3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
22 The source of C<isl> can be obtained either as a tarball
23 or from the git repository. Both are available from
24 L<http://freshmeat.net/projects/isl/>.
25 The installation process depends on how you obtained
28 =head2 Installation from the git repository
32 =item 1 Clone or update the repository
34 The first time the source is obtained, you need to clone
37 git clone git://repo.or.cz/isl.git
39 To obtain updates, you need to pull in the latest changes
43 =item 2 Get submodule (optional)
45 C<isl> can optionally use the C<piplib> library and provides
46 this library as a submodule. If you want to use it, then
47 after you have cloned C<isl>, you need to grab the submodules
52 To obtain updates, you only need
56 Note that C<isl> currently does not use any C<piplib>
57 functionality by default.
59 =item 3 Generate C<configure>
65 After performing the above steps, continue
66 with the L<Common installation instructions>.
68 =head2 Common installation instructions
74 Building C<isl> requires C<GMP>, including its headers files.
75 Your distribution may not provide these header files by default
76 and you may need to install a package called C<gmp-devel> or something
77 similar. Alternatively, C<GMP> can be built from
78 source, available from L<http://gmplib.org/>.
82 C<isl> uses the standard C<autoconf> C<configure> script.
87 optionally followed by some configure options.
88 A complete list of options can be obtained by running
92 Below we discuss some of the more common options.
94 C<isl> can optionally use C<piplib>, but no
95 C<piplib> functionality is currently used by default.
96 The C<--with-piplib> option can
97 be used to specify which C<piplib>
98 library to use, either an installed version (C<system>),
99 an externally built version (C<build>), a bundled version (C<bundled>)
100 or no version (C<no>). The option C<build> is mostly useful
101 in C<configure> scripts of larger projects that bundle both C<isl>
108 Installation prefix for C<isl>
110 =item C<--with-gmp-prefix>
112 Installation prefix for C<GMP> (architecture-independent files).
114 =item C<--with-gmp-exec-prefix>
116 Installation prefix for C<GMP> (architecture-dependent files).
118 =item C<--with-piplib>
120 Which copy of C<piplib> to use, either C<no> (default), C<system>, C<build>
121 or C<bundled>. Note that C<bundled> only works if you have obtained
122 C<isl> and its submodules from the git repository.
124 =item C<--with-piplib-prefix>
126 Installation prefix for C<system> C<piplib> (architecture-independent files).
128 =item C<--with-piplib-exec-prefix>
130 Installation prefix for C<system> C<piplib> (architecture-dependent files).
132 =item C<--with-piplib-builddir>
134 Location where C<build> C<piplib> was built.
142 =item 4 Install (optional)
150 =head2 Initialization
152 All manipulations of integer sets and relations occur within
153 the context of an C<isl_ctx>.
154 A given C<isl_ctx> can only be used within a single thread.
155 All arguments of a function are required to have been allocated
156 within the same context.
157 There are currently no functions available for moving an object
158 from one C<isl_ctx> to another C<isl_ctx>. This means that
159 there is currently no way of safely moving an object from one
160 thread to another, unless the whole C<isl_ctx> is moved.
162 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
163 freed using C<isl_ctx_free>.
164 All objects allocated within an C<isl_ctx> should be freed
165 before the C<isl_ctx> itself is freed.
167 isl_ctx *isl_ctx_alloc();
168 void isl_ctx_free(isl_ctx *ctx);
172 All operations on integers, mainly the coefficients
173 of the constraints describing the sets and relations,
174 are performed in exact integer arithmetic using C<GMP>.
175 However, to allow future versions of C<isl> to optionally
176 support fixed integer arithmetic, all calls to C<GMP>
177 are wrapped inside C<isl> specific macros.
178 The basic type is C<isl_int> and the following operations
179 are available on this type.
183 =item isl_int_init(i)
185 =item isl_int_clear(i)
187 =item isl_int_set(r,i)
189 =item isl_int_set_si(r,i)
191 =item isl_int_abs(r,i)
193 =item isl_int_neg(r,i)
195 =item isl_int_swap(i,j)
197 =item isl_int_swap_or_set(i,j)
199 =item isl_int_add_ui(r,i,j)
201 =item isl_int_sub_ui(r,i,j)
203 =item isl_int_add(r,i,j)
205 =item isl_int_sub(r,i,j)
207 =item isl_int_mul(r,i,j)
209 =item isl_int_mul_ui(r,i,j)
211 =item isl_int_addmul(r,i,j)
213 =item isl_int_submul(r,i,j)
215 =item isl_int_gcd(r,i,j)
217 =item isl_int_lcm(r,i,j)
219 =item isl_int_divexact(r,i,j)
221 =item isl_int_cdiv_q(r,i,j)
223 =item isl_int_fdiv_q(r,i,j)
225 =item isl_int_fdiv_r(r,i,j)
227 =item isl_int_fdiv_q_ui(r,i,j)
229 =item isl_int_read(r,s)
231 =item isl_int_print(out,i,width)
235 =item isl_int_cmp(i,j)
237 =item isl_int_cmp_si(i,si)
239 =item isl_int_eq(i,j)
241 =item isl_int_ne(i,j)
243 =item isl_int_lt(i,j)
245 =item isl_int_le(i,j)
247 =item isl_int_gt(i,j)
249 =item isl_int_ge(i,j)
251 =item isl_int_abs_eq(i,j)
253 =item isl_int_abs_ne(i,j)
255 =item isl_int_abs_lt(i,j)
257 =item isl_int_abs_gt(i,j)
259 =item isl_int_abs_ge(i,j)
261 =item isl_int_is_zero(i)
263 =item isl_int_is_one(i)
265 =item isl_int_is_negone(i)
267 =item isl_int_is_pos(i)
269 =item isl_int_is_neg(i)
271 =item isl_int_is_nonpos(i)
273 =item isl_int_is_nonneg(i)
275 =item isl_int_is_divisible_by(i,j)
279 =head2 Sets and Relations
281 C<isl> uses four types of objects for representing sets and relations,
282 C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
283 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
284 can be described as a conjunction of affine constraints, while
285 C<isl_set> and C<isl_map> represent unions of
286 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
287 The difference between sets and relations (maps) is that sets have
288 one set of variables, while relations have two sets of variables,
289 input variables and output variables.
291 =head2 Memory Management
293 Since a high-level operation on sets and/or relations usually involves
294 several substeps and since the user is usually not interested in
295 the intermediate results, most functions that return a new object
296 will also release all the objects passed as arguments.
297 If the user still wants to use one or more of these arguments
298 after the function call, she should pass along a copy of the
299 object rather than the object itself.
300 The user is then responsible for make sure that the original
301 object gets used somewhere else or is explicitly freed.
303 The arguments and return values of all documents functions are
304 annotated to make clear which arguments are released and which
305 arguments are preserved. In particular, the following annotations
312 C<__isl_give> means that a new object is returned.
313 The user should make sure that the returned pointer is
314 used exactly once as a value for an C<__isl_take> argument.
315 In between, it can be used as a value for as many
316 C<__isl_keep> arguments as the user likes.
317 There is one exception, and that is the case where the
318 pointer returned is C<NULL>. Is this case, the user
319 is free to use it as an C<__isl_take> argument or not.
323 C<__isl_take> means that the object the argument points to
324 is taken over by the function and may no longer be used
325 by the user as an argument to any other function.
326 The pointer value must be one returned by a function
327 returning an C<__isl_give> pointer.
328 If the user passes in a C<NULL> value, then this will
329 be treated as an error in the sense that the function will
330 not perform its usual operation. However, it will still
331 make sure that all the the other C<__isl_take> arguments
336 C<__isl_keep> means that the function will only use the object
337 temporarily. After the function has finished, the user
338 can still use it as an argument to other functions.
339 A C<NULL> value will be treated in the same way as
340 a C<NULL> value for an C<__isl_take> argument.
344 =head2 Dimension Specifications
346 Whenever a new set or relation is created from scratch,
347 its dimension needs to be specified using an C<isl_dim>.
350 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
351 unsigned nparam, unsigned n_in, unsigned n_out);
352 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
353 unsigned nparam, unsigned dim);
354 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
355 void isl_dim_free(__isl_take isl_dim *dim);
356 unsigned isl_dim_size(__isl_keep isl_dim *dim,
357 enum isl_dim_type type);
359 The dimension specification used for creating a set
360 needs to be created using C<isl_dim_set_alloc>, while
361 that for creating a relation
362 needs to be created using C<isl_dim_alloc>.
363 C<isl_dim_size> can be used
364 to find out the number of dimensions of each type in
365 a dimension specification, where type may be
366 C<isl_dim_param>, C<isl_dim_in> (only for relations),
367 C<isl_dim_out> (only for relations), C<isl_dim_set>
368 (only for sets) or C<isl_dim_all>.
370 =head2 Input and Output
372 Proper input and output functions are still in development.
373 However, some functions are provided to read and write
374 to foreign file formats.
379 __isl_give isl_basic_set *isl_basic_set_read_from_file(
380 isl_ctx *ctx, FILE *input, unsigned nparam);
381 __isl_give isl_basic_set *isl_basic_set_read_from_str(
382 isl_ctx *ctx, const char *str, unsigned nparam);
383 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
384 FILE *input, unsigned nparam);
387 __isl_give isl_basic_map *isl_basic_map_read_from_file(
388 isl_ctx *ctx, FILE *input, unsigned nparam);
390 The input may be either in C<PolyLib> format or in an
391 C<Omega>-like format.
392 C<nparam> specifies how many of the final columns in
393 the C<PolyLib> format correspond to parameters. It should
394 be zero when C<Omega>-like input is expected.
399 void isl_basic_set_print(__isl_keep isl_basic_set *bset,
400 FILE *out, int indent,
401 const char *prefix, const char *suffix,
402 unsigned output_format);
403 void isl_set_print(__isl_keep struct isl_set *set,
404 FILE *out, int indent, unsigned output_format);
406 C<input_format> must be C<ISL_FORMAT_POLYLIB>.
407 Each line in the output is indented by C<indent> spaces,
408 prefixed by C<prefix> and suffixed by C<suffix>.
409 The coefficients of the existentially quantified variables
410 appear between those of the set variables and those
413 =head3 Dumping the internal state
415 For lack of proper output functions, the following functions
416 can be used to dump the internal state of a set or relation.
417 The user should not depend on the output format of these functions.
419 void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
420 FILE *out, int indent);
421 void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
422 FILE *out, int indent);
423 void isl_set_dump(__isl_keep isl_set *set,
424 FILE *out, int indent);
425 void isl_map_dump(__isl_keep isl_map *map,
426 FILE *out, int indent);
428 =head2 Creating New Sets and Relations
430 C<isl> has functions for creating some standard sets and relations.
434 =item * Empty sets and relations
436 __isl_give isl_basic_set *isl_basic_set_empty(
437 __isl_take isl_dim *dim);
438 __isl_give isl_basic_map *isl_basic_map_empty(
439 __isl_take isl_dim *dim);
440 __isl_give isl_set *isl_set_empty(
441 __isl_take isl_dim *dim);
442 __isl_give isl_map *isl_map_empty(
443 __isl_take isl_dim *dim);
445 =item * Universe sets and relations
447 __isl_give isl_basic_set *isl_basic_set_universe(
448 __isl_take isl_dim *dim);
449 __isl_give isl_basic_map *isl_basic_map_universe(
450 __isl_take isl_dim *dim);
451 __isl_give isl_set *isl_set_universe(
452 __isl_take isl_dim *dim);
453 __isl_give isl_map *isl_map_universe(
454 __isl_take isl_dim *dim);
456 =item * Identity relations
458 __isl_give isl_basic_map *isl_basic_map_identity(
459 __isl_take isl_dim *set_dim);
460 __isl_give isl_map *isl_map_identity(
461 __isl_take isl_dim *set_dim);
463 These functions take a dimension specification for a B<set>
464 and return an identity relation between two such sets.
466 =item * Lexicographic order
468 __isl_give isl_map *isl_map_lex_lt(
469 __isl_take isl_dim *set_dim);
470 __isl_give isl_map *isl_map_lex_le(
471 __isl_take isl_dim *set_dim);
472 __isl_give isl_map *isl_map_lex_gt(
473 __isl_take isl_dim *set_dim);
474 __isl_give isl_map *isl_map_lex_ge(
475 __isl_take isl_dim *set_dim);
477 These functions take a dimension specification for a B<set>
478 and return relations that express that the elements in the domain
479 are lexicograhically less
480 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
481 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
482 than the elements in the range.
486 A basic set or relation can be converted to a set or relation
487 using the following functions.
489 __isl_give isl_set *isl_set_from_basic_set(
490 __isl_take isl_basic_set *bset);
491 __isl_give isl_map *isl_map_from_basic_map(
492 __isl_take isl_basic_map *bmap);
494 Sets and relations can be copied and freed again using the following
497 __isl_give isl_basic_set *isl_basic_set_copy(
498 __isl_keep isl_basic_set *bset);
499 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
500 __isl_give isl_basic_map *isl_basic_map_copy(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
503 void isl_basic_set_free(__isl_take isl_basic_set *bset);
504 void isl_set_free(__isl_take isl_set *set);
505 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
506 void isl_map_free(__isl_take isl_map *map);
508 Other sets and relations can be constructed by starting
509 from a universe set or relation, adding equality and/or
510 inequality constraints and then projecting out the
511 existentially quantified variables, if any.
512 Constraints can be constructed, manipulated and
513 added to basic sets and relations using the following functions.
515 #include <isl_constraint.h>
516 __isl_give isl_constraint *isl_equality_alloc(
517 __isl_take isl_dim *dim);
518 __isl_give isl_constraint *isl_inequality_alloc(
519 __isl_take isl_dim *dim);
520 void isl_constraint_set_constant(
521 __isl_keep isl_constraint *constraint, isl_int v);
522 void isl_constraint_set_coefficient(
523 __isl_keep isl_constraint *constraint,
524 enum isl_dim_type type, int pos, isl_int v);
525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
526 __isl_take isl_basic_map *bmap,
527 __isl_take isl_constraint *constraint);
528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
529 __isl_take isl_basic_set *bset,
530 __isl_take isl_constraint *constraint);
532 For example, to create a set containing the even integers
533 between 10 and 42, you would use the following code.
537 struct isl_constraint *c;
538 struct isl_basic_set *bset;
541 dim = isl_dim_set_alloc(ctx, 0, 2);
542 bset = isl_basic_set_universe(isl_dim_copy(dim));
544 c = isl_equality_alloc(isl_dim_copy(dim));
545 isl_int_set_si(v, -1);
546 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
547 isl_int_set_si(v, 2);
548 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
549 bset = isl_basic_set_add_constraint(bset, c);
551 c = isl_inequality_alloc(isl_dim_copy(dim));
552 isl_int_set_si(v, -10);
553 isl_constraint_set_constant(c, v);
554 isl_int_set_si(v, 1);
555 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
556 bset = isl_basic_set_add_constraint(bset, c);
558 c = isl_inequality_alloc(dim);
559 isl_int_set_si(v, 42);
560 isl_constraint_set_constant(c, v);
561 isl_int_set_si(v, -1);
562 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
563 bset = isl_basic_set_add_constraint(bset, c);
565 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
571 =head3 Unary Properties
577 The following functions test whether the given set or relation
578 contains any integer points. The ``fast'' variants do not perform
579 any computations, but simply check if the given set or relation
580 is already known to be empty.
582 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
583 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
584 int isl_set_is_empty(__isl_keep isl_set *set);
585 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
586 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
587 int isl_map_fast_is_empty(__isl_keep isl_map *map);
588 int isl_map_is_empty(__isl_keep isl_map *map);
592 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
593 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
597 =head3 Binary Properties
603 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
604 __isl_keep isl_set *set2);
605 int isl_set_is_equal(__isl_keep isl_set *set1,
606 __isl_keep isl_set *set2);
607 int isl_map_is_equal(__isl_keep isl_map *map1,
608 __isl_keep isl_map *map2);
609 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
610 __isl_keep isl_map *map2);
611 int isl_basic_map_is_equal(
612 __isl_keep isl_basic_map *bmap1,
613 __isl_keep isl_basic_map *bmap2);
617 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
618 __isl_keep isl_set *set2);
622 int isl_set_is_subset(__isl_keep isl_set *set1,
623 __isl_keep isl_set *set2);
624 int isl_set_is_strict_subset(
625 __isl_keep isl_set *set1,
626 __isl_keep isl_set *set2);
627 int isl_basic_map_is_subset(
628 __isl_keep isl_basic_map *bmap1,
629 __isl_keep isl_basic_map *bmap2);
630 int isl_basic_map_is_strict_subset(
631 __isl_keep isl_basic_map *bmap1,
632 __isl_keep isl_basic_map *bmap2);
633 int isl_map_is_subset(
634 __isl_keep isl_map *map1,
635 __isl_keep isl_map *map2);
636 int isl_map_is_strict_subset(
637 __isl_keep isl_map *map1,
638 __isl_keep isl_map *map2);
642 =head2 Unary Operations
648 __isl_give isl_basic_set *isl_basic_set_project_out(
649 __isl_take isl_basic_set *bset,
650 enum isl_dim_type type, unsigned first, unsigned n);
651 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
652 enum isl_dim_type type, unsigned first, unsigned n);
653 __isl_give isl_basic_set *isl_basic_map_domain(
654 __isl_take isl_basic_map *bmap);
655 __isl_give isl_basic_set *isl_basic_map_range(
656 __isl_take isl_basic_map *bmap);
657 __isl_give isl_set *isl_map_domain(
658 __isl_take isl_map *bmap);
659 __isl_give isl_set *isl_map_range(
660 __isl_take isl_map *map);
662 C<isl_basic_set_project_out> currently only supports projecting
663 out the final C<isl_dim_set> dimensions.
667 Simplify the representation of a set or relation by trying
668 to combine pairs of basic sets or relations into a single
669 basic set or relation.
671 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
672 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
676 __isl_give isl_basic_set *isl_set_convex_hull(
677 __isl_take isl_set *set);
678 __isl_give isl_basic_map *isl_map_convex_hull(
679 __isl_take isl_map *map);
681 If the input set or relation has any existentially quantified
682 variables, then the result of these operations is currently undefined.
686 __isl_give isl_basic_set *isl_basic_set_affine_hull(
687 __isl_take isl_basic_set *bset);
688 __isl_give isl_basic_set *isl_set_affine_hull(
689 __isl_take isl_set *set);
690 __isl_give isl_basic_map *isl_basic_map_affine_hull(
691 __isl_take isl_basic_map *bmap);
692 __isl_give isl_basic_map *isl_map_affine_hull(
693 __isl_take isl_map *map);
697 =head2 Binary Operations
699 The two arguments of a binary operation not only need to live
700 in the same C<isl_ctx>, they currently also need to have
701 the same (number of) parameters.
703 =head3 Basic Operations
709 __isl_give isl_basic_set *isl_basic_set_intersect(
710 __isl_take isl_basic_set *bset1,
711 __isl_take isl_basic_set *bset2);
712 __isl_give isl_set *isl_set_intersect(
713 __isl_take isl_set *set1,
714 __isl_take isl_set *set2);
715 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
716 __isl_take isl_basic_map *bmap,
717 __isl_take isl_basic_set *bset);
718 __isl_give isl_basic_map *isl_basic_map_intersect_range(
719 __isl_take isl_basic_map *bmap,
720 __isl_take isl_basic_set *bset);
721 __isl_give isl_basic_map *isl_basic_map_intersect(
722 __isl_take isl_basic_map *bmap1,
723 __isl_take isl_basic_map *bmap2);
724 __isl_give isl_map *isl_map_intersect_domain(
725 __isl_take isl_map *map,
726 __isl_take isl_set *set);
727 __isl_give isl_map *isl_map_intersect_range(
728 __isl_take isl_map *map,
729 __isl_take isl_set *set);
730 __isl_give isl_map *isl_map_intersect(
731 __isl_take isl_map *map1,
732 __isl_take isl_map *map2);
736 __isl_give isl_set *isl_basic_set_union(
737 __isl_take isl_basic_set *bset1,
738 __isl_take isl_basic_set *bset2);
739 __isl_give isl_map *isl_basic_map_union(
740 __isl_take isl_basic_map *bmap1,
741 __isl_take isl_basic_map *bmap2);
742 __isl_give isl_set *isl_set_union(
743 __isl_take isl_set *set1,
744 __isl_take isl_set *set2);
745 __isl_give isl_map *isl_map_union(
746 __isl_take isl_map *map1,
747 __isl_take isl_map *map2);
749 =item * Set difference
751 __isl_give isl_set *isl_set_subtract(
752 __isl_take isl_set *set1,
753 __isl_take isl_set *set2);
754 __isl_give isl_map *isl_map_subtract(
755 __isl_take isl_map *map1,
756 __isl_take isl_map *map2);
760 __isl_give isl_basic_set *isl_basic_set_apply(
761 __isl_take isl_basic_set *bset,
762 __isl_take isl_basic_map *bmap);
763 __isl_give isl_set *isl_set_apply(
764 __isl_take isl_set *set,
765 __isl_take isl_map *map);
766 __isl_give isl_basic_map *isl_basic_map_apply_domain(
767 __isl_take isl_basic_map *bmap1,
768 __isl_take isl_basic_map *bmap2);
769 __isl_give isl_basic_map *isl_basic_map_apply_range(
770 __isl_take isl_basic_map *bmap1,
771 __isl_take isl_basic_map *bmap2);
772 __isl_give isl_map *isl_map_apply_domain(
773 __isl_take isl_map *map1,
774 __isl_take isl_map *map2);
775 __isl_give isl_map *isl_map_apply_range(
776 __isl_take isl_map *map1,
777 __isl_take isl_map *map2);
781 =head3 Lexicographic Optimization
783 Given a basic set C<bset> and a zero-dimensional domain C<dom>,
784 the following functions
785 compute a set that contains the lexicographic minimum or maximum
786 of the elements in C<bset> for those values of the parameters
788 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
789 that contains the parameter values in C<dom> for which C<bset>
791 In other words, the union of the parameter values
792 for which the result is non-empty and of C<*empty>
795 __isl_give isl_set *isl_basic_set_partial_lexmin(
796 __isl_take isl_basic_set *bset,
797 __isl_take isl_basic_set *dom,
798 __isl_give isl_set **empty);
799 __isl_give isl_set *isl_basic_set_partial_lexmax(
800 __isl_take isl_basic_set *bset,
801 __isl_take isl_basic_set *dom,
802 __isl_give isl_set **empty);
804 Given a basic set C<bset>, the following functions simply
805 return a set containing the lexicographic minimum or maximum
806 of the elements in C<bset>.
808 __isl_give isl_set *isl_basic_set_lexmin(
809 __isl_take isl_basic_set *bset);
810 __isl_give isl_set *isl_basic_set_lexmax(
811 __isl_take isl_basic_set *bset);
813 Given a basic relation C<bmap> and a domain C<dom>,
814 the following functions
815 compute a relation that maps each element of C<dom>
816 to the single lexicographic minimum or maximum
817 of the elements that are associated to that same
819 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
820 that contains the elements in C<dom> that do not map
821 to any elements in C<bmap>.
822 In other words, the union of the domain of the result and of C<*empty>
825 __isl_give isl_map *isl_basic_map_partial_lexmax(
826 __isl_take isl_basic_map *bmap,
827 __isl_take isl_basic_set *dom,
828 __isl_give isl_set **empty);
829 __isl_give isl_map *isl_basic_map_partial_lexmin(
830 __isl_take isl_basic_map *bmap,
831 __isl_take isl_basic_set *dom,
832 __isl_give isl_set **empty);
834 Given a basic map C<bmap>, the following functions simply
835 return a map mapping each element in the domain of
836 C<bmap> to the lexicographic minimum or maximum
837 of all elements associated to that element.
839 __isl_give isl_map *isl_basic_map_lexmin(
840 __isl_take isl_basic_map *bmap);
841 __isl_give isl_map *isl_basic_map_lexmax(
842 __isl_take isl_basic_map *bmap);
846 Although C<isl> is mainly meant to be used as a library,
847 it also contains some basic applications that use some
848 of the functionality of C<isl>.
849 Since C<isl> does not have its own input format yet, these
850 applications currently take input in C<PolyLib> style.
851 That is, a line with the number of rows and columns,
852 where the number of rows is equal to the number of constraints
853 and the number of columns is equal to two plus the number of variables,
854 followed by the actual rows.
855 In each row, the first column indicates whether the constraint
856 is an equality (C<0>) or inequality (C<1>). The final column
857 corresponds to the constant term.
859 =head2 C<isl_polyhedron_sample>
861 C<isl_polyhedron_sample>
862 takes a polyhedron in C<PolyLib> format as input and prints
863 an integer element of the polyhedron, if there is any.
864 The first column in the output is the denominator and is always
865 equal to 1. If the polyhedron contains no integer points,
866 then a vector of length zero is printed.
870 C<isl_pip> takes the same input as the C<example> program
871 from the C<piplib> distribution, i.e., a set of constraints
872 on the parameters in C<PolyLib> format,
873 a line contains only -1 and finally a set
874 of constraints on a parametric polyhedron, again in C<PolyLib> format.
875 The coefficients of the parameters appear in the last columns
876 (but before the final constant column).
877 The output is the lexicographic minimum of the parametric polyhedron.
878 As C<isl> currently does not have its own output format, the output
879 is just a dump of the internal state.
881 =head2 C<isl_polyhedron_minimize>
883 C<isl_polyhedron_minimize> computes the minimum of some linear
884 or affine objective function over the integer points in a polyhedron.
885 The input is in C<PolyLib> format. If an affine objective function
886 is given, then the constant should appear in the last column.
888 =head2 C<isl_polytope_scan>
890 Given a polytope in C<PolyLib> format, C<isl_polytope_scan> prints
891 all integer points in the polytope.
893 =head1 C<isl-polylib>
895 The C<isl-polylib> library provides the following functions for converting
896 between C<isl> objects and C<PolyLib> objects.
897 The library is distributed separately for licensing reasons.
899 #include <isl_set_polylib.h>
900 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
901 Polyhedron *P, __isl_take isl_dim *dim);
902 Polyhedron *isl_basic_set_to_polylib(
903 __isl_keep isl_basic_set *bset);
904 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
905 __isl_take isl_dim *dim);
906 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
908 #include <isl_map_polylib.h>
909 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
910 Polyhedron *P, __isl_take isl_dim *dim);
911 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
912 __isl_take isl_dim *dim);
913 Polyhedron *isl_basic_map_to_polylib(
914 __isl_keep isl_basic_map *bmap);
915 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);