 = isl_mat_lin_to_aff(H1);
 355         C = isl_mat_inverse_product(H1, C);
 356         if (!C)
 357                 goto error;
 358         isl_mat_free(H);
 359
 360         if (!isl_int_is_one(C->row[0][0])) {
 361                 int i;
 362                 isl_int g;
 363
 364                 isl_int_init(g);
 365                 for (i = 0; i < n_eq; ++i) {
 366                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 367                         isl_int_gcd(g, g, C->row[0][0]);
 368                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 369                                 break;
 370                 }
 371                 isl_int_clear(g);
 372
 373                 if (i < n_eq) {
 374                         isl_mat_free(C);
 375                         isl_mat_free(U);
 376                         isl_mat_free(Q);
 377                         return isl_morph_empty(bset);
 378                 }
 379
 380                 C = isl_mat_normalize(C);
 381         }
 382
 383         U1 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, 0, n_eq);
 384         U1 = isl_mat_lin_to_aff(U1);
 385         U2 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, n_eq, U->n_row - n_eq);
 386         U2 = isl_mat_lin_to_aff(U2);
 387         isl_mat_free(U);
 388
 389         C = isl_mat_product(U1, C);
 390         C = isl_mat_aff_direct_sum(C, U2);
 391         C = insert_parameter_rows(C, otype - 1);
 392         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 393
 394         dim = isl_dim_copy(bset->dim);
 395         dim = isl_dim_drop(dim, type, 0, ntype);
 396         dim = isl_dim_add(dim, type, ntype - n_eq);
 397         ran = isl_basic_set_universe(dim);
 398         dom = copy_equalities(bset, f_eq, n_eq);
 399
 400         return isl_morph_alloc(dom, ran, Q, C);
 401 error:
 402         isl_mat_free(C);
 403         isl_mat_free(H);
 404         isl_mat_free(U);
 405         isl_mat_free(Q);
 406         return NULL;
 407 }
 408
 409 /* Construct a parameter compression for "bset".
 410  * We basically just call isl_mat_parameter_compression with the right input
 411  * and then extend the resulting matrix to include the variables.
 412  *
 413  * Let the equalities be given as
 414  *
 415  *      B(p) + A x = 0
 416  *
 417  * and let [H 0] be the Hermite Normal Form of A, then
 418  *
 419  *      H^-1 B(p)
 420  *
 421  * needs to be integer, so we impose that each row is divisible by
 422  * the denominator.
 423  */
 424 __isl_give isl_morph *isl_basic_set_parameter_compression(
 425         __isl_keep isl_basic_set *bset)
 426 {
 427         unsigned nparam;
 428         unsigned nvar;
 429         int n_eq;
 430         isl_mat *H, *B;
 431         isl_vec *d;
 432         isl_mat *map, *inv;
 433         isl_basic_set *dom, *ran;
 434
 435         if (!bset)
 436                 return NULL;
 437
 438         if (isl_basic_set_fast_is_empty(bset))
 439                 return isl_morph_empty(bset);
 440         if (bset->n_eq == 0)
 441                 return isl_morph_identity(bset);
 442
 443         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 444
 445         n_eq = bset->n_eq;
 446         nparam = isl_basic_set_dim(bset, isl_dim_param);
 447         nvar = isl_basic_set_dim(bset, isl_dim_set);
 448
 449         isl_assert(bset->ctx, n_eq <= nvar, return NULL);
 450
 451         d = isl_vec_alloc(bset->ctx, n_eq);
 452         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 453         H = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
 454         H = isl_mat_left_hermite(H, 0, NULL, NULL);
 455         H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
 456         H = isl_mat_lin_to_aff(H);
 457         H = isl_mat_right_inverse(H);
 458         if (!H || !d)
 459                 goto error;
 460         isl_seq_set(d->el, H->row[0][0], d->size);
 461         H = isl_mat_drop_rows(H, 0, 1);
 462         H = isl_mat_drop_cols(H, 0, 1);
 463         B = isl_mat_product(H, B);
 464         inv = isl_mat_parameter_compression(B, d);
 465         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 466         map = isl_mat_right_inverse(isl_mat_copy(inv));
 467
 468         dom = isl_basic_set_universe(isl_dim_copy(bset->dim));
 469         ran = isl_basic_set_universe(isl_dim_copy(bset->dim));
 470
 471         return isl_morph_alloc(dom, ran, map, inv);
 472 error:
 473         isl_mat_free(H);
 474         isl_mat_free(B);
 475         isl_vec_free(d);
 476         return NULL;
 477 }
 478
 479 /* Add stride constraints to "bset" based on the inverse mapping
 480  * that was plugged in.  In particular, if morph maps x' to x,
 481  * the the constraints of the original input
 482  *
 483  *      A x' + b >= 0
 484  *
 485  * have been rewritten to
 486  *
 487  *      A inv x + b >= 0
 488  *
 489  * However, this substitution may loose information on the integrality of x',
 490  * so we need to impose that
 491  *
 492  *      inv x
 493  *
 494  * is integral.  If inv = B/d, this means that we need to impose that
 495  *
 496  *      B x = 0         mod d
 497  *
 498  * or
 499  *
 500  *      exists alpha in Z^m: B x = d alpha
 501  *
 502  */
 503 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 504         __isl_keep isl_morph *morph)
 505 {
 506         int i, div, k;
 507         isl_int gcd;
 508
 509         if (isl_int_is_one(morph->inv->row[0][0]))
 510                 return bset;
 511
 512         isl_int_init(gcd);
 513
 514         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 515                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 516                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 517                         continue;
 518                 div = isl_basic_set_alloc_div(bset);
 519                 if (div < 0)
 520                         goto error;
 521                 k = isl_basic_set_alloc_equality(bset);
 522                 if (k < 0)
 523                         goto error;
 524                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 525                             morph->inv->n_col);
 526                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 527                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 528                             morph->inv->row[0][0]);
 529         }
 530
 531         isl_int_clear(gcd);
 532
 533         return bset;
 534 error:
 535         isl_int_clear(gcd);
 536         isl_basic_set_free(bset);
 537         return NULL;
 538 }
 539
 540 /* Apply the morphism to the basic set.
 541  * We basically just compute the preimage of "bset" under the inverse mapping
 542  * in morph, add in stride constraints and intersect with the range
 543  * of the morphism.
 544  */
 545 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 546         __isl_take isl_basic_set *bset)
 547 {
 548         isl_basic_set *res = NULL;
 549         isl_mat *mat = NULL;
 550         int i, k;
 551         int max_stride;
 552
 553         if (!morph || !bset)
 554                 goto error;
 555
 556         isl_assert(bset->ctx, isl_dim_equal(bset->dim, morph->dom->dim),
 557                     goto error);
 558
 559         max_stride = morph->inv->n_row - 1;
 560         if (isl_int_is_one(morph->inv->row[0][0]))
 561                 max_stride = 0;
 562         res = isl_basic_set_alloc_dim(isl_dim_copy(morph->ran->dim),
 563                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 564
 565         for (i = 0; i < bset->n_div; ++i)
 566                 if (isl_basic_set_alloc_div(res) < 0)
 567                         goto error;
 568
 569         mat = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq,
 570                                         0, morph->inv->n_row);
 571         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 572         if (!mat)
 573                 goto error;
 574         for (i = 0; i < bset->n_eq; ++i) {
 575                 k = isl_basic_set_alloc_equality(res);
 576                 if (k < 0)
 577                         goto error;
 578                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 579                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 580                                 morph->inv->row[0][0], bset->n_div);
 581         }
 582         isl_mat_free(mat);
 583
 584         mat = isl_mat_sub_alloc(bset->ctx, bset->ineq, 0, bset->n_ineq,
 585                                         0, morph->inv->n_row);
 586         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 587         if (!mat)
 588                 goto error;
 589         for (i = 0; i < bset->n_ineq; ++i) {
 590                 k = isl_basic_set_alloc_inequality(res);
 591                 if (k < 0)
 592                         goto error;
 593                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 594                 isl_seq_scale(res->ineq[k] + mat->n_col,
 595                                 bset->ineq[i] + mat->n_col,
 596                                 morph->inv->row[0][0], bset->n_div);
 597         }
 598         isl_mat_free(mat);
 599
 600         mat = isl_mat_sub_alloc(bset->ctx, bset->div, 0, bset->n_div,
 601                                         1, morph->inv->n_row);
 602         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 603         if (!mat)
 604                 goto error;
 605         for (i = 0; i < bset->n_div; ++i) {
 606                 isl_int_mul(res->div[i][0],
 607                                 morph->inv->row[0][0], bset->div[i][0]);
 608                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 609                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 610                                 bset->div[i] + 1 + mat->n_col,
 611                                 morph->inv->row[0][0], bset->n_div);
 612         }
 613         isl_mat_free(mat);
 614
 615         res = add_strides(res, morph);
 616
 617         res = isl_basic_set_simplify(res);
 618         res = isl_basic_set_finalize(res);
 619
 620         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 621
 622         isl_morph_free(morph);
 623         isl_basic_set_free(bset);
 624         return res;
 625 error:
 626         isl_mat_free(mat);
 627         isl_morph_free(morph);
 628         isl_basic_set_free(bset);
 629         isl_basic_set_free(res);
 630         return NULL;
 631 }
 632
 633 /* Apply the morphism to the set.
 634  */
 635 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 636         __isl_take isl_set *set)
 637 {
 638         int i;
 639
 640         if (!morph || !set)
 641                 goto error;
 642
 643         isl_assert(set->ctx, isl_dim_equal(set->dim, morph->dom->dim), goto error);
 644
 645         set = isl_set_cow(set);
 646         if (!set)
 647                 goto error;
 648
 649         isl_dim_free(set->dim);
 650         set->dim = isl_dim_copy(morph->ran->dim);
 651         if (!set->dim)
 652                 goto error;
 653
 654         for (i = 0; i < set->n; ++i) {
 655                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 656                 if (!set->p[i])
 657                         goto error;
 658         }
 659
 660         isl_morph_free(morph);
 661
 662         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 663
 664         return set;
 665 error:
 666         isl_set_free(set);
 667         isl_morph_free(morph);
 668         return NULL;
 669 }
 670
 671 /* Construct a morphism that first does morph2 and then morph1.
 672  */
 673 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 674         __isl_take isl_morph *morph2)
 675 {
 676         isl_mat *map, *inv;
 677         isl_basic_set *dom, *ran;
 678
 679         if (!morph1 || !morph2)
 680                 goto error;
 681
 682         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 683         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 684         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 685                                   isl_basic_set_copy(morph1->dom));
 686         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 687         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 688                                   isl_basic_set_copy(morph2->ran));
 689         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 690
 691         isl_morph_free(morph1);
 692         isl_morph_free(morph2);
 693
 694         return isl_morph_alloc(dom, ran, map, inv);
 695 error:
 696         isl_morph_free(morph1);
 697         isl_morph_free(morph2);
 698         return NULL;
 699 }
 700
 701 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 702 {
 703         isl_basic_set *bset;
 704         isl_mat *mat;
 705
 706         morph = isl_morph_cow(morph);
 707         if (!morph)
 708                 return NULL;
 709
 710         bset = morph->dom;
 711         morph->dom = morph->ran;
 712         morph->ran = bset;
 713
 714         mat = morph->map;
 715         morph->map = morph->inv;
 716         morph->inv = mat;
 717
 718         return morph;
 719 }
 720
 721 __isl_give isl_morph *isl_basic_set_full_compression(
 722         __isl_keep isl_basic_set *bset)
 723 {
 724         isl_morph *morph, *morph2;
 725
 726         bset = isl_basic_set_copy(bset);
 727
 728         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 729         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 730
 731         morph2 = isl_basic_set_parameter_compression(bset);
 732         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 733
 734         morph = isl_morph_compose(morph2, morph);
 735
 736         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 737         isl_basic_set_free(bset);
 738
 739         morph = isl_morph_compose(morph2, morph);
 740
 741         return morph;
 742 }