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 C<isl> supports its own input/output format, which is similar
373 to the C<Omega> format, but also supports the C<PolyLib> format
378 The C<isl> format is similar to that of C<Omega>, but has a different
379 syntax for describing the parameters and allows for the definition
380 of an existentially quantified variable as the integer division
381 of an affine expression.
382 For example, the set of integers C<i> between C<0> and C<n>
383 such that C<i % 10 <= 6> can be described as
385 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
388 A set or relation can have several disjuncts, separated
389 by the keyword C<or>. Each disjunct is either a conjunction
390 of constraints or a projection (C<exists>) of a conjunction
391 of constraints. The constraints are separated by the keyword
394 =head3 C<PolyLib> format
396 If the represented set is a union, then the first line
397 contains a single number representing the number of disjuncts.
398 Otherwise, a line containing the number C<1> is optional.
400 Each disjunct is represented by a matrix of constraints.
401 The first line contains two numbers representing
402 the number of rows and columns,
403 where the number of rows is equal to the number of constraints
404 and the number of columns is equal to two plus the number of variables.
405 The following lines contain the actual rows of the constraint matrix.
406 In each row, the first column indicates whether the constraint
407 is an equality (C<0>) or inequality (C<1>). The final column
408 corresponds to the constant term.
410 If the set is parametric, then the coefficients of the parameters
411 appear in the last columns before the constant column.
412 The coefficients of any existentially quantified variables appear
413 between those of the set variables and those of the parameters.
418 __isl_give isl_basic_set *isl_basic_set_read_from_file(
419 isl_ctx *ctx, FILE *input, int nparam);
420 __isl_give isl_basic_set *isl_basic_set_read_from_str(
421 isl_ctx *ctx, const char *str, int nparam);
422 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
423 FILE *input, int nparam);
424 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
425 const char *str, int nparam);
428 __isl_give isl_basic_map *isl_basic_map_read_from_file(
429 isl_ctx *ctx, FILE *input, int nparam);
430 __isl_give isl_basic_map *isl_basic_map_read_from_str(
431 isl_ctx *ctx, const char *str, int nparam);
432 __isl_give isl_map *isl_map_read_from_file(
433 struct isl_ctx *ctx, FILE *input, int nparam);
434 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
435 const char *str, int nparam);
437 The input format is autodetected and may be either the C<PolyLib> format
438 or the C<isl> format.
439 C<nparam> specifies how many of the final columns in
440 the C<PolyLib> format correspond to parameters.
441 If input is given in the C<isl> format, then the number
442 of parameters needs to be equal to C<nparam>.
443 If C<nparam> is negative, then any number of parameters
444 is accepted in the C<isl> format and zero parameters
445 are assumed in the C<PolyLib> format.
450 void isl_basic_set_print(__isl_keep isl_basic_set *bset,
451 FILE *out, int indent,
452 const char *prefix, const char *suffix,
453 unsigned output_format);
454 void isl_set_print(__isl_keep struct isl_set *set,
455 FILE *out, int indent, unsigned output_format);
458 void isl_basic_map_print(__isl_keep isl_basic_map *bmap,
459 FILE *out, int indent,
460 const char *prefix, const char *suffix,
461 unsigned output_format);
462 void isl_map_print(__isl_keep struct isl_map *map,
463 FILE *out, int indent, unsigned output_format);
465 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
466 or C<ISL_FORMAT_POLYLIB>.
467 Each line in the output is indented by C<indent> spaces,
468 prefixed by C<prefix> and suffixed by C<suffix>.
469 In the C<PolyLib> format output,
470 the coefficients of the existentially quantified variables
471 appear between those of the set variables and those
474 =head3 Dumping the internal state
476 For lack of proper output functions, the following functions
477 can be used to dump the internal state of a set or relation.
478 The user should not depend on the output format of these functions.
480 void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
481 FILE *out, int indent);
482 void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
483 FILE *out, int indent);
484 void isl_set_dump(__isl_keep isl_set *set,
485 FILE *out, int indent);
486 void isl_map_dump(__isl_keep isl_map *map,
487 FILE *out, int indent);
489 =head2 Creating New Sets and Relations
491 C<isl> has functions for creating some standard sets and relations.
495 =item * Empty sets and relations
497 __isl_give isl_basic_set *isl_basic_set_empty(
498 __isl_take isl_dim *dim);
499 __isl_give isl_basic_map *isl_basic_map_empty(
500 __isl_take isl_dim *dim);
501 __isl_give isl_set *isl_set_empty(
502 __isl_take isl_dim *dim);
503 __isl_give isl_map *isl_map_empty(
504 __isl_take isl_dim *dim);
506 =item * Universe sets and relations
508 __isl_give isl_basic_set *isl_basic_set_universe(
509 __isl_take isl_dim *dim);
510 __isl_give isl_basic_map *isl_basic_map_universe(
511 __isl_take isl_dim *dim);
512 __isl_give isl_set *isl_set_universe(
513 __isl_take isl_dim *dim);
514 __isl_give isl_map *isl_map_universe(
515 __isl_take isl_dim *dim);
517 =item * Identity relations
519 __isl_give isl_basic_map *isl_basic_map_identity(
520 __isl_take isl_dim *set_dim);
521 __isl_give isl_map *isl_map_identity(
522 __isl_take isl_dim *set_dim);
524 These functions take a dimension specification for a B<set>
525 and return an identity relation between two such sets.
527 =item * Lexicographic order
529 __isl_give isl_map *isl_map_lex_lt(
530 __isl_take isl_dim *set_dim);
531 __isl_give isl_map *isl_map_lex_le(
532 __isl_take isl_dim *set_dim);
533 __isl_give isl_map *isl_map_lex_gt(
534 __isl_take isl_dim *set_dim);
535 __isl_give isl_map *isl_map_lex_ge(
536 __isl_take isl_dim *set_dim);
538 These functions take a dimension specification for a B<set>
539 and return relations that express that the elements in the domain
540 are lexicographically less
541 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
542 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
543 than the elements in the range.
547 A basic set or relation can be converted to a set or relation
548 using the following functions.
550 __isl_give isl_set *isl_set_from_basic_set(
551 __isl_take isl_basic_set *bset);
552 __isl_give isl_map *isl_map_from_basic_map(
553 __isl_take isl_basic_map *bmap);
555 Sets and relations can be copied and freed again using the following
558 __isl_give isl_basic_set *isl_basic_set_copy(
559 __isl_keep isl_basic_set *bset);
560 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
561 __isl_give isl_basic_map *isl_basic_map_copy(
562 __isl_keep isl_basic_map *bmap);
563 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
564 void isl_basic_set_free(__isl_take isl_basic_set *bset);
565 void isl_set_free(__isl_take isl_set *set);
566 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
567 void isl_map_free(__isl_take isl_map *map);
569 Other sets and relations can be constructed by starting
570 from a universe set or relation, adding equality and/or
571 inequality constraints and then projecting out the
572 existentially quantified variables, if any.
573 Constraints can be constructed, manipulated and
574 added to basic sets and relations using the following functions.
576 #include <isl_constraint.h>
577 __isl_give isl_constraint *isl_equality_alloc(
578 __isl_take isl_dim *dim);
579 __isl_give isl_constraint *isl_inequality_alloc(
580 __isl_take isl_dim *dim);
581 void isl_constraint_set_constant(
582 __isl_keep isl_constraint *constraint, isl_int v);
583 void isl_constraint_set_coefficient(
584 __isl_keep isl_constraint *constraint,
585 enum isl_dim_type type, int pos, isl_int v);
586 __isl_give isl_basic_map *isl_basic_map_add_constraint(
587 __isl_take isl_basic_map *bmap,
588 __isl_take isl_constraint *constraint);
589 __isl_give isl_basic_set *isl_basic_set_add_constraint(
590 __isl_take isl_basic_set *bset,
591 __isl_take isl_constraint *constraint);
593 For example, to create a set containing the even integers
594 between 10 and 42, you would use the following code.
598 struct isl_constraint *c;
599 struct isl_basic_set *bset;
602 dim = isl_dim_set_alloc(ctx, 0, 2);
603 bset = isl_basic_set_universe(isl_dim_copy(dim));
605 c = isl_equality_alloc(isl_dim_copy(dim));
606 isl_int_set_si(v, -1);
607 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
608 isl_int_set_si(v, 2);
609 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
610 bset = isl_basic_set_add_constraint(bset, c);
612 c = isl_inequality_alloc(isl_dim_copy(dim));
613 isl_int_set_si(v, -10);
614 isl_constraint_set_constant(c, v);
615 isl_int_set_si(v, 1);
616 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
617 bset = isl_basic_set_add_constraint(bset, c);
619 c = isl_inequality_alloc(dim);
620 isl_int_set_si(v, 42);
621 isl_constraint_set_constant(c, v);
622 isl_int_set_si(v, -1);
623 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
624 bset = isl_basic_set_add_constraint(bset, c);
626 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
632 struct isl_basic_set *bset;
633 bset = isl_basic_set_read_from_str(ctx,
634 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
638 =head3 Unary Properties
644 The following functions test whether the given set or relation
645 contains any integer points. The ``fast'' variants do not perform
646 any computations, but simply check if the given set or relation
647 is already known to be empty.
649 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
650 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
651 int isl_set_is_empty(__isl_keep isl_set *set);
652 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
653 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
654 int isl_map_fast_is_empty(__isl_keep isl_map *map);
655 int isl_map_is_empty(__isl_keep isl_map *map);
659 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
660 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
664 =head3 Binary Properties
670 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
671 __isl_keep isl_set *set2);
672 int isl_set_is_equal(__isl_keep isl_set *set1,
673 __isl_keep isl_set *set2);
674 int isl_map_is_equal(__isl_keep isl_map *map1,
675 __isl_keep isl_map *map2);
676 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
677 __isl_keep isl_map *map2);
678 int isl_basic_map_is_equal(
679 __isl_keep isl_basic_map *bmap1,
680 __isl_keep isl_basic_map *bmap2);
684 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
685 __isl_keep isl_set *set2);
689 int isl_set_is_subset(__isl_keep isl_set *set1,
690 __isl_keep isl_set *set2);
691 int isl_set_is_strict_subset(
692 __isl_keep isl_set *set1,
693 __isl_keep isl_set *set2);
694 int isl_basic_map_is_subset(
695 __isl_keep isl_basic_map *bmap1,
696 __isl_keep isl_basic_map *bmap2);
697 int isl_basic_map_is_strict_subset(
698 __isl_keep isl_basic_map *bmap1,
699 __isl_keep isl_basic_map *bmap2);
700 int isl_map_is_subset(
701 __isl_keep isl_map *map1,
702 __isl_keep isl_map *map2);
703 int isl_map_is_strict_subset(
704 __isl_keep isl_map *map1,
705 __isl_keep isl_map *map2);
709 =head2 Unary Operations
715 __isl_give isl_basic_set *isl_basic_set_project_out(
716 __isl_take isl_basic_set *bset,
717 enum isl_dim_type type, unsigned first, unsigned n);
718 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
719 enum isl_dim_type type, unsigned first, unsigned n);
720 __isl_give isl_basic_set *isl_basic_map_domain(
721 __isl_take isl_basic_map *bmap);
722 __isl_give isl_basic_set *isl_basic_map_range(
723 __isl_take isl_basic_map *bmap);
724 __isl_give isl_set *isl_map_domain(
725 __isl_take isl_map *bmap);
726 __isl_give isl_set *isl_map_range(
727 __isl_take isl_map *map);
729 C<isl_basic_set_project_out> currently only supports projecting
730 out the final C<isl_dim_set> dimensions.
734 Simplify the representation of a set or relation by trying
735 to combine pairs of basic sets or relations into a single
736 basic set or relation.
738 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
739 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
743 __isl_give isl_basic_set *isl_set_convex_hull(
744 __isl_take isl_set *set);
745 __isl_give isl_basic_map *isl_map_convex_hull(
746 __isl_take isl_map *map);
748 If the input set or relation has any existentially quantified
749 variables, then the result of these operations is currently undefined.
753 __isl_give isl_basic_set *isl_basic_set_affine_hull(
754 __isl_take isl_basic_set *bset);
755 __isl_give isl_basic_set *isl_set_affine_hull(
756 __isl_take isl_set *set);
757 __isl_give isl_basic_map *isl_basic_map_affine_hull(
758 __isl_take isl_basic_map *bmap);
759 __isl_give isl_basic_map *isl_map_affine_hull(
760 __isl_take isl_map *map);
764 =head2 Binary Operations
766 The two arguments of a binary operation not only need to live
767 in the same C<isl_ctx>, they currently also need to have
768 the same (number of) parameters.
770 =head3 Basic Operations
776 __isl_give isl_basic_set *isl_basic_set_intersect(
777 __isl_take isl_basic_set *bset1,
778 __isl_take isl_basic_set *bset2);
779 __isl_give isl_set *isl_set_intersect(
780 __isl_take isl_set *set1,
781 __isl_take isl_set *set2);
782 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
783 __isl_take isl_basic_map *bmap,
784 __isl_take isl_basic_set *bset);
785 __isl_give isl_basic_map *isl_basic_map_intersect_range(
786 __isl_take isl_basic_map *bmap,
787 __isl_take isl_basic_set *bset);
788 __isl_give isl_basic_map *isl_basic_map_intersect(
789 __isl_take isl_basic_map *bmap1,
790 __isl_take isl_basic_map *bmap2);
791 __isl_give isl_map *isl_map_intersect_domain(
792 __isl_take isl_map *map,
793 __isl_take isl_set *set);
794 __isl_give isl_map *isl_map_intersect_range(
795 __isl_take isl_map *map,
796 __isl_take isl_set *set);
797 __isl_give isl_map *isl_map_intersect(
798 __isl_take isl_map *map1,
799 __isl_take isl_map *map2);
803 __isl_give isl_set *isl_basic_set_union(
804 __isl_take isl_basic_set *bset1,
805 __isl_take isl_basic_set *bset2);
806 __isl_give isl_map *isl_basic_map_union(
807 __isl_take isl_basic_map *bmap1,
808 __isl_take isl_basic_map *bmap2);
809 __isl_give isl_set *isl_set_union(
810 __isl_take isl_set *set1,
811 __isl_take isl_set *set2);
812 __isl_give isl_map *isl_map_union(
813 __isl_take isl_map *map1,
814 __isl_take isl_map *map2);
816 =item * Set difference
818 __isl_give isl_set *isl_set_subtract(
819 __isl_take isl_set *set1,
820 __isl_take isl_set *set2);
821 __isl_give isl_map *isl_map_subtract(
822 __isl_take isl_map *map1,
823 __isl_take isl_map *map2);
827 __isl_give isl_basic_set *isl_basic_set_apply(
828 __isl_take isl_basic_set *bset,
829 __isl_take isl_basic_map *bmap);
830 __isl_give isl_set *isl_set_apply(
831 __isl_take isl_set *set,
832 __isl_take isl_map *map);
833 __isl_give isl_basic_map *isl_basic_map_apply_domain(
834 __isl_take isl_basic_map *bmap1,
835 __isl_take isl_basic_map *bmap2);
836 __isl_give isl_basic_map *isl_basic_map_apply_range(
837 __isl_take isl_basic_map *bmap1,
838 __isl_take isl_basic_map *bmap2);
839 __isl_give isl_map *isl_map_apply_domain(
840 __isl_take isl_map *map1,
841 __isl_take isl_map *map2);
842 __isl_give isl_map *isl_map_apply_range(
843 __isl_take isl_map *map1,
844 __isl_take isl_map *map2);
848 =head3 Lexicographic Optimization
850 Given a basic set C<bset> and a zero-dimensional domain C<dom>,
851 the following functions
852 compute a set that contains the lexicographic minimum or maximum
853 of the elements in C<bset> for those values of the parameters
855 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
856 that contains the parameter values in C<dom> for which C<bset>
858 In other words, the union of the parameter values
859 for which the result is non-empty and of C<*empty>
862 __isl_give isl_set *isl_basic_set_partial_lexmin(
863 __isl_take isl_basic_set *bset,
864 __isl_take isl_basic_set *dom,
865 __isl_give isl_set **empty);
866 __isl_give isl_set *isl_basic_set_partial_lexmax(
867 __isl_take isl_basic_set *bset,
868 __isl_take isl_basic_set *dom,
869 __isl_give isl_set **empty);
871 Given a basic set C<bset>, the following functions simply
872 return a set containing the lexicographic minimum or maximum
873 of the elements in C<bset>.
875 __isl_give isl_set *isl_basic_set_lexmin(
876 __isl_take isl_basic_set *bset);
877 __isl_give isl_set *isl_basic_set_lexmax(
878 __isl_take isl_basic_set *bset);
880 Given a basic relation C<bmap> and a domain C<dom>,
881 the following functions
882 compute a relation that maps each element of C<dom>
883 to the single lexicographic minimum or maximum
884 of the elements that are associated to that same
886 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
887 that contains the elements in C<dom> that do not map
888 to any elements in C<bmap>.
889 In other words, the union of the domain of the result and of C<*empty>
892 __isl_give isl_map *isl_basic_map_partial_lexmax(
893 __isl_take isl_basic_map *bmap,
894 __isl_take isl_basic_set *dom,
895 __isl_give isl_set **empty);
896 __isl_give isl_map *isl_basic_map_partial_lexmin(
897 __isl_take isl_basic_map *bmap,
898 __isl_take isl_basic_set *dom,
899 __isl_give isl_set **empty);
901 Given a basic map C<bmap>, the following functions simply
902 return a map mapping each element in the domain of
903 C<bmap> to the lexicographic minimum or maximum
904 of all elements associated to that element.
906 __isl_give isl_map *isl_basic_map_lexmin(
907 __isl_take isl_basic_map *bmap);
908 __isl_give isl_map *isl_basic_map_lexmax(
909 __isl_take isl_basic_map *bmap);
913 Although C<isl> is mainly meant to be used as a library,
914 it also contains some basic applications that use some
915 of the functionality of C<isl>.
916 The input may specified either in the L<isl format>
917 or the L<PolyLib format>.
919 =head2 C<isl_polyhedron_sample>
921 C<isl_polyhedron_sample> takes a polyhedron as input and prints
922 an integer element of the polyhedron, if there is any.
923 The first column in the output is the denominator and is always
924 equal to 1. If the polyhedron contains no integer points,
925 then a vector of length zero is printed.
929 C<isl_pip> takes the same input as the C<example> program
930 from the C<piplib> distribution, i.e., a set of constraints
931 on the parameters, a line contains only -1 and finally a set
932 of constraints on a parametric polyhedron.
933 The coefficients of the parameters appear in the last columns
934 (but before the final constant column).
935 The output is the lexicographic minimum of the parametric polyhedron.
936 As C<isl> currently does not have its own output format, the output
937 is just a dump of the internal state.
939 =head2 C<isl_polyhedron_minimize>
941 C<isl_polyhedron_minimize> computes the minimum of some linear
942 or affine objective function over the integer points in a polyhedron.
943 If an affine objective function
944 is given, then the constant should appear in the last column.
946 =head2 C<isl_polytope_scan>
948 Given a polytope, C<isl_polytope_scan> prints
949 all integer points in the polytope.
951 =head1 C<isl-polylib>
953 The C<isl-polylib> library provides the following functions for converting
954 between C<isl> objects and C<PolyLib> objects.
955 The library is distributed separately for licensing reasons.
957 #include <isl_set_polylib.h>
958 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
959 Polyhedron *P, __isl_take isl_dim *dim);
960 Polyhedron *isl_basic_set_to_polylib(
961 __isl_keep isl_basic_set *bset);
962 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
963 __isl_take isl_dim *dim);
964 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
966 #include <isl_map_polylib.h>
967 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
968 Polyhedron *P, __isl_take isl_dim *dim);
969 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
970 __isl_take isl_dim *dim);
971 Polyhedron *isl_basic_map_to_polylib(
972 __isl_keep isl_basic_map *bmap);
973 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);