isl_val.c

   1 /*
   2  * Copyright 2013      Ecole Normale Superieure
   3  *
   4  * Use of this software is governed by the MIT license
   5  *
   6  * Written by Sven Verdoolaege,
   7  * Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
   8  */
   9
  10 #include <isl_int.h>
  11 #include <isl_ctx_private.h>
  12 #include <isl_val_private.h>
  13
  14 #undef BASE
  15 #define BASE val
  16
  17 #include <isl_list_templ.c>
  18
  19 /* Allocate an isl_val object with indeterminate value.
  20  */
  21 __isl_give isl_val *isl_val_alloc(isl_ctx *ctx)
  22 {
  23         isl_val *v;
  24
  25         v = isl_alloc_type(ctx, struct isl_val);
  26         if (!v)
  27                 return NULL;
  28
  29         v->ctx = ctx;
  30         isl_ctx_ref(ctx);
  31         v->ref = 1;
  32         isl_int_init(v->n);
  33         isl_int_init(v->d);
  34
  35         return v;
  36 }
  37
  38 /* Return a reference to an isl_val representing zero.
  39  */
  40 __isl_give isl_val *isl_val_zero(isl_ctx *ctx)
  41 {
  42         return isl_val_int_from_si(ctx, 0);
  43 }
  44
  45 /* Return a reference to an isl_val representing one.
  46  */
  47 __isl_give isl_val *isl_val_one(isl_ctx *ctx)
  48 {
  49         return isl_val_int_from_si(ctx, 1);
  50 }
  51
  52 /* Return a reference to an isl_val representing negative one.
  53  */
  54 __isl_give isl_val *isl_val_negone(isl_ctx *ctx)
  55 {
  56         return isl_val_int_from_si(ctx, -1);
  57 }
  58
  59 /* Return a reference to an isl_val representing NaN.
  60  */
  61 __isl_give isl_val *isl_val_nan(isl_ctx *ctx)
  62 {
  63         isl_val *v;
  64
  65         v = isl_val_alloc(ctx);
  66         if (!v)
  67                 return NULL;
  68
  69         isl_int_set_si(v->n, 0);
  70         isl_int_set_si(v->d, 0);
  71
  72         return v;
  73 }
  74
  75 /* Change "v" into a NaN.
  76  */
  77 __isl_give isl_val *isl_val_set_nan(__isl_take isl_val *v)
  78 {
  79         if (!v)
  80                 return NULL;
  81         if (isl_val_is_nan(v))
  82                 return v;
  83         v = isl_val_cow(v);
  84         if (!v)
  85                 return NULL;
  86
  87         isl_int_set_si(v->n, 0);
  88         isl_int_set_si(v->d, 0);
  89
  90         return v;
  91 }
  92
  93 /* Return a reference to an isl_val representing +infinity.
  94  */
  95 __isl_give isl_val *isl_val_infty(isl_ctx *ctx)
  96 {
  97         isl_val *v;
  98
  99         v = isl_val_alloc(ctx);
 100         if (!v)
 101                 return NULL;
 102
 103         isl_int_set_si(v->n, 1);
 104         isl_int_set_si(v->d, 0);
 105
 106         return v;
 107 }
 108
 109 /* Return a reference to an isl_val representing -infinity.
 110  */
 111 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx)
 112 {
 113         isl_val *v;
 114
 115         v = isl_val_alloc(ctx);
 116         if (!v)
 117                 return NULL;
 118
 119         isl_int_set_si(v->n, -1);
 120         isl_int_set_si(v->d, 0);
 121
 122         return v;
 123 }
 124
 125 /* Return a reference to an isl_val representing the integer "i".
 126  */
 127 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx, long i)
 128 {
 129         isl_val *v;
 130
 131         v = isl_val_alloc(ctx);
 132         if (!v)
 133                 return NULL;
 134
 135         isl_int_set_si(v->n, i);
 136         isl_int_set_si(v->d, 1);
 137
 138         return v;
 139 }
 140
 141 /* Change the value of "v" to be equal to the integer "i".
 142  */
 143 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v, long i)
 144 {
 145         if (!v)
 146                 return NULL;
 147         if (isl_val_is_int(v) && isl_int_cmp_si(v->n, i) == 0)
 148                 return v;
 149         v = isl_val_cow(v);
 150         if (!v)
 151                 return NULL;
 152
 153         isl_int_set_si(v->n, i);
 154         isl_int_set_si(v->d, 1);
 155
 156         return v;
 157 }
 158
 159 /* Change the value of "v" to be equal to zero.
 160  */
 161 __isl_give isl_val *isl_val_set_zero(__isl_take isl_val *v)
 162 {
 163         return isl_val_set_si(v, 0);
 164 }
 165
 166 /* Return a reference to an isl_val representing the unsigned integer "u".
 167  */
 168 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx, unsigned long u)
 169 {
 170         isl_val *v;
 171
 172         v = isl_val_alloc(ctx);
 173         if (!v)
 174                 return NULL;
 175
 176         isl_int_set_ui(v->n, u);
 177         isl_int_set_si(v->d, 1);
 178
 179         return v;
 180 }
 181
 182 /* Return a reference to an isl_val representing the integer "n".
 183  */
 184 __isl_give isl_val *isl_val_int_from_isl_int(isl_ctx *ctx, isl_int n)
 185 {
 186         isl_val *v;
 187
 188         v = isl_val_alloc(ctx);
 189         if (!v)
 190                 return NULL;
 191
 192         isl_int_set(v->n, n);
 193         isl_int_set_si(v->d, 1);
 194
 195         return v;
 196 }
 197
 198 /* Return a reference to an isl_val representing the rational value "n"/"d".
 199  * Normalizing the isl_val (if needed) is left to the caller.
 200  */
 201 __isl_give isl_val *isl_val_rat_from_isl_int(isl_ctx *ctx,
 202         isl_int n, isl_int d)
 203 {
 204         isl_val *v;
 205
 206         v = isl_val_alloc(ctx);
 207         if (!v)
 208                 return NULL;
 209
 210         isl_int_set(v->n, n);
 211         isl_int_set(v->d, d);
 212
 213         return v;
 214 }
 215
 216 /* Return a new reference to "v".
 217  */
 218 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v)
 219 {
 220         if (!v)
 221                 return NULL;
 222
 223         v->ref++;
 224         return v;
 225 }
 226
 227 /* Return a fresh copy of "val".
 228  */
 229 __isl_give isl_val *isl_val_dup(__isl_keep isl_val *val)
 230 {
 231         isl_val *dup;
 232
 233         if (!val)
 234                 return NULL;
 235
 236         dup = isl_val_alloc(isl_val_get_ctx(val));
 237         if (!dup)
 238                 return NULL;
 239
 240         isl_int_set(dup->n, val->n);
 241         isl_int_set(dup->d, val->d);
 242
 243         return dup;
 244 }
 245
 246 /* Return an isl_val that is equal to "val" and that has only
 247  * a single reference.
 248  */
 249 __isl_give isl_val *isl_val_cow(__isl_take isl_val *val)
 250 {
 251         if (!val)
 252                 return NULL;
 253
 254         if (val->ref == 1)
 255                 return val;
 256         val->ref--;
 257         return isl_val_dup(val);
 258 }
 259
 260 /* Free "v" and return NULL.
 261  */
 262 __isl_null isl_val *isl_val_free(__isl_take isl_val *v)
 263 {
 264         if (!v)
 265                 return NULL;
 266
 267         if (--v->ref > 0)
 268                 return NULL;
 269
 270         isl_ctx_deref(v->ctx);
 271         isl_int_clear(v->n);
 272         isl_int_clear(v->d);
 273         free(v);
 274         return NULL;
 275 }
 276
 277 /* Extract the numerator of a rational value "v" as an integer.
 278  *
 279  * If "v" is not a rational value, then the result is undefined.
 280  */
 281 long isl_val_get_num_si(__isl_keep isl_val *v)
 282 {
 283         if (!v)
 284                 return 0;
 285         if (!isl_val_is_rat(v))
 286                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 287                         "expecting rational value", return 0);
 288         if (!isl_int_fits_slong(v->n))
 289                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 290                         "numerator too large", return 0);
 291         return isl_int_get_si(v->n);
 292 }
 293
 294 /* Extract the numerator of a rational value "v" as an isl_int.
 295  *
 296  * If "v" is not a rational value, then the result is undefined.
 297  */
 298 int isl_val_get_num_isl_int(__isl_keep isl_val *v, isl_int *n)
 299 {
 300         if (!v)
 301                 return -1;
 302         if (!isl_val_is_rat(v))
 303                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 304                         "expecting rational value", return -1);
 305         isl_int_set(*n, v->n);
 306         return 0;
 307 }
 308
 309 /* Extract the denominator of a rational value "v" as an integer.
 310  *
 311  * If "v" is not a rational value, then the result is undefined.
 312  */
 313 long isl_val_get_den_si(__isl_keep isl_val *v)
 314 {
 315         if (!v)
 316                 return 0;
 317         if (!isl_val_is_rat(v))
 318                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 319                         "expecting rational value", return 0);
 320         if (!isl_int_fits_slong(v->d))
 321                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 322                         "denominator too large", return 0);
 323         return isl_int_get_si(v->d);
 324 }
 325
 326 /* Extract the denominator of a rational value "v" as an isl_val.
 327  *
 328  * If "v" is not a rational value, then the result is undefined.
 329  */
 330 __isl_give isl_val *isl_val_get_den_val(__isl_keep isl_val *v)
 331 {
 332         if (!v)
 333                 return NULL;
 334         if (!isl_val_is_rat(v))
 335                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 336                         "expecting rational value", return NULL);
 337         return isl_val_int_from_isl_int(isl_val_get_ctx(v), v->d);
 338 }
 339
 340 /* Return an approximation of "v" as a double.
 341  */
 342 double isl_val_get_d(__isl_keep isl_val *v)
 343 {
 344         if (!v)
 345                 return 0;
 346         if (!isl_val_is_rat(v))
 347                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 348                         "expecting rational value", return 0);
 349         return isl_int_get_d(v->n) / isl_int_get_d(v->d);
 350 }
 351
 352 /* Return the isl_ctx to which "val" belongs.
 353  */
 354 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val)
 355 {
 356         return val ? val->ctx : NULL;
 357 }
 358
 359 /* Return a hash value that digests "val".
 360  */
 361 uint32_t isl_val_get_hash(__isl_keep isl_val *val)
 362 {
 363         uint32_t hash;
 364
 365         if (!val)
 366                 return 0;
 367
 368         hash = isl_hash_init();
 369         hash = isl_int_hash(val->n, hash);
 370         hash = isl_int_hash(val->d, hash);
 371
 372         return hash;
 373 }
 374
 375 /* Normalize "v".
 376  *
 377  * In particular, make sure that the denominator of a rational value
 378  * is positive and the numerator and denominator do not have any
 379  * common divisors.
 380  *
 381  * This function should not be called by an external user
 382  * since it will only be given normalized values.
 383  */
 384 __isl_give isl_val *isl_val_normalize(__isl_take isl_val *v)
 385 {
 386         isl_ctx *ctx;
 387
 388         if (!v)
 389                 return NULL;
 390         if (isl_val_is_int(v))
 391                 return v;
 392         if (!isl_val_is_rat(v))
 393                 return v;
 394         if (isl_int_is_neg(v->d)) {
 395                 isl_int_neg(v->d, v->d);
 396                 isl_int_neg(v->n, v->n);
 397         }
 398         ctx = isl_val_get_ctx(v);
 399         isl_int_gcd(ctx->normalize_gcd, v->n, v->d);
 400         if (isl_int_is_one(ctx->normalize_gcd))
 401                 return v;
 402         isl_int_divexact(v->n, v->n, ctx->normalize_gcd);
 403         isl_int_divexact(v->d, v->d, ctx->normalize_gcd);
 404         return v;
 405 }
 406
 407 /* Return the opposite of "v".
 408  */
 409 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v)
 410 {
 411         if (!v)
 412                 return NULL;
 413         if (isl_val_is_nan(v))
 414                 return v;
 415         if (isl_val_is_zero(v))
 416                 return v;
 417
 418         v = isl_val_cow(v);
 419         if (!v)
 420                 return NULL;
 421         isl_int_neg(v->n, v->n);
 422
 423         return v;
 424 }
 425
 426 /* Return the inverse of "v".
 427  */
 428 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v)
 429 {
 430         if (!v)
 431                 return NULL;
 432         if (isl_val_is_nan(v))
 433                 return v;
 434         if (isl_val_is_zero(v)) {
 435                 isl_ctx *ctx = isl_val_get_ctx(v);
 436                 isl_val_free(v);
 437                 return isl_val_nan(ctx);
 438         }
 439         if (isl_val_is_infty(v) || isl_val_is_neginfty(v)) {
 440                 isl_ctx *ctx = isl_val_get_ctx(v);
 441                 isl_val_free(v);
 442                 return isl_val_zero(ctx);
 443         }
 444
 445         v = isl_val_cow(v);
 446         if (!v)
 447                 return NULL;
 448         isl_int_swap(v->n, v->d);
 449
 450         return isl_val_normalize(v);
 451 }
 452
 453 /* Return the absolute value of "v".
 454  */
 455 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v)
 456 {
 457         if (!v)
 458                 return NULL;
 459         if (isl_val_is_nan(v))
 460                 return v;
 461         if (isl_val_is_nonneg(v))
 462                 return v;
 463         return isl_val_neg(v);
 464 }
 465
 466 /* Return the "floor" (greatest integer part) of "v".
 467  * That is, return the result of rounding towards -infinity.
 468  */
 469 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v)
 470 {
 471         if (!v)
 472                 return NULL;
 473         if (isl_val_is_int(v))
 474                 return v;
 475         if (!isl_val_is_rat(v))
 476                 return v;
 477
 478         v = isl_val_cow(v);
 479         if (!v)
 480                 return NULL;
 481         isl_int_fdiv_q(v->n, v->n, v->d);
 482         isl_int_set_si(v->d, 1);
 483
 484         return v;
 485 }
 486
 487 /* Return the "ceiling" of "v".
 488  * That is, return the result of rounding towards +infinity.
 489  */
 490 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v)
 491 {
 492         if (!v)
 493                 return NULL;
 494         if (isl_val_is_int(v))
 495                 return v;
 496         if (!isl_val_is_rat(v))
 497                 return v;
 498
 499         v = isl_val_cow(v);
 500         if (!v)
 501                 return NULL;
 502         isl_int_cdiv_q(v->n, v->n, v->d);
 503         isl_int_set_si(v->d, 1);
 504
 505         return v;
 506 }
 507
 508 /* Truncate "v".
 509  * That is, return the result of rounding towards zero.
 510  */
 511 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v)
 512 {
 513         if (!v)
 514                 return NULL;
 515         if (isl_val_is_int(v))
 516                 return v;
 517         if (!isl_val_is_rat(v))
 518                 return v;
 519
 520         v = isl_val_cow(v);
 521         if (!v)
 522                 return NULL;
 523         isl_int_tdiv_q(v->n, v->n, v->d);
 524         isl_int_set_si(v->d, 1);
 525
 526         return v;
 527 }
 528
 529 /* Return 2^v, where v is an integer (that is not too large).
 530  */
 531 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v)
 532 {
 533         unsigned long exp;
 534         int neg;
 535
 536         v = isl_val_cow(v);
 537         if (!v)
 538                 return NULL;
 539         if (!isl_val_is_int(v))
 540                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 541                         "can only compute integer powers",
 542                         return isl_val_free(v));
 543         neg = isl_val_is_neg(v);
 544         if (neg)
 545                 isl_int_neg(v->n, v->n);
 546         if (!isl_int_fits_ulong(v->n))
 547                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 548                         "exponent too large", return isl_val_free(v));
 549         exp = isl_int_get_ui(v->n);
 550         if (neg) {
 551                 isl_int_mul_2exp(v->d, v->d, exp);
 552                 isl_int_set_si(v->n, 1);
 553         } else {
 554                 isl_int_mul_2exp(v->n, v->d, exp);
 555         }
 556
 557         return v;
 558 }
 559
 560 /* Return the minimum of "v1" and "v2".
 561  */
 562 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1, __isl_take isl_val *v2)
 563 {
 564         if (!v1 || !v2)
 565                 goto error;
 566
 567         if (isl_val_is_nan(v1)) {
 568                 isl_val_free(v2);
 569                 return v1;
 570         }
 571         if (isl_val_is_nan(v2)) {
 572                 isl_val_free(v1);
 573                 return v2;
 574         }
 575         if (isl_val_le(v1, v2)) {
 576                 isl_val_free(v2);
 577                 return v1;
 578         } else {
 579                 isl_val_free(v1);
 580                 return v2;
 581         }
 582 error:
 583         isl_val_free(v1);
 584         isl_val_free(v2);
 585         return NULL;
 586 }
 587
 588 /* Return the maximum of "v1" and "v2".
 589  */
 590 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1, __isl_take isl_val *v2)
 591 {
 592         if (!v1 || !v2)
 593                 goto error;
 594
 595         if (isl_val_is_nan(v1)) {
 596                 isl_val_free(v2);
 597                 return v1;
 598         }
 599         if (isl_val_is_nan(v2)) {
 600                 isl_val_free(v1);
 601                 return v2;
 602         }
 603         if (isl_val_ge(v1, v2)) {
 604                 isl_val_free(v2);
 605                 return v1;
 606         } else {
 607                 isl_val_free(v1);
 608                 return v2;
 609         }
 610 error:
 611         isl_val_free(v1);
 612         isl_val_free(v2);
 613         return NULL;
 614 }
 615
 616 /* Return the sum of "v1" and "v2".
 617  */
 618 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1, __isl_take isl_val *v2)
 619 {
 620         if (!v1 || !v2)
 621                 goto error;
 622         if (isl_val_is_nan(v1)) {
 623                 isl_val_free(v2);
 624                 return v1;
 625         }
 626         if (isl_val_is_nan(v2)) {
 627                 isl_val_free(v1);
 628                 return v2;
 629         }
 630         if ((isl_val_is_infty(v1) && isl_val_is_neginfty(v2)) ||
 631             (isl_val_is_neginfty(v1) && isl_val_is_infty(v2))) {
 632                 isl_val_free(v2);
 633                 return isl_val_set_nan(v1);
 634         }
 635         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 636                 isl_val_free(v2);
 637                 return v1;
 638         }
 639         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 640                 isl_val_free(v1);
 641                 return v2;
 642         }
 643         if (isl_val_is_zero(v1)) {
 644                 isl_val_free(v1);
 645                 return v2;
 646         }
 647         if (isl_val_is_zero(v2)) {
 648                 isl_val_free(v2);
 649                 return v1;
 650         }
 651
 652         v1 = isl_val_cow(v1);
 653         if (!v1)
 654                 goto error;
 655         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 656                 isl_int_add(v1->n, v1->n, v2->n);
 657         else {
 658                 if (isl_int_eq(v1->d, v2->d))
 659                         isl_int_add(v1->n, v1->n, v2->n);
 660                 else {
 661                         isl_int_mul(v1->n, v1->n, v2->d);
 662                         isl_int_addmul(v1->n, v2->n, v1->d);
 663                         isl_int_mul(v1->d, v1->d, v2->d);
 664                 }
 665                 v1 = isl_val_normalize(v1);
 666         }
 667         isl_val_free(v2);
 668         return v1;
 669 error:
 670         isl_val_free(v1);
 671         isl_val_free(v2);
 672         return NULL;
 673 }
 674
 675 /* Return the sum of "v1" and "v2".
 676  */
 677 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1, unsigned long v2)
 678 {
 679         if (!v1)
 680                 return NULL;
 681         if (!isl_val_is_rat(v1))
 682                 return v1;
 683         if (v2 == 0)
 684                 return v1;
 685         v1 = isl_val_cow(v1);
 686         if (!v1)
 687                 return NULL;
 688
 689         isl_int_addmul_ui(v1->n, v1->d, v2);
 690
 691         return v1;
 692 }
 693
 694 /* Subtract "v2" from "v1".
 695  */
 696 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1, __isl_take isl_val *v2)
 697 {
 698         if (!v1 || !v2)
 699                 goto error;
 700         if (isl_val_is_nan(v1)) {
 701                 isl_val_free(v2);
 702                 return v1;
 703         }
 704         if (isl_val_is_nan(v2)) {
 705                 isl_val_free(v1);
 706                 return v2;
 707         }
 708         if ((isl_val_is_infty(v1) && isl_val_is_infty(v2)) ||
 709             (isl_val_is_neginfty(v1) && isl_val_is_neginfty(v2))) {
 710                 isl_val_free(v2);
 711                 return isl_val_set_nan(v1);
 712         }
 713         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 714                 isl_val_free(v2);
 715                 return v1;
 716         }
 717         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 718                 isl_val_free(v1);
 719                 return isl_val_neg(v2);
 720         }
 721         if (isl_val_is_zero(v2)) {
 722                 isl_val_free(v2);
 723                 return v1;
 724         }
 725         if (isl_val_is_zero(v1)) {
 726                 isl_val_free(v1);
 727                 return isl_val_neg(v2);
 728         }
 729
 730         v1 = isl_val_cow(v1);
 731         if (!v1)
 732                 goto error;
 733         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 734                 isl_int_sub(v1->n, v1->n, v2->n);
 735         else {
 736                 if (isl_int_eq(v1->d, v2->d))
 737                         isl_int_sub(v1->n, v1->n, v2->n);
 738                 else {
 739                         isl_int_mul(v1->n, v1->n, v2->d);
 740                         isl_int_submul(v1->n, v2->n, v1->d);
 741                         isl_int_mul(v1->d, v1->d, v2->d);
 742                 }
 743                 v1 = isl_val_normalize(v1);
 744         }
 745         isl_val_free(v2);
 746         return v1;
 747 error:
 748         isl_val_free(v1);
 749         isl_val_free(v2);
 750         return NULL;
 751 }
 752
 753 /* Subtract "v2" from "v1".
 754  */
 755 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1, unsigned long v2)
 756 {
 757         if (!v1)
 758                 return NULL;
 759         if (!isl_val_is_rat(v1))
 760                 return v1;
 761         if (v2 == 0)
 762                 return v1;
 763         v1 = isl_val_cow(v1);
 764         if (!v1)
 765                 return NULL;
 766
 767         isl_int_submul_ui(v1->n, v1->d, v2);
 768
 769         return v1;
 770 }
 771
 772 /* Return the product of "v1" and "v2".
 773  */
 774 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1, __isl_take isl_val *v2)
 775 {
 776         if (!v1 || !v2)
 777                 goto error;
 778         if (isl_val_is_nan(v1)) {
 779                 isl_val_free(v2);
 780                 return v1;
 781         }
 782         if (isl_val_is_nan(v2)) {
 783                 isl_val_free(v1);
 784                 return v2;
 785         }
 786         if ((!isl_val_is_rat(v1) && isl_val_is_zero(v2)) ||
 787             (isl_val_is_zero(v1) && !isl_val_is_rat(v2))) {
 788                 isl_val_free(v2);
 789                 return isl_val_set_nan(v1);
 790         }
 791         if (isl_val_is_zero(v1)) {
 792                 isl_val_free(v2);
 793                 return v1;
 794         }
 795         if (isl_val_is_zero(v2)) {
 796                 isl_val_free(v1);
 797                 return v2;
 798         }
 799         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 800                 if (isl_val_is_neg(v2))
 801                         v1 = isl_val_neg(v1);
 802                 isl_val_free(v2);
 803                 return v1;
 804         }
 805         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 806                 if (isl_val_is_neg(v1))
 807                         v2 = isl_val_neg(v2);
 808                 isl_val_free(v1);
 809                 return v2;
 810         }
 811
 812         v1 = isl_val_cow(v1);
 813         if (!v1)
 814                 goto error;
 815         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 816                 isl_int_mul(v1->n, v1->n, v2->n);
 817         else {
 818                 isl_int_mul(v1->n, v1->n, v2->n);
 819                 isl_int_mul(v1->d, v1->d, v2->d);
 820                 v1 = isl_val_normalize(v1);
 821         }
 822         isl_val_free(v2);
 823         return v1;
 824 error:
 825         isl_val_free(v1);
 826         isl_val_free(v2);
 827         return NULL;
 828 }
 829
 830 /* Return the product of "v1" and "v2".
 831  *
 832  * This is a private copy of isl_val_mul for use in the generic
 833  * isl_multi_*_scale_val instantiated for isl_val.
 834  */
 835 __isl_give isl_val *isl_val_scale_val(__isl_take isl_val *v1,
 836         __isl_take isl_val *v2)
 837 {
 838         return isl_val_mul(v1, v2);
 839 }
 840
 841 /* Return the product of "v1" and "v2".
 842  */
 843 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1, unsigned long v2)
 844 {
 845         if (!v1)
 846                 return NULL;
 847         if (isl_val_is_nan(v1))
 848                 return v1;
 849         if (!isl_val_is_rat(v1)) {
 850                 if (v2 == 0)
 851                         v1 = isl_val_set_nan(v1);
 852                 return v1;
 853         }
 854         if (v2 == 1)
 855                 return v1;
 856         v1 = isl_val_cow(v1);
 857         if (!v1)
 858                 return NULL;
 859
 860         isl_int_mul_ui(v1->n, v1->n, v2);
 861
 862         return isl_val_normalize(v1);
 863 }
 864
 865 /* Divide "v1" by "v2".
 866  */
 867 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1, __isl_take isl_val *v2)
 868 {
 869         if (!v1 || !v2)
 870                 goto error;
 871         if (isl_val_is_nan(v1)) {
 872                 isl_val_free(v2);
 873                 return v1;
 874         }
 875         if (isl_val_is_nan(v2)) {
 876                 isl_val_free(v1);
 877                 return v2;
 878         }
 879         if (isl_val_is_zero(v2) ||
 880             (!isl_val_is_rat(v1) && !isl_val_is_rat(v2))) {
 881                 isl_val_free(v2);
 882                 return isl_val_set_nan(v1);
 883         }
 884         if (isl_val_is_zero(v1)) {
 885                 isl_val_free(v2);
 886                 return v1;
 887         }
 888         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 889                 if (isl_val_is_neg(v2))
 890                         v1 = isl_val_neg(v1);
 891                 isl_val_free(v2);
 892                 return v1;
 893         }
 894         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 895                 isl_val_free(v2);
 896                 return isl_val_set_zero(v1);
 897         }
 898
 899         v1 = isl_val_cow(v1);
 900         if (!v1)
 901                 goto error;
 902         if (isl_val_is_int(v2)) {
 903                 isl_int_mul(v1->d, v1->d, v2->n);
 904                 v1 = isl_val_normalize(v1);
 905         } else {
 906                 isl_int_mul(v1->d, v1->d, v2->n);
 907                 isl_int_mul(v1->n, v1->n, v2->d);
 908                 v1 = isl_val_normalize(v1);
 909         }
 910         isl_val_free(v2);
 911         return v1;
 912 error:
 913         isl_val_free(v1);
 914         isl_val_free(v2);
 915         return NULL;
 916 }
 917
 918 /* Divide "v1" by "v2".
 919  *
 920  * This is a private copy of isl_val_div for use in the generic
 921  * isl_multi_*_scale_down_val instantiated for isl_val.
 922  */
 923 __isl_give isl_val *isl_val_scale_down_val(__isl_take isl_val *v1,
 924         __isl_take isl_val *v2)
 925 {
 926         return isl_val_div(v1, v2);
 927 }
 928
 929 /* Given two integer values "v1" and "v2", check if "v1" is divisible by "v2".
 930  */
 931 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
 932 {
 933         if (!v1 || !v2)
 934                 return isl_bool_error;
 935
 936         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 937                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 938                         "expecting two integers", return isl_bool_error);
 939
 940         return isl_int_is_divisible_by(v1->n, v2->n);
 941 }
 942
 943 /* Given two integer values "v1" and "v2", return the residue of "v1"
 944  * modulo "v2".
 945  */
 946 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1, __isl_take isl_val *v2)
 947 {
 948         if (!v1 || !v2)
 949                 goto error;
 950         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 951                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 952                         "expecting two integers", goto error);
 953         if (isl_val_is_nonneg(v1) && isl_val_lt(v1, v2)) {
 954                 isl_val_free(v2);
 955                 return v1;
 956         }
 957         v1 = isl_val_cow(v1);
 958         if (!v1)
 959                 goto error;
 960         isl_int_fdiv_r(v1->n, v1->n, v2->n);
 961         isl_val_free(v2);
 962         return v1;
 963 error:
 964         isl_val_free(v1);
 965         isl_val_free(v2);
 966         return NULL;
 967 }
 968
 969 /* Given two integer values "v1" and "v2", return the residue of "v1"
 970  * modulo "v2".
 971  *
 972  * This is a private copy of isl_val_mod for use in the generic
 973  * isl_multi_*_mod_multi_val instantiated for isl_val.
 974  */
 975 __isl_give isl_val *isl_val_mod_val(__isl_take isl_val *v1,
 976         __isl_take isl_val *v2)
 977 {
 978         return isl_val_mod(v1, v2);
 979 }
 980
 981 /* Given two integer values, return their greatest common divisor.
 982  */
 983 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1, __isl_take isl_val *v2)
 984 {
 985         if (!v1 || !v2)
 986                 goto error;
 987         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 988                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 989                         "expecting two integers", goto error);
 990         if (isl_val_eq(v1, v2)) {
 991                 isl_val_free(v2);
 992                 return v1;
 993         }
 994         if (isl_val_is_one(v1)) {
 995                 isl_val_free(v2);
 996                 return v1;
 997         }
 998         if (isl_val_is_one(v2)) {
 999                 isl_val_free(v1);
1000                 return v2;
1001         }
1002         v1 = isl_val_cow(v1);
1003         if (!v1)
1004                 goto error;
1005         isl_int_gcd(v1->n, v1->n, v2->n);
1006         isl_val_free(v2);
1007         return v1;
1008 error:
1009         isl_val_free(v1);
1010         isl_val_free(v2);
1011         return NULL;
1012 }
1013
1014 /* Compute x, y and g such that g = gcd(a,b) and a*x+b*y = g.
1015  */
1016 static void isl_int_gcdext(isl_int *g, isl_int *x, isl_int *y,
1017         isl_int a, isl_int b)
1018 {
1019         isl_int d, tmp;
1020         isl_int a_copy, b_copy;
1021
1022         isl_int_init(a_copy);
1023         isl_int_init(b_copy);
1024         isl_int_init(d);
1025         isl_int_init(tmp);
1026         isl_int_set(a_copy, a);
1027         isl_int_set(b_copy, b);
1028         isl_int_abs(*g, a_copy);
1029         isl_int_abs(d, b_copy);
1030         isl_int_set_si(*x, 1);
1031         isl_int_set_si(*y, 0);
1032         while (isl_int_is_pos(d)) {
1033                 isl_int_fdiv_q(tmp, *g, d);
1034                 isl_int_submul(*x, tmp, *y);
1035                 isl_int_submul(*g, tmp, d);
1036                 isl_int_swap(*g, d);
1037                 isl_int_swap(*x, *y);
1038         }
1039         if (isl_int_is_zero(a_copy))
1040                 isl_int_set_si(*x, 0);
1041         else if (isl_int_is_neg(a_copy))
1042                 isl_int_neg(*x, *x);
1043         if (isl_int_is_zero(b_copy))
1044                 isl_int_set_si(*y, 0);
1045         else {
1046                 isl_int_mul(tmp, a_copy, *x);
1047                 isl_int_sub(tmp, *g, tmp);
1048                 isl_int_divexact(*y, tmp, b_copy);
1049         }
1050         isl_int_clear(d);
1051         isl_int_clear(tmp);
1052         isl_int_clear(a_copy);
1053         isl_int_clear(b_copy);
1054 }
1055
1056 /* Given two integer values v1 and v2, return their greatest common divisor g,
1057  * as well as two integers x and y such that x * v1 + y * v2 = g.
1058  */
1059 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
1060         __isl_take isl_val *v2, __isl_give isl_val **x, __isl_give isl_val **y)
1061 {
1062         isl_ctx *ctx;
1063         isl_val *a = NULL, *b = NULL;
1064
1065         if (!x && !y)
1066                 return isl_val_gcd(v1, v2);
1067
1068         if (!v1 || !v2)
1069                 goto error;
1070
1071         ctx = isl_val_get_ctx(v1);
1072         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
1073                 isl_die(ctx, isl_error_invalid,
1074                         "expecting two integers", goto error);
1075
1076         v1 = isl_val_cow(v1);
1077         a = isl_val_alloc(ctx);
1078         b = isl_val_alloc(ctx);
1079         if (!v1 || !a || !b)
1080                 goto error;
1081         isl_int_gcdext(&v1->n, &a->n, &b->n, v1->n, v2->n);
1082         if (x) {
1083                 isl_int_set_si(a->d, 1);
1084                 *x = a;
1085         } else
1086                 isl_val_free(a);
1087         if (y) {
1088                 isl_int_set_si(b->d, 1);
1089                 *y = b;
1090         } else
1091                 isl_val_free(b);
1092         isl_val_free(v2);
1093         return v1;
1094 error:
1095         isl_val_free(v1);
1096         isl_val_free(v2);
1097         isl_val_free(a);
1098         isl_val_free(b);
1099         if (x)
1100                 *x = NULL;
1101         if (y)
1102                 *y = NULL;
1103         return NULL;
1104 }
1105
1106 /* Does "v" represent an integer value?
1107  */
1108 isl_bool isl_val_is_int(__isl_keep isl_val *v)
1109 {
1110         if (!v)
1111                 return isl_bool_error;
1112
1113         return isl_int_is_one(v->d);
1114 }
1115
1116 /* Does "v" represent a rational value?
1117  */
1118 isl_bool isl_val_is_rat(__isl_keep isl_val *v)
1119 {
1120         if (!v)
1121                 return isl_bool_error;
1122
1123         return !isl_int_is_zero(v->d);
1124 }
1125
1126 /* Does "v" represent NaN?
1127  */
1128 isl_bool isl_val_is_nan(__isl_keep isl_val *v)
1129 {
1130         if (!v)
1131                 return isl_bool_error;
1132
1133         return isl_int_is_zero(v->n) && isl_int_is_zero(v->d);
1134 }
1135
1136 /* Does "v" represent +infinity?
1137  */
1138 isl_bool isl_val_is_infty(__isl_keep isl_val *v)
1139 {
1140         if (!v)
1141                 return isl_bool_error;
1142
1143         return isl_int_is_pos(v->n) && isl_int_is_zero(v->d);
1144 }
1145
1146 /* Does "v" represent -infinity?
1147  */
1148 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v)
1149 {
1150         if (!v)
1151                 return isl_bool_error;
1152
1153         return isl_int_is_neg(v->n) && isl_int_is_zero(v->d);
1154 }
1155
1156 /* Does "v" represent the integer zero?
1157  */
1158 isl_bool isl_val_is_zero(__isl_keep isl_val *v)
1159 {
1160         if (!v)
1161                 return isl_bool_error;
1162
1163         return isl_int_is_zero(v->n) && !isl_int_is_zero(v->d);
1164 }
1165
1166 /* Does "v" represent the integer one?
1167  */
1168 isl_bool isl_val_is_one(__isl_keep isl_val *v)
1169 {
1170         if (!v)
1171                 return isl_bool_error;
1172
1173         if (isl_val_is_nan(v))
1174                 return isl_bool_false;
1175
1176         return isl_int_eq(v->n, v->d);
1177 }
1178
1179 /* Does "v" represent the integer negative one?
1180  */
1181 isl_bool isl_val_is_negone(__isl_keep isl_val *v)
1182 {
1183         if (!v)
1184                 return isl_bool_error;
1185
1186         return isl_int_is_neg(v->n) && isl_int_abs_eq(v->n, v->d);
1187 }
1188
1189 /* Is "v" (strictly) positive?
1190  */
1191 isl_bool isl_val_is_pos(__isl_keep isl_val *v)
1192 {
1193         if (!v)
1194                 return isl_bool_error;
1195
1196         return isl_int_is_pos(v->n);
1197 }
1198
1199 /* Is "v" (strictly) negative?
1200  */
1201 isl_bool isl_val_is_neg(__isl_keep isl_val *v)
1202 {
1203         if (!v)
1204                 return isl_bool_error;
1205
1206         return isl_int_is_neg(v->n);
1207 }
1208
1209 /* Is "v" non-negative?
1210  */
1211 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v)
1212 {
1213         if (!v)
1214                 return isl_bool_error;
1215
1216         if (isl_val_is_nan(v))
1217                 return isl_bool_false;
1218
1219         return isl_int_is_nonneg(v->n);
1220 }
1221
1222 /* Is "v" non-positive?
1223  */
1224 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v)
1225 {
1226         if (!v)
1227                 return isl_bool_error;
1228
1229         if (isl_val_is_nan(v))
1230                 return isl_bool_false;
1231
1232         return isl_int_is_nonpos(v->n);
1233 }
1234
1235 /* Return the sign of "v".
1236  *
1237  * The sign of NaN is undefined.
1238  */
1239 int isl_val_sgn(__isl_keep isl_val *v)
1240 {
1241         if (!v)
1242                 return 0;
1243         if (isl_val_is_zero(v))
1244                 return 0;
1245         if (isl_val_is_pos(v))
1246                 return 1;
1247         return -1;
1248 }
1249
1250 /* Is "v1" (strictly) less than "v2"?
1251  */
1252 isl_bool isl_val_lt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1253 {
1254         isl_int t;
1255         isl_bool lt;
1256
1257         if (!v1 || !v2)
1258                 return isl_bool_error;
1259         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1260                 return isl_int_lt(v1->n, v2->n);
1261         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1262                 return isl_bool_false;
1263         if (isl_val_eq(v1, v2))
1264                 return isl_bool_false;
1265         if (isl_val_is_infty(v2))
1266                 return isl_bool_true;
1267         if (isl_val_is_infty(v1))
1268                 return isl_bool_false;
1269         if (isl_val_is_neginfty(v1))
1270                 return isl_bool_true;
1271         if (isl_val_is_neginfty(v2))
1272                 return isl_bool_false;
1273
1274         isl_int_init(t);
1275         isl_int_mul(t, v1->n, v2->d);
1276         isl_int_submul(t, v2->n, v1->d);
1277         lt = isl_int_is_neg(t);
1278         isl_int_clear(t);
1279
1280         return lt;
1281 }
1282
1283 /* Is "v1" (strictly) greater than "v2"?
1284  */
1285 isl_bool isl_val_gt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1286 {
1287         return isl_val_lt(v2, v1);
1288 }
1289
1290 /* Is "v1" less than or equal to "v2"?
1291  */
1292 isl_bool isl_val_le(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1293 {
1294         isl_int t;
1295         isl_bool le;
1296
1297         if (!v1 || !v2)
1298                 return isl_bool_error;
1299         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1300                 return isl_int_le(v1->n, v2->n);
1301         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1302                 return isl_bool_false;
1303         if (isl_val_eq(v1, v2))
1304                 return isl_bool_true;
1305         if (isl_val_is_infty(v2))
1306                 return isl_bool_true;
1307         if (isl_val_is_infty(v1))
1308                 return isl_bool_false;
1309         if (isl_val_is_neginfty(v1))
1310                 return isl_bool_true;
1311         if (isl_val_is_neginfty(v2))
1312                 return isl_bool_false;
1313
1314         isl_int_init(t);
1315         isl_int_mul(t, v1->n, v2->d);
1316         isl_int_submul(t, v2->n, v1->d);
1317         le = isl_int_is_nonpos(t);
1318         isl_int_clear(t);
1319
1320         return le;
1321 }
1322
1323 /* Is "v1" greater than or equal to "v2"?
1324  */
1325 isl_bool isl_val_ge(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1326 {
1327         return isl_val_le(v2, v1);
1328 }
1329
1330 /* How does "v" compare to "i"?
1331  *
1332  * Return 1 if v is greater, -1 if v is smaller and 0 if v is equal to i.
1333  *
1334  * If v is NaN (or NULL), then the result is undefined.
1335  */
1336 int isl_val_cmp_si(__isl_keep isl_val *v, long i)
1337 {
1338         isl_int t;
1339         int cmp;
1340
1341         if (!v)
1342                 return 0;
1343         if (isl_val_is_int(v))
1344                 return isl_int_cmp_si(v->n, i);
1345         if (isl_val_is_nan(v))
1346                 return 0;
1347         if (isl_val_is_infty(v))
1348                 return 1;
1349         if (isl_val_is_neginfty(v))
1350                 return -1;
1351
1352         isl_int_init(t);
1353         isl_int_mul_si(t, v->d, i);
1354         isl_int_sub(t, v->n, t);
1355         cmp = isl_int_sgn(t);
1356         isl_int_clear(t);
1357
1358         return cmp;
1359 }
1360
1361 /* Is "v1" equal to "v2"?
1362  */
1363 isl_bool isl_val_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1364 {
1365         if (!v1 || !v2)
1366                 return isl_bool_error;
1367         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1368                 return isl_bool_false;
1369
1370         return isl_int_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1371 }
1372
1373 /* Is "v1" equal to "v2" in absolute value?
1374  */
1375 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1376 {
1377         if (!v1 || !v2)
1378                 return isl_bool_error;
1379         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1380                 return isl_bool_false;
1381
1382         return isl_int_abs_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1383 }
1384
1385 /* Is "v1" different from "v2"?
1386  */
1387 isl_bool isl_val_ne(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1388 {
1389         if (!v1 || !v2)
1390                 return isl_bool_error;
1391         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1392                 return isl_bool_false;
1393
1394         return isl_int_ne(v1->n, v2->n) || isl_int_ne(v1->d, v2->d);
1395 }
1396
1397 /* Print a textual representation of "v" onto "p".
1398  */
1399 __isl_give isl_printer *isl_printer_print_val(__isl_take isl_printer *p,
1400         __isl_keep isl_val *v)
1401 {
1402         int neg;
1403
1404         if (!p || !v)
1405                 return isl_printer_free(p);
1406
1407         neg = isl_int_is_neg(v->n);
1408         if (neg) {
1409                 p = isl_printer_print_str(p, "-");
1410                 isl_int_neg(v->n, v->n);
1411         }
1412         if (isl_int_is_zero(v->d)) {
1413                 int sgn = isl_int_sgn(v->n);
1414                 p = isl_printer_print_str(p, sgn < 0 ? "-infty" :
1415                                             sgn == 0 ? "NaN" : "infty");
1416         } else
1417                 p = isl_printer_print_isl_int(p, v->n);
1418         if (neg)
1419                 isl_int_neg(v->n, v->n);
1420         if (!isl_int_is_zero(v->d) && !isl_int_is_one(v->d)) {
1421                 p = isl_printer_print_str(p, "/");
1422                 p = isl_printer_print_isl_int(p, v->d);
1423         }
1424
1425         return p;
1426 }
1427
1428 /* Is "val1" (obviously) equal to "val2"?
1429  *
1430  * This is a private copy of isl_val_eq for use in the generic
1431  * isl_multi_*_plain_is_equal instantiated for isl_val.
1432  */
1433 int isl_val_plain_is_equal(__isl_keep isl_val *val1, __isl_keep isl_val *val2)
1434 {
1435         return isl_val_eq(val1, val2);
1436 }
1437
1438 /* Does "v" have any non-zero coefficients
1439  * for any dimension in the given range?
1440  *
1441  * This function is only meant to be used in the generic isl_multi_*
1442  * functions which have to deal with base objects that have an associated
1443  * space.  Since an isl_val does not have any coefficients, this function
1444  * always return 0.
1445  */
1446 int isl_val_involves_dims(__isl_keep isl_val *v, enum isl_dim_type type,
1447         unsigned first, unsigned n)
1448 {
1449         if (!v)
1450                 return -1;
1451
1452         return 0;
1453 }
1454
1455 /* Insert "n" dimensions of type "type" at position "first".
1456  *
1457  * This function is only meant to be used in the generic isl_multi_*
1458  * functions which have to deal with base objects that have an associated
1459  * space.  Since an isl_val does not have an associated space, this function
1460  * does not do anything.
1461  */
1462 __isl_give isl_val *isl_val_insert_dims(__isl_take isl_val *v,
1463         enum isl_dim_type type, unsigned first, unsigned n)
1464 {
1465         return v;
1466 }
1467
1468 /* Drop the the "n" first dimensions of type "type" at position "first".
1469  *
1470  * This function is only meant to be used in the generic isl_multi_*
1471  * functions which have to deal with base objects that have an associated
1472  * space.  Since an isl_val does not have an associated space, this function
1473  * does not do anything.
1474  */
1475 __isl_give isl_val *isl_val_drop_dims(__isl_take isl_val *v,
1476         enum isl_dim_type type, unsigned first, unsigned n)
1477 {
1478         return v;
1479 }
1480
1481 /* Change the name of the dimension of type "type" at position "pos" to "s".
1482  *
1483  * This function is only meant to be used in the generic isl_multi_*
1484  * functions which have to deal with base objects that have an associated
1485  * space.  Since an isl_val does not have an associated space, this function
1486  * does not do anything.
1487  */
1488 __isl_give isl_val *isl_val_set_dim_name(__isl_take isl_val *v,
1489         enum isl_dim_type type, unsigned pos, const char *s)
1490 {
1491         return v;
1492 }
1493
1494 /* Return the space of "v".
1495  *
1496  * This function is only meant to be used in the generic isl_multi_*
1497  * functions which have to deal with base objects that have an associated
1498  * space.  The conditions surrounding the call to this function make sure
1499  * that this function will never actually get called.  We return a valid
1500  * space anyway, just in case.
1501  */
1502 __isl_give isl_space *isl_val_get_space(__isl_keep isl_val *v)
1503 {
1504         if (!v)
1505                 return NULL;
1506
1507         return isl_space_params_alloc(isl_val_get_ctx(v), 0);
1508 }
1509
1510 /* Reset the domain space of "v" to "space".
1511  *
1512  * This function is only meant to be used in the generic isl_multi_*
1513  * functions which have to deal with base objects that have an associated
1514  * space.  Since an isl_val does not have an associated space, this function
1515  * does not do anything, apart from error handling and cleaning up memory.
1516  */
1517 __isl_give isl_val *isl_val_reset_domain_space(__isl_take isl_val *v,
1518         __isl_take isl_space *space)
1519 {
1520         if (!space)
1521                 return isl_val_free(v);
1522         isl_space_free(space);
1523         return v;
1524 }
1525
1526 /* Align the parameters of "v" to those of "space".
1527  *
1528  * This function is only meant to be used in the generic isl_multi_*
1529  * functions which have to deal with base objects that have an associated
1530  * space.  Since an isl_val does not have an associated space, this function
1531  * does not do anything, apart from error handling and cleaning up memory.
1532  * Note that the conditions surrounding the call to this function make sure
1533  * that this function will never actually get called.
1534  */
1535 __isl_give isl_val *isl_val_align_params(__isl_take isl_val *v,
1536         __isl_take isl_space *space)
1537 {
1538         if (!space)
1539                 return isl_val_free(v);
1540         isl_space_free(space);
1541         return v;
1542 }
1543
1544 /* Reorder the dimensions of the domain of "v" according
1545  * to the given reordering.
1546  *
1547  * This function is only meant to be used in the generic isl_multi_*
1548  * functions which have to deal with base objects that have an associated
1549  * space.  Since an isl_val does not have an associated space, this function
1550  * does not do anything, apart from error handling and cleaning up memory.
1551  */
1552 __isl_give isl_val *isl_val_realign_domain(__isl_take isl_val *v,
1553         __isl_take isl_reordering *r)
1554 {
1555         if (!r)
1556                 return isl_val_free(v);
1557         isl_reordering_free(r);
1558         return v;
1559 }
1560
1561 /* Return an isl_val that is zero on "ls".
1562  *
1563  * This function is only meant to be used in the generic isl_multi_*
1564  * functions which have to deal with base objects that have an associated
1565  * space.  Since an isl_val does not have an associated space, this function
1566  * simply returns a zero isl_val in the same context as "ls".
1567  */
1568 __isl_give isl_val *isl_val_zero_on_domain(__isl_take isl_local_space *ls)
1569 {
1570         isl_ctx *ctx;
1571
1572         if (!ls)
1573                 return NULL;
1574         ctx = isl_local_space_get_ctx(ls);
1575         isl_local_space_free(ls);
1576         return isl_val_zero(ctx);
1577 }
1578
1579 /* Do the parameters of "v" match those of "space"?
1580  *
1581  * This function is only meant to be used in the generic isl_multi_*
1582  * functions which have to deal with base objects that have an associated
1583  * space.  Since an isl_val does not have an associated space, this function
1584  * simply returns 1, except if "v" or "space" are NULL.
1585  */
1586 int isl_val_matching_params(__isl_keep isl_val *v, __isl_keep isl_space *space)
1587 {
1588         if (!v || !space)
1589                 return -1;
1590         return 1;
1591 }
1592
1593 /* Check that the domain space of "v" matches "space".
1594  *
1595  * Return 0 on success and -1 on error.
1596  *
1597  * This function is only meant to be used in the generic isl_multi_*
1598  * functions which have to deal with base objects that have an associated
1599  * space.  Since an isl_val does not have an associated space, this function
1600  * simply returns 0, except if "v" or "space" are NULL.
1601  */
1602 int isl_val_check_match_domain_space(__isl_keep isl_val *v,
1603         __isl_keep isl_space *space)
1604 {
1605         if (!v || !space)
1606                 return -1;
1607         return 0;
1608 }
1609
1610 #undef BASE
1611 #define BASE val
1612
1613 #define NO_DOMAIN
1614 #define NO_IDENTITY
1615 #define NO_FROM_BASE
1616 #define NO_MOVE_DIMS
1617 #include <isl_multi_templ.c>
1618
1619 /* Apply "fn" to each of the elements of "mv" with as second argument "v".
1620  */
1621 static __isl_give isl_multi_val *isl_multi_val_fn_val(
1622         __isl_take isl_multi_val *mv,
1623         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
1624                                         __isl_take isl_val *v2),
1625         __isl_take isl_val *v)
1626 {
1627         int i;
1628
1629         mv = isl_multi_val_cow(mv);
1630         if (!mv || !v)
1631                 goto error;
1632
1633         for (i = 0; i < mv->n; ++i) {
1634                 mv->p[i] = fn(mv->p[i], isl_val_copy(v));
1635                 if (!mv->p[i])
1636                         goto error;
1637         }
1638
1639         isl_val_free(v);
1640         return mv;
1641 error:
1642         isl_val_free(v);
1643         isl_multi_val_free(mv);
1644         return NULL;
1645 }
1646
1647 /* Add "v" to each of the elements of "mv".
1648  */
1649 __isl_give isl_multi_val *isl_multi_val_add_val(__isl_take isl_multi_val *mv,
1650         __isl_take isl_val *v)
1651 {
1652         if (!v)
1653                 return isl_multi_val_free(mv);
1654         if (isl_val_is_zero(v)) {
1655                 isl_val_free(v);
1656                 return mv;
1657         }
1658         return isl_multi_val_fn_val(mv, &isl_val_add, v);
1659 }
1660
1661 /* Reduce the elements of "mv" modulo "v".
1662  */
1663 __isl_give isl_multi_val *isl_multi_val_mod_val(__isl_take isl_multi_val *mv,
1664         __isl_take isl_val *v)
1665 {
1666         return isl_multi_val_fn_val(mv, &isl_val_mod, v);
1667 }