isl_polynomial.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 <stdlib.h>
  12 #include <isl_seq.h>
  13 #include <isl_polynomial_private.h>
  14 #include <isl_point_private.h>
  15 #include <isl_dim.h>
  16 #include <isl_map_private.h>
  17
  18 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
  19 {
  20         switch (type) {
  21         case isl_dim_param:     return 0;
  22         case isl_dim_in:        return dim->nparam;
  23         case isl_dim_out:       return dim->nparam + dim->n_in;
  24         }
  25 }
  26
  27 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
  28 {
  29         if (!up)
  30                 return -1;
  31
  32         return up->var < 0;
  33 }
  34
  35 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
  36 {
  37         if (!up)
  38                 return NULL;
  39
  40         isl_assert(up->ctx, up->var < 0, return NULL);
  41
  42         return (struct isl_upoly_cst *)up;
  43 }
  44
  45 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
  46 {
  47         if (!up)
  48                 return NULL;
  49
  50         isl_assert(up->ctx, up->var >= 0, return NULL);
  51
  52         return (struct isl_upoly_rec *)up;
  53 }
  54
  55 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
  56         __isl_keep struct isl_upoly *up2)
  57 {
  58         int i;
  59         struct isl_upoly_rec *rec1, *rec2;
  60
  61         if (!up1 || !up2)
  62                 return -1;
  63         if (up1 == up2)
  64                 return 1;
  65         if (up1->var != up2->var)
  66                 return 0;
  67         if (isl_upoly_is_cst(up1)) {
  68                 struct isl_upoly_cst *cst1, *cst2;
  69                 cst1 = isl_upoly_as_cst(up1);
  70                 cst2 = isl_upoly_as_cst(up2);
  71                 if (!cst1 || !cst2)
  72                         return -1;
  73                 return isl_int_eq(cst1->n, cst2->n) &&
  74                        isl_int_eq(cst1->d, cst2->d);
  75         }
  76
  77         rec1 = isl_upoly_as_rec(up1);
  78         rec2 = isl_upoly_as_rec(up2);
  79         if (!rec1 || !rec2)
  80                 return -1;
  81
  82         if (rec1->n != rec2->n)
  83                 return 0;
  84
  85         for (i = 0; i < rec1->n; ++i) {
  86                 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
  87                 if (eq < 0 || !eq)
  88                         return eq;
  89         }
  90
  91         return 1;
  92 }
  93
  94 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
  95 {
  96         struct isl_upoly_cst *cst;
  97
  98         if (!up)
  99                 return -1;
 100         if (!isl_upoly_is_cst(up))
 101                 return 0;
 102
 103         cst = isl_upoly_as_cst(up);
 104         if (!cst)
 105                 return -1;
 106
 107         return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
 108 }
 109
 110 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
 111 {
 112         struct isl_upoly_cst *cst;
 113
 114         if (!up)
 115                 return 0;
 116         if (!isl_upoly_is_cst(up))
 117                 return 0;
 118
 119         cst = isl_upoly_as_cst(up);
 120         if (!cst)
 121                 return 0;
 122
 123         return isl_int_sgn(cst->n);
 124 }
 125
 126 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
 127 {
 128         struct isl_upoly_cst *cst;
 129
 130         if (!up)
 131                 return -1;
 132         if (!isl_upoly_is_cst(up))
 133                 return 0;
 134
 135         cst = isl_upoly_as_cst(up);
 136         if (!cst)
 137                 return -1;
 138
 139         return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
 140 }
 141
 142 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
 143 {
 144         struct isl_upoly_cst *cst;
 145
 146         if (!up)
 147                 return -1;
 148         if (!isl_upoly_is_cst(up))
 149                 return 0;
 150
 151         cst = isl_upoly_as_cst(up);
 152         if (!cst)
 153                 return -1;
 154
 155         return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
 156 }
 157
 158 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
 159 {
 160         struct isl_upoly_cst *cst;
 161
 162         if (!up)
 163                 return -1;
 164         if (!isl_upoly_is_cst(up))
 165                 return 0;
 166
 167         cst = isl_upoly_as_cst(up);
 168         if (!cst)
 169                 return -1;
 170
 171         return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
 172 }
 173
 174 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
 175 {
 176         struct isl_upoly_cst *cst;
 177
 178         if (!up)
 179                 return -1;
 180         if (!isl_upoly_is_cst(up))
 181                 return 0;
 182
 183         cst = isl_upoly_as_cst(up);
 184         if (!cst)
 185                 return -1;
 186
 187         return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
 188 }
 189
 190 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
 191 {
 192         struct isl_upoly_cst *cst;
 193
 194         if (!up)
 195                 return -1;
 196         if (!isl_upoly_is_cst(up))
 197                 return 0;
 198
 199         cst = isl_upoly_as_cst(up);
 200         if (!cst)
 201                 return -1;
 202
 203         return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
 204 }
 205
 206 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
 207 {
 208         struct isl_upoly_cst *cst;
 209
 210         cst = isl_alloc_type(ctx, struct isl_upoly_cst);
 211         if (!cst)
 212                 return NULL;
 213
 214         cst->up.ref = 1;
 215         cst->up.ctx = ctx;
 216         isl_ctx_ref(ctx);
 217         cst->up.var = -1;
 218
 219         isl_int_init(cst->n);
 220         isl_int_init(cst->d);
 221
 222         return cst;
 223 }
 224
 225 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
 226 {
 227         struct isl_upoly_cst *cst;
 228
 229         cst = isl_upoly_cst_alloc(ctx);
 230         if (!cst)
 231                 return NULL;
 232
 233         isl_int_set_si(cst->n, 0);
 234         isl_int_set_si(cst->d, 1);
 235
 236         return &cst->up;
 237 }
 238
 239 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
 240 {
 241         struct isl_upoly_cst *cst;
 242
 243         cst = isl_upoly_cst_alloc(ctx);
 244         if (!cst)
 245                 return NULL;
 246
 247         isl_int_set_si(cst->n, 1);
 248         isl_int_set_si(cst->d, 0);
 249
 250         return &cst->up;
 251 }
 252
 253 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
 254 {
 255         struct isl_upoly_cst *cst;
 256
 257         cst = isl_upoly_cst_alloc(ctx);
 258         if (!cst)
 259                 return NULL;
 260
 261         isl_int_set_si(cst->n, 0);
 262         isl_int_set_si(cst->d, 0);
 263
 264         return &cst->up;
 265 }
 266
 267 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
 268         isl_int n, isl_int d)
 269 {
 270         struct isl_upoly_cst *cst;
 271
 272         cst = isl_upoly_cst_alloc(ctx);
 273         if (!cst)
 274                 return NULL;
 275
 276         isl_int_set(cst->n, n);
 277         isl_int_set(cst->d, d);
 278
 279         return &cst->up;
 280 }
 281
 282 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
 283         int var, int size)
 284 {
 285         struct isl_upoly_rec *rec;
 286
 287         isl_assert(ctx, var >= 0, return NULL);
 288         isl_assert(ctx, size >= 0, return NULL);
 289         rec = isl_calloc(dim->ctx, struct isl_upoly_rec,
 290                         sizeof(struct isl_upoly_rec) +
 291                         (size - 1) * sizeof(struct isl_upoly *));
 292         if (!rec)
 293                 return NULL;
 294
 295         rec->up.ref = 1;
 296         rec->up.ctx = ctx;
 297         isl_ctx_ref(ctx);
 298         rec->up.var = var;
 299
 300         rec->n = 0;
 301         rec->size = size;
 302
 303         return rec;
 304 error:
 305         isl_upoly_free(&rec->up);
 306         return NULL;
 307 }
 308
 309 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
 310 {
 311         return qp ? qp->dim->ctx : NULL;
 312 }
 313
 314 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
 315 {
 316         return qp ? isl_upoly_is_zero(qp->upoly) : -1;
 317 }
 318
 319 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
 320 {
 321         return qp ? isl_upoly_is_one(qp->upoly) : -1;
 322 }
 323
 324 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
 325 {
 326         return qp ? isl_upoly_is_nan(qp->upoly) : -1;
 327 }
 328
 329 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
 330 {
 331         return qp ? isl_upoly_is_infty(qp->upoly) : -1;
 332 }
 333
 334 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
 335 {
 336         return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
 337 }
 338
 339 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
 340 {
 341         return qp ? isl_upoly_sgn(qp->upoly) : 0;
 342 }
 343
 344 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
 345 {
 346         isl_int_clear(cst->n);
 347         isl_int_clear(cst->d);
 348 }
 349
 350 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
 351 {
 352         int i;
 353
 354         for (i = 0; i < rec->n; ++i)
 355                 isl_upoly_free(rec->p[i]);
 356 }
 357
 358 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
 359 {
 360         if (!up)
 361                 return NULL;
 362
 363         up->ref++;
 364         return up;
 365 }
 366
 367 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
 368 {
 369         struct isl_upoly_cst *cst;
 370         struct isl_upoly_cst *dup;
 371
 372         cst = isl_upoly_as_cst(up);
 373         if (!cst)
 374                 return NULL;
 375
 376         dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
 377         if (!dup)
 378                 return NULL;
 379         isl_int_set(dup->n, cst->n);
 380         isl_int_set(dup->d, cst->d);
 381
 382         return &dup->up;
 383 }
 384
 385 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
 386 {
 387         int i;
 388         struct isl_upoly_rec *rec;
 389         struct isl_upoly_rec *dup;
 390
 391         rec = isl_upoly_as_rec(up);
 392         if (!rec)
 393                 return NULL;
 394
 395         dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
 396         if (!dup)
 397                 return NULL;
 398
 399         for (i = 0; i < rec->n; ++i) {
 400                 dup->p[i] = isl_upoly_copy(rec->p[i]);
 401                 if (!dup->p[i])
 402                         goto error;
 403                 dup->n++;
 404         }
 405
 406         return &dup->up;
 407 error:
 408         isl_upoly_free(&dup->up);
 409         return NULL;
 410 }
 411
 412 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
 413 {
 414         struct isl_upoly *dup;
 415
 416         if (!up)
 417                 return NULL;
 418
 419         if (isl_upoly_is_cst(up))
 420                 return isl_upoly_dup_cst(up);
 421         else
 422                 return isl_upoly_dup_rec(up);
 423 }
 424
 425 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
 426 {
 427         if (!up)
 428                 return NULL;
 429
 430         if (up->ref == 1)
 431                 return up;
 432         up->ref--;
 433         return isl_upoly_dup(up);
 434 }
 435
 436 void isl_upoly_free(__isl_take struct isl_upoly *up)
 437 {
 438         if (!up)
 439                 return;
 440
 441         if (--up->ref > 0)
 442                 return;
 443
 444         if (up->var < 0)
 445                 upoly_free_cst((struct isl_upoly_cst *)up);
 446         else
 447                 upoly_free_rec((struct isl_upoly_rec *)up);
 448
 449         isl_ctx_deref(up->ctx);
 450         free(up);
 451 }
 452
 453 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
 454 {
 455         isl_int gcd;
 456
 457         isl_int_init(gcd);
 458         isl_int_gcd(gcd, cst->n, cst->d);
 459         if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
 460                 isl_int_divexact(cst->n, cst->n, gcd);
 461                 isl_int_divexact(cst->d, cst->d, gcd);
 462         }
 463         isl_int_clear(gcd);
 464 }
 465
 466 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
 467         __isl_take struct isl_upoly *up2)
 468 {
 469         struct isl_upoly_cst *cst1;
 470         struct isl_upoly_cst *cst2;
 471
 472         up1 = isl_upoly_cow(up1);
 473         if (!up1 || !up2)
 474                 goto error;
 475
 476         cst1 = isl_upoly_as_cst(up1);
 477         cst2 = isl_upoly_as_cst(up2);
 478
 479         if (isl_int_eq(cst1->d, cst2->d))
 480                 isl_int_add(cst1->n, cst1->n, cst2->n);
 481         else {
 482                 isl_int_mul(cst1->n, cst1->n, cst2->d);
 483                 isl_int_addmul(cst1->n, cst2->n, cst1->d);
 484                 isl_int_mul(cst1->d, cst1->d, cst2->d);
 485         }
 486
 487         isl_upoly_cst_reduce(cst1);
 488
 489         isl_upoly_free(up2);
 490         return up1;
 491 error:
 492         isl_upoly_free(up1);
 493         isl_upoly_free(up2);
 494         return NULL;
 495 }
 496
 497 static __isl_give struct isl_upoly *replace_by_zero(
 498         __isl_take struct isl_upoly *up)
 499 {
 500         struct isl_ctx *ctx;
 501
 502         if (!up)
 503                 return NULL;
 504         ctx = up->ctx;
 505         isl_upoly_free(up);
 506         return isl_upoly_zero(ctx);
 507 }
 508
 509 static __isl_give struct isl_upoly *replace_by_constant_term(
 510         __isl_take struct isl_upoly *up)
 511 {
 512         struct isl_upoly_rec *rec;
 513         struct isl_upoly *cst;
 514
 515         if (!up)
 516                 return NULL;
 517
 518         rec = isl_upoly_as_rec(up);
 519         if (!rec)
 520                 goto error;
 521         cst = isl_upoly_copy(rec->p[0]);
 522         isl_upoly_free(up);
 523         return cst;
 524 error:
 525         isl_upoly_free(up);
 526         return NULL;
 527 }
 528
 529 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
 530         __isl_take struct isl_upoly *up2)
 531 {
 532         int i;
 533         struct isl_upoly_rec *rec1, *rec2;
 534
 535         if (!up1 || !up2)
 536                 goto error;
 537
 538         if (isl_upoly_is_nan(up1)) {
 539                 isl_upoly_free(up2);
 540                 return up1;
 541         }
 542
 543         if (isl_upoly_is_nan(up2)) {
 544                 isl_upoly_free(up1);
 545                 return up2;
 546         }
 547
 548         if (isl_upoly_is_zero(up1)) {
 549                 isl_upoly_free(up1);
 550                 return up2;
 551         }
 552
 553         if (isl_upoly_is_zero(up2)) {
 554                 isl_upoly_free(up2);
 555                 return up1;
 556         }
 557
 558         if (up1->var < up2->var)
 559                 return isl_upoly_sum(up2, up1);
 560
 561         if (up2->var < up1->var) {
 562                 struct isl_upoly_rec *rec;
 563                 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
 564                         isl_upoly_free(up1);
 565                         return up2;
 566                 }
 567                 up1 = isl_upoly_cow(up1);
 568                 rec = isl_upoly_as_rec(up1);
 569                 if (!rec)
 570                         goto error;
 571                 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
 572                 if (rec->n == 1)
 573                         up1 = replace_by_constant_term(up1);
 574                 return up1;
 575         }
 576
 577         if (isl_upoly_is_cst(up1))
 578                 return isl_upoly_sum_cst(up1, up2);
 579
 580         rec1 = isl_upoly_as_rec(up1);
 581         rec2 = isl_upoly_as_rec(up2);
 582         if (!rec1 || !rec2)
 583                 goto error;
 584
 585         if (rec1->n < rec2->n)
 586                 return isl_upoly_sum(up2, up1);
 587
 588         up1 = isl_upoly_cow(up1);
 589         rec1 = isl_upoly_as_rec(up1);
 590         if (!rec1)
 591                 goto error;
 592
 593         for (i = rec2->n - 1; i >= 0; --i) {
 594                 rec1->p[i] = isl_upoly_sum(rec1->p[i],
 595                                             isl_upoly_copy(rec2->p[i]));
 596                 if (!rec1->p[i])
 597                         goto error;
 598                 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
 599                         isl_upoly_free(rec1->p[i]);
 600                         rec1->n--;
 601                 }
 602         }
 603
 604         if (rec1->n == 0)
 605                 up1 = replace_by_zero(up1);
 606         else if (rec1->n == 1)
 607                 up1 = replace_by_constant_term(up1);
 608
 609         isl_upoly_free(up2);
 610
 611         return up1;
 612 error:
 613         isl_upoly_free(up1);
 614         isl_upoly_free(up2);
 615         return NULL;
 616 }
 617
 618 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
 619 {
 620         struct isl_upoly_cst *cst;
 621
 622         if (isl_upoly_is_zero(up))
 623                 return up;
 624
 625         up = isl_upoly_cow(up);
 626         if (!up)
 627                 return NULL;
 628
 629         cst = isl_upoly_as_cst(up);
 630
 631         isl_int_neg(cst->n, cst->n);
 632
 633         return up;
 634 }
 635
 636 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
 637 {
 638         int i;
 639         struct isl_upoly_rec *rec;
 640
 641         if (!up)
 642                 return NULL;
 643
 644         if (isl_upoly_is_cst(up))
 645                 return isl_upoly_neg_cst(up);
 646
 647         up = isl_upoly_cow(up);
 648         rec = isl_upoly_as_rec(up);
 649         if (!rec)
 650                 goto error;
 651
 652         for (i = 0; i < rec->n; ++i) {
 653                 rec->p[i] = isl_upoly_neg(rec->p[i]);
 654                 if (!rec->p[i])
 655                         goto error;
 656         }
 657
 658         return up;
 659 error:
 660         isl_upoly_free(up);
 661         return NULL;
 662 }
 663
 664 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
 665         __isl_take struct isl_upoly *up2)
 666 {
 667         struct isl_upoly_cst *cst1;
 668         struct isl_upoly_cst *cst2;
 669
 670         up1 = isl_upoly_cow(up1);
 671         if (!up1 || !up2)
 672                 goto error;
 673
 674         cst1 = isl_upoly_as_cst(up1);
 675         cst2 = isl_upoly_as_cst(up2);
 676
 677         isl_int_mul(cst1->n, cst1->n, cst2->n);
 678         isl_int_mul(cst1->d, cst1->d, cst2->d);
 679
 680         isl_upoly_cst_reduce(cst1);
 681
 682         isl_upoly_free(up2);
 683         return up1;
 684 error:
 685         isl_upoly_free(up1);
 686         isl_upoly_free(up2);
 687         return NULL;
 688 }
 689
 690 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
 691         __isl_take struct isl_upoly *up2)
 692 {
 693         struct isl_upoly_rec *rec1;
 694         struct isl_upoly_rec *rec2;
 695         struct isl_upoly_rec *res;
 696         int i, j;
 697         int size;
 698
 699         rec1 = isl_upoly_as_rec(up1);
 700         rec2 = isl_upoly_as_rec(up2);
 701         if (!rec1 || !rec2)
 702                 goto error;
 703         size = rec1->n + rec2->n - 1;
 704         res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
 705         if (!res)
 706                 goto error;
 707
 708         for (i = 0; i < rec1->n; ++i) {
 709                 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
 710                                             isl_upoly_copy(rec1->p[i]));
 711                 if (!res->p[i])
 712                         goto error;
 713                 res->n++;
 714         }
 715         for (; i < size; ++i) {
 716                 res->p[i] = isl_upoly_zero(up1->ctx);
 717                 if (!res->p[i])
 718                         goto error;
 719                 res->n++;
 720         }
 721         for (i = 0; i < rec1->n; ++i) {
 722                 for (j = 1; j < rec2->n; ++j) {
 723                         struct isl_upoly *up;
 724                         up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
 725                                             isl_upoly_copy(rec1->p[i]));
 726                         res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
 727                         if (!res->p[i + j])
 728                                 goto error;
 729                 }
 730         }
 731
 732         isl_upoly_free(up1);
 733         isl_upoly_free(up2);
 734
 735         return &res->up;
 736 error:
 737         isl_upoly_free(up1);
 738         isl_upoly_free(up2);
 739         isl_upoly_free(&res->up);
 740         return NULL;
 741 }
 742
 743 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
 744         __isl_take struct isl_upoly *up2)
 745 {
 746         if (!up1 || !up2)
 747                 goto error;
 748
 749         if (isl_upoly_is_nan(up1)) {
 750                 isl_upoly_free(up2);
 751                 return up1;
 752         }
 753
 754         if (isl_upoly_is_nan(up2)) {
 755                 isl_upoly_free(up1);
 756                 return up2;
 757         }
 758
 759         if (isl_upoly_is_zero(up1)) {
 760                 isl_upoly_free(up2);
 761                 return up1;
 762         }
 763
 764         if (isl_upoly_is_zero(up2)) {
 765                 isl_upoly_free(up1);
 766                 return up2;
 767         }
 768
 769         if (isl_upoly_is_one(up1)) {
 770                 isl_upoly_free(up1);
 771                 return up2;
 772         }
 773
 774         if (isl_upoly_is_one(up2)) {
 775                 isl_upoly_free(up2);
 776                 return up1;
 777         }
 778
 779         if (up1->var < up2->var)
 780                 return isl_upoly_mul(up2, up1);
 781
 782         if (up2->var < up1->var) {
 783                 int i;
 784                 struct isl_upoly_rec *rec;
 785                 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
 786                         isl_ctx *ctx = up1->ctx;
 787                         isl_upoly_free(up1);
 788                         isl_upoly_free(up2);
 789                         return isl_upoly_nan(ctx);
 790                 }
 791                 up1 = isl_upoly_cow(up1);
 792                 rec = isl_upoly_as_rec(up1);
 793                 if (!rec)
 794                         goto error;
 795
 796                 for (i = 0; i < rec->n; ++i) {
 797                         rec->p[i] = isl_upoly_mul(rec->p[i],
 798                                                     isl_upoly_copy(up2));
 799                         if (!rec->p[i])
 800                                 goto error;
 801                 }
 802                 isl_upoly_free(up2);
 803                 return up1;
 804         }
 805
 806         if (isl_upoly_is_cst(up1))
 807                 return isl_upoly_mul_cst(up1, up2);
 808
 809         return isl_upoly_mul_rec(up1, up2);
 810 error:
 811         isl_upoly_free(up1);
 812         isl_upoly_free(up2);
 813         return NULL;
 814 }
 815
 816 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
 817         unsigned n_div, __isl_take struct isl_upoly *up)
 818 {
 819         struct isl_qpolynomial *qp = NULL;
 820         unsigned total;
 821
 822         if (!dim || !up)
 823                 goto error;
 824
 825         total = isl_dim_total(dim);
 826
 827         qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
 828         if (!qp)
 829                 goto error;
 830
 831         qp->ref = 1;
 832         qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
 833         if (!qp->div)
 834                 goto error;
 835
 836         qp->dim = dim;
 837         qp->upoly = up;
 838
 839         return qp;
 840 error:
 841         isl_dim_free(dim);
 842         isl_upoly_free(up);
 843         isl_qpolynomial_free(qp);
 844         return NULL;
 845 }
 846
 847 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
 848 {
 849         if (!qp)
 850                 return NULL;
 851
 852         qp->ref++;
 853         return qp;
 854 }
 855
 856 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
 857 {
 858         struct isl_qpolynomial *dup;
 859
 860         if (!qp)
 861                 return NULL;
 862
 863         dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
 864                                     isl_upoly_copy(qp->upoly));
 865         if (!dup)
 866                 return NULL;
 867         isl_mat_free(dup->div);
 868         dup->div = isl_mat_copy(qp->div);
 869         if (!dup->div)
 870                 goto error;
 871
 872         return dup;
 873 error:
 874         isl_qpolynomial_free(dup);
 875         return NULL;
 876 }
 877
 878 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
 879 {
 880         if (!qp)
 881                 return NULL;
 882
 883         if (qp->ref == 1)
 884                 return qp;
 885         qp->ref--;
 886         return isl_qpolynomial_dup(qp);
 887 }
 888
 889 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
 890 {
 891         if (!qp)
 892                 return;
 893
 894         if (--qp->ref > 0)
 895                 return;
 896
 897         isl_dim_free(qp->dim);
 898         isl_mat_free(qp->div);
 899         isl_upoly_free(qp->upoly);
 900
 901         free(qp);
 902 }
 903
 904 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
 905 {
 906         int n_row, n_col;
 907         int equal;
 908
 909         isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
 910                                 div1->n_col >= div2->n_col, return -1);
 911
 912         if (div1->n_row == div2->n_row)
 913                 return isl_mat_is_equal(div1, div2);
 914
 915         n_row = div1->n_row;
 916         n_col = div1->n_col;
 917         div1->n_row = div2->n_row;
 918         div1->n_col = div2->n_col;
 919
 920         equal = isl_mat_is_equal(div1, div2);
 921
 922         div1->n_row = n_row;
 923         div1->n_col = n_col;
 924
 925         return equal;
 926 }
 927
 928 static void expand_row(__isl_keep isl_mat *dst, int d,
 929         __isl_keep isl_mat *src, int s, int *exp)
 930 {
 931         int i;
 932         unsigned c = src->n_col - src->n_row;
 933
 934         isl_seq_cpy(dst->row[d], src->row[s], c);
 935         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 936
 937         for (i = 0; i < s; ++i)
 938                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 939 }
 940
 941 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
 942 {
 943         int li, lj;
 944
 945         li = isl_seq_last_non_zero(div->row[i], div->n_col);
 946         lj = isl_seq_last_non_zero(div->row[j], div->n_col);
 947
 948         if (li != lj)
 949                 return li - lj;
 950
 951         return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
 952 }
 953
 954 struct isl_div_sort_info {
 955         isl_mat *div;
 956         int      row;
 957 };
 958
 959 static int div_sort_cmp(const void *p1, const void *p2)
 960 {
 961         const struct isl_div_sort_info *i1, *i2;
 962         i1 = (const struct isl_div_sort_info *) p1;
 963         i2 = (const struct isl_div_sort_info *) p2;
 964
 965         return cmp_row(i1->div, i1->row, i2->row);
 966 }
 967
 968 static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div)
 969 {
 970         int i;
 971         struct isl_div_sort_info *array = NULL;
 972         int *pos = NULL;
 973
 974         if (!div)
 975                 return NULL;
 976         if (div->n_row <= 1)
 977                 return div;
 978
 979         array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row);
 980         pos = isl_alloc_array(div->ctx, int, div->n_row);
 981         if (!array || !pos)
 982                 goto error;
 983
 984         for (i = 0; i < div->n_row; ++i) {
 985                 array[i].div = div;
 986                 array[i].row = i;
 987                 pos[i] = i;
 988         }
 989
 990         qsort(array, div->n_row, sizeof(struct isl_div_sort_info),
 991                 div_sort_cmp);
 992
 993         for (i = 0; i < div->n_row; ++i) {
 994                 int t;
 995                 if (pos[array[i].row] == i)
 996                         continue;
 997                 div = isl_mat_cow(div);
 998                 div = isl_mat_swap_rows(div, i, pos[array[i].row]);
 999                 t = pos[array[i].row];
1000                 pos[array[i].row] = pos[i];
1001                 pos[i] = t;
1002         }
1003
1004         free(array);
1005
1006         return div;
1007 error:
1008         free(pos);
1009         free(array);
1010         isl_mat_free(div);
1011         return NULL;
1012 }
1013
1014 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1015         __isl_keep isl_mat *div2, int *exp1, int *exp2)
1016 {
1017         int i, j, k;
1018         isl_mat *div = NULL;
1019         unsigned d = div1->n_col - div1->n_row;
1020
1021         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1022                                 d + div1->n_row + div2->n_row);
1023         if (!div)
1024                 return NULL;
1025
1026         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1027                 int cmp;
1028
1029                 expand_row(div, k, div1, i, exp1);
1030                 expand_row(div, k + 1, div2, j, exp2);
1031
1032                 cmp = cmp_row(div, k, k + 1);
1033                 if (cmp == 0) {
1034                         exp1[i++] = k;
1035                         exp2[j++] = k;
1036                 } else if (cmp < 0) {
1037                         exp1[i++] = k;
1038                 } else {
1039                         exp2[j++] = k;
1040                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1041                 }
1042         }
1043         for (; i < div1->n_row; ++i, ++k) {
1044                 expand_row(div, k, div1, i, exp1);
1045                 exp1[i] = k;
1046         }
1047         for (; j < div2->n_row; ++j, ++k) {
1048                 expand_row(div, k, div2, j, exp2);
1049                 exp2[j] = k;
1050         }
1051
1052         div->n_row = k;
1053         div->n_col = d + k;
1054
1055         return div;
1056 }
1057
1058 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1059         int *exp, int first)
1060 {
1061         int i;
1062         struct isl_upoly_rec *rec;
1063
1064         if (isl_upoly_is_cst(up))
1065                 return up;
1066
1067         if (up->var < first)
1068                 return up;
1069
1070         if (exp[up->var - first] == up->var - first)
1071                 return up;
1072
1073         up = isl_upoly_cow(up);
1074         if (!up)
1075                 goto error;
1076
1077         up->var = exp[up->var - first] + first;
1078
1079         rec = isl_upoly_as_rec(up);
1080         if (!rec)
1081                 goto error;
1082
1083         for (i = 0; i < rec->n; ++i) {
1084                 rec->p[i] = expand(rec->p[i], exp, first);
1085                 if (!rec->p[i])
1086                         goto error;
1087         }
1088
1089         return up;
1090 error:
1091         isl_upoly_free(up);
1092         return NULL;
1093 }
1094
1095 static __isl_give isl_qpolynomial *with_merged_divs(
1096         __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1097                                           __isl_take isl_qpolynomial *qp2),
1098         __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1099 {
1100         int *exp1 = NULL;
1101         int *exp2 = NULL;
1102         isl_mat *div = NULL;
1103
1104         qp1 = isl_qpolynomial_cow(qp1);
1105         qp2 = isl_qpolynomial_cow(qp2);
1106
1107         if (!qp1 || !qp2)
1108                 goto error;
1109
1110         isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1111                                 qp1->div->n_col >= qp2->div->n_col, goto error);
1112
1113         exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1114         exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1115         if (!exp1 || !exp2)
1116                 goto error;
1117
1118         div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1119         if (!div)
1120                 goto error;
1121
1122         isl_mat_free(qp1->div);
1123         qp1->div = isl_mat_copy(div);
1124         isl_mat_free(qp2->div);
1125         qp2->div = isl_mat_copy(div);
1126
1127         qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1128         qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1129
1130         if (!qp1->upoly || !qp2->upoly)
1131                 goto error;
1132
1133         isl_mat_free(div);
1134         free(exp1);
1135         free(exp2);
1136
1137         return fn(qp1, qp2);
1138 error:
1139         isl_mat_free(div);
1140         free(exp1);
1141         free(exp2);
1142         isl_qpolynomial_free(qp1);
1143         isl_qpolynomial_free(qp2);
1144         return NULL;
1145 }
1146
1147 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1148         __isl_take isl_qpolynomial *qp2)
1149 {
1150         qp1 = isl_qpolynomial_cow(qp1);
1151
1152         if (!qp1 || !qp2)
1153                 goto error;
1154
1155         if (qp1->div->n_row < qp2->div->n_row)
1156                 return isl_qpolynomial_add(qp2, qp1);
1157
1158         isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1159         if (!compatible_divs(qp1->div, qp2->div))
1160                 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1161
1162         qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1163         if (!qp1->upoly)
1164                 goto error;
1165
1166         isl_qpolynomial_free(qp2);
1167
1168         return qp1;
1169 error:
1170         isl_qpolynomial_free(qp1);
1171         isl_qpolynomial_free(qp2);
1172         return NULL;
1173 }
1174
1175 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1176         __isl_take isl_qpolynomial *qp2)
1177 {
1178         return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1179 }
1180
1181 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1182 {
1183         qp = isl_qpolynomial_cow(qp);
1184
1185         if (!qp)
1186                 return NULL;
1187
1188         qp->upoly = isl_upoly_neg(qp->upoly);
1189         if (!qp->upoly)
1190                 goto error;
1191
1192         return qp;
1193 error:
1194         isl_qpolynomial_free(qp);
1195         return NULL;
1196 }
1197
1198 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1199         __isl_take isl_qpolynomial *qp2)
1200 {
1201         qp1 = isl_qpolynomial_cow(qp1);
1202
1203         if (!qp1 || !qp2)
1204                 goto error;
1205
1206         if (qp1->div->n_row < qp2->div->n_row)
1207                 return isl_qpolynomial_mul(qp2, qp1);
1208
1209         isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1210         if (!compatible_divs(qp1->div, qp2->div))
1211                 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1212
1213         qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1214         if (!qp1->upoly)
1215                 goto error;
1216
1217         isl_qpolynomial_free(qp2);
1218
1219         return qp1;
1220 error:
1221         isl_qpolynomial_free(qp1);
1222         isl_qpolynomial_free(qp2);
1223         return NULL;
1224 }
1225
1226 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1227 {
1228         return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1229 }
1230
1231 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1232 {
1233         return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1234 }
1235
1236 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1237 {
1238         return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1239 }
1240
1241 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1242         isl_int v)
1243 {
1244         struct isl_qpolynomial *qp;
1245         struct isl_upoly_cst *cst;
1246
1247         qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1248         if (!qp)
1249                 return NULL;
1250
1251         cst = isl_upoly_as_cst(qp->upoly);
1252         isl_int_set(cst->n, v);
1253
1254         return qp;
1255 error:
1256         isl_qpolynomial_free(qp);
1257         return NULL;
1258 }
1259
1260 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1261         isl_int *n, isl_int *d)
1262 {
1263         struct isl_upoly_cst *cst;
1264
1265         if (!qp)
1266                 return -1;
1267
1268         if (!isl_upoly_is_cst(qp->upoly))
1269                 return 0;
1270
1271         cst = isl_upoly_as_cst(qp->upoly);
1272         if (!cst)
1273                 return -1;
1274
1275         if (n)
1276                 isl_int_set(*n, cst->n);
1277         if (d)
1278                 isl_int_set(*d, cst->d);
1279
1280         return 1;
1281 }
1282
1283 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1284 {
1285         int is_cst;
1286         struct isl_upoly_rec *rec;
1287
1288         if (!up)
1289                 return -1;
1290
1291         if (up->var < 0)
1292                 return 1;
1293
1294         rec = isl_upoly_as_rec(up);
1295         if (!rec)
1296                 return -1;
1297
1298         if (rec->n > 2)
1299                 return 0;
1300
1301         isl_assert(up->ctx, rec->n > 1, return -1);
1302
1303         is_cst = isl_upoly_is_cst(rec->p[1]);
1304         if (is_cst < 0)
1305                 return -1;
1306         if (!is_cst)
1307                 return 0;
1308
1309         return isl_upoly_is_affine(rec->p[0]);
1310 }
1311
1312 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1313 {
1314         if (!qp)
1315                 return -1;
1316
1317         if (qp->div->n_row > 0)
1318                 return 0;
1319
1320         return isl_upoly_is_affine(qp->upoly);
1321 }
1322
1323 static void update_coeff(__isl_keep isl_vec *aff,
1324         __isl_keep struct isl_upoly_cst *cst, int pos)
1325 {
1326         isl_int gcd;
1327         isl_int f;
1328
1329         if (isl_int_is_zero(cst->n))
1330                 return;
1331
1332         isl_int_init(gcd);
1333         isl_int_init(f);
1334         isl_int_gcd(gcd, cst->d, aff->el[0]);
1335         isl_int_divexact(f, cst->d, gcd);
1336         isl_int_divexact(gcd, aff->el[0], gcd);
1337         isl_seq_scale(aff->el, aff->el, f, aff->size);
1338         isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1339         isl_int_clear(gcd);
1340         isl_int_clear(f);
1341 }
1342
1343 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1344         __isl_keep isl_vec *aff)
1345 {
1346         struct isl_upoly_cst *cst;
1347         struct isl_upoly_rec *rec;
1348
1349         if (!up || !aff)
1350                 return -1;
1351
1352         if (up->var < 0) {
1353                 struct isl_upoly_cst *cst;
1354
1355                 cst = isl_upoly_as_cst(up);
1356                 if (!cst)
1357                         return -1;
1358                 update_coeff(aff, cst, 0);
1359                 return 0;
1360         }
1361
1362         rec = isl_upoly_as_rec(up);
1363         if (!rec)
1364                 return -1;
1365         isl_assert(up->ctx, rec->n == 2, return -1);
1366
1367         cst = isl_upoly_as_cst(rec->p[1]);
1368         if (!cst)
1369                 return -1;
1370         update_coeff(aff, cst, 1 + up->var);
1371
1372         return isl_upoly_update_affine(rec->p[0], aff);
1373 }
1374
1375 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1376         __isl_keep isl_qpolynomial *qp)
1377 {
1378         isl_vec *aff;
1379         unsigned d;
1380
1381         if (!qp)
1382                 return NULL;
1383
1384         isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1385         d = isl_dim_total(qp->dim);
1386         aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1387         if (!aff)
1388                 return NULL;
1389
1390         isl_seq_clr(aff->el + 1, 1 + d);
1391         isl_int_set_si(aff->el[0], 1);
1392
1393         if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1394                 goto error;
1395
1396         return aff;
1397 error:
1398         isl_vec_free(aff);
1399         return NULL;
1400 }
1401
1402 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1403         __isl_keep isl_qpolynomial *qp2)
1404 {
1405         if (!qp1 || !qp2)
1406                 return -1;
1407
1408         return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1409 }
1410
1411 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1412 {
1413         int i;
1414         struct isl_upoly_rec *rec;
1415
1416         if (isl_upoly_is_cst(up)) {
1417                 struct isl_upoly_cst *cst;
1418                 cst = isl_upoly_as_cst(up);
1419                 if (!cst)
1420                         return;
1421                 isl_int_lcm(*d, *d, cst->d);
1422                 return;
1423         }
1424
1425         rec = isl_upoly_as_rec(up);
1426         if (!rec)
1427                 return;
1428
1429         for (i = 0; i < rec->n; ++i)
1430                 upoly_update_den(rec->p[i], d);
1431 }
1432
1433 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1434 {
1435         isl_int_set_si(*d, 1);
1436         if (!qp)
1437                 return;
1438         upoly_update_den(qp->upoly, d);
1439 }
1440
1441 __isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
1442 {
1443         int i;
1444         struct isl_upoly *up;
1445         struct isl_upoly_rec *rec;
1446         struct isl_upoly_cst *cst;
1447
1448         rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1449         if (!rec)
1450                 return NULL;
1451         for (i = 0; i < 1 + power; ++i) {
1452                 rec->p[i] = isl_upoly_zero(ctx);
1453                 if (!rec->p[i])
1454                         goto error;
1455                 rec->n++;
1456         }
1457         cst = isl_upoly_as_cst(rec->p[power]);
1458         isl_int_set_si(cst->n, 1);
1459
1460         return &rec->up;
1461 error:
1462         isl_upoly_free(&rec->up);
1463         return NULL;
1464 }
1465
1466 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
1467         int pos, int power)
1468 {
1469         struct isl_ctx *ctx;
1470
1471         if (!dim)
1472                 return NULL;
1473
1474         ctx = dim->ctx;
1475
1476         return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
1477 }
1478
1479 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1480         enum isl_dim_type type, unsigned pos)
1481 {
1482         if (!dim)
1483                 return NULL;
1484
1485         isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1486         isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1487
1488         if (type == isl_dim_set)
1489                 pos += isl_dim_size(dim, isl_dim_param);
1490
1491         return isl_qpolynomial_pow(dim, pos, 1);
1492 error:
1493         isl_dim_free(dim);
1494         return NULL;
1495 }
1496
1497 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
1498         int power)
1499 {
1500         struct isl_qpolynomial *qp = NULL;
1501         struct isl_upoly_rec *rec;
1502         struct isl_upoly_cst *cst;
1503         int i;
1504         int pos;
1505
1506         if (!div)
1507                 return NULL;
1508         isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
1509
1510         pos = isl_dim_total(div->bmap->dim);
1511         rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
1512         qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1,
1513                                    &rec->up);
1514         if (!qp)
1515                 goto error;
1516
1517         isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
1518         isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
1519
1520         for (i = 0; i < 1 + power; ++i) {
1521                 rec->p[i] = isl_upoly_zero(div->ctx);
1522                 if (!rec->p[i])
1523                         goto error;
1524                 rec->n++;
1525         }
1526         cst = isl_upoly_as_cst(rec->p[power]);
1527         isl_int_set_si(cst->n, 1);
1528
1529         isl_div_free(div);
1530
1531         return qp;
1532 error:
1533         isl_qpolynomial_free(qp);
1534         isl_div_free(div);
1535         return NULL;
1536 }
1537
1538 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
1539 {
1540         return isl_qpolynomial_div_pow(div, 1);
1541 }
1542
1543 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
1544         const isl_int n, const isl_int d)
1545 {
1546         struct isl_qpolynomial *qp;
1547         struct isl_upoly_cst *cst;
1548
1549         qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1550         if (!qp)
1551                 return NULL;
1552
1553         cst = isl_upoly_as_cst(qp->upoly);
1554         isl_int_set(cst->n, n);
1555         isl_int_set(cst->d, d);
1556
1557         return qp;
1558 error:
1559         isl_qpolynomial_free(qp);
1560         return NULL;
1561 }
1562
1563 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
1564 {
1565         struct isl_upoly_rec *rec;
1566         int i;
1567
1568         if (!up)
1569                 return -1;
1570
1571         if (isl_upoly_is_cst(up))
1572                 return 0;
1573
1574         if (up->var < d)
1575                 active[up->var] = 1;
1576
1577         rec = isl_upoly_as_rec(up);
1578         for (i = 0; i < rec->n; ++i)
1579                 if (up_set_active(rec->p[i], active, d) < 0)
1580                         return -1;
1581
1582         return 0;
1583 }
1584
1585 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
1586 {
1587         int i, j;
1588         int d = isl_dim_total(qp->dim);
1589
1590         if (!qp || !active)
1591                 return -1;
1592
1593         for (i = 0; i < d; ++i)
1594                 for (j = 0; j < qp->div->n_row; ++j) {
1595                         if (isl_int_is_zero(qp->div->row[j][2 + i]))
1596                                 continue;
1597                         active[i] = 1;
1598                         break;
1599                 }
1600
1601         return up_set_active(qp->upoly, active, d);
1602 }
1603
1604 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
1605         enum isl_dim_type type, unsigned first, unsigned n)
1606 {
1607         int i;
1608         int *active = NULL;
1609         int involves = 0;
1610
1611         if (!qp)
1612                 return -1;
1613         if (n == 0)
1614                 return 0;
1615
1616         isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1617                         return -1);
1618         isl_assert(qp->dim->ctx, type == isl_dim_param ||
1619                                  type == isl_dim_set, return -1);
1620
1621         active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
1622         if (set_active(qp, active) < 0)
1623                 goto error;
1624
1625         if (type == isl_dim_set)
1626                 first += isl_dim_size(qp->dim, isl_dim_param);
1627         for (i = 0; i < n; ++i)
1628                 if (active[first + i]) {
1629                         involves = 1;
1630                         break;
1631                 }
1632
1633         free(active);
1634
1635         return involves;
1636 error:
1637         free(active);
1638         return -1;
1639 }
1640
1641 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
1642         unsigned first, unsigned n)
1643 {
1644         int i;
1645         struct isl_upoly_rec *rec;
1646
1647         if (!up)
1648                 return NULL;
1649         if (n == 0 || up->var < 0 || up->var < first)
1650                 return up;
1651         if (up->var < first + n) {
1652                 up = replace_by_constant_term(up);
1653                 return isl_upoly_drop(up, first, n);
1654         }
1655         up = isl_upoly_cow(up);
1656         if (!up)
1657                 return NULL;
1658         up->var -= n;
1659         rec = isl_upoly_as_rec(up);
1660         if (!rec)
1661                 goto error;
1662
1663         for (i = 0; i < rec->n; ++i) {
1664                 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
1665                 if (!rec->p[i])
1666                         goto error;
1667         }
1668
1669         return up;
1670 error:
1671         isl_upoly_free(up);
1672         return NULL;
1673 }
1674
1675 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
1676         __isl_take isl_qpolynomial *qp,
1677         enum isl_dim_type type, unsigned first, unsigned n)
1678 {
1679         if (!qp)
1680                 return NULL;
1681         if (n == 0)
1682                 return qp;
1683
1684         qp = isl_qpolynomial_cow(qp);
1685         if (!qp)
1686                 return NULL;
1687
1688         isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
1689                         goto error);
1690         isl_assert(qp->dim->ctx, type == isl_dim_param ||
1691                                  type == isl_dim_set, goto error);
1692
1693         qp->dim = isl_dim_drop(qp->dim, type, first, n);
1694         if (!qp->dim)
1695                 goto error;
1696
1697         if (type == isl_dim_set)
1698                 first += isl_dim_size(qp->dim, isl_dim_param);
1699
1700         qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
1701         if (!qp->div)
1702                 goto error;
1703
1704         qp->upoly = isl_upoly_drop(qp->upoly, first, n);
1705         if (!qp->upoly)
1706                 goto error;
1707
1708         return qp;
1709 error:
1710         isl_qpolynomial_free(qp);
1711         return NULL;
1712 }
1713
1714 #undef PW
1715 #define PW isl_pw_qpolynomial
1716 #undef EL
1717 #define EL isl_qpolynomial
1718 #undef IS_ZERO
1719 #define IS_ZERO is_zero
1720 #undef FIELD
1721 #define FIELD qp
1722 #undef ADD
1723 #define ADD(d,e1,e2)    isl_qpolynomial_add(e1,e2)
1724
1725 #include <isl_pw_templ.c>
1726
1727 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
1728 {
1729         if (!pwqp)
1730                 return -1;
1731
1732         if (pwqp->n != -1)
1733                 return 0;
1734
1735         if (!isl_set_fast_is_universe(pwqp->p[0].set))
1736                 return 0;
1737
1738         return isl_qpolynomial_is_one(pwqp->p[0].qp);
1739 }
1740
1741 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1742         __isl_take isl_pw_qpolynomial *pwqp1,
1743         __isl_take isl_pw_qpolynomial *pwqp2)
1744 {
1745         int i, j, n;
1746         struct isl_pw_qpolynomial *res;
1747         isl_set *set;
1748
1749         if (!pwqp1 || !pwqp2)
1750                 goto error;
1751
1752         isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
1753                         goto error);
1754
1755         if (isl_pw_qpolynomial_is_zero(pwqp1)) {
1756                 isl_pw_qpolynomial_free(pwqp2);
1757                 return pwqp1;
1758         }
1759
1760         if (isl_pw_qpolynomial_is_zero(pwqp2)) {
1761                 isl_pw_qpolynomial_free(pwqp1);
1762                 return pwqp2;
1763         }
1764
1765         if (isl_pw_qpolynomial_is_one(pwqp1)) {
1766                 isl_pw_qpolynomial_free(pwqp1);
1767                 return pwqp2;
1768         }
1769
1770         if (isl_pw_qpolynomial_is_one(pwqp2)) {
1771                 isl_pw_qpolynomial_free(pwqp2);
1772                 return pwqp1;
1773         }
1774
1775         n = pwqp1->n * pwqp2->n;
1776         res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
1777
1778         for (i = 0; i < pwqp1->n; ++i) {
1779                 for (j = 0; j < pwqp2->n; ++j) {
1780                         struct isl_set *common;
1781                         struct isl_qpolynomial *prod;
1782                         common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
1783                                                 isl_set_copy(pwqp2->p[j].set));
1784                         if (isl_set_fast_is_empty(common)) {
1785                                 isl_set_free(common);
1786                                 continue;
1787                         }
1788
1789                         prod = isl_qpolynomial_mul(
1790                                 isl_qpolynomial_copy(pwqp1->p[i].qp),
1791                                 isl_qpolynomial_copy(pwqp2->p[j].qp));
1792
1793                         res = isl_pw_qpolynomial_add_piece(res, common, prod);
1794                 }
1795         }
1796
1797         isl_pw_qpolynomial_free(pwqp1);
1798         isl_pw_qpolynomial_free(pwqp2);
1799
1800         return res;
1801 error:
1802         isl_pw_qpolynomial_free(pwqp1);
1803         isl_pw_qpolynomial_free(pwqp2);
1804         return NULL;
1805 }
1806
1807 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1808         __isl_take isl_pw_qpolynomial *pwqp)
1809 {
1810         int i, j, n;
1811         struct isl_pw_qpolynomial *res;
1812         isl_set *set;
1813
1814         if (!pwqp)
1815                 return NULL;
1816
1817         if (isl_pw_qpolynomial_is_zero(pwqp))
1818                 return pwqp;
1819
1820         pwqp = isl_pw_qpolynomial_cow(pwqp);
1821
1822         for (i = 0; i < pwqp->n; ++i) {
1823                 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
1824                 if (!pwqp->p[i].qp)
1825                         goto error;
1826         }
1827
1828         return pwqp;
1829 error:
1830         isl_pw_qpolynomial_free(pwqp);
1831         return NULL;
1832 }
1833
1834 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1835         __isl_take isl_pw_qpolynomial *pwqp1,
1836         __isl_take isl_pw_qpolynomial *pwqp2)
1837 {
1838         return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
1839 }
1840
1841 __isl_give struct isl_upoly *isl_upoly_eval(
1842         __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
1843 {
1844         int i;
1845         struct isl_upoly_rec *rec;
1846         struct isl_upoly *res;
1847         struct isl_upoly *base;
1848
1849         if (isl_upoly_is_cst(up)) {
1850                 isl_vec_free(vec);
1851                 return up;
1852         }
1853
1854         rec = isl_upoly_as_rec(up);
1855         if (!rec)
1856                 goto error;
1857
1858         isl_assert(up->ctx, rec->n >= 1, goto error);
1859
1860         base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
1861
1862         res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
1863                                 isl_vec_copy(vec));
1864
1865         for (i = rec->n - 2; i >= 0; --i) {
1866                 res = isl_upoly_mul(res, isl_upoly_copy(base));
1867                 res = isl_upoly_sum(res,
1868                             isl_upoly_eval(isl_upoly_copy(rec->p[i]),
1869                                                             isl_vec_copy(vec)));
1870         }
1871
1872         isl_upoly_free(base);
1873         isl_upoly_free(up);
1874         isl_vec_free(vec);
1875         return res;
1876 error:
1877         isl_upoly_free(up);
1878         isl_vec_free(vec);
1879         return NULL;
1880 }
1881
1882 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
1883         __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
1884 {
1885         isl_vec *ext;
1886         struct isl_upoly *up;
1887         isl_dim *dim;
1888
1889         if (!qp || !pnt)
1890                 goto error;
1891         isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
1892
1893         if (qp->div->n_row == 0)
1894                 ext = isl_vec_copy(pnt->vec);
1895         else {
1896                 int i;
1897                 unsigned dim = isl_dim_total(qp->dim);
1898                 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
1899                 if (!ext)
1900                         goto error;
1901
1902                 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
1903                 for (i = 0; i < qp->div->n_row; ++i) {
1904                         isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
1905                                                 1 + dim + i, &ext->el[1+dim+i]);
1906                         isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
1907                                         qp->div->row[i][0]);
1908                 }
1909         }
1910
1911         up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
1912         if (!up)
1913                 goto error;
1914
1915         dim = isl_dim_copy(qp->dim);
1916         isl_qpolynomial_free(qp);
1917         isl_point_free(pnt);
1918
1919         return isl_qpolynomial_alloc(dim, 0, up);
1920 error:
1921         isl_qpolynomial_free(qp);
1922         isl_point_free(pnt);
1923         return NULL;
1924 }
1925
1926 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
1927         __isl_keep struct isl_upoly_cst *cst2)
1928 {
1929         int cmp;
1930         isl_int t;
1931         isl_int_init(t);
1932         isl_int_mul(t, cst1->n, cst2->d);
1933         isl_int_submul(t, cst2->n, cst1->d);
1934         cmp = isl_int_sgn(t);
1935         isl_int_clear(t);
1936         return cmp;
1937 }
1938
1939 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
1940         __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1941 {
1942         struct isl_upoly_cst *cst1, *cst2;
1943         int cmp;
1944
1945         if (!qp1 || !qp2)
1946                 goto error;
1947         isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
1948         isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
1949         cst1 = isl_upoly_as_cst(qp1->upoly);
1950         cst2 = isl_upoly_as_cst(qp2->upoly);
1951         cmp = isl_upoly_cmp(cst1, cst2);
1952
1953         if (cmp <= 0) {
1954                 isl_qpolynomial_free(qp2);
1955         } else {
1956                 isl_qpolynomial_free(qp1);
1957                 qp1 = qp2;
1958         }
1959         return qp1;
1960 error:
1961         isl_qpolynomial_free(qp1);
1962         isl_qpolynomial_free(qp2);
1963         return NULL;
1964 }
1965
1966 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
1967         __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1968 {
1969         struct isl_upoly_cst *cst1, *cst2;
1970         int cmp;
1971
1972         if (!qp1 || !qp2)
1973                 goto error;
1974         isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
1975         isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
1976         cst1 = isl_upoly_as_cst(qp1->upoly);
1977         cst2 = isl_upoly_as_cst(qp2->upoly);
1978         cmp = isl_upoly_cmp(cst1, cst2);
1979
1980         if (cmp >= 0) {
1981                 isl_qpolynomial_free(qp2);
1982         } else {
1983                 isl_qpolynomial_free(qp1);
1984                 qp1 = qp2;
1985         }
1986         return qp1;
1987 error:
1988         isl_qpolynomial_free(qp1);
1989         isl_qpolynomial_free(qp2);
1990         return NULL;
1991 }
1992
1993 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
1994         __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
1995 {
1996         unsigned total;
1997         unsigned g_pos;
1998         int *exp;
1999
2000         if (n == 0)
2001                 return qp;
2002
2003         qp = isl_qpolynomial_cow(qp);
2004         if (!qp)
2005                 return NULL;
2006
2007         g_pos = pos(qp->dim, type) + isl_dim_size(qp->dim, type);
2008
2009         qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2010         if (!qp->div)
2011                 goto error;
2012
2013         total = qp->div->n_col - 2;
2014         if (total > g_pos) {
2015                 int i;
2016                 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2017                 if (!exp)
2018                         goto error;
2019                 for (i = 0; i < total - g_pos; ++i)
2020                         exp[i] = i + n;
2021                 qp->upoly = expand(qp->upoly, exp, g_pos);
2022                 free(exp);
2023                 if (!qp->upoly)
2024                         goto error;
2025         }
2026
2027         qp->dim = isl_dim_add(qp->dim, type, n);
2028         if (!qp->dim)
2029                 goto error;
2030
2031         return qp;
2032 error:
2033         isl_qpolynomial_free(qp);
2034         return NULL;
2035 }
2036
2037 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2038         __isl_take isl_pw_qpolynomial *pwqp,
2039         enum isl_dim_type type, unsigned n)
2040 {
2041         int i;
2042
2043         if (n == 0)
2044                 return pwqp;
2045
2046         pwqp = isl_pw_qpolynomial_cow(pwqp);
2047         if (!pwqp)
2048                 return NULL;
2049
2050         pwqp->dim = isl_dim_add(pwqp->dim, type, n);
2051         if (!pwqp->dim)
2052                 goto error;
2053
2054         for (i = 0; i < pwqp->n; ++i) {
2055                 pwqp->p[i].set = isl_set_add(pwqp->p[i].set, type, n);
2056                 if (!pwqp->p[i].set)
2057                         goto error;
2058                 pwqp->p[i].qp = isl_qpolynomial_add_dims(pwqp->p[i].qp, type, n);
2059                 if (!pwqp->p[i].qp)
2060                         goto error;
2061         }
2062
2063         return pwqp;
2064 error:
2065         isl_pw_qpolynomial_free(pwqp);
2066         return NULL;
2067 }
2068
2069 static int *reordering_move(isl_ctx *ctx,
2070         unsigned len, unsigned dst, unsigned src, unsigned n)
2071 {
2072         int i;
2073         int *reordering;
2074
2075         reordering = isl_alloc_array(ctx, int, len);
2076         if (!reordering)
2077                 return NULL;
2078
2079         if (dst <= src) {
2080                 for (i = 0; i < dst; ++i)
2081                         reordering[i] = i;
2082                 for (i = 0; i < n; ++i)
2083                         reordering[src + i] = dst + i;
2084                 for (i = 0; i < src - dst; ++i)
2085                         reordering[dst + i] = dst + n + i;
2086                 for (i = 0; i < len - src - n; ++i)
2087                         reordering[src + n + i] = src + n + i;
2088         } else {
2089                 for (i = 0; i < src; ++i)
2090                         reordering[i] = i;
2091                 for (i = 0; i < n; ++i)
2092                         reordering[src + i] = dst + i;
2093                 for (i = 0; i < dst - src; ++i)
2094                         reordering[src + n + i] = src + i;
2095                 for (i = 0; i < len - dst - n; ++i)
2096                         reordering[dst + n + i] = dst + n + i;
2097         }
2098
2099         return reordering;
2100 }
2101
2102 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
2103         int *r)
2104 {
2105         int i;
2106         struct isl_upoly_rec *rec;
2107         struct isl_upoly *base;
2108         struct isl_upoly *res;
2109
2110         if (isl_upoly_is_cst(up))
2111                 return up;
2112
2113         rec = isl_upoly_as_rec(up);
2114         if (!rec)
2115                 goto error;
2116
2117         isl_assert(up->ctx, rec->n >= 1, goto error);
2118
2119         base = isl_upoly_pow(up->ctx, r[up->var], 1);
2120         res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
2121
2122         for (i = rec->n - 2; i >= 0; --i) {
2123                 res = isl_upoly_mul(res, isl_upoly_copy(base));
2124                 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
2125         }
2126
2127         isl_upoly_free(base);
2128         isl_upoly_free(up);
2129
2130         return res;
2131 error:
2132         isl_upoly_free(up);
2133         return NULL;
2134 }
2135
2136 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2137         __isl_take isl_qpolynomial *qp,
2138         enum isl_dim_type dst_type, unsigned dst_pos,
2139         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2140 {
2141         unsigned g_dst_pos;
2142         unsigned g_src_pos;
2143         int *reordering;
2144
2145         qp = isl_qpolynomial_cow(qp);
2146         if (!qp)
2147                 return NULL;
2148
2149         isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2150                 goto error);
2151
2152         g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2153         g_src_pos = pos(qp->dim, src_type) + src_pos;
2154         if (dst_type > src_type)
2155                 g_dst_pos -= n;
2156
2157         qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2158         qp->div = sort_divs(qp->div);
2159         if (!qp->div)
2160                 goto error;
2161
2162         reordering = reordering_move(qp->dim->ctx,
2163                                 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2164         if (!reordering)
2165                 goto error;
2166
2167         qp->upoly = reorder(qp->upoly, reordering);
2168         free(reordering);
2169         if (!qp->upoly)
2170                 goto error;
2171
2172         qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2173         if (!qp->dim)
2174                 goto error;
2175
2176         return qp;
2177 error:
2178         isl_qpolynomial_free(qp);
2179         return NULL;
2180 }
2181
2182 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_move(
2183         __isl_take isl_pw_qpolynomial *pwqp,
2184         enum isl_dim_type dst_type, unsigned dst_pos,
2185         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2186 {
2187         int i;
2188
2189         pwqp = isl_pw_qpolynomial_cow(pwqp);
2190         if (!pwqp)
2191                 return NULL;
2192
2193         pwqp->dim = isl_dim_move(pwqp->dim,
2194                                     dst_type, dst_pos, src_type, src_pos, n);
2195         if (!pwqp->dim)
2196                 goto error;
2197
2198         for (i = 0; i < pwqp->n; ++i) {
2199                 pwqp->p[i].set = isl_set_move_dims(pwqp->p[i].set,
2200                                                 dst_type, dst_pos,
2201                                                 src_type, src_pos, n);
2202                 if (!pwqp->p[i].set)
2203                         goto error;
2204                 pwqp->p[i].qp = isl_qpolynomial_move_dims(pwqp->p[i].qp,
2205                                         dst_type, dst_pos, src_type, src_pos, n);
2206                 if (!pwqp->p[i].qp)
2207                         goto error;
2208         }
2209
2210         return pwqp;
2211 error:
2212         isl_pw_qpolynomial_free(pwqp);
2213         return NULL;
2214 }
2215
2216 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
2217         __isl_take isl_mat *div)
2218 {
2219         isl_term *term;
2220         int n;
2221
2222         if (!dim || !div)
2223                 goto error;
2224
2225         n = isl_dim_total(dim) + div->n_row;
2226
2227         term = isl_calloc(dim->ctx, struct isl_term,
2228                         sizeof(struct isl_term) + (n - 1) * sizeof(int));
2229         if (!term)
2230                 goto error;
2231
2232         term->ref = 1;
2233         term->dim = dim;
2234         term->div = div;
2235         isl_int_init(term->n);
2236         isl_int_init(term->d);
2237
2238         return term;
2239 error:
2240         isl_dim_free(dim);
2241         isl_mat_free(div);
2242         return NULL;
2243 }
2244
2245 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
2246 {
2247         if (!term)
2248                 return NULL;
2249
2250         term->ref++;
2251         return term;
2252 }
2253
2254 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
2255 {
2256         int i;
2257         isl_term *dup;
2258         unsigned total;
2259
2260         if (term)
2261                 return NULL;
2262
2263         total = isl_dim_total(term->dim) + term->div->n_row;
2264
2265         dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
2266         if (!dup)
2267                 return NULL;
2268
2269         isl_int_set(dup->n, term->n);
2270         isl_int_set(dup->d, term->d);
2271
2272         for (i = 0; i < total; ++i)
2273                 dup->pow[i] = term->pow[i];
2274
2275         return dup;
2276 }
2277
2278 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
2279 {
2280         if (!term)
2281                 return NULL;
2282
2283         if (term->ref == 1)
2284                 return term;
2285         term->ref--;
2286         return isl_term_dup(term);
2287 }
2288
2289 void isl_term_free(__isl_take isl_term *term)
2290 {
2291         if (!term)
2292                 return;
2293
2294         if (--term->ref > 0)
2295                 return;
2296
2297         isl_dim_free(term->dim);
2298         isl_mat_free(term->div);
2299         isl_int_clear(term->n);
2300         isl_int_clear(term->d);
2301         free(term);
2302 }
2303
2304 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
2305 {
2306         if (!term)
2307                 return 0;
2308
2309         switch (type) {
2310         case isl_dim_param:
2311         case isl_dim_in:
2312         case isl_dim_out:       return isl_dim_size(term->dim, type);
2313         case isl_dim_div:       return term->div->n_row;
2314         case isl_dim_all:       return isl_dim_total(term->dim) + term->div->n_row;
2315         }
2316 }
2317
2318 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
2319 {
2320         return term ? term->dim->ctx : NULL;
2321 }
2322
2323 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
2324 {
2325         if (!term)
2326                 return;
2327         isl_int_set(*n, term->n);
2328 }
2329
2330 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
2331 {
2332         if (!term)
2333                 return;
2334         isl_int_set(*d, term->d);
2335 }
2336
2337 int isl_term_get_exp(__isl_keep isl_term *term,
2338         enum isl_dim_type type, unsigned pos)
2339 {
2340         if (!term)
2341                 return -1;
2342
2343         isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
2344
2345         if (type >= isl_dim_set)
2346                 pos += isl_dim_size(term->dim, isl_dim_param);
2347         if (type >= isl_dim_div)
2348                 pos += isl_dim_size(term->dim, isl_dim_set);
2349
2350         return term->pow[pos];
2351 }
2352
2353 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
2354 {
2355         isl_basic_map *bmap;
2356         unsigned total;
2357         int k;
2358
2359         if (!term)
2360                 return NULL;
2361
2362         isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
2363                         return NULL);
2364
2365         total = term->div->n_col - term->div->n_row - 2;
2366         /* No nested divs for now */
2367         isl_assert(term->dim->ctx,
2368                 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
2369                                         term->div->n_row) == -1,
2370                 return NULL);
2371
2372         bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
2373         if ((k = isl_basic_map_alloc_div(bmap)) < 0)
2374                 goto error;
2375
2376         isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
2377
2378         return isl_basic_map_div(bmap, k);
2379 error:
2380         isl_basic_map_free(bmap);
2381         return NULL;
2382 }
2383
2384 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
2385         int (*fn)(__isl_take isl_term *term, void *user),
2386         __isl_take isl_term *term, void *user)
2387 {
2388         int i;
2389         struct isl_upoly_rec *rec;
2390
2391         if (!up || !term)
2392                 goto error;
2393
2394         if (isl_upoly_is_zero(up))
2395                 return term;
2396
2397         isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
2398         isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
2399         isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
2400
2401         if (isl_upoly_is_cst(up)) {
2402                 struct isl_upoly_cst *cst;
2403                 cst = isl_upoly_as_cst(up);
2404                 if (!cst)
2405                         goto error;
2406                 term = isl_term_cow(term);
2407                 if (!term)
2408                         goto error;
2409                 isl_int_set(term->n, cst->n);
2410                 isl_int_set(term->d, cst->d);
2411                 if (fn(isl_term_copy(term), user) < 0)
2412                         goto error;
2413                 return term;
2414         }
2415
2416         rec = isl_upoly_as_rec(up);
2417         if (!rec)
2418                 goto error;
2419
2420         for (i = 0; i < rec->n; ++i) {
2421                 term = isl_term_cow(term);
2422                 if (!term)
2423                         goto error;
2424                 term->pow[up->var] = i;
2425                 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
2426                 if (!term)
2427                         goto error;
2428         }
2429         term->pow[up->var] = 0;
2430
2431         return term;
2432 error:
2433         isl_term_free(term);
2434         return NULL;
2435 }
2436
2437 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
2438         int (*fn)(__isl_take isl_term *term, void *user), void *user)
2439 {
2440         isl_term *term;
2441
2442         if (!qp)
2443                 return -1;
2444
2445         term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
2446         if (!term)
2447                 return -1;
2448
2449         term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
2450
2451         isl_term_free(term);
2452
2453         return term ? 0 : -1;
2454 }
2455
2456 int isl_pw_qpolynomial_foreach_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2457         int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2458                     void *user), void *user)
2459 {
2460         int i;
2461
2462         if (!pwqp)
2463                 return -1;
2464
2465         for (i = 0; i < pwqp->n; ++i)
2466                 if (fn(isl_set_copy(pwqp->p[i].set),
2467                                 isl_qpolynomial_copy(pwqp->p[i].qp), user) < 0)
2468                         return -1;
2469
2470         return 0;
2471 }
2472
2473 static int any_divs(__isl_keep isl_set *set)
2474 {
2475         int i;
2476
2477         if (!set)
2478                 return -1;
2479
2480         for (i = 0; i < set->n; ++i)
2481                 if (set->p[i]->n_div > 0)
2482                         return 1;
2483
2484         return 0;
2485 }
2486
2487 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
2488         __isl_take isl_dim *dim)
2489 {
2490         if (!qp || !dim)
2491                 goto error;
2492
2493         if (isl_dim_equal(qp->dim, dim)) {
2494                 isl_dim_free(dim);
2495                 return qp;
2496         }
2497
2498         qp = isl_qpolynomial_cow(qp);
2499         if (!qp)
2500                 goto error;
2501
2502         if (qp->div->n_row) {
2503                 int i;
2504                 int extra;
2505                 unsigned total;
2506                 int *exp;
2507
2508                 extra = isl_dim_size(dim, isl_dim_set) -
2509                                 isl_dim_size(qp->dim, isl_dim_set);
2510                 total = isl_dim_total(qp->dim);
2511                 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
2512                 if (!exp)
2513                         goto error;
2514                 for (i = 0; i < qp->div->n_row; ++i)
2515                         exp[i] = extra + i;
2516                 qp->upoly = expand(qp->upoly, exp, total);
2517                 free(exp);
2518                 if (!qp->upoly)
2519                         goto error;
2520                 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
2521                 if (!qp->div)
2522                         goto error;
2523                 for (i = 0; i < qp->div->n_row; ++i)
2524                         isl_seq_clr(qp->div->row[i] + 2 + total, extra);
2525         }
2526
2527         isl_dim_free(qp->dim);
2528         qp->dim = dim;
2529
2530         return qp;
2531 error:
2532         isl_dim_free(dim);
2533         isl_qpolynomial_free(qp);
2534         return NULL;
2535 }
2536
2537 static int foreach_lifted_subset(__isl_take isl_set *set,
2538         __isl_take isl_qpolynomial *qp,
2539         int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2540                     void *user), void *user)
2541 {
2542         int i;
2543
2544         if (!set || !qp)
2545                 goto error;
2546
2547         for (i = 0; i < set->n; ++i) {
2548                 isl_set *lift;
2549                 isl_qpolynomial *copy;
2550
2551                 lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i]));
2552                 lift = isl_set_lift(lift);
2553
2554                 copy = isl_qpolynomial_copy(qp);
2555                 copy = isl_qpolynomial_lift(copy, isl_set_get_dim(lift));
2556
2557                 if (fn(lift, copy, user) < 0)
2558                         goto error;
2559         }
2560
2561         isl_set_free(set);
2562         isl_qpolynomial_free(qp);
2563
2564         return 0;
2565 error:
2566         isl_set_free(set);
2567         isl_qpolynomial_free(qp);
2568         return -1;
2569 }
2570
2571 int isl_pw_qpolynomial_foreach_lifted_piece(__isl_keep isl_pw_qpolynomial *pwqp,
2572         int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
2573                     void *user), void *user)
2574 {
2575         int i;
2576
2577         if (!pwqp)
2578                 return -1;
2579
2580         for (i = 0; i < pwqp->n; ++i) {
2581                 isl_set *set;
2582                 isl_qpolynomial *qp;
2583
2584                 set = isl_set_copy(pwqp->p[i].set);
2585                 qp = isl_qpolynomial_copy(pwqp->p[i].qp);
2586                 if (!any_divs(set)) {
2587                         if (fn(set, qp, user) < 0)
2588                                 return -1;
2589                         continue;
2590                 }
2591                 if (foreach_lifted_subset(set, qp, fn, user) < 0)
2592                         return -1;
2593         }
2594
2595         return 0;
2596 }
2597
2598 /* For each parameter or variable that does not appear in qp,
2599  * first eliminate the variable from all constraints and then set it to zero.
2600  */
2601 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
2602         __isl_keep isl_qpolynomial *qp)
2603 {
2604         int *active = NULL;
2605         int i;
2606         int d;
2607         unsigned nparam;
2608         unsigned nvar;
2609
2610         if (!set || !qp)
2611                 goto error;
2612
2613         d = isl_dim_total(set->dim);
2614         active = isl_calloc_array(set->ctx, int, d);
2615         if (set_active(qp, active) < 0)
2616                 goto error;
2617
2618         for (i = 0; i < d; ++i)
2619                 if (!active[i])
2620                         break;
2621
2622         if (i == d) {
2623                 free(active);
2624                 return set;
2625         }
2626
2627         nparam = isl_dim_size(set->dim, isl_dim_param);
2628         nvar = isl_dim_size(set->dim, isl_dim_set);
2629         for (i = 0; i < nparam; ++i) {
2630                 if (active[i])
2631                         continue;
2632                 set = isl_set_eliminate(set, isl_dim_param, i, 1);
2633                 set = isl_set_fix_si(set, isl_dim_param, i, 0);
2634         }
2635         for (i = 0; i < nvar; ++i) {
2636                 if (active[nparam + i])
2637                         continue;
2638                 set = isl_set_eliminate(set, isl_dim_set, i, 1);
2639                 set = isl_set_fix_si(set, isl_dim_set, i, 0);
2640         }
2641
2642         free(active);
2643
2644         return set;
2645 error:
2646         free(active);
2647         isl_set_free(set);
2648         return NULL;
2649 }
2650
2651 struct isl_opt_data {
2652         isl_qpolynomial *qp;
2653         int first;
2654         isl_qpolynomial *opt;
2655         int max;
2656 };
2657
2658 static int opt_fn(__isl_take isl_point *pnt, void *user)
2659 {
2660         struct isl_opt_data *data = (struct isl_opt_data *)user;
2661         isl_qpolynomial *val;
2662
2663         val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
2664         if (data->first) {
2665                 data->first = 0;
2666                 data->opt = val;
2667         } else if (data->max) {
2668                 data->opt = isl_qpolynomial_max_cst(data->opt, val);
2669         } else {
2670                 data->opt = isl_qpolynomial_min_cst(data->opt, val);
2671         }
2672
2673         return 0;
2674 }
2675
2676 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
2677         __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
2678 {
2679         struct isl_opt_data data = { NULL, 1, NULL, max };
2680
2681         if (!set || !qp)
2682                 goto error;
2683
2684         if (isl_upoly_is_cst(qp->upoly)) {
2685                 isl_set_free(set);
2686                 return qp;
2687         }
2688
2689         set = fix_inactive(set, qp);
2690
2691         data.qp = qp;
2692         if (isl_set_foreach_point(set, opt_fn, &data) < 0)
2693                 goto error;
2694
2695         isl_set_free(set);
2696         isl_qpolynomial_free(qp);
2697         return data.opt;
2698 error:
2699         isl_set_free(set);
2700         isl_qpolynomial_free(qp);
2701         isl_qpolynomial_free(data.opt);
2702         return NULL;
2703 }