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, int nparam);
381 __isl_give isl_basic_set *isl_basic_set_read_from_str(
382 isl_ctx *ctx, const char *str, int nparam);
383 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
384 FILE *input, int nparam);
387 __isl_give isl_basic_map *isl_basic_map_read_from_file(
388 isl_ctx *ctx, FILE *input, int nparam);
389 __isl_give isl_basic_map *isl_basic_map_read_from_str(
390 isl_ctx *ctx, const char *str, int nparam);
391 __isl_give isl_map *isl_map_read_from_file(
392 struct isl_ctx *ctx, FILE *input, int nparam);
393 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
394 const char *str, int nparam);
396 The input may be either in C<PolyLib> format or in the
397 C<isl> format, which is similar to the C<Omega> format.
398 C<nparam> specifies how many of the final columns in
399 the C<PolyLib> format correspond to parameters.
400 If input is given in the C<isl> format, then the number
401 of parameters needs to be equal to C<nparam>.
402 If C<nparam> is negative, then any number of parameters
403 is accepted in the C<isl> format and zero parameters
404 are assumed in the C<PolyLib> format.
409 void isl_basic_set_print(__isl_keep isl_basic_set *bset,
410 FILE *out, int indent,
411 const char *prefix, const char *suffix,
412 unsigned output_format);
413 void isl_set_print(__isl_keep struct isl_set *set,
414 FILE *out, int indent, unsigned output_format);
416 C<input_format> must be C<ISL_FORMAT_POLYLIB>.
417 Each line in the output is indented by C<indent> spaces,
418 prefixed by C<prefix> and suffixed by C<suffix>.
419 The coefficients of the existentially quantified variables
420 appear between those of the set variables and those
423 =head3 Dumping the internal state
425 For lack of proper output functions, the following functions
426 can be used to dump the internal state of a set or relation.
427 The user should not depend on the output format of these functions.
429 void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
430 FILE *out, int indent);
431 void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
432 FILE *out, int indent);
433 void isl_set_dump(__isl_keep isl_set *set,
434 FILE *out, int indent);
435 void isl_map_dump(__isl_keep isl_map *map,
436 FILE *out, int indent);
438 =head2 Creating New Sets and Relations
440 C<isl> has functions for creating some standard sets and relations.
444 =item * Empty sets and relations
446 __isl_give isl_basic_set *isl_basic_set_empty(
447 __isl_take isl_dim *dim);
448 __isl_give isl_basic_map *isl_basic_map_empty(
449 __isl_take isl_dim *dim);
450 __isl_give isl_set *isl_set_empty(
451 __isl_take isl_dim *dim);
452 __isl_give isl_map *isl_map_empty(
453 __isl_take isl_dim *dim);
455 =item * Universe sets and relations
457 __isl_give isl_basic_set *isl_basic_set_universe(
458 __isl_take isl_dim *dim);
459 __isl_give isl_basic_map *isl_basic_map_universe(
460 __isl_take isl_dim *dim);
461 __isl_give isl_set *isl_set_universe(
462 __isl_take isl_dim *dim);
463 __isl_give isl_map *isl_map_universe(
464 __isl_take isl_dim *dim);
466 =item * Identity relations
468 __isl_give isl_basic_map *isl_basic_map_identity(
469 __isl_take isl_dim *set_dim);
470 __isl_give isl_map *isl_map_identity(
471 __isl_take isl_dim *set_dim);
473 These functions take a dimension specification for a B<set>
474 and return an identity relation between two such sets.
476 =item * Lexicographic order
478 __isl_give isl_map *isl_map_lex_lt(
479 __isl_take isl_dim *set_dim);
480 __isl_give isl_map *isl_map_lex_le(
481 __isl_take isl_dim *set_dim);
482 __isl_give isl_map *isl_map_lex_gt(
483 __isl_take isl_dim *set_dim);
484 __isl_give isl_map *isl_map_lex_ge(
485 __isl_take isl_dim *set_dim);
487 These functions take a dimension specification for a B<set>
488 and return relations that express that the elements in the domain
489 are lexicograhically less
490 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
491 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
492 than the elements in the range.
496 A basic set or relation can be converted to a set or relation
497 using the following functions.
499 __isl_give isl_set *isl_set_from_basic_set(
500 __isl_take isl_basic_set *bset);
501 __isl_give isl_map *isl_map_from_basic_map(
502 __isl_take isl_basic_map *bmap);
504 Sets and relations can be copied and freed again using the following
507 __isl_give isl_basic_set *isl_basic_set_copy(
508 __isl_keep isl_basic_set *bset);
509 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
510 __isl_give isl_basic_map *isl_basic_map_copy(
511 __isl_keep isl_basic_map *bmap);
512 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
513 void isl_basic_set_free(__isl_take isl_basic_set *bset);
514 void isl_set_free(__isl_take isl_set *set);
515 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
516 void isl_map_free(__isl_take isl_map *map);
518 Other sets and relations can be constructed by starting
519 from a universe set or relation, adding equality and/or
520 inequality constraints and then projecting out the
521 existentially quantified variables, if any.
522 Constraints can be constructed, manipulated and
523 added to basic sets and relations using the following functions.
525 #include <isl_constraint.h>
526 __isl_give isl_constraint *isl_equality_alloc(
527 __isl_take isl_dim *dim);
528 __isl_give isl_constraint *isl_inequality_alloc(
529 __isl_take isl_dim *dim);
530 void isl_constraint_set_constant(
531 __isl_keep isl_constraint *constraint, isl_int v);
532 void isl_constraint_set_coefficient(
533 __isl_keep isl_constraint *constraint,
534 enum isl_dim_type type, int pos, isl_int v);
535 __isl_give isl_basic_map *isl_basic_map_add_constraint(
536 __isl_take isl_basic_map *bmap,
537 __isl_take isl_constraint *constraint);
538 __isl_give isl_basic_set *isl_basic_set_add_constraint(
539 __isl_take isl_basic_set *bset,
540 __isl_take isl_constraint *constraint);
542 For example, to create a set containing the even integers
543 between 10 and 42, you would use the following code.
547 struct isl_constraint *c;
548 struct isl_basic_set *bset;
551 dim = isl_dim_set_alloc(ctx, 0, 2);
552 bset = isl_basic_set_universe(isl_dim_copy(dim));
554 c = isl_equality_alloc(isl_dim_copy(dim));
555 isl_int_set_si(v, -1);
556 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
557 isl_int_set_si(v, 2);
558 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
559 bset = isl_basic_set_add_constraint(bset, c);
561 c = isl_inequality_alloc(isl_dim_copy(dim));
562 isl_int_set_si(v, -10);
563 isl_constraint_set_constant(c, v);
564 isl_int_set_si(v, 1);
565 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
566 bset = isl_basic_set_add_constraint(bset, c);
568 c = isl_inequality_alloc(dim);
569 isl_int_set_si(v, 42);
570 isl_constraint_set_constant(c, v);
571 isl_int_set_si(v, -1);
572 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
573 bset = isl_basic_set_add_constraint(bset, c);
575 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
581 =head3 Unary Properties
587 The following functions test whether the given set or relation
588 contains any integer points. The ``fast'' variants do not perform
589 any computations, but simply check if the given set or relation
590 is already known to be empty.
592 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
593 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
594 int isl_set_is_empty(__isl_keep isl_set *set);
595 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
596 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
597 int isl_map_fast_is_empty(__isl_keep isl_map *map);
598 int isl_map_is_empty(__isl_keep isl_map *map);
602 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
603 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
607 =head3 Binary Properties
613 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
614 __isl_keep isl_set *set2);
615 int isl_set_is_equal(__isl_keep isl_set *set1,
616 __isl_keep isl_set *set2);
617 int isl_map_is_equal(__isl_keep isl_map *map1,
618 __isl_keep isl_map *map2);
619 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
620 __isl_keep isl_map *map2);
621 int isl_basic_map_is_equal(
622 __isl_keep isl_basic_map *bmap1,
623 __isl_keep isl_basic_map *bmap2);
627 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
628 __isl_keep isl_set *set2);
632 int isl_set_is_subset(__isl_keep isl_set *set1,
633 __isl_keep isl_set *set2);
634 int isl_set_is_strict_subset(
635 __isl_keep isl_set *set1,
636 __isl_keep isl_set *set2);
637 int isl_basic_map_is_subset(
638 __isl_keep isl_basic_map *bmap1,
639 __isl_keep isl_basic_map *bmap2);
640 int isl_basic_map_is_strict_subset(
641 __isl_keep isl_basic_map *bmap1,
642 __isl_keep isl_basic_map *bmap2);
643 int isl_map_is_subset(
644 __isl_keep isl_map *map1,
645 __isl_keep isl_map *map2);
646 int isl_map_is_strict_subset(
647 __isl_keep isl_map *map1,
648 __isl_keep isl_map *map2);
652 =head2 Unary Operations
658 __isl_give isl_basic_set *isl_basic_set_project_out(
659 __isl_take isl_basic_set *bset,
660 enum isl_dim_type type, unsigned first, unsigned n);
661 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
662 enum isl_dim_type type, unsigned first, unsigned n);
663 __isl_give isl_basic_set *isl_basic_map_domain(
664 __isl_take isl_basic_map *bmap);
665 __isl_give isl_basic_set *isl_basic_map_range(
666 __isl_take isl_basic_map *bmap);
667 __isl_give isl_set *isl_map_domain(
668 __isl_take isl_map *bmap);
669 __isl_give isl_set *isl_map_range(
670 __isl_take isl_map *map);
672 C<isl_basic_set_project_out> currently only supports projecting
673 out the final C<isl_dim_set> dimensions.
677 Simplify the representation of a set or relation by trying
678 to combine pairs of basic sets or relations into a single
679 basic set or relation.
681 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
682 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
686 __isl_give isl_basic_set *isl_set_convex_hull(
687 __isl_take isl_set *set);
688 __isl_give isl_basic_map *isl_map_convex_hull(
689 __isl_take isl_map *map);
691 If the input set or relation has any existentially quantified
692 variables, then the result of these operations is currently undefined.
696 __isl_give isl_basic_set *isl_basic_set_affine_hull(
697 __isl_take isl_basic_set *bset);
698 __isl_give isl_basic_set *isl_set_affine_hull(
699 __isl_take isl_set *set);
700 __isl_give isl_basic_map *isl_basic_map_affine_hull(
701 __isl_take isl_basic_map *bmap);
702 __isl_give isl_basic_map *isl_map_affine_hull(
703 __isl_take isl_map *map);
707 =head2 Binary Operations
709 The two arguments of a binary operation not only need to live
710 in the same C<isl_ctx>, they currently also need to have
711 the same (number of) parameters.
713 =head3 Basic Operations
719 __isl_give isl_basic_set *isl_basic_set_intersect(
720 __isl_take isl_basic_set *bset1,
721 __isl_take isl_basic_set *bset2);
722 __isl_give isl_set *isl_set_intersect(
723 __isl_take isl_set *set1,
724 __isl_take isl_set *set2);
725 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
726 __isl_take isl_basic_map *bmap,
727 __isl_take isl_basic_set *bset);
728 __isl_give isl_basic_map *isl_basic_map_intersect_range(
729 __isl_take isl_basic_map *bmap,
730 __isl_take isl_basic_set *bset);
731 __isl_give isl_basic_map *isl_basic_map_intersect(
732 __isl_take isl_basic_map *bmap1,
733 __isl_take isl_basic_map *bmap2);
734 __isl_give isl_map *isl_map_intersect_domain(
735 __isl_take isl_map *map,
736 __isl_take isl_set *set);
737 __isl_give isl_map *isl_map_intersect_range(
738 __isl_take isl_map *map,
739 __isl_take isl_set *set);
740 __isl_give isl_map *isl_map_intersect(
741 __isl_take isl_map *map1,
742 __isl_take isl_map *map2);
746 __isl_give isl_set *isl_basic_set_union(
747 __isl_take isl_basic_set *bset1,
748 __isl_take isl_basic_set *bset2);
749 __isl_give isl_map *isl_basic_map_union(
750 __isl_take isl_basic_map *bmap1,
751 __isl_take isl_basic_map *bmap2);
752 __isl_give isl_set *isl_set_union(
753 __isl_take isl_set *set1,
754 __isl_take isl_set *set2);
755 __isl_give isl_map *isl_map_union(
756 __isl_take isl_map *map1,
757 __isl_take isl_map *map2);
759 =item * Set difference
761 __isl_give isl_set *isl_set_subtract(
762 __isl_take isl_set *set1,
763 __isl_take isl_set *set2);
764 __isl_give isl_map *isl_map_subtract(
765 __isl_take isl_map *map1,
766 __isl_take isl_map *map2);
770 __isl_give isl_basic_set *isl_basic_set_apply(
771 __isl_take isl_basic_set *bset,
772 __isl_take isl_basic_map *bmap);
773 __isl_give isl_set *isl_set_apply(
774 __isl_take isl_set *set,
775 __isl_take isl_map *map);
776 __isl_give isl_basic_map *isl_basic_map_apply_domain(
777 __isl_take isl_basic_map *bmap1,
778 __isl_take isl_basic_map *bmap2);
779 __isl_give isl_basic_map *isl_basic_map_apply_range(
780 __isl_take isl_basic_map *bmap1,
781 __isl_take isl_basic_map *bmap2);
782 __isl_give isl_map *isl_map_apply_domain(
783 __isl_take isl_map *map1,
784 __isl_take isl_map *map2);
785 __isl_give isl_map *isl_map_apply_range(
786 __isl_take isl_map *map1,
787 __isl_take isl_map *map2);
791 =head3 Lexicographic Optimization
793 Given a basic set C<bset> and a zero-dimensional domain C<dom>,
794 the following functions
795 compute a set that contains the lexicographic minimum or maximum
796 of the elements in C<bset> for those values of the parameters
798 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
799 that contains the parameter values in C<dom> for which C<bset>
801 In other words, the union of the parameter values
802 for which the result is non-empty and of C<*empty>
805 __isl_give isl_set *isl_basic_set_partial_lexmin(
806 __isl_take isl_basic_set *bset,
807 __isl_take isl_basic_set *dom,
808 __isl_give isl_set **empty);
809 __isl_give isl_set *isl_basic_set_partial_lexmax(
810 __isl_take isl_basic_set *bset,
811 __isl_take isl_basic_set *dom,
812 __isl_give isl_set **empty);
814 Given a basic set C<bset>, the following functions simply
815 return a set containing the lexicographic minimum or maximum
816 of the elements in C<bset>.
818 __isl_give isl_set *isl_basic_set_lexmin(
819 __isl_take isl_basic_set *bset);
820 __isl_give isl_set *isl_basic_set_lexmax(
821 __isl_take isl_basic_set *bset);
823 Given a basic relation C<bmap> and a domain C<dom>,
824 the following functions
825 compute a relation that maps each element of C<dom>
826 to the single lexicographic minimum or maximum
827 of the elements that are associated to that same
829 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
830 that contains the elements in C<dom> that do not map
831 to any elements in C<bmap>.
832 In other words, the union of the domain of the result and of C<*empty>
835 __isl_give isl_map *isl_basic_map_partial_lexmax(
836 __isl_take isl_basic_map *bmap,
837 __isl_take isl_basic_set *dom,
838 __isl_give isl_set **empty);
839 __isl_give isl_map *isl_basic_map_partial_lexmin(
840 __isl_take isl_basic_map *bmap,
841 __isl_take isl_basic_set *dom,
842 __isl_give isl_set **empty);
844 Given a basic map C<bmap>, the following functions simply
845 return a map mapping each element in the domain of
846 C<bmap> to the lexicographic minimum or maximum
847 of all elements associated to that element.
849 __isl_give isl_map *isl_basic_map_lexmin(
850 __isl_take isl_basic_map *bmap);
851 __isl_give isl_map *isl_basic_map_lexmax(
852 __isl_take isl_basic_map *bmap);
856 Although C<isl> is mainly meant to be used as a library,
857 it also contains some basic applications that use some
858 of the functionality of C<isl>.
859 Since C<isl> does not have its own input format yet, these
860 applications currently take input in C<PolyLib> style.
861 That is, a line with the number of rows and columns,
862 where the number of rows is equal to the number of constraints
863 and the number of columns is equal to two plus the number of variables,
864 followed by the actual rows.
865 In each row, the first column indicates whether the constraint
866 is an equality (C<0>) or inequality (C<1>). The final column
867 corresponds to the constant term.
869 =head2 C<isl_polyhedron_sample>
871 C<isl_polyhedron_sample>
872 takes a polyhedron in C<PolyLib> format as input and prints
873 an integer element of the polyhedron, if there is any.
874 The first column in the output is the denominator and is always
875 equal to 1. If the polyhedron contains no integer points,
876 then a vector of length zero is printed.
880 C<isl_pip> takes the same input as the C<example> program
881 from the C<piplib> distribution, i.e., a set of constraints
882 on the parameters in C<PolyLib> format,
883 a line contains only -1 and finally a set
884 of constraints on a parametric polyhedron, again in C<PolyLib> format.
885 The coefficients of the parameters appear in the last columns
886 (but before the final constant column).
887 The output is the lexicographic minimum of the parametric polyhedron.
888 As C<isl> currently does not have its own output format, the output
889 is just a dump of the internal state.
891 =head2 C<isl_polyhedron_minimize>
893 C<isl_polyhedron_minimize> computes the minimum of some linear
894 or affine objective function over the integer points in a polyhedron.
895 The input is in C<PolyLib> format. If an affine objective function
896 is given, then the constant should appear in the last column.
898 =head2 C<isl_polytope_scan>
900 Given a polytope in C<PolyLib> format, C<isl_polytope_scan> prints
901 all integer points in the polytope.
903 =head1 C<isl-polylib>
905 The C<isl-polylib> library provides the following functions for converting
906 between C<isl> objects and C<PolyLib> objects.
907 The library is distributed separately for licensing reasons.
909 #include <isl_set_polylib.h>
910 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
911 Polyhedron *P, __isl_take isl_dim *dim);
912 Polyhedron *isl_basic_set_to_polylib(
913 __isl_keep isl_basic_set *bset);
914 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
915 __isl_take isl_dim *dim);
916 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
918 #include <isl_map_polylib.h>
919 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
920 Polyhedron *P, __isl_take isl_dim *dim);
921 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
922 __isl_take isl_dim *dim);
923 Polyhedron *isl_basic_map_to_polylib(
924 __isl_keep isl_basic_map *bmap);
925 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);