isl_fold.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_map_private.h>
  12 #include <isl_union_map_private.h>
  13 #include <isl_polynomial_private.h>
  14 #include <isl_point_private.h>
  15 #include <isl_dim_private.h>
  16 #include <isl/lp.h>
  17 #include <isl/seq.h>
  18 #include <isl_mat_private.h>
  19
  20 enum isl_fold isl_fold_type_negate(enum isl_fold type)
  21 {
  22         switch (type) {
  23         case isl_fold_min:
  24                 return isl_fold_max;
  25         case isl_fold_max:
  26                 return isl_fold_min;
  27         case isl_fold_list:
  28                 return isl_fold_list;
  29         }
  30 }
  31
  32 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  33         enum isl_fold type, __isl_take isl_dim *dim, int n)
  34 {
  35         isl_qpolynomial_fold *fold;
  36
  37         if (!dim)
  38                 goto error;
  39
  40         isl_assert(dim->ctx, n >= 0, goto error);
  41         fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
  42                         sizeof(struct isl_qpolynomial_fold) +
  43                         (n - 1) * sizeof(struct isl_qpolynomial *));
  44         if (!fold)
  45                 goto error;
  46
  47         fold->ref = 1;
  48         fold->size = n;
  49         fold->n = 0;
  50         fold->type = type;
  51         fold->dim = dim;
  52
  53         return fold;
  54 error:
  55         isl_dim_free(dim);
  56         return NULL;
  57 }
  58
  59 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
  60 {
  61         return fold ? fold->dim->ctx : NULL;
  62 }
  63
  64 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_dim(
  65         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_dim *dim)
  66 {
  67         int i;
  68
  69         fold = isl_qpolynomial_fold_cow(fold);
  70         if (!fold || !dim)
  71                 goto error;
  72
  73         for (i = 0; i < fold->n; ++i) {
  74                 fold->qp[i] = isl_qpolynomial_reset_dim(fold->qp[i],
  75                                                         isl_dim_copy(dim));
  76                 if (!fold->qp[i])
  77                         goto error;
  78         }
  79
  80         isl_dim_free(fold->dim);
  81         fold->dim = dim;
  82
  83         return fold;
  84 error:
  85         isl_qpolynomial_fold_free(fold);
  86         isl_dim_free(dim);
  87         return NULL;
  88 }
  89
  90 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
  91         enum isl_dim_type type, unsigned first, unsigned n)
  92 {
  93         int i;
  94
  95         if (!fold)
  96                 return -1;
  97         if (fold->n == 0 || n == 0)
  98                 return 0;
  99
 100         for (i = 0; i < fold->n; ++i) {
 101                 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
 102                                                             type, first, n);
 103                 if (involves < 0 || involves)
 104                         return involves;
 105         }
 106         return 0;
 107 }
 108
 109 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
 110         __isl_take isl_qpolynomial_fold *fold,
 111         enum isl_dim_type type, unsigned pos, const char *s)
 112 {
 113         int i;
 114
 115         fold = isl_qpolynomial_fold_cow(fold);
 116         if (!fold)
 117                 return NULL;
 118         fold->dim = isl_dim_set_name(fold->dim, type, pos, s);
 119         if (!fold->dim)
 120                 goto error;
 121
 122         for (i = 0; i < fold->n; ++i) {
 123                 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
 124                                                             type, pos, s);
 125                 if (!fold->qp[i])
 126                         goto error;
 127         }
 128
 129         return fold;
 130 error:
 131         isl_qpolynomial_fold_free(fold);
 132         return NULL;
 133 }
 134
 135 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
 136         __isl_take isl_qpolynomial_fold *fold,
 137         enum isl_dim_type type, unsigned first, unsigned n)
 138 {
 139         int i;
 140
 141         if (!fold)
 142                 return NULL;
 143         if (n == 0)
 144                 return fold;
 145
 146         fold = isl_qpolynomial_fold_cow(fold);
 147         if (!fold)
 148                 return NULL;
 149         fold->dim = isl_dim_drop(fold->dim, type, first, n);
 150         if (!fold->dim)
 151                 goto error;
 152
 153         for (i = 0; i < fold->n; ++i) {
 154                 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
 155                                                             type, first, n);
 156                 if (!fold->qp[i])
 157                         goto error;
 158         }
 159
 160         return fold;
 161 error:
 162         isl_qpolynomial_fold_free(fold);
 163         return NULL;
 164 }
 165
 166 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
 167         __isl_take isl_qpolynomial_fold *fold,
 168         enum isl_dim_type type, unsigned first, unsigned n)
 169 {
 170         int i;
 171
 172         if (!fold)
 173                 return NULL;
 174         if (n == 0 && !isl_dim_is_named_or_nested(fold->dim, type))
 175                 return fold;
 176
 177         fold = isl_qpolynomial_fold_cow(fold);
 178         if (!fold)
 179                 return NULL;
 180         fold->dim = isl_dim_insert(fold->dim, type, first, n);
 181         if (!fold->dim)
 182                 goto error;
 183
 184         for (i = 0; i < fold->n; ++i) {
 185                 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
 186                                                             type, first, n);
 187                 if (!fold->qp[i])
 188                         goto error;
 189         }
 190
 191         return fold;
 192 error:
 193         isl_qpolynomial_fold_free(fold);
 194         return NULL;
 195 }
 196
 197 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
 198 {
 199         struct isl_upoly_cst *cst;
 200
 201         cst = isl_upoly_as_cst(qp->upoly);
 202         if (!cst)
 203                 return 0;
 204
 205         return isl_int_sgn(cst->n) < 0 ? -1 : 1;
 206 }
 207
 208 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
 209         __isl_keep isl_qpolynomial *qp)
 210 {
 211         enum isl_lp_result res;
 212         isl_vec *aff;
 213         isl_int opt;
 214         int sgn = 0;
 215
 216         aff = isl_qpolynomial_extract_affine(qp);
 217         if (!aff)
 218                 return 0;
 219
 220         isl_int_init(opt);
 221
 222         res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
 223                                 &opt, NULL, NULL);
 224         if (res == isl_lp_error)
 225                 goto done;
 226         if (res == isl_lp_empty ||
 227             (res == isl_lp_ok && !isl_int_is_neg(opt))) {
 228                 sgn = 1;
 229                 goto done;
 230         }
 231
 232         res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
 233                                 &opt, NULL, NULL);
 234         if (res == isl_lp_ok && !isl_int_is_pos(opt))
 235                 sgn = -1;
 236
 237 done:
 238         isl_int_clear(opt);
 239         isl_vec_free(aff);
 240         return sgn;
 241 }
 242
 243 /* Determine, if possible, the sign of the quasipolynomial "qp" on
 244  * the domain "set".
 245  *
 246  * If qp is a constant, then the problem is trivial.
 247  * If qp is linear, then we check if the minimum of the corresponding
 248  * affine constraint is non-negative or if the maximum is non-positive.
 249  *
 250  * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 251  * in "set".  If so, we write qp(v,v') as
 252  *
 253  *      q(v,v') * (v - l) + r(v')
 254  *
 255  * if q(v,v') and r(v') have the same known sign, then the original
 256  * quasipolynomial has the same sign as well.
 257  *
 258  * Return
 259  *      -1 if qp <= 0
 260  *       1 if qp >= 0
 261  *       0 if unknown
 262  */
 263 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
 264         __isl_keep isl_qpolynomial *qp)
 265 {
 266         int d;
 267         int i;
 268         int is;
 269         struct isl_upoly_rec *rec;
 270         isl_vec *v;
 271         isl_int l;
 272         enum isl_lp_result res;
 273         int sgn = 0;
 274
 275         is = isl_qpolynomial_is_cst(qp, NULL, NULL);
 276         if (is < 0)
 277                 return 0;
 278         if (is)
 279                 return isl_qpolynomial_cst_sign(qp);
 280
 281         is = isl_qpolynomial_is_affine(qp);
 282         if (is < 0)
 283                 return 0;
 284         if (is)
 285                 return isl_qpolynomial_aff_sign(set, qp);
 286
 287         if (qp->div->n_row > 0)
 288                 return 0;
 289
 290         rec = isl_upoly_as_rec(qp->upoly);
 291         if (!rec)
 292                 return 0;
 293
 294         d = isl_dim_total(qp->dim);
 295         v = isl_vec_alloc(set->ctx, 2 + d);
 296         if (!v)
 297                 return 0;
 298
 299         isl_seq_clr(v->el + 1, 1 + d);
 300         isl_int_set_si(v->el[0], 1);
 301         isl_int_set_si(v->el[2 + qp->upoly->var], 1);
 302
 303         isl_int_init(l);
 304
 305         res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
 306         if (res == isl_lp_ok) {
 307                 isl_qpolynomial *min;
 308                 isl_qpolynomial *base;
 309                 isl_qpolynomial *r, *q;
 310                 isl_qpolynomial *t;
 311
 312                 min = isl_qpolynomial_cst(isl_dim_copy(qp->dim), l);
 313                 base = isl_qpolynomial_var_pow(isl_dim_copy(qp->dim),
 314                                                 qp->upoly->var, 1);
 315
 316                 r = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
 317                                           isl_upoly_copy(rec->p[rec->n - 1]));
 318                 q = isl_qpolynomial_copy(r);
 319
 320                 for (i = rec->n - 2; i >= 0; --i) {
 321                         r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
 322                         t = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
 323                                                   isl_upoly_copy(rec->p[i]));
 324                         r = isl_qpolynomial_add(r, t);
 325                         if (i == 0)
 326                                 break;
 327                         q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
 328                         q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
 329                 }
 330
 331                 if (isl_qpolynomial_is_zero(q))
 332                         sgn = isl_qpolynomial_sign(set, r);
 333                 else if (isl_qpolynomial_is_zero(r))
 334                         sgn = isl_qpolynomial_sign(set, q);
 335                 else {
 336                         int sgn_q, sgn_r;
 337                         sgn_r = isl_qpolynomial_sign(set, r);
 338                         sgn_q = isl_qpolynomial_sign(set, q);
 339                         if (sgn_r == sgn_q)
 340                                 sgn = sgn_r;
 341                 }
 342
 343                 isl_qpolynomial_free(min);
 344                 isl_qpolynomial_free(base);
 345                 isl_qpolynomial_free(q);
 346                 isl_qpolynomial_free(r);
 347         }
 348
 349         isl_int_clear(l);
 350
 351         isl_vec_free(v);
 352
 353         return sgn;
 354 }
 355
 356 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
 357         __isl_keep isl_set *set,
 358         __isl_take isl_qpolynomial_fold *fold1,
 359         __isl_take isl_qpolynomial_fold *fold2)
 360 {
 361         int i, j;
 362         int n1;
 363         struct isl_qpolynomial_fold *res = NULL;
 364         int better;
 365
 366         if (!fold1 || !fold2)
 367                 goto error;
 368
 369         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 370         isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
 371                         goto error);
 372
 373         better = fold1->type == isl_fold_max ? -1 : 1;
 374
 375         if (isl_qpolynomial_fold_is_empty(fold1)) {
 376                 isl_qpolynomial_fold_free(fold1);
 377                 return fold2;
 378         }
 379
 380         if (isl_qpolynomial_fold_is_empty(fold2)) {
 381                 isl_qpolynomial_fold_free(fold2);
 382                 return fold1;
 383         }
 384
 385         res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
 386                                         fold1->n + fold2->n);
 387         if (!res)
 388                 goto error;
 389
 390         for (i = 0; i < fold1->n; ++i) {
 391                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 392                 if (!res->qp[res->n])
 393                         goto error;
 394                 res->n++;
 395         }
 396         n1 = res->n;
 397
 398         for (i = 0; i < fold2->n; ++i) {
 399                 for (j = n1 - 1; j >= 0; --j) {
 400                         isl_qpolynomial *d;
 401                         int sgn;
 402                         d = isl_qpolynomial_sub(
 403                                 isl_qpolynomial_copy(res->qp[j]),
 404                                 isl_qpolynomial_copy(fold2->qp[i]));
 405                         sgn = isl_qpolynomial_sign(set, d);
 406                         isl_qpolynomial_free(d);
 407                         if (sgn == 0)
 408                                 continue;
 409                         if (sgn != better)
 410                                 break;
 411                         isl_qpolynomial_free(res->qp[j]);
 412                         if (j != n1 - 1)
 413                                 res->qp[j] = res->qp[n1 - 1];
 414                         n1--;
 415                         if (n1 != res->n - 1)
 416                                 res->qp[n1] = res->qp[res->n - 1];
 417                         res->n--;
 418                 }
 419                 if (j >= 0)
 420                         continue;
 421                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 422                 if (!res->qp[res->n])
 423                         goto error;
 424                 res->n++;
 425         }
 426
 427         isl_qpolynomial_fold_free(fold1);
 428         isl_qpolynomial_fold_free(fold2);
 429
 430         return res;
 431 error:
 432         isl_qpolynomial_fold_free(res);
 433         isl_qpolynomial_fold_free(fold1);
 434         isl_qpolynomial_fold_free(fold2);
 435         return NULL;
 436 }
 437
 438 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
 439         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
 440 {
 441         int i;
 442
 443         if (!fold || !qp)
 444                 goto error;
 445
 446         if (isl_qpolynomial_is_zero(qp)) {
 447                 isl_qpolynomial_free(qp);
 448                 return fold;
 449         }
 450
 451         fold = isl_qpolynomial_fold_cow(fold);
 452         if (!fold)
 453                 goto error;
 454
 455         for (i = 0; i < fold->n; ++i) {
 456                 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
 457                                                 isl_qpolynomial_copy(qp));
 458                 if (!fold->qp[i])
 459                         goto error;
 460         }
 461
 462         isl_qpolynomial_free(qp);
 463         return fold;
 464 error:
 465         isl_qpolynomial_fold_free(fold);
 466         isl_qpolynomial_free(qp);
 467         return NULL;
 468 }
 469
 470 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
 471         __isl_keep isl_set *dom,
 472         __isl_take isl_qpolynomial_fold *fold1,
 473         __isl_take isl_qpolynomial_fold *fold2)
 474 {
 475         int i;
 476         isl_qpolynomial_fold *res = NULL;
 477
 478         if (!fold1 || !fold2)
 479                 goto error;
 480
 481         if (isl_qpolynomial_fold_is_empty(fold1)) {
 482                 isl_qpolynomial_fold_free(fold1);
 483                 return fold2;
 484         }
 485
 486         if (isl_qpolynomial_fold_is_empty(fold2)) {
 487                 isl_qpolynomial_fold_free(fold2);
 488                 return fold1;
 489         }
 490
 491         if (fold1->n == 1 && fold2->n != 1)
 492                 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
 493
 494         if (fold2->n == 1) {
 495                 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
 496                                         isl_qpolynomial_copy(fold2->qp[0]));
 497                 isl_qpolynomial_fold_free(fold2);
 498                 return res;
 499         }
 500
 501         res = isl_qpolynomial_fold_add_qpolynomial(
 502                                 isl_qpolynomial_fold_copy(fold1),
 503                                 isl_qpolynomial_copy(fold2->qp[0]));
 504
 505         for (i = 1; i < fold2->n; ++i) {
 506                 isl_qpolynomial_fold *res_i;
 507                 res_i = isl_qpolynomial_fold_add_qpolynomial(
 508                                         isl_qpolynomial_fold_copy(fold1),
 509                                         isl_qpolynomial_copy(fold2->qp[i]));
 510                 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
 511         }
 512
 513         isl_qpolynomial_fold_free(fold1);
 514         isl_qpolynomial_fold_free(fold2);
 515         return res;
 516 error:
 517         isl_qpolynomial_fold_free(res);
 518         isl_qpolynomial_fold_free(fold1);
 519         isl_qpolynomial_fold_free(fold2);
 520         return NULL;
 521 }
 522
 523 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
 524         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
 525 {
 526         int i;
 527
 528         if (!fold || !eq)
 529                 goto error;
 530
 531         fold = isl_qpolynomial_fold_cow(fold);
 532         if (!fold)
 533                 return NULL;
 534
 535         for (i = 0; i < fold->n; ++i) {
 536                 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
 537                                                         isl_basic_set_copy(eq));
 538                 if (!fold->qp[i])
 539                         goto error;
 540         }
 541
 542         isl_basic_set_free(eq);
 543         return fold;
 544 error:
 545         isl_basic_set_free(eq);
 546         isl_qpolynomial_fold_free(fold);
 547         return NULL;
 548 }
 549
 550 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
 551         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 552 {
 553         int i;
 554
 555         if (!fold || !context)
 556                 goto error;
 557
 558         fold = isl_qpolynomial_fold_cow(fold);
 559         if (!fold)
 560                 return NULL;
 561
 562         for (i = 0; i < fold->n; ++i) {
 563                 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
 564                                                         isl_set_copy(context));
 565                 if (!fold->qp[i])
 566                         goto error;
 567         }
 568
 569         isl_set_free(context);
 570         return fold;
 571 error:
 572         isl_set_free(context);
 573         isl_qpolynomial_fold_free(fold);
 574         return NULL;
 575 }
 576
 577 #define HAS_TYPE
 578
 579 #undef PW
 580 #define PW isl_pw_qpolynomial_fold
 581 #undef EL
 582 #define EL isl_qpolynomial_fold
 583 #undef IS_ZERO
 584 #define IS_ZERO is_empty
 585 #undef FIELD
 586 #define FIELD fold
 587
 588 #include <isl_pw_templ.c>
 589
 590 #undef UNION
 591 #define UNION isl_union_pw_qpolynomial_fold
 592 #undef PART
 593 #define PART isl_pw_qpolynomial_fold
 594 #undef PARTS
 595 #define PARTS pw_qpolynomial_fold
 596
 597 #include <isl_union_templ.c>
 598
 599 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 600         __isl_take isl_dim *dim)
 601 {
 602         return qpolynomial_fold_alloc(type, dim, 0);
 603 }
 604
 605 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 606         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 607 {
 608         isl_qpolynomial_fold *fold;
 609
 610         if (!qp)
 611                 return NULL;
 612
 613         fold = qpolynomial_fold_alloc(type, isl_dim_copy(qp->dim), 1);
 614         if (!fold)
 615                 goto error;
 616
 617         fold->qp[0] = qp;
 618         fold->n++;
 619
 620         return fold;
 621 error:
 622         isl_qpolynomial_fold_free(fold);
 623         isl_qpolynomial_free(qp);
 624         return NULL;
 625 }
 626
 627 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 628         __isl_keep isl_qpolynomial_fold *fold)
 629 {
 630         if (!fold)
 631                 return NULL;
 632
 633         fold->ref++;
 634         return fold;
 635 }
 636
 637 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 638         __isl_keep isl_qpolynomial_fold *fold)
 639 {
 640         int i;
 641         isl_qpolynomial_fold *dup;
 642
 643         if (!fold)
 644                 return NULL;
 645         dup = qpolynomial_fold_alloc(fold->type,
 646                                         isl_dim_copy(fold->dim), fold->n);
 647         if (!dup)
 648                 return NULL;
 649
 650         dup->n = fold->n;
 651         for (i = 0; i < fold->n; ++i) {
 652                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 653                 if (!dup->qp[i])
 654                         goto error;
 655         }
 656
 657         return dup;
 658 error:
 659         isl_qpolynomial_fold_free(dup);
 660         return NULL;
 661 }
 662
 663 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 664         __isl_take isl_qpolynomial_fold *fold)
 665 {
 666         if (!fold)
 667                 return NULL;
 668
 669         if (fold->ref == 1)
 670                 return fold;
 671         fold->ref--;
 672         return isl_qpolynomial_fold_dup(fold);
 673 }
 674
 675 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 676 {
 677         int i;
 678
 679         if (!fold)
 680                 return;
 681         if (--fold->ref > 0)
 682                 return;
 683
 684         for (i = 0; i < fold->n; ++i)
 685                 isl_qpolynomial_free(fold->qp[i]);
 686         isl_dim_free(fold->dim);
 687         free(fold);
 688 }
 689
 690 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 691 {
 692         if (!fold)
 693                 return -1;
 694
 695         return fold->n == 0;
 696 }
 697
 698 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 699         __isl_take isl_qpolynomial_fold *fold1,
 700         __isl_take isl_qpolynomial_fold *fold2)
 701 {
 702         int i;
 703         struct isl_qpolynomial_fold *res = NULL;
 704
 705         if (!fold1 || !fold2)
 706                 goto error;
 707
 708         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 709         isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
 710                         goto error);
 711
 712         if (isl_qpolynomial_fold_is_empty(fold1)) {
 713                 isl_qpolynomial_fold_free(fold1);
 714                 return fold2;
 715         }
 716
 717         if (isl_qpolynomial_fold_is_empty(fold2)) {
 718                 isl_qpolynomial_fold_free(fold2);
 719                 return fold1;
 720         }
 721
 722         res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
 723                                         fold1->n + fold2->n);
 724         if (!res)
 725                 goto error;
 726
 727         for (i = 0; i < fold1->n; ++i) {
 728                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 729                 if (!res->qp[res->n])
 730                         goto error;
 731                 res->n++;
 732         }
 733
 734         for (i = 0; i < fold2->n; ++i) {
 735                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 736                 if (!res->qp[res->n])
 737                         goto error;
 738                 res->n++;
 739         }
 740
 741         isl_qpolynomial_fold_free(fold1);
 742         isl_qpolynomial_fold_free(fold2);
 743
 744         return res;
 745 error:
 746         isl_qpolynomial_fold_free(res);
 747         isl_qpolynomial_fold_free(fold1);
 748         isl_qpolynomial_fold_free(fold2);
 749         return NULL;
 750 }
 751
 752 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 753         __isl_take isl_pw_qpolynomial_fold *pw1,
 754         __isl_take isl_pw_qpolynomial_fold *pw2)
 755 {
 756         int i, j, n;
 757         struct isl_pw_qpolynomial_fold *res;
 758         isl_set *set;
 759
 760         if (!pw1 || !pw2)
 761                 goto error;
 762
 763         isl_assert(pw1->dim->ctx, isl_dim_equal(pw1->dim, pw2->dim), goto error);
 764
 765         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 766                 isl_pw_qpolynomial_fold_free(pw1);
 767                 return pw2;
 768         }
 769
 770         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 771                 isl_pw_qpolynomial_fold_free(pw2);
 772                 return pw1;
 773         }
 774
 775         if (pw1->type != pw2->type)
 776                 isl_die(set->ctx, isl_error_invalid, "fold types don't match",
 777                         goto error);
 778
 779         n = (pw1->n + 1) * (pw2->n + 1);
 780         res = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pw1->dim),
 781                                                 pw1->type, n);
 782
 783         for (i = 0; i < pw1->n; ++i) {
 784                 set = isl_set_copy(pw1->p[i].set);
 785                 for (j = 0; j < pw2->n; ++j) {
 786                         struct isl_set *common;
 787                         isl_qpolynomial_fold *sum;
 788                         set = isl_set_subtract(set,
 789                                         isl_set_copy(pw2->p[j].set));
 790                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 791                                                 isl_set_copy(pw2->p[j].set));
 792                         if (isl_set_fast_is_empty(common)) {
 793                                 isl_set_free(common);
 794                                 continue;
 795                         }
 796
 797                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 798                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 799                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 800
 801                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 802                 }
 803                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 804                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 805         }
 806
 807         for (j = 0; j < pw2->n; ++j) {
 808                 set = isl_set_copy(pw2->p[j].set);
 809                 for (i = 0; i < pw1->n; ++i)
 810                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 811                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 812                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 813         }
 814
 815         isl_pw_qpolynomial_fold_free(pw1);
 816         isl_pw_qpolynomial_fold_free(pw2);
 817
 818         return res;
 819 error:
 820         isl_pw_qpolynomial_fold_free(pw1);
 821         isl_pw_qpolynomial_fold_free(pw2);
 822         return NULL;
 823 }
 824
 825 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 826         __isl_take isl_union_pw_qpolynomial_fold *u,
 827         __isl_take isl_pw_qpolynomial_fold *part)
 828 {
 829         uint32_t hash;
 830         struct isl_hash_table_entry *entry;
 831
 832         u = isl_union_pw_qpolynomial_fold_cow(u);
 833
 834         if (!part || !u)
 835                 goto error;
 836
 837         isl_assert(u->dim->ctx, isl_dim_match(part->dim, isl_dim_param, u->dim,
 838                                               isl_dim_param), goto error);
 839
 840         hash = isl_dim_get_hash(part->dim);
 841         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 842                                     &has_dim, part->dim, 1);
 843         if (!entry)
 844                 goto error;
 845
 846         if (!entry->data)
 847                 entry->data = part;
 848         else {
 849                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 850                                             isl_pw_qpolynomial_fold_copy(part));
 851                 if (!entry->data)
 852                         goto error;
 853                 isl_pw_qpolynomial_fold_free(part);
 854         }
 855
 856         return u;
 857 error:
 858         isl_pw_qpolynomial_fold_free(part);
 859         isl_union_pw_qpolynomial_fold_free(u);
 860         return NULL;
 861 }
 862
 863 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 864 {
 865         isl_union_pw_qpolynomial_fold **u;
 866         u = (isl_union_pw_qpolynomial_fold **)user;
 867
 868         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 869
 870         return 0;
 871 }
 872
 873 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 874         __isl_take isl_union_pw_qpolynomial_fold *u1,
 875         __isl_take isl_union_pw_qpolynomial_fold *u2)
 876 {
 877         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 878
 879         if (!u1 || !u2)
 880                 goto error;
 881
 882         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 883                                                         &fold_part, &u1) < 0)
 884                 goto error;
 885
 886         isl_union_pw_qpolynomial_fold_free(u2);
 887
 888         return u1;
 889 error:
 890         isl_union_pw_qpolynomial_fold_free(u1);
 891         isl_union_pw_qpolynomial_fold_free(u2);
 892         return NULL;
 893 }
 894
 895 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 896         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 897 {
 898         int i;
 899         isl_pw_qpolynomial_fold *pwf;
 900
 901         if (!pwqp)
 902                 return NULL;
 903
 904         pwf = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp->dim), type,
 905                                                 pwqp->n);
 906
 907         for (i = 0; i < pwqp->n; ++i)
 908                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 909                         isl_set_copy(pwqp->p[i].set),
 910                         isl_qpolynomial_fold_alloc(type,
 911                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 912
 913         isl_pw_qpolynomial_free(pwqp);
 914
 915         return pwf;
 916 }
 917
 918 int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 919         __isl_keep isl_qpolynomial_fold *fold2)
 920 {
 921         int i;
 922
 923         if (!fold1 || !fold2)
 924                 return -1;
 925
 926         if (fold1->n != fold2->n)
 927                 return 0;
 928
 929         /* We probably want to sort the qps first... */
 930         for (i = 0; i < fold1->n; ++i) {
 931                 int eq = isl_qpolynomial_is_equal(fold1->qp[i], fold2->qp[i]);
 932                 if (eq < 0 || !eq)
 933                         return eq;
 934         }
 935
 936         return 1;
 937 }
 938
 939 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
 940         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
 941 {
 942         isl_qpolynomial *qp;
 943
 944         if (!fold || !pnt)
 945                 goto error;
 946         isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, fold->dim), goto error);
 947         isl_assert(pnt->dim->ctx,
 948                 fold->type == isl_fold_max || fold->type == isl_fold_min,
 949                 goto error);
 950
 951         if (fold->n == 0)
 952                 qp = isl_qpolynomial_zero(isl_dim_copy(fold->dim));
 953         else {
 954                 int i;
 955                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
 956                                                 isl_point_copy(pnt));
 957                 for (i = 1; i < fold->n; ++i) {
 958                         isl_qpolynomial *qp_i;
 959                         qp_i = isl_qpolynomial_eval(
 960                                             isl_qpolynomial_copy(fold->qp[i]),
 961                                             isl_point_copy(pnt));
 962                         if (fold->type == isl_fold_max)
 963                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
 964                         else
 965                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
 966                 }
 967         }
 968         isl_qpolynomial_fold_free(fold);
 969         isl_point_free(pnt);
 970
 971         return qp;
 972 error:
 973         isl_qpolynomial_fold_free(fold);
 974         isl_point_free(pnt);
 975         return NULL;
 976 }
 977
 978 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
 979 {
 980         int i;
 981         size_t n = 0;
 982
 983         for (i = 0; i < pwf->n; ++i)
 984                 n += pwf->p[i].fold->n;
 985
 986         return n;
 987 }
 988
 989 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
 990         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
 991 {
 992         int i;
 993         isl_qpolynomial *opt;
 994
 995         if (!set || !fold)
 996                 goto error;
 997
 998         if (fold->n == 0) {
 999                 isl_dim *dim = isl_dim_copy(fold->dim);
1000                 isl_set_free(set);
1001                 isl_qpolynomial_fold_free(fold);
1002                 return isl_qpolynomial_zero(dim);
1003         }
1004
1005         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1006                                                 isl_set_copy(set), max);
1007         for (i = 1; i < fold->n; ++i) {
1008                 isl_qpolynomial *opt_i;
1009                 opt_i = isl_qpolynomial_opt_on_domain(
1010                                 isl_qpolynomial_copy(fold->qp[i]),
1011                                 isl_set_copy(set), max);
1012                 if (max)
1013                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1014                 else
1015                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1016         }
1017
1018         isl_set_free(set);
1019         isl_qpolynomial_fold_free(fold);
1020
1021         return opt;
1022 error:
1023         isl_set_free(set);
1024         isl_qpolynomial_fold_free(fold);
1025         return NULL;
1026 }
1027
1028 /* Check whether for each quasi-polynomial in "fold2" there is
1029  * a quasi-polynomial in "fold1" that dominates it on "set".
1030  */
1031 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1032         __isl_keep isl_qpolynomial_fold *fold1,
1033         __isl_keep isl_qpolynomial_fold *fold2)
1034 {
1035         int i, j;
1036         int covers;
1037
1038         if (!set || !fold1 || !fold2)
1039                 return -1;
1040
1041         covers = fold1->type == isl_fold_max ? 1 : -1;
1042
1043         for (i = 0; i < fold2->n; ++i) {
1044                 for (j = 0; j < fold1->n; ++j) {
1045                         isl_qpolynomial *d;
1046                         int sgn;
1047
1048                         d = isl_qpolynomial_sub(
1049                                 isl_qpolynomial_copy(fold1->qp[j]),
1050                                 isl_qpolynomial_copy(fold2->qp[i]));
1051                         sgn = isl_qpolynomial_sign(set, d);
1052                         isl_qpolynomial_free(d);
1053                         if (sgn == covers)
1054                                 break;
1055                 }
1056                 if (j >= fold1->n)
1057                         return 0;
1058         }
1059
1060         return 1;
1061 }
1062
1063 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1064  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1065  * that of pwf2.
1066  */
1067 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1068         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1069 {
1070         int i, j;
1071         isl_set *dom1, *dom2;
1072         int is_subset;
1073
1074         if (!pwf1 || !pwf2)
1075                 return -1;
1076
1077         if (pwf2->n == 0)
1078                 return 1;
1079         if (pwf1->n == 0)
1080                 return 0;
1081
1082         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1083         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1084         is_subset = isl_set_is_subset(dom2, dom1);
1085         isl_set_free(dom1);
1086         isl_set_free(dom2);
1087
1088         if (is_subset < 0 || !is_subset)
1089                 return is_subset;
1090
1091         for (i = 0; i < pwf2->n; ++i) {
1092                 for (j = 0; j < pwf1->n; ++j) {
1093                         int is_empty;
1094                         isl_set *common;
1095                         int covers;
1096
1097                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1098                                                    isl_set_copy(pwf2->p[i].set));
1099                         is_empty = isl_set_is_empty(common);
1100                         if (is_empty < 0 || is_empty) {
1101                                 isl_set_free(common);
1102                                 if (is_empty < 0)
1103                                         return -1;
1104                                 continue;
1105                         }
1106                         covers = qpolynomial_fold_covers_on_domain(common,
1107                                         pwf1->p[j].fold, pwf2->p[i].fold);
1108                         isl_set_free(common);
1109                         if (covers < 0 || !covers)
1110                                 return covers;
1111                 }
1112         }
1113
1114         return 1;
1115 }
1116
1117 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph(
1118         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1119 {
1120         int i;
1121         isl_ctx *ctx;
1122
1123         if (!fold || !morph)
1124                 goto error;
1125
1126         ctx = fold->dim->ctx;
1127         isl_assert(ctx, isl_dim_equal(fold->dim, morph->dom->dim), goto error);
1128
1129         fold = isl_qpolynomial_fold_cow(fold);
1130         if (!fold)
1131                 goto error;
1132
1133         isl_dim_free(fold->dim);
1134         fold->dim = isl_dim_copy(morph->ran->dim);
1135         if (!fold->dim)
1136                 goto error;
1137
1138         for (i = 0; i < fold->n; ++i) {
1139                 fold->qp[i] = isl_qpolynomial_morph(fold->qp[i],
1140                                                 isl_morph_copy(morph));
1141                 if (!fold->qp[i])
1142                         goto error;
1143         }
1144
1145         isl_morph_free(morph);
1146
1147         return fold;
1148 error:
1149         isl_qpolynomial_fold_free(fold);
1150         isl_morph_free(morph);
1151         return NULL;
1152 }
1153
1154 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1155 {
1156         if (!fold)
1157                 return isl_fold_list;
1158         return fold->type;
1159 }
1160
1161 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1162         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1163 {
1164         if (!upwf)
1165                 return isl_fold_list;
1166         return upwf->type;
1167 }
1168
1169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1170         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_dim *dim)
1171 {
1172         int i;
1173         isl_ctx *ctx;
1174
1175         if (!fold || !dim)
1176                 goto error;
1177
1178         if (isl_dim_equal(fold->dim, dim)) {
1179                 isl_dim_free(dim);
1180                 return fold;
1181         }
1182
1183         fold = isl_qpolynomial_fold_cow(fold);
1184         if (!fold)
1185                 goto error;
1186
1187         isl_dim_free(fold->dim);
1188         fold->dim = isl_dim_copy(dim);
1189         if (!fold->dim)
1190                 goto error;
1191
1192         for (i = 0; i < fold->n; ++i) {
1193                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1194                                                 isl_dim_copy(dim));
1195                 if (!fold->qp[i])
1196                         goto error;
1197         }
1198
1199         isl_dim_free(dim);
1200
1201         return fold;
1202 error:
1203         isl_qpolynomial_fold_free(fold);
1204         isl_dim_free(dim);
1205         return NULL;
1206 }
1207
1208 int isl_qpolynomial_fold_foreach_qpolynomial(
1209         __isl_keep isl_qpolynomial_fold *fold,
1210         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1211 {
1212         int i;
1213
1214         if (!fold)
1215                 return -1;
1216
1217         for (i = 0; i < fold->n; ++i)
1218                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1219                         return -1;
1220
1221         return 0;
1222 }
1223
1224 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1225         __isl_take isl_qpolynomial_fold *fold,
1226         enum isl_dim_type dst_type, unsigned dst_pos,
1227         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1228 {
1229         int i;
1230
1231         if (n == 0)
1232                 return fold;
1233
1234         fold = isl_qpolynomial_fold_cow(fold);
1235         if (!fold)
1236                 return NULL;
1237
1238         fold->dim = isl_dim_move(fold->dim, dst_type, dst_pos,
1239                                                 src_type, src_pos, n);
1240         if (!fold->dim)
1241                 goto error;
1242
1243         for (i = 0; i < fold->n; ++i) {
1244                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1245                                 dst_type, dst_pos, src_type, src_pos, n);
1246                 if (!fold->qp[i])
1247                         goto error;
1248         }
1249
1250         return fold;
1251 error:
1252         isl_qpolynomial_fold_free(fold);
1253         return NULL;
1254 }
1255
1256 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1257  * in fold->qp[k] by subs[i].
1258  */
1259 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1260         __isl_take isl_qpolynomial_fold *fold,
1261         enum isl_dim_type type, unsigned first, unsigned n,
1262         __isl_keep isl_qpolynomial **subs)
1263 {
1264         int i;
1265
1266         if (n == 0)
1267                 return fold;
1268
1269         fold = isl_qpolynomial_fold_cow(fold);
1270         if (!fold)
1271                 return NULL;
1272
1273         for (i = 0; i < fold->n; ++i) {
1274                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1275                                 type, first, n, subs);
1276                 if (!fold->qp[i])
1277                         goto error;
1278         }
1279
1280         return fold;
1281 error:
1282         isl_qpolynomial_fold_free(fold);
1283         return NULL;
1284 }
1285
1286 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1287 {
1288         isl_ctx *ctx;
1289         isl_pw_qpolynomial_fold *pwf;
1290         isl_union_pw_qpolynomial_fold **upwf;
1291         uint32_t hash;
1292         struct isl_hash_table_entry *entry;
1293
1294         upwf = (isl_union_pw_qpolynomial_fold **)user;
1295
1296         ctx = pwqp->dim->ctx;
1297         hash = isl_dim_get_hash(pwqp->dim);
1298         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1299                                      hash, &has_dim, pwqp->dim, 1);
1300         if (!entry)
1301                 goto error;
1302
1303         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1304         if (!entry->data)
1305                 entry->data = pwf;
1306         else {
1307                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1308                 if (!entry->data)
1309                         return -1;
1310                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1311                         isl_pw_qpolynomial_fold_free(entry->data);
1312                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1313                 }
1314         }
1315
1316         return 0;
1317 error:
1318         isl_pw_qpolynomial_free(pwqp);
1319         return -1;
1320 }
1321
1322 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1323         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1324         __isl_take isl_union_pw_qpolynomial *upwqp)
1325 {
1326         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1327                                 isl_union_pw_qpolynomial_get_dim(upwqp));
1328         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1329                                 isl_union_pw_qpolynomial_fold_get_dim(upwf));
1330
1331         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1332         if (!upwf || !upwqp)
1333                 goto error;
1334
1335         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1336                                                          &upwf) < 0)
1337                 goto error;
1338
1339         isl_union_pw_qpolynomial_free(upwqp);
1340
1341         return upwf;
1342 error:
1343         isl_union_pw_qpolynomial_fold_free(upwf);
1344         isl_union_pw_qpolynomial_free(upwqp);
1345         return NULL;
1346 }
1347
1348 static int compatible_range(__isl_keep isl_dim *dim1, __isl_keep isl_dim *dim2)
1349 {
1350         int m;
1351         m = isl_dim_match(dim1, isl_dim_param, dim2, isl_dim_param);
1352         if (m < 0 || !m)
1353                 return m;
1354         return isl_dim_tuple_match(dim1, isl_dim_out, dim2, isl_dim_set);
1355 }
1356
1357 /* Compute the intersection of the range of the map and the domain
1358  * of the piecewise quasipolynomial reduction and then compute a bound
1359  * on the associated quasipolynomial reduction over all elements
1360  * in this intersection.
1361  *
1362  * We first introduce some unconstrained dimensions in the
1363  * piecewise quasipolynomial, intersect the resulting domain
1364  * with the wrapped map and the compute the sum.
1365  */
1366 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1367         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1368         int *tight)
1369 {
1370         isl_ctx *ctx;
1371         isl_set *dom;
1372         isl_dim *map_dim;
1373         isl_dim *pwf_dim;
1374         unsigned n_in;
1375         int ok;
1376
1377         ctx = isl_map_get_ctx(map);
1378         if (!ctx)
1379                 goto error;
1380
1381         map_dim = isl_map_get_dim(map);
1382         pwf_dim = isl_pw_qpolynomial_fold_get_dim(pwf);
1383         ok = compatible_range(map_dim, pwf_dim);
1384         isl_dim_free(map_dim);
1385         isl_dim_free(pwf_dim);
1386         if (!ok)
1387                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1388                         goto error);
1389
1390         n_in = isl_map_dim(map, isl_dim_in);
1391         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_set, 0, n_in);
1392
1393         dom = isl_map_wrap(map);
1394         pwf = isl_pw_qpolynomial_fold_reset_dim(pwf, isl_set_get_dim(dom));
1395
1396         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1397         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1398
1399         return pwf;
1400 error:
1401         isl_map_free(map);
1402         isl_pw_qpolynomial_fold_free(pwf);
1403         return NULL;
1404 }
1405
1406 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1407         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1408         int *tight)
1409 {
1410         isl_map *map;
1411
1412         map = isl_map_from_range(set);
1413         return isl_map_apply_pw_qpolynomial_fold(map, pwf, tight);
1414 }
1415
1416 struct isl_apply_fold_data {
1417         isl_union_pw_qpolynomial_fold *upwf;
1418         isl_union_pw_qpolynomial_fold *res;
1419         isl_map *map;
1420         int tight;
1421 };
1422
1423 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1424         void *user)
1425 {
1426         isl_dim *map_dim;
1427         isl_dim *pwf_dim;
1428         struct isl_apply_fold_data *data = user;
1429         int ok;
1430
1431         map_dim = isl_map_get_dim(data->map);
1432         pwf_dim = isl_pw_qpolynomial_fold_get_dim(pwf);
1433         ok = compatible_range(map_dim, pwf_dim);
1434         isl_dim_free(map_dim);
1435         isl_dim_free(pwf_dim);
1436
1437         if (ok) {
1438                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1439                                     pwf, data->tight ? &data->tight : NULL);
1440                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1441                                                         data->res, pwf);
1442         } else
1443                 isl_pw_qpolynomial_fold_free(pwf);
1444
1445         return 0;
1446 }
1447
1448 static int map_apply(__isl_take isl_map *map, void *user)
1449 {
1450         struct isl_apply_fold_data *data = user;
1451         int r;
1452
1453         data->map = map;
1454         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1455                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1456
1457         isl_map_free(map);
1458         return r;
1459 }
1460
1461 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1462         __isl_take isl_union_map *umap,
1463         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1464 {
1465         isl_dim *dim;
1466         enum isl_fold type;
1467         struct isl_apply_fold_data data;
1468
1469         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1470                                 isl_union_map_get_dim(umap));
1471         umap = isl_union_map_align_params(umap,
1472                                 isl_union_pw_qpolynomial_fold_get_dim(upwf));
1473
1474         data.upwf = upwf;
1475         data.tight = tight ? 1 : 0;
1476         dim = isl_union_pw_qpolynomial_fold_get_dim(upwf);
1477         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1478         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1479         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1480                 goto error;
1481
1482         isl_union_map_free(umap);
1483         isl_union_pw_qpolynomial_fold_free(upwf);
1484
1485         if (tight)
1486                 *tight = data.tight;
1487
1488         return data.res;
1489 error:
1490         isl_union_map_free(umap);
1491         isl_union_pw_qpolynomial_fold_free(upwf);
1492         isl_union_pw_qpolynomial_fold_free(data.res);
1493         return NULL;
1494 }
1495
1496 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1497         __isl_take isl_union_set *uset,
1498         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1499 {
1500         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1501 }
1502
1503 /* Reorder the dimension of "fold" according to the given reordering.
1504  */
1505 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign(
1506         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1507 {
1508         int i;
1509
1510         fold = isl_qpolynomial_fold_cow(fold);
1511         if (!fold || !r)
1512                 goto error;
1513
1514         for (i = 0; i < fold->n; ++i) {
1515                 fold->qp[i] = isl_qpolynomial_realign(fold->qp[i],
1516                                                     isl_reordering_copy(r));
1517                 if (!fold->qp[i])
1518                         goto error;
1519         }
1520
1521         fold = isl_qpolynomial_fold_reset_dim(fold, isl_dim_copy(r->dim));
1522
1523         isl_reordering_free(r);
1524
1525         return fold;
1526 error:
1527         isl_qpolynomial_fold_free(fold);
1528         isl_reordering_free(r);
1529         return NULL;
1530 }
1531
1532 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1533         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1534 {
1535         int i;
1536
1537         if (isl_int_is_one(v))
1538                 return fold;
1539         if (fold && isl_int_is_zero(v)) {
1540                 isl_qpolynomial_fold *zero;
1541                 isl_dim *dim = isl_dim_copy(fold->dim);
1542                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1543                 isl_qpolynomial_fold_free(fold);
1544                 return zero;
1545         }
1546
1547         fold = isl_qpolynomial_fold_cow(fold);
1548         if (!fold)
1549                 return NULL;
1550
1551         if (isl_int_is_neg(v))
1552                 fold->type = isl_fold_type_negate(fold->type);
1553         for (i = 0; i < fold->n; ++i) {
1554                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1555                 if (!fold->qp[i])
1556                         goto error;
1557         }
1558
1559         return fold;
1560 error:
1561         isl_qpolynomial_fold_free(fold);
1562         return NULL;
1563 }