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 /* Return an approximation of "v" as a double.
 327  */
 328 double isl_val_get_d(__isl_keep isl_val *v)
 329 {
 330         if (!v)
 331                 return 0;
 332         if (!isl_val_is_rat(v))
 333                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 334                         "expecting rational value", return 0);
 335         return isl_int_get_d(v->n) / isl_int_get_d(v->d);
 336 }
 337
 338 /* Return the isl_ctx to which "val" belongs.
 339  */
 340 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val)
 341 {
 342         return val ? val->ctx : NULL;
 343 }
 344
 345 /* Normalize "v".
 346  *
 347  * In particular, make sure that the denominator of a rational value
 348  * is positive and the numerator and denominator do not have any
 349  * common divisors.
 350  *
 351  * This function should not be called by an external user
 352  * since it will only be given normalized values.
 353  */
 354 __isl_give isl_val *isl_val_normalize(__isl_take isl_val *v)
 355 {
 356         isl_ctx *ctx;
 357
 358         if (!v)
 359                 return NULL;
 360         if (isl_val_is_int(v))
 361                 return v;
 362         if (!isl_val_is_rat(v))
 363                 return v;
 364         if (isl_int_is_neg(v->d)) {
 365                 isl_int_neg(v->d, v->d);
 366                 isl_int_neg(v->n, v->n);
 367         }
 368         ctx = isl_val_get_ctx(v);
 369         isl_int_gcd(ctx->normalize_gcd, v->n, v->d);
 370         if (isl_int_is_one(ctx->normalize_gcd))
 371                 return v;
 372         isl_int_divexact(v->n, v->n, ctx->normalize_gcd);
 373         isl_int_divexact(v->d, v->d, ctx->normalize_gcd);
 374         return v;
 375 }
 376
 377 /* Return the opposite of "v".
 378  */
 379 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v)
 380 {
 381         if (!v)
 382                 return NULL;
 383         if (isl_val_is_nan(v))
 384                 return v;
 385         if (isl_val_is_zero(v))
 386                 return v;
 387
 388         v = isl_val_cow(v);
 389         if (!v)
 390                 return NULL;
 391         isl_int_neg(v->n, v->n);
 392
 393         return v;
 394 }
 395
 396 /* Return the inverse of "v".
 397  */
 398 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v)
 399 {
 400         if (!v)
 401                 return NULL;
 402         if (isl_val_is_nan(v))
 403                 return v;
 404         if (isl_val_is_zero(v)) {
 405                 isl_ctx *ctx = isl_val_get_ctx(v);
 406                 isl_val_free(v);
 407                 return isl_val_nan(ctx);
 408         }
 409         if (isl_val_is_infty(v) || isl_val_is_neginfty(v)) {
 410                 isl_ctx *ctx = isl_val_get_ctx(v);
 411                 isl_val_free(v);
 412                 return isl_val_zero(ctx);
 413         }
 414
 415         v = isl_val_cow(v);
 416         if (!v)
 417                 return NULL;
 418         isl_int_swap(v->n, v->d);
 419
 420         return isl_val_normalize(v);
 421 }
 422
 423 /* Return the absolute value of "v".
 424  */
 425 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v)
 426 {
 427         if (!v)
 428                 return NULL;
 429         if (isl_val_is_nan(v))
 430                 return v;
 431         if (isl_val_is_nonneg(v))
 432                 return v;
 433         return isl_val_neg(v);
 434 }
 435
 436 /* Return the "floor" (greatest integer part) of "v".
 437  * That is, return the result of rounding towards -infinity.
 438  */
 439 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v)
 440 {
 441         if (!v)
 442                 return NULL;
 443         if (isl_val_is_int(v))
 444                 return v;
 445         if (!isl_val_is_rat(v))
 446                 return v;
 447
 448         v = isl_val_cow(v);
 449         if (!v)
 450                 return NULL;
 451         isl_int_fdiv_q(v->n, v->n, v->d);
 452         isl_int_set_si(v->d, 1);
 453
 454         return v;
 455 }
 456
 457 /* Return the "ceiling" of "v".
 458  * That is, return the result of rounding towards +infinity.
 459  */
 460 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v)
 461 {
 462         if (!v)
 463                 return NULL;
 464         if (isl_val_is_int(v))
 465                 return v;
 466         if (!isl_val_is_rat(v))
 467                 return v;
 468
 469         v = isl_val_cow(v);
 470         if (!v)
 471                 return NULL;
 472         isl_int_cdiv_q(v->n, v->n, v->d);
 473         isl_int_set_si(v->d, 1);
 474
 475         return v;
 476 }
 477
 478 /* Truncate "v".
 479  * That is, return the result of rounding towards zero.
 480  */
 481 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v)
 482 {
 483         if (!v)
 484                 return NULL;
 485         if (isl_val_is_int(v))
 486                 return v;
 487         if (!isl_val_is_rat(v))
 488                 return v;
 489
 490         v = isl_val_cow(v);
 491         if (!v)
 492                 return NULL;
 493         isl_int_tdiv_q(v->n, v->n, v->d);
 494         isl_int_set_si(v->d, 1);
 495
 496         return v;
 497 }
 498
 499 /* Return 2^v, where v is an integer (that is not too large).
 500  */
 501 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v)
 502 {
 503         unsigned long exp;
 504         int neg;
 505
 506         v = isl_val_cow(v);
 507         if (!v)
 508                 return NULL;
 509         if (!isl_val_is_int(v))
 510                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 511                         "can only compute integer powers",
 512                         return isl_val_free(v));
 513         neg = isl_val_is_neg(v);
 514         if (neg)
 515                 isl_int_neg(v->n, v->n);
 516         if (!isl_int_fits_ulong(v->n))
 517                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 518                         "exponent too large", return isl_val_free(v));
 519         exp = isl_int_get_ui(v->n);
 520         if (neg) {
 521                 isl_int_mul_2exp(v->d, v->d, exp);
 522                 isl_int_set_si(v->n, 1);
 523         } else {
 524                 isl_int_mul_2exp(v->n, v->d, exp);
 525         }
 526
 527         return v;
 528 }
 529
 530 /* Return the minimum of "v1" and "v2".
 531  */
 532 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1, __isl_take isl_val *v2)
 533 {
 534         if (!v1 || !v2)
 535                 goto error;
 536
 537         if (isl_val_is_nan(v1)) {
 538                 isl_val_free(v2);
 539                 return v1;
 540         }
 541         if (isl_val_is_nan(v2)) {
 542                 isl_val_free(v1);
 543                 return v2;
 544         }
 545         if (isl_val_le(v1, v2)) {
 546                 isl_val_free(v2);
 547                 return v1;
 548         } else {
 549                 isl_val_free(v1);
 550                 return v2;
 551         }
 552 error:
 553         isl_val_free(v1);
 554         isl_val_free(v2);
 555         return NULL;
 556 }
 557
 558 /* Return the maximum of "v1" and "v2".
 559  */
 560 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1, __isl_take isl_val *v2)
 561 {
 562         if (!v1 || !v2)
 563                 goto error;
 564
 565         if (isl_val_is_nan(v1)) {
 566                 isl_val_free(v2);
 567                 return v1;
 568         }
 569         if (isl_val_is_nan(v2)) {
 570                 isl_val_free(v1);
 571                 return v2;
 572         }
 573         if (isl_val_ge(v1, v2)) {
 574                 isl_val_free(v2);
 575                 return v1;
 576         } else {
 577                 isl_val_free(v1);
 578                 return v2;
 579         }
 580 error:
 581         isl_val_free(v1);
 582         isl_val_free(v2);
 583         return NULL;
 584 }
 585
 586 /* Return the sum of "v1" and "v2".
 587  */
 588 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1, __isl_take isl_val *v2)
 589 {
 590         if (!v1 || !v2)
 591                 goto error;
 592         if (isl_val_is_nan(v1)) {
 593                 isl_val_free(v2);
 594                 return v1;
 595         }
 596         if (isl_val_is_nan(v2)) {
 597                 isl_val_free(v1);
 598                 return v2;
 599         }
 600         if ((isl_val_is_infty(v1) && isl_val_is_neginfty(v2)) ||
 601             (isl_val_is_neginfty(v1) && isl_val_is_infty(v2))) {
 602                 isl_val_free(v2);
 603                 return isl_val_set_nan(v1);
 604         }
 605         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 606                 isl_val_free(v2);
 607                 return v1;
 608         }
 609         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 610                 isl_val_free(v1);
 611                 return v2;
 612         }
 613         if (isl_val_is_zero(v1)) {
 614                 isl_val_free(v1);
 615                 return v2;
 616         }
 617         if (isl_val_is_zero(v2)) {
 618                 isl_val_free(v2);
 619                 return v1;
 620         }
 621
 622         v1 = isl_val_cow(v1);
 623         if (!v1)
 624                 goto error;
 625         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 626                 isl_int_add(v1->n, v1->n, v2->n);
 627         else {
 628                 if (isl_int_eq(v1->d, v2->d))
 629                         isl_int_add(v1->n, v1->n, v2->n);
 630                 else {
 631                         isl_int_mul(v1->n, v1->n, v2->d);
 632                         isl_int_addmul(v1->n, v2->n, v1->d);
 633                         isl_int_mul(v1->d, v1->d, v2->d);
 634                 }
 635                 v1 = isl_val_normalize(v1);
 636         }
 637         isl_val_free(v2);
 638         return v1;
 639 error:
 640         isl_val_free(v1);
 641         isl_val_free(v2);
 642         return NULL;
 643 }
 644
 645 /* Return the sum of "v1" and "v2".
 646  */
 647 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1, unsigned long v2)
 648 {
 649         if (!v1)
 650                 return NULL;
 651         if (!isl_val_is_rat(v1))
 652                 return v1;
 653         if (v2 == 0)
 654                 return v1;
 655         v1 = isl_val_cow(v1);
 656         if (!v1)
 657                 return NULL;
 658
 659         isl_int_addmul_ui(v1->n, v1->d, v2);
 660
 661         return v1;
 662 }
 663
 664 /* Subtract "v2" from "v1".
 665  */
 666 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1, __isl_take isl_val *v2)
 667 {
 668         if (!v1 || !v2)
 669                 goto error;
 670         if (isl_val_is_nan(v1)) {
 671                 isl_val_free(v2);
 672                 return v1;
 673         }
 674         if (isl_val_is_nan(v2)) {
 675                 isl_val_free(v1);
 676                 return v2;
 677         }
 678         if ((isl_val_is_infty(v1) && isl_val_is_infty(v2)) ||
 679             (isl_val_is_neginfty(v1) && isl_val_is_neginfty(v2))) {
 680                 isl_val_free(v2);
 681                 return isl_val_set_nan(v1);
 682         }
 683         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 684                 isl_val_free(v2);
 685                 return v1;
 686         }
 687         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 688                 isl_val_free(v1);
 689                 return isl_val_neg(v2);
 690         }
 691         if (isl_val_is_zero(v2)) {
 692                 isl_val_free(v2);
 693                 return v1;
 694         }
 695         if (isl_val_is_zero(v1)) {
 696                 isl_val_free(v1);
 697                 return isl_val_neg(v2);
 698         }
 699
 700         v1 = isl_val_cow(v1);
 701         if (!v1)
 702                 goto error;
 703         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 704                 isl_int_sub(v1->n, v1->n, v2->n);
 705         else {
 706                 if (isl_int_eq(v1->d, v2->d))
 707                         isl_int_sub(v1->n, v1->n, v2->n);
 708                 else {
 709                         isl_int_mul(v1->n, v1->n, v2->d);
 710                         isl_int_submul(v1->n, v2->n, v1->d);
 711                         isl_int_mul(v1->d, v1->d, v2->d);
 712                 }
 713                 v1 = isl_val_normalize(v1);
 714         }
 715         isl_val_free(v2);
 716         return v1;
 717 error:
 718         isl_val_free(v1);
 719         isl_val_free(v2);
 720         return NULL;
 721 }
 722
 723 /* Subtract "v2" from "v1".
 724  */
 725 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1, unsigned long v2)
 726 {
 727         if (!v1)
 728                 return NULL;
 729         if (!isl_val_is_rat(v1))
 730                 return v1;
 731         if (v2 == 0)
 732                 return v1;
 733         v1 = isl_val_cow(v1);
 734         if (!v1)
 735                 return NULL;
 736
 737         isl_int_submul_ui(v1->n, v1->d, v2);
 738
 739         return v1;
 740 }
 741
 742 /* Return the product of "v1" and "v2".
 743  */
 744 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1, __isl_take isl_val *v2)
 745 {
 746         if (!v1 || !v2)
 747                 goto error;
 748         if (isl_val_is_nan(v1)) {
 749                 isl_val_free(v2);
 750                 return v1;
 751         }
 752         if (isl_val_is_nan(v2)) {
 753                 isl_val_free(v1);
 754                 return v2;
 755         }
 756         if ((!isl_val_is_rat(v1) && isl_val_is_zero(v2)) ||
 757             (isl_val_is_zero(v1) && !isl_val_is_rat(v2))) {
 758                 isl_val_free(v2);
 759                 return isl_val_set_nan(v1);
 760         }
 761         if (isl_val_is_zero(v1)) {
 762                 isl_val_free(v2);
 763                 return v1;
 764         }
 765         if (isl_val_is_zero(v2)) {
 766                 isl_val_free(v1);
 767                 return v2;
 768         }
 769         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 770                 if (isl_val_is_neg(v2))
 771                         v1 = isl_val_neg(v1);
 772                 isl_val_free(v2);
 773                 return v1;
 774         }
 775         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 776                 if (isl_val_is_neg(v1))
 777                         v2 = isl_val_neg(v2);
 778                 isl_val_free(v1);
 779                 return v2;
 780         }
 781
 782         v1 = isl_val_cow(v1);
 783         if (!v1)
 784                 goto error;
 785         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 786                 isl_int_mul(v1->n, v1->n, v2->n);
 787         else {
 788                 isl_int_mul(v1->n, v1->n, v2->n);
 789                 isl_int_mul(v1->d, v1->d, v2->d);
 790                 v1 = isl_val_normalize(v1);
 791         }
 792         isl_val_free(v2);
 793         return v1;
 794 error:
 795         isl_val_free(v1);
 796         isl_val_free(v2);
 797         return NULL;
 798 }
 799
 800 /* Return the product of "v1" and "v2".
 801  *
 802  * This is a private copy of isl_val_mul for use in the generic
 803  * isl_multi_*_scale_val instantiated for isl_val.
 804  */
 805 __isl_give isl_val *isl_val_scale_val(__isl_take isl_val *v1,
 806         __isl_take isl_val *v2)
 807 {
 808         return isl_val_mul(v1, v2);
 809 }
 810
 811 /* Return the product of "v1" and "v2".
 812  */
 813 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1, unsigned long v2)
 814 {
 815         if (!v1)
 816                 return NULL;
 817         if (isl_val_is_nan(v1))
 818                 return v1;
 819         if (!isl_val_is_rat(v1)) {
 820                 if (v2 == 0)
 821                         v1 = isl_val_set_nan(v1);
 822                 return v1;
 823         }
 824         if (v2 == 1)
 825                 return v1;
 826         v1 = isl_val_cow(v1);
 827         if (!v1)
 828                 return NULL;
 829
 830         isl_int_mul_ui(v1->n, v1->n, v2);
 831
 832         return isl_val_normalize(v1);
 833 }
 834
 835 /* Divide "v1" by "v2".
 836  */
 837 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1, __isl_take isl_val *v2)
 838 {
 839         if (!v1 || !v2)
 840                 goto error;
 841         if (isl_val_is_nan(v1)) {
 842                 isl_val_free(v2);
 843                 return v1;
 844         }
 845         if (isl_val_is_nan(v2)) {
 846                 isl_val_free(v1);
 847                 return v2;
 848         }
 849         if (isl_val_is_zero(v2) ||
 850             (!isl_val_is_rat(v1) && !isl_val_is_rat(v2))) {
 851                 isl_val_free(v2);
 852                 return isl_val_set_nan(v1);
 853         }
 854         if (isl_val_is_zero(v1)) {
 855                 isl_val_free(v2);
 856                 return v1;
 857         }
 858         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 859                 if (isl_val_is_neg(v2))
 860                         v1 = isl_val_neg(v1);
 861                 isl_val_free(v2);
 862                 return v1;
 863         }
 864         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 865                 isl_val_free(v2);
 866                 return isl_val_set_zero(v1);
 867         }
 868
 869         v1 = isl_val_cow(v1);
 870         if (!v1)
 871                 goto error;
 872         if (isl_val_is_int(v2)) {
 873                 isl_int_mul(v1->d, v1->d, v2->n);
 874                 v1 = isl_val_normalize(v1);
 875         } else {
 876                 isl_int_mul(v1->d, v1->d, v2->n);
 877                 isl_int_mul(v1->n, v1->n, v2->d);
 878                 v1 = isl_val_normalize(v1);
 879         }
 880         isl_val_free(v2);
 881         return v1;
 882 error:
 883         isl_val_free(v1);
 884         isl_val_free(v2);
 885         return NULL;
 886 }
 887
 888 /* Divide "v1" by "v2".
 889  *
 890  * This is a private copy of isl_val_div for use in the generic
 891  * isl_multi_*_scale_down_val instantiated for isl_val.
 892  */
 893 __isl_give isl_val *isl_val_scale_down_val(__isl_take isl_val *v1,
 894         __isl_take isl_val *v2)
 895 {
 896         return isl_val_div(v1, v2);
 897 }
 898
 899 /* Given two integer values "v1" and "v2", check if "v1" is divisible by "v2".
 900  */
 901 int isl_val_is_divisible_by(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
 902 {
 903         if (!v1 || !v2)
 904                 return -1;
 905
 906         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 907                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 908                         "expecting two integers", return -1);
 909
 910         return isl_int_is_divisible_by(v1->n, v2->n);
 911 }
 912
 913 /* Given two integer values "v1" and "v2", return the residue of "v1"
 914  * modulo "v2".
 915  */
 916 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1, __isl_take isl_val *v2)
 917 {
 918         if (!v1 || !v2)
 919                 goto error;
 920         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 921                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 922                         "expecting two integers", goto error);
 923         if (isl_val_is_nonneg(v1) && isl_val_lt(v1, v2)) {
 924                 isl_val_free(v2);
 925                 return v1;
 926         }
 927         v1 = isl_val_cow(v1);
 928         if (!v1)
 929                 goto error;
 930         isl_int_fdiv_r(v1->n, v1->n, v2->n);
 931         isl_val_free(v2);
 932         return v1;
 933 error:
 934         isl_val_free(v1);
 935         isl_val_free(v2);
 936         return NULL;
 937 }
 938
 939 /* Given two integer values, return their greatest common divisor.
 940  */
 941 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1, __isl_take isl_val *v2)
 942 {
 943         if (!v1 || !v2)
 944                 goto error;
 945         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 946                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 947                         "expecting two integers", goto error);
 948         if (isl_val_eq(v1, v2)) {
 949                 isl_val_free(v2);
 950                 return v1;
 951         }
 952         if (isl_val_is_one(v1)) {
 953                 isl_val_free(v2);
 954                 return v1;
 955         }
 956         if (isl_val_is_one(v2)) {
 957                 isl_val_free(v1);
 958                 return v2;
 959         }
 960         v1 = isl_val_cow(v1);
 961         if (!v1)
 962                 goto error;
 963         isl_int_gcd(v1->n, v1->n, v2->n);
 964         isl_val_free(v2);
 965         return v1;
 966 error:
 967         isl_val_free(v1);
 968         isl_val_free(v2);
 969         return NULL;
 970 }
 971
 972 /* Compute x, y and g such that g = gcd(a,b) and a*x+b*y = g.
 973  */
 974 static void isl_int_gcdext(isl_int g, isl_int x, isl_int y,
 975         isl_int a, isl_int b)
 976 {
 977         isl_int d, tmp;
 978         isl_int a_copy, b_copy;
 979
 980         isl_int_init(a_copy);
 981         isl_int_init(b_copy);
 982         isl_int_init(d);
 983         isl_int_init(tmp);
 984         isl_int_set(a_copy, a);
 985         isl_int_set(b_copy, b);
 986         isl_int_abs(g, a_copy);
 987         isl_int_abs(d, b_copy);
 988         isl_int_set_si(x, 1);
 989         isl_int_set_si(y, 0);
 990         while (isl_int_is_pos(d)) {
 991                 isl_int_fdiv_q(tmp, g, d);
 992                 isl_int_submul(x, tmp, y);
 993                 isl_int_submul(g, tmp, d);
 994                 isl_int_swap(g, d);
 995                 isl_int_swap(x, y);
 996         }
 997         if (isl_int_is_zero(a_copy))
 998                 isl_int_set_si(x, 0);
 999         else if (isl_int_is_neg(a_copy))
1000                 isl_int_neg(x, x);
1001         if (isl_int_is_zero(b_copy))
1002                 isl_int_set_si(y, 0);
1003         else {
1004                 isl_int_mul(tmp, a_copy, x);
1005                 isl_int_sub(tmp, g, tmp);
1006                 isl_int_divexact(y, tmp, b_copy);
1007         }
1008         isl_int_clear(d);
1009         isl_int_clear(tmp);
1010         isl_int_clear(a_copy);
1011         isl_int_clear(b_copy);
1012 }
1013
1014 /* Given two integer values v1 and v2, return their greatest common divisor g,
1015  * as well as two integers x and y such that x * v1 + y * v2 = g.
1016  */
1017 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
1018         __isl_take isl_val *v2, __isl_give isl_val **x, __isl_give isl_val **y)
1019 {
1020         isl_ctx *ctx;
1021         isl_val *a = NULL, *b = NULL;
1022
1023         if (!x && !y)
1024                 return isl_val_gcd(v1, v2);
1025
1026         if (!v1 || !v2)
1027                 goto error;
1028
1029         ctx = isl_val_get_ctx(v1);
1030         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
1031                 isl_die(ctx, isl_error_invalid,
1032                         "expecting two integers", goto error);
1033
1034         v1 = isl_val_cow(v1);
1035         a = isl_val_alloc(ctx);
1036         b = isl_val_alloc(ctx);
1037         if (!v1 || !a || !b)
1038                 goto error;
1039         isl_int_gcdext(v1->n, a->n, b->n, v1->n, v2->n);
1040         if (x) {
1041                 isl_int_set_si(a->d, 1);
1042                 *x = a;
1043         } else
1044                 isl_val_free(a);
1045         if (y) {
1046                 isl_int_set_si(b->d, 1);
1047                 *y = b;
1048         } else
1049                 isl_val_free(b);
1050         isl_val_free(v2);
1051         return v1;
1052 error:
1053         isl_val_free(v1);
1054         isl_val_free(v2);
1055         isl_val_free(a);
1056         isl_val_free(b);
1057         if (x)
1058                 *x = NULL;
1059         if (y)
1060                 *y = NULL;
1061         return NULL;
1062 }
1063
1064 /* Does "v" represent an integer value?
1065  */
1066 int isl_val_is_int(__isl_keep isl_val *v)
1067 {
1068         if (!v)
1069                 return -1;
1070
1071         return isl_int_is_one(v->d);
1072 }
1073
1074 /* Does "v" represent a rational value?
1075  */
1076 int isl_val_is_rat(__isl_keep isl_val *v)
1077 {
1078         if (!v)
1079                 return -1;
1080
1081         return !isl_int_is_zero(v->d);
1082 }
1083
1084 /* Does "v" represent NaN?
1085  */
1086 int isl_val_is_nan(__isl_keep isl_val *v)
1087 {
1088         if (!v)
1089                 return -1;
1090
1091         return isl_int_is_zero(v->n) && isl_int_is_zero(v->d);
1092 }
1093
1094 /* Does "v" represent +infinity?
1095  */
1096 int isl_val_is_infty(__isl_keep isl_val *v)
1097 {
1098         if (!v)
1099                 return -1;
1100
1101         return isl_int_is_pos(v->n) && isl_int_is_zero(v->d);
1102 }
1103
1104 /* Does "v" represent -infinity?
1105  */
1106 int isl_val_is_neginfty(__isl_keep isl_val *v)
1107 {
1108         if (!v)
1109                 return -1;
1110
1111         return isl_int_is_neg(v->n) && isl_int_is_zero(v->d);
1112 }
1113
1114 /* Does "v" represent the integer zero?
1115  */
1116 int isl_val_is_zero(__isl_keep isl_val *v)
1117 {
1118         if (!v)
1119                 return -1;
1120
1121         return isl_int_is_zero(v->n) && !isl_int_is_zero(v->d);
1122 }
1123
1124 /* Does "v" represent the integer one?
1125  */
1126 int isl_val_is_one(__isl_keep isl_val *v)
1127 {
1128         if (!v)
1129                 return -1;
1130
1131         return isl_int_eq(v->n, v->d);
1132 }
1133
1134 /* Does "v" represent the integer negative one?
1135  */
1136 int isl_val_is_negone(__isl_keep isl_val *v)
1137 {
1138         if (!v)
1139                 return -1;
1140
1141         return isl_int_is_neg(v->n) && isl_int_abs_eq(v->n, v->d);
1142 }
1143
1144 /* Is "v" (strictly) positive?
1145  */
1146 int isl_val_is_pos(__isl_keep isl_val *v)
1147 {
1148         if (!v)
1149                 return -1;
1150
1151         return isl_int_is_pos(v->n);
1152 }
1153
1154 /* Is "v" (strictly) negative?
1155  */
1156 int isl_val_is_neg(__isl_keep isl_val *v)
1157 {
1158         if (!v)
1159                 return -1;
1160
1161         return isl_int_is_neg(v->n);
1162 }
1163
1164 /* Is "v" non-negative?
1165  */
1166 int isl_val_is_nonneg(__isl_keep isl_val *v)
1167 {
1168         if (!v)
1169                 return -1;
1170
1171         if (isl_val_is_nan(v))
1172                 return 0;
1173
1174         return isl_int_is_nonneg(v->n);
1175 }
1176
1177 /* Is "v" non-positive?
1178  */
1179 int isl_val_is_nonpos(__isl_keep isl_val *v)
1180 {
1181         if (!v)
1182                 return -1;
1183
1184         if (isl_val_is_nan(v))
1185                 return 0;
1186
1187         return isl_int_is_nonpos(v->n);
1188 }
1189
1190 /* Return the sign of "v".
1191  *
1192  * The sign of NaN is undefined.
1193  */
1194 int isl_val_sgn(__isl_keep isl_val *v)
1195 {
1196         if (!v)
1197                 return 0;
1198         if (isl_val_is_zero(v))
1199                 return 0;
1200         if (isl_val_is_pos(v))
1201                 return 1;
1202         return -1;
1203 }
1204
1205 /* Is "v1" (strictly) less than "v2"?
1206  */
1207 int isl_val_lt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1208 {
1209         isl_int t;
1210         int lt;
1211
1212         if (!v1 || !v2)
1213                 return -1;
1214         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1215                 return isl_int_lt(v1->n, v2->n);
1216         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1217                 return 0;
1218         if (isl_val_eq(v1, v2))
1219                 return 0;
1220         if (isl_val_is_infty(v2))
1221                 return 1;
1222         if (isl_val_is_infty(v1))
1223                 return 0;
1224         if (isl_val_is_neginfty(v1))
1225                 return 1;
1226         if (isl_val_is_neginfty(v2))
1227                 return 0;
1228
1229         isl_int_init(t);
1230         isl_int_mul(t, v1->n, v2->d);
1231         isl_int_submul(t, v2->n, v1->d);
1232         lt = isl_int_is_neg(t);
1233         isl_int_clear(t);
1234
1235         return lt;
1236 }
1237
1238 /* Is "v1" (strictly) greater than "v2"?
1239  */
1240 int isl_val_gt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1241 {
1242         return isl_val_lt(v2, v1);
1243 }
1244
1245 /* Is "v1" less than or equal to "v2"?
1246  */
1247 int isl_val_le(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1248 {
1249         isl_int t;
1250         int le;
1251
1252         if (!v1 || !v2)
1253                 return -1;
1254         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1255                 return isl_int_le(v1->n, v2->n);
1256         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1257                 return 0;
1258         if (isl_val_eq(v1, v2))
1259                 return 1;
1260         if (isl_val_is_infty(v2))
1261                 return 1;
1262         if (isl_val_is_infty(v1))
1263                 return 0;
1264         if (isl_val_is_neginfty(v1))
1265                 return 1;
1266         if (isl_val_is_neginfty(v2))
1267                 return 0;
1268
1269         isl_int_init(t);
1270         isl_int_mul(t, v1->n, v2->d);
1271         isl_int_submul(t, v2->n, v1->d);
1272         le = isl_int_is_nonpos(t);
1273         isl_int_clear(t);
1274
1275         return le;
1276 }
1277
1278 /* Is "v1" greater than or equal to "v2"?
1279  */
1280 int isl_val_ge(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1281 {
1282         return isl_val_le(v2, v1);
1283 }
1284
1285 /* How does "v" compare to "i"?
1286  *
1287  * Return 1 if v is greater, -1 if v is smaller and 0 if v is equal to i.
1288  *
1289  * If v is NaN (or NULL), then the result is undefined.
1290  */
1291 int isl_val_cmp_si(__isl_keep isl_val *v, long i)
1292 {
1293         isl_int t;
1294         int cmp;
1295
1296         if (!v)
1297                 return 0;
1298         if (isl_val_is_int(v))
1299                 return isl_int_cmp_si(v->n, i);
1300         if (isl_val_is_nan(v))
1301                 return 0;
1302         if (isl_val_is_infty(v))
1303                 return 1;
1304         if (isl_val_is_neginfty(v))
1305                 return -1;
1306
1307         isl_int_init(t);
1308         isl_int_mul_si(t, v->d, i);
1309         isl_int_sub(t, v->n, t);
1310         cmp = isl_int_sgn(t);
1311         isl_int_clear(t);
1312
1313         return cmp;
1314 }
1315
1316 /* Is "v1" equal to "v2"?
1317  */
1318 int isl_val_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1319 {
1320         if (!v1 || !v2)
1321                 return -1;
1322         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1323                 return 0;
1324
1325         return isl_int_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1326 }
1327
1328 /* Is "v1" equal to "v2" in absolute value?
1329  */
1330 int isl_val_abs_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1331 {
1332         if (!v1 || !v2)
1333                 return -1;
1334         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1335                 return 0;
1336
1337         return isl_int_abs_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1338 }
1339
1340 /* Is "v1" different from "v2"?
1341  */
1342 int isl_val_ne(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1343 {
1344         if (!v1 || !v2)
1345                 return -1;
1346         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1347                 return 0;
1348
1349         return isl_int_ne(v1->n, v2->n) || isl_int_ne(v1->d, v2->d);
1350 }
1351
1352 /* Print a textual representation of "v" onto "p".
1353  */
1354 __isl_give isl_printer *isl_printer_print_val(__isl_take isl_printer *p,
1355         __isl_keep isl_val *v)
1356 {
1357         int neg;
1358
1359         if (!p || !v)
1360                 return isl_printer_free(p);
1361
1362         neg = isl_int_is_neg(v->n);
1363         if (neg) {
1364                 p = isl_printer_print_str(p, "-");
1365                 isl_int_neg(v->n, v->n);
1366         }
1367         if (isl_int_is_zero(v->d)) {
1368                 int sgn = isl_int_sgn(v->n);
1369                 p = isl_printer_print_str(p, sgn < 0 ? "-infty" :
1370                                             sgn == 0 ? "NaN" : "infty");
1371         } else
1372                 p = isl_printer_print_isl_int(p, v->n);
1373         if (neg)
1374                 isl_int_neg(v->n, v->n);
1375         if (!isl_int_is_zero(v->d) && !isl_int_is_one(v->d)) {
1376                 p = isl_printer_print_str(p, "/");
1377                 p = isl_printer_print_isl_int(p, v->d);
1378         }
1379
1380         return p;
1381 }
1382
1383 /* Is "val1" (obviously) equal to "val2"?
1384  *
1385  * This is a private copy of isl_val_eq for use in the generic
1386  * isl_multi_*_plain_is_equal instantiated for isl_val.
1387  */
1388 int isl_val_plain_is_equal(__isl_keep isl_val *val1, __isl_keep isl_val *val2)
1389 {
1390         return isl_val_eq(val1, val2);
1391 }
1392
1393 /* Does "v" have any non-zero coefficients
1394  * for any dimension in the given range?
1395  *
1396  * This function is only meant to be used in the generic isl_multi_*
1397  * functions which have to deal with base objects that have an associated
1398  * space.  Since an isl_val does not have any coefficients, this function
1399  * always return 0.
1400  */
1401 int isl_val_involves_dims(__isl_keep isl_val *v, enum isl_dim_type type,
1402         unsigned first, unsigned n)
1403 {
1404         if (!v)
1405                 return -1;
1406
1407         return 0;
1408 }
1409
1410 /* Insert "n" dimensions of type "type" at position "first".
1411  *
1412  * This function is only meant to be used in the generic isl_multi_*
1413  * functions which have to deal with base objects that have an associated
1414  * space.  Since an isl_val does not have an associated space, this function
1415  * does not do anything.
1416  */
1417 __isl_give isl_val *isl_val_insert_dims(__isl_take isl_val *v,
1418         enum isl_dim_type type, unsigned first, unsigned n)
1419 {
1420         return v;
1421 }
1422
1423 /* Drop the the "n" first dimensions of type "type" at position "first".
1424  *
1425  * This function is only meant to be used in the generic isl_multi_*
1426  * functions which have to deal with base objects that have an associated
1427  * space.  Since an isl_val does not have an associated space, this function
1428  * does not do anything.
1429  */
1430 __isl_give isl_val *isl_val_drop_dims(__isl_take isl_val *v,
1431         enum isl_dim_type type, unsigned first, unsigned n)
1432 {
1433         return v;
1434 }
1435
1436 /* Change the name of the dimension of type "type" at position "pos" to "s".
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 an associated space, this function
1441  * does not do anything.
1442  */
1443 __isl_give isl_val *isl_val_set_dim_name(__isl_take isl_val *v,
1444         enum isl_dim_type type, unsigned pos, const char *s)
1445 {
1446         return v;
1447 }
1448
1449 /* Return the space of "v".
1450  *
1451  * This function is only meant to be used in the generic isl_multi_*
1452  * functions which have to deal with base objects that have an associated
1453  * space.  The conditions surrounding the call to this function make sure
1454  * that this function will never actually get called.  We return a valid
1455  * space anyway, just in case.
1456  */
1457 __isl_give isl_space *isl_val_get_space(__isl_keep isl_val *v)
1458 {
1459         if (!v)
1460                 return NULL;
1461
1462         return isl_space_params_alloc(isl_val_get_ctx(v), 0);
1463 }
1464
1465 /* Reset the domain space of "v" to "space".
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, apart from error handling and cleaning up memory.
1471  */
1472 __isl_give isl_val *isl_val_reset_domain_space(__isl_take isl_val *v,
1473         __isl_take isl_space *space)
1474 {
1475         if (!space)
1476                 return isl_val_free(v);
1477         isl_space_free(space);
1478         return v;
1479 }
1480
1481 /* Align the parameters of "v" to those of "space".
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, apart from error handling and cleaning up memory.
1487  * Note that the conditions surrounding the call to this function make sure
1488  * that this function will never actually get called.
1489  */
1490 __isl_give isl_val *isl_val_align_params(__isl_take isl_val *v,
1491         __isl_take isl_space *space)
1492 {
1493         if (!space)
1494                 return isl_val_free(v);
1495         isl_space_free(space);
1496         return v;
1497 }
1498
1499 /* Reorder the dimensions of the domain of "v" according
1500  * to the given reordering.
1501  *
1502  * This function is only meant to be used in the generic isl_multi_*
1503  * functions which have to deal with base objects that have an associated
1504  * space.  Since an isl_val does not have an associated space, this function
1505  * does not do anything, apart from error handling and cleaning up memory.
1506  */
1507 __isl_give isl_val *isl_val_realign_domain(__isl_take isl_val *v,
1508         __isl_take isl_reordering *r)
1509 {
1510         if (!r)
1511                 return isl_val_free(v);
1512         isl_reordering_free(r);
1513         return v;
1514 }
1515
1516 /* Return an isl_val that is zero on "ls".
1517  *
1518  * This function is only meant to be used in the generic isl_multi_*
1519  * functions which have to deal with base objects that have an associated
1520  * space.  Since an isl_val does not have an associated space, this function
1521  * simply returns a zero isl_val in the same context as "ls".
1522  */
1523 __isl_give isl_val *isl_val_zero_on_domain(__isl_take isl_local_space *ls)
1524 {
1525         isl_ctx *ctx;
1526
1527         if (!ls)
1528                 return NULL;
1529         ctx = isl_local_space_get_ctx(ls);
1530         isl_local_space_free(ls);
1531         return isl_val_zero(ctx);
1532 }
1533
1534 /* Do the parameters of "v" match those of "space"?
1535  *
1536  * This function is only meant to be used in the generic isl_multi_*
1537  * functions which have to deal with base objects that have an associated
1538  * space.  Since an isl_val does not have an associated space, this function
1539  * simply returns 1, except if "v" or "space" are NULL.
1540  */
1541 int isl_val_matching_params(__isl_keep isl_val *v, __isl_keep isl_space *space)
1542 {
1543         if (!v || !space)
1544                 return -1;
1545         return 1;
1546 }
1547
1548 /* Check that the domain space of "v" matches "space".
1549  *
1550  * Return 0 on success and -1 on error.
1551  *
1552  * This function is only meant to be used in the generic isl_multi_*
1553  * functions which have to deal with base objects that have an associated
1554  * space.  Since an isl_val does not have an associated space, this function
1555  * simply returns 0, except if "v" or "space" are NULL.
1556  */
1557 int isl_val_check_match_domain_space(__isl_keep isl_val *v,
1558         __isl_keep isl_space *space)
1559 {
1560         if (!v || !space)
1561                 return -1;
1562         return 0;
1563 }
1564
1565 #undef BASE
1566 #define BASE val
1567
1568 #define NO_DOMAIN
1569 #define NO_INTERSECT_DOMAIN
1570 #define NO_GIST
1571 #define NO_IDENTITY
1572 #define NO_FROM_BASE
1573 #define NO_MOVE_DIMS
1574 #include <isl_multi_templ.c>
1575
1576 /* Apply "fn" to each of the elements of "mv" with as second argument "v".
1577  */
1578 static __isl_give isl_multi_val *isl_multi_val_fn_val(
1579         __isl_take isl_multi_val *mv,
1580         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
1581                                         __isl_take isl_val *v2),
1582         __isl_take isl_val *v)
1583 {
1584         int i;
1585
1586         mv = isl_multi_val_cow(mv);
1587         if (!mv || !v)
1588                 goto error;
1589
1590         for (i = 0; i < mv->n; ++i) {
1591                 mv->p[i] = fn(mv->p[i], isl_val_copy(v));
1592                 if (!mv->p[i])
1593                         goto error;
1594         }
1595
1596         isl_val_free(v);
1597         return mv;
1598 error:
1599         isl_val_free(v);
1600         isl_multi_val_free(mv);
1601         return NULL;
1602 }
1603
1604 /* Add "v" to each of the elements of "mv".
1605  */
1606 __isl_give isl_multi_val *isl_multi_val_add_val(__isl_take isl_multi_val *mv,
1607         __isl_take isl_val *v)
1608 {
1609         if (!v)
1610                 return isl_multi_val_free(mv);
1611         if (isl_val_is_zero(v)) {
1612                 isl_val_free(v);
1613                 return mv;
1614         }
1615         return isl_multi_val_fn_val(mv, &isl_val_add, v);
1616 }
1617
1618 /* Reduce the elements of "mv" modulo "v".
1619  */
1620 __isl_give isl_multi_val *isl_multi_val_mod_val(__isl_take isl_multi_val *mv,
1621         __isl_take isl_val *v)
1622 {
1623         return isl_multi_val_fn_val(mv, &isl_val_mod, v);
1624 }