isl_morph.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the MIT 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_map_private.h>
  12 #include <isl_morph.h>
  13 #include <isl/seq.h>
  14 #include <isl_mat_private.h>
  15 #include <isl_space_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_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
  92 {
  93         if (!morph)
  94                 return NULL;
  95
  96         return isl_space_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_space_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_space_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 /* Project domain of morph onto its parameter domain.
 170  */
 171 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
 172 {
 173         unsigned n;
 174
 175         morph = isl_morph_cow(morph);
 176         if (!morph)
 177                 return NULL;
 178         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 179         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 180         if (!morph)
 181                 return NULL;
 182         morph->dom = isl_basic_set_params(morph->dom);
 183         if (morph->dom)
 184                 return morph;
 185
 186         isl_morph_free(morph);
 187         return NULL;
 188 }
 189
 190 /* Project range of morph onto its parameter domain.
 191  */
 192 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 193 {
 194         unsigned n;
 195
 196         morph = isl_morph_cow(morph);
 197         if (!morph)
 198                 return NULL;
 199         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 200         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 201         if (!morph)
 202                 return NULL;
 203         morph->ran = isl_basic_set_params(morph->ran);
 204         if (morph->ran)
 205                 return morph;
 206
 207         isl_morph_free(morph);
 208         return NULL;
 209 }
 210
 211 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 212 {
 213         if (!morph)
 214                 return;
 215
 216         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 217         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 218         isl_mat_print_internal(morph->map, out, 4);
 219         isl_mat_print_internal(morph->inv, out, 4);
 220 }
 221
 222 void isl_morph_dump(__isl_take isl_morph *morph)
 223 {
 224         isl_morph_print_internal(morph, stderr);
 225 }
 226
 227 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 228 {
 229         isl_mat *id;
 230         isl_basic_set *universe;
 231         unsigned total;
 232
 233         if (!bset)
 234                 return NULL;
 235
 236         total = isl_basic_set_total_dim(bset);
 237         id = isl_mat_identity(bset->ctx, 1 + total);
 238         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 239
 240         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 241                 id, isl_mat_copy(id));
 242 }
 243
 244 /* Create a(n identity) morphism between empty sets of the same dimension
 245  * a "bset".
 246  */
 247 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 248 {
 249         isl_mat *id;
 250         isl_basic_set *empty;
 251         unsigned total;
 252
 253         if (!bset)
 254                 return NULL;
 255
 256         total = isl_basic_set_total_dim(bset);
 257         id = isl_mat_identity(bset->ctx, 1 + total);
 258         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 259
 260         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 261                 id, isl_mat_copy(id));
 262 }
 263
 264 /* Given a matrix that maps a (possibly) parametric domain to
 265  * a parametric domain, add in rows that map the "nparam" parameters onto
 266  * themselves.
 267  */
 268 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 269         unsigned nparam)
 270 {
 271         int i;
 272
 273         if (nparam == 0)
 274                 return mat;
 275         if (!mat)
 276                 return NULL;
 277
 278         mat = isl_mat_insert_rows(mat, 1, nparam);
 279         if (!mat)
 280                 return NULL;
 281
 282         for (i = 0; i < nparam; ++i) {
 283                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 284                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 285         }
 286
 287         return mat;
 288 }
 289
 290 /* Construct a basic set described by the "n" equalities of "bset" starting
 291  * at "first".
 292  */
 293 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 294         unsigned first, unsigned n)
 295 {
 296         int i, k;
 297         isl_basic_set *eq;
 298         unsigned total;
 299
 300         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 301
 302         total = isl_basic_set_total_dim(bset);
 303         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 304         if (!eq)
 305                 return NULL;
 306         for (i = 0; i < n; ++i) {
 307                 k = isl_basic_set_alloc_equality(eq);
 308                 if (k < 0)
 309                         goto error;
 310                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 311         }
 312
 313         return eq;
 314 error:
 315         isl_basic_set_free(eq);
 316         return NULL;
 317 }
 318
 319 /* Given a basic set, exploit the equalties in the basic set to construct
 320  * a morphishm that maps the basic set to a lower-dimensional space.
 321  * Specifically, the morphism reduces the number of dimensions of type "type".
 322  *
 323  * This function is a slight generalization of isl_mat_variable_compression
 324  * in that it allows the input to be parametric and that it allows for the
 325  * compression of either parameters or set variables.
 326  *
 327  * We first select the equalities of interest, that is those that involve
 328  * variables of type "type" and no later variables.
 329  * Denote those equalities as
 330  *
 331  *              -C(p) + M x = 0
 332  *
 333  * where C(p) depends on the parameters if type == isl_dim_set and
 334  * is a constant if type == isl_dim_param.
 335  *
 336  * First compute the (left) Hermite normal form of M,
 337  *
 338  *              M [U1 U2] = M U = H = [H1 0]
 339  * or
 340  *                            M = H Q = [H1 0] [Q1]
 341  *                                             [Q2]
 342  *
 343  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 344  * Define the transformed variables as
 345  *
 346  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 347  *                          [ x2' ]           [Q2]
 348  *
 349  * The equalities then become
 350  *
 351  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 352  *
 353  * If the denominator of the constant term does not divide the
 354  * the common denominator of the parametric terms, then every
 355  * integer point is mapped to a non-integer point and then the original set has no
 356  * integer solutions (since the x' are a unimodular transformation
 357  * of the x).  In this case, an empty morphism is returned.
 358  * Otherwise, the transformation is given by
 359  *
 360  *              x = U1 H1^{-1} C(p) + U2 x2'
 361  *
 362  * The inverse transformation is simply
 363  *
 364  *              x2' = Q2 x
 365  *
 366  * Both matrices are extended to map the full original space to the full
 367  * compressed space.
 368  */
 369 __isl_give isl_morph *isl_basic_set_variable_compression(
 370         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 371 {
 372         unsigned otype;
 373         unsigned ntype;
 374         unsigned orest;
 375         unsigned nrest;
 376         int f_eq, n_eq;
 377         isl_space *dim;
 378         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 379         isl_basic_set *dom, *ran;
 380
 381         if (!bset)
 382                 return NULL;
 383
 384         if (isl_basic_set_plain_is_empty(bset))
 385                 return isl_morph_empty(bset);
 386
 387         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 388
 389         otype = 1 + isl_space_offset(bset->dim, type);
 390         ntype = isl_basic_set_dim(bset, type);
 391         orest = otype + ntype;
 392         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 393
 394         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 395                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 396                         break;
 397         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 398                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 399                         break;
 400         if (n_eq == 0)
 401                 return isl_morph_identity(bset);
 402
 403         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 404         H = isl_mat_left_hermite(H, 0, &U, &Q);
 405         if (!H || !U || !Q)
 406                 goto error;
 407         Q = isl_mat_drop_rows(Q, 0, n_eq);
 408         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 409         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 410         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 411         if (!C)
 412                 goto error;
 413         isl_int_set_si(C->row[0][0], 1);
 414         isl_seq_clr(C->row[0] + 1, otype - 1);
 415         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 416         H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
 417         H1 = isl_mat_lin_to_aff(H1);
 418         C = isl_mat_inverse_product(H1, C);
 419         if (!C)
 420                 goto error;
 421         isl_mat_free(H);
 422
 423         if (!isl_int_is_one(C->row[0][0])) {
 424                 int i;
 425                 isl_int g;
 426
 427                 isl_int_init(g);
 428                 for (i = 0; i < n_eq; ++i) {
 429                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 430                         isl_int_gcd(g, g, C->row[0][0]);
 431                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 432                                 break;
 433                 }
 434                 isl_int_clear(g);
 435
 436                 if (i < n_eq) {
 437                         isl_mat_free(C);
 438                         isl_mat_free(U);
 439                         isl_mat_free(Q);
 440                         return isl_morph_empty(bset);
 441                 }
 442
 443                 C = isl_mat_normalize(C);
 444         }
 445
 446         U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
 447         U1 = isl_mat_lin_to_aff(U1);
 448         U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
 449         U2 = isl_mat_lin_to_aff(U2);
 450         isl_mat_free(U);
 451
 452         C = isl_mat_product(U1, C);
 453         C = isl_mat_aff_direct_sum(C, U2);
 454         C = insert_parameter_rows(C, otype - 1);
 455         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 456
 457         dim = isl_space_copy(bset->dim);
 458         dim = isl_space_drop_dims(dim, type, 0, ntype);
 459         dim = isl_space_add_dims(dim, type, ntype - n_eq);
 460         ran = isl_basic_set_universe(dim);
 461         dom = copy_equalities(bset, f_eq, n_eq);
 462
 463         return isl_morph_alloc(dom, ran, Q, C);
 464 error:
 465         isl_mat_free(C);
 466         isl_mat_free(H);
 467         isl_mat_free(U);
 468         isl_mat_free(Q);
 469         return NULL;
 470 }
 471
 472 /* Construct a parameter compression for "bset".
 473  * We basically just call isl_mat_parameter_compression with the right input
 474  * and then extend the resulting matrix to include the variables.
 475  *
 476  * Let the equalities be given as
 477  *
 478  *      B(p) + A x = 0
 479  *
 480  * and let [H 0] be the Hermite Normal Form of A, then
 481  *
 482  *      H^-1 B(p)
 483  *
 484  * needs to be integer, so we impose that each row is divisible by
 485  * the denominator.
 486  */
 487 __isl_give isl_morph *isl_basic_set_parameter_compression(
 488         __isl_keep isl_basic_set *bset)
 489 {
 490         unsigned nparam;
 491         unsigned nvar;
 492         int n_eq;
 493         isl_mat *H, *B;
 494         isl_vec *d;
 495         isl_mat *map, *inv;
 496         isl_basic_set *dom, *ran;
 497
 498         if (!bset)
 499                 return NULL;
 500
 501         if (isl_basic_set_plain_is_empty(bset))
 502                 return isl_morph_empty(bset);
 503         if (bset->n_eq == 0)
 504                 return isl_morph_identity(bset);
 505
 506         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 507
 508         n_eq = bset->n_eq;
 509         nparam = isl_basic_set_dim(bset, isl_dim_param);
 510         nvar = isl_basic_set_dim(bset, isl_dim_set);
 511
 512         isl_assert(bset->ctx, n_eq <= nvar, return NULL);
 513
 514         d = isl_vec_alloc(bset->ctx, n_eq);
 515         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 516         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
 517         H = isl_mat_left_hermite(H, 0, NULL, NULL);
 518         H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
 519         H = isl_mat_lin_to_aff(H);
 520         H = isl_mat_right_inverse(H);
 521         if (!H || !d)
 522                 goto error;
 523         d = isl_vec_set(d, H->row[0][0]);
 524         H = isl_mat_drop_rows(H, 0, 1);
 525         H = isl_mat_drop_cols(H, 0, 1);
 526         B = isl_mat_product(H, B);
 527         inv = isl_mat_parameter_compression(B, d);
 528         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 529         map = isl_mat_right_inverse(isl_mat_copy(inv));
 530
 531         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 532         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 533
 534         return isl_morph_alloc(dom, ran, map, inv);
 535 error:
 536         isl_mat_free(H);
 537         isl_mat_free(B);
 538         isl_vec_free(d);
 539         return NULL;
 540 }
 541
 542 /* Add stride constraints to "bset" based on the inverse mapping
 543  * that was plugged in.  In particular, if morph maps x' to x,
 544  * the the constraints of the original input
 545  *
 546  *      A x' + b >= 0
 547  *
 548  * have been rewritten to
 549  *
 550  *      A inv x + b >= 0
 551  *
 552  * However, this substitution may loose information on the integrality of x',
 553  * so we need to impose that
 554  *
 555  *      inv x
 556  *
 557  * is integral.  If inv = B/d, this means that we need to impose that
 558  *
 559  *      B x = 0         mod d
 560  *
 561  * or
 562  *
 563  *      exists alpha in Z^m: B x = d alpha
 564  *
 565  */
 566 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 567         __isl_keep isl_morph *morph)
 568 {
 569         int i, div, k;
 570         isl_int gcd;
 571
 572         if (isl_int_is_one(morph->inv->row[0][0]))
 573                 return bset;
 574
 575         isl_int_init(gcd);
 576
 577         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 578                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 579                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 580                         continue;
 581                 div = isl_basic_set_alloc_div(bset);
 582                 if (div < 0)
 583                         goto error;
 584                 isl_int_set_si(bset->div[div][0], 0);
 585                 k = isl_basic_set_alloc_equality(bset);
 586                 if (k < 0)
 587                         goto error;
 588                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 589                             morph->inv->n_col);
 590                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 591                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 592                             morph->inv->row[0][0]);
 593         }
 594
 595         isl_int_clear(gcd);
 596
 597         return bset;
 598 error:
 599         isl_int_clear(gcd);
 600         isl_basic_set_free(bset);
 601         return NULL;
 602 }
 603
 604 /* Apply the morphism to the basic set.
 605  * We basically just compute the preimage of "bset" under the inverse mapping
 606  * in morph, add in stride constraints and intersect with the range
 607  * of the morphism.
 608  */
 609 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 610         __isl_take isl_basic_set *bset)
 611 {
 612         isl_basic_set *res = NULL;
 613         isl_mat *mat = NULL;
 614         int i, k;
 615         int max_stride;
 616
 617         if (!morph || !bset)
 618                 goto error;
 619
 620         isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
 621                     goto error);
 622
 623         max_stride = morph->inv->n_row - 1;
 624         if (isl_int_is_one(morph->inv->row[0][0]))
 625                 max_stride = 0;
 626         res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
 627                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 628
 629         for (i = 0; i < bset->n_div; ++i)
 630                 if (isl_basic_set_alloc_div(res) < 0)
 631                         goto error;
 632
 633         mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
 634                                         0, morph->inv->n_row);
 635         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 636         if (!mat)
 637                 goto error;
 638         for (i = 0; i < bset->n_eq; ++i) {
 639                 k = isl_basic_set_alloc_equality(res);
 640                 if (k < 0)
 641                         goto error;
 642                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 643                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 644                                 morph->inv->row[0][0], bset->n_div);
 645         }
 646         isl_mat_free(mat);
 647
 648         mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
 649                                         0, morph->inv->n_row);
 650         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 651         if (!mat)
 652                 goto error;
 653         for (i = 0; i < bset->n_ineq; ++i) {
 654                 k = isl_basic_set_alloc_inequality(res);
 655                 if (k < 0)
 656                         goto error;
 657                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 658                 isl_seq_scale(res->ineq[k] + mat->n_col,
 659                                 bset->ineq[i] + mat->n_col,
 660                                 morph->inv->row[0][0], bset->n_div);
 661         }
 662         isl_mat_free(mat);
 663
 664         mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
 665                                         1, morph->inv->n_row);
 666         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 667         if (!mat)
 668                 goto error;
 669         for (i = 0; i < bset->n_div; ++i) {
 670                 isl_int_mul(res->div[i][0],
 671                                 morph->inv->row[0][0], bset->div[i][0]);
 672                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 673                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 674                                 bset->div[i] + 1 + mat->n_col,
 675                                 morph->inv->row[0][0], bset->n_div);
 676         }
 677         isl_mat_free(mat);
 678
 679         res = add_strides(res, morph);
 680
 681         if (isl_basic_set_is_rational(bset))
 682                 res = isl_basic_set_set_rational(res);
 683
 684         res = isl_basic_set_simplify(res);
 685         res = isl_basic_set_finalize(res);
 686
 687         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 688
 689         isl_morph_free(morph);
 690         isl_basic_set_free(bset);
 691         return res;
 692 error:
 693         isl_mat_free(mat);
 694         isl_morph_free(morph);
 695         isl_basic_set_free(bset);
 696         isl_basic_set_free(res);
 697         return NULL;
 698 }
 699
 700 /* Apply the morphism to the set.
 701  */
 702 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 703         __isl_take isl_set *set)
 704 {
 705         int i;
 706
 707         if (!morph || !set)
 708                 goto error;
 709
 710         isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
 711
 712         set = isl_set_cow(set);
 713         if (!set)
 714                 goto error;
 715
 716         isl_space_free(set->dim);
 717         set->dim = isl_space_copy(morph->ran->dim);
 718         if (!set->dim)
 719                 goto error;
 720
 721         for (i = 0; i < set->n; ++i) {
 722                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 723                 if (!set->p[i])
 724                         goto error;
 725         }
 726
 727         isl_morph_free(morph);
 728
 729         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 730
 731         return set;
 732 error:
 733         isl_set_free(set);
 734         isl_morph_free(morph);
 735         return NULL;
 736 }
 737
 738 /* Construct a morphism that first does morph2 and then morph1.
 739  */
 740 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 741         __isl_take isl_morph *morph2)
 742 {
 743         isl_mat *map, *inv;
 744         isl_basic_set *dom, *ran;
 745
 746         if (!morph1 || !morph2)
 747                 goto error;
 748
 749         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 750         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 751         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 752                                   isl_basic_set_copy(morph1->dom));
 753         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 754         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 755                                   isl_basic_set_copy(morph2->ran));
 756         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 757
 758         isl_morph_free(morph1);
 759         isl_morph_free(morph2);
 760
 761         return isl_morph_alloc(dom, ran, map, inv);
 762 error:
 763         isl_morph_free(morph1);
 764         isl_morph_free(morph2);
 765         return NULL;
 766 }
 767
 768 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 769 {
 770         isl_basic_set *bset;
 771         isl_mat *mat;
 772
 773         morph = isl_morph_cow(morph);
 774         if (!morph)
 775                 return NULL;
 776
 777         bset = morph->dom;
 778         morph->dom = morph->ran;
 779         morph->ran = bset;
 780
 781         mat = morph->map;
 782         morph->map = morph->inv;
 783         morph->inv = mat;
 784
 785         return morph;
 786 }
 787
 788 /* We detect all the equalities first to avoid implicit equalties
 789  * being discovered during the computations.  In particular,
 790  * the compression on the variables could expose additional stride
 791  * constraints on the parameters.  This would result in existentially
 792  * quantified variables after applying the resulting morph, which
 793  * in turn could break invariants of the calling functions.
 794  */
 795 __isl_give isl_morph *isl_basic_set_full_compression(
 796         __isl_keep isl_basic_set *bset)
 797 {
 798         isl_morph *morph, *morph2;
 799
 800         bset = isl_basic_set_copy(bset);
 801         bset = isl_basic_set_detect_equalities(bset);
 802
 803         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 804         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 805
 806         morph2 = isl_basic_set_parameter_compression(bset);
 807         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 808
 809         morph = isl_morph_compose(morph2, morph);
 810
 811         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 812         isl_basic_set_free(bset);
 813
 814         morph = isl_morph_compose(morph2, morph);
 815
 816         return morph;
 817 }
 818
 819 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
 820         __isl_take isl_vec *vec)
 821 {
 822         if (!morph)
 823                 goto error;
 824
 825         vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
 826
 827         isl_morph_free(morph);
 828         return vec;
 829 error:
 830         isl_morph_free(morph);
 831         isl_vec_free(vec);
 832         return NULL;
 833 }