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_mat_private.h>
  15 #include <isl_dim_private.h>
  16 #include <isl_equalities.h>
  17
  18 __isl_give isl_morph *isl_morph_alloc(
  19         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  20         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  21 {
  22         isl_morph *morph;
  23
  24         if (!dom || !ran || !map || !inv)
  25                 goto error;
  26
  27         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  28         if (!morph)
  29                 goto error;
  30
  31         morph->ref = 1;
  32         morph->dom = dom;
  33         morph->ran = ran;
  34         morph->map = map;
  35         morph->inv = inv;
  36
  37         return morph;
  38 error:
  39         isl_basic_set_free(dom);
  40         isl_basic_set_free(ran);
  41         isl_mat_free(map);
  42         isl_mat_free(inv);
  43         return NULL;
  44 }
  45
  46 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  47 {
  48         if (!morph)
  49                 return NULL;
  50
  51         morph->ref++;
  52         return morph;
  53 }
  54
  55 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  56 {
  57         if (!morph)
  58                 return NULL;
  59
  60         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  61                 isl_basic_set_copy(morph->ran),
  62                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  63 }
  64
  65 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  66 {
  67         if (!morph)
  68                 return NULL;
  69
  70         if (morph->ref == 1)
  71                 return morph;
  72         morph->ref--;
  73         return isl_morph_dup(morph);
  74 }
  75
  76 void isl_morph_free(__isl_take isl_morph *morph)
  77 {
  78         if (!morph)
  79                 return;
  80
  81         if (--morph->ref > 0)
  82                 return;
  83
  84         isl_basic_set_free(morph->dom);
  85         isl_basic_set_free(morph->ran);
  86         isl_mat_free(morph->map);
  87         isl_mat_free(morph->inv);
  88         free(morph);
  89 }
  90
  91 __isl_give isl_dim *isl_morph_get_ran_dim(__isl_keep isl_morph *morph)
  92 {
  93         if (!morph)
  94                 return NULL;
  95
  96         return isl_dim_copy(morph->ran->dim);
  97 }
  98
  99 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 100 {
 101         if (!morph)
 102                 return 0;
 103
 104         return isl_basic_set_dim(morph->dom, type);
 105 }
 106
 107 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 108 {
 109         if (!morph)
 110                 return 0;
 111
 112         return isl_basic_set_dim(morph->ran, type);
 113 }
 114
 115 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 116         enum isl_dim_type type, unsigned first, unsigned n)
 117 {
 118         unsigned dom_offset;
 119
 120         if (n == 0)
 121                 return morph;
 122
 123         morph = isl_morph_cow(morph);
 124         if (!morph)
 125                 return NULL;
 126
 127         dom_offset = 1 + isl_dim_offset(morph->dom->dim, type);
 128
 129         morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
 130
 131         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 132
 133         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 134
 135         if (morph->dom && morph->ran && morph->map && morph->inv)
 136                 return morph;
 137
 138         isl_morph_free(morph);
 139         return NULL;
 140 }
 141
 142 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 143         enum isl_dim_type type, unsigned first, unsigned n)
 144 {
 145         unsigned ran_offset;
 146
 147         if (n == 0)
 148                 return morph;
 149
 150         morph = isl_morph_cow(morph);
 151         if (!morph)
 152                 return NULL;
 153
 154         ran_offset = 1 + isl_dim_offset(morph->ran->dim, type);
 155
 156         morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
 157
 158         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 159
 160         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 161
 162         if (morph->dom && morph->ran && morph->map && morph->inv)
 163                 return morph;
 164
 165         isl_morph_free(morph);
 166         return NULL;
 167 }
 168
 169 void isl_morph_dump(__isl_take isl_morph *morph, FILE *out)
 170 {
 171         if (!morph)
 172                 return;
 173
 174         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 175         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 176         isl_mat_dump(morph->map, out, 4);
 177         isl_mat_dump(morph->inv, out, 4);
 178 }
 179
 180 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 181 {
 182         isl_mat *id;
 183         isl_basic_set *universe;
 184         unsigned total;
 185
 186         if (!bset)
 187                 return NULL;
 188
 189         total = isl_basic_set_total_dim(bset);
 190         id = isl_mat_identity(bset->ctx, 1 + total);
 191         universe = isl_basic_set_universe(isl_dim_copy(bset->dim));
 192
 193         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 194                 id, isl_mat_copy(id));
 195 }
 196
 197 /* Create a(n identity) morphism between empty sets of the same dimension
 198  * a "bset".
 199  */
 200 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 201 {
 202         isl_mat *id;
 203         isl_basic_set *empty;
 204         unsigned total;
 205
 206         if (!bset)
 207                 return NULL;
 208
 209         total = isl_basic_set_total_dim(bset);
 210         id = isl_mat_identity(bset->ctx, 1 + total);
 211         empty = isl_basic_set_empty(isl_dim_copy(bset->dim));
 212
 213         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 214                 id, isl_mat_copy(id));
 215 }
 216
 217 /* Given a matrix that maps a (possibly) parametric domain to
 218  * a parametric domain, add in rows that map the "nparam" parameters onto
 219  * themselves.
 220  */
 221 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 222         unsigned nparam)
 223 {
 224         int i;
 225
 226         if (nparam == 0)
 227                 return mat;
 228         if (!mat)
 229                 return NULL;
 230
 231         mat = isl_mat_insert_rows(mat, 1, nparam);
 232         if (!mat)
 233                 return NULL;
 234
 235         for (i = 0; i < nparam; ++i) {
 236                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 237                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 238         }
 239
 240         return mat;
 241 }
 242
 243 /* Construct a basic set described by the "n" equalities of "bset" starting
 244  * at "first".
 245  */
 246 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 247         unsigned first, unsigned n)
 248 {
 249         int i, k;
 250         isl_basic_set *eq;
 251         unsigned total;
 252
 253         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 254
 255         total = isl_basic_set_total_dim(bset);
 256         eq = isl_basic_set_alloc_dim(isl_dim_copy(bset->dim), 0, n, 0);
 257         if (!eq)
 258                 return NULL;
 259         for (i = 0; i < n; ++i) {
 260                 k = isl_basic_set_alloc_equality(eq);
 261                 if (k < 0)
 262                         goto error;
 263                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 264         }
 265
 266         return eq;
 267 error:
 268         isl_basic_set_free(eq);
 269         return NULL;
 270 }
 271
 272 /* Given a basic set, exploit the equalties in the a basic set to construct
 273  * a morphishm that maps the basic set to a lower-dimensional space.
 274  * Specifically, the morphism reduces the number of dimensions of type "type".
 275  *
 276  * This function is a slight generalization of isl_mat_variable_compression
 277  * in that it allows the input to be parametric and that it allows for the
 278  * compression of either parameters or set variables.
 279  *
 280  * We first select the equalities of interest, that is those that involve
 281  * variables of type "type" and no later variables.
 282  * Denote those equalities as
 283  *
 284  *              -C(p) + M x = 0
 285  *
 286  * where C(p) depends on the parameters if type == isl_dim_set and
 287  * is a constant if type == isl_dim_param.
 288  *
 289  * First compute the (left) Hermite normal form of M,
 290  *
 291  *              M [U1 U2] = M U = H = [H1 0]
 292  * or
 293  *                            M = H Q = [H1 0] [Q1]
 294  *                                             [Q2]
 295  *
 296  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 297  * Define the transformed variables as
 298  *
 299  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 300  *                          [ x2' ]           [Q2]
 301  *
 302  * The equalities then become
 303  *
 304  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 305  *
 306  * If the denominator of the constant term does not divide the
 307  * the common denominator of the parametric terms, then every
 308  * integer point is mapped to a non-integer point and then the original set has no
 309  * integer solutions (since the x' are a unimodular transformation
 310  * of the x).  In this case, an empty morphism is returned.
 311  * Otherwise, the transformation is given by
 312  *
 313  *              x = U1 H1^{-1} C(p) + U2 x2'
 314  *
 315  * The inverse transformation is simply
 316  *
 317  *              x2' = Q2 x
 318  *
 319  * Both matrices are extended to map the full original space to the full
 320  * compressed space.
 321  */
 322 __isl_give isl_morph *isl_basic_set_variable_compression(
 323         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 324 {
 325         unsigned otype;
 326         unsigned ntype;
 327         unsigned orest;
 328         unsigned nrest;
 329         unsigned total;
 330         int f_eq, n_eq;
 331         isl_dim *dim;
 332         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 333         isl_basic_set *dom, *ran;
 334
 335         if (!bset)
 336                 return NULL;
 337
 338         if (isl_basic_set_fast_is_empty(bset))
 339                 return isl_morph_empty(bset);
 340
 341         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 342
 343         otype = 1 + isl_dim_offset(bset->dim, type);
 344         ntype = isl_basic_set_dim(bset, type);
 345         orest = otype + ntype;
 346         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 347
 348         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 349                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 350                         break;
 351         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 352                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 353                         break;
 354         if (n_eq == 0)
 355                 return isl_morph_identity(bset);
 356
 357         H = isl_mat_sub_alloc(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 358         H = isl_mat_left_hermite(H, 0, &U, &Q);
 359         if (!H || !U || !Q)
 360                 goto error;
 361         Q = isl_mat_drop_rows(Q, 0, n_eq);
 362         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 363         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 364         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 365         if (!C)
 366                 goto error;
 367         isl_int_set_si(C->row[0][0], 1);
 368         isl_seq_clr(C->row[0] + 1, otype - 1);
 369         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 370         H1 = isl_mat_sub_alloc(H->ctx, H->row, 0, H->n_row, 0, H->n_row);
 371         H1 = isl_mat_lin_to_aff(H1);
 372         C = isl_mat_inverse_product(H1, C);
 373         if (!C)
 374                 goto error;
 375         isl_mat_free(H);
 376
 377         if (!isl_int_is_one(C->row[0][0])) {
 378                 int i;
 379                 isl_int g;
 380
 381                 isl_int_init(g);
 382                 for (i = 0; i < n_eq; ++i) {
 383                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 384                         isl_int_gcd(g, g, C->row[0][0]);
 385                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 386                                 break;
 387                 }
 388                 isl_int_clear(g);
 389
 390                 if (i < n_eq) {
 391                         isl_mat_free(C);
 392                         isl_mat_free(U);
 393                         isl_mat_free(Q);
 394                         return isl_morph_empty(bset);
 395                 }
 396
 397                 C = isl_mat_normalize(C);
 398         }
 399
 400         U1 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, 0, n_eq);
 401         U1 = isl_mat_lin_to_aff(U1);
 402         U2 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, n_eq, U->n_row - n_eq);
 403         U2 = isl_mat_lin_to_aff(U2);
 404         isl_mat_free(U);
 405
 406         C = isl_mat_product(U1, C);
 407         C = isl_mat_aff_direct_sum(C, U2);
 408         C = insert_parameter_rows(C, otype - 1);
 409         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 410
 411         dim = isl_dim_copy(bset->dim);
 412         dim = isl_dim_drop(dim, type, 0, ntype);
 413         dim = isl_dim_add(dim, type, ntype - n_eq);
 414         ran = isl_basic_set_universe(dim);
 415         dom = copy_equalities(bset, f_eq, n_eq);
 416
 417         return isl_morph_alloc(dom, ran, Q, C);
 418 error:
 419         isl_mat_free(C);
 420         isl_mat_free(H);
 421         isl_mat_free(U);
 422         isl_mat_free(Q);
 423         return NULL;
 424 }
 425
 426 /* Construct a parameter compression for "bset".
 427  * We basically just call isl_mat_parameter_compression with the right input
 428  * and then extend the resulting matrix to include the variables.
 429  *
 430  * Let the equalities be given as
 431  *
 432  *      B(p) + A x = 0
 433  *
 434  * and let [H 0] be the Hermite Normal Form of A, then
 435  *
 436  *      H^-1 B(p)
 437  *
 438  * needs to be integer, so we impose that each row is divisible by
 439  * the denominator.
 440  */
 441 __isl_give isl_morph *isl_basic_set_parameter_compression(
 442         __isl_keep isl_basic_set *bset)
 443 {
 444         unsigned nparam;
 445         unsigned nvar;
 446         int n_eq;
 447         isl_mat *H, *B;
 448         isl_vec *d;
 449         isl_mat *map, *inv;
 450         isl_basic_set *dom, *ran;
 451
 452         if (!bset)
 453                 return NULL;
 454
 455         if (isl_basic_set_fast_is_empty(bset))
 456                 return isl_morph_empty(bset);
 457         if (bset->n_eq == 0)
 458                 return isl_morph_identity(bset);
 459
 460         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 461
 462         n_eq = bset->n_eq;
 463         nparam = isl_basic_set_dim(bset, isl_dim_param);
 464         nvar = isl_basic_set_dim(bset, isl_dim_set);
 465
 466         isl_assert(bset->ctx, n_eq <= nvar, return NULL);
 467
 468         d = isl_vec_alloc(bset->ctx, n_eq);
 469         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 470         H = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
 471         H = isl_mat_left_hermite(H, 0, NULL, NULL);
 472         H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
 473         H = isl_mat_lin_to_aff(H);
 474         H = isl_mat_right_inverse(H);
 475         if (!H || !d)
 476                 goto error;
 477         isl_seq_set(d->el, H->row[0][0], d->size);
 478         H = isl_mat_drop_rows(H, 0, 1);
 479         H = isl_mat_drop_cols(H, 0, 1);
 480         B = isl_mat_product(H, B);
 481         inv = isl_mat_parameter_compression(B, d);
 482         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 483         map = isl_mat_right_inverse(isl_mat_copy(inv));
 484
 485         dom = isl_basic_set_universe(isl_dim_copy(bset->dim));
 486         ran = isl_basic_set_universe(isl_dim_copy(bset->dim));
 487
 488         return isl_morph_alloc(dom, ran, map, inv);
 489 error:
 490         isl_mat_free(H);
 491         isl_mat_free(B);
 492         isl_vec_free(d);
 493         return NULL;
 494 }
 495
 496 /* Add stride constraints to "bset" based on the inverse mapping
 497  * that was plugged in.  In particular, if morph maps x' to x,
 498  * the the constraints of the original input
 499  *
 500  *      A x' + b >= 0
 501  *
 502  * have been rewritten to
 503  *
 504  *      A inv x + b >= 0
 505  *
 506  * However, this substitution may loose information on the integrality of x',
 507  * so we need to impose that
 508  *
 509  *      inv x
 510  *
 511  * is integral.  If inv = B/d, this means that we need to impose that
 512  *
 513  *      B x = 0         mod d
 514  *
 515  * or
 516  *
 517  *      exists alpha in Z^m: B x = d alpha
 518  *
 519  */
 520 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 521         __isl_keep isl_morph *morph)
 522 {
 523         int i, div, k;
 524         isl_int gcd;
 525
 526         if (isl_int_is_one(morph->inv->row[0][0]))
 527                 return bset;
 528
 529         isl_int_init(gcd);
 530
 531         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 532                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 533                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 534                         continue;
 535                 div = isl_basic_set_alloc_div(bset);
 536                 if (div < 0)
 537                         goto error;
 538                 k = isl_basic_set_alloc_equality(bset);
 539                 if (k < 0)
 540                         goto error;
 541                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 542                             morph->inv->n_col);
 543                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 544                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 545                             morph->inv->row[0][0]);
 546         }
 547
 548         isl_int_clear(gcd);
 549
 550         return bset;
 551 error:
 552         isl_int_clear(gcd);
 553         isl_basic_set_free(bset);
 554         return NULL;
 555 }
 556
 557 /* Apply the morphism to the basic set.
 558  * We basically just compute the preimage of "bset" under the inverse mapping
 559  * in morph, add in stride constraints and intersect with the range
 560  * of the morphism.
 561  */
 562 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 563         __isl_take isl_basic_set *bset)
 564 {
 565         isl_basic_set *res = NULL;
 566         isl_mat *mat = NULL;
 567         int i, k;
 568         int max_stride;
 569
 570         if (!morph || !bset)
 571                 goto error;
 572
 573         isl_assert(bset->ctx, isl_dim_equal(bset->dim, morph->dom->dim),
 574                     goto error);
 575
 576         max_stride = morph->inv->n_row - 1;
 577         if (isl_int_is_one(morph->inv->row[0][0]))
 578                 max_stride = 0;
 579         res = isl_basic_set_alloc_dim(isl_dim_copy(morph->ran->dim),
 580                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 581
 582         for (i = 0; i < bset->n_div; ++i)
 583                 if (isl_basic_set_alloc_div(res) < 0)
 584                         goto error;
 585
 586         mat = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq,
 587                                         0, morph->inv->n_row);
 588         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 589         if (!mat)
 590                 goto error;
 591         for (i = 0; i < bset->n_eq; ++i) {
 592                 k = isl_basic_set_alloc_equality(res);
 593                 if (k < 0)
 594                         goto error;
 595                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 596                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 597                                 morph->inv->row[0][0], bset->n_div);
 598         }
 599         isl_mat_free(mat);
 600
 601         mat = isl_mat_sub_alloc(bset->ctx, bset->ineq, 0, bset->n_ineq,
 602                                         0, morph->inv->n_row);
 603         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 604         if (!mat)
 605                 goto error;
 606         for (i = 0; i < bset->n_ineq; ++i) {
 607                 k = isl_basic_set_alloc_inequality(res);
 608                 if (k < 0)
 609                         goto error;
 610                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 611                 isl_seq_scale(res->ineq[k] + mat->n_col,
 612                                 bset->ineq[i] + mat->n_col,
 613                                 morph->inv->row[0][0], bset->n_div);
 614         }
 615         isl_mat_free(mat);
 616
 617         mat = isl_mat_sub_alloc(bset->ctx, bset->div, 0, bset->n_div,
 618                                         1, morph->inv->n_row);
 619         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 620         if (!mat)
 621                 goto error;
 622         for (i = 0; i < bset->n_div; ++i) {
 623                 isl_int_mul(res->div[i][0],
 624                                 morph->inv->row[0][0], bset->div[i][0]);
 625                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 626                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 627                                 bset->div[i] + 1 + mat->n_col,
 628                                 morph->inv->row[0][0], bset->n_div);
 629         }
 630         isl_mat_free(mat);
 631
 632         res = add_strides(res, morph);
 633
 634         res = isl_basic_set_simplify(res);
 635         res = isl_basic_set_finalize(res);
 636
 637         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 638
 639         isl_morph_free(morph);
 640         isl_basic_set_free(bset);
 641         return res;
 642 error:
 643         isl_mat_free(mat);
 644         isl_morph_free(morph);
 645         isl_basic_set_free(bset);
 646         isl_basic_set_free(res);
 647         return NULL;
 648 }
 649
 650 /* Apply the morphism to the set.
 651  */
 652 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 653         __isl_take isl_set *set)
 654 {
 655         int i;
 656
 657         if (!morph || !set)
 658                 goto error;
 659
 660         isl_assert(set->ctx, isl_dim_equal(set->dim, morph->dom->dim), goto error);
 661
 662         set = isl_set_cow(set);
 663         if (!set)
 664                 goto error;
 665
 666         isl_dim_free(set->dim);
 667         set->dim = isl_dim_copy(morph->ran->dim);
 668         if (!set->dim)
 669                 goto error;
 670
 671         for (i = 0; i < set->n; ++i) {
 672                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 673                 if (!set->p[i])
 674                         goto error;
 675         }
 676
 677         isl_morph_free(morph);
 678
 679         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 680
 681         return set;
 682 error:
 683         isl_set_free(set);
 684         isl_morph_free(morph);
 685         return NULL;
 686 }
 687
 688 /* Construct a morphism that first does morph2 and then morph1.
 689  */
 690 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 691         __isl_take isl_morph *morph2)
 692 {
 693         isl_mat *map, *inv;
 694         isl_basic_set *dom, *ran;
 695
 696         if (!morph1 || !morph2)
 697                 goto error;
 698
 699         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 700         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 701         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 702                                   isl_basic_set_copy(morph1->dom));
 703         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 704         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 705                                   isl_basic_set_copy(morph2->ran));
 706         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 707
 708         isl_morph_free(morph1);
 709         isl_morph_free(morph2);
 710
 711         return isl_morph_alloc(dom, ran, map, inv);
 712 error:
 713         isl_morph_free(morph1);
 714         isl_morph_free(morph2);
 715         return NULL;
 716 }
 717
 718 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 719 {
 720         isl_basic_set *bset;
 721         isl_mat *mat;
 722
 723         morph = isl_morph_cow(morph);
 724         if (!morph)
 725                 return NULL;
 726
 727         bset = morph->dom;
 728         morph->dom = morph->ran;
 729         morph->ran = bset;
 730
 731         mat = morph->map;
 732         morph->map = morph->inv;
 733         morph->inv = mat;
 734
 735         return morph;
 736 }
 737
 738 __isl_give isl_morph *isl_basic_set_full_compression(
 739         __isl_keep isl_basic_set *bset)
 740 {
 741         isl_morph *morph, *morph2;
 742
 743         bset = isl_basic_set_copy(bset);
 744
 745         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 746         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 747
 748         morph2 = isl_basic_set_parameter_compression(bset);
 749         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 750
 751         morph = isl_morph_compose(morph2, morph);
 752
 753         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 754         isl_basic_set_free(bset);
 755
 756         morph = isl_morph_compose(morph2, morph);
 757
 758         return morph;
 759 }