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_ctx *isl_morph_get_ctx(__isl_keep isl_morph *morph)
  19 {
  20         if (!morph)
  21                 return NULL;
  22         return isl_basic_set_get_ctx(morph->dom);
  23 }
  24
  25 __isl_give isl_morph *isl_morph_alloc(
  26         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  27         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  28 {
  29         isl_morph *morph;
  30
  31         if (!dom || !ran || !map || !inv)
  32                 goto error;
  33
  34         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  35         if (!morph)
  36                 goto error;
  37
  38         morph->ref = 1;
  39         morph->dom = dom;
  40         morph->ran = ran;
  41         morph->map = map;
  42         morph->inv = inv;
  43
  44         return morph;
  45 error:
  46         isl_basic_set_free(dom);
  47         isl_basic_set_free(ran);
  48         isl_mat_free(map);
  49         isl_mat_free(inv);
  50         return NULL;
  51 }
  52
  53 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  54 {
  55         if (!morph)
  56                 return NULL;
  57
  58         morph->ref++;
  59         return morph;
  60 }
  61
  62 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  63 {
  64         if (!morph)
  65                 return NULL;
  66
  67         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  68                 isl_basic_set_copy(morph->ran),
  69                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  70 }
  71
  72 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  73 {
  74         if (!morph)
  75                 return NULL;
  76
  77         if (morph->ref == 1)
  78                 return morph;
  79         morph->ref--;
  80         return isl_morph_dup(morph);
  81 }
  82
  83 void isl_morph_free(__isl_take isl_morph *morph)
  84 {
  85         if (!morph)
  86                 return;
  87
  88         if (--morph->ref > 0)
  89                 return;
  90
  91         isl_basic_set_free(morph->dom);
  92         isl_basic_set_free(morph->ran);
  93         isl_mat_free(morph->map);
  94         isl_mat_free(morph->inv);
  95         free(morph);
  96 }
  97
  98 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
  99 {
 100         if (!morph)
 101                 return NULL;
 102
 103         return isl_space_copy(morph->ran->dim);
 104 }
 105
 106 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 107 {
 108         if (!morph)
 109                 return 0;
 110
 111         return isl_basic_set_dim(morph->dom, type);
 112 }
 113
 114 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 115 {
 116         if (!morph)
 117                 return 0;
 118
 119         return isl_basic_set_dim(morph->ran, type);
 120 }
 121
 122 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 123         enum isl_dim_type type, unsigned first, unsigned n)
 124 {
 125         unsigned dom_offset;
 126
 127         if (n == 0)
 128                 return morph;
 129
 130         morph = isl_morph_cow(morph);
 131         if (!morph)
 132                 return NULL;
 133
 134         dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
 135
 136         morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
 137
 138         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 139
 140         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 141
 142         if (morph->dom && morph->ran && morph->map && morph->inv)
 143                 return morph;
 144
 145         isl_morph_free(morph);
 146         return NULL;
 147 }
 148
 149 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 150         enum isl_dim_type type, unsigned first, unsigned n)
 151 {
 152         unsigned ran_offset;
 153
 154         if (n == 0)
 155                 return morph;
 156
 157         morph = isl_morph_cow(morph);
 158         if (!morph)
 159                 return NULL;
 160
 161         ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
 162
 163         morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
 164
 165         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 166
 167         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 168
 169         if (morph->dom && morph->ran && morph->map && morph->inv)
 170                 return morph;
 171
 172         isl_morph_free(morph);
 173         return NULL;
 174 }
 175
 176 /* Project domain of morph onto its parameter domain.
 177  */
 178 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
 179 {
 180         unsigned n;
 181
 182         morph = isl_morph_cow(morph);
 183         if (!morph)
 184                 return NULL;
 185         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 186         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 187         if (!morph)
 188                 return NULL;
 189         morph->dom = isl_basic_set_params(morph->dom);
 190         if (morph->dom)
 191                 return morph;
 192
 193         isl_morph_free(morph);
 194         return NULL;
 195 }
 196
 197 /* Project range of morph onto its parameter domain.
 198  */
 199 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 200 {
 201         unsigned n;
 202
 203         morph = isl_morph_cow(morph);
 204         if (!morph)
 205                 return NULL;
 206         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 207         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 208         if (!morph)
 209                 return NULL;
 210         morph->ran = isl_basic_set_params(morph->ran);
 211         if (morph->ran)
 212                 return morph;
 213
 214         isl_morph_free(morph);
 215         return NULL;
 216 }
 217
 218 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 219 {
 220         if (!morph)
 221                 return;
 222
 223         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 224         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 225         isl_mat_print_internal(morph->map, out, 4);
 226         isl_mat_print_internal(morph->inv, out, 4);
 227 }
 228
 229 void isl_morph_dump(__isl_take isl_morph *morph)
 230 {
 231         isl_morph_print_internal(morph, stderr);
 232 }
 233
 234 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 235 {
 236         isl_mat *id;
 237         isl_basic_set *universe;
 238         unsigned total;
 239
 240         if (!bset)
 241                 return NULL;
 242
 243         total = isl_basic_set_total_dim(bset);
 244         id = isl_mat_identity(bset->ctx, 1 + total);
 245         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 246
 247         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 248                 id, isl_mat_copy(id));
 249 }
 250
 251 /* Create a(n identity) morphism between empty sets of the same dimension
 252  * a "bset".
 253  */
 254 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 255 {
 256         isl_mat *id;
 257         isl_basic_set *empty;
 258         unsigned total;
 259
 260         if (!bset)
 261                 return NULL;
 262
 263         total = isl_basic_set_total_dim(bset);
 264         id = isl_mat_identity(bset->ctx, 1 + total);
 265         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 266
 267         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 268                 id, isl_mat_copy(id));
 269 }
 270
 271 /* Given a matrix that maps a (possibly) parametric domain to
 272  * a parametric domain, add in rows that map the "nparam" parameters onto
 273  * themselves.
 274  */
 275 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 276         unsigned nparam)
 277 {
 278         int i;
 279
 280         if (nparam == 0)
 281                 return mat;
 282         if (!mat)
 283                 return NULL;
 284
 285         mat = isl_mat_insert_rows(mat, 1, nparam);
 286         if (!mat)
 287                 return NULL;
 288
 289         for (i = 0; i < nparam; ++i) {
 290                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 291                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 292         }
 293
 294         return mat;
 295 }
 296
 297 /* Construct a basic set described by the "n" equalities of "bset" starting
 298  * at "first".
 299  */
 300 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 301         unsigned first, unsigned n)
 302 {
 303         int i, k;
 304         isl_basic_set *eq;
 305         unsigned total;
 306
 307         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 308
 309         total = isl_basic_set_total_dim(bset);
 310         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 311         if (!eq)
 312                 return NULL;
 313         for (i = 0; i < n; ++i) {
 314                 k = isl_basic_set_alloc_equality(eq);
 315                 if (k < 0)
 316                         goto error;
 317                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 318         }
 319
 320         return eq;
 321 error:
 322         isl_basic_set_free(eq);
 323         return NULL;
 324 }
 325
 326 /* Given a basic set, exploit the equalties in the basic set to construct
 327  * a morphishm that maps the basic set to a lower-dimensional space.
 328  * Specifically, the morphism reduces the number of dimensions of type "type".
 329  *
 330  * This function is a slight generalization of isl_mat_variable_compression
 331  * in that it allows the input to be parametric and that it allows for the
 332  * compression of either parameters or set variables.
 333  *
 334  * We first select the equalities of interest, that is those that involve
 335  * variables of type "type" and no later variables.
 336  * Denote those equalities as
 337  *
 338  *              -C(p) + M x = 0
 339  *
 340  * where C(p) depends on the parameters if type == isl_dim_set and
 341  * is a constant if type == isl_dim_param.
 342  *
 343  * First compute the (left) Hermite normal form of M,
 344  *
 345  *              M [U1 U2] = M U = H = [H1 0]
 346  * or
 347  *                            M = H Q = [H1 0] [Q1]
 348  *                                             [Q2]
 349  *
 350  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 351  * Define the transformed variables as
 352  *
 353  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 354  *                          [ x2' ]           [Q2]
 355  *
 356  * The equalities then become
 357  *
 358  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 359  *
 360  * If the denominator of the constant term does not divide the
 361  * the common denominator of the parametric terms, then every
 362  * integer point is mapped to a non-integer point and then the original set has no
 363  * integer solutions (since the x' are a unimodular transformation
 364  * of the x).  In this case, an empty morphism is returned.
 365  * Otherwise, the transformation is given by
 366  *
 367  *              x = U1 H1^{-1} C(p) + U2 x2'
 368  *
 369  * The inverse transformation is simply
 370  *
 371  *              x2' = Q2 x
 372  *
 373  * Both matrices are extended to map the full original space to the full
 374  * compressed space.
 375  */
 376 __isl_give isl_morph *isl_basic_set_variable_compression(
 377         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 378 {
 379         unsigned otype;
 380         unsigned ntype;
 381         unsigned orest;
 382         unsigned nrest;
 383         int f_eq, n_eq;
 384         isl_space *dim;
 385         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 386         isl_basic_set *dom, *ran;
 387
 388         if (!bset)
 389                 return NULL;
 390
 391         if (isl_basic_set_plain_is_empty(bset))
 392                 return isl_morph_empty(bset);
 393
 394         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 395
 396         otype = 1 + isl_space_offset(bset->dim, type);
 397         ntype = isl_basic_set_dim(bset, type);
 398         orest = otype + ntype;
 399         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 400
 401         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 402                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 403                         break;
 404         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 405                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 406                         break;
 407         if (n_eq == 0)
 408                 return isl_morph_identity(bset);
 409
 410         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 411         H = isl_mat_left_hermite(H, 0, &U, &Q);
 412         if (!H || !U || !Q)
 413                 goto error;
 414         Q = isl_mat_drop_rows(Q, 0, n_eq);
 415         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 416         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 417         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 418         if (!C)
 419                 goto error;
 420         isl_int_set_si(C->row[0][0], 1);
 421         isl_seq_clr(C->row[0] + 1, otype - 1);
 422         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 423         H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
 424         H1 = isl_mat_lin_to_aff(H1);
 425         C = isl_mat_inverse_product(H1, C);
 426         if (!C)
 427                 goto error;
 428         isl_mat_free(H);
 429
 430         if (!isl_int_is_one(C->row[0][0])) {
 431                 int i;
 432                 isl_int g;
 433
 434                 isl_int_init(g);
 435                 for (i = 0; i < n_eq; ++i) {
 436                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 437                         isl_int_gcd(g, g, C->row[0][0]);
 438                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 439                                 break;
 440                 }
 441                 isl_int_clear(g);
 442
 443                 if (i < n_eq) {
 444                         isl_mat_free(C);
 445                         isl_mat_free(U);
 446                         isl_mat_free(Q);
 447                         return isl_morph_empty(bset);
 448                 }
 449
 450                 C = isl_mat_normalize(C);
 451         }
 452
 453         U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
 454         U1 = isl_mat_lin_to_aff(U1);
 455         U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
 456         U2 = isl_mat_lin_to_aff(U2);
 457         isl_mat_free(U);
 458
 459         C = isl_mat_product(U1, C);
 460         C = isl_mat_aff_direct_sum(C, U2);
 461         C = insert_parameter_rows(C, otype - 1);
 462         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 463
 464         dim = isl_space_copy(bset->dim);
 465         dim = isl_space_drop_dims(dim, type, 0, ntype);
 466         dim = isl_space_add_dims(dim, type, ntype - n_eq);
 467         ran = isl_basic_set_universe(dim);
 468         dom = copy_equalities(bset, f_eq, n_eq);
 469
 470         return isl_morph_alloc(dom, ran, Q, C);
 471 error:
 472         isl_mat_free(C);
 473         isl_mat_free(H);
 474         isl_mat_free(U);
 475         isl_mat_free(Q);
 476         return NULL;
 477 }
 478
 479 /* Construct a parameter compression for "bset".
 480  * We basically just call isl_mat_parameter_compression with the right input
 481  * and then extend the resulting matrix to include the variables.
 482  *
 483  * The implementation assumes that "bset" does not have any equalities
 484  * that only involve the parameters and that isl_basic_set_gauss has
 485  * been applied to "bset".
 486  *
 487  * Let the equalities be given as
 488  *
 489  *      B(p) + A x = 0.
 490  *
 491  * We use isl_mat_parameter_compression_ext to compute the compression
 492  *
 493  *      p = T p'.
 494  */
 495 __isl_give isl_morph *isl_basic_set_parameter_compression(
 496         __isl_keep isl_basic_set *bset)
 497 {
 498         unsigned nparam;
 499         unsigned nvar;
 500         unsigned n_div;
 501         int n_eq;
 502         isl_mat *H, *B;
 503         isl_mat *map, *inv;
 504         isl_basic_set *dom, *ran;
 505
 506         if (!bset)
 507                 return NULL;
 508
 509         if (isl_basic_set_plain_is_empty(bset))
 510                 return isl_morph_empty(bset);
 511         if (bset->n_eq == 0)
 512                 return isl_morph_identity(bset);
 513
 514         n_eq = bset->n_eq;
 515         nparam = isl_basic_set_dim(bset, isl_dim_param);
 516         nvar = isl_basic_set_dim(bset, isl_dim_set);
 517         n_div = isl_basic_set_dim(bset, isl_dim_div);
 518
 519         if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,
 520                                     nvar + n_div) == -1)
 521                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 522                         "input not allowed to have parameter equalities",
 523                         return NULL);
 524         if (n_eq > nvar + n_div)
 525                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 526                         "input not gaussed", return NULL);
 527
 528         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 529         H = isl_mat_sub_alloc6(bset->ctx, bset->eq,
 530                                 0, n_eq, 1 + nparam, nvar + n_div);
 531         inv = isl_mat_parameter_compression_ext(B, H);
 532         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 533         map = isl_mat_right_inverse(isl_mat_copy(inv));
 534
 535         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 536         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 537
 538         return isl_morph_alloc(dom, ran, map, inv);
 539 }
 540
 541 /* Add stride constraints to "bset" based on the inverse mapping
 542  * that was plugged in.  In particular, if morph maps x' to x,
 543  * the the constraints of the original input
 544  *
 545  *      A x' + b >= 0
 546  *
 547  * have been rewritten to
 548  *
 549  *      A inv x + b >= 0
 550  *
 551  * However, this substitution may loose information on the integrality of x',
 552  * so we need to impose that
 553  *
 554  *      inv x
 555  *
 556  * is integral.  If inv = B/d, this means that we need to impose that
 557  *
 558  *      B x = 0         mod d
 559  *
 560  * or
 561  *
 562  *      exists alpha in Z^m: B x = d alpha
 563  *
 564  * This function is similar to add_strides in isl_affine_hull.c
 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 }