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 absolute value of "v".
 397  */
 398 __isl_give isl_val *isl_val_abs(__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_nonneg(v))
 405                 return v;
 406         return isl_val_neg(v);
 407 }
 408
 409 /* Return the "floor" (greatest integer part) of "v".
 410  * That is, return the result of rounding towards -infinity.
 411  */
 412 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v)
 413 {
 414         if (!v)
 415                 return NULL;
 416         if (isl_val_is_int(v))
 417                 return v;
 418         if (!isl_val_is_rat(v))
 419                 return v;
 420
 421         v = isl_val_cow(v);
 422         if (!v)
 423                 return NULL;
 424         isl_int_fdiv_q(v->n, v->n, v->d);
 425         isl_int_set_si(v->d, 1);
 426
 427         return v;
 428 }
 429
 430 /* Return the "ceiling" of "v".
 431  * That is, return the result of rounding towards +infinity.
 432  */
 433 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v)
 434 {
 435         if (!v)
 436                 return NULL;
 437         if (isl_val_is_int(v))
 438                 return v;
 439         if (!isl_val_is_rat(v))
 440                 return v;
 441
 442         v = isl_val_cow(v);
 443         if (!v)
 444                 return NULL;
 445         isl_int_cdiv_q(v->n, v->n, v->d);
 446         isl_int_set_si(v->d, 1);
 447
 448         return v;
 449 }
 450
 451 /* Truncate "v".
 452  * That is, return the result of rounding towards zero.
 453  */
 454 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v)
 455 {
 456         if (!v)
 457                 return NULL;
 458         if (isl_val_is_int(v))
 459                 return v;
 460         if (!isl_val_is_rat(v))
 461                 return v;
 462
 463         v = isl_val_cow(v);
 464         if (!v)
 465                 return NULL;
 466         isl_int_tdiv_q(v->n, v->n, v->d);
 467         isl_int_set_si(v->d, 1);
 468
 469         return v;
 470 }
 471
 472 /* Return 2^v, where v is an integer (that is not too large).
 473  */
 474 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v)
 475 {
 476         unsigned long exp;
 477         int neg;
 478
 479         v = isl_val_cow(v);
 480         if (!v)
 481                 return NULL;
 482         if (!isl_val_is_int(v))
 483                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 484                         "can only compute integer powers",
 485                         return isl_val_free(v));
 486         neg = isl_val_is_neg(v);
 487         if (neg)
 488                 isl_int_neg(v->n, v->n);
 489         if (!isl_int_fits_ulong(v->n))
 490                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
 491                         "exponent too large", return isl_val_free(v));
 492         exp = isl_int_get_ui(v->n);
 493         if (neg) {
 494                 isl_int_mul_2exp(v->d, v->d, exp);
 495                 isl_int_set_si(v->n, 1);
 496         } else {
 497                 isl_int_mul_2exp(v->n, v->d, exp);
 498         }
 499
 500         return v;
 501 }
 502
 503 /* Return the minimum of "v1" and "v2".
 504  */
 505 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1, __isl_take isl_val *v2)
 506 {
 507         if (!v1 || !v2)
 508                 goto error;
 509
 510         if (isl_val_is_nan(v1)) {
 511                 isl_val_free(v2);
 512                 return v1;
 513         }
 514         if (isl_val_is_nan(v2)) {
 515                 isl_val_free(v1);
 516                 return v2;
 517         }
 518         if (isl_val_le(v1, v2)) {
 519                 isl_val_free(v2);
 520                 return v1;
 521         } else {
 522                 isl_val_free(v1);
 523                 return v2;
 524         }
 525 error:
 526         isl_val_free(v1);
 527         isl_val_free(v2);
 528         return NULL;
 529 }
 530
 531 /* Return the maximum of "v1" and "v2".
 532  */
 533 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1, __isl_take isl_val *v2)
 534 {
 535         if (!v1 || !v2)
 536                 goto error;
 537
 538         if (isl_val_is_nan(v1)) {
 539                 isl_val_free(v2);
 540                 return v1;
 541         }
 542         if (isl_val_is_nan(v2)) {
 543                 isl_val_free(v1);
 544                 return v2;
 545         }
 546         if (isl_val_ge(v1, v2)) {
 547                 isl_val_free(v2);
 548                 return v1;
 549         } else {
 550                 isl_val_free(v1);
 551                 return v2;
 552         }
 553 error:
 554         isl_val_free(v1);
 555         isl_val_free(v2);
 556         return NULL;
 557 }
 558
 559 /* Return the sum of "v1" and "v2".
 560  */
 561 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1, __isl_take isl_val *v2)
 562 {
 563         if (!v1 || !v2)
 564                 goto error;
 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_is_infty(v1) && isl_val_is_neginfty(v2)) ||
 574             (isl_val_is_neginfty(v1) && isl_val_is_infty(v2))) {
 575                 isl_val_free(v2);
 576                 return isl_val_set_nan(v1);
 577         }
 578         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 579                 isl_val_free(v2);
 580                 return v1;
 581         }
 582         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 583                 isl_val_free(v1);
 584                 return v2;
 585         }
 586         if (isl_val_is_zero(v1)) {
 587                 isl_val_free(v1);
 588                 return v2;
 589         }
 590         if (isl_val_is_zero(v2)) {
 591                 isl_val_free(v2);
 592                 return v1;
 593         }
 594
 595         v1 = isl_val_cow(v1);
 596         if (!v1)
 597                 goto error;
 598         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 599                 isl_int_add(v1->n, v1->n, v2->n);
 600         else {
 601                 if (isl_int_eq(v1->d, v2->d))
 602                         isl_int_add(v1->n, v1->n, v2->n);
 603                 else {
 604                         isl_int_mul(v1->n, v1->n, v2->d);
 605                         isl_int_addmul(v1->n, v2->n, v1->d);
 606                         isl_int_mul(v1->d, v1->d, v2->d);
 607                 }
 608                 v1 = isl_val_normalize(v1);
 609         }
 610         isl_val_free(v2);
 611         return v1;
 612 error:
 613         isl_val_free(v1);
 614         isl_val_free(v2);
 615         return NULL;
 616 }
 617
 618 /* Return the sum of "v1" and "v2".
 619  */
 620 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1, unsigned long v2)
 621 {
 622         if (!v1)
 623                 return NULL;
 624         if (!isl_val_is_rat(v1))
 625                 return v1;
 626         if (v2 == 0)
 627                 return v1;
 628         v1 = isl_val_cow(v1);
 629         if (!v1)
 630                 return NULL;
 631
 632         isl_int_addmul_ui(v1->n, v1->d, v2);
 633
 634         return v1;
 635 }
 636
 637 /* Subtract "v2" from "v1".
 638  */
 639 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1, __isl_take isl_val *v2)
 640 {
 641         if (!v1 || !v2)
 642                 goto error;
 643         if (isl_val_is_nan(v1)) {
 644                 isl_val_free(v2);
 645                 return v1;
 646         }
 647         if (isl_val_is_nan(v2)) {
 648                 isl_val_free(v1);
 649                 return v2;
 650         }
 651         if ((isl_val_is_infty(v1) && isl_val_is_infty(v2)) ||
 652             (isl_val_is_neginfty(v1) && isl_val_is_neginfty(v2))) {
 653                 isl_val_free(v2);
 654                 return isl_val_set_nan(v1);
 655         }
 656         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 657                 isl_val_free(v2);
 658                 return v1;
 659         }
 660         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 661                 isl_val_free(v1);
 662                 return isl_val_neg(v2);
 663         }
 664         if (isl_val_is_zero(v2)) {
 665                 isl_val_free(v2);
 666                 return v1;
 667         }
 668         if (isl_val_is_zero(v1)) {
 669                 isl_val_free(v1);
 670                 return isl_val_neg(v2);
 671         }
 672
 673         v1 = isl_val_cow(v1);
 674         if (!v1)
 675                 goto error;
 676         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 677                 isl_int_sub(v1->n, v1->n, v2->n);
 678         else {
 679                 if (isl_int_eq(v1->d, v2->d))
 680                         isl_int_sub(v1->n, v1->n, v2->n);
 681                 else {
 682                         isl_int_mul(v1->n, v1->n, v2->d);
 683                         isl_int_submul(v1->n, v2->n, v1->d);
 684                         isl_int_mul(v1->d, v1->d, v2->d);
 685                 }
 686                 v1 = isl_val_normalize(v1);
 687         }
 688         isl_val_free(v2);
 689         return v1;
 690 error:
 691         isl_val_free(v1);
 692         isl_val_free(v2);
 693         return NULL;
 694 }
 695
 696 /* Subtract "v2" from "v1".
 697  */
 698 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1, unsigned long v2)
 699 {
 700         if (!v1)
 701                 return NULL;
 702         if (!isl_val_is_rat(v1))
 703                 return v1;
 704         if (v2 == 0)
 705                 return v1;
 706         v1 = isl_val_cow(v1);
 707         if (!v1)
 708                 return NULL;
 709
 710         isl_int_submul_ui(v1->n, v1->d, v2);
 711
 712         return v1;
 713 }
 714
 715 /* Return the product of "v1" and "v2".
 716  */
 717 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1, __isl_take isl_val *v2)
 718 {
 719         if (!v1 || !v2)
 720                 goto error;
 721         if (isl_val_is_nan(v1)) {
 722                 isl_val_free(v2);
 723                 return v1;
 724         }
 725         if (isl_val_is_nan(v2)) {
 726                 isl_val_free(v1);
 727                 return v2;
 728         }
 729         if ((!isl_val_is_rat(v1) && isl_val_is_zero(v2)) ||
 730             (isl_val_is_zero(v1) && !isl_val_is_rat(v2))) {
 731                 isl_val_free(v2);
 732                 return isl_val_set_nan(v1);
 733         }
 734         if (isl_val_is_zero(v1)) {
 735                 isl_val_free(v2);
 736                 return v1;
 737         }
 738         if (isl_val_is_zero(v2)) {
 739                 isl_val_free(v1);
 740                 return v2;
 741         }
 742         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 743                 if (isl_val_is_neg(v2))
 744                         v1 = isl_val_neg(v1);
 745                 isl_val_free(v2);
 746                 return v1;
 747         }
 748         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 749                 if (isl_val_is_neg(v1))
 750                         v2 = isl_val_neg(v2);
 751                 isl_val_free(v1);
 752                 return v2;
 753         }
 754
 755         v1 = isl_val_cow(v1);
 756         if (!v1)
 757                 goto error;
 758         if (isl_val_is_int(v1) && isl_val_is_int(v2))
 759                 isl_int_mul(v1->n, v1->n, v2->n);
 760         else {
 761                 isl_int_mul(v1->n, v1->n, v2->n);
 762                 isl_int_mul(v1->d, v1->d, v2->d);
 763                 v1 = isl_val_normalize(v1);
 764         }
 765         isl_val_free(v2);
 766         return v1;
 767 error:
 768         isl_val_free(v1);
 769         isl_val_free(v2);
 770         return NULL;
 771 }
 772
 773 /* Return the product of "v1" and "v2".
 774  *
 775  * This is a private copy of isl_val_mul for use in the generic
 776  * isl_multi_*_scale_val instantiated for isl_val.
 777  */
 778 __isl_give isl_val *isl_val_scale_val(__isl_take isl_val *v1,
 779         __isl_take isl_val *v2)
 780 {
 781         return isl_val_mul(v1, v2);
 782 }
 783
 784 /* Return the product of "v1" and "v2".
 785  */
 786 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1, unsigned long v2)
 787 {
 788         if (!v1)
 789                 return NULL;
 790         if (isl_val_is_nan(v1))
 791                 return v1;
 792         if (!isl_val_is_rat(v1)) {
 793                 if (v2 == 0)
 794                         v1 = isl_val_set_nan(v1);
 795                 return v1;
 796         }
 797         if (v2 == 1)
 798                 return v1;
 799         v1 = isl_val_cow(v1);
 800         if (!v1)
 801                 return NULL;
 802
 803         isl_int_mul_ui(v1->n, v1->n, v2);
 804
 805         return isl_val_normalize(v1);
 806 }
 807
 808 /* Divide "v1" by "v2".
 809  */
 810 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1, __isl_take isl_val *v2)
 811 {
 812         if (!v1 || !v2)
 813                 goto error;
 814         if (isl_val_is_nan(v1)) {
 815                 isl_val_free(v2);
 816                 return v1;
 817         }
 818         if (isl_val_is_nan(v2)) {
 819                 isl_val_free(v1);
 820                 return v2;
 821         }
 822         if (isl_val_is_zero(v2) ||
 823             (!isl_val_is_rat(v1) && !isl_val_is_rat(v2))) {
 824                 isl_val_free(v2);
 825                 return isl_val_set_nan(v1);
 826         }
 827         if (isl_val_is_zero(v1)) {
 828                 isl_val_free(v2);
 829                 return v1;
 830         }
 831         if (isl_val_is_infty(v1) || isl_val_is_neginfty(v1)) {
 832                 if (isl_val_is_neg(v2))
 833                         v1 = isl_val_neg(v1);
 834                 isl_val_free(v2);
 835                 return v1;
 836         }
 837         if (isl_val_is_infty(v2) || isl_val_is_neginfty(v2)) {
 838                 isl_val_free(v2);
 839                 return isl_val_set_zero(v1);
 840         }
 841
 842         v1 = isl_val_cow(v1);
 843         if (!v1)
 844                 goto error;
 845         if (isl_val_is_int(v2)) {
 846                 isl_int_mul(v1->d, v1->d, v2->n);
 847                 v1 = isl_val_normalize(v1);
 848         } else {
 849                 isl_int_mul(v1->d, v1->d, v2->n);
 850                 isl_int_mul(v1->n, v1->n, v2->d);
 851                 v1 = isl_val_normalize(v1);
 852         }
 853         isl_val_free(v2);
 854         return v1;
 855 error:
 856         isl_val_free(v1);
 857         isl_val_free(v2);
 858         return NULL;
 859 }
 860
 861 /* Divide "v1" by "v2".
 862  *
 863  * This is a private copy of isl_val_div for use in the generic
 864  * isl_multi_*_scale_down_val instantiated for isl_val.
 865  */
 866 __isl_give isl_val *isl_val_scale_down_val(__isl_take isl_val *v1,
 867         __isl_take isl_val *v2)
 868 {
 869         return isl_val_div(v1, v2);
 870 }
 871
 872 /* Given two integer values "v1" and "v2", check if "v1" is divisible by "v2".
 873  */
 874 int isl_val_is_divisible_by(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
 875 {
 876         if (!v1 || !v2)
 877                 return -1;
 878
 879         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 880                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 881                         "expecting two integers", return -1);
 882
 883         return isl_int_is_divisible_by(v1->n, v2->n);
 884 }
 885
 886 /* Given two integer values "v1" and "v2", return the residue of "v1"
 887  * modulo "v2".
 888  */
 889 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1, __isl_take isl_val *v2)
 890 {
 891         if (!v1 || !v2)
 892                 goto error;
 893         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 894                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 895                         "expecting two integers", goto error);
 896         if (isl_val_is_nonneg(v1) && isl_val_lt(v1, v2)) {
 897                 isl_val_free(v2);
 898                 return v1;
 899         }
 900         v1 = isl_val_cow(v1);
 901         if (!v1)
 902                 goto error;
 903         isl_int_fdiv_r(v1->n, v1->n, v2->n);
 904         isl_val_free(v2);
 905         return v1;
 906 error:
 907         isl_val_free(v1);
 908         isl_val_free(v2);
 909         return NULL;
 910 }
 911
 912 /* Given two integer values, return their greatest common divisor.
 913  */
 914 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1, __isl_take isl_val *v2)
 915 {
 916         if (!v1 || !v2)
 917                 goto error;
 918         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 919                 isl_die(isl_val_get_ctx(v1), isl_error_invalid,
 920                         "expecting two integers", goto error);
 921         if (isl_val_eq(v1, v2)) {
 922                 isl_val_free(v2);
 923                 return v1;
 924         }
 925         if (isl_val_is_one(v1)) {
 926                 isl_val_free(v2);
 927                 return v1;
 928         }
 929         if (isl_val_is_one(v2)) {
 930                 isl_val_free(v1);
 931                 return v2;
 932         }
 933         v1 = isl_val_cow(v1);
 934         if (!v1)
 935                 goto error;
 936         isl_int_gcd(v1->n, v1->n, v2->n);
 937         isl_val_free(v2);
 938         return v1;
 939 error:
 940         isl_val_free(v1);
 941         isl_val_free(v2);
 942         return NULL;
 943 }
 944
 945 /* Given two integer values v1 and v2, return their greatest common divisor g,
 946  * as well as two integers x and y such that x * v1 + y * v2 = g.
 947  */
 948 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
 949         __isl_take isl_val *v2, __isl_give isl_val **x, __isl_give isl_val **y)
 950 {
 951         isl_ctx *ctx;
 952         isl_val *a = NULL, *b = NULL;
 953
 954         if (!x && !y)
 955                 return isl_val_gcd(v1, v2);
 956
 957         if (!v1 || !v2)
 958                 goto error;
 959
 960         ctx = isl_val_get_ctx(v1);
 961         if (!isl_val_is_int(v1) || !isl_val_is_int(v2))
 962                 isl_die(ctx, isl_error_invalid,
 963                         "expecting two integers", goto error);
 964
 965         v1 = isl_val_cow(v1);
 966         a = isl_val_alloc(ctx);
 967         b = isl_val_alloc(ctx);
 968         if (!v1 || !a || !b)
 969                 goto error;
 970         isl_int_gcdext(v1->n, a->n, b->n, v1->n, v2->n);
 971         if (x) {
 972                 isl_int_set_si(a->d, 1);
 973                 *x = a;
 974         } else
 975                 isl_val_free(a);
 976         if (y) {
 977                 isl_int_set_si(b->d, 1);
 978                 *y = b;
 979         } else
 980                 isl_val_free(b);
 981         isl_val_free(v2);
 982         return v1;
 983 error:
 984         isl_val_free(v1);
 985         isl_val_free(v2);
 986         isl_val_free(a);
 987         isl_val_free(b);
 988         if (x)
 989                 *x = NULL;
 990         if (y)
 991                 *y = NULL;
 992         return NULL;
 993 }
 994
 995 /* Does "v" represent an integer value?
 996  */
 997 int isl_val_is_int(__isl_keep isl_val *v)
 998 {
 999         if (!v)
1000                 return -1;
1001
1002         return isl_int_is_one(v->d);
1003 }
1004
1005 /* Does "v" represent a rational value?
1006  */
1007 int isl_val_is_rat(__isl_keep isl_val *v)
1008 {
1009         if (!v)
1010                 return -1;
1011
1012         return !isl_int_is_zero(v->d);
1013 }
1014
1015 /* Does "v" represent NaN?
1016  */
1017 int isl_val_is_nan(__isl_keep isl_val *v)
1018 {
1019         if (!v)
1020                 return -1;
1021
1022         return isl_int_is_zero(v->n) && isl_int_is_zero(v->d);
1023 }
1024
1025 /* Does "v" represent +infinity?
1026  */
1027 int isl_val_is_infty(__isl_keep isl_val *v)
1028 {
1029         if (!v)
1030                 return -1;
1031
1032         return isl_int_is_pos(v->n) && isl_int_is_zero(v->d);
1033 }
1034
1035 /* Does "v" represent -infinity?
1036  */
1037 int isl_val_is_neginfty(__isl_keep isl_val *v)
1038 {
1039         if (!v)
1040                 return -1;
1041
1042         return isl_int_is_neg(v->n) && isl_int_is_zero(v->d);
1043 }
1044
1045 /* Does "v" represent the integer zero?
1046  */
1047 int isl_val_is_zero(__isl_keep isl_val *v)
1048 {
1049         if (!v)
1050                 return -1;
1051
1052         return isl_int_is_zero(v->n) && !isl_int_is_zero(v->d);
1053 }
1054
1055 /* Does "v" represent the integer one?
1056  */
1057 int isl_val_is_one(__isl_keep isl_val *v)
1058 {
1059         if (!v)
1060                 return -1;
1061
1062         return isl_int_eq(v->n, v->d);
1063 }
1064
1065 /* Does "v" represent the integer negative one?
1066  */
1067 int isl_val_is_negone(__isl_keep isl_val *v)
1068 {
1069         if (!v)
1070                 return -1;
1071
1072         return isl_int_is_neg(v->n) && isl_int_abs_eq(v->n, v->d);
1073 }
1074
1075 /* Is "v" (strictly) positive?
1076  */
1077 int isl_val_is_pos(__isl_keep isl_val *v)
1078 {
1079         if (!v)
1080                 return -1;
1081
1082         return isl_int_is_pos(v->n);
1083 }
1084
1085 /* Is "v" (strictly) negative?
1086  */
1087 int isl_val_is_neg(__isl_keep isl_val *v)
1088 {
1089         if (!v)
1090                 return -1;
1091
1092         return isl_int_is_neg(v->n);
1093 }
1094
1095 /* Is "v" non-negative?
1096  */
1097 int isl_val_is_nonneg(__isl_keep isl_val *v)
1098 {
1099         if (!v)
1100                 return -1;
1101
1102         if (isl_val_is_nan(v))
1103                 return 0;
1104
1105         return isl_int_is_nonneg(v->n);
1106 }
1107
1108 /* Is "v" non-positive?
1109  */
1110 int isl_val_is_nonpos(__isl_keep isl_val *v)
1111 {
1112         if (!v)
1113                 return -1;
1114
1115         if (isl_val_is_nan(v))
1116                 return 0;
1117
1118         return isl_int_is_nonpos(v->n);
1119 }
1120
1121 /* Return the sign of "v".
1122  *
1123  * The sign of NaN is undefined.
1124  */
1125 int isl_val_sgn(__isl_keep isl_val *v)
1126 {
1127         if (!v)
1128                 return 0;
1129         if (isl_val_is_zero(v))
1130                 return 0;
1131         if (isl_val_is_pos(v))
1132                 return 1;
1133         return -1;
1134 }
1135
1136 /* Is "v1" (strictly) less than "v2"?
1137  */
1138 int isl_val_lt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1139 {
1140         isl_int t;
1141         int lt;
1142
1143         if (!v1 || !v2)
1144                 return -1;
1145         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1146                 return isl_int_lt(v1->n, v2->n);
1147         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1148                 return 0;
1149         if (isl_val_eq(v1, v2))
1150                 return 0;
1151         if (isl_val_is_infty(v2))
1152                 return 1;
1153         if (isl_val_is_infty(v1))
1154                 return 0;
1155         if (isl_val_is_neginfty(v1))
1156                 return 1;
1157         if (isl_val_is_neginfty(v2))
1158                 return 0;
1159
1160         isl_int_init(t);
1161         isl_int_mul(t, v1->n, v2->d);
1162         isl_int_submul(t, v2->n, v1->d);
1163         lt = isl_int_is_neg(t);
1164         isl_int_clear(t);
1165
1166         return lt;
1167 }
1168
1169 /* Is "v1" (strictly) greater than "v2"?
1170  */
1171 int isl_val_gt(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1172 {
1173         return isl_val_lt(v2, v1);
1174 }
1175
1176 /* Is "v1" less than or equal to "v2"?
1177  */
1178 int isl_val_le(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1179 {
1180         isl_int t;
1181         int le;
1182
1183         if (!v1 || !v2)
1184                 return -1;
1185         if (isl_val_is_int(v1) && isl_val_is_int(v2))
1186                 return isl_int_le(v1->n, v2->n);
1187         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1188                 return 0;
1189         if (isl_val_eq(v1, v2))
1190                 return 1;
1191         if (isl_val_is_infty(v2))
1192                 return 1;
1193         if (isl_val_is_infty(v1))
1194                 return 0;
1195         if (isl_val_is_neginfty(v1))
1196                 return 1;
1197         if (isl_val_is_neginfty(v2))
1198                 return 0;
1199
1200         isl_int_init(t);
1201         isl_int_mul(t, v1->n, v2->d);
1202         isl_int_submul(t, v2->n, v1->d);
1203         le = isl_int_is_nonpos(t);
1204         isl_int_clear(t);
1205
1206         return le;
1207 }
1208
1209 /* Is "v1" greater than or equal to "v2"?
1210  */
1211 int isl_val_ge(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1212 {
1213         return isl_val_le(v2, v1);
1214 }
1215
1216 /* How does "v" compare to "i"?
1217  *
1218  * Return 1 if v is greater, -1 if v is smaller and 0 if v is equal to i.
1219  *
1220  * If v is NaN (or NULL), then the result is undefined.
1221  */
1222 int isl_val_cmp_si(__isl_keep isl_val *v, long i)
1223 {
1224         isl_int t;
1225         int cmp;
1226
1227         if (!v)
1228                 return 0;
1229         if (isl_val_is_int(v))
1230                 return isl_int_cmp_si(v->n, i);
1231         if (isl_val_is_nan(v))
1232                 return 0;
1233         if (isl_val_is_infty(v))
1234                 return 1;
1235         if (isl_val_is_neginfty(v))
1236                 return -1;
1237
1238         isl_int_init(t);
1239         isl_int_mul_si(t, v->d, i);
1240         isl_int_sub(t, v->n, t);
1241         cmp = isl_int_sgn(t);
1242         isl_int_clear(t);
1243
1244         return cmp;
1245 }
1246
1247 /* Is "v1" equal to "v2"?
1248  */
1249 int isl_val_eq(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1250 {
1251         if (!v1 || !v2)
1252                 return -1;
1253         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1254                 return 0;
1255
1256         return isl_int_eq(v1->n, v2->n) && isl_int_eq(v1->d, v2->d);
1257 }
1258
1259 /* Is "v1" different from "v2"?
1260  */
1261 int isl_val_ne(__isl_keep isl_val *v1, __isl_keep isl_val *v2)
1262 {
1263         if (!v1 || !v2)
1264                 return -1;
1265         if (isl_val_is_nan(v1) || isl_val_is_nan(v2))
1266                 return 0;
1267
1268         return isl_int_ne(v1->n, v2->n) || isl_int_ne(v1->d, v2->d);
1269 }
1270
1271 /* Print a textual representation of "v" onto "p".
1272  */
1273 __isl_give isl_printer *isl_printer_print_val(__isl_take isl_printer *p,
1274         __isl_keep isl_val *v)
1275 {
1276         int neg;
1277
1278         if (!p || !v)
1279                 return isl_printer_free(p);
1280
1281         neg = isl_int_is_neg(v->n);
1282         if (neg) {
1283                 p = isl_printer_print_str(p, "-");
1284                 isl_int_neg(v->n, v->n);
1285         }
1286         if (isl_int_is_zero(v->d)) {
1287                 int sgn = isl_int_sgn(v->n);
1288                 p = isl_printer_print_str(p, sgn < 0 ? "-infty" :
1289                                             sgn == 0 ? "NaN" : "infty");
1290         } else
1291                 p = isl_printer_print_isl_int(p, v->n);
1292         if (neg)
1293                 isl_int_neg(v->n, v->n);
1294         if (!isl_int_is_zero(v->d) && !isl_int_is_one(v->d)) {
1295                 p = isl_printer_print_str(p, "/");
1296                 p = isl_printer_print_isl_int(p, v->d);
1297         }
1298
1299         return p;
1300 }
1301
1302 /* Is "val1" (obviously) equal to "val2"?
1303  *
1304  * This is a private copy of isl_val_eq for use in the generic
1305  * isl_multi_*_plain_is_equal instantiated for isl_val.
1306  */
1307 int isl_val_plain_is_equal(__isl_keep isl_val *val1, __isl_keep isl_val *val2)
1308 {
1309         return isl_val_eq(val1, val2);
1310 }
1311
1312 /* Does "v" have any non-zero coefficients
1313  * for any dimension in the given range?
1314  *
1315  * This function is only meant to be used in the generic isl_multi_*
1316  * functions which have to deal with base objects that have an associated
1317  * space.  Since an isl_val does not have any coefficients, this function
1318  * always return 0.
1319  */
1320 int isl_val_involves_dims(__isl_keep isl_val *v, enum isl_dim_type type,
1321         unsigned first, unsigned n)
1322 {
1323         if (!v)
1324                 return -1;
1325
1326         return 0;
1327 }
1328
1329 /* Insert "n" dimensions of type "type" at position "first".
1330  *
1331  * This function is only meant to be used in the generic isl_multi_*
1332  * functions which have to deal with base objects that have an associated
1333  * space.  Since an isl_val does not have an associated space, this function
1334  * does not do anything.
1335  */
1336 __isl_give isl_val *isl_val_insert_dims(__isl_take isl_val *v,
1337         enum isl_dim_type type, unsigned first, unsigned n)
1338 {
1339         return v;
1340 }
1341
1342 /* Drop the the "n" first dimensions of type "type" at position "first".
1343  *
1344  * This function is only meant to be used in the generic isl_multi_*
1345  * functions which have to deal with base objects that have an associated
1346  * space.  Since an isl_val does not have an associated space, this function
1347  * does not do anything.
1348  */
1349 __isl_give isl_val *isl_val_drop_dims(__isl_take isl_val *v,
1350         enum isl_dim_type type, unsigned first, unsigned n)
1351 {
1352         return v;
1353 }
1354
1355 /* Change the name of the dimension of type "type" at position "pos" to "s".
1356  *
1357  * This function is only meant to be used in the generic isl_multi_*
1358  * functions which have to deal with base objects that have an associated
1359  * space.  Since an isl_val does not have an associated space, this function
1360  * does not do anything.
1361  */
1362 __isl_give isl_val *isl_val_set_dim_name(__isl_take isl_val *v,
1363         enum isl_dim_type type, unsigned pos, const char *s)
1364 {
1365         return v;
1366 }
1367
1368 /* Return the space of "v".
1369  *
1370  * This function is only meant to be used in the generic isl_multi_*
1371  * functions which have to deal with base objects that have an associated
1372  * space.  The conditions surrounding the call to this function make sure
1373  * that this function will never actually get called.  We return a valid
1374  * space anyway, just in case.
1375  */
1376 __isl_give isl_space *isl_val_get_space(__isl_keep isl_val *v)
1377 {
1378         if (!v)
1379                 return NULL;
1380
1381         return isl_space_params_alloc(isl_val_get_ctx(v), 0);
1382 }
1383
1384 /* Reset the domain space of "v" to "space".
1385  *
1386  * This function is only meant to be used in the generic isl_multi_*
1387  * functions which have to deal with base objects that have an associated
1388  * space.  Since an isl_val does not have an associated space, this function
1389  * does not do anything, apart from error handling and cleaning up memory.
1390  */
1391 __isl_give isl_val *isl_val_reset_domain_space(__isl_take isl_val *v,
1392         __isl_take isl_space *space)
1393 {
1394         if (!space)
1395                 return isl_val_free(v);
1396         isl_space_free(space);
1397         return v;
1398 }
1399
1400 /* Align the parameters of "v" to those of "space".
1401  *
1402  * This function is only meant to be used in the generic isl_multi_*
1403  * functions which have to deal with base objects that have an associated
1404  * space.  Since an isl_val does not have an associated space, this function
1405  * does not do anything, apart from error handling and cleaning up memory.
1406  * Note that the conditions surrounding the call to this function make sure
1407  * that this function will never actually get called.
1408  */
1409 __isl_give isl_val *isl_val_align_params(__isl_take isl_val *v,
1410         __isl_take isl_space *space)
1411 {
1412         if (!space)
1413                 return isl_val_free(v);
1414         isl_space_free(space);
1415         return v;
1416 }
1417
1418 /* Reorder the dimensions of the domain of "v" according
1419  * to the given reordering.
1420  *
1421  * This function is only meant to be used in the generic isl_multi_*
1422  * functions which have to deal with base objects that have an associated
1423  * space.  Since an isl_val does not have an associated space, this function
1424  * does not do anything, apart from error handling and cleaning up memory.
1425  */
1426 __isl_give isl_val *isl_val_realign_domain(__isl_take isl_val *v,
1427         __isl_take isl_reordering *r)
1428 {
1429         if (!r)
1430                 return isl_val_free(v);
1431         isl_reordering_free(r);
1432         return v;
1433 }
1434
1435 /* Return an isl_val that is zero on "ls".
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  * simply returns a zero isl_val in the same context as "ls".
1441  */
1442 __isl_give isl_val *isl_val_zero_on_domain(__isl_take isl_local_space *ls)
1443 {
1444         isl_ctx *ctx;
1445
1446         if (!ls)
1447                 return NULL;
1448         ctx = isl_local_space_get_ctx(ls);
1449         isl_local_space_free(ls);
1450         return isl_val_zero(ctx);
1451 }
1452
1453 /* Do the parameters of "v" match those of "space"?
1454  *
1455  * This function is only meant to be used in the generic isl_multi_*
1456  * functions which have to deal with base objects that have an associated
1457  * space.  Since an isl_val does not have an associated space, this function
1458  * simply returns 1, except if "v" or "space" are NULL.
1459  */
1460 int isl_val_matching_params(__isl_keep isl_val *v, __isl_keep isl_space *space)
1461 {
1462         if (!v || !space)
1463                 return -1;
1464         return 1;
1465 }
1466
1467 /* Check that the domain space of "v" matches "space".
1468  *
1469  * Return 0 on success and -1 on error.
1470  *
1471  * This function is only meant to be used in the generic isl_multi_*
1472  * functions which have to deal with base objects that have an associated
1473  * space.  Since an isl_val does not have an associated space, this function
1474  * simply returns 0, except if "v" or "space" are NULL.
1475  */
1476 int isl_val_check_match_domain_space(__isl_keep isl_val *v,
1477         __isl_keep isl_space *space)
1478 {
1479         if (!v || !space)
1480                 return -1;
1481         return 0;
1482 }
1483
1484 #undef BASE
1485 #define BASE val
1486
1487 #define NO_DOMAIN
1488 #define NO_INTERSECT_DOMAIN
1489 #define NO_GIST
1490 #define NO_IDENTITY
1491 #define NO_FROM_BASE
1492 #define NO_MOVE_DIMS
1493 #include <isl_multi_templ.c>
1494
1495 /* Apply "fn" to each of the elements of "mv" with as second argument "v".
1496  */
1497 static __isl_give isl_multi_val *isl_multi_val_fn_val(
1498         __isl_take isl_multi_val *mv,
1499         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
1500                                         __isl_take isl_val *v2),
1501         __isl_take isl_val *v)
1502 {
1503         int i;
1504
1505         mv = isl_multi_val_cow(mv);
1506         if (!mv || !v)
1507                 goto error;
1508
1509         for (i = 0; i < mv->n; ++i) {
1510                 mv->p[i] = fn(mv->p[i], isl_val_copy(v));
1511                 if (!mv->p[i])
1512                         goto error;
1513         }
1514
1515         isl_val_free(v);
1516         return mv;
1517 error:
1518         isl_val_free(v);
1519         isl_multi_val_free(mv);
1520         return NULL;
1521 }
1522
1523 /* Add "v" to each of the elements of "mv".
1524  */
1525 __isl_give isl_multi_val *isl_multi_val_add_val(__isl_take isl_multi_val *mv,
1526         __isl_take isl_val *v)
1527 {
1528         if (!v)
1529                 return isl_multi_val_free(mv);
1530         if (isl_val_is_zero(v)) {
1531                 isl_val_free(v);
1532                 return mv;
1533         }
1534         return isl_multi_val_fn_val(mv, &isl_val_add, v);
1535 }
1536
1537 /* Reduce the elements of "mv" modulo "v".
1538  */
1539 __isl_give isl_multi_val *isl_multi_val_mod_val(__isl_take isl_multi_val *mv,
1540         __isl_take isl_val *v)
1541 {
1542         return isl_multi_val_fn_val(mv, &isl_val_mod, v);
1543 }