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 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
 902 {
 903         if (!v1 || !v2)
 904                 return isl_bool_error;
 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 isl_bool_error);
 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 "v1" and "v2", return the residue of "v1"
 940  * modulo "v2".
 941  *
 942  * This is a private copy of isl_val_mod for use in the generic
 943  * isl_multi_*_mod_multi_val instantiated for isl_val.
 944  */
 945 __isl_give isl_val *isl_val_mod_val(__isl_take isl_val *v1,
 946         __isl_take isl_val *v2)
 947 {
 948         return isl_val_mod(v1, v2);
 949 }
 950
 951 /* Given two integer values, return their greatest common divisor.
 952  */
 953 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1, __isl_take isl_val *v2)
 954 {
 955         if (!v1 || !v2)
 956                 goto error;
 957         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 958                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 959                         "expecting two integers", goto error);
 960         if (isl_val_eq(v1, v2)) {
 961                 isl_val_free(v2);
 962                 return v1;
 963         }
 964         if (isl_val_is_one(v1)) {
 965                 isl_val_free(v2);
 966                 return v1;
 967         }
 968         if (isl_val_is_one(v2)) {
 969                 isl_val_free(v1);
 970                 return v2;
 971         }
 972         v1 = isl_val_cow(v1);
 973         if (!v1)
 974                 goto error;
 975         isl_int_gcd(v1->n, v1->n, v2->n);
 976         isl_val_free(v2);
 977         return v1;
 978 error:
 979         isl_val_free(v1);
 980         isl_val_free(v2);
 981         return NULL;
 982 }
 983
 984 /* Compute x, y and g such that g = gcd(a,b) and a*x+b*y = g.
 985  */
 986 static void isl_int_gcdext(isl_int g, isl_int x, isl_int y,
 987         isl_int a, isl_int b)
 988 {
 989         isl_int d, tmp;
 990         isl_int a_copy, b_copy;
 991
 992         isl_int_init(a_copy);
 993         isl_int_init(b_copy);
 994         isl_int_init(d);
 995         isl_int_init(tmp);
 996         isl_int_set(a_copy, a);
 997         isl_int_set(b_copy, b);
 998         isl_int_abs(g, a_copy);
 999         isl_int_abs(d, b_copy);
1000         isl_int_set_si(x, 1);
1001         isl_int_set_si(y, 0);
1002         while (isl_int_is_pos(d)) {
1003                 isl_int_fdiv_q(tmp, g, d);
1004                 isl_int_submul(x, tmp, y);
1005                 isl_int_submul(g, tmp, d);
1006                 isl_int_swap(g, d);
1007                 isl_int_swap(x, y);
1008         }
1009         if (isl_int_is_zero(a_copy))
1010                 isl_int_set_si(x, 0);
1011         else if (isl_int_is_neg(a_copy))
1012                 isl_int_neg(x, x);
1013         if (isl_int_is_zero(b_copy))
1014                 isl_int_set_si(y, 0);
1015         else {
1016                 isl_int_mul(tmp, a_copy, x);
1017                 isl_int_sub(tmp, g, tmp);
1018                 isl_int_divexact(y, tmp, b_copy);
1019         }
1020         isl_int_clear(d);
1021         isl_int_clear(tmp);
1022         isl_int_clear(a_copy);
1023         isl_int_clear(b_copy);
1024 }
1025
1026 /* Given two integer values v1 and v2, return their greatest common divisor g,
1027  * as well as two integers x and y such that x * v1 + y * v2 = g.
1028  */
1029 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
1030         __isl_take isl_val *v2, __isl_give isl_val **x, __isl_give isl_val **y)
1031 {
1032         isl_ctx *ctx;
1033         isl_val *a = NULL, *b = NULL;
1034
1035         if (!x && !y)
1036                 return isl_val_gcd(v1, v2);
1037
1038         if (!v1 || !v2)
1039                 goto error;
1040
1041         ctx = isl_val_get_ctx(v1);
1042         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
1043                 isl_die(ctx, isl_error_invalid,
1044                         "expecting two integers", goto error);
1045
1046         v1 = isl_val_cow(v1);
1047         a = isl_val_alloc(ctx);
1048         b = isl_val_alloc(ctx);
1049         if (!v1 || !a || !b)
1050                 goto error;
1051         isl_int_gcdext(v1->n, a->n, b->n, v1->n, v2->n);
1052         if (x) {
1053                 isl_int_set_si(a->d, 1);
1054                 *x = a;
1055         } else
1056                 isl_val_free(a);
1057         if (y) {
1058                 isl_int_set_si(b->d, 1);
1059                 *y = b;
1060         } else
1061                 isl_val_free(b);
1062         isl_val_free(v2);
1063         return v1;
1064 error:
1065         isl_val_free(v1);
1066         isl_val_free(v2);
1067         isl_val_free(a);
1068         isl_val_free(b);
1069         if (x)
1070                 *x = NULL;
1071         if (y)
1072                 *y = NULL;
1073         return NULL;
1074 }
1075
1076 /* Does "v" represent an integer value?
1077  */
1078 isl_bool isl_val_is_int(__isl_keep isl_val *v)
1079 {
1080         if (!v)
1081                 return isl_bool_error;
1082
1083         return isl_int_is_one(v->d);
1084 }
1085
1086 /* Does "v" represent a rational value?
1087  */
1088 isl_bool isl_val_is_rat(__isl_keep isl_val *v)
1089 {
1090         if (!v)
1091                 return isl_bool_error;
1092
1093         return !isl_int_is_zero(v->d);
1094 }
1095
1096 /* Does "v" represent NaN?
1097  */
1098 isl_bool isl_val_is_nan(__isl_keep isl_val *v)
1099 {
1100         if (!v)
1101                 return isl_bool_error;
1102
1103         return isl_int_is_zero(v->n) && isl_int_is_zero(v->d);
1104 }
1105
1106 /* Does "v" represent +infinity?
1107  */
1108 isl_bool isl_val_is_infty(__isl_keep isl_val *v)
1109 {
1110         if (!v)
1111                 return isl_bool_error;
1112
1113         return isl_int_is_pos(v->n) && isl_int_is_zero(v->d);
1114 }
1115
1116 /* Does "v" represent -infinity?
1117  */
1118 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v)
1119 {
1120         if (!v)
1121                 return isl_bool_error;
1122
1123         return isl_int_is_neg(v->n) && isl_int_is_zero(v->d);
1124 }
1125
1126 /* Does "v" represent the integer zero?
1127  */
1128 isl_bool isl_val_is_zero(__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 the integer one?
1137  */
1138 isl_bool isl_val_is_one(__isl_keep isl_val *v)
1139 {
1140         if (!v)
1141                 return isl_bool_error;
1142
1143         return isl_int_eq(v->n, v->d);
1144 }
1145
1146 /* Does "v" represent the integer negative one?
1147  */
1148 isl_bool isl_val_is_negone(__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_abs_eq(v->n, v->d);
1154 }
1155
1156 /* Is "v" (strictly) positive?
1157  */
1158 isl_bool isl_val_is_pos(__isl_keep isl_val *v)
1159 {
1160         if (!v)
1161                 return isl_bool_error;
1162
1163         return isl_int_is_pos(v->n);
1164 }
1165
1166 /* Is "v" (strictly) negative?
1167  */
1168 isl_bool isl_val_is_neg(__isl_keep isl_val *v)
1169 {
1170         if (!v)
1171                 return isl_bool_error;
1172
1173         return isl_int_is_neg(v->n);
1174 }
1175
1176 /* Is "v" non-negative?
1177  */
1178 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v)
1179 {
1180         if (!v)
1181                 return isl_bool_error;
1182
1183         if (isl_val_is_nan(v))
1184                 return isl_bool_false;
1185
1186         return isl_int_is_nonneg(v->n);
1187 }
1188
1189 /* Is "v" non-positive?
1190  */
1191 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v)
1192 {
1193         if (!v)
1194                 return isl_bool_error;
1195
1196         if (isl_val_is_nan(v))
1197                 return isl_bool_false;
1198
1199         return isl_int_is_nonpos(v->n);
1200 }
1201
1202 /* Return the sign of "v".
1203  *
1204  * The sign of NaN is undefined.
1205  */
1206 int isl_val_sgn(__isl_keep isl_val *v)
1207 {
1208         if (!v)
1209                 return 0;
1210         if (isl_val_is_zero(v))
1211                 return 0;
1212         if (isl_val_is_pos(v))
1213                 return 1;
1214         return -1;
1215 }
1216
1217 /* Is "v1" (strictly) less than "v2"?
1218  */
1219 isl_bool isl_val_lt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1220 {
1221         isl_int t;
1222         isl_bool lt;
1223
1224         if (!v1 || !v2)
1225                 return isl_bool_error;
1226         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1227                 return isl_int_lt(v1->n, v2->n);
1228         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1229                 return isl_bool_false;
1230         if (isl_val_eq(v1, v2))
1231                 return isl_bool_false;
1232         if (isl_val_is_infty(v2))
1233                 return isl_bool_true;
1234         if (isl_val_is_infty(v1))
1235                 return isl_bool_false;
1236         if (isl_val_is_neginfty(v1))
1237                 return isl_bool_true;
1238         if (isl_val_is_neginfty(v2))
1239                 return isl_bool_false;
1240
1241         isl_int_init(t);
1242         isl_int_mul(t, v1->n, v2->d);
1243         isl_int_submul(t, v2->n, v1->d);
1244         lt = isl_int_is_neg(t);
1245         isl_int_clear(t);
1246
1247         return lt;
1248 }
1249
1250 /* Is "v1" (strictly) greater than "v2"?
1251  */
1252 isl_bool isl_val_gt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1253 {
1254         return isl_val_lt(v2, v1);
1255 }
1256
1257 /* Is "v1" less than or equal to "v2"?
1258  */
1259 isl_bool isl_val_le(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1260 {
1261         isl_int t;
1262         isl_bool le;
1263
1264         if (!v1 || !v2)
1265                 return isl_bool_error;
1266         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1267                 return isl_int_le(v1->n, v2->n);
1268         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1269                 return isl_bool_false;
1270         if (isl_val_eq(v1, v2))
1271                 return isl_bool_true;
1272         if (isl_val_is_infty(v2))
1273                 return isl_bool_true;
1274         if (isl_val_is_infty(v1))
1275                 return isl_bool_false;
1276         if (isl_val_is_neginfty(v1))
1277                 return isl_bool_true;
1278         if (isl_val_is_neginfty(v2))
1279                 return isl_bool_false;
1280
1281         isl_int_init(t);
1282         isl_int_mul(t, v1->n, v2->d);
1283         isl_int_submul(t, v2->n, v1->d);
1284         le = isl_int_is_nonpos(t);
1285         isl_int_clear(t);
1286
1287         return le;
1288 }
1289
1290 /* Is "v1" greater than or equal to "v2"?
1291  */
1292 isl_bool isl_val_ge(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1293 {
1294         return isl_val_le(v2, v1);
1295 }
1296
1297 /* How does "v" compare to "i"?
1298  *
1299  * Return 1 if v is greater, -1 if v is smaller and 0 if v is equal to i.
1300  *
1301  * If v is NaN (or NULL), then the result is undefined.
1302  */
1303 int isl_val_cmp_si(__isl_keep isl_val *v, long i)
1304 {
1305         isl_int t;
1306         int cmp;
1307
1308         if (!v)
1309                 return 0;
1310         if (isl_val_is_int(v))
1311                 return isl_int_cmp_si(v->n, i);
1312         if (isl_val_is_nan(v))
1313                 return 0;
1314         if (isl_val_is_infty(v))
1315                 return 1;
1316         if (isl_val_is_neginfty(v))
1317                 return -1;
1318
1319         isl_int_init(t);
1320         isl_int_mul_si(t, v->d, i);
1321         isl_int_sub(t, v->n, t);
1322         cmp = isl_int_sgn(t);
1323         isl_int_clear(t);
1324
1325         return cmp;
1326 }
1327
1328 /* Is "v1" equal to "v2"?
1329  */
1330 isl_bool isl_val_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1331 {
1332         if (!v1 || !v2)
1333                 return isl_bool_error;
1334         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1335                 return isl_bool_false;
1336
1337         return isl_int_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1338 }
1339
1340 /* Is "v1" equal to "v2" in absolute value?
1341  */
1342 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1343 {
1344         if (!v1 || !v2)
1345                 return isl_bool_error;
1346         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1347                 return isl_bool_false;
1348
1349         return isl_int_abs_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1350 }
1351
1352 /* Is "v1" different from "v2"?
1353  */
1354 isl_bool isl_val_ne(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1355 {
1356         if (!v1 || !v2)
1357                 return isl_bool_error;
1358         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1359                 return isl_bool_false;
1360
1361         return isl_int_ne(v1->n, v2->n) || isl_int_ne(v1->d, v2->d);
1362 }
1363
1364 /* Print a textual representation of "v" onto "p".
1365  */
1366 __isl_give isl_printer *isl_printer_print_val(__isl_take isl_printer *p,
1367         __isl_keep isl_val *v)
1368 {
1369         int neg;
1370
1371         if (!p || !v)
1372                 return isl_printer_free(p);
1373
1374         neg = isl_int_is_neg(v->n);
1375         if (neg) {
1376                 p = isl_printer_print_str(p, "-");
1377                 isl_int_neg(v->n, v->n);
1378         }
1379         if (isl_int_is_zero(v->d)) {
1380                 int sgn = isl_int_sgn(v->n);
1381                 p = isl_printer_print_str(p, sgn < 0 ? "-infty" :
1382                                             sgn == 0 ? "NaN" : "infty");
1383         } else
1384                 p = isl_printer_print_isl_int(p, v->n);
1385         if (neg)
1386                 isl_int_neg(v->n, v->n);
1387         if (!isl_int_is_zero(v->d) && !isl_int_is_one(v->d)) {
1388                 p = isl_printer_print_str(p, "/");
1389                 p = isl_printer_print_isl_int(p, v->d);
1390         }
1391
1392         return p;
1393 }
1394
1395 /* Is "val1" (obviously) equal to "val2"?
1396  *
1397  * This is a private copy of isl_val_eq for use in the generic
1398  * isl_multi_*_plain_is_equal instantiated for isl_val.
1399  */
1400 int isl_val_plain_is_equal(__isl_keep isl_val *val1, __isl_keep isl_val *val2)
1401 {
1402         return isl_val_eq(val1, val2);
1403 }
1404
1405 /* Does "v" have any non-zero coefficients
1406  * for any dimension in the given range?
1407  *
1408  * This function is only meant to be used in the generic isl_multi_*
1409  * functions which have to deal with base objects that have an associated
1410  * space.  Since an isl_val does not have any coefficients, this function
1411  * always return 0.
1412  */
1413 int isl_val_involves_dims(__isl_keep isl_val *v, enum isl_dim_type type,
1414         unsigned first, unsigned n)
1415 {
1416         if (!v)
1417                 return -1;
1418
1419         return 0;
1420 }
1421
1422 /* Insert "n" dimensions of type "type" at position "first".
1423  *
1424  * This function is only meant to be used in the generic isl_multi_*
1425  * functions which have to deal with base objects that have an associated
1426  * space.  Since an isl_val does not have an associated space, this function
1427  * does not do anything.
1428  */
1429 __isl_give isl_val *isl_val_insert_dims(__isl_take isl_val *v,
1430         enum isl_dim_type type, unsigned first, unsigned n)
1431 {
1432         return v;
1433 }
1434
1435 /* Drop the the "n" first dimensions of type "type" at position "first".
1436  *
1437  * This function is only meant to be used in the generic isl_multi_*
1438  * functions which have to deal with base objects that have an associated
1439  * space.  Since an isl_val does not have an associated space, this function
1440  * does not do anything.
1441  */
1442 __isl_give isl_val *isl_val_drop_dims(__isl_take isl_val *v,
1443         enum isl_dim_type type, unsigned first, unsigned n)
1444 {
1445         return v;
1446 }
1447
1448 /* Change the name of the dimension of type "type" at position "pos" to "s".
1449  *
1450  * This function is only meant to be used in the generic isl_multi_*
1451  * functions which have to deal with base objects that have an associated
1452  * space.  Since an isl_val does not have an associated space, this function
1453  * does not do anything.
1454  */
1455 __isl_give isl_val *isl_val_set_dim_name(__isl_take isl_val *v,
1456         enum isl_dim_type type, unsigned pos, const char *s)
1457 {
1458         return v;
1459 }
1460
1461 /* Return the space of "v".
1462  *
1463  * This function is only meant to be used in the generic isl_multi_*
1464  * functions which have to deal with base objects that have an associated
1465  * space.  The conditions surrounding the call to this function make sure
1466  * that this function will never actually get called.  We return a valid
1467  * space anyway, just in case.
1468  */
1469 __isl_give isl_space *isl_val_get_space(__isl_keep isl_val *v)
1470 {
1471         if (!v)
1472                 return NULL;
1473
1474         return isl_space_params_alloc(isl_val_get_ctx(v), 0);
1475 }
1476
1477 /* Reset the domain space of "v" to "space".
1478  *
1479  * This function is only meant to be used in the generic isl_multi_*
1480  * functions which have to deal with base objects that have an associated
1481  * space.  Since an isl_val does not have an associated space, this function
1482  * does not do anything, apart from error handling and cleaning up memory.
1483  */
1484 __isl_give isl_val *isl_val_reset_domain_space(__isl_take isl_val *v,
1485         __isl_take isl_space *space)
1486 {
1487         if (!space)
1488                 return isl_val_free(v);
1489         isl_space_free(space);
1490         return v;
1491 }
1492
1493 /* Align the parameters of "v" to those of "space".
1494  *
1495  * This function is only meant to be used in the generic isl_multi_*
1496  * functions which have to deal with base objects that have an associated
1497  * space.  Since an isl_val does not have an associated space, this function
1498  * does not do anything, apart from error handling and cleaning up memory.
1499  * Note that the conditions surrounding the call to this function make sure
1500  * that this function will never actually get called.
1501  */
1502 __isl_give isl_val *isl_val_align_params(__isl_take isl_val *v,
1503         __isl_take isl_space *space)
1504 {
1505         if (!space)
1506                 return isl_val_free(v);
1507         isl_space_free(space);
1508         return v;
1509 }
1510
1511 /* Reorder the dimensions of the domain of "v" according
1512  * to the given reordering.
1513  *
1514  * This function is only meant to be used in the generic isl_multi_*
1515  * functions which have to deal with base objects that have an associated
1516  * space.  Since an isl_val does not have an associated space, this function
1517  * does not do anything, apart from error handling and cleaning up memory.
1518  */
1519 __isl_give isl_val *isl_val_realign_domain(__isl_take isl_val *v,
1520         __isl_take isl_reordering *r)
1521 {
1522         if (!r)
1523                 return isl_val_free(v);
1524         isl_reordering_free(r);
1525         return v;
1526 }
1527
1528 /* Return an isl_val that is zero on "ls".
1529  *
1530  * This function is only meant to be used in the generic isl_multi_*
1531  * functions which have to deal with base objects that have an associated
1532  * space.  Since an isl_val does not have an associated space, this function
1533  * simply returns a zero isl_val in the same context as "ls".
1534  */
1535 __isl_give isl_val *isl_val_zero_on_domain(__isl_take isl_local_space *ls)
1536 {
1537         isl_ctx *ctx;
1538
1539         if (!ls)
1540                 return NULL;
1541         ctx = isl_local_space_get_ctx(ls);
1542         isl_local_space_free(ls);
1543         return isl_val_zero(ctx);
1544 }
1545
1546 /* Do the parameters of "v" match those of "space"?
1547  *
1548  * This function is only meant to be used in the generic isl_multi_*
1549  * functions which have to deal with base objects that have an associated
1550  * space.  Since an isl_val does not have an associated space, this function
1551  * simply returns 1, except if "v" or "space" are NULL.
1552  */
1553 int isl_val_matching_params(__isl_keep isl_val *v, __isl_keep isl_space *space)
1554 {
1555         if (!v || !space)
1556                 return -1;
1557         return 1;
1558 }
1559
1560 /* Check that the domain space of "v" matches "space".
1561  *
1562  * Return 0 on success and -1 on error.
1563  *
1564  * This function is only meant to be used in the generic isl_multi_*
1565  * functions which have to deal with base objects that have an associated
1566  * space.  Since an isl_val does not have an associated space, this function
1567  * simply returns 0, except if "v" or "space" are NULL.
1568  */
1569 int isl_val_check_match_domain_space(__isl_keep isl_val *v,
1570         __isl_keep isl_space *space)
1571 {
1572         if (!v || !space)
1573                 return -1;
1574         return 0;
1575 }
1576
1577 #undef BASE
1578 #define BASE val
1579
1580 #define NO_DOMAIN
1581 #define NO_IDENTITY
1582 #define NO_FROM_BASE
1583 #define NO_MOVE_DIMS
1584 #include <isl_multi_templ.c>
1585
1586 /* Apply "fn" to each of the elements of "mv" with as second argument "v".
1587  */
1588 static __isl_give isl_multi_val *isl_multi_val_fn_val(
1589         __isl_take isl_multi_val *mv,
1590         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
1591                                         __isl_take isl_val *v2),
1592         __isl_take isl_val *v)
1593 {
1594         int i;
1595
1596         mv = isl_multi_val_cow(mv);
1597         if (!mv || !v)
1598                 goto error;
1599
1600         for (i = 0; i < mv->n; ++i) {
1601                 mv->p[i] = fn(mv->p[i], isl_val_copy(v));
1602                 if (!mv->p[i])
1603                         goto error;
1604         }
1605
1606         isl_val_free(v);
1607         return mv;
1608 error:
1609         isl_val_free(v);
1610         isl_multi_val_free(mv);
1611         return NULL;
1612 }
1613
1614 /* Add "v" to each of the elements of "mv".
1615  */
1616 __isl_give isl_multi_val *isl_multi_val_add_val(__isl_take isl_multi_val *mv,
1617         __isl_take isl_val *v)
1618 {
1619         if (!v)
1620                 return isl_multi_val_free(mv);
1621         if (isl_val_is_zero(v)) {
1622                 isl_val_free(v);
1623                 return mv;
1624         }
1625         return isl_multi_val_fn_val(mv, &isl_val_add, v);
1626 }
1627
1628 /* Reduce the elements of "mv" modulo "v".
1629  */
1630 __isl_give isl_multi_val *isl_multi_val_mod_val(__isl_take isl_multi_val *mv,
1631         __isl_take isl_val *v)
1632 {
1633         return isl_multi_val_fn_val(mv, &isl_val_mod, v);
1634 }