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         return isl_int_eq(v->n, v->d);
1174 }
1175
1176 /* Does "v" represent the integer negative one?
1177  */
1178 isl_bool isl_val_is_negone(__isl_keep isl_val *v)
1179 {
1180         if (!v)
1181                 return isl_bool_error;
1182
1183         return isl_int_is_neg(v->n) && isl_int_abs_eq(v->n, v->d);
1184 }
1185
1186 /* Is "v" (strictly) positive?
1187  */
1188 isl_bool isl_val_is_pos(__isl_keep isl_val *v)
1189 {
1190         if (!v)
1191                 return isl_bool_error;
1192
1193         return isl_int_is_pos(v->n);
1194 }
1195
1196 /* Is "v" (strictly) negative?
1197  */
1198 isl_bool isl_val_is_neg(__isl_keep isl_val *v)
1199 {
1200         if (!v)
1201                 return isl_bool_error;
1202
1203         return isl_int_is_neg(v->n);
1204 }
1205
1206 /* Is "v" non-negative?
1207  */
1208 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v)
1209 {
1210         if (!v)
1211                 return isl_bool_error;
1212
1213         if (isl_val_is_nan(v))
1214                 return isl_bool_false;
1215
1216         return isl_int_is_nonneg(v->n);
1217 }
1218
1219 /* Is "v" non-positive?
1220  */
1221 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v)
1222 {
1223         if (!v)
1224                 return isl_bool_error;
1225
1226         if (isl_val_is_nan(v))
1227                 return isl_bool_false;
1228
1229         return isl_int_is_nonpos(v->n);
1230 }
1231
1232 /* Return the sign of "v".
1233  *
1234  * The sign of NaN is undefined.
1235  */
1236 int isl_val_sgn(__isl_keep isl_val *v)
1237 {
1238         if (!v)
1239                 return 0;
1240         if (isl_val_is_zero(v))
1241                 return 0;
1242         if (isl_val_is_pos(v))
1243                 return 1;
1244         return -1;
1245 }
1246
1247 /* Is "v1" (strictly) less than "v2"?
1248  */
1249 isl_bool isl_val_lt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1250 {
1251         isl_int t;
1252         isl_bool lt;
1253
1254         if (!v1 || !v2)
1255                 return isl_bool_error;
1256         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1257                 return isl_int_lt(v1->n, v2->n);
1258         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1259                 return isl_bool_false;
1260         if (isl_val_eq(v1, v2))
1261                 return isl_bool_false;
1262         if (isl_val_is_infty(v2))
1263                 return isl_bool_true;
1264         if (isl_val_is_infty(v1))
1265                 return isl_bool_false;
1266         if (isl_val_is_neginfty(v1))
1267                 return isl_bool_true;
1268         if (isl_val_is_neginfty(v2))
1269                 return isl_bool_false;
1270
1271         isl_int_init(t);
1272         isl_int_mul(t, v1->n, v2->d);
1273         isl_int_submul(t, v2->n, v1->d);
1274         lt = isl_int_is_neg(t);
1275         isl_int_clear(t);
1276
1277         return lt;
1278 }
1279
1280 /* Is "v1" (strictly) greater than "v2"?
1281  */
1282 isl_bool isl_val_gt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1283 {
1284         return isl_val_lt(v2, v1);
1285 }
1286
1287 /* Is "v1" less than or equal to "v2"?
1288  */
1289 isl_bool isl_val_le(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1290 {
1291         isl_int t;
1292         isl_bool le;
1293
1294         if (!v1 || !v2)
1295                 return isl_bool_error;
1296         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1297                 return isl_int_le(v1->n, v2->n);
1298         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1299                 return isl_bool_false;
1300         if (isl_val_eq(v1, v2))
1301                 return isl_bool_true;
1302         if (isl_val_is_infty(v2))
1303                 return isl_bool_true;
1304         if (isl_val_is_infty(v1))
1305                 return isl_bool_false;
1306         if (isl_val_is_neginfty(v1))
1307                 return isl_bool_true;
1308         if (isl_val_is_neginfty(v2))
1309                 return isl_bool_false;
1310
1311         isl_int_init(t);
1312         isl_int_mul(t, v1->n, v2->d);
1313         isl_int_submul(t, v2->n, v1->d);
1314         le = isl_int_is_nonpos(t);
1315         isl_int_clear(t);
1316
1317         return le;
1318 }
1319
1320 /* Is "v1" greater than or equal to "v2"?
1321  */
1322 isl_bool isl_val_ge(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1323 {
1324         return isl_val_le(v2, v1);
1325 }
1326
1327 /* How does "v" compare to "i"?
1328  *
1329  * Return 1 if v is greater, -1 if v is smaller and 0 if v is equal to i.
1330  *
1331  * If v is NaN (or NULL), then the result is undefined.
1332  */
1333 int isl_val_cmp_si(__isl_keep isl_val *v, long i)
1334 {
1335         isl_int t;
1336         int cmp;
1337
1338         if (!v)
1339                 return 0;
1340         if (isl_val_is_int(v))
1341                 return isl_int_cmp_si(v->n, i);
1342         if (isl_val_is_nan(v))
1343                 return 0;
1344         if (isl_val_is_infty(v))
1345                 return 1;
1346         if (isl_val_is_neginfty(v))
1347                 return -1;
1348
1349         isl_int_init(t);
1350         isl_int_mul_si(t, v->d, i);
1351         isl_int_sub(t, v->n, t);
1352         cmp = isl_int_sgn(t);
1353         isl_int_clear(t);
1354
1355         return cmp;
1356 }
1357
1358 /* Is "v1" equal to "v2"?
1359  */
1360 isl_bool isl_val_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1361 {
1362         if (!v1 || !v2)
1363                 return isl_bool_error;
1364         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1365                 return isl_bool_false;
1366
1367         return isl_int_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1368 }
1369
1370 /* Is "v1" equal to "v2" in absolute value?
1371  */
1372 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1373 {
1374         if (!v1 || !v2)
1375                 return isl_bool_error;
1376         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1377                 return isl_bool_false;
1378
1379         return isl_int_abs_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1380 }
1381
1382 /* Is "v1" different from "v2"?
1383  */
1384 isl_bool isl_val_ne(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1385 {
1386         if (!v1 || !v2)
1387                 return isl_bool_error;
1388         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1389                 return isl_bool_false;
1390
1391         return isl_int_ne(v1->n, v2->n) || isl_int_ne(v1->d, v2->d);
1392 }
1393
1394 /* Print a textual representation of "v" onto "p".
1395  */
1396 __isl_give isl_printer *isl_printer_print_val(__isl_take isl_printer *p,
1397         __isl_keep isl_val *v)
1398 {
1399         int neg;
1400
1401         if (!p || !v)
1402                 return isl_printer_free(p);
1403
1404         neg = isl_int_is_neg(v->n);
1405         if (neg) {
1406                 p = isl_printer_print_str(p, "-");
1407                 isl_int_neg(v->n, v->n);
1408         }
1409         if (isl_int_is_zero(v->d)) {
1410                 int sgn = isl_int_sgn(v->n);
1411                 p = isl_printer_print_str(p, sgn < 0 ? "-infty" :
1412                                             sgn == 0 ? "NaN" : "infty");
1413         } else
1414                 p = isl_printer_print_isl_int(p, v->n);
1415         if (neg)
1416                 isl_int_neg(v->n, v->n);
1417         if (!isl_int_is_zero(v->d) && !isl_int_is_one(v->d)) {
1418                 p = isl_printer_print_str(p, "/");
1419                 p = isl_printer_print_isl_int(p, v->d);
1420         }
1421
1422         return p;
1423 }
1424
1425 /* Is "val1" (obviously) equal to "val2"?
1426  *
1427  * This is a private copy of isl_val_eq for use in the generic
1428  * isl_multi_*_plain_is_equal instantiated for isl_val.
1429  */
1430 int isl_val_plain_is_equal(__isl_keep isl_val *val1, __isl_keep isl_val *val2)
1431 {
1432         return isl_val_eq(val1, val2);
1433 }
1434
1435 /* Does "v" have any non-zero coefficients
1436  * for any dimension in the given range?
1437  *
1438  * This function is only meant to be used in the generic isl_multi_*
1439  * functions which have to deal with base objects that have an associated
1440  * space.  Since an isl_val does not have any coefficients, this function
1441  * always return 0.
1442  */
1443 int isl_val_involves_dims(__isl_keep isl_val *v, enum isl_dim_type type,
1444         unsigned first, unsigned n)
1445 {
1446         if (!v)
1447                 return -1;
1448
1449         return 0;
1450 }
1451
1452 /* Insert "n" dimensions of type "type" at position "first".
1453  *
1454  * This function is only meant to be used in the generic isl_multi_*
1455  * functions which have to deal with base objects that have an associated
1456  * space.  Since an isl_val does not have an associated space, this function
1457  * does not do anything.
1458  */
1459 __isl_give isl_val *isl_val_insert_dims(__isl_take isl_val *v,
1460         enum isl_dim_type type, unsigned first, unsigned n)
1461 {
1462         return v;
1463 }
1464
1465 /* Drop the the "n" first dimensions of type "type" at position "first".
1466  *
1467  * This function is only meant to be used in the generic isl_multi_*
1468  * functions which have to deal with base objects that have an associated
1469  * space.  Since an isl_val does not have an associated space, this function
1470  * does not do anything.
1471  */
1472 __isl_give isl_val *isl_val_drop_dims(__isl_take isl_val *v,
1473         enum isl_dim_type type, unsigned first, unsigned n)
1474 {
1475         return v;
1476 }
1477
1478 /* Change the name of the dimension of type "type" at position "pos" to "s".
1479  *
1480  * This function is only meant to be used in the generic isl_multi_*
1481  * functions which have to deal with base objects that have an associated
1482  * space.  Since an isl_val does not have an associated space, this function
1483  * does not do anything.
1484  */
1485 __isl_give isl_val *isl_val_set_dim_name(__isl_take isl_val *v,
1486         enum isl_dim_type type, unsigned pos, const char *s)
1487 {
1488         return v;
1489 }
1490
1491 /* Return the space of "v".
1492  *
1493  * This function is only meant to be used in the generic isl_multi_*
1494  * functions which have to deal with base objects that have an associated
1495  * space.  The conditions surrounding the call to this function make sure
1496  * that this function will never actually get called.  We return a valid
1497  * space anyway, just in case.
1498  */
1499 __isl_give isl_space *isl_val_get_space(__isl_keep isl_val *v)
1500 {
1501         if (!v)
1502                 return NULL;
1503
1504         return isl_space_params_alloc(isl_val_get_ctx(v), 0);
1505 }
1506
1507 /* Reset the domain space of "v" to "space".
1508  *
1509  * This function is only meant to be used in the generic isl_multi_*
1510  * functions which have to deal with base objects that have an associated
1511  * space.  Since an isl_val does not have an associated space, this function
1512  * does not do anything, apart from error handling and cleaning up memory.
1513  */
1514 __isl_give isl_val *isl_val_reset_domain_space(__isl_take isl_val *v,
1515         __isl_take isl_space *space)
1516 {
1517         if (!space)
1518                 return isl_val_free(v);
1519         isl_space_free(space);
1520         return v;
1521 }
1522
1523 /* Align the parameters of "v" to those of "space".
1524  *
1525  * This function is only meant to be used in the generic isl_multi_*
1526  * functions which have to deal with base objects that have an associated
1527  * space.  Since an isl_val does not have an associated space, this function
1528  * does not do anything, apart from error handling and cleaning up memory.
1529  * Note that the conditions surrounding the call to this function make sure
1530  * that this function will never actually get called.
1531  */
1532 __isl_give isl_val *isl_val_align_params(__isl_take isl_val *v,
1533         __isl_take isl_space *space)
1534 {
1535         if (!space)
1536                 return isl_val_free(v);
1537         isl_space_free(space);
1538         return v;
1539 }
1540
1541 /* Reorder the dimensions of the domain of "v" according
1542  * to the given reordering.
1543  *
1544  * This function is only meant to be used in the generic isl_multi_*
1545  * functions which have to deal with base objects that have an associated
1546  * space.  Since an isl_val does not have an associated space, this function
1547  * does not do anything, apart from error handling and cleaning up memory.
1548  */
1549 __isl_give isl_val *isl_val_realign_domain(__isl_take isl_val *v,
1550         __isl_take isl_reordering *r)
1551 {
1552         if (!r)
1553                 return isl_val_free(v);
1554         isl_reordering_free(r);
1555         return v;
1556 }
1557
1558 /* Return an isl_val that is zero on "ls".
1559  *
1560  * This function is only meant to be used in the generic isl_multi_*
1561  * functions which have to deal with base objects that have an associated
1562  * space.  Since an isl_val does not have an associated space, this function
1563  * simply returns a zero isl_val in the same context as "ls".
1564  */
1565 __isl_give isl_val *isl_val_zero_on_domain(__isl_take isl_local_space *ls)
1566 {
1567         isl_ctx *ctx;
1568
1569         if (!ls)
1570                 return NULL;
1571         ctx = isl_local_space_get_ctx(ls);
1572         isl_local_space_free(ls);
1573         return isl_val_zero(ctx);
1574 }
1575
1576 /* Do the parameters of "v" match those of "space"?
1577  *
1578  * This function is only meant to be used in the generic isl_multi_*
1579  * functions which have to deal with base objects that have an associated
1580  * space.  Since an isl_val does not have an associated space, this function
1581  * simply returns true, except if "v" or "space" are NULL.
1582  */
1583 isl_bool isl_val_matching_params(__isl_keep isl_val *v,
1584         __isl_keep isl_space *space)
1585 {
1586         if (!v || !space)
1587                 return isl_bool_error;
1588         return isl_bool_true;
1589 }
1590
1591 /* Check that the domain space of "v" matches "space".
1592  *
1593  * This function is only meant to be used in the generic isl_multi_*
1594  * functions which have to deal with base objects that have an associated
1595  * space.  Since an isl_val does not have an associated space, this function
1596  * simply returns 0, except if "v" or "space" are NULL.
1597  */
1598 isl_stat isl_val_check_match_domain_space(__isl_keep isl_val *v,
1599         __isl_keep isl_space *space)
1600 {
1601         if (!v || !space)
1602                 return isl_stat_error;
1603         return isl_stat_ok;
1604 }
1605
1606 #define isl_val_involves_nan isl_val_is_nan
1607
1608 #undef BASE
1609 #define BASE val
1610
1611 #define NO_DOMAIN
1612 #define NO_IDENTITY
1613 #define NO_FROM_BASE
1614 #define NO_MOVE_DIMS
1615 #include <isl_multi_templ.c>
1616
1617 /* Apply "fn" to each of the elements of "mv" with as second argument "v".
1618  */
1619 static __isl_give isl_multi_val *isl_multi_val_fn_val(
1620         __isl_take isl_multi_val *mv,
1621         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
1622                                         __isl_take isl_val *v2),
1623         __isl_take isl_val *v)
1624 {
1625         int i;
1626
1627         mv = isl_multi_val_cow(mv);
1628         if (!mv || !v)
1629                 goto error;
1630
1631         for (i = 0; i < mv->n; ++i) {
1632                 mv->p[i] = fn(mv->p[i], isl_val_copy(v));
1633                 if (!mv->p[i])
1634                         goto error;
1635         }
1636
1637         isl_val_free(v);
1638         return mv;
1639 error:
1640         isl_val_free(v);
1641         isl_multi_val_free(mv);
1642         return NULL;
1643 }
1644
1645 /* Add "v" to each of the elements of "mv".
1646  */
1647 __isl_give isl_multi_val *isl_multi_val_add_val(__isl_take isl_multi_val *mv,
1648         __isl_take isl_val *v)
1649 {
1650         if (!v)
1651                 return isl_multi_val_free(mv);
1652         if (isl_val_is_zero(v)) {
1653                 isl_val_free(v);
1654                 return mv;
1655         }
1656         return isl_multi_val_fn_val(mv, &isl_val_add, v);
1657 }
1658
1659 /* Reduce the elements of "mv" modulo "v".
1660  */
1661 __isl_give isl_multi_val *isl_multi_val_mod_val(__isl_take isl_multi_val *mv,
1662         __isl_take isl_val *v)
1663 {
1664         return isl_multi_val_fn_val(mv, &isl_val_mod, v);
1665 }