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.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
119 The source of C<isl> can be obtained either as a tarball
120 or from the git repository. Both are available from
121 L<http://freshmeat.net/projects/isl/>.
122 The installation process depends on how you obtained
125 =head2 Installation from the git repository
129 =item 1 Clone or update the repository
131 The first time the source is obtained, you need to clone
134 git clone git://repo.or.cz/isl.git
136 To obtain updates, you need to pull in the latest changes
140 =item 2 Generate C<configure>
146 After performing the above steps, continue
147 with the L<Common installation instructions>.
149 =head2 Common installation instructions
153 =item 1 Obtain C<GMP>
155 Building C<isl> requires C<GMP>, including its headers files.
156 Your distribution may not provide these header files by default
157 and you may need to install a package called C<gmp-devel> or something
158 similar. Alternatively, C<GMP> can be built from
159 source, available from L<http://gmplib.org/>.
163 C<isl> uses the standard C<autoconf> C<configure> script.
168 optionally followed by some configure options.
169 A complete list of options can be obtained by running
173 Below we discuss some of the more common options.
175 C<isl> can optionally use C<piplib>, but no
176 C<piplib> functionality is currently used by default.
177 The C<--with-piplib> option can
178 be used to specify which C<piplib>
179 library to use, either an installed version (C<system>),
180 an externally built version (C<build>)
181 or no version (C<no>). The option C<build> is mostly useful
182 in C<configure> scripts of larger projects that bundle both C<isl>
189 Installation prefix for C<isl>
191 =item C<--with-gmp-prefix>
193 Installation prefix for C<GMP> (architecture-independent files).
195 =item C<--with-gmp-exec-prefix>
197 Installation prefix for C<GMP> (architecture-dependent files).
199 =item C<--with-piplib>
201 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
203 =item C<--with-piplib-prefix>
205 Installation prefix for C<system> C<piplib> (architecture-independent files).
207 =item C<--with-piplib-exec-prefix>
209 Installation prefix for C<system> C<piplib> (architecture-dependent files).
211 =item C<--with-piplib-builddir>
213 Location where C<build> C<piplib> was built.
221 =item 4 Install (optional)
229 =head2 Initialization
231 All manipulations of integer sets and relations occur within
232 the context of an C<isl_ctx>.
233 A given C<isl_ctx> can only be used within a single thread.
234 All arguments of a function are required to have been allocated
235 within the same context.
236 There are currently no functions available for moving an object
237 from one C<isl_ctx> to another C<isl_ctx>. This means that
238 there is currently no way of safely moving an object from one
239 thread to another, unless the whole C<isl_ctx> is moved.
241 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
242 freed using C<isl_ctx_free>.
243 All objects allocated within an C<isl_ctx> should be freed
244 before the C<isl_ctx> itself is freed.
246 isl_ctx *isl_ctx_alloc();
247 void isl_ctx_free(isl_ctx *ctx);
251 All operations on integers, mainly the coefficients
252 of the constraints describing the sets and relations,
253 are performed in exact integer arithmetic using C<GMP>.
254 However, to allow future versions of C<isl> to optionally
255 support fixed integer arithmetic, all calls to C<GMP>
256 are wrapped inside C<isl> specific macros.
257 The basic type is C<isl_int> and the operations below
258 are available on this type.
259 The meanings of these operations are essentially the same
260 as their C<GMP> C<mpz_> counterparts.
261 As always with C<GMP> types, C<isl_int>s need to be
262 initialized with C<isl_int_init> before they can be used
263 and they need to be released with C<isl_int_clear>
265 The user should not assume that an C<isl_int> is represented
266 as a C<mpz_t>, but should instead explicitly convert between
267 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
268 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
272 =item isl_int_init(i)
274 =item isl_int_clear(i)
276 =item isl_int_set(r,i)
278 =item isl_int_set_si(r,i)
280 =item isl_int_set_gmp(r,g)
282 =item isl_int_get_gmp(i,g)
284 =item isl_int_abs(r,i)
286 =item isl_int_neg(r,i)
288 =item isl_int_swap(i,j)
290 =item isl_int_swap_or_set(i,j)
292 =item isl_int_add_ui(r,i,j)
294 =item isl_int_sub_ui(r,i,j)
296 =item isl_int_add(r,i,j)
298 =item isl_int_sub(r,i,j)
300 =item isl_int_mul(r,i,j)
302 =item isl_int_mul_ui(r,i,j)
304 =item isl_int_addmul(r,i,j)
306 =item isl_int_submul(r,i,j)
308 =item isl_int_gcd(r,i,j)
310 =item isl_int_lcm(r,i,j)
312 =item isl_int_divexact(r,i,j)
314 =item isl_int_cdiv_q(r,i,j)
316 =item isl_int_fdiv_q(r,i,j)
318 =item isl_int_fdiv_r(r,i,j)
320 =item isl_int_fdiv_q_ui(r,i,j)
322 =item isl_int_read(r,s)
324 =item isl_int_print(out,i,width)
328 =item isl_int_cmp(i,j)
330 =item isl_int_cmp_si(i,si)
332 =item isl_int_eq(i,j)
334 =item isl_int_ne(i,j)
336 =item isl_int_lt(i,j)
338 =item isl_int_le(i,j)
340 =item isl_int_gt(i,j)
342 =item isl_int_ge(i,j)
344 =item isl_int_abs_eq(i,j)
346 =item isl_int_abs_ne(i,j)
348 =item isl_int_abs_lt(i,j)
350 =item isl_int_abs_gt(i,j)
352 =item isl_int_abs_ge(i,j)
354 =item isl_int_is_zero(i)
356 =item isl_int_is_one(i)
358 =item isl_int_is_negone(i)
360 =item isl_int_is_pos(i)
362 =item isl_int_is_neg(i)
364 =item isl_int_is_nonpos(i)
366 =item isl_int_is_nonneg(i)
368 =item isl_int_is_divisible_by(i,j)
372 =head2 Sets and Relations
374 C<isl> uses six types of objects for representing sets and relations,
375 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
376 C<isl_union_set> and C<isl_union_map>.
377 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
378 can be described as a conjunction of affine constraints, while
379 C<isl_set> and C<isl_map> represent unions of
380 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
381 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
382 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
383 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
384 where spaces are considered different if they have a different number
385 of dimensions and/or different names (see L<"Spaces">).
386 The difference between sets and relations (maps) is that sets have
387 one set of variables, while relations have two sets of variables,
388 input variables and output variables.
390 =head2 Memory Management
392 Since a high-level operation on sets and/or relations usually involves
393 several substeps and since the user is usually not interested in
394 the intermediate results, most functions that return a new object
395 will also release all the objects passed as arguments.
396 If the user still wants to use one or more of these arguments
397 after the function call, she should pass along a copy of the
398 object rather than the object itself.
399 The user is then responsible for making sure that the original
400 object gets used somewhere else or is explicitly freed.
402 The arguments and return values of all documented functions are
403 annotated to make clear which arguments are released and which
404 arguments are preserved. In particular, the following annotations
411 C<__isl_give> means that a new object is returned.
412 The user should make sure that the returned pointer is
413 used exactly once as a value for an C<__isl_take> argument.
414 In between, it can be used as a value for as many
415 C<__isl_keep> arguments as the user likes.
416 There is one exception, and that is the case where the
417 pointer returned is C<NULL>. Is this case, the user
418 is free to use it as an C<__isl_take> argument or not.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
445 Identifiers are used to identify both individual dimensions
446 and tuples of dimensions. They consist of a name and an optional
447 pointer. Identifiers with the same name but different pointer values
448 are considered to be distinct.
449 Identifiers can be constructed, copied, freed, inspected and printed
450 using the following functions.
453 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
454 __isl_keep const char *name, void *user);
455 __isl_give isl_id *isl_id_copy(isl_id *id);
456 void *isl_id_free(__isl_take isl_id *id);
458 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
459 void *isl_id_get_user(__isl_keep isl_id *id);
460 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
462 __isl_give isl_printer *isl_printer_print_id(
463 __isl_take isl_printer *p, __isl_keep isl_id *id);
465 Note that C<isl_id_get_name> returns a pointer to some internal
466 data structure, so the result can only be used while the
467 corresponding C<isl_id> is alive.
471 Whenever a new set or relation is created from scratch,
472 the space in which it lives needs to be specified using an C<isl_space>.
474 #include <isl/space.h>
475 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
476 unsigned nparam, unsigned n_in, unsigned n_out);
477 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
479 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
480 unsigned nparam, unsigned dim);
481 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
482 void isl_space_free(__isl_take isl_space *space);
483 unsigned isl_space_dim(__isl_keep isl_space *space,
484 enum isl_dim_type type);
486 The space used for creating a parameter domain
487 needs to be created using C<isl_space_params_alloc>.
488 For other sets, the space
489 needs to be created using C<isl_space_set_alloc>, while
490 for a relation, the space
491 needs to be created using C<isl_space_alloc>.
492 C<isl_space_dim> can be used
493 to find out the number of dimensions of each type in
494 a space, where type may be
495 C<isl_dim_param>, C<isl_dim_in> (only for relations),
496 C<isl_dim_out> (only for relations), C<isl_dim_set>
497 (only for sets) or C<isl_dim_all>.
499 To check whether a given space is that of a set or a map
500 or whether it is a parameter space, use these functions:
502 #include <isl/space.h>
503 int isl_space_is_params(__isl_keep isl_space *space);
504 int isl_space_is_set(__isl_keep isl_space *space);
506 It is often useful to create objects that live in the
507 same space as some other object. This can be accomplished
508 by creating the new objects
509 (see L<Creating New Sets and Relations> or
510 L<Creating New (Piecewise) Quasipolynomials>) based on the space
511 of the original object.
514 __isl_give isl_space *isl_basic_set_get_space(
515 __isl_keep isl_basic_set *bset);
516 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
518 #include <isl/union_set.h>
519 __isl_give isl_space *isl_union_set_get_space(
520 __isl_keep isl_union_set *uset);
523 __isl_give isl_space *isl_basic_map_get_space(
524 __isl_keep isl_basic_map *bmap);
525 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
527 #include <isl/union_map.h>
528 __isl_give isl_space *isl_union_map_get_space(
529 __isl_keep isl_union_map *umap);
531 #include <isl/constraint.h>
532 __isl_give isl_space *isl_constraint_get_space(
533 __isl_keep isl_constraint *constraint);
535 #include <isl/polynomial.h>
536 __isl_give isl_space *isl_qpolynomial_get_space(
537 __isl_keep isl_qpolynomial *qp);
538 __isl_give isl_space *isl_qpolynomial_fold_get_space(
539 __isl_keep isl_qpolynomial_fold *fold);
540 __isl_give isl_space *isl_pw_qpolynomial_get_space(
541 __isl_keep isl_pw_qpolynomial *pwqp);
542 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
543 __isl_keep isl_union_pw_qpolynomial *upwqp);
544 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
545 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
548 __isl_give isl_space *isl_aff_get_space(
549 __isl_keep isl_aff *aff);
550 __isl_give isl_space *isl_pw_aff_get_space(
551 __isl_keep isl_pw_aff *pwaff);
553 #include <isl/point.h>
554 __isl_give isl_space *isl_point_get_space(
555 __isl_keep isl_point *pnt);
557 The identifiers or names of the individual dimensions may be set or read off
558 using the following functions.
560 #include <isl/space.h>
561 __isl_give isl_space *isl_space_set_dim_id(
562 __isl_take isl_space *space,
563 enum isl_dim_type type, unsigned pos,
564 __isl_take isl_id *id);
565 int isl_space_has_dim_id(__isl_keep isl_space *space,
566 enum isl_dim_type type, unsigned pos);
567 __isl_give isl_id *isl_space_get_dim_id(
568 __isl_keep isl_space *space,
569 enum isl_dim_type type, unsigned pos);
570 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
571 enum isl_dim_type type, unsigned pos,
572 __isl_keep const char *name);
573 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
574 enum isl_dim_type type, unsigned pos);
576 Note that C<isl_space_get_name> returns a pointer to some internal
577 data structure, so the result can only be used while the
578 corresponding C<isl_space> is alive.
579 Also note that every function that operates on two sets or relations
580 requires that both arguments have the same parameters. This also
581 means that if one of the arguments has named parameters, then the
582 other needs to have named parameters too and the names need to match.
583 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
584 arguments may have different parameters (as long as they are named),
585 in which case the result will have as parameters the union of the parameters of
588 Given the identifier of a dimension (typically a parameter),
589 its position can be obtained from the following function.
591 #include <isl/space.h>
592 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
593 enum isl_dim_type type, __isl_keep isl_id *id);
595 The identifiers or names of entire spaces may be set or read off
596 using the following functions.
598 #include <isl/space.h>
599 __isl_give isl_space *isl_space_set_tuple_id(
600 __isl_take isl_space *space,
601 enum isl_dim_type type, __isl_take isl_id *id);
602 __isl_give isl_space *isl_space_reset_tuple_id(
603 __isl_take isl_space *space, enum isl_dim_type type);
604 int isl_space_has_tuple_id(__isl_keep isl_space *space,
605 enum isl_dim_type type);
606 __isl_give isl_id *isl_space_get_tuple_id(
607 __isl_keep isl_space *space, enum isl_dim_type type);
608 __isl_give isl_space *isl_space_set_tuple_name(
609 __isl_take isl_space *space,
610 enum isl_dim_type type, const char *s);
611 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
612 enum isl_dim_type type);
614 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
615 or C<isl_dim_set>. As with C<isl_space_get_name>,
616 the C<isl_space_get_tuple_name> function returns a pointer to some internal
618 Binary operations require the corresponding spaces of their arguments
619 to have the same name.
621 Spaces can be nested. In particular, the domain of a set or
622 the domain or range of a relation can be a nested relation.
623 The following functions can be used to construct and deconstruct
626 #include <isl/space.h>
627 int isl_space_is_wrapping(__isl_keep isl_space *space);
628 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
629 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
631 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
632 be the space of a set, while that of
633 C<isl_space_wrap> should be the space of a relation.
634 Conversely, the output of C<isl_space_unwrap> is the space
635 of a relation, while that of C<isl_space_wrap> is the space of a set.
637 Spaces can be created from other spaces
638 using the following functions.
640 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
641 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
642 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
643 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
644 __isl_give isl_space *isl_space_params(
645 __isl_take isl_space *space);
646 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
647 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
648 __isl_take isl_space *right);
649 __isl_give isl_space *isl_space_align_params(
650 __isl_take isl_space *space1, __isl_take isl_space *space2)
651 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
652 enum isl_dim_type type, unsigned pos, unsigned n);
653 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
654 enum isl_dim_type type, unsigned n);
655 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
656 enum isl_dim_type type, unsigned first, unsigned n);
657 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
658 enum isl_dim_type dst_type, unsigned dst_pos,
659 enum isl_dim_type src_type, unsigned src_pos,
661 __isl_give isl_space *isl_space_map_from_set(
662 __isl_take isl_space *space);
663 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
665 Note that if dimensions are added or removed from a space, then
666 the name and the internal structure are lost.
670 A local space is essentially a space with
671 zero or more existentially quantified variables.
672 The local space of a basic set or relation can be obtained
673 using the following functions.
676 __isl_give isl_local_space *isl_basic_set_get_local_space(
677 __isl_keep isl_basic_set *bset);
680 __isl_give isl_local_space *isl_basic_map_get_local_space(
681 __isl_keep isl_basic_map *bmap);
683 A new local space can be created from a space using
685 #include <isl/local_space.h>
686 __isl_give isl_local_space *isl_local_space_from_space(
687 __isl_take isl_space *space);
689 They can be inspected, copied and freed using the following functions.
691 #include <isl/local_space.h>
692 isl_ctx *isl_local_space_get_ctx(
693 __isl_keep isl_local_space *ls);
694 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
695 int isl_local_space_dim(__isl_keep isl_local_space *ls,
696 enum isl_dim_type type);
697 const char *isl_local_space_get_dim_name(
698 __isl_keep isl_local_space *ls,
699 enum isl_dim_type type, unsigned pos);
700 __isl_give isl_local_space *isl_local_space_set_dim_name(
701 __isl_take isl_local_space *ls,
702 enum isl_dim_type type, unsigned pos, const char *s);
703 __isl_give isl_space *isl_local_space_get_space(
704 __isl_keep isl_local_space *ls);
705 __isl_give isl_div *isl_local_space_get_div(
706 __isl_keep isl_local_space *ls, int pos);
707 __isl_give isl_local_space *isl_local_space_copy(
708 __isl_keep isl_local_space *ls);
709 void *isl_local_space_free(__isl_take isl_local_space *ls);
711 Two local spaces can be compared using
713 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
714 __isl_keep isl_local_space *ls2);
716 Local spaces can be created from other local spaces
717 using the following functions.
719 __isl_give isl_local_space *isl_local_space_domain(
720 __isl_take isl_local_space *ls);
721 __isl_give isl_local_space *isl_local_space_from_domain(
722 __isl_take isl_local_space *ls);
723 __isl_give isl_local_space *isl_local_space_add_dims(
724 __isl_take isl_local_space *ls,
725 enum isl_dim_type type, unsigned n);
726 __isl_give isl_local_space *isl_local_space_insert_dims(
727 __isl_take isl_local_space *ls,
728 enum isl_dim_type type, unsigned first, unsigned n);
729 __isl_give isl_local_space *isl_local_space_drop_dims(
730 __isl_take isl_local_space *ls,
731 enum isl_dim_type type, unsigned first, unsigned n);
733 =head2 Input and Output
735 C<isl> supports its own input/output format, which is similar
736 to the C<Omega> format, but also supports the C<PolyLib> format
741 The C<isl> format is similar to that of C<Omega>, but has a different
742 syntax for describing the parameters and allows for the definition
743 of an existentially quantified variable as the integer division
744 of an affine expression.
745 For example, the set of integers C<i> between C<0> and C<n>
746 such that C<i % 10 <= 6> can be described as
748 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
751 A set or relation can have several disjuncts, separated
752 by the keyword C<or>. Each disjunct is either a conjunction
753 of constraints or a projection (C<exists>) of a conjunction
754 of constraints. The constraints are separated by the keyword
757 =head3 C<PolyLib> format
759 If the represented set is a union, then the first line
760 contains a single number representing the number of disjuncts.
761 Otherwise, a line containing the number C<1> is optional.
763 Each disjunct is represented by a matrix of constraints.
764 The first line contains two numbers representing
765 the number of rows and columns,
766 where the number of rows is equal to the number of constraints
767 and the number of columns is equal to two plus the number of variables.
768 The following lines contain the actual rows of the constraint matrix.
769 In each row, the first column indicates whether the constraint
770 is an equality (C<0>) or inequality (C<1>). The final column
771 corresponds to the constant term.
773 If the set is parametric, then the coefficients of the parameters
774 appear in the last columns before the constant column.
775 The coefficients of any existentially quantified variables appear
776 between those of the set variables and those of the parameters.
778 =head3 Extended C<PolyLib> format
780 The extended C<PolyLib> format is nearly identical to the
781 C<PolyLib> format. The only difference is that the line
782 containing the number of rows and columns of a constraint matrix
783 also contains four additional numbers:
784 the number of output dimensions, the number of input dimensions,
785 the number of local dimensions (i.e., the number of existentially
786 quantified variables) and the number of parameters.
787 For sets, the number of ``output'' dimensions is equal
788 to the number of set dimensions, while the number of ``input''
794 __isl_give isl_basic_set *isl_basic_set_read_from_file(
795 isl_ctx *ctx, FILE *input, int nparam);
796 __isl_give isl_basic_set *isl_basic_set_read_from_str(
797 isl_ctx *ctx, const char *str, int nparam);
798 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
799 FILE *input, int nparam);
800 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
801 const char *str, int nparam);
804 __isl_give isl_basic_map *isl_basic_map_read_from_file(
805 isl_ctx *ctx, FILE *input, int nparam);
806 __isl_give isl_basic_map *isl_basic_map_read_from_str(
807 isl_ctx *ctx, const char *str, int nparam);
808 __isl_give isl_map *isl_map_read_from_file(
809 isl_ctx *ctx, FILE *input, int nparam);
810 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
811 const char *str, int nparam);
813 #include <isl/union_set.h>
814 __isl_give isl_union_set *isl_union_set_read_from_file(
815 isl_ctx *ctx, FILE *input);
816 __isl_give isl_union_set *isl_union_set_read_from_str(
817 isl_ctx *ctx, const char *str);
819 #include <isl/union_map.h>
820 __isl_give isl_union_map *isl_union_map_read_from_file(
821 isl_ctx *ctx, FILE *input);
822 __isl_give isl_union_map *isl_union_map_read_from_str(
823 isl_ctx *ctx, const char *str);
825 The input format is autodetected and may be either the C<PolyLib> format
826 or the C<isl> format.
827 C<nparam> specifies how many of the final columns in
828 the C<PolyLib> format correspond to parameters.
829 If input is given in the C<isl> format, then the number
830 of parameters needs to be equal to C<nparam>.
831 If C<nparam> is negative, then any number of parameters
832 is accepted in the C<isl> format and zero parameters
833 are assumed in the C<PolyLib> format.
837 Before anything can be printed, an C<isl_printer> needs to
840 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
842 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
843 void isl_printer_free(__isl_take isl_printer *printer);
844 __isl_give char *isl_printer_get_str(
845 __isl_keep isl_printer *printer);
847 The behavior of the printer can be modified in various ways
849 __isl_give isl_printer *isl_printer_set_output_format(
850 __isl_take isl_printer *p, int output_format);
851 __isl_give isl_printer *isl_printer_set_indent(
852 __isl_take isl_printer *p, int indent);
853 __isl_give isl_printer *isl_printer_indent(
854 __isl_take isl_printer *p, int indent);
855 __isl_give isl_printer *isl_printer_set_prefix(
856 __isl_take isl_printer *p, const char *prefix);
857 __isl_give isl_printer *isl_printer_set_suffix(
858 __isl_take isl_printer *p, const char *suffix);
860 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
861 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
862 and defaults to C<ISL_FORMAT_ISL>.
863 Each line in the output is indented by C<indent> (set by
864 C<isl_printer_set_indent>) spaces
865 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
866 In the C<PolyLib> format output,
867 the coefficients of the existentially quantified variables
868 appear between those of the set variables and those
870 The function C<isl_printer_indent> increases the indentation
871 by the specified amount (which may be negative).
873 To actually print something, use
876 __isl_give isl_printer *isl_printer_print_basic_set(
877 __isl_take isl_printer *printer,
878 __isl_keep isl_basic_set *bset);
879 __isl_give isl_printer *isl_printer_print_set(
880 __isl_take isl_printer *printer,
881 __isl_keep isl_set *set);
884 __isl_give isl_printer *isl_printer_print_basic_map(
885 __isl_take isl_printer *printer,
886 __isl_keep isl_basic_map *bmap);
887 __isl_give isl_printer *isl_printer_print_map(
888 __isl_take isl_printer *printer,
889 __isl_keep isl_map *map);
891 #include <isl/union_set.h>
892 __isl_give isl_printer *isl_printer_print_union_set(
893 __isl_take isl_printer *p,
894 __isl_keep isl_union_set *uset);
896 #include <isl/union_map.h>
897 __isl_give isl_printer *isl_printer_print_union_map(
898 __isl_take isl_printer *p,
899 __isl_keep isl_union_map *umap);
901 When called on a file printer, the following function flushes
902 the file. When called on a string printer, the buffer is cleared.
904 __isl_give isl_printer *isl_printer_flush(
905 __isl_take isl_printer *p);
907 =head2 Creating New Sets and Relations
909 C<isl> has functions for creating some standard sets and relations.
913 =item * Empty sets and relations
915 __isl_give isl_basic_set *isl_basic_set_empty(
916 __isl_take isl_space *space);
917 __isl_give isl_basic_map *isl_basic_map_empty(
918 __isl_take isl_space *space);
919 __isl_give isl_set *isl_set_empty(
920 __isl_take isl_space *space);
921 __isl_give isl_map *isl_map_empty(
922 __isl_take isl_space *space);
923 __isl_give isl_union_set *isl_union_set_empty(
924 __isl_take isl_space *space);
925 __isl_give isl_union_map *isl_union_map_empty(
926 __isl_take isl_space *space);
928 For C<isl_union_set>s and C<isl_union_map>s, the space
929 is only used to specify the parameters.
931 =item * Universe sets and relations
933 __isl_give isl_basic_set *isl_basic_set_universe(
934 __isl_take isl_space *space);
935 __isl_give isl_basic_map *isl_basic_map_universe(
936 __isl_take isl_space *space);
937 __isl_give isl_set *isl_set_universe(
938 __isl_take isl_space *space);
939 __isl_give isl_map *isl_map_universe(
940 __isl_take isl_space *space);
941 __isl_give isl_union_set *isl_union_set_universe(
942 __isl_take isl_union_set *uset);
943 __isl_give isl_union_map *isl_union_map_universe(
944 __isl_take isl_union_map *umap);
946 The sets and relations constructed by the functions above
947 contain all integer values, while those constructed by the
948 functions below only contain non-negative values.
950 __isl_give isl_basic_set *isl_basic_set_nat_universe(
951 __isl_take isl_space *space);
952 __isl_give isl_basic_map *isl_basic_map_nat_universe(
953 __isl_take isl_space *space);
954 __isl_give isl_set *isl_set_nat_universe(
955 __isl_take isl_space *space);
956 __isl_give isl_map *isl_map_nat_universe(
957 __isl_take isl_space *space);
959 =item * Identity relations
961 __isl_give isl_basic_map *isl_basic_map_identity(
962 __isl_take isl_space *space);
963 __isl_give isl_map *isl_map_identity(
964 __isl_take isl_space *space);
966 The number of input and output dimensions in C<space> needs
969 =item * Lexicographic order
971 __isl_give isl_map *isl_map_lex_lt(
972 __isl_take isl_space *set_space);
973 __isl_give isl_map *isl_map_lex_le(
974 __isl_take isl_space *set_space);
975 __isl_give isl_map *isl_map_lex_gt(
976 __isl_take isl_space *set_space);
977 __isl_give isl_map *isl_map_lex_ge(
978 __isl_take isl_space *set_space);
979 __isl_give isl_map *isl_map_lex_lt_first(
980 __isl_take isl_space *space, unsigned n);
981 __isl_give isl_map *isl_map_lex_le_first(
982 __isl_take isl_space *space, unsigned n);
983 __isl_give isl_map *isl_map_lex_gt_first(
984 __isl_take isl_space *space, unsigned n);
985 __isl_give isl_map *isl_map_lex_ge_first(
986 __isl_take isl_space *space, unsigned n);
988 The first four functions take a space for a B<set>
989 and return relations that express that the elements in the domain
990 are lexicographically less
991 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
992 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
993 than the elements in the range.
994 The last four functions take a space for a map
995 and return relations that express that the first C<n> dimensions
996 in the domain are lexicographically less
997 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
998 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
999 than the first C<n> dimensions in the range.
1003 A basic set or relation can be converted to a set or relation
1004 using the following functions.
1006 __isl_give isl_set *isl_set_from_basic_set(
1007 __isl_take isl_basic_set *bset);
1008 __isl_give isl_map *isl_map_from_basic_map(
1009 __isl_take isl_basic_map *bmap);
1011 Sets and relations can be converted to union sets and relations
1012 using the following functions.
1014 __isl_give isl_union_map *isl_union_map_from_map(
1015 __isl_take isl_map *map);
1016 __isl_give isl_union_set *isl_union_set_from_set(
1017 __isl_take isl_set *set);
1019 The inverse conversions below can only be used if the input
1020 union set or relation is known to contain elements in exactly one
1023 __isl_give isl_set *isl_set_from_union_set(
1024 __isl_take isl_union_set *uset);
1025 __isl_give isl_map *isl_map_from_union_map(
1026 __isl_take isl_union_map *umap);
1028 Sets and relations can be copied and freed again using the following
1031 __isl_give isl_basic_set *isl_basic_set_copy(
1032 __isl_keep isl_basic_set *bset);
1033 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1034 __isl_give isl_union_set *isl_union_set_copy(
1035 __isl_keep isl_union_set *uset);
1036 __isl_give isl_basic_map *isl_basic_map_copy(
1037 __isl_keep isl_basic_map *bmap);
1038 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1039 __isl_give isl_union_map *isl_union_map_copy(
1040 __isl_keep isl_union_map *umap);
1041 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1042 void isl_set_free(__isl_take isl_set *set);
1043 void *isl_union_set_free(__isl_take isl_union_set *uset);
1044 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1045 void isl_map_free(__isl_take isl_map *map);
1046 void *isl_union_map_free(__isl_take isl_union_map *umap);
1048 Other sets and relations can be constructed by starting
1049 from a universe set or relation, adding equality and/or
1050 inequality constraints and then projecting out the
1051 existentially quantified variables, if any.
1052 Constraints can be constructed, manipulated and
1053 added to (or removed from) (basic) sets and relations
1054 using the following functions.
1056 #include <isl/constraint.h>
1057 __isl_give isl_constraint *isl_equality_alloc(
1058 __isl_take isl_space *space);
1059 __isl_give isl_constraint *isl_inequality_alloc(
1060 __isl_take isl_space *space);
1061 __isl_give isl_constraint *isl_constraint_set_constant(
1062 __isl_take isl_constraint *constraint, isl_int v);
1063 __isl_give isl_constraint *isl_constraint_set_constant_si(
1064 __isl_take isl_constraint *constraint, int v);
1065 __isl_give isl_constraint *isl_constraint_set_coefficient(
1066 __isl_take isl_constraint *constraint,
1067 enum isl_dim_type type, int pos, isl_int v);
1068 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1069 __isl_take isl_constraint *constraint,
1070 enum isl_dim_type type, int pos, int v);
1071 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1072 __isl_take isl_basic_map *bmap,
1073 __isl_take isl_constraint *constraint);
1074 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1075 __isl_take isl_basic_set *bset,
1076 __isl_take isl_constraint *constraint);
1077 __isl_give isl_map *isl_map_add_constraint(
1078 __isl_take isl_map *map,
1079 __isl_take isl_constraint *constraint);
1080 __isl_give isl_set *isl_set_add_constraint(
1081 __isl_take isl_set *set,
1082 __isl_take isl_constraint *constraint);
1083 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1084 __isl_take isl_basic_set *bset,
1085 __isl_take isl_constraint *constraint);
1087 For example, to create a set containing the even integers
1088 between 10 and 42, you would use the following code.
1093 isl_basic_set *bset;
1096 space = isl_space_set_alloc(ctx, 0, 2);
1097 bset = isl_basic_set_universe(isl_space_copy(space));
1099 c = isl_equality_alloc(isl_space_copy(space));
1100 isl_int_set_si(v, -1);
1101 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1102 isl_int_set_si(v, 2);
1103 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1104 bset = isl_basic_set_add_constraint(bset, c);
1106 c = isl_inequality_alloc(isl_space_copy(space));
1107 isl_int_set_si(v, -10);
1108 isl_constraint_set_constant(c, v);
1109 isl_int_set_si(v, 1);
1110 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1111 bset = isl_basic_set_add_constraint(bset, c);
1113 c = isl_inequality_alloc(space);
1114 isl_int_set_si(v, 42);
1115 isl_constraint_set_constant(c, v);
1116 isl_int_set_si(v, -1);
1117 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1118 bset = isl_basic_set_add_constraint(bset, c);
1120 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1126 isl_basic_set *bset;
1127 bset = isl_basic_set_read_from_str(ctx,
1128 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1130 A basic set or relation can also be constructed from two matrices
1131 describing the equalities and the inequalities.
1133 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1134 __isl_take isl_space *space,
1135 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1136 enum isl_dim_type c1,
1137 enum isl_dim_type c2, enum isl_dim_type c3,
1138 enum isl_dim_type c4);
1139 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1140 __isl_take isl_space *space,
1141 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1142 enum isl_dim_type c1,
1143 enum isl_dim_type c2, enum isl_dim_type c3,
1144 enum isl_dim_type c4, enum isl_dim_type c5);
1146 The C<isl_dim_type> arguments indicate the order in which
1147 different kinds of variables appear in the input matrices
1148 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1149 C<isl_dim_set> and C<isl_dim_div> for sets and
1150 of C<isl_dim_cst>, C<isl_dim_param>,
1151 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1153 A (basic) set or relation can also be constructed from a (piecewise)
1155 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1157 __isl_give isl_basic_map *isl_basic_map_from_aff(
1158 __isl_take isl_aff *aff);
1159 __isl_give isl_set *isl_set_from_pw_aff(
1160 __isl_take isl_pw_aff *pwaff);
1161 __isl_give isl_map *isl_map_from_pw_aff(
1162 __isl_take isl_pw_aff *pwaff);
1163 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1164 __isl_take isl_space *domain_space,
1165 __isl_take isl_aff_list *list);
1167 The C<domain_dim> argument describes the domain of the resulting
1168 basic relation. It is required because the C<list> may consist
1169 of zero affine expressions.
1171 =head2 Inspecting Sets and Relations
1173 Usually, the user should not have to care about the actual constraints
1174 of the sets and maps, but should instead apply the abstract operations
1175 explained in the following sections.
1176 Occasionally, however, it may be required to inspect the individual
1177 coefficients of the constraints. This section explains how to do so.
1178 In these cases, it may also be useful to have C<isl> compute
1179 an explicit representation of the existentially quantified variables.
1181 __isl_give isl_set *isl_set_compute_divs(
1182 __isl_take isl_set *set);
1183 __isl_give isl_map *isl_map_compute_divs(
1184 __isl_take isl_map *map);
1185 __isl_give isl_union_set *isl_union_set_compute_divs(
1186 __isl_take isl_union_set *uset);
1187 __isl_give isl_union_map *isl_union_map_compute_divs(
1188 __isl_take isl_union_map *umap);
1190 This explicit representation defines the existentially quantified
1191 variables as integer divisions of the other variables, possibly
1192 including earlier existentially quantified variables.
1193 An explicitly represented existentially quantified variable therefore
1194 has a unique value when the values of the other variables are known.
1195 If, furthermore, the same existentials, i.e., existentials
1196 with the same explicit representations, should appear in the
1197 same order in each of the disjuncts of a set or map, then the user should call
1198 either of the following functions.
1200 __isl_give isl_set *isl_set_align_divs(
1201 __isl_take isl_set *set);
1202 __isl_give isl_map *isl_map_align_divs(
1203 __isl_take isl_map *map);
1205 Alternatively, the existentially quantified variables can be removed
1206 using the following functions, which compute an overapproximation.
1208 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1209 __isl_take isl_basic_set *bset);
1210 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1211 __isl_take isl_basic_map *bmap);
1212 __isl_give isl_set *isl_set_remove_divs(
1213 __isl_take isl_set *set);
1214 __isl_give isl_map *isl_map_remove_divs(
1215 __isl_take isl_map *map);
1217 To iterate over all the sets or maps in a union set or map, use
1219 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1220 int (*fn)(__isl_take isl_set *set, void *user),
1222 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1223 int (*fn)(__isl_take isl_map *map, void *user),
1226 The number of sets or maps in a union set or map can be obtained
1229 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1230 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1232 To extract the set or map in a given space from a union, use
1234 __isl_give isl_set *isl_union_set_extract_set(
1235 __isl_keep isl_union_set *uset,
1236 __isl_take isl_space *space);
1237 __isl_give isl_map *isl_union_map_extract_map(
1238 __isl_keep isl_union_map *umap,
1239 __isl_take isl_space *space);
1241 To iterate over all the basic sets or maps in a set or map, use
1243 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1244 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1246 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1247 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1250 The callback function C<fn> should return 0 if successful and
1251 -1 if an error occurs. In the latter case, or if any other error
1252 occurs, the above functions will return -1.
1254 It should be noted that C<isl> does not guarantee that
1255 the basic sets or maps passed to C<fn> are disjoint.
1256 If this is required, then the user should call one of
1257 the following functions first.
1259 __isl_give isl_set *isl_set_make_disjoint(
1260 __isl_take isl_set *set);
1261 __isl_give isl_map *isl_map_make_disjoint(
1262 __isl_take isl_map *map);
1264 The number of basic sets in a set can be obtained
1267 int isl_set_n_basic_set(__isl_keep isl_set *set);
1269 To iterate over the constraints of a basic set or map, use
1271 #include <isl/constraint.h>
1273 int isl_basic_map_foreach_constraint(
1274 __isl_keep isl_basic_map *bmap,
1275 int (*fn)(__isl_take isl_constraint *c, void *user),
1277 void *isl_constraint_free(__isl_take isl_constraint *c);
1279 Again, the callback function C<fn> should return 0 if successful and
1280 -1 if an error occurs. In the latter case, or if any other error
1281 occurs, the above functions will return -1.
1282 The constraint C<c> represents either an equality or an inequality.
1283 Use the following function to find out whether a constraint
1284 represents an equality. If not, it represents an inequality.
1286 int isl_constraint_is_equality(
1287 __isl_keep isl_constraint *constraint);
1289 The coefficients of the constraints can be inspected using
1290 the following functions.
1292 void isl_constraint_get_constant(
1293 __isl_keep isl_constraint *constraint, isl_int *v);
1294 void isl_constraint_get_coefficient(
1295 __isl_keep isl_constraint *constraint,
1296 enum isl_dim_type type, int pos, isl_int *v);
1297 int isl_constraint_involves_dims(
1298 __isl_keep isl_constraint *constraint,
1299 enum isl_dim_type type, unsigned first, unsigned n);
1301 The explicit representations of the existentially quantified
1302 variables can be inspected using the following functions.
1303 Note that the user is only allowed to use these functions
1304 if the inspected set or map is the result of a call
1305 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1307 __isl_give isl_div *isl_constraint_div(
1308 __isl_keep isl_constraint *constraint, int pos);
1309 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1310 void isl_div_get_constant(__isl_keep isl_div *div,
1312 void isl_div_get_denominator(__isl_keep isl_div *div,
1314 void isl_div_get_coefficient(__isl_keep isl_div *div,
1315 enum isl_dim_type type, int pos, isl_int *v);
1317 To obtain the constraints of a basic set or map in matrix
1318 form, use the following functions.
1320 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1321 __isl_keep isl_basic_set *bset,
1322 enum isl_dim_type c1, enum isl_dim_type c2,
1323 enum isl_dim_type c3, enum isl_dim_type c4);
1324 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1325 __isl_keep isl_basic_set *bset,
1326 enum isl_dim_type c1, enum isl_dim_type c2,
1327 enum isl_dim_type c3, enum isl_dim_type c4);
1328 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1329 __isl_keep isl_basic_map *bmap,
1330 enum isl_dim_type c1,
1331 enum isl_dim_type c2, enum isl_dim_type c3,
1332 enum isl_dim_type c4, enum isl_dim_type c5);
1333 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1334 __isl_keep isl_basic_map *bmap,
1335 enum isl_dim_type c1,
1336 enum isl_dim_type c2, enum isl_dim_type c3,
1337 enum isl_dim_type c4, enum isl_dim_type c5);
1339 The C<isl_dim_type> arguments dictate the order in which
1340 different kinds of variables appear in the resulting matrix
1341 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1342 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1344 The number of parameters, input, output or set dimensions can
1345 be obtained using the following functions.
1347 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1348 enum isl_dim_type type);
1349 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1350 enum isl_dim_type type);
1351 unsigned isl_set_dim(__isl_keep isl_set *set,
1352 enum isl_dim_type type);
1353 unsigned isl_map_dim(__isl_keep isl_map *map,
1354 enum isl_dim_type type);
1356 To check whether the description of a set or relation depends
1357 on one or more given dimensions, it is not necessary to iterate over all
1358 constraints. Instead the following functions can be used.
1360 int isl_basic_set_involves_dims(
1361 __isl_keep isl_basic_set *bset,
1362 enum isl_dim_type type, unsigned first, unsigned n);
1363 int isl_set_involves_dims(__isl_keep isl_set *set,
1364 enum isl_dim_type type, unsigned first, unsigned n);
1365 int isl_basic_map_involves_dims(
1366 __isl_keep isl_basic_map *bmap,
1367 enum isl_dim_type type, unsigned first, unsigned n);
1368 int isl_map_involves_dims(__isl_keep isl_map *map,
1369 enum isl_dim_type type, unsigned first, unsigned n);
1371 Similarly, the following functions can be used to check whether
1372 a given dimension is involved in any lower or upper bound.
1374 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1375 enum isl_dim_type type, unsigned pos);
1376 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1377 enum isl_dim_type type, unsigned pos);
1379 The identifiers or names of the domain and range spaces of a set
1380 or relation can be read off or set using the following functions.
1382 __isl_give isl_set *isl_set_set_tuple_id(
1383 __isl_take isl_set *set, __isl_take isl_id *id);
1384 __isl_give isl_set *isl_set_reset_tuple_id(
1385 __isl_take isl_set *set);
1386 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1387 __isl_give isl_id *isl_set_get_tuple_id(
1388 __isl_keep isl_set *set);
1389 __isl_give isl_map *isl_map_set_tuple_id(
1390 __isl_take isl_map *map, enum isl_dim_type type,
1391 __isl_take isl_id *id);
1392 __isl_give isl_map *isl_map_reset_tuple_id(
1393 __isl_take isl_map *map, enum isl_dim_type type);
1394 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1395 enum isl_dim_type type);
1396 __isl_give isl_id *isl_map_get_tuple_id(
1397 __isl_keep isl_map *map, enum isl_dim_type type);
1399 const char *isl_basic_set_get_tuple_name(
1400 __isl_keep isl_basic_set *bset);
1401 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1402 __isl_take isl_basic_set *set, const char *s);
1403 const char *isl_set_get_tuple_name(
1404 __isl_keep isl_set *set);
1405 const char *isl_basic_map_get_tuple_name(
1406 __isl_keep isl_basic_map *bmap,
1407 enum isl_dim_type type);
1408 const char *isl_map_get_tuple_name(
1409 __isl_keep isl_map *map,
1410 enum isl_dim_type type);
1412 As with C<isl_space_get_tuple_name>, the value returned points to
1413 an internal data structure.
1414 The identifiers, positions or names of individual dimensions can be
1415 read off using the following functions.
1417 __isl_give isl_set *isl_set_set_dim_id(
1418 __isl_take isl_set *set, enum isl_dim_type type,
1419 unsigned pos, __isl_take isl_id *id);
1420 int isl_set_has_dim_id(__isl_keep isl_set *set,
1421 enum isl_dim_type type, unsigned pos);
1422 __isl_give isl_id *isl_set_get_dim_id(
1423 __isl_keep isl_set *set, enum isl_dim_type type,
1425 __isl_give isl_map *isl_map_set_dim_id(
1426 __isl_take isl_map *map, enum isl_dim_type type,
1427 unsigned pos, __isl_take isl_id *id);
1428 int isl_map_has_dim_id(__isl_keep isl_map *map,
1429 enum isl_dim_type type, unsigned pos);
1430 __isl_give isl_id *isl_map_get_dim_id(
1431 __isl_keep isl_map *map, enum isl_dim_type type,
1434 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1435 enum isl_dim_type type, __isl_keep isl_id *id);
1436 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1437 enum isl_dim_type type, __isl_keep isl_id *id);
1439 const char *isl_constraint_get_dim_name(
1440 __isl_keep isl_constraint *constraint,
1441 enum isl_dim_type type, unsigned pos);
1442 const char *isl_basic_set_get_dim_name(
1443 __isl_keep isl_basic_set *bset,
1444 enum isl_dim_type type, unsigned pos);
1445 const char *isl_set_get_dim_name(
1446 __isl_keep isl_set *set,
1447 enum isl_dim_type type, unsigned pos);
1448 const char *isl_basic_map_get_dim_name(
1449 __isl_keep isl_basic_map *bmap,
1450 enum isl_dim_type type, unsigned pos);
1451 const char *isl_map_get_dim_name(
1452 __isl_keep isl_map *map,
1453 enum isl_dim_type type, unsigned pos);
1455 These functions are mostly useful to obtain the identifiers, positions
1456 or names of the parameters. Identifiers of individual dimensions are
1457 essentially only useful for printing. They are ignored by all other
1458 operations and may not be preserved across those operations.
1462 =head3 Unary Properties
1468 The following functions test whether the given set or relation
1469 contains any integer points. The ``plain'' variants do not perform
1470 any computations, but simply check if the given set or relation
1471 is already known to be empty.
1473 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1474 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1475 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1476 int isl_set_is_empty(__isl_keep isl_set *set);
1477 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1478 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1479 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1480 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1481 int isl_map_is_empty(__isl_keep isl_map *map);
1482 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1484 =item * Universality
1486 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1487 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1488 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1490 =item * Single-valuedness
1492 int isl_map_is_single_valued(__isl_keep isl_map *map);
1493 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1497 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1498 int isl_map_is_injective(__isl_keep isl_map *map);
1499 int isl_union_map_plain_is_injective(
1500 __isl_keep isl_union_map *umap);
1501 int isl_union_map_is_injective(
1502 __isl_keep isl_union_map *umap);
1506 int isl_map_is_bijective(__isl_keep isl_map *map);
1507 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1511 int isl_basic_map_plain_is_fixed(
1512 __isl_keep isl_basic_map *bmap,
1513 enum isl_dim_type type, unsigned pos,
1515 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1516 enum isl_dim_type type, unsigned pos,
1519 Check if the relation obviously lies on a hyperplane where the given dimension
1520 has a fixed value and if so, return that value in C<*val>.
1524 To check whether a set is a parameter domain, use this function:
1526 int isl_set_is_params(__isl_keep isl_set *set);
1530 The following functions check whether the domain of the given
1531 (basic) set is a wrapped relation.
1533 int isl_basic_set_is_wrapping(
1534 __isl_keep isl_basic_set *bset);
1535 int isl_set_is_wrapping(__isl_keep isl_set *set);
1537 =item * Internal Product
1539 int isl_basic_map_can_zip(
1540 __isl_keep isl_basic_map *bmap);
1541 int isl_map_can_zip(__isl_keep isl_map *map);
1543 Check whether the product of domain and range of the given relation
1545 i.e., whether both domain and range are nested relations.
1549 =head3 Binary Properties
1555 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1556 __isl_keep isl_set *set2);
1557 int isl_set_is_equal(__isl_keep isl_set *set1,
1558 __isl_keep isl_set *set2);
1559 int isl_union_set_is_equal(
1560 __isl_keep isl_union_set *uset1,
1561 __isl_keep isl_union_set *uset2);
1562 int isl_basic_map_is_equal(
1563 __isl_keep isl_basic_map *bmap1,
1564 __isl_keep isl_basic_map *bmap2);
1565 int isl_map_is_equal(__isl_keep isl_map *map1,
1566 __isl_keep isl_map *map2);
1567 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1568 __isl_keep isl_map *map2);
1569 int isl_union_map_is_equal(
1570 __isl_keep isl_union_map *umap1,
1571 __isl_keep isl_union_map *umap2);
1573 =item * Disjointness
1575 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1576 __isl_keep isl_set *set2);
1580 int isl_set_is_subset(__isl_keep isl_set *set1,
1581 __isl_keep isl_set *set2);
1582 int isl_set_is_strict_subset(
1583 __isl_keep isl_set *set1,
1584 __isl_keep isl_set *set2);
1585 int isl_union_set_is_subset(
1586 __isl_keep isl_union_set *uset1,
1587 __isl_keep isl_union_set *uset2);
1588 int isl_union_set_is_strict_subset(
1589 __isl_keep isl_union_set *uset1,
1590 __isl_keep isl_union_set *uset2);
1591 int isl_basic_map_is_subset(
1592 __isl_keep isl_basic_map *bmap1,
1593 __isl_keep isl_basic_map *bmap2);
1594 int isl_basic_map_is_strict_subset(
1595 __isl_keep isl_basic_map *bmap1,
1596 __isl_keep isl_basic_map *bmap2);
1597 int isl_map_is_subset(
1598 __isl_keep isl_map *map1,
1599 __isl_keep isl_map *map2);
1600 int isl_map_is_strict_subset(
1601 __isl_keep isl_map *map1,
1602 __isl_keep isl_map *map2);
1603 int isl_union_map_is_subset(
1604 __isl_keep isl_union_map *umap1,
1605 __isl_keep isl_union_map *umap2);
1606 int isl_union_map_is_strict_subset(
1607 __isl_keep isl_union_map *umap1,
1608 __isl_keep isl_union_map *umap2);
1612 =head2 Unary Operations
1618 __isl_give isl_set *isl_set_complement(
1619 __isl_take isl_set *set);
1623 __isl_give isl_basic_map *isl_basic_map_reverse(
1624 __isl_take isl_basic_map *bmap);
1625 __isl_give isl_map *isl_map_reverse(
1626 __isl_take isl_map *map);
1627 __isl_give isl_union_map *isl_union_map_reverse(
1628 __isl_take isl_union_map *umap);
1632 __isl_give isl_basic_set *isl_basic_set_project_out(
1633 __isl_take isl_basic_set *bset,
1634 enum isl_dim_type type, unsigned first, unsigned n);
1635 __isl_give isl_basic_map *isl_basic_map_project_out(
1636 __isl_take isl_basic_map *bmap,
1637 enum isl_dim_type type, unsigned first, unsigned n);
1638 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1639 enum isl_dim_type type, unsigned first, unsigned n);
1640 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1641 enum isl_dim_type type, unsigned first, unsigned n);
1642 __isl_give isl_basic_set *isl_basic_set_params(
1643 __isl_take isl_basic_set *bset);
1644 __isl_give isl_basic_set *isl_basic_map_domain(
1645 __isl_take isl_basic_map *bmap);
1646 __isl_give isl_basic_set *isl_basic_map_range(
1647 __isl_take isl_basic_map *bmap);
1648 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1649 __isl_give isl_set *isl_map_domain(
1650 __isl_take isl_map *bmap);
1651 __isl_give isl_set *isl_map_range(
1652 __isl_take isl_map *map);
1653 __isl_give isl_union_set *isl_union_map_domain(
1654 __isl_take isl_union_map *umap);
1655 __isl_give isl_union_set *isl_union_map_range(
1656 __isl_take isl_union_map *umap);
1658 __isl_give isl_basic_map *isl_basic_map_domain_map(
1659 __isl_take isl_basic_map *bmap);
1660 __isl_give isl_basic_map *isl_basic_map_range_map(
1661 __isl_take isl_basic_map *bmap);
1662 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1663 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1664 __isl_give isl_union_map *isl_union_map_domain_map(
1665 __isl_take isl_union_map *umap);
1666 __isl_give isl_union_map *isl_union_map_range_map(
1667 __isl_take isl_union_map *umap);
1669 The functions above construct a (basic, regular or union) relation
1670 that maps (a wrapped version of) the input relation to its domain or range.
1674 __isl_give isl_set *isl_set_eliminate(
1675 __isl_take isl_set *set, enum isl_dim_type type,
1676 unsigned first, unsigned n);
1678 Eliminate the coefficients for the given dimensions from the constraints,
1679 without removing the dimensions.
1683 __isl_give isl_basic_set *isl_basic_set_fix(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type, unsigned pos,
1687 __isl_give isl_basic_set *isl_basic_set_fix_si(
1688 __isl_take isl_basic_set *bset,
1689 enum isl_dim_type type, unsigned pos, int value);
1690 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1691 enum isl_dim_type type, unsigned pos,
1693 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1694 enum isl_dim_type type, unsigned pos, int value);
1695 __isl_give isl_basic_map *isl_basic_map_fix_si(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, unsigned pos, int value);
1698 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1699 enum isl_dim_type type, unsigned pos, int value);
1701 Intersect the set or relation with the hyperplane where the given
1702 dimension has the fixed given value.
1704 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1705 enum isl_dim_type type1, int pos1,
1706 enum isl_dim_type type2, int pos2);
1707 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1708 enum isl_dim_type type1, int pos1,
1709 enum isl_dim_type type2, int pos2);
1711 Intersect the set or relation with the hyperplane where the given
1712 dimensions are equal to each other.
1714 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1715 enum isl_dim_type type1, int pos1,
1716 enum isl_dim_type type2, int pos2);
1718 Intersect the relation with the hyperplane where the given
1719 dimensions have opposite values.
1723 __isl_give isl_map *isl_set_identity(
1724 __isl_take isl_set *set);
1725 __isl_give isl_union_map *isl_union_set_identity(
1726 __isl_take isl_union_set *uset);
1728 Construct an identity relation on the given (union) set.
1732 __isl_give isl_basic_set *isl_basic_map_deltas(
1733 __isl_take isl_basic_map *bmap);
1734 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1735 __isl_give isl_union_set *isl_union_map_deltas(
1736 __isl_take isl_union_map *umap);
1738 These functions return a (basic) set containing the differences
1739 between image elements and corresponding domain elements in the input.
1741 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1742 __isl_take isl_basic_map *bmap);
1743 __isl_give isl_map *isl_map_deltas_map(
1744 __isl_take isl_map *map);
1745 __isl_give isl_union_map *isl_union_map_deltas_map(
1746 __isl_take isl_union_map *umap);
1748 The functions above construct a (basic, regular or union) relation
1749 that maps (a wrapped version of) the input relation to its delta set.
1753 Simplify the representation of a set or relation by trying
1754 to combine pairs of basic sets or relations into a single
1755 basic set or relation.
1757 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1758 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1759 __isl_give isl_union_set *isl_union_set_coalesce(
1760 __isl_take isl_union_set *uset);
1761 __isl_give isl_union_map *isl_union_map_coalesce(
1762 __isl_take isl_union_map *umap);
1764 =item * Detecting equalities
1766 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1767 __isl_take isl_basic_set *bset);
1768 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1769 __isl_take isl_basic_map *bmap);
1770 __isl_give isl_set *isl_set_detect_equalities(
1771 __isl_take isl_set *set);
1772 __isl_give isl_map *isl_map_detect_equalities(
1773 __isl_take isl_map *map);
1774 __isl_give isl_union_set *isl_union_set_detect_equalities(
1775 __isl_take isl_union_set *uset);
1776 __isl_give isl_union_map *isl_union_map_detect_equalities(
1777 __isl_take isl_union_map *umap);
1779 Simplify the representation of a set or relation by detecting implicit
1782 =item * Removing redundant constraints
1784 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1785 __isl_take isl_basic_set *bset);
1786 __isl_give isl_set *isl_set_remove_redundancies(
1787 __isl_take isl_set *set);
1788 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1789 __isl_take isl_basic_map *bmap);
1790 __isl_give isl_map *isl_map_remove_redundancies(
1791 __isl_take isl_map *map);
1795 __isl_give isl_basic_set *isl_set_convex_hull(
1796 __isl_take isl_set *set);
1797 __isl_give isl_basic_map *isl_map_convex_hull(
1798 __isl_take isl_map *map);
1800 If the input set or relation has any existentially quantified
1801 variables, then the result of these operations is currently undefined.
1805 __isl_give isl_basic_set *isl_set_simple_hull(
1806 __isl_take isl_set *set);
1807 __isl_give isl_basic_map *isl_map_simple_hull(
1808 __isl_take isl_map *map);
1809 __isl_give isl_union_map *isl_union_map_simple_hull(
1810 __isl_take isl_union_map *umap);
1812 These functions compute a single basic set or relation
1813 that contains the whole input set or relation.
1814 In particular, the output is described by translates
1815 of the constraints describing the basic sets or relations in the input.
1819 (See \autoref{s:simple hull}.)
1825 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1826 __isl_take isl_basic_set *bset);
1827 __isl_give isl_basic_set *isl_set_affine_hull(
1828 __isl_take isl_set *set);
1829 __isl_give isl_union_set *isl_union_set_affine_hull(
1830 __isl_take isl_union_set *uset);
1831 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1832 __isl_take isl_basic_map *bmap);
1833 __isl_give isl_basic_map *isl_map_affine_hull(
1834 __isl_take isl_map *map);
1835 __isl_give isl_union_map *isl_union_map_affine_hull(
1836 __isl_take isl_union_map *umap);
1838 In case of union sets and relations, the affine hull is computed
1841 =item * Polyhedral hull
1843 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1844 __isl_take isl_set *set);
1845 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1846 __isl_take isl_map *map);
1847 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1848 __isl_take isl_union_set *uset);
1849 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1850 __isl_take isl_union_map *umap);
1852 These functions compute a single basic set or relation
1853 not involving any existentially quantified variables
1854 that contains the whole input set or relation.
1855 In case of union sets and relations, the polyhedral hull is computed
1858 =item * Optimization
1860 #include <isl/ilp.h>
1861 enum isl_lp_result isl_basic_set_max(
1862 __isl_keep isl_basic_set *bset,
1863 __isl_keep isl_aff *obj, isl_int *opt)
1864 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1865 __isl_keep isl_aff *obj, isl_int *opt);
1866 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1867 __isl_keep isl_aff *obj, isl_int *opt);
1869 Compute the minimum or maximum of the integer affine expression C<obj>
1870 over the points in C<set>, returning the result in C<opt>.
1871 The return value may be one of C<isl_lp_error>,
1872 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1874 =item * Parametric optimization
1876 __isl_give isl_pw_aff *isl_set_dim_min(
1877 __isl_take isl_set *set, int pos);
1878 __isl_give isl_pw_aff *isl_set_dim_max(
1879 __isl_take isl_set *set, int pos);
1881 Compute the minimum or maximum of the given set dimension as a function of the
1882 parameters, but independently of the other set dimensions.
1883 For lexicographic optimization, see L<"Lexicographic Optimization">.
1887 The following functions compute either the set of (rational) coefficient
1888 values of valid constraints for the given set or the set of (rational)
1889 values satisfying the constraints with coefficients from the given set.
1890 Internally, these two sets of functions perform essentially the
1891 same operations, except that the set of coefficients is assumed to
1892 be a cone, while the set of values may be any polyhedron.
1893 The current implementation is based on the Farkas lemma and
1894 Fourier-Motzkin elimination, but this may change or be made optional
1895 in future. In particular, future implementations may use different
1896 dualization algorithms or skip the elimination step.
1898 __isl_give isl_basic_set *isl_basic_set_coefficients(
1899 __isl_take isl_basic_set *bset);
1900 __isl_give isl_basic_set *isl_set_coefficients(
1901 __isl_take isl_set *set);
1902 __isl_give isl_union_set *isl_union_set_coefficients(
1903 __isl_take isl_union_set *bset);
1904 __isl_give isl_basic_set *isl_basic_set_solutions(
1905 __isl_take isl_basic_set *bset);
1906 __isl_give isl_basic_set *isl_set_solutions(
1907 __isl_take isl_set *set);
1908 __isl_give isl_union_set *isl_union_set_solutions(
1909 __isl_take isl_union_set *bset);
1913 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1915 __isl_give isl_union_map *isl_union_map_power(
1916 __isl_take isl_union_map *umap, int *exact);
1918 Compute a parametric representation for all positive powers I<k> of C<map>.
1919 The result maps I<k> to a nested relation corresponding to the
1920 I<k>th power of C<map>.
1921 The result may be an overapproximation. If the result is known to be exact,
1922 then C<*exact> is set to C<1>.
1924 =item * Transitive closure
1926 __isl_give isl_map *isl_map_transitive_closure(
1927 __isl_take isl_map *map, int *exact);
1928 __isl_give isl_union_map *isl_union_map_transitive_closure(
1929 __isl_take isl_union_map *umap, int *exact);
1931 Compute the transitive closure of C<map>.
1932 The result may be an overapproximation. If the result is known to be exact,
1933 then C<*exact> is set to C<1>.
1935 =item * Reaching path lengths
1937 __isl_give isl_map *isl_map_reaching_path_lengths(
1938 __isl_take isl_map *map, int *exact);
1940 Compute a relation that maps each element in the range of C<map>
1941 to the lengths of all paths composed of edges in C<map> that
1942 end up in the given element.
1943 The result may be an overapproximation. If the result is known to be exact,
1944 then C<*exact> is set to C<1>.
1945 To compute the I<maximal> path length, the resulting relation
1946 should be postprocessed by C<isl_map_lexmax>.
1947 In particular, if the input relation is a dependence relation
1948 (mapping sources to sinks), then the maximal path length corresponds
1949 to the free schedule.
1950 Note, however, that C<isl_map_lexmax> expects the maximum to be
1951 finite, so if the path lengths are unbounded (possibly due to
1952 the overapproximation), then you will get an error message.
1956 __isl_give isl_basic_set *isl_basic_map_wrap(
1957 __isl_take isl_basic_map *bmap);
1958 __isl_give isl_set *isl_map_wrap(
1959 __isl_take isl_map *map);
1960 __isl_give isl_union_set *isl_union_map_wrap(
1961 __isl_take isl_union_map *umap);
1962 __isl_give isl_basic_map *isl_basic_set_unwrap(
1963 __isl_take isl_basic_set *bset);
1964 __isl_give isl_map *isl_set_unwrap(
1965 __isl_take isl_set *set);
1966 __isl_give isl_union_map *isl_union_set_unwrap(
1967 __isl_take isl_union_set *uset);
1971 Remove any internal structure of domain (and range) of the given
1972 set or relation. If there is any such internal structure in the input,
1973 then the name of the space is also removed.
1975 __isl_give isl_basic_set *isl_basic_set_flatten(
1976 __isl_take isl_basic_set *bset);
1977 __isl_give isl_set *isl_set_flatten(
1978 __isl_take isl_set *set);
1979 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1980 __isl_take isl_basic_map *bmap);
1981 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1982 __isl_take isl_basic_map *bmap);
1983 __isl_give isl_map *isl_map_flatten_range(
1984 __isl_take isl_map *map);
1985 __isl_give isl_map *isl_map_flatten_domain(
1986 __isl_take isl_map *map);
1987 __isl_give isl_basic_map *isl_basic_map_flatten(
1988 __isl_take isl_basic_map *bmap);
1989 __isl_give isl_map *isl_map_flatten(
1990 __isl_take isl_map *map);
1992 __isl_give isl_map *isl_set_flatten_map(
1993 __isl_take isl_set *set);
1995 The function above constructs a relation
1996 that maps the input set to a flattened version of the set.
2000 Lift the input set to a space with extra dimensions corresponding
2001 to the existentially quantified variables in the input.
2002 In particular, the result lives in a wrapped map where the domain
2003 is the original space and the range corresponds to the original
2004 existentially quantified variables.
2006 __isl_give isl_basic_set *isl_basic_set_lift(
2007 __isl_take isl_basic_set *bset);
2008 __isl_give isl_set *isl_set_lift(
2009 __isl_take isl_set *set);
2010 __isl_give isl_union_set *isl_union_set_lift(
2011 __isl_take isl_union_set *uset);
2013 =item * Internal Product
2015 __isl_give isl_basic_map *isl_basic_map_zip(
2016 __isl_take isl_basic_map *bmap);
2017 __isl_give isl_map *isl_map_zip(
2018 __isl_take isl_map *map);
2019 __isl_give isl_union_map *isl_union_map_zip(
2020 __isl_take isl_union_map *umap);
2022 Given a relation with nested relations for domain and range,
2023 interchange the range of the domain with the domain of the range.
2025 =item * Aligning parameters
2027 __isl_give isl_set *isl_set_align_params(
2028 __isl_take isl_set *set,
2029 __isl_take isl_space *model);
2030 __isl_give isl_map *isl_map_align_params(
2031 __isl_take isl_map *map,
2032 __isl_take isl_space *model);
2034 Change the order of the parameters of the given set or relation
2035 such that the first parameters match those of C<model>.
2036 This may involve the introduction of extra parameters.
2037 All parameters need to be named.
2039 =item * Dimension manipulation
2041 __isl_give isl_set *isl_set_add_dims(
2042 __isl_take isl_set *set,
2043 enum isl_dim_type type, unsigned n);
2044 __isl_give isl_map *isl_map_add_dims(
2045 __isl_take isl_map *map,
2046 enum isl_dim_type type, unsigned n);
2047 __isl_give isl_set *isl_set_insert_dims(
2048 __isl_take isl_set *set,
2049 enum isl_dim_type type, unsigned pos, unsigned n);
2050 __isl_give isl_map *isl_map_insert_dims(
2051 __isl_take isl_map *map,
2052 enum isl_dim_type type, unsigned pos, unsigned n);
2054 It is usually not advisable to directly change the (input or output)
2055 space of a set or a relation as this removes the name and the internal
2056 structure of the space. However, the above functions can be useful
2057 to add new parameters, assuming
2058 C<isl_set_align_params> and C<isl_map_align_params>
2063 =head2 Binary Operations
2065 The two arguments of a binary operation not only need to live
2066 in the same C<isl_ctx>, they currently also need to have
2067 the same (number of) parameters.
2069 =head3 Basic Operations
2073 =item * Intersection
2075 __isl_give isl_basic_set *isl_basic_set_intersect(
2076 __isl_take isl_basic_set *bset1,
2077 __isl_take isl_basic_set *bset2);
2078 __isl_give isl_set *isl_set_intersect_params(
2079 __isl_take isl_set *set,
2080 __isl_take isl_set *params);
2081 __isl_give isl_set *isl_set_intersect(
2082 __isl_take isl_set *set1,
2083 __isl_take isl_set *set2);
2084 __isl_give isl_union_set *isl_union_set_intersect(
2085 __isl_take isl_union_set *uset1,
2086 __isl_take isl_union_set *uset2);
2087 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2088 __isl_take isl_basic_map *bmap,
2089 __isl_take isl_basic_set *bset);
2090 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2091 __isl_take isl_basic_map *bmap,
2092 __isl_take isl_basic_set *bset);
2093 __isl_give isl_basic_map *isl_basic_map_intersect(
2094 __isl_take isl_basic_map *bmap1,
2095 __isl_take isl_basic_map *bmap2);
2096 __isl_give isl_map *isl_map_intersect_params(
2097 __isl_take isl_map *map,
2098 __isl_take isl_set *params);
2099 __isl_give isl_map *isl_map_intersect_domain(
2100 __isl_take isl_map *map,
2101 __isl_take isl_set *set);
2102 __isl_give isl_map *isl_map_intersect_range(
2103 __isl_take isl_map *map,
2104 __isl_take isl_set *set);
2105 __isl_give isl_map *isl_map_intersect(
2106 __isl_take isl_map *map1,
2107 __isl_take isl_map *map2);
2108 __isl_give isl_union_map *isl_union_map_intersect_domain(
2109 __isl_take isl_union_map *umap,
2110 __isl_take isl_union_set *uset);
2111 __isl_give isl_union_map *isl_union_map_intersect_range(
2112 __isl_take isl_union_map *umap,
2113 __isl_take isl_union_set *uset);
2114 __isl_give isl_union_map *isl_union_map_intersect(
2115 __isl_take isl_union_map *umap1,
2116 __isl_take isl_union_map *umap2);
2120 __isl_give isl_set *isl_basic_set_union(
2121 __isl_take isl_basic_set *bset1,
2122 __isl_take isl_basic_set *bset2);
2123 __isl_give isl_map *isl_basic_map_union(
2124 __isl_take isl_basic_map *bmap1,
2125 __isl_take isl_basic_map *bmap2);
2126 __isl_give isl_set *isl_set_union(
2127 __isl_take isl_set *set1,
2128 __isl_take isl_set *set2);
2129 __isl_give isl_map *isl_map_union(
2130 __isl_take isl_map *map1,
2131 __isl_take isl_map *map2);
2132 __isl_give isl_union_set *isl_union_set_union(
2133 __isl_take isl_union_set *uset1,
2134 __isl_take isl_union_set *uset2);
2135 __isl_give isl_union_map *isl_union_map_union(
2136 __isl_take isl_union_map *umap1,
2137 __isl_take isl_union_map *umap2);
2139 =item * Set difference
2141 __isl_give isl_set *isl_set_subtract(
2142 __isl_take isl_set *set1,
2143 __isl_take isl_set *set2);
2144 __isl_give isl_map *isl_map_subtract(
2145 __isl_take isl_map *map1,
2146 __isl_take isl_map *map2);
2147 __isl_give isl_union_set *isl_union_set_subtract(
2148 __isl_take isl_union_set *uset1,
2149 __isl_take isl_union_set *uset2);
2150 __isl_give isl_union_map *isl_union_map_subtract(
2151 __isl_take isl_union_map *umap1,
2152 __isl_take isl_union_map *umap2);
2156 __isl_give isl_basic_set *isl_basic_set_apply(
2157 __isl_take isl_basic_set *bset,
2158 __isl_take isl_basic_map *bmap);
2159 __isl_give isl_set *isl_set_apply(
2160 __isl_take isl_set *set,
2161 __isl_take isl_map *map);
2162 __isl_give isl_union_set *isl_union_set_apply(
2163 __isl_take isl_union_set *uset,
2164 __isl_take isl_union_map *umap);
2165 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2166 __isl_take isl_basic_map *bmap1,
2167 __isl_take isl_basic_map *bmap2);
2168 __isl_give isl_basic_map *isl_basic_map_apply_range(
2169 __isl_take isl_basic_map *bmap1,
2170 __isl_take isl_basic_map *bmap2);
2171 __isl_give isl_map *isl_map_apply_domain(
2172 __isl_take isl_map *map1,
2173 __isl_take isl_map *map2);
2174 __isl_give isl_union_map *isl_union_map_apply_domain(
2175 __isl_take isl_union_map *umap1,
2176 __isl_take isl_union_map *umap2);
2177 __isl_give isl_map *isl_map_apply_range(
2178 __isl_take isl_map *map1,
2179 __isl_take isl_map *map2);
2180 __isl_give isl_union_map *isl_union_map_apply_range(
2181 __isl_take isl_union_map *umap1,
2182 __isl_take isl_union_map *umap2);
2184 =item * Cartesian Product
2186 __isl_give isl_set *isl_set_product(
2187 __isl_take isl_set *set1,
2188 __isl_take isl_set *set2);
2189 __isl_give isl_union_set *isl_union_set_product(
2190 __isl_take isl_union_set *uset1,
2191 __isl_take isl_union_set *uset2);
2192 __isl_give isl_basic_map *isl_basic_map_domain_product(
2193 __isl_take isl_basic_map *bmap1,
2194 __isl_take isl_basic_map *bmap2);
2195 __isl_give isl_basic_map *isl_basic_map_range_product(
2196 __isl_take isl_basic_map *bmap1,
2197 __isl_take isl_basic_map *bmap2);
2198 __isl_give isl_map *isl_map_domain_product(
2199 __isl_take isl_map *map1,
2200 __isl_take isl_map *map2);
2201 __isl_give isl_map *isl_map_range_product(
2202 __isl_take isl_map *map1,
2203 __isl_take isl_map *map2);
2204 __isl_give isl_union_map *isl_union_map_range_product(
2205 __isl_take isl_union_map *umap1,
2206 __isl_take isl_union_map *umap2);
2207 __isl_give isl_map *isl_map_product(
2208 __isl_take isl_map *map1,
2209 __isl_take isl_map *map2);
2210 __isl_give isl_union_map *isl_union_map_product(
2211 __isl_take isl_union_map *umap1,
2212 __isl_take isl_union_map *umap2);
2214 The above functions compute the cross product of the given
2215 sets or relations. The domains and ranges of the results
2216 are wrapped maps between domains and ranges of the inputs.
2217 To obtain a ``flat'' product, use the following functions
2220 __isl_give isl_basic_set *isl_basic_set_flat_product(
2221 __isl_take isl_basic_set *bset1,
2222 __isl_take isl_basic_set *bset2);
2223 __isl_give isl_set *isl_set_flat_product(
2224 __isl_take isl_set *set1,
2225 __isl_take isl_set *set2);
2226 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2227 __isl_take isl_basic_map *bmap1,
2228 __isl_take isl_basic_map *bmap2);
2229 __isl_give isl_map *isl_map_flat_domain_product(
2230 __isl_take isl_map *map1,
2231 __isl_take isl_map *map2);
2232 __isl_give isl_map *isl_map_flat_range_product(
2233 __isl_take isl_map *map1,
2234 __isl_take isl_map *map2);
2235 __isl_give isl_union_map *isl_union_map_flat_range_product(
2236 __isl_take isl_union_map *umap1,
2237 __isl_take isl_union_map *umap2);
2238 __isl_give isl_basic_map *isl_basic_map_flat_product(
2239 __isl_take isl_basic_map *bmap1,
2240 __isl_take isl_basic_map *bmap2);
2241 __isl_give isl_map *isl_map_flat_product(
2242 __isl_take isl_map *map1,
2243 __isl_take isl_map *map2);
2245 =item * Simplification
2247 __isl_give isl_basic_set *isl_basic_set_gist(
2248 __isl_take isl_basic_set *bset,
2249 __isl_take isl_basic_set *context);
2250 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2251 __isl_take isl_set *context);
2252 __isl_give isl_union_set *isl_union_set_gist(
2253 __isl_take isl_union_set *uset,
2254 __isl_take isl_union_set *context);
2255 __isl_give isl_basic_map *isl_basic_map_gist(
2256 __isl_take isl_basic_map *bmap,
2257 __isl_take isl_basic_map *context);
2258 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2259 __isl_take isl_map *context);
2260 __isl_give isl_union_map *isl_union_map_gist(
2261 __isl_take isl_union_map *umap,
2262 __isl_take isl_union_map *context);
2264 The gist operation returns a set or relation that has the
2265 same intersection with the context as the input set or relation.
2266 Any implicit equality in the intersection is made explicit in the result,
2267 while all inequalities that are redundant with respect to the intersection
2269 In case of union sets and relations, the gist operation is performed
2274 =head3 Lexicographic Optimization
2276 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2277 the following functions
2278 compute a set that contains the lexicographic minimum or maximum
2279 of the elements in C<set> (or C<bset>) for those values of the parameters
2280 that satisfy C<dom>.
2281 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2282 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2284 In other words, the union of the parameter values
2285 for which the result is non-empty and of C<*empty>
2288 __isl_give isl_set *isl_basic_set_partial_lexmin(
2289 __isl_take isl_basic_set *bset,
2290 __isl_take isl_basic_set *dom,
2291 __isl_give isl_set **empty);
2292 __isl_give isl_set *isl_basic_set_partial_lexmax(
2293 __isl_take isl_basic_set *bset,
2294 __isl_take isl_basic_set *dom,
2295 __isl_give isl_set **empty);
2296 __isl_give isl_set *isl_set_partial_lexmin(
2297 __isl_take isl_set *set, __isl_take isl_set *dom,
2298 __isl_give isl_set **empty);
2299 __isl_give isl_set *isl_set_partial_lexmax(
2300 __isl_take isl_set *set, __isl_take isl_set *dom,
2301 __isl_give isl_set **empty);
2303 Given a (basic) set C<set> (or C<bset>), the following functions simply
2304 return a set containing the lexicographic minimum or maximum
2305 of the elements in C<set> (or C<bset>).
2306 In case of union sets, the optimum is computed per space.
2308 __isl_give isl_set *isl_basic_set_lexmin(
2309 __isl_take isl_basic_set *bset);
2310 __isl_give isl_set *isl_basic_set_lexmax(
2311 __isl_take isl_basic_set *bset);
2312 __isl_give isl_set *isl_set_lexmin(
2313 __isl_take isl_set *set);
2314 __isl_give isl_set *isl_set_lexmax(
2315 __isl_take isl_set *set);
2316 __isl_give isl_union_set *isl_union_set_lexmin(
2317 __isl_take isl_union_set *uset);
2318 __isl_give isl_union_set *isl_union_set_lexmax(
2319 __isl_take isl_union_set *uset);
2321 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2322 the following functions
2323 compute a relation that maps each element of C<dom>
2324 to the single lexicographic minimum or maximum
2325 of the elements that are associated to that same
2326 element in C<map> (or C<bmap>).
2327 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2328 that contains the elements in C<dom> that do not map
2329 to any elements in C<map> (or C<bmap>).
2330 In other words, the union of the domain of the result and of C<*empty>
2333 __isl_give isl_map *isl_basic_map_partial_lexmax(
2334 __isl_take isl_basic_map *bmap,
2335 __isl_take isl_basic_set *dom,
2336 __isl_give isl_set **empty);
2337 __isl_give isl_map *isl_basic_map_partial_lexmin(
2338 __isl_take isl_basic_map *bmap,
2339 __isl_take isl_basic_set *dom,
2340 __isl_give isl_set **empty);
2341 __isl_give isl_map *isl_map_partial_lexmax(
2342 __isl_take isl_map *map, __isl_take isl_set *dom,
2343 __isl_give isl_set **empty);
2344 __isl_give isl_map *isl_map_partial_lexmin(
2345 __isl_take isl_map *map, __isl_take isl_set *dom,
2346 __isl_give isl_set **empty);
2348 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2349 return a map mapping each element in the domain of
2350 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2351 of all elements associated to that element.
2352 In case of union relations, the optimum is computed per space.
2354 __isl_give isl_map *isl_basic_map_lexmin(
2355 __isl_take isl_basic_map *bmap);
2356 __isl_give isl_map *isl_basic_map_lexmax(
2357 __isl_take isl_basic_map *bmap);
2358 __isl_give isl_map *isl_map_lexmin(
2359 __isl_take isl_map *map);
2360 __isl_give isl_map *isl_map_lexmax(
2361 __isl_take isl_map *map);
2362 __isl_give isl_union_map *isl_union_map_lexmin(
2363 __isl_take isl_union_map *umap);
2364 __isl_give isl_union_map *isl_union_map_lexmax(
2365 __isl_take isl_union_map *umap);
2369 Lists are defined over several element types, including
2370 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2371 Here we take lists of C<isl_set>s as an example.
2372 Lists can be created, copied and freed using the following functions.
2374 #include <isl/list.h>
2375 __isl_give isl_set_list *isl_set_list_from_set(
2376 __isl_take isl_set *el);
2377 __isl_give isl_set_list *isl_set_list_alloc(
2378 isl_ctx *ctx, int n);
2379 __isl_give isl_set_list *isl_set_list_copy(
2380 __isl_keep isl_set_list *list);
2381 __isl_give isl_set_list *isl_set_list_add(
2382 __isl_take isl_set_list *list,
2383 __isl_take isl_set *el);
2384 __isl_give isl_set_list *isl_set_list_concat(
2385 __isl_take isl_set_list *list1,
2386 __isl_take isl_set_list *list2);
2387 void *isl_set_list_free(__isl_take isl_set_list *list);
2389 C<isl_set_list_alloc> creates an empty list with a capacity for
2390 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2393 Lists can be inspected using the following functions.
2395 #include <isl/list.h>
2396 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2397 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2398 __isl_give isl_set *isl_set_list_get_set(
2399 __isl_keep isl_set_list *list, int index);
2400 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2401 int (*fn)(__isl_take isl_set *el, void *user),
2404 Lists can be printed using
2406 #include <isl/list.h>
2407 __isl_give isl_printer *isl_printer_print_set_list(
2408 __isl_take isl_printer *p,
2409 __isl_keep isl_set_list *list);
2413 Matrices can be created, copied and freed using the following functions.
2415 #include <isl/mat.h>
2416 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2417 unsigned n_row, unsigned n_col);
2418 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2419 void isl_mat_free(__isl_take isl_mat *mat);
2421 Note that the elements of a newly created matrix may have arbitrary values.
2422 The elements can be changed and inspected using the following functions.
2424 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2425 int isl_mat_rows(__isl_keep isl_mat *mat);
2426 int isl_mat_cols(__isl_keep isl_mat *mat);
2427 int isl_mat_get_element(__isl_keep isl_mat *mat,
2428 int row, int col, isl_int *v);
2429 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2430 int row, int col, isl_int v);
2431 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2432 int row, int col, int v);
2434 C<isl_mat_get_element> will return a negative value if anything went wrong.
2435 In that case, the value of C<*v> is undefined.
2437 The following function can be used to compute the (right) inverse
2438 of a matrix, i.e., a matrix such that the product of the original
2439 and the inverse (in that order) is a multiple of the identity matrix.
2440 The input matrix is assumed to be of full row-rank.
2442 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2444 The following function can be used to compute the (right) kernel
2445 (or null space) of a matrix, i.e., a matrix such that the product of
2446 the original and the kernel (in that order) is the zero matrix.
2448 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2450 =head2 Piecewise Quasi Affine Expressions
2452 The zero quasi affine expression can be created using
2454 __isl_give isl_aff *isl_aff_zero(
2455 __isl_take isl_local_space *ls);
2457 A quasi affine expression can also be initialized from an C<isl_div>:
2459 #include <isl/div.h>
2460 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2462 An empty piecewise quasi affine expression (one with no cells)
2463 or a piecewise quasi affine expression with a single cell can
2464 be created using the following functions.
2466 #include <isl/aff.h>
2467 __isl_give isl_pw_aff *isl_pw_aff_empty(
2468 __isl_take isl_space *space);
2469 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2470 __isl_take isl_set *set, __isl_take isl_aff *aff);
2471 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2472 __isl_take isl_aff *aff);
2474 Quasi affine expressions can be copied and freed using
2476 #include <isl/aff.h>
2477 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2478 void *isl_aff_free(__isl_take isl_aff *aff);
2480 __isl_give isl_pw_aff *isl_pw_aff_copy(
2481 __isl_keep isl_pw_aff *pwaff);
2482 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2484 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2485 using the following function. The constraint is required to have
2486 a non-zero coefficient for the specified dimension.
2488 #include <isl/constraint.h>
2489 __isl_give isl_aff *isl_constraint_get_bound(
2490 __isl_keep isl_constraint *constraint,
2491 enum isl_dim_type type, int pos);
2493 The entire affine expression of the constraint can also be extracted
2494 using the following function.
2496 #include <isl/constraint.h>
2497 __isl_give isl_aff *isl_constraint_get_aff(
2498 __isl_keep isl_constraint *constraint);
2500 Conversely, an equality constraint equating
2501 the affine expression to zero or an inequality constraint enforcing
2502 the affine expression to be non-negative, can be constructed using
2504 __isl_give isl_constraint *isl_equality_from_aff(
2505 __isl_take isl_aff *aff);
2506 __isl_give isl_constraint *isl_inequality_from_aff(
2507 __isl_take isl_aff *aff);
2509 The expression can be inspected using
2511 #include <isl/aff.h>
2512 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2513 int isl_aff_dim(__isl_keep isl_aff *aff,
2514 enum isl_dim_type type);
2515 __isl_give isl_local_space *isl_aff_get_local_space(
2516 __isl_keep isl_aff *aff);
2517 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2518 enum isl_dim_type type, unsigned pos);
2519 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2521 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2522 enum isl_dim_type type, int pos, isl_int *v);
2523 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2525 __isl_give isl_div *isl_aff_get_div(
2526 __isl_keep isl_aff *aff, int pos);
2528 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2529 int (*fn)(__isl_take isl_set *set,
2530 __isl_take isl_aff *aff,
2531 void *user), void *user);
2533 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2534 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2536 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2537 enum isl_dim_type type, unsigned first, unsigned n);
2538 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2539 enum isl_dim_type type, unsigned first, unsigned n);
2541 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2542 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2543 enum isl_dim_type type);
2544 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2546 It can be modified using
2548 #include <isl/aff.h>
2549 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2550 __isl_take isl_pw_aff *pwaff,
2551 __isl_take isl_id *id);
2552 __isl_give isl_aff *isl_aff_set_dim_name(
2553 __isl_take isl_aff *aff, enum isl_dim_type type,
2554 unsigned pos, const char *s);
2555 __isl_give isl_aff *isl_aff_set_constant(
2556 __isl_take isl_aff *aff, isl_int v);
2557 __isl_give isl_aff *isl_aff_set_constant_si(
2558 __isl_take isl_aff *aff, int v);
2559 __isl_give isl_aff *isl_aff_set_coefficient(
2560 __isl_take isl_aff *aff,
2561 enum isl_dim_type type, int pos, isl_int v);
2562 __isl_give isl_aff *isl_aff_set_coefficient_si(
2563 __isl_take isl_aff *aff,
2564 enum isl_dim_type type, int pos, int v);
2565 __isl_give isl_aff *isl_aff_set_denominator(
2566 __isl_take isl_aff *aff, isl_int v);
2568 __isl_give isl_aff *isl_aff_add_constant(
2569 __isl_take isl_aff *aff, isl_int v);
2570 __isl_give isl_aff *isl_aff_add_constant_si(
2571 __isl_take isl_aff *aff, int v);
2572 __isl_give isl_aff *isl_aff_add_coefficient(
2573 __isl_take isl_aff *aff,
2574 enum isl_dim_type type, int pos, isl_int v);
2575 __isl_give isl_aff *isl_aff_add_coefficient_si(
2576 __isl_take isl_aff *aff,
2577 enum isl_dim_type type, int pos, int v);
2579 __isl_give isl_aff *isl_aff_insert_dims(
2580 __isl_take isl_aff *aff,
2581 enum isl_dim_type type, unsigned first, unsigned n);
2582 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2583 __isl_take isl_pw_aff *pwaff,
2584 enum isl_dim_type type, unsigned first, unsigned n);
2585 __isl_give isl_aff *isl_aff_add_dims(
2586 __isl_take isl_aff *aff,
2587 enum isl_dim_type type, unsigned n);
2588 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2589 __isl_take isl_pw_aff *pwaff,
2590 enum isl_dim_type type, unsigned n);
2591 __isl_give isl_aff *isl_aff_drop_dims(
2592 __isl_take isl_aff *aff,
2593 enum isl_dim_type type, unsigned first, unsigned n);
2594 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2595 __isl_take isl_pw_aff *pwaff,
2596 enum isl_dim_type type, unsigned first, unsigned n);
2598 Note that the C<set_constant> and C<set_coefficient> functions
2599 set the I<numerator> of the constant or coefficient, while
2600 C<add_constant> and C<add_coefficient> add an integer value to
2601 the possibly rational constant or coefficient.
2603 To check whether an affine expressions is obviously zero
2604 or obviously equal to some other affine expression, use
2606 #include <isl/aff.h>
2607 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2608 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2609 __isl_keep isl_aff *aff2);
2613 #include <isl/aff.h>
2614 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2615 __isl_take isl_aff *aff2);
2616 __isl_give isl_pw_aff *isl_pw_aff_add(
2617 __isl_take isl_pw_aff *pwaff1,
2618 __isl_take isl_pw_aff *pwaff2);
2619 __isl_give isl_pw_aff *isl_pw_aff_min(
2620 __isl_take isl_pw_aff *pwaff1,
2621 __isl_take isl_pw_aff *pwaff2);
2622 __isl_give isl_pw_aff *isl_pw_aff_max(
2623 __isl_take isl_pw_aff *pwaff1,
2624 __isl_take isl_pw_aff *pwaff2);
2625 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2626 __isl_take isl_aff *aff2);
2627 __isl_give isl_pw_aff *isl_pw_aff_sub(
2628 __isl_take isl_pw_aff *pwaff1,
2629 __isl_take isl_pw_aff *pwaff2);
2630 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2631 __isl_give isl_pw_aff *isl_pw_aff_neg(
2632 __isl_take isl_pw_aff *pwaff);
2633 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2634 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2635 __isl_take isl_pw_aff *pwaff);
2636 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2637 __isl_give isl_pw_aff *isl_pw_aff_floor(
2638 __isl_take isl_pw_aff *pwaff);
2639 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2641 __isl_give isl_pw_aff *isl_pw_aff_mod(
2642 __isl_take isl_pw_aff *pwaff, isl_int mod);
2643 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2645 __isl_give isl_pw_aff *isl_pw_aff_scale(
2646 __isl_take isl_pw_aff *pwaff, isl_int f);
2647 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2649 __isl_give isl_aff *isl_aff_scale_down_ui(
2650 __isl_take isl_aff *aff, unsigned f);
2651 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2652 __isl_take isl_pw_aff *pwaff, isl_int f);
2654 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2655 __isl_take isl_pw_aff_list *list);
2656 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2657 __isl_take isl_pw_aff_list *list);
2659 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2660 __isl_take isl_pw_aff *pwqp);
2662 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2663 __isl_take isl_pw_aff *pwaff,
2664 __isl_take isl_space *model);
2666 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2667 __isl_take isl_set *context);
2668 __isl_give isl_pw_aff *isl_pw_aff_gist(
2669 __isl_take isl_pw_aff *pwaff,
2670 __isl_take isl_set *context);
2672 __isl_give isl_set *isl_pw_aff_domain(
2673 __isl_take isl_pw_aff *pwaff);
2675 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2676 __isl_take isl_aff *aff2);
2677 __isl_give isl_pw_aff *isl_pw_aff_mul(
2678 __isl_take isl_pw_aff *pwaff1,
2679 __isl_take isl_pw_aff *pwaff2);
2681 When multiplying two affine expressions, at least one of the two needs
2684 #include <isl/aff.h>
2685 __isl_give isl_basic_set *isl_aff_le_basic_set(
2686 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2687 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2688 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2689 __isl_give isl_set *isl_pw_aff_eq_set(
2690 __isl_take isl_pw_aff *pwaff1,
2691 __isl_take isl_pw_aff *pwaff2);
2692 __isl_give isl_set *isl_pw_aff_ne_set(
2693 __isl_take isl_pw_aff *pwaff1,
2694 __isl_take isl_pw_aff *pwaff2);
2695 __isl_give isl_set *isl_pw_aff_le_set(
2696 __isl_take isl_pw_aff *pwaff1,
2697 __isl_take isl_pw_aff *pwaff2);
2698 __isl_give isl_set *isl_pw_aff_lt_set(
2699 __isl_take isl_pw_aff *pwaff1,
2700 __isl_take isl_pw_aff *pwaff2);
2701 __isl_give isl_set *isl_pw_aff_ge_set(
2702 __isl_take isl_pw_aff *pwaff1,
2703 __isl_take isl_pw_aff *pwaff2);
2704 __isl_give isl_set *isl_pw_aff_gt_set(
2705 __isl_take isl_pw_aff *pwaff1,
2706 __isl_take isl_pw_aff *pwaff2);
2708 __isl_give isl_set *isl_pw_aff_list_eq_set(
2709 __isl_take isl_pw_aff_list *list1,
2710 __isl_take isl_pw_aff_list *list2);
2711 __isl_give isl_set *isl_pw_aff_list_ne_set(
2712 __isl_take isl_pw_aff_list *list1,
2713 __isl_take isl_pw_aff_list *list2);
2714 __isl_give isl_set *isl_pw_aff_list_le_set(
2715 __isl_take isl_pw_aff_list *list1,
2716 __isl_take isl_pw_aff_list *list2);
2717 __isl_give isl_set *isl_pw_aff_list_lt_set(
2718 __isl_take isl_pw_aff_list *list1,
2719 __isl_take isl_pw_aff_list *list2);
2720 __isl_give isl_set *isl_pw_aff_list_ge_set(
2721 __isl_take isl_pw_aff_list *list1,
2722 __isl_take isl_pw_aff_list *list2);
2723 __isl_give isl_set *isl_pw_aff_list_gt_set(
2724 __isl_take isl_pw_aff_list *list1,
2725 __isl_take isl_pw_aff_list *list2);
2727 The function C<isl_aff_ge_basic_set> returns a basic set
2728 containing those elements in the shared space
2729 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2730 The function C<isl_aff_ge_set> returns a set
2731 containing those elements in the shared domain
2732 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2733 The functions operating on C<isl_pw_aff_list> apply the corresponding
2734 C<isl_pw_aff> function to each pair of elements in the two lists.
2736 #include <isl/aff.h>
2737 __isl_give isl_set *isl_pw_aff_nonneg_set(
2738 __isl_take isl_pw_aff *pwaff);
2739 __isl_give isl_set *isl_pw_aff_zero_set(
2740 __isl_take isl_pw_aff *pwaff);
2741 __isl_give isl_set *isl_pw_aff_non_zero_set(
2742 __isl_take isl_pw_aff *pwaff);
2744 The function C<isl_pw_aff_nonneg_set> returns a set
2745 containing those elements in the domain
2746 of C<pwaff> where C<pwaff> is non-negative.
2748 #include <isl/aff.h>
2749 __isl_give isl_pw_aff *isl_pw_aff_cond(
2750 __isl_take isl_set *cond,
2751 __isl_take isl_pw_aff *pwaff_true,
2752 __isl_take isl_pw_aff *pwaff_false);
2754 The function C<isl_pw_aff_cond> performs a conditional operator
2755 and returns an expression that is equal to C<pwaff_true>
2756 for elements in C<cond> and equal to C<pwaff_false> for elements
2759 #include <isl/aff.h>
2760 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2761 __isl_take isl_pw_aff *pwaff1,
2762 __isl_take isl_pw_aff *pwaff2);
2763 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2764 __isl_take isl_pw_aff *pwaff1,
2765 __isl_take isl_pw_aff *pwaff2);
2767 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2768 expression with a domain that is the union of those of C<pwaff1> and
2769 C<pwaff2> and such that on each cell, the quasi-affine expression is
2770 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2771 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2772 associated expression is the defined one.
2774 An expression can be printed using
2776 #include <isl/aff.h>
2777 __isl_give isl_printer *isl_printer_print_aff(
2778 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2780 __isl_give isl_printer *isl_printer_print_pw_aff(
2781 __isl_take isl_printer *p,
2782 __isl_keep isl_pw_aff *pwaff);
2786 Points are elements of a set. They can be used to construct
2787 simple sets (boxes) or they can be used to represent the
2788 individual elements of a set.
2789 The zero point (the origin) can be created using
2791 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2793 The coordinates of a point can be inspected, set and changed
2796 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2797 enum isl_dim_type type, int pos, isl_int *v);
2798 __isl_give isl_point *isl_point_set_coordinate(
2799 __isl_take isl_point *pnt,
2800 enum isl_dim_type type, int pos, isl_int v);
2802 __isl_give isl_point *isl_point_add_ui(
2803 __isl_take isl_point *pnt,
2804 enum isl_dim_type type, int pos, unsigned val);
2805 __isl_give isl_point *isl_point_sub_ui(
2806 __isl_take isl_point *pnt,
2807 enum isl_dim_type type, int pos, unsigned val);
2809 Other properties can be obtained using
2811 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2813 Points can be copied or freed using
2815 __isl_give isl_point *isl_point_copy(
2816 __isl_keep isl_point *pnt);
2817 void isl_point_free(__isl_take isl_point *pnt);
2819 A singleton set can be created from a point using
2821 __isl_give isl_basic_set *isl_basic_set_from_point(
2822 __isl_take isl_point *pnt);
2823 __isl_give isl_set *isl_set_from_point(
2824 __isl_take isl_point *pnt);
2826 and a box can be created from two opposite extremal points using
2828 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2829 __isl_take isl_point *pnt1,
2830 __isl_take isl_point *pnt2);
2831 __isl_give isl_set *isl_set_box_from_points(
2832 __isl_take isl_point *pnt1,
2833 __isl_take isl_point *pnt2);
2835 All elements of a B<bounded> (union) set can be enumerated using
2836 the following functions.
2838 int isl_set_foreach_point(__isl_keep isl_set *set,
2839 int (*fn)(__isl_take isl_point *pnt, void *user),
2841 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2842 int (*fn)(__isl_take isl_point *pnt, void *user),
2845 The function C<fn> is called for each integer point in
2846 C<set> with as second argument the last argument of
2847 the C<isl_set_foreach_point> call. The function C<fn>
2848 should return C<0> on success and C<-1> on failure.
2849 In the latter case, C<isl_set_foreach_point> will stop
2850 enumerating and return C<-1> as well.
2851 If the enumeration is performed successfully and to completion,
2852 then C<isl_set_foreach_point> returns C<0>.
2854 To obtain a single point of a (basic) set, use
2856 __isl_give isl_point *isl_basic_set_sample_point(
2857 __isl_take isl_basic_set *bset);
2858 __isl_give isl_point *isl_set_sample_point(
2859 __isl_take isl_set *set);
2861 If C<set> does not contain any (integer) points, then the
2862 resulting point will be ``void'', a property that can be
2865 int isl_point_is_void(__isl_keep isl_point *pnt);
2867 =head2 Piecewise Quasipolynomials
2869 A piecewise quasipolynomial is a particular kind of function that maps
2870 a parametric point to a rational value.
2871 More specifically, a quasipolynomial is a polynomial expression in greatest
2872 integer parts of affine expressions of parameters and variables.
2873 A piecewise quasipolynomial is a subdivision of a given parametric
2874 domain into disjoint cells with a quasipolynomial associated to
2875 each cell. The value of the piecewise quasipolynomial at a given
2876 point is the value of the quasipolynomial associated to the cell
2877 that contains the point. Outside of the union of cells,
2878 the value is assumed to be zero.
2879 For example, the piecewise quasipolynomial
2881 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2883 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2884 A given piecewise quasipolynomial has a fixed domain dimension.
2885 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2886 defined over different domains.
2887 Piecewise quasipolynomials are mainly used by the C<barvinok>
2888 library for representing the number of elements in a parametric set or map.
2889 For example, the piecewise quasipolynomial above represents
2890 the number of points in the map
2892 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2894 =head3 Printing (Piecewise) Quasipolynomials
2896 Quasipolynomials and piecewise quasipolynomials can be printed
2897 using the following functions.
2899 __isl_give isl_printer *isl_printer_print_qpolynomial(
2900 __isl_take isl_printer *p,
2901 __isl_keep isl_qpolynomial *qp);
2903 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2904 __isl_take isl_printer *p,
2905 __isl_keep isl_pw_qpolynomial *pwqp);
2907 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2908 __isl_take isl_printer *p,
2909 __isl_keep isl_union_pw_qpolynomial *upwqp);
2911 The output format of the printer
2912 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2913 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2915 In case of printing in C<ISL_FORMAT_C>, the user may want
2916 to set the names of all dimensions
2918 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2919 __isl_take isl_qpolynomial *qp,
2920 enum isl_dim_type type, unsigned pos,
2922 __isl_give isl_pw_qpolynomial *
2923 isl_pw_qpolynomial_set_dim_name(
2924 __isl_take isl_pw_qpolynomial *pwqp,
2925 enum isl_dim_type type, unsigned pos,
2928 =head3 Creating New (Piecewise) Quasipolynomials
2930 Some simple quasipolynomials can be created using the following functions.
2931 More complicated quasipolynomials can be created by applying
2932 operations such as addition and multiplication
2933 on the resulting quasipolynomials
2935 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2936 __isl_take isl_space *dim);
2937 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2938 __isl_take isl_space *dim);
2939 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2940 __isl_take isl_space *dim);
2941 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2942 __isl_take isl_space *dim);
2943 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2944 __isl_take isl_space *dim);
2945 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2946 __isl_take isl_space *dim,
2947 const isl_int n, const isl_int d);
2948 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2949 __isl_take isl_div *div);
2950 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2951 __isl_take isl_space *dim,
2952 enum isl_dim_type type, unsigned pos);
2953 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2954 __isl_take isl_aff *aff);
2956 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2957 with a single cell can be created using the following functions.
2958 Multiple of these single cell piecewise quasipolynomials can
2959 be combined to create more complicated piecewise quasipolynomials.
2961 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2962 __isl_take isl_space *space);
2963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2964 __isl_take isl_set *set,
2965 __isl_take isl_qpolynomial *qp);
2966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2967 __isl_take isl_qpolynomial *qp);
2968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2969 __isl_take isl_pw_aff *pwaff);
2971 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2972 __isl_take isl_space *space);
2973 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2974 __isl_take isl_pw_qpolynomial *pwqp);
2975 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2976 __isl_take isl_union_pw_qpolynomial *upwqp,
2977 __isl_take isl_pw_qpolynomial *pwqp);
2979 Quasipolynomials can be copied and freed again using the following
2982 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2983 __isl_keep isl_qpolynomial *qp);
2984 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2986 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2987 __isl_keep isl_pw_qpolynomial *pwqp);
2988 void *isl_pw_qpolynomial_free(
2989 __isl_take isl_pw_qpolynomial *pwqp);
2991 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2992 __isl_keep isl_union_pw_qpolynomial *upwqp);
2993 void isl_union_pw_qpolynomial_free(
2994 __isl_take isl_union_pw_qpolynomial *upwqp);
2996 =head3 Inspecting (Piecewise) Quasipolynomials
2998 To iterate over all piecewise quasipolynomials in a union
2999 piecewise quasipolynomial, use the following function
3001 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3002 __isl_keep isl_union_pw_qpolynomial *upwqp,
3003 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3006 To extract the piecewise quasipolynomial in a given space from a union, use
3008 __isl_give isl_pw_qpolynomial *
3009 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3010 __isl_keep isl_union_pw_qpolynomial *upwqp,
3011 __isl_take isl_space *space);
3013 To iterate over the cells in a piecewise quasipolynomial,
3014 use either of the following two functions
3016 int isl_pw_qpolynomial_foreach_piece(
3017 __isl_keep isl_pw_qpolynomial *pwqp,
3018 int (*fn)(__isl_take isl_set *set,
3019 __isl_take isl_qpolynomial *qp,
3020 void *user), void *user);
3021 int isl_pw_qpolynomial_foreach_lifted_piece(
3022 __isl_keep isl_pw_qpolynomial *pwqp,
3023 int (*fn)(__isl_take isl_set *set,
3024 __isl_take isl_qpolynomial *qp,
3025 void *user), void *user);
3027 As usual, the function C<fn> should return C<0> on success
3028 and C<-1> on failure. The difference between
3029 C<isl_pw_qpolynomial_foreach_piece> and
3030 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3031 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3032 compute unique representations for all existentially quantified
3033 variables and then turn these existentially quantified variables
3034 into extra set variables, adapting the associated quasipolynomial
3035 accordingly. This means that the C<set> passed to C<fn>
3036 will not have any existentially quantified variables, but that
3037 the dimensions of the sets may be different for different
3038 invocations of C<fn>.
3040 To iterate over all terms in a quasipolynomial,
3043 int isl_qpolynomial_foreach_term(
3044 __isl_keep isl_qpolynomial *qp,
3045 int (*fn)(__isl_take isl_term *term,
3046 void *user), void *user);
3048 The terms themselves can be inspected and freed using
3051 unsigned isl_term_dim(__isl_keep isl_term *term,
3052 enum isl_dim_type type);
3053 void isl_term_get_num(__isl_keep isl_term *term,
3055 void isl_term_get_den(__isl_keep isl_term *term,
3057 int isl_term_get_exp(__isl_keep isl_term *term,
3058 enum isl_dim_type type, unsigned pos);
3059 __isl_give isl_div *isl_term_get_div(
3060 __isl_keep isl_term *term, unsigned pos);
3061 void isl_term_free(__isl_take isl_term *term);
3063 Each term is a product of parameters, set variables and
3064 integer divisions. The function C<isl_term_get_exp>
3065 returns the exponent of a given dimensions in the given term.
3066 The C<isl_int>s in the arguments of C<isl_term_get_num>
3067 and C<isl_term_get_den> need to have been initialized
3068 using C<isl_int_init> before calling these functions.
3070 =head3 Properties of (Piecewise) Quasipolynomials
3072 To check whether a quasipolynomial is actually a constant,
3073 use the following function.
3075 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3076 isl_int *n, isl_int *d);
3078 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3079 then the numerator and denominator of the constant
3080 are returned in C<*n> and C<*d>, respectively.
3082 =head3 Operations on (Piecewise) Quasipolynomials
3084 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3085 __isl_take isl_qpolynomial *qp, isl_int v);
3086 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3087 __isl_take isl_qpolynomial *qp);
3088 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3089 __isl_take isl_qpolynomial *qp1,
3090 __isl_take isl_qpolynomial *qp2);
3091 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3092 __isl_take isl_qpolynomial *qp1,
3093 __isl_take isl_qpolynomial *qp2);
3094 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3095 __isl_take isl_qpolynomial *qp1,
3096 __isl_take isl_qpolynomial *qp2);
3097 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3098 __isl_take isl_qpolynomial *qp, unsigned exponent);
3100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3101 __isl_take isl_pw_qpolynomial *pwqp1,
3102 __isl_take isl_pw_qpolynomial *pwqp2);
3103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3104 __isl_take isl_pw_qpolynomial *pwqp1,
3105 __isl_take isl_pw_qpolynomial *pwqp2);
3106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3107 __isl_take isl_pw_qpolynomial *pwqp1,
3108 __isl_take isl_pw_qpolynomial *pwqp2);
3109 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3110 __isl_take isl_pw_qpolynomial *pwqp);
3111 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3112 __isl_take isl_pw_qpolynomial *pwqp1,
3113 __isl_take isl_pw_qpolynomial *pwqp2);
3114 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3115 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3117 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3118 __isl_take isl_union_pw_qpolynomial *upwqp1,
3119 __isl_take isl_union_pw_qpolynomial *upwqp2);
3120 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3121 __isl_take isl_union_pw_qpolynomial *upwqp1,
3122 __isl_take isl_union_pw_qpolynomial *upwqp2);
3123 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3124 __isl_take isl_union_pw_qpolynomial *upwqp1,
3125 __isl_take isl_union_pw_qpolynomial *upwqp2);
3127 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3128 __isl_take isl_pw_qpolynomial *pwqp,
3129 __isl_take isl_point *pnt);
3131 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3132 __isl_take isl_union_pw_qpolynomial *upwqp,
3133 __isl_take isl_point *pnt);
3135 __isl_give isl_set *isl_pw_qpolynomial_domain(
3136 __isl_take isl_pw_qpolynomial *pwqp);
3137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3138 __isl_take isl_pw_qpolynomial *pwpq,
3139 __isl_take isl_set *set);
3141 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3142 __isl_take isl_union_pw_qpolynomial *upwqp);
3143 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3144 __isl_take isl_union_pw_qpolynomial *upwpq,
3145 __isl_take isl_union_set *uset);
3147 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3148 __isl_take isl_qpolynomial *qp,
3149 __isl_take isl_space *model);
3151 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3152 __isl_take isl_qpolynomial *qp);
3153 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3154 __isl_take isl_pw_qpolynomial *pwqp);
3156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3157 __isl_take isl_union_pw_qpolynomial *upwqp);
3159 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3160 __isl_take isl_qpolynomial *qp,
3161 __isl_take isl_set *context);
3163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3164 __isl_take isl_pw_qpolynomial *pwqp,
3165 __isl_take isl_set *context);
3167 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3168 __isl_take isl_union_pw_qpolynomial *upwqp,
3169 __isl_take isl_union_set *context);
3171 The gist operation applies the gist operation to each of
3172 the cells in the domain of the input piecewise quasipolynomial.
3173 The context is also exploited
3174 to simplify the quasipolynomials associated to each cell.
3176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3177 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3178 __isl_give isl_union_pw_qpolynomial *
3179 isl_union_pw_qpolynomial_to_polynomial(
3180 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3182 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3183 the polynomial will be an overapproximation. If C<sign> is negative,
3184 it will be an underapproximation. If C<sign> is zero, the approximation
3185 will lie somewhere in between.
3187 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3189 A piecewise quasipolynomial reduction is a piecewise
3190 reduction (or fold) of quasipolynomials.
3191 In particular, the reduction can be maximum or a minimum.
3192 The objects are mainly used to represent the result of
3193 an upper or lower bound on a quasipolynomial over its domain,
3194 i.e., as the result of the following function.
3196 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3197 __isl_take isl_pw_qpolynomial *pwqp,
3198 enum isl_fold type, int *tight);
3200 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3201 __isl_take isl_union_pw_qpolynomial *upwqp,
3202 enum isl_fold type, int *tight);
3204 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3205 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3206 is the returned bound is known be tight, i.e., for each value
3207 of the parameters there is at least
3208 one element in the domain that reaches the bound.
3209 If the domain of C<pwqp> is not wrapping, then the bound is computed
3210 over all elements in that domain and the result has a purely parametric
3211 domain. If the domain of C<pwqp> is wrapping, then the bound is
3212 computed over the range of the wrapped relation. The domain of the
3213 wrapped relation becomes the domain of the result.
3215 A (piecewise) quasipolynomial reduction can be copied or freed using the
3216 following functions.
3218 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3219 __isl_keep isl_qpolynomial_fold *fold);
3220 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3221 __isl_keep isl_pw_qpolynomial_fold *pwf);
3222 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3223 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3224 void isl_qpolynomial_fold_free(
3225 __isl_take isl_qpolynomial_fold *fold);
3226 void *isl_pw_qpolynomial_fold_free(
3227 __isl_take isl_pw_qpolynomial_fold *pwf);
3228 void isl_union_pw_qpolynomial_fold_free(
3229 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3231 =head3 Printing Piecewise Quasipolynomial Reductions
3233 Piecewise quasipolynomial reductions can be printed
3234 using the following function.
3236 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3237 __isl_take isl_printer *p,
3238 __isl_keep isl_pw_qpolynomial_fold *pwf);
3239 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3240 __isl_take isl_printer *p,
3241 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3243 For C<isl_printer_print_pw_qpolynomial_fold>,
3244 output format of the printer
3245 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3246 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3247 output format of the printer
3248 needs to be set to C<ISL_FORMAT_ISL>.
3249 In case of printing in C<ISL_FORMAT_C>, the user may want
3250 to set the names of all dimensions
3252 __isl_give isl_pw_qpolynomial_fold *
3253 isl_pw_qpolynomial_fold_set_dim_name(
3254 __isl_take isl_pw_qpolynomial_fold *pwf,
3255 enum isl_dim_type type, unsigned pos,
3258 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3260 To iterate over all piecewise quasipolynomial reductions in a union
3261 piecewise quasipolynomial reduction, use the following function
3263 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3264 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3265 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3266 void *user), void *user);
3268 To iterate over the cells in a piecewise quasipolynomial reduction,
3269 use either of the following two functions
3271 int isl_pw_qpolynomial_fold_foreach_piece(
3272 __isl_keep isl_pw_qpolynomial_fold *pwf,
3273 int (*fn)(__isl_take isl_set *set,
3274 __isl_take isl_qpolynomial_fold *fold,
3275 void *user), void *user);
3276 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3277 __isl_keep isl_pw_qpolynomial_fold *pwf,
3278 int (*fn)(__isl_take isl_set *set,
3279 __isl_take isl_qpolynomial_fold *fold,
3280 void *user), void *user);
3282 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3283 of the difference between these two functions.
3285 To iterate over all quasipolynomials in a reduction, use
3287 int isl_qpolynomial_fold_foreach_qpolynomial(
3288 __isl_keep isl_qpolynomial_fold *fold,
3289 int (*fn)(__isl_take isl_qpolynomial *qp,
3290 void *user), void *user);
3292 =head3 Operations on Piecewise Quasipolynomial Reductions
3294 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3295 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3297 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3298 __isl_take isl_pw_qpolynomial_fold *pwf1,
3299 __isl_take isl_pw_qpolynomial_fold *pwf2);
3301 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3302 __isl_take isl_pw_qpolynomial_fold *pwf1,
3303 __isl_take isl_pw_qpolynomial_fold *pwf2);
3305 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3306 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3307 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3309 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3310 __isl_take isl_pw_qpolynomial_fold *pwf,
3311 __isl_take isl_point *pnt);
3313 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3314 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3315 __isl_take isl_point *pnt);
3317 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3318 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3319 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3320 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3321 __isl_take isl_union_set *uset);
3323 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3324 __isl_take isl_pw_qpolynomial_fold *pwf);
3326 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3327 __isl_take isl_pw_qpolynomial_fold *pwf);
3329 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3330 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3332 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3333 __isl_take isl_pw_qpolynomial_fold *pwf,
3334 __isl_take isl_set *context);
3336 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3337 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3338 __isl_take isl_union_set *context);
3340 The gist operation applies the gist operation to each of
3341 the cells in the domain of the input piecewise quasipolynomial reduction.
3342 In future, the operation will also exploit the context
3343 to simplify the quasipolynomial reductions associated to each cell.
3345 __isl_give isl_pw_qpolynomial_fold *
3346 isl_set_apply_pw_qpolynomial_fold(
3347 __isl_take isl_set *set,
3348 __isl_take isl_pw_qpolynomial_fold *pwf,
3350 __isl_give isl_pw_qpolynomial_fold *
3351 isl_map_apply_pw_qpolynomial_fold(
3352 __isl_take isl_map *map,
3353 __isl_take isl_pw_qpolynomial_fold *pwf,
3355 __isl_give isl_union_pw_qpolynomial_fold *
3356 isl_union_set_apply_union_pw_qpolynomial_fold(
3357 __isl_take isl_union_set *uset,
3358 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3360 __isl_give isl_union_pw_qpolynomial_fold *
3361 isl_union_map_apply_union_pw_qpolynomial_fold(
3362 __isl_take isl_union_map *umap,
3363 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3366 The functions taking a map
3367 compose the given map with the given piecewise quasipolynomial reduction.
3368 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3369 over all elements in the intersection of the range of the map
3370 and the domain of the piecewise quasipolynomial reduction
3371 as a function of an element in the domain of the map.
3372 The functions taking a set compute a bound over all elements in the
3373 intersection of the set and the domain of the
3374 piecewise quasipolynomial reduction.
3376 =head2 Dependence Analysis
3378 C<isl> contains specialized functionality for performing
3379 array dataflow analysis. That is, given a I<sink> access relation
3380 and a collection of possible I<source> access relations,
3381 C<isl> can compute relations that describe
3382 for each iteration of the sink access, which iteration
3383 of which of the source access relations was the last
3384 to access the same data element before the given iteration
3386 To compute standard flow dependences, the sink should be
3387 a read, while the sources should be writes.
3388 If any of the source accesses are marked as being I<may>
3389 accesses, then there will be a dependence to the last
3390 I<must> access B<and> to any I<may> access that follows
3391 this last I<must> access.
3392 In particular, if I<all> sources are I<may> accesses,
3393 then memory based dependence analysis is performed.
3394 If, on the other hand, all sources are I<must> accesses,
3395 then value based dependence analysis is performed.
3397 #include <isl/flow.h>
3399 typedef int (*isl_access_level_before)(void *first, void *second);
3401 __isl_give isl_access_info *isl_access_info_alloc(
3402 __isl_take isl_map *sink,
3403 void *sink_user, isl_access_level_before fn,
3405 __isl_give isl_access_info *isl_access_info_add_source(
3406 __isl_take isl_access_info *acc,
3407 __isl_take isl_map *source, int must,
3409 void isl_access_info_free(__isl_take isl_access_info *acc);
3411 __isl_give isl_flow *isl_access_info_compute_flow(
3412 __isl_take isl_access_info *acc);
3414 int isl_flow_foreach(__isl_keep isl_flow *deps,
3415 int (*fn)(__isl_take isl_map *dep, int must,
3416 void *dep_user, void *user),
3418 __isl_give isl_map *isl_flow_get_no_source(
3419 __isl_keep isl_flow *deps, int must);
3420 void isl_flow_free(__isl_take isl_flow *deps);
3422 The function C<isl_access_info_compute_flow> performs the actual
3423 dependence analysis. The other functions are used to construct
3424 the input for this function or to read off the output.
3426 The input is collected in an C<isl_access_info>, which can
3427 be created through a call to C<isl_access_info_alloc>.
3428 The arguments to this functions are the sink access relation
3429 C<sink>, a token C<sink_user> used to identify the sink
3430 access to the user, a callback function for specifying the
3431 relative order of source and sink accesses, and the number
3432 of source access relations that will be added.
3433 The callback function has type C<int (*)(void *first, void *second)>.
3434 The function is called with two user supplied tokens identifying
3435 either a source or the sink and it should return the shared nesting
3436 level and the relative order of the two accesses.
3437 In particular, let I<n> be the number of loops shared by
3438 the two accesses. If C<first> precedes C<second> textually,
3439 then the function should return I<2 * n + 1>; otherwise,
3440 it should return I<2 * n>.
3441 The sources can be added to the C<isl_access_info> by performing
3442 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3443 C<must> indicates whether the source is a I<must> access
3444 or a I<may> access. Note that a multi-valued access relation
3445 should only be marked I<must> if every iteration in the domain
3446 of the relation accesses I<all> elements in its image.
3447 The C<source_user> token is again used to identify
3448 the source access. The range of the source access relation
3449 C<source> should have the same dimension as the range
3450 of the sink access relation.
3451 The C<isl_access_info_free> function should usually not be
3452 called explicitly, because it is called implicitly by
3453 C<isl_access_info_compute_flow>.
3455 The result of the dependence analysis is collected in an
3456 C<isl_flow>. There may be elements of
3457 the sink access for which no preceding source access could be
3458 found or for which all preceding sources are I<may> accesses.
3459 The relations containing these elements can be obtained through
3460 calls to C<isl_flow_get_no_source>, the first with C<must> set
3461 and the second with C<must> unset.
3462 In the case of standard flow dependence analysis,
3463 with the sink a read and the sources I<must> writes,
3464 the first relation corresponds to the reads from uninitialized
3465 array elements and the second relation is empty.
3466 The actual flow dependences can be extracted using
3467 C<isl_flow_foreach>. This function will call the user-specified
3468 callback function C<fn> for each B<non-empty> dependence between
3469 a source and the sink. The callback function is called
3470 with four arguments, the actual flow dependence relation
3471 mapping source iterations to sink iterations, a boolean that
3472 indicates whether it is a I<must> or I<may> dependence, a token
3473 identifying the source and an additional C<void *> with value
3474 equal to the third argument of the C<isl_flow_foreach> call.
3475 A dependence is marked I<must> if it originates from a I<must>
3476 source and if it is not followed by any I<may> sources.
3478 After finishing with an C<isl_flow>, the user should call
3479 C<isl_flow_free> to free all associated memory.
3481 A higher-level interface to dependence analysis is provided
3482 by the following function.
3484 #include <isl/flow.h>
3486 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3487 __isl_take isl_union_map *must_source,
3488 __isl_take isl_union_map *may_source,
3489 __isl_take isl_union_map *schedule,
3490 __isl_give isl_union_map **must_dep,
3491 __isl_give isl_union_map **may_dep,
3492 __isl_give isl_union_map **must_no_source,
3493 __isl_give isl_union_map **may_no_source);
3495 The arrays are identified by the tuple names of the ranges
3496 of the accesses. The iteration domains by the tuple names
3497 of the domains of the accesses and of the schedule.
3498 The relative order of the iteration domains is given by the
3499 schedule. The relations returned through C<must_no_source>
3500 and C<may_no_source> are subsets of C<sink>.
3501 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3502 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3503 any of the other arguments is treated as an error.
3507 B<The functionality described in this section is fairly new
3508 and may be subject to change.>
3510 The following function can be used to compute a schedule
3511 for a union of domains. The generated schedule respects
3512 all C<validity> dependences. That is, all dependence distances
3513 over these dependences in the scheduled space are lexicographically
3514 positive. The generated schedule schedule also tries to minimize
3515 the dependence distances over C<proximity> dependences.
3516 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3517 for groups of domains where the dependence distances have only
3518 non-negative values.
3519 The algorithm used to construct the schedule is similar to that
3522 #include <isl/schedule.h>
3523 __isl_give isl_schedule *isl_union_set_compute_schedule(
3524 __isl_take isl_union_set *domain,
3525 __isl_take isl_union_map *validity,
3526 __isl_take isl_union_map *proximity);
3527 void *isl_schedule_free(__isl_take isl_schedule *sched);
3529 A mapping from the domains to the scheduled space can be obtained
3530 from an C<isl_schedule> using the following function.
3532 __isl_give isl_union_map *isl_schedule_get_map(
3533 __isl_keep isl_schedule *sched);
3535 A representation of the schedule can be printed using
3537 __isl_give isl_printer *isl_printer_print_schedule(
3538 __isl_take isl_printer *p,
3539 __isl_keep isl_schedule *schedule);
3541 A representation of the schedule as a forest of bands can be obtained
3542 using the following function.
3544 __isl_give isl_band_list *isl_schedule_get_band_forest(
3545 __isl_keep isl_schedule *schedule);
3547 The list can be manipulated as explained in L<"Lists">.
3548 The bands inside the list can be copied and freed using the following
3551 #include <isl/band.h>
3552 __isl_give isl_band *isl_band_copy(
3553 __isl_keep isl_band *band);
3554 void *isl_band_free(__isl_take isl_band *band);
3556 Each band contains zero or more scheduling dimensions.
3557 These are referred to as the members of the band.
3558 The section of the schedule that corresponds to the band is
3559 referred to as the partial schedule of the band.
3560 For those nodes that participate in a band, the outer scheduling
3561 dimensions form the prefix schedule, while the inner scheduling
3562 dimensions form the suffix schedule.
3563 That is, if we take a cut of the band forest, then the union of
3564 the concatenations of the prefix, partial and suffix schedules of
3565 each band in the cut is equal to the entire schedule (modulo
3566 some possible padding at the end with zero scheduling dimensions).
3567 The properties of a band can be inspected using the following functions.
3569 #include <isl/band.h>
3570 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3572 int isl_band_has_children(__isl_keep isl_band *band);
3573 __isl_give isl_band_list *isl_band_get_children(
3574 __isl_keep isl_band *band);
3576 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3577 __isl_keep isl_band *band);
3578 __isl_give isl_union_map *isl_band_get_partial_schedule(
3579 __isl_keep isl_band *band);
3580 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3581 __isl_keep isl_band *band);
3583 int isl_band_n_member(__isl_keep isl_band *band);
3584 int isl_band_member_is_zero_distance(
3585 __isl_keep isl_band *band, int pos);
3587 Note that a scheduling dimension is considered to be ``zero
3588 distance'' if it does not carry any proximity dependences
3590 That is, if the dependence distances of the proximity
3591 dependences are all zero in that direction (for fixed
3592 iterations of outer bands).
3594 A representation of the band can be printed using
3596 #include <isl/band.h>
3597 __isl_give isl_printer *isl_printer_print_band(
3598 __isl_take isl_printer *p,
3599 __isl_keep isl_band *band);
3601 =head2 Parametric Vertex Enumeration
3603 The parametric vertex enumeration described in this section
3604 is mainly intended to be used internally and by the C<barvinok>
3607 #include <isl/vertices.h>
3608 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3609 __isl_keep isl_basic_set *bset);
3611 The function C<isl_basic_set_compute_vertices> performs the
3612 actual computation of the parametric vertices and the chamber
3613 decomposition and store the result in an C<isl_vertices> object.
3614 This information can be queried by either iterating over all
3615 the vertices or iterating over all the chambers or cells
3616 and then iterating over all vertices that are active on the chamber.
3618 int isl_vertices_foreach_vertex(
3619 __isl_keep isl_vertices *vertices,
3620 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3623 int isl_vertices_foreach_cell(
3624 __isl_keep isl_vertices *vertices,
3625 int (*fn)(__isl_take isl_cell *cell, void *user),
3627 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3628 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3631 Other operations that can be performed on an C<isl_vertices> object are
3634 isl_ctx *isl_vertices_get_ctx(
3635 __isl_keep isl_vertices *vertices);
3636 int isl_vertices_get_n_vertices(
3637 __isl_keep isl_vertices *vertices);
3638 void isl_vertices_free(__isl_take isl_vertices *vertices);
3640 Vertices can be inspected and destroyed using the following functions.
3642 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3643 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3644 __isl_give isl_basic_set *isl_vertex_get_domain(
3645 __isl_keep isl_vertex *vertex);
3646 __isl_give isl_basic_set *isl_vertex_get_expr(
3647 __isl_keep isl_vertex *vertex);
3648 void isl_vertex_free(__isl_take isl_vertex *vertex);
3650 C<isl_vertex_get_expr> returns a singleton parametric set describing
3651 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3653 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3654 B<rational> basic sets, so they should mainly be used for inspection
3655 and should not be mixed with integer sets.
3657 Chambers can be inspected and destroyed using the following functions.
3659 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3660 __isl_give isl_basic_set *isl_cell_get_domain(
3661 __isl_keep isl_cell *cell);
3662 void isl_cell_free(__isl_take isl_cell *cell);
3666 Although C<isl> is mainly meant to be used as a library,
3667 it also contains some basic applications that use some
3668 of the functionality of C<isl>.
3669 The input may be specified in either the L<isl format>
3670 or the L<PolyLib format>.
3672 =head2 C<isl_polyhedron_sample>
3674 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3675 an integer element of the polyhedron, if there is any.
3676 The first column in the output is the denominator and is always
3677 equal to 1. If the polyhedron contains no integer points,
3678 then a vector of length zero is printed.
3682 C<isl_pip> takes the same input as the C<example> program
3683 from the C<piplib> distribution, i.e., a set of constraints
3684 on the parameters, a line containing only -1 and finally a set
3685 of constraints on a parametric polyhedron.
3686 The coefficients of the parameters appear in the last columns
3687 (but before the final constant column).
3688 The output is the lexicographic minimum of the parametric polyhedron.
3689 As C<isl> currently does not have its own output format, the output
3690 is just a dump of the internal state.
3692 =head2 C<isl_polyhedron_minimize>
3694 C<isl_polyhedron_minimize> computes the minimum of some linear
3695 or affine objective function over the integer points in a polyhedron.
3696 If an affine objective function
3697 is given, then the constant should appear in the last column.
3699 =head2 C<isl_polytope_scan>
3701 Given a polytope, C<isl_polytope_scan> prints
3702 all integer points in the polytope.