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_dim(__isl_keep isl_local_space *ls,
695 enum isl_dim_type type);
696 const char *isl_local_space_get_dim_name(
697 __isl_keep isl_local_space *ls,
698 enum isl_dim_type type, unsigned pos);
699 __isl_give isl_local_space *isl_local_space_set_dim_name(
700 __isl_take isl_local_space *ls,
701 enum isl_dim_type type, unsigned pos, const char *s);
702 __isl_give isl_space *isl_local_space_get_space(
703 __isl_keep isl_local_space *ls);
704 __isl_give isl_div *isl_local_space_get_div(
705 __isl_keep isl_local_space *ls, int pos);
706 __isl_give isl_local_space *isl_local_space_copy(
707 __isl_keep isl_local_space *ls);
708 void *isl_local_space_free(__isl_take isl_local_space *ls);
710 Two local spaces can be compared using
712 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
713 __isl_keep isl_local_space *ls2);
715 Local spaces can be created from other local spaces
716 using the following functions.
718 __isl_give isl_local_space *isl_local_space_domain(
719 __isl_take isl_local_space *ls);
720 __isl_give isl_local_space *isl_local_space_from_domain(
721 __isl_take isl_local_space *ls);
722 __isl_give isl_local_space *isl_local_space_add_dims(
723 __isl_take isl_local_space *ls,
724 enum isl_dim_type type, unsigned n);
725 __isl_give isl_local_space *isl_local_space_insert_dims(
726 __isl_take isl_local_space *ls,
727 enum isl_dim_type type, unsigned first, unsigned n);
728 __isl_give isl_local_space *isl_local_space_drop_dims(
729 __isl_take isl_local_space *ls,
730 enum isl_dim_type type, unsigned first, unsigned n);
732 =head2 Input and Output
734 C<isl> supports its own input/output format, which is similar
735 to the C<Omega> format, but also supports the C<PolyLib> format
740 The C<isl> format is similar to that of C<Omega>, but has a different
741 syntax for describing the parameters and allows for the definition
742 of an existentially quantified variable as the integer division
743 of an affine expression.
744 For example, the set of integers C<i> between C<0> and C<n>
745 such that C<i % 10 <= 6> can be described as
747 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
750 A set or relation can have several disjuncts, separated
751 by the keyword C<or>. Each disjunct is either a conjunction
752 of constraints or a projection (C<exists>) of a conjunction
753 of constraints. The constraints are separated by the keyword
756 =head3 C<PolyLib> format
758 If the represented set is a union, then the first line
759 contains a single number representing the number of disjuncts.
760 Otherwise, a line containing the number C<1> is optional.
762 Each disjunct is represented by a matrix of constraints.
763 The first line contains two numbers representing
764 the number of rows and columns,
765 where the number of rows is equal to the number of constraints
766 and the number of columns is equal to two plus the number of variables.
767 The following lines contain the actual rows of the constraint matrix.
768 In each row, the first column indicates whether the constraint
769 is an equality (C<0>) or inequality (C<1>). The final column
770 corresponds to the constant term.
772 If the set is parametric, then the coefficients of the parameters
773 appear in the last columns before the constant column.
774 The coefficients of any existentially quantified variables appear
775 between those of the set variables and those of the parameters.
777 =head3 Extended C<PolyLib> format
779 The extended C<PolyLib> format is nearly identical to the
780 C<PolyLib> format. The only difference is that the line
781 containing the number of rows and columns of a constraint matrix
782 also contains four additional numbers:
783 the number of output dimensions, the number of input dimensions,
784 the number of local dimensions (i.e., the number of existentially
785 quantified variables) and the number of parameters.
786 For sets, the number of ``output'' dimensions is equal
787 to the number of set dimensions, while the number of ``input''
793 __isl_give isl_basic_set *isl_basic_set_read_from_file(
794 isl_ctx *ctx, FILE *input, int nparam);
795 __isl_give isl_basic_set *isl_basic_set_read_from_str(
796 isl_ctx *ctx, const char *str, int nparam);
797 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
798 FILE *input, int nparam);
799 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
800 const char *str, int nparam);
803 __isl_give isl_basic_map *isl_basic_map_read_from_file(
804 isl_ctx *ctx, FILE *input, int nparam);
805 __isl_give isl_basic_map *isl_basic_map_read_from_str(
806 isl_ctx *ctx, const char *str, int nparam);
807 __isl_give isl_map *isl_map_read_from_file(
808 isl_ctx *ctx, FILE *input, int nparam);
809 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
810 const char *str, int nparam);
812 #include <isl/union_set.h>
813 __isl_give isl_union_set *isl_union_set_read_from_file(
814 isl_ctx *ctx, FILE *input);
815 __isl_give isl_union_set *isl_union_set_read_from_str(
816 isl_ctx *ctx, const char *str);
818 #include <isl/union_map.h>
819 __isl_give isl_union_map *isl_union_map_read_from_file(
820 isl_ctx *ctx, FILE *input);
821 __isl_give isl_union_map *isl_union_map_read_from_str(
822 isl_ctx *ctx, const char *str);
824 The input format is autodetected and may be either the C<PolyLib> format
825 or the C<isl> format.
826 C<nparam> specifies how many of the final columns in
827 the C<PolyLib> format correspond to parameters.
828 If input is given in the C<isl> format, then the number
829 of parameters needs to be equal to C<nparam>.
830 If C<nparam> is negative, then any number of parameters
831 is accepted in the C<isl> format and zero parameters
832 are assumed in the C<PolyLib> format.
836 Before anything can be printed, an C<isl_printer> needs to
839 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
841 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
842 void isl_printer_free(__isl_take isl_printer *printer);
843 __isl_give char *isl_printer_get_str(
844 __isl_keep isl_printer *printer);
846 The behavior of the printer can be modified in various ways
848 __isl_give isl_printer *isl_printer_set_output_format(
849 __isl_take isl_printer *p, int output_format);
850 __isl_give isl_printer *isl_printer_set_indent(
851 __isl_take isl_printer *p, int indent);
852 __isl_give isl_printer *isl_printer_indent(
853 __isl_take isl_printer *p, int indent);
854 __isl_give isl_printer *isl_printer_set_prefix(
855 __isl_take isl_printer *p, const char *prefix);
856 __isl_give isl_printer *isl_printer_set_suffix(
857 __isl_take isl_printer *p, const char *suffix);
859 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
860 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
861 and defaults to C<ISL_FORMAT_ISL>.
862 Each line in the output is indented by C<indent> (set by
863 C<isl_printer_set_indent>) spaces
864 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
865 In the C<PolyLib> format output,
866 the coefficients of the existentially quantified variables
867 appear between those of the set variables and those
869 The function C<isl_printer_indent> increases the indentation
870 by the specified amount (which may be negative).
872 To actually print something, use
875 __isl_give isl_printer *isl_printer_print_basic_set(
876 __isl_take isl_printer *printer,
877 __isl_keep isl_basic_set *bset);
878 __isl_give isl_printer *isl_printer_print_set(
879 __isl_take isl_printer *printer,
880 __isl_keep isl_set *set);
883 __isl_give isl_printer *isl_printer_print_basic_map(
884 __isl_take isl_printer *printer,
885 __isl_keep isl_basic_map *bmap);
886 __isl_give isl_printer *isl_printer_print_map(
887 __isl_take isl_printer *printer,
888 __isl_keep isl_map *map);
890 #include <isl/union_set.h>
891 __isl_give isl_printer *isl_printer_print_union_set(
892 __isl_take isl_printer *p,
893 __isl_keep isl_union_set *uset);
895 #include <isl/union_map.h>
896 __isl_give isl_printer *isl_printer_print_union_map(
897 __isl_take isl_printer *p,
898 __isl_keep isl_union_map *umap);
900 When called on a file printer, the following function flushes
901 the file. When called on a string printer, the buffer is cleared.
903 __isl_give isl_printer *isl_printer_flush(
904 __isl_take isl_printer *p);
906 =head2 Creating New Sets and Relations
908 C<isl> has functions for creating some standard sets and relations.
912 =item * Empty sets and relations
914 __isl_give isl_basic_set *isl_basic_set_empty(
915 __isl_take isl_space *space);
916 __isl_give isl_basic_map *isl_basic_map_empty(
917 __isl_take isl_space *space);
918 __isl_give isl_set *isl_set_empty(
919 __isl_take isl_space *space);
920 __isl_give isl_map *isl_map_empty(
921 __isl_take isl_space *space);
922 __isl_give isl_union_set *isl_union_set_empty(
923 __isl_take isl_space *space);
924 __isl_give isl_union_map *isl_union_map_empty(
925 __isl_take isl_space *space);
927 For C<isl_union_set>s and C<isl_union_map>s, the space
928 is only used to specify the parameters.
930 =item * Universe sets and relations
932 __isl_give isl_basic_set *isl_basic_set_universe(
933 __isl_take isl_space *space);
934 __isl_give isl_basic_map *isl_basic_map_universe(
935 __isl_take isl_space *space);
936 __isl_give isl_set *isl_set_universe(
937 __isl_take isl_space *space);
938 __isl_give isl_map *isl_map_universe(
939 __isl_take isl_space *space);
940 __isl_give isl_union_set *isl_union_set_universe(
941 __isl_take isl_union_set *uset);
942 __isl_give isl_union_map *isl_union_map_universe(
943 __isl_take isl_union_map *umap);
945 The sets and relations constructed by the functions above
946 contain all integer values, while those constructed by the
947 functions below only contain non-negative values.
949 __isl_give isl_basic_set *isl_basic_set_nat_universe(
950 __isl_take isl_space *space);
951 __isl_give isl_basic_map *isl_basic_map_nat_universe(
952 __isl_take isl_space *space);
953 __isl_give isl_set *isl_set_nat_universe(
954 __isl_take isl_space *space);
955 __isl_give isl_map *isl_map_nat_universe(
956 __isl_take isl_space *space);
958 =item * Identity relations
960 __isl_give isl_basic_map *isl_basic_map_identity(
961 __isl_take isl_space *space);
962 __isl_give isl_map *isl_map_identity(
963 __isl_take isl_space *space);
965 The number of input and output dimensions in C<space> needs
968 =item * Lexicographic order
970 __isl_give isl_map *isl_map_lex_lt(
971 __isl_take isl_space *set_space);
972 __isl_give isl_map *isl_map_lex_le(
973 __isl_take isl_space *set_space);
974 __isl_give isl_map *isl_map_lex_gt(
975 __isl_take isl_space *set_space);
976 __isl_give isl_map *isl_map_lex_ge(
977 __isl_take isl_space *set_space);
978 __isl_give isl_map *isl_map_lex_lt_first(
979 __isl_take isl_space *space, unsigned n);
980 __isl_give isl_map *isl_map_lex_le_first(
981 __isl_take isl_space *space, unsigned n);
982 __isl_give isl_map *isl_map_lex_gt_first(
983 __isl_take isl_space *space, unsigned n);
984 __isl_give isl_map *isl_map_lex_ge_first(
985 __isl_take isl_space *space, unsigned n);
987 The first four functions take a space for a B<set>
988 and return relations that express that the elements in the domain
989 are lexicographically less
990 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
991 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
992 than the elements in the range.
993 The last four functions take a space for a map
994 and return relations that express that the first C<n> dimensions
995 in the domain are lexicographically less
996 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
997 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
998 than the first C<n> dimensions in the range.
1002 A basic set or relation can be converted to a set or relation
1003 using the following functions.
1005 __isl_give isl_set *isl_set_from_basic_set(
1006 __isl_take isl_basic_set *bset);
1007 __isl_give isl_map *isl_map_from_basic_map(
1008 __isl_take isl_basic_map *bmap);
1010 Sets and relations can be converted to union sets and relations
1011 using the following functions.
1013 __isl_give isl_union_map *isl_union_map_from_map(
1014 __isl_take isl_map *map);
1015 __isl_give isl_union_set *isl_union_set_from_set(
1016 __isl_take isl_set *set);
1018 The inverse conversions below can only be used if the input
1019 union set or relation is known to contain elements in exactly one
1022 __isl_give isl_set *isl_set_from_union_set(
1023 __isl_take isl_union_set *uset);
1024 __isl_give isl_map *isl_map_from_union_map(
1025 __isl_take isl_union_map *umap);
1027 Sets and relations can be copied and freed again using the following
1030 __isl_give isl_basic_set *isl_basic_set_copy(
1031 __isl_keep isl_basic_set *bset);
1032 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1033 __isl_give isl_union_set *isl_union_set_copy(
1034 __isl_keep isl_union_set *uset);
1035 __isl_give isl_basic_map *isl_basic_map_copy(
1036 __isl_keep isl_basic_map *bmap);
1037 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1038 __isl_give isl_union_map *isl_union_map_copy(
1039 __isl_keep isl_union_map *umap);
1040 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1041 void isl_set_free(__isl_take isl_set *set);
1042 void *isl_union_set_free(__isl_take isl_union_set *uset);
1043 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1044 void isl_map_free(__isl_take isl_map *map);
1045 void *isl_union_map_free(__isl_take isl_union_map *umap);
1047 Other sets and relations can be constructed by starting
1048 from a universe set or relation, adding equality and/or
1049 inequality constraints and then projecting out the
1050 existentially quantified variables, if any.
1051 Constraints can be constructed, manipulated and
1052 added to (or removed from) (basic) sets and relations
1053 using the following functions.
1055 #include <isl/constraint.h>
1056 __isl_give isl_constraint *isl_equality_alloc(
1057 __isl_take isl_space *space);
1058 __isl_give isl_constraint *isl_inequality_alloc(
1059 __isl_take isl_space *space);
1060 __isl_give isl_constraint *isl_constraint_set_constant(
1061 __isl_take isl_constraint *constraint, isl_int v);
1062 __isl_give isl_constraint *isl_constraint_set_constant_si(
1063 __isl_take isl_constraint *constraint, int v);
1064 __isl_give isl_constraint *isl_constraint_set_coefficient(
1065 __isl_take isl_constraint *constraint,
1066 enum isl_dim_type type, int pos, isl_int v);
1067 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1068 __isl_take isl_constraint *constraint,
1069 enum isl_dim_type type, int pos, int v);
1070 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1071 __isl_take isl_basic_map *bmap,
1072 __isl_take isl_constraint *constraint);
1073 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1074 __isl_take isl_basic_set *bset,
1075 __isl_take isl_constraint *constraint);
1076 __isl_give isl_map *isl_map_add_constraint(
1077 __isl_take isl_map *map,
1078 __isl_take isl_constraint *constraint);
1079 __isl_give isl_set *isl_set_add_constraint(
1080 __isl_take isl_set *set,
1081 __isl_take isl_constraint *constraint);
1082 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1083 __isl_take isl_basic_set *bset,
1084 __isl_take isl_constraint *constraint);
1086 For example, to create a set containing the even integers
1087 between 10 and 42, you would use the following code.
1092 isl_basic_set *bset;
1095 space = isl_space_set_alloc(ctx, 0, 2);
1096 bset = isl_basic_set_universe(isl_space_copy(space));
1098 c = isl_equality_alloc(isl_space_copy(space));
1099 isl_int_set_si(v, -1);
1100 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1101 isl_int_set_si(v, 2);
1102 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1103 bset = isl_basic_set_add_constraint(bset, c);
1105 c = isl_inequality_alloc(isl_space_copy(space));
1106 isl_int_set_si(v, -10);
1107 isl_constraint_set_constant(c, v);
1108 isl_int_set_si(v, 1);
1109 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1110 bset = isl_basic_set_add_constraint(bset, c);
1112 c = isl_inequality_alloc(space);
1113 isl_int_set_si(v, 42);
1114 isl_constraint_set_constant(c, v);
1115 isl_int_set_si(v, -1);
1116 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1117 bset = isl_basic_set_add_constraint(bset, c);
1119 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1125 isl_basic_set *bset;
1126 bset = isl_basic_set_read_from_str(ctx,
1127 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1129 A basic set or relation can also be constructed from two matrices
1130 describing the equalities and the inequalities.
1132 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1133 __isl_take isl_space *space,
1134 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1135 enum isl_dim_type c1,
1136 enum isl_dim_type c2, enum isl_dim_type c3,
1137 enum isl_dim_type c4);
1138 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1139 __isl_take isl_space *space,
1140 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1141 enum isl_dim_type c1,
1142 enum isl_dim_type c2, enum isl_dim_type c3,
1143 enum isl_dim_type c4, enum isl_dim_type c5);
1145 The C<isl_dim_type> arguments indicate the order in which
1146 different kinds of variables appear in the input matrices
1147 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1148 C<isl_dim_set> and C<isl_dim_div> for sets and
1149 of C<isl_dim_cst>, C<isl_dim_param>,
1150 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1152 A (basic) set or relation can also be constructed from a (piecewise)
1154 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1156 __isl_give isl_basic_map *isl_basic_map_from_aff(
1157 __isl_take isl_aff *aff);
1158 __isl_give isl_set *isl_set_from_pw_aff(
1159 __isl_take isl_pw_aff *pwaff);
1160 __isl_give isl_map *isl_map_from_pw_aff(
1161 __isl_take isl_pw_aff *pwaff);
1162 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1163 __isl_take isl_space *domain_space,
1164 __isl_take isl_aff_list *list);
1166 The C<domain_dim> argument describes the domain of the resulting
1167 basic relation. It is required because the C<list> may consist
1168 of zero affine expressions.
1170 =head2 Inspecting Sets and Relations
1172 Usually, the user should not have to care about the actual constraints
1173 of the sets and maps, but should instead apply the abstract operations
1174 explained in the following sections.
1175 Occasionally, however, it may be required to inspect the individual
1176 coefficients of the constraints. This section explains how to do so.
1177 In these cases, it may also be useful to have C<isl> compute
1178 an explicit representation of the existentially quantified variables.
1180 __isl_give isl_set *isl_set_compute_divs(
1181 __isl_take isl_set *set);
1182 __isl_give isl_map *isl_map_compute_divs(
1183 __isl_take isl_map *map);
1184 __isl_give isl_union_set *isl_union_set_compute_divs(
1185 __isl_take isl_union_set *uset);
1186 __isl_give isl_union_map *isl_union_map_compute_divs(
1187 __isl_take isl_union_map *umap);
1189 This explicit representation defines the existentially quantified
1190 variables as integer divisions of the other variables, possibly
1191 including earlier existentially quantified variables.
1192 An explicitly represented existentially quantified variable therefore
1193 has a unique value when the values of the other variables are known.
1194 If, furthermore, the same existentials, i.e., existentials
1195 with the same explicit representations, should appear in the
1196 same order in each of the disjuncts of a set or map, then the user should call
1197 either of the following functions.
1199 __isl_give isl_set *isl_set_align_divs(
1200 __isl_take isl_set *set);
1201 __isl_give isl_map *isl_map_align_divs(
1202 __isl_take isl_map *map);
1204 Alternatively, the existentially quantified variables can be removed
1205 using the following functions, which compute an overapproximation.
1207 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1208 __isl_take isl_basic_set *bset);
1209 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1210 __isl_take isl_basic_map *bmap);
1211 __isl_give isl_set *isl_set_remove_divs(
1212 __isl_take isl_set *set);
1213 __isl_give isl_map *isl_map_remove_divs(
1214 __isl_take isl_map *map);
1216 To iterate over all the sets or maps in a union set or map, use
1218 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1219 int (*fn)(__isl_take isl_set *set, void *user),
1221 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1222 int (*fn)(__isl_take isl_map *map, void *user),
1225 The number of sets or maps in a union set or map can be obtained
1228 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1229 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1231 To extract the set or map in a given space from a union, use
1233 __isl_give isl_set *isl_union_set_extract_set(
1234 __isl_keep isl_union_set *uset,
1235 __isl_take isl_space *space);
1236 __isl_give isl_map *isl_union_map_extract_map(
1237 __isl_keep isl_union_map *umap,
1238 __isl_take isl_space *space);
1240 To iterate over all the basic sets or maps in a set or map, use
1242 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1243 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1245 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1246 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1249 The callback function C<fn> should return 0 if successful and
1250 -1 if an error occurs. In the latter case, or if any other error
1251 occurs, the above functions will return -1.
1253 It should be noted that C<isl> does not guarantee that
1254 the basic sets or maps passed to C<fn> are disjoint.
1255 If this is required, then the user should call one of
1256 the following functions first.
1258 __isl_give isl_set *isl_set_make_disjoint(
1259 __isl_take isl_set *set);
1260 __isl_give isl_map *isl_map_make_disjoint(
1261 __isl_take isl_map *map);
1263 The number of basic sets in a set can be obtained
1266 int isl_set_n_basic_set(__isl_keep isl_set *set);
1268 To iterate over the constraints of a basic set or map, use
1270 #include <isl/constraint.h>
1272 int isl_basic_map_foreach_constraint(
1273 __isl_keep isl_basic_map *bmap,
1274 int (*fn)(__isl_take isl_constraint *c, void *user),
1276 void *isl_constraint_free(__isl_take isl_constraint *c);
1278 Again, the callback function C<fn> should return 0 if successful and
1279 -1 if an error occurs. In the latter case, or if any other error
1280 occurs, the above functions will return -1.
1281 The constraint C<c> represents either an equality or an inequality.
1282 Use the following function to find out whether a constraint
1283 represents an equality. If not, it represents an inequality.
1285 int isl_constraint_is_equality(
1286 __isl_keep isl_constraint *constraint);
1288 The coefficients of the constraints can be inspected using
1289 the following functions.
1291 void isl_constraint_get_constant(
1292 __isl_keep isl_constraint *constraint, isl_int *v);
1293 void isl_constraint_get_coefficient(
1294 __isl_keep isl_constraint *constraint,
1295 enum isl_dim_type type, int pos, isl_int *v);
1296 int isl_constraint_involves_dims(
1297 __isl_keep isl_constraint *constraint,
1298 enum isl_dim_type type, unsigned first, unsigned n);
1300 The explicit representations of the existentially quantified
1301 variables can be inspected using the following functions.
1302 Note that the user is only allowed to use these functions
1303 if the inspected set or map is the result of a call
1304 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1306 __isl_give isl_div *isl_constraint_div(
1307 __isl_keep isl_constraint *constraint, int pos);
1308 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1309 void isl_div_get_constant(__isl_keep isl_div *div,
1311 void isl_div_get_denominator(__isl_keep isl_div *div,
1313 void isl_div_get_coefficient(__isl_keep isl_div *div,
1314 enum isl_dim_type type, int pos, isl_int *v);
1316 To obtain the constraints of a basic set or map in matrix
1317 form, use the following functions.
1319 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1320 __isl_keep isl_basic_set *bset,
1321 enum isl_dim_type c1, enum isl_dim_type c2,
1322 enum isl_dim_type c3, enum isl_dim_type c4);
1323 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1324 __isl_keep isl_basic_set *bset,
1325 enum isl_dim_type c1, enum isl_dim_type c2,
1326 enum isl_dim_type c3, enum isl_dim_type c4);
1327 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1328 __isl_keep isl_basic_map *bmap,
1329 enum isl_dim_type c1,
1330 enum isl_dim_type c2, enum isl_dim_type c3,
1331 enum isl_dim_type c4, enum isl_dim_type c5);
1332 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1333 __isl_keep isl_basic_map *bmap,
1334 enum isl_dim_type c1,
1335 enum isl_dim_type c2, enum isl_dim_type c3,
1336 enum isl_dim_type c4, enum isl_dim_type c5);
1338 The C<isl_dim_type> arguments dictate the order in which
1339 different kinds of variables appear in the resulting matrix
1340 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1341 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1343 The number of parameters, input, output or set dimensions can
1344 be obtained using the following functions.
1346 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1347 enum isl_dim_type type);
1348 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1349 enum isl_dim_type type);
1350 unsigned isl_set_dim(__isl_keep isl_set *set,
1351 enum isl_dim_type type);
1352 unsigned isl_map_dim(__isl_keep isl_map *map,
1353 enum isl_dim_type type);
1355 To check whether the description of a set or relation depends
1356 on one or more given dimensions, it is not necessary to iterate over all
1357 constraints. Instead the following functions can be used.
1359 int isl_basic_set_involves_dims(
1360 __isl_keep isl_basic_set *bset,
1361 enum isl_dim_type type, unsigned first, unsigned n);
1362 int isl_set_involves_dims(__isl_keep isl_set *set,
1363 enum isl_dim_type type, unsigned first, unsigned n);
1364 int isl_basic_map_involves_dims(
1365 __isl_keep isl_basic_map *bmap,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1367 int isl_map_involves_dims(__isl_keep isl_map *map,
1368 enum isl_dim_type type, unsigned first, unsigned n);
1370 Similarly, the following functions can be used to check whether
1371 a given dimension is involved in any lower or upper bound.
1373 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1374 enum isl_dim_type type, unsigned pos);
1375 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1376 enum isl_dim_type type, unsigned pos);
1378 The identifiers or names of the domain and range spaces of a set
1379 or relation can be read off or set using the following functions.
1381 __isl_give isl_set *isl_set_set_tuple_id(
1382 __isl_take isl_set *set, __isl_take isl_id *id);
1383 __isl_give isl_set *isl_set_reset_tuple_id(
1384 __isl_take isl_set *set);
1385 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1386 __isl_give isl_id *isl_set_get_tuple_id(
1387 __isl_keep isl_set *set);
1388 __isl_give isl_map *isl_map_set_tuple_id(
1389 __isl_take isl_map *map, enum isl_dim_type type,
1390 __isl_take isl_id *id);
1391 __isl_give isl_map *isl_map_reset_tuple_id(
1392 __isl_take isl_map *map, enum isl_dim_type type);
1393 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1394 enum isl_dim_type type);
1395 __isl_give isl_id *isl_map_get_tuple_id(
1396 __isl_keep isl_map *map, enum isl_dim_type type);
1398 const char *isl_basic_set_get_tuple_name(
1399 __isl_keep isl_basic_set *bset);
1400 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1401 __isl_take isl_basic_set *set, const char *s);
1402 const char *isl_set_get_tuple_name(
1403 __isl_keep isl_set *set);
1404 const char *isl_basic_map_get_tuple_name(
1405 __isl_keep isl_basic_map *bmap,
1406 enum isl_dim_type type);
1407 const char *isl_map_get_tuple_name(
1408 __isl_keep isl_map *map,
1409 enum isl_dim_type type);
1411 As with C<isl_space_get_tuple_name>, the value returned points to
1412 an internal data structure.
1413 The identifiers, positions or names of individual dimensions can be
1414 read off using the following functions.
1416 __isl_give isl_set *isl_set_set_dim_id(
1417 __isl_take isl_set *set, enum isl_dim_type type,
1418 unsigned pos, __isl_take isl_id *id);
1419 int isl_set_has_dim_id(__isl_keep isl_set *set,
1420 enum isl_dim_type type, unsigned pos);
1421 __isl_give isl_id *isl_set_get_dim_id(
1422 __isl_keep isl_set *set, enum isl_dim_type type,
1424 __isl_give isl_map *isl_map_set_dim_id(
1425 __isl_take isl_map *map, enum isl_dim_type type,
1426 unsigned pos, __isl_take isl_id *id);
1427 int isl_map_has_dim_id(__isl_keep isl_map *map,
1428 enum isl_dim_type type, unsigned pos);
1429 __isl_give isl_id *isl_map_get_dim_id(
1430 __isl_keep isl_map *map, enum isl_dim_type type,
1433 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1434 enum isl_dim_type type, __isl_keep isl_id *id);
1435 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1436 enum isl_dim_type type, __isl_keep isl_id *id);
1438 const char *isl_constraint_get_dim_name(
1439 __isl_keep isl_constraint *constraint,
1440 enum isl_dim_type type, unsigned pos);
1441 const char *isl_basic_set_get_dim_name(
1442 __isl_keep isl_basic_set *bset,
1443 enum isl_dim_type type, unsigned pos);
1444 const char *isl_set_get_dim_name(
1445 __isl_keep isl_set *set,
1446 enum isl_dim_type type, unsigned pos);
1447 const char *isl_basic_map_get_dim_name(
1448 __isl_keep isl_basic_map *bmap,
1449 enum isl_dim_type type, unsigned pos);
1450 const char *isl_map_get_dim_name(
1451 __isl_keep isl_map *map,
1452 enum isl_dim_type type, unsigned pos);
1454 These functions are mostly useful to obtain the identifiers, positions
1455 or names of the parameters. Identifiers of individual dimensions are
1456 essentially only useful for printing. They are ignored by all other
1457 operations and may not be preserved across those operations.
1461 =head3 Unary Properties
1467 The following functions test whether the given set or relation
1468 contains any integer points. The ``plain'' variants do not perform
1469 any computations, but simply check if the given set or relation
1470 is already known to be empty.
1472 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1473 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1474 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1475 int isl_set_is_empty(__isl_keep isl_set *set);
1476 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1477 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1478 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1479 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1480 int isl_map_is_empty(__isl_keep isl_map *map);
1481 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1483 =item * Universality
1485 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1486 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1487 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1489 =item * Single-valuedness
1491 int isl_map_is_single_valued(__isl_keep isl_map *map);
1492 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1496 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1497 int isl_map_is_injective(__isl_keep isl_map *map);
1498 int isl_union_map_plain_is_injective(
1499 __isl_keep isl_union_map *umap);
1500 int isl_union_map_is_injective(
1501 __isl_keep isl_union_map *umap);
1505 int isl_map_is_bijective(__isl_keep isl_map *map);
1506 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1510 int isl_basic_map_plain_is_fixed(
1511 __isl_keep isl_basic_map *bmap,
1512 enum isl_dim_type type, unsigned pos,
1514 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1515 enum isl_dim_type type, unsigned pos,
1518 Check if the relation obviously lies on a hyperplane where the given dimension
1519 has a fixed value and if so, return that value in C<*val>.
1523 To check whether a set is a parameter domain, use this function:
1525 int isl_set_is_params(__isl_keep isl_set *set);
1529 The following functions check whether the domain of the given
1530 (basic) set is a wrapped relation.
1532 int isl_basic_set_is_wrapping(
1533 __isl_keep isl_basic_set *bset);
1534 int isl_set_is_wrapping(__isl_keep isl_set *set);
1536 =item * Internal Product
1538 int isl_basic_map_can_zip(
1539 __isl_keep isl_basic_map *bmap);
1540 int isl_map_can_zip(__isl_keep isl_map *map);
1542 Check whether the product of domain and range of the given relation
1544 i.e., whether both domain and range are nested relations.
1548 =head3 Binary Properties
1554 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1555 __isl_keep isl_set *set2);
1556 int isl_set_is_equal(__isl_keep isl_set *set1,
1557 __isl_keep isl_set *set2);
1558 int isl_union_set_is_equal(
1559 __isl_keep isl_union_set *uset1,
1560 __isl_keep isl_union_set *uset2);
1561 int isl_basic_map_is_equal(
1562 __isl_keep isl_basic_map *bmap1,
1563 __isl_keep isl_basic_map *bmap2);
1564 int isl_map_is_equal(__isl_keep isl_map *map1,
1565 __isl_keep isl_map *map2);
1566 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1567 __isl_keep isl_map *map2);
1568 int isl_union_map_is_equal(
1569 __isl_keep isl_union_map *umap1,
1570 __isl_keep isl_union_map *umap2);
1572 =item * Disjointness
1574 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1575 __isl_keep isl_set *set2);
1579 int isl_set_is_subset(__isl_keep isl_set *set1,
1580 __isl_keep isl_set *set2);
1581 int isl_set_is_strict_subset(
1582 __isl_keep isl_set *set1,
1583 __isl_keep isl_set *set2);
1584 int isl_union_set_is_subset(
1585 __isl_keep isl_union_set *uset1,
1586 __isl_keep isl_union_set *uset2);
1587 int isl_union_set_is_strict_subset(
1588 __isl_keep isl_union_set *uset1,
1589 __isl_keep isl_union_set *uset2);
1590 int isl_basic_map_is_subset(
1591 __isl_keep isl_basic_map *bmap1,
1592 __isl_keep isl_basic_map *bmap2);
1593 int isl_basic_map_is_strict_subset(
1594 __isl_keep isl_basic_map *bmap1,
1595 __isl_keep isl_basic_map *bmap2);
1596 int isl_map_is_subset(
1597 __isl_keep isl_map *map1,
1598 __isl_keep isl_map *map2);
1599 int isl_map_is_strict_subset(
1600 __isl_keep isl_map *map1,
1601 __isl_keep isl_map *map2);
1602 int isl_union_map_is_subset(
1603 __isl_keep isl_union_map *umap1,
1604 __isl_keep isl_union_map *umap2);
1605 int isl_union_map_is_strict_subset(
1606 __isl_keep isl_union_map *umap1,
1607 __isl_keep isl_union_map *umap2);
1611 =head2 Unary Operations
1617 __isl_give isl_set *isl_set_complement(
1618 __isl_take isl_set *set);
1622 __isl_give isl_basic_map *isl_basic_map_reverse(
1623 __isl_take isl_basic_map *bmap);
1624 __isl_give isl_map *isl_map_reverse(
1625 __isl_take isl_map *map);
1626 __isl_give isl_union_map *isl_union_map_reverse(
1627 __isl_take isl_union_map *umap);
1631 __isl_give isl_basic_set *isl_basic_set_project_out(
1632 __isl_take isl_basic_set *bset,
1633 enum isl_dim_type type, unsigned first, unsigned n);
1634 __isl_give isl_basic_map *isl_basic_map_project_out(
1635 __isl_take isl_basic_map *bmap,
1636 enum isl_dim_type type, unsigned first, unsigned n);
1637 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1638 enum isl_dim_type type, unsigned first, unsigned n);
1639 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1640 enum isl_dim_type type, unsigned first, unsigned n);
1641 __isl_give isl_basic_set *isl_basic_set_params(
1642 __isl_take isl_basic_set *bset);
1643 __isl_give isl_basic_set *isl_basic_map_domain(
1644 __isl_take isl_basic_map *bmap);
1645 __isl_give isl_basic_set *isl_basic_map_range(
1646 __isl_take isl_basic_map *bmap);
1647 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1648 __isl_give isl_set *isl_map_domain(
1649 __isl_take isl_map *bmap);
1650 __isl_give isl_set *isl_map_range(
1651 __isl_take isl_map *map);
1652 __isl_give isl_union_set *isl_union_map_domain(
1653 __isl_take isl_union_map *umap);
1654 __isl_give isl_union_set *isl_union_map_range(
1655 __isl_take isl_union_map *umap);
1657 __isl_give isl_basic_map *isl_basic_map_domain_map(
1658 __isl_take isl_basic_map *bmap);
1659 __isl_give isl_basic_map *isl_basic_map_range_map(
1660 __isl_take isl_basic_map *bmap);
1661 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1662 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1663 __isl_give isl_union_map *isl_union_map_domain_map(
1664 __isl_take isl_union_map *umap);
1665 __isl_give isl_union_map *isl_union_map_range_map(
1666 __isl_take isl_union_map *umap);
1668 The functions above construct a (basic, regular or union) relation
1669 that maps (a wrapped version of) the input relation to its domain or range.
1673 __isl_give isl_set *isl_set_eliminate(
1674 __isl_take isl_set *set, enum isl_dim_type type,
1675 unsigned first, unsigned n);
1677 Eliminate the coefficients for the given dimensions from the constraints,
1678 without removing the dimensions.
1682 __isl_give isl_basic_set *isl_basic_set_fix(
1683 __isl_take isl_basic_set *bset,
1684 enum isl_dim_type type, unsigned pos,
1686 __isl_give isl_basic_set *isl_basic_set_fix_si(
1687 __isl_take isl_basic_set *bset,
1688 enum isl_dim_type type, unsigned pos, int value);
1689 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1690 enum isl_dim_type type, unsigned pos,
1692 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1693 enum isl_dim_type type, unsigned pos, int value);
1694 __isl_give isl_basic_map *isl_basic_map_fix_si(
1695 __isl_take isl_basic_map *bmap,
1696 enum isl_dim_type type, unsigned pos, int value);
1697 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1698 enum isl_dim_type type, unsigned pos, int value);
1700 Intersect the set or relation with the hyperplane where the given
1701 dimension has the fixed given value.
1703 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1704 enum isl_dim_type type1, int pos1,
1705 enum isl_dim_type type2, int pos2);
1706 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1707 enum isl_dim_type type1, int pos1,
1708 enum isl_dim_type type2, int pos2);
1710 Intersect the set or relation with the hyperplane where the given
1711 dimensions are equal to each other.
1713 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1714 enum isl_dim_type type1, int pos1,
1715 enum isl_dim_type type2, int pos2);
1717 Intersect the relation with the hyperplane where the given
1718 dimensions have opposite values.
1722 __isl_give isl_map *isl_set_identity(
1723 __isl_take isl_set *set);
1724 __isl_give isl_union_map *isl_union_set_identity(
1725 __isl_take isl_union_set *uset);
1727 Construct an identity relation on the given (union) set.
1731 __isl_give isl_basic_set *isl_basic_map_deltas(
1732 __isl_take isl_basic_map *bmap);
1733 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1734 __isl_give isl_union_set *isl_union_map_deltas(
1735 __isl_take isl_union_map *umap);
1737 These functions return a (basic) set containing the differences
1738 between image elements and corresponding domain elements in the input.
1740 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1741 __isl_take isl_basic_map *bmap);
1742 __isl_give isl_map *isl_map_deltas_map(
1743 __isl_take isl_map *map);
1744 __isl_give isl_union_map *isl_union_map_deltas_map(
1745 __isl_take isl_union_map *umap);
1747 The functions above construct a (basic, regular or union) relation
1748 that maps (a wrapped version of) the input relation to its delta set.
1752 Simplify the representation of a set or relation by trying
1753 to combine pairs of basic sets or relations into a single
1754 basic set or relation.
1756 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1757 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1758 __isl_give isl_union_set *isl_union_set_coalesce(
1759 __isl_take isl_union_set *uset);
1760 __isl_give isl_union_map *isl_union_map_coalesce(
1761 __isl_take isl_union_map *umap);
1763 =item * Detecting equalities
1765 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1766 __isl_take isl_basic_set *bset);
1767 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1768 __isl_take isl_basic_map *bmap);
1769 __isl_give isl_set *isl_set_detect_equalities(
1770 __isl_take isl_set *set);
1771 __isl_give isl_map *isl_map_detect_equalities(
1772 __isl_take isl_map *map);
1773 __isl_give isl_union_set *isl_union_set_detect_equalities(
1774 __isl_take isl_union_set *uset);
1775 __isl_give isl_union_map *isl_union_map_detect_equalities(
1776 __isl_take isl_union_map *umap);
1778 Simplify the representation of a set or relation by detecting implicit
1781 =item * Removing redundant constraints
1783 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1784 __isl_take isl_basic_set *bset);
1785 __isl_give isl_set *isl_set_remove_redundancies(
1786 __isl_take isl_set *set);
1787 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1788 __isl_take isl_basic_map *bmap);
1789 __isl_give isl_map *isl_map_remove_redundancies(
1790 __isl_take isl_map *map);
1794 __isl_give isl_basic_set *isl_set_convex_hull(
1795 __isl_take isl_set *set);
1796 __isl_give isl_basic_map *isl_map_convex_hull(
1797 __isl_take isl_map *map);
1799 If the input set or relation has any existentially quantified
1800 variables, then the result of these operations is currently undefined.
1804 __isl_give isl_basic_set *isl_set_simple_hull(
1805 __isl_take isl_set *set);
1806 __isl_give isl_basic_map *isl_map_simple_hull(
1807 __isl_take isl_map *map);
1808 __isl_give isl_union_map *isl_union_map_simple_hull(
1809 __isl_take isl_union_map *umap);
1811 These functions compute a single basic set or relation
1812 that contains the whole input set or relation.
1813 In particular, the output is described by translates
1814 of the constraints describing the basic sets or relations in the input.
1818 (See \autoref{s:simple hull}.)
1824 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1825 __isl_take isl_basic_set *bset);
1826 __isl_give isl_basic_set *isl_set_affine_hull(
1827 __isl_take isl_set *set);
1828 __isl_give isl_union_set *isl_union_set_affine_hull(
1829 __isl_take isl_union_set *uset);
1830 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1831 __isl_take isl_basic_map *bmap);
1832 __isl_give isl_basic_map *isl_map_affine_hull(
1833 __isl_take isl_map *map);
1834 __isl_give isl_union_map *isl_union_map_affine_hull(
1835 __isl_take isl_union_map *umap);
1837 In case of union sets and relations, the affine hull is computed
1840 =item * Polyhedral hull
1842 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1843 __isl_take isl_set *set);
1844 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1845 __isl_take isl_map *map);
1846 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1847 __isl_take isl_union_set *uset);
1848 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1849 __isl_take isl_union_map *umap);
1851 These functions compute a single basic set or relation
1852 not involving any existentially quantified variables
1853 that contains the whole input set or relation.
1854 In case of union sets and relations, the polyhedral hull is computed
1857 =item * Optimization
1859 #include <isl/ilp.h>
1860 enum isl_lp_result isl_basic_set_max(
1861 __isl_keep isl_basic_set *bset,
1862 __isl_keep isl_aff *obj, isl_int *opt)
1863 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1864 __isl_keep isl_aff *obj, isl_int *opt);
1865 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1866 __isl_keep isl_aff *obj, isl_int *opt);
1868 Compute the minimum or maximum of the integer affine expression C<obj>
1869 over the points in C<set>, returning the result in C<opt>.
1870 The return value may be one of C<isl_lp_error>,
1871 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1873 =item * Parametric optimization
1875 __isl_give isl_pw_aff *isl_set_dim_min(
1876 __isl_take isl_set *set, int pos);
1877 __isl_give isl_pw_aff *isl_set_dim_max(
1878 __isl_take isl_set *set, int pos);
1880 Compute the minimum or maximum of the given set dimension as a function of the
1881 parameters, but independently of the other set dimensions.
1882 For lexicographic optimization, see L<"Lexicographic Optimization">.
1886 The following functions compute either the set of (rational) coefficient
1887 values of valid constraints for the given set or the set of (rational)
1888 values satisfying the constraints with coefficients from the given set.
1889 Internally, these two sets of functions perform essentially the
1890 same operations, except that the set of coefficients is assumed to
1891 be a cone, while the set of values may be any polyhedron.
1892 The current implementation is based on the Farkas lemma and
1893 Fourier-Motzkin elimination, but this may change or be made optional
1894 in future. In particular, future implementations may use different
1895 dualization algorithms or skip the elimination step.
1897 __isl_give isl_basic_set *isl_basic_set_coefficients(
1898 __isl_take isl_basic_set *bset);
1899 __isl_give isl_basic_set *isl_set_coefficients(
1900 __isl_take isl_set *set);
1901 __isl_give isl_union_set *isl_union_set_coefficients(
1902 __isl_take isl_union_set *bset);
1903 __isl_give isl_basic_set *isl_basic_set_solutions(
1904 __isl_take isl_basic_set *bset);
1905 __isl_give isl_basic_set *isl_set_solutions(
1906 __isl_take isl_set *set);
1907 __isl_give isl_union_set *isl_union_set_solutions(
1908 __isl_take isl_union_set *bset);
1912 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1914 __isl_give isl_union_map *isl_union_map_power(
1915 __isl_take isl_union_map *umap, int *exact);
1917 Compute a parametric representation for all positive powers I<k> of C<map>.
1918 The result maps I<k> to a nested relation corresponding to the
1919 I<k>th power of C<map>.
1920 The result may be an overapproximation. If the result is known to be exact,
1921 then C<*exact> is set to C<1>.
1923 =item * Transitive closure
1925 __isl_give isl_map *isl_map_transitive_closure(
1926 __isl_take isl_map *map, int *exact);
1927 __isl_give isl_union_map *isl_union_map_transitive_closure(
1928 __isl_take isl_union_map *umap, int *exact);
1930 Compute the transitive closure of C<map>.
1931 The result may be an overapproximation. If the result is known to be exact,
1932 then C<*exact> is set to C<1>.
1934 =item * Reaching path lengths
1936 __isl_give isl_map *isl_map_reaching_path_lengths(
1937 __isl_take isl_map *map, int *exact);
1939 Compute a relation that maps each element in the range of C<map>
1940 to the lengths of all paths composed of edges in C<map> that
1941 end up in the given element.
1942 The result may be an overapproximation. If the result is known to be exact,
1943 then C<*exact> is set to C<1>.
1944 To compute the I<maximal> path length, the resulting relation
1945 should be postprocessed by C<isl_map_lexmax>.
1946 In particular, if the input relation is a dependence relation
1947 (mapping sources to sinks), then the maximal path length corresponds
1948 to the free schedule.
1949 Note, however, that C<isl_map_lexmax> expects the maximum to be
1950 finite, so if the path lengths are unbounded (possibly due to
1951 the overapproximation), then you will get an error message.
1955 __isl_give isl_basic_set *isl_basic_map_wrap(
1956 __isl_take isl_basic_map *bmap);
1957 __isl_give isl_set *isl_map_wrap(
1958 __isl_take isl_map *map);
1959 __isl_give isl_union_set *isl_union_map_wrap(
1960 __isl_take isl_union_map *umap);
1961 __isl_give isl_basic_map *isl_basic_set_unwrap(
1962 __isl_take isl_basic_set *bset);
1963 __isl_give isl_map *isl_set_unwrap(
1964 __isl_take isl_set *set);
1965 __isl_give isl_union_map *isl_union_set_unwrap(
1966 __isl_take isl_union_set *uset);
1970 Remove any internal structure of domain (and range) of the given
1971 set or relation. If there is any such internal structure in the input,
1972 then the name of the space is also removed.
1974 __isl_give isl_basic_set *isl_basic_set_flatten(
1975 __isl_take isl_basic_set *bset);
1976 __isl_give isl_set *isl_set_flatten(
1977 __isl_take isl_set *set);
1978 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1981 __isl_take isl_basic_map *bmap);
1982 __isl_give isl_map *isl_map_flatten_range(
1983 __isl_take isl_map *map);
1984 __isl_give isl_map *isl_map_flatten_domain(
1985 __isl_take isl_map *map);
1986 __isl_give isl_basic_map *isl_basic_map_flatten(
1987 __isl_take isl_basic_map *bmap);
1988 __isl_give isl_map *isl_map_flatten(
1989 __isl_take isl_map *map);
1991 __isl_give isl_map *isl_set_flatten_map(
1992 __isl_take isl_set *set);
1994 The function above constructs a relation
1995 that maps the input set to a flattened version of the set.
1999 Lift the input set to a space with extra dimensions corresponding
2000 to the existentially quantified variables in the input.
2001 In particular, the result lives in a wrapped map where the domain
2002 is the original space and the range corresponds to the original
2003 existentially quantified variables.
2005 __isl_give isl_basic_set *isl_basic_set_lift(
2006 __isl_take isl_basic_set *bset);
2007 __isl_give isl_set *isl_set_lift(
2008 __isl_take isl_set *set);
2009 __isl_give isl_union_set *isl_union_set_lift(
2010 __isl_take isl_union_set *uset);
2012 =item * Internal Product
2014 __isl_give isl_basic_map *isl_basic_map_zip(
2015 __isl_take isl_basic_map *bmap);
2016 __isl_give isl_map *isl_map_zip(
2017 __isl_take isl_map *map);
2018 __isl_give isl_union_map *isl_union_map_zip(
2019 __isl_take isl_union_map *umap);
2021 Given a relation with nested relations for domain and range,
2022 interchange the range of the domain with the domain of the range.
2024 =item * Aligning parameters
2026 __isl_give isl_set *isl_set_align_params(
2027 __isl_take isl_set *set,
2028 __isl_take isl_space *model);
2029 __isl_give isl_map *isl_map_align_params(
2030 __isl_take isl_map *map,
2031 __isl_take isl_space *model);
2033 Change the order of the parameters of the given set or relation
2034 such that the first parameters match those of C<model>.
2035 This may involve the introduction of extra parameters.
2036 All parameters need to be named.
2038 =item * Dimension manipulation
2040 __isl_give isl_set *isl_set_add_dims(
2041 __isl_take isl_set *set,
2042 enum isl_dim_type type, unsigned n);
2043 __isl_give isl_map *isl_map_add_dims(
2044 __isl_take isl_map *map,
2045 enum isl_dim_type type, unsigned n);
2046 __isl_give isl_set *isl_set_insert_dims(
2047 __isl_take isl_set *set,
2048 enum isl_dim_type type, unsigned pos, unsigned n);
2049 __isl_give isl_map *isl_map_insert_dims(
2050 __isl_take isl_map *map,
2051 enum isl_dim_type type, unsigned pos, unsigned n);
2053 It is usually not advisable to directly change the (input or output)
2054 space of a set or a relation as this removes the name and the internal
2055 structure of the space. However, the above functions can be useful
2056 to add new parameters, assuming
2057 C<isl_set_align_params> and C<isl_map_align_params>
2062 =head2 Binary Operations
2064 The two arguments of a binary operation not only need to live
2065 in the same C<isl_ctx>, they currently also need to have
2066 the same (number of) parameters.
2068 =head3 Basic Operations
2072 =item * Intersection
2074 __isl_give isl_basic_set *isl_basic_set_intersect(
2075 __isl_take isl_basic_set *bset1,
2076 __isl_take isl_basic_set *bset2);
2077 __isl_give isl_set *isl_set_intersect_params(
2078 __isl_take isl_set *set,
2079 __isl_take isl_set *params);
2080 __isl_give isl_set *isl_set_intersect(
2081 __isl_take isl_set *set1,
2082 __isl_take isl_set *set2);
2083 __isl_give isl_union_set *isl_union_set_intersect(
2084 __isl_take isl_union_set *uset1,
2085 __isl_take isl_union_set *uset2);
2086 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2087 __isl_take isl_basic_map *bmap,
2088 __isl_take isl_basic_set *bset);
2089 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2090 __isl_take isl_basic_map *bmap,
2091 __isl_take isl_basic_set *bset);
2092 __isl_give isl_basic_map *isl_basic_map_intersect(
2093 __isl_take isl_basic_map *bmap1,
2094 __isl_take isl_basic_map *bmap2);
2095 __isl_give isl_map *isl_map_intersect_params(
2096 __isl_take isl_map *map,
2097 __isl_take isl_set *params);
2098 __isl_give isl_map *isl_map_intersect_domain(
2099 __isl_take isl_map *map,
2100 __isl_take isl_set *set);
2101 __isl_give isl_map *isl_map_intersect_range(
2102 __isl_take isl_map *map,
2103 __isl_take isl_set *set);
2104 __isl_give isl_map *isl_map_intersect(
2105 __isl_take isl_map *map1,
2106 __isl_take isl_map *map2);
2107 __isl_give isl_union_map *isl_union_map_intersect_domain(
2108 __isl_take isl_union_map *umap,
2109 __isl_take isl_union_set *uset);
2110 __isl_give isl_union_map *isl_union_map_intersect_range(
2111 __isl_take isl_union_map *umap,
2112 __isl_take isl_union_set *uset);
2113 __isl_give isl_union_map *isl_union_map_intersect(
2114 __isl_take isl_union_map *umap1,
2115 __isl_take isl_union_map *umap2);
2119 __isl_give isl_set *isl_basic_set_union(
2120 __isl_take isl_basic_set *bset1,
2121 __isl_take isl_basic_set *bset2);
2122 __isl_give isl_map *isl_basic_map_union(
2123 __isl_take isl_basic_map *bmap1,
2124 __isl_take isl_basic_map *bmap2);
2125 __isl_give isl_set *isl_set_union(
2126 __isl_take isl_set *set1,
2127 __isl_take isl_set *set2);
2128 __isl_give isl_map *isl_map_union(
2129 __isl_take isl_map *map1,
2130 __isl_take isl_map *map2);
2131 __isl_give isl_union_set *isl_union_set_union(
2132 __isl_take isl_union_set *uset1,
2133 __isl_take isl_union_set *uset2);
2134 __isl_give isl_union_map *isl_union_map_union(
2135 __isl_take isl_union_map *umap1,
2136 __isl_take isl_union_map *umap2);
2138 =item * Set difference
2140 __isl_give isl_set *isl_set_subtract(
2141 __isl_take isl_set *set1,
2142 __isl_take isl_set *set2);
2143 __isl_give isl_map *isl_map_subtract(
2144 __isl_take isl_map *map1,
2145 __isl_take isl_map *map2);
2146 __isl_give isl_union_set *isl_union_set_subtract(
2147 __isl_take isl_union_set *uset1,
2148 __isl_take isl_union_set *uset2);
2149 __isl_give isl_union_map *isl_union_map_subtract(
2150 __isl_take isl_union_map *umap1,
2151 __isl_take isl_union_map *umap2);
2155 __isl_give isl_basic_set *isl_basic_set_apply(
2156 __isl_take isl_basic_set *bset,
2157 __isl_take isl_basic_map *bmap);
2158 __isl_give isl_set *isl_set_apply(
2159 __isl_take isl_set *set,
2160 __isl_take isl_map *map);
2161 __isl_give isl_union_set *isl_union_set_apply(
2162 __isl_take isl_union_set *uset,
2163 __isl_take isl_union_map *umap);
2164 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2165 __isl_take isl_basic_map *bmap1,
2166 __isl_take isl_basic_map *bmap2);
2167 __isl_give isl_basic_map *isl_basic_map_apply_range(
2168 __isl_take isl_basic_map *bmap1,
2169 __isl_take isl_basic_map *bmap2);
2170 __isl_give isl_map *isl_map_apply_domain(
2171 __isl_take isl_map *map1,
2172 __isl_take isl_map *map2);
2173 __isl_give isl_union_map *isl_union_map_apply_domain(
2174 __isl_take isl_union_map *umap1,
2175 __isl_take isl_union_map *umap2);
2176 __isl_give isl_map *isl_map_apply_range(
2177 __isl_take isl_map *map1,
2178 __isl_take isl_map *map2);
2179 __isl_give isl_union_map *isl_union_map_apply_range(
2180 __isl_take isl_union_map *umap1,
2181 __isl_take isl_union_map *umap2);
2183 =item * Cartesian Product
2185 __isl_give isl_set *isl_set_product(
2186 __isl_take isl_set *set1,
2187 __isl_take isl_set *set2);
2188 __isl_give isl_union_set *isl_union_set_product(
2189 __isl_take isl_union_set *uset1,
2190 __isl_take isl_union_set *uset2);
2191 __isl_give isl_basic_map *isl_basic_map_domain_product(
2192 __isl_take isl_basic_map *bmap1,
2193 __isl_take isl_basic_map *bmap2);
2194 __isl_give isl_basic_map *isl_basic_map_range_product(
2195 __isl_take isl_basic_map *bmap1,
2196 __isl_take isl_basic_map *bmap2);
2197 __isl_give isl_map *isl_map_domain_product(
2198 __isl_take isl_map *map1,
2199 __isl_take isl_map *map2);
2200 __isl_give isl_map *isl_map_range_product(
2201 __isl_take isl_map *map1,
2202 __isl_take isl_map *map2);
2203 __isl_give isl_union_map *isl_union_map_range_product(
2204 __isl_take isl_union_map *umap1,
2205 __isl_take isl_union_map *umap2);
2206 __isl_give isl_map *isl_map_product(
2207 __isl_take isl_map *map1,
2208 __isl_take isl_map *map2);
2209 __isl_give isl_union_map *isl_union_map_product(
2210 __isl_take isl_union_map *umap1,
2211 __isl_take isl_union_map *umap2);
2213 The above functions compute the cross product of the given
2214 sets or relations. The domains and ranges of the results
2215 are wrapped maps between domains and ranges of the inputs.
2216 To obtain a ``flat'' product, use the following functions
2219 __isl_give isl_basic_set *isl_basic_set_flat_product(
2220 __isl_take isl_basic_set *bset1,
2221 __isl_take isl_basic_set *bset2);
2222 __isl_give isl_set *isl_set_flat_product(
2223 __isl_take isl_set *set1,
2224 __isl_take isl_set *set2);
2225 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2226 __isl_take isl_basic_map *bmap1,
2227 __isl_take isl_basic_map *bmap2);
2228 __isl_give isl_map *isl_map_flat_domain_product(
2229 __isl_take isl_map *map1,
2230 __isl_take isl_map *map2);
2231 __isl_give isl_map *isl_map_flat_range_product(
2232 __isl_take isl_map *map1,
2233 __isl_take isl_map *map2);
2234 __isl_give isl_union_map *isl_union_map_flat_range_product(
2235 __isl_take isl_union_map *umap1,
2236 __isl_take isl_union_map *umap2);
2237 __isl_give isl_basic_map *isl_basic_map_flat_product(
2238 __isl_take isl_basic_map *bmap1,
2239 __isl_take isl_basic_map *bmap2);
2240 __isl_give isl_map *isl_map_flat_product(
2241 __isl_take isl_map *map1,
2242 __isl_take isl_map *map2);
2244 =item * Simplification
2246 __isl_give isl_basic_set *isl_basic_set_gist(
2247 __isl_take isl_basic_set *bset,
2248 __isl_take isl_basic_set *context);
2249 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2250 __isl_take isl_set *context);
2251 __isl_give isl_union_set *isl_union_set_gist(
2252 __isl_take isl_union_set *uset,
2253 __isl_take isl_union_set *context);
2254 __isl_give isl_basic_map *isl_basic_map_gist(
2255 __isl_take isl_basic_map *bmap,
2256 __isl_take isl_basic_map *context);
2257 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2258 __isl_take isl_map *context);
2259 __isl_give isl_union_map *isl_union_map_gist(
2260 __isl_take isl_union_map *umap,
2261 __isl_take isl_union_map *context);
2263 The gist operation returns a set or relation that has the
2264 same intersection with the context as the input set or relation.
2265 Any implicit equality in the intersection is made explicit in the result,
2266 while all inequalities that are redundant with respect to the intersection
2268 In case of union sets and relations, the gist operation is performed
2273 =head3 Lexicographic Optimization
2275 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2276 the following functions
2277 compute a set that contains the lexicographic minimum or maximum
2278 of the elements in C<set> (or C<bset>) for those values of the parameters
2279 that satisfy C<dom>.
2280 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2281 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2283 In other words, the union of the parameter values
2284 for which the result is non-empty and of C<*empty>
2287 __isl_give isl_set *isl_basic_set_partial_lexmin(
2288 __isl_take isl_basic_set *bset,
2289 __isl_take isl_basic_set *dom,
2290 __isl_give isl_set **empty);
2291 __isl_give isl_set *isl_basic_set_partial_lexmax(
2292 __isl_take isl_basic_set *bset,
2293 __isl_take isl_basic_set *dom,
2294 __isl_give isl_set **empty);
2295 __isl_give isl_set *isl_set_partial_lexmin(
2296 __isl_take isl_set *set, __isl_take isl_set *dom,
2297 __isl_give isl_set **empty);
2298 __isl_give isl_set *isl_set_partial_lexmax(
2299 __isl_take isl_set *set, __isl_take isl_set *dom,
2300 __isl_give isl_set **empty);
2302 Given a (basic) set C<set> (or C<bset>), the following functions simply
2303 return a set containing the lexicographic minimum or maximum
2304 of the elements in C<set> (or C<bset>).
2305 In case of union sets, the optimum is computed per space.
2307 __isl_give isl_set *isl_basic_set_lexmin(
2308 __isl_take isl_basic_set *bset);
2309 __isl_give isl_set *isl_basic_set_lexmax(
2310 __isl_take isl_basic_set *bset);
2311 __isl_give isl_set *isl_set_lexmin(
2312 __isl_take isl_set *set);
2313 __isl_give isl_set *isl_set_lexmax(
2314 __isl_take isl_set *set);
2315 __isl_give isl_union_set *isl_union_set_lexmin(
2316 __isl_take isl_union_set *uset);
2317 __isl_give isl_union_set *isl_union_set_lexmax(
2318 __isl_take isl_union_set *uset);
2320 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2321 the following functions
2322 compute a relation that maps each element of C<dom>
2323 to the single lexicographic minimum or maximum
2324 of the elements that are associated to that same
2325 element in C<map> (or C<bmap>).
2326 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2327 that contains the elements in C<dom> that do not map
2328 to any elements in C<map> (or C<bmap>).
2329 In other words, the union of the domain of the result and of C<*empty>
2332 __isl_give isl_map *isl_basic_map_partial_lexmax(
2333 __isl_take isl_basic_map *bmap,
2334 __isl_take isl_basic_set *dom,
2335 __isl_give isl_set **empty);
2336 __isl_give isl_map *isl_basic_map_partial_lexmin(
2337 __isl_take isl_basic_map *bmap,
2338 __isl_take isl_basic_set *dom,
2339 __isl_give isl_set **empty);
2340 __isl_give isl_map *isl_map_partial_lexmax(
2341 __isl_take isl_map *map, __isl_take isl_set *dom,
2342 __isl_give isl_set **empty);
2343 __isl_give isl_map *isl_map_partial_lexmin(
2344 __isl_take isl_map *map, __isl_take isl_set *dom,
2345 __isl_give isl_set **empty);
2347 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2348 return a map mapping each element in the domain of
2349 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2350 of all elements associated to that element.
2351 In case of union relations, the optimum is computed per space.
2353 __isl_give isl_map *isl_basic_map_lexmin(
2354 __isl_take isl_basic_map *bmap);
2355 __isl_give isl_map *isl_basic_map_lexmax(
2356 __isl_take isl_basic_map *bmap);
2357 __isl_give isl_map *isl_map_lexmin(
2358 __isl_take isl_map *map);
2359 __isl_give isl_map *isl_map_lexmax(
2360 __isl_take isl_map *map);
2361 __isl_give isl_union_map *isl_union_map_lexmin(
2362 __isl_take isl_union_map *umap);
2363 __isl_give isl_union_map *isl_union_map_lexmax(
2364 __isl_take isl_union_map *umap);
2368 Lists are defined over several element types, including
2369 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2370 Here we take lists of C<isl_set>s as an example.
2371 Lists can be created, copied and freed using the following functions.
2373 #include <isl/list.h>
2374 __isl_give isl_set_list *isl_set_list_from_set(
2375 __isl_take isl_set *el);
2376 __isl_give isl_set_list *isl_set_list_alloc(
2377 isl_ctx *ctx, int n);
2378 __isl_give isl_set_list *isl_set_list_copy(
2379 __isl_keep isl_set_list *list);
2380 __isl_give isl_set_list *isl_set_list_add(
2381 __isl_take isl_set_list *list,
2382 __isl_take isl_set *el);
2383 __isl_give isl_set_list *isl_set_list_concat(
2384 __isl_take isl_set_list *list1,
2385 __isl_take isl_set_list *list2);
2386 void *isl_set_list_free(__isl_take isl_set_list *list);
2388 C<isl_set_list_alloc> creates an empty list with a capacity for
2389 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2392 Lists can be inspected using the following functions.
2394 #include <isl/list.h>
2395 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2396 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2397 __isl_give isl_set *isl_set_list_get_set(
2398 __isl_keep isl_set_list *list, int index);
2399 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2400 int (*fn)(__isl_take isl_set *el, void *user),
2403 Lists can be printed using
2405 #include <isl/list.h>
2406 __isl_give isl_printer *isl_printer_print_set_list(
2407 __isl_take isl_printer *p,
2408 __isl_keep isl_set_list *list);
2412 Matrices can be created, copied and freed using the following functions.
2414 #include <isl/mat.h>
2415 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2416 unsigned n_row, unsigned n_col);
2417 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2418 void isl_mat_free(__isl_take isl_mat *mat);
2420 Note that the elements of a newly created matrix may have arbitrary values.
2421 The elements can be changed and inspected using the following functions.
2423 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2424 int isl_mat_rows(__isl_keep isl_mat *mat);
2425 int isl_mat_cols(__isl_keep isl_mat *mat);
2426 int isl_mat_get_element(__isl_keep isl_mat *mat,
2427 int row, int col, isl_int *v);
2428 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2429 int row, int col, isl_int v);
2430 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2431 int row, int col, int v);
2433 C<isl_mat_get_element> will return a negative value if anything went wrong.
2434 In that case, the value of C<*v> is undefined.
2436 The following function can be used to compute the (right) inverse
2437 of a matrix, i.e., a matrix such that the product of the original
2438 and the inverse (in that order) is a multiple of the identity matrix.
2439 The input matrix is assumed to be of full row-rank.
2441 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2443 The following function can be used to compute the (right) kernel
2444 (or null space) of a matrix, i.e., a matrix such that the product of
2445 the original and the kernel (in that order) is the zero matrix.
2447 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2449 =head2 Piecewise Quasi Affine Expressions
2451 The zero quasi affine expression can be created using
2453 __isl_give isl_aff *isl_aff_zero(
2454 __isl_take isl_local_space *ls);
2456 A quasi affine expression can also be initialized from an C<isl_div>:
2458 #include <isl/div.h>
2459 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2461 An empty piecewise quasi affine expression (one with no cells)
2462 or a piecewise quasi affine expression with a single cell can
2463 be created using the following functions.
2465 #include <isl/aff.h>
2466 __isl_give isl_pw_aff *isl_pw_aff_empty(
2467 __isl_take isl_space *space);
2468 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2469 __isl_take isl_set *set, __isl_take isl_aff *aff);
2470 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2471 __isl_take isl_aff *aff);
2473 Quasi affine expressions can be copied and freed using
2475 #include <isl/aff.h>
2476 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2477 void *isl_aff_free(__isl_take isl_aff *aff);
2479 __isl_give isl_pw_aff *isl_pw_aff_copy(
2480 __isl_keep isl_pw_aff *pwaff);
2481 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2483 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2484 using the following function. The constraint is required to have
2485 a non-zero coefficient for the specified dimension.
2487 #include <isl/constraint.h>
2488 __isl_give isl_aff *isl_constraint_get_bound(
2489 __isl_keep isl_constraint *constraint,
2490 enum isl_dim_type type, int pos);
2492 The entire affine expression of the constraint can also be extracted
2493 using the following function.
2495 #include <isl/constraint.h>
2496 __isl_give isl_aff *isl_constraint_get_aff(
2497 __isl_keep isl_constraint *constraint);
2499 Conversely, an equality constraint equating
2500 the affine expression to zero or an inequality constraint enforcing
2501 the affine expression to be non-negative, can be constructed using
2503 __isl_give isl_constraint *isl_equality_from_aff(
2504 __isl_take isl_aff *aff);
2505 __isl_give isl_constraint *isl_inequality_from_aff(
2506 __isl_take isl_aff *aff);
2508 The expression can be inspected using
2510 #include <isl/aff.h>
2511 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2512 int isl_aff_dim(__isl_keep isl_aff *aff,
2513 enum isl_dim_type type);
2514 __isl_give isl_local_space *isl_aff_get_local_space(
2515 __isl_keep isl_aff *aff);
2516 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2517 enum isl_dim_type type, unsigned pos);
2518 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2520 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2521 enum isl_dim_type type, int pos, isl_int *v);
2522 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2524 __isl_give isl_div *isl_aff_get_div(
2525 __isl_keep isl_aff *aff, int pos);
2527 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2528 int (*fn)(__isl_take isl_set *set,
2529 __isl_take isl_aff *aff,
2530 void *user), void *user);
2532 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2533 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2535 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2536 enum isl_dim_type type, unsigned first, unsigned n);
2537 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2538 enum isl_dim_type type, unsigned first, unsigned n);
2540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2541 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2542 enum isl_dim_type type);
2543 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2545 It can be modified using
2547 #include <isl/aff.h>
2548 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2549 __isl_take isl_pw_aff *pwaff,
2550 __isl_take isl_id *id);
2551 __isl_give isl_aff *isl_aff_set_dim_name(
2552 __isl_take isl_aff *aff, enum isl_dim_type type,
2553 unsigned pos, const char *s);
2554 __isl_give isl_aff *isl_aff_set_constant(
2555 __isl_take isl_aff *aff, isl_int v);
2556 __isl_give isl_aff *isl_aff_set_constant_si(
2557 __isl_take isl_aff *aff, int v);
2558 __isl_give isl_aff *isl_aff_set_coefficient(
2559 __isl_take isl_aff *aff,
2560 enum isl_dim_type type, int pos, isl_int v);
2561 __isl_give isl_aff *isl_aff_set_coefficient_si(
2562 __isl_take isl_aff *aff,
2563 enum isl_dim_type type, int pos, int v);
2564 __isl_give isl_aff *isl_aff_set_denominator(
2565 __isl_take isl_aff *aff, isl_int v);
2567 __isl_give isl_aff *isl_aff_add_constant(
2568 __isl_take isl_aff *aff, isl_int v);
2569 __isl_give isl_aff *isl_aff_add_constant_si(
2570 __isl_take isl_aff *aff, int v);
2571 __isl_give isl_aff *isl_aff_add_coefficient(
2572 __isl_take isl_aff *aff,
2573 enum isl_dim_type type, int pos, isl_int v);
2574 __isl_give isl_aff *isl_aff_add_coefficient_si(
2575 __isl_take isl_aff *aff,
2576 enum isl_dim_type type, int pos, int v);
2578 __isl_give isl_aff *isl_aff_insert_dims(
2579 __isl_take isl_aff *aff,
2580 enum isl_dim_type type, unsigned first, unsigned n);
2581 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2582 __isl_take isl_pw_aff *pwaff,
2583 enum isl_dim_type type, unsigned first, unsigned n);
2584 __isl_give isl_aff *isl_aff_add_dims(
2585 __isl_take isl_aff *aff,
2586 enum isl_dim_type type, unsigned n);
2587 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2588 __isl_take isl_pw_aff *pwaff,
2589 enum isl_dim_type type, unsigned n);
2590 __isl_give isl_aff *isl_aff_drop_dims(
2591 __isl_take isl_aff *aff,
2592 enum isl_dim_type type, unsigned first, unsigned n);
2593 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2594 __isl_take isl_pw_aff *pwaff,
2595 enum isl_dim_type type, unsigned first, unsigned n);
2597 Note that the C<set_constant> and C<set_coefficient> functions
2598 set the I<numerator> of the constant or coefficient, while
2599 C<add_constant> and C<add_coefficient> add an integer value to
2600 the possibly rational constant or coefficient.
2602 To check whether an affine expressions is obviously zero
2603 or obviously equal to some other affine expression, use
2605 #include <isl/aff.h>
2606 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2607 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2608 __isl_keep isl_aff *aff2);
2612 #include <isl/aff.h>
2613 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2614 __isl_take isl_aff *aff2);
2615 __isl_give isl_pw_aff *isl_pw_aff_add(
2616 __isl_take isl_pw_aff *pwaff1,
2617 __isl_take isl_pw_aff *pwaff2);
2618 __isl_give isl_pw_aff *isl_pw_aff_min(
2619 __isl_take isl_pw_aff *pwaff1,
2620 __isl_take isl_pw_aff *pwaff2);
2621 __isl_give isl_pw_aff *isl_pw_aff_max(
2622 __isl_take isl_pw_aff *pwaff1,
2623 __isl_take isl_pw_aff *pwaff2);
2624 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2625 __isl_take isl_aff *aff2);
2626 __isl_give isl_pw_aff *isl_pw_aff_sub(
2627 __isl_take isl_pw_aff *pwaff1,
2628 __isl_take isl_pw_aff *pwaff2);
2629 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2630 __isl_give isl_pw_aff *isl_pw_aff_neg(
2631 __isl_take isl_pw_aff *pwaff);
2632 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2633 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2634 __isl_take isl_pw_aff *pwaff);
2635 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2636 __isl_give isl_pw_aff *isl_pw_aff_floor(
2637 __isl_take isl_pw_aff *pwaff);
2638 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2640 __isl_give isl_pw_aff *isl_pw_aff_mod(
2641 __isl_take isl_pw_aff *pwaff, isl_int mod);
2642 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2644 __isl_give isl_pw_aff *isl_pw_aff_scale(
2645 __isl_take isl_pw_aff *pwaff, isl_int f);
2646 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2648 __isl_give isl_aff *isl_aff_scale_down_ui(
2649 __isl_take isl_aff *aff, unsigned f);
2650 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2651 __isl_take isl_pw_aff *pwaff, isl_int f);
2653 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2654 __isl_take isl_pw_aff_list *list);
2655 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2656 __isl_take isl_pw_aff_list *list);
2658 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2659 __isl_take isl_pw_aff *pwqp);
2661 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2662 __isl_take isl_pw_aff *pwaff,
2663 __isl_take isl_space *model);
2665 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2666 __isl_take isl_set *context);
2667 __isl_give isl_pw_aff *isl_pw_aff_gist(
2668 __isl_take isl_pw_aff *pwaff,
2669 __isl_take isl_set *context);
2671 __isl_give isl_set *isl_pw_aff_domain(
2672 __isl_take isl_pw_aff *pwaff);
2674 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2675 __isl_take isl_aff *aff2);
2676 __isl_give isl_pw_aff *isl_pw_aff_mul(
2677 __isl_take isl_pw_aff *pwaff1,
2678 __isl_take isl_pw_aff *pwaff2);
2680 When multiplying two affine expressions, at least one of the two needs
2683 #include <isl/aff.h>
2684 __isl_give isl_basic_set *isl_aff_le_basic_set(
2685 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2686 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2687 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2688 __isl_give isl_set *isl_pw_aff_eq_set(
2689 __isl_take isl_pw_aff *pwaff1,
2690 __isl_take isl_pw_aff *pwaff2);
2691 __isl_give isl_set *isl_pw_aff_ne_set(
2692 __isl_take isl_pw_aff *pwaff1,
2693 __isl_take isl_pw_aff *pwaff2);
2694 __isl_give isl_set *isl_pw_aff_le_set(
2695 __isl_take isl_pw_aff *pwaff1,
2696 __isl_take isl_pw_aff *pwaff2);
2697 __isl_give isl_set *isl_pw_aff_lt_set(
2698 __isl_take isl_pw_aff *pwaff1,
2699 __isl_take isl_pw_aff *pwaff2);
2700 __isl_give isl_set *isl_pw_aff_ge_set(
2701 __isl_take isl_pw_aff *pwaff1,
2702 __isl_take isl_pw_aff *pwaff2);
2703 __isl_give isl_set *isl_pw_aff_gt_set(
2704 __isl_take isl_pw_aff *pwaff1,
2705 __isl_take isl_pw_aff *pwaff2);
2707 __isl_give isl_set *isl_pw_aff_list_eq_set(
2708 __isl_take isl_pw_aff_list *list1,
2709 __isl_take isl_pw_aff_list *list2);
2710 __isl_give isl_set *isl_pw_aff_list_ne_set(
2711 __isl_take isl_pw_aff_list *list1,
2712 __isl_take isl_pw_aff_list *list2);
2713 __isl_give isl_set *isl_pw_aff_list_le_set(
2714 __isl_take isl_pw_aff_list *list1,
2715 __isl_take isl_pw_aff_list *list2);
2716 __isl_give isl_set *isl_pw_aff_list_lt_set(
2717 __isl_take isl_pw_aff_list *list1,
2718 __isl_take isl_pw_aff_list *list2);
2719 __isl_give isl_set *isl_pw_aff_list_ge_set(
2720 __isl_take isl_pw_aff_list *list1,
2721 __isl_take isl_pw_aff_list *list2);
2722 __isl_give isl_set *isl_pw_aff_list_gt_set(
2723 __isl_take isl_pw_aff_list *list1,
2724 __isl_take isl_pw_aff_list *list2);
2726 The function C<isl_aff_ge_basic_set> returns a basic set
2727 containing those elements in the shared space
2728 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2729 The function C<isl_aff_ge_set> returns a set
2730 containing those elements in the shared domain
2731 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2732 The functions operating on C<isl_pw_aff_list> apply the corresponding
2733 C<isl_pw_aff> function to each pair of elements in the two lists.
2735 #include <isl/aff.h>
2736 __isl_give isl_set *isl_pw_aff_nonneg_set(
2737 __isl_take isl_pw_aff *pwaff);
2738 __isl_give isl_set *isl_pw_aff_zero_set(
2739 __isl_take isl_pw_aff *pwaff);
2740 __isl_give isl_set *isl_pw_aff_non_zero_set(
2741 __isl_take isl_pw_aff *pwaff);
2743 The function C<isl_pw_aff_nonneg_set> returns a set
2744 containing those elements in the domain
2745 of C<pwaff> where C<pwaff> is non-negative.
2747 #include <isl/aff.h>
2748 __isl_give isl_pw_aff *isl_pw_aff_cond(
2749 __isl_take isl_set *cond,
2750 __isl_take isl_pw_aff *pwaff_true,
2751 __isl_take isl_pw_aff *pwaff_false);
2753 The function C<isl_pw_aff_cond> performs a conditional operator
2754 and returns an expression that is equal to C<pwaff_true>
2755 for elements in C<cond> and equal to C<pwaff_false> for elements
2758 #include <isl/aff.h>
2759 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2760 __isl_take isl_pw_aff *pwaff1,
2761 __isl_take isl_pw_aff *pwaff2);
2762 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2763 __isl_take isl_pw_aff *pwaff1,
2764 __isl_take isl_pw_aff *pwaff2);
2766 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2767 expression with a domain that is the union of those of C<pwaff1> and
2768 C<pwaff2> and such that on each cell, the quasi-affine expression is
2769 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2770 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2771 associated expression is the defined one.
2773 An expression can be printed using
2775 #include <isl/aff.h>
2776 __isl_give isl_printer *isl_printer_print_aff(
2777 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2779 __isl_give isl_printer *isl_printer_print_pw_aff(
2780 __isl_take isl_printer *p,
2781 __isl_keep isl_pw_aff *pwaff);
2785 Points are elements of a set. They can be used to construct
2786 simple sets (boxes) or they can be used to represent the
2787 individual elements of a set.
2788 The zero point (the origin) can be created using
2790 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2792 The coordinates of a point can be inspected, set and changed
2795 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2796 enum isl_dim_type type, int pos, isl_int *v);
2797 __isl_give isl_point *isl_point_set_coordinate(
2798 __isl_take isl_point *pnt,
2799 enum isl_dim_type type, int pos, isl_int v);
2801 __isl_give isl_point *isl_point_add_ui(
2802 __isl_take isl_point *pnt,
2803 enum isl_dim_type type, int pos, unsigned val);
2804 __isl_give isl_point *isl_point_sub_ui(
2805 __isl_take isl_point *pnt,
2806 enum isl_dim_type type, int pos, unsigned val);
2808 Other properties can be obtained using
2810 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2812 Points can be copied or freed using
2814 __isl_give isl_point *isl_point_copy(
2815 __isl_keep isl_point *pnt);
2816 void isl_point_free(__isl_take isl_point *pnt);
2818 A singleton set can be created from a point using
2820 __isl_give isl_basic_set *isl_basic_set_from_point(
2821 __isl_take isl_point *pnt);
2822 __isl_give isl_set *isl_set_from_point(
2823 __isl_take isl_point *pnt);
2825 and a box can be created from two opposite extremal points using
2827 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2828 __isl_take isl_point *pnt1,
2829 __isl_take isl_point *pnt2);
2830 __isl_give isl_set *isl_set_box_from_points(
2831 __isl_take isl_point *pnt1,
2832 __isl_take isl_point *pnt2);
2834 All elements of a B<bounded> (union) set can be enumerated using
2835 the following functions.
2837 int isl_set_foreach_point(__isl_keep isl_set *set,
2838 int (*fn)(__isl_take isl_point *pnt, void *user),
2840 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2841 int (*fn)(__isl_take isl_point *pnt, void *user),
2844 The function C<fn> is called for each integer point in
2845 C<set> with as second argument the last argument of
2846 the C<isl_set_foreach_point> call. The function C<fn>
2847 should return C<0> on success and C<-1> on failure.
2848 In the latter case, C<isl_set_foreach_point> will stop
2849 enumerating and return C<-1> as well.
2850 If the enumeration is performed successfully and to completion,
2851 then C<isl_set_foreach_point> returns C<0>.
2853 To obtain a single point of a (basic) set, use
2855 __isl_give isl_point *isl_basic_set_sample_point(
2856 __isl_take isl_basic_set *bset);
2857 __isl_give isl_point *isl_set_sample_point(
2858 __isl_take isl_set *set);
2860 If C<set> does not contain any (integer) points, then the
2861 resulting point will be ``void'', a property that can be
2864 int isl_point_is_void(__isl_keep isl_point *pnt);
2866 =head2 Piecewise Quasipolynomials
2868 A piecewise quasipolynomial is a particular kind of function that maps
2869 a parametric point to a rational value.
2870 More specifically, a quasipolynomial is a polynomial expression in greatest
2871 integer parts of affine expressions of parameters and variables.
2872 A piecewise quasipolynomial is a subdivision of a given parametric
2873 domain into disjoint cells with a quasipolynomial associated to
2874 each cell. The value of the piecewise quasipolynomial at a given
2875 point is the value of the quasipolynomial associated to the cell
2876 that contains the point. Outside of the union of cells,
2877 the value is assumed to be zero.
2878 For example, the piecewise quasipolynomial
2880 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2882 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2883 A given piecewise quasipolynomial has a fixed domain dimension.
2884 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2885 defined over different domains.
2886 Piecewise quasipolynomials are mainly used by the C<barvinok>
2887 library for representing the number of elements in a parametric set or map.
2888 For example, the piecewise quasipolynomial above represents
2889 the number of points in the map
2891 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2893 =head3 Printing (Piecewise) Quasipolynomials
2895 Quasipolynomials and piecewise quasipolynomials can be printed
2896 using the following functions.
2898 __isl_give isl_printer *isl_printer_print_qpolynomial(
2899 __isl_take isl_printer *p,
2900 __isl_keep isl_qpolynomial *qp);
2902 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2903 __isl_take isl_printer *p,
2904 __isl_keep isl_pw_qpolynomial *pwqp);
2906 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2907 __isl_take isl_printer *p,
2908 __isl_keep isl_union_pw_qpolynomial *upwqp);
2910 The output format of the printer
2911 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2912 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2914 In case of printing in C<ISL_FORMAT_C>, the user may want
2915 to set the names of all dimensions
2917 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2918 __isl_take isl_qpolynomial *qp,
2919 enum isl_dim_type type, unsigned pos,
2921 __isl_give isl_pw_qpolynomial *
2922 isl_pw_qpolynomial_set_dim_name(
2923 __isl_take isl_pw_qpolynomial *pwqp,
2924 enum isl_dim_type type, unsigned pos,
2927 =head3 Creating New (Piecewise) Quasipolynomials
2929 Some simple quasipolynomials can be created using the following functions.
2930 More complicated quasipolynomials can be created by applying
2931 operations such as addition and multiplication
2932 on the resulting quasipolynomials
2934 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2935 __isl_take isl_space *dim);
2936 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2937 __isl_take isl_space *dim);
2938 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2939 __isl_take isl_space *dim);
2940 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2941 __isl_take isl_space *dim);
2942 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2943 __isl_take isl_space *dim);
2944 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2945 __isl_take isl_space *dim,
2946 const isl_int n, const isl_int d);
2947 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2948 __isl_take isl_div *div);
2949 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2950 __isl_take isl_space *dim,
2951 enum isl_dim_type type, unsigned pos);
2952 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2953 __isl_take isl_aff *aff);
2955 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2956 with a single cell can be created using the following functions.
2957 Multiple of these single cell piecewise quasipolynomials can
2958 be combined to create more complicated piecewise quasipolynomials.
2960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2961 __isl_take isl_space *space);
2962 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2963 __isl_take isl_set *set,
2964 __isl_take isl_qpolynomial *qp);
2965 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2966 __isl_take isl_qpolynomial *qp);
2967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2968 __isl_take isl_pw_aff *pwaff);
2970 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2971 __isl_take isl_space *space);
2972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2973 __isl_take isl_pw_qpolynomial *pwqp);
2974 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2975 __isl_take isl_union_pw_qpolynomial *upwqp,
2976 __isl_take isl_pw_qpolynomial *pwqp);
2978 Quasipolynomials can be copied and freed again using the following
2981 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2982 __isl_keep isl_qpolynomial *qp);
2983 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2985 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2986 __isl_keep isl_pw_qpolynomial *pwqp);
2987 void *isl_pw_qpolynomial_free(
2988 __isl_take isl_pw_qpolynomial *pwqp);
2990 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2991 __isl_keep isl_union_pw_qpolynomial *upwqp);
2992 void isl_union_pw_qpolynomial_free(
2993 __isl_take isl_union_pw_qpolynomial *upwqp);
2995 =head3 Inspecting (Piecewise) Quasipolynomials
2997 To iterate over all piecewise quasipolynomials in a union
2998 piecewise quasipolynomial, use the following function
3000 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3001 __isl_keep isl_union_pw_qpolynomial *upwqp,
3002 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3005 To extract the piecewise quasipolynomial in a given space from a union, use
3007 __isl_give isl_pw_qpolynomial *
3008 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3009 __isl_keep isl_union_pw_qpolynomial *upwqp,
3010 __isl_take isl_space *space);
3012 To iterate over the cells in a piecewise quasipolynomial,
3013 use either of the following two functions
3015 int isl_pw_qpolynomial_foreach_piece(
3016 __isl_keep isl_pw_qpolynomial *pwqp,
3017 int (*fn)(__isl_take isl_set *set,
3018 __isl_take isl_qpolynomial *qp,
3019 void *user), void *user);
3020 int isl_pw_qpolynomial_foreach_lifted_piece(
3021 __isl_keep isl_pw_qpolynomial *pwqp,
3022 int (*fn)(__isl_take isl_set *set,
3023 __isl_take isl_qpolynomial *qp,
3024 void *user), void *user);
3026 As usual, the function C<fn> should return C<0> on success
3027 and C<-1> on failure. The difference between
3028 C<isl_pw_qpolynomial_foreach_piece> and
3029 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3030 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3031 compute unique representations for all existentially quantified
3032 variables and then turn these existentially quantified variables
3033 into extra set variables, adapting the associated quasipolynomial
3034 accordingly. This means that the C<set> passed to C<fn>
3035 will not have any existentially quantified variables, but that
3036 the dimensions of the sets may be different for different
3037 invocations of C<fn>.
3039 To iterate over all terms in a quasipolynomial,
3042 int isl_qpolynomial_foreach_term(
3043 __isl_keep isl_qpolynomial *qp,
3044 int (*fn)(__isl_take isl_term *term,
3045 void *user), void *user);
3047 The terms themselves can be inspected and freed using
3050 unsigned isl_term_dim(__isl_keep isl_term *term,
3051 enum isl_dim_type type);
3052 void isl_term_get_num(__isl_keep isl_term *term,
3054 void isl_term_get_den(__isl_keep isl_term *term,
3056 int isl_term_get_exp(__isl_keep isl_term *term,
3057 enum isl_dim_type type, unsigned pos);
3058 __isl_give isl_div *isl_term_get_div(
3059 __isl_keep isl_term *term, unsigned pos);
3060 void isl_term_free(__isl_take isl_term *term);
3062 Each term is a product of parameters, set variables and
3063 integer divisions. The function C<isl_term_get_exp>
3064 returns the exponent of a given dimensions in the given term.
3065 The C<isl_int>s in the arguments of C<isl_term_get_num>
3066 and C<isl_term_get_den> need to have been initialized
3067 using C<isl_int_init> before calling these functions.
3069 =head3 Properties of (Piecewise) Quasipolynomials
3071 To check whether a quasipolynomial is actually a constant,
3072 use the following function.
3074 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3075 isl_int *n, isl_int *d);
3077 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3078 then the numerator and denominator of the constant
3079 are returned in C<*n> and C<*d>, respectively.
3081 =head3 Operations on (Piecewise) Quasipolynomials
3083 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3084 __isl_take isl_qpolynomial *qp, isl_int v);
3085 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3086 __isl_take isl_qpolynomial *qp);
3087 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3088 __isl_take isl_qpolynomial *qp1,
3089 __isl_take isl_qpolynomial *qp2);
3090 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3091 __isl_take isl_qpolynomial *qp1,
3092 __isl_take isl_qpolynomial *qp2);
3093 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3094 __isl_take isl_qpolynomial *qp1,
3095 __isl_take isl_qpolynomial *qp2);
3096 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3097 __isl_take isl_qpolynomial *qp, unsigned exponent);
3099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3100 __isl_take isl_pw_qpolynomial *pwqp1,
3101 __isl_take isl_pw_qpolynomial *pwqp2);
3102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3103 __isl_take isl_pw_qpolynomial *pwqp1,
3104 __isl_take isl_pw_qpolynomial *pwqp2);
3105 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3106 __isl_take isl_pw_qpolynomial *pwqp1,
3107 __isl_take isl_pw_qpolynomial *pwqp2);
3108 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3109 __isl_take isl_pw_qpolynomial *pwqp);
3110 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3111 __isl_take isl_pw_qpolynomial *pwqp1,
3112 __isl_take isl_pw_qpolynomial *pwqp2);
3113 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3114 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3116 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3117 __isl_take isl_union_pw_qpolynomial *upwqp1,
3118 __isl_take isl_union_pw_qpolynomial *upwqp2);
3119 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3120 __isl_take isl_union_pw_qpolynomial *upwqp1,
3121 __isl_take isl_union_pw_qpolynomial *upwqp2);
3122 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3123 __isl_take isl_union_pw_qpolynomial *upwqp1,
3124 __isl_take isl_union_pw_qpolynomial *upwqp2);
3126 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3127 __isl_take isl_pw_qpolynomial *pwqp,
3128 __isl_take isl_point *pnt);
3130 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3131 __isl_take isl_union_pw_qpolynomial *upwqp,
3132 __isl_take isl_point *pnt);
3134 __isl_give isl_set *isl_pw_qpolynomial_domain(
3135 __isl_take isl_pw_qpolynomial *pwqp);
3136 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3137 __isl_take isl_pw_qpolynomial *pwpq,
3138 __isl_take isl_set *set);
3140 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3141 __isl_take isl_union_pw_qpolynomial *upwqp);
3142 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3143 __isl_take isl_union_pw_qpolynomial *upwpq,
3144 __isl_take isl_union_set *uset);
3146 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3147 __isl_take isl_qpolynomial *qp,
3148 __isl_take isl_space *model);
3150 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3151 __isl_take isl_qpolynomial *qp);
3152 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3153 __isl_take isl_pw_qpolynomial *pwqp);
3155 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3156 __isl_take isl_union_pw_qpolynomial *upwqp);
3158 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3159 __isl_take isl_qpolynomial *qp,
3160 __isl_take isl_set *context);
3162 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3163 __isl_take isl_pw_qpolynomial *pwqp,
3164 __isl_take isl_set *context);
3166 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3167 __isl_take isl_union_pw_qpolynomial *upwqp,
3168 __isl_take isl_union_set *context);
3170 The gist operation applies the gist operation to each of
3171 the cells in the domain of the input piecewise quasipolynomial.
3172 The context is also exploited
3173 to simplify the quasipolynomials associated to each cell.
3175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3176 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3177 __isl_give isl_union_pw_qpolynomial *
3178 isl_union_pw_qpolynomial_to_polynomial(
3179 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3181 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3182 the polynomial will be an overapproximation. If C<sign> is negative,
3183 it will be an underapproximation. If C<sign> is zero, the approximation
3184 will lie somewhere in between.
3186 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3188 A piecewise quasipolynomial reduction is a piecewise
3189 reduction (or fold) of quasipolynomials.
3190 In particular, the reduction can be maximum or a minimum.
3191 The objects are mainly used to represent the result of
3192 an upper or lower bound on a quasipolynomial over its domain,
3193 i.e., as the result of the following function.
3195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3196 __isl_take isl_pw_qpolynomial *pwqp,
3197 enum isl_fold type, int *tight);
3199 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3200 __isl_take isl_union_pw_qpolynomial *upwqp,
3201 enum isl_fold type, int *tight);
3203 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3204 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3205 is the returned bound is known be tight, i.e., for each value
3206 of the parameters there is at least
3207 one element in the domain that reaches the bound.
3208 If the domain of C<pwqp> is not wrapping, then the bound is computed
3209 over all elements in that domain and the result has a purely parametric
3210 domain. If the domain of C<pwqp> is wrapping, then the bound is
3211 computed over the range of the wrapped relation. The domain of the
3212 wrapped relation becomes the domain of the result.
3214 A (piecewise) quasipolynomial reduction can be copied or freed using the
3215 following functions.
3217 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3218 __isl_keep isl_qpolynomial_fold *fold);
3219 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3220 __isl_keep isl_pw_qpolynomial_fold *pwf);
3221 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3222 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3223 void isl_qpolynomial_fold_free(
3224 __isl_take isl_qpolynomial_fold *fold);
3225 void *isl_pw_qpolynomial_fold_free(
3226 __isl_take isl_pw_qpolynomial_fold *pwf);
3227 void isl_union_pw_qpolynomial_fold_free(
3228 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3230 =head3 Printing Piecewise Quasipolynomial Reductions
3232 Piecewise quasipolynomial reductions can be printed
3233 using the following function.
3235 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3236 __isl_take isl_printer *p,
3237 __isl_keep isl_pw_qpolynomial_fold *pwf);
3238 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3239 __isl_take isl_printer *p,
3240 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3242 For C<isl_printer_print_pw_qpolynomial_fold>,
3243 output format of the printer
3244 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3245 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3246 output format of the printer
3247 needs to be set to C<ISL_FORMAT_ISL>.
3248 In case of printing in C<ISL_FORMAT_C>, the user may want
3249 to set the names of all dimensions
3251 __isl_give isl_pw_qpolynomial_fold *
3252 isl_pw_qpolynomial_fold_set_dim_name(
3253 __isl_take isl_pw_qpolynomial_fold *pwf,
3254 enum isl_dim_type type, unsigned pos,
3257 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3259 To iterate over all piecewise quasipolynomial reductions in a union
3260 piecewise quasipolynomial reduction, use the following function
3262 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3263 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3264 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3265 void *user), void *user);
3267 To iterate over the cells in a piecewise quasipolynomial reduction,
3268 use either of the following two functions
3270 int isl_pw_qpolynomial_fold_foreach_piece(
3271 __isl_keep isl_pw_qpolynomial_fold *pwf,
3272 int (*fn)(__isl_take isl_set *set,
3273 __isl_take isl_qpolynomial_fold *fold,
3274 void *user), void *user);
3275 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3276 __isl_keep isl_pw_qpolynomial_fold *pwf,
3277 int (*fn)(__isl_take isl_set *set,
3278 __isl_take isl_qpolynomial_fold *fold,
3279 void *user), void *user);
3281 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3282 of the difference between these two functions.
3284 To iterate over all quasipolynomials in a reduction, use
3286 int isl_qpolynomial_fold_foreach_qpolynomial(
3287 __isl_keep isl_qpolynomial_fold *fold,
3288 int (*fn)(__isl_take isl_qpolynomial *qp,
3289 void *user), void *user);
3291 =head3 Operations on Piecewise Quasipolynomial Reductions
3293 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3294 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3296 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3297 __isl_take isl_pw_qpolynomial_fold *pwf1,
3298 __isl_take isl_pw_qpolynomial_fold *pwf2);
3300 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3301 __isl_take isl_pw_qpolynomial_fold *pwf1,
3302 __isl_take isl_pw_qpolynomial_fold *pwf2);
3304 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3305 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3306 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3308 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3309 __isl_take isl_pw_qpolynomial_fold *pwf,
3310 __isl_take isl_point *pnt);
3312 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3313 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3314 __isl_take isl_point *pnt);
3316 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3317 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3318 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3319 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3320 __isl_take isl_union_set *uset);
3322 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3323 __isl_take isl_pw_qpolynomial_fold *pwf);
3325 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3326 __isl_take isl_pw_qpolynomial_fold *pwf);
3328 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3329 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3331 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3332 __isl_take isl_pw_qpolynomial_fold *pwf,
3333 __isl_take isl_set *context);
3335 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3337 __isl_take isl_union_set *context);
3339 The gist operation applies the gist operation to each of
3340 the cells in the domain of the input piecewise quasipolynomial reduction.
3341 In future, the operation will also exploit the context
3342 to simplify the quasipolynomial reductions associated to each cell.
3344 __isl_give isl_pw_qpolynomial_fold *
3345 isl_set_apply_pw_qpolynomial_fold(
3346 __isl_take isl_set *set,
3347 __isl_take isl_pw_qpolynomial_fold *pwf,
3349 __isl_give isl_pw_qpolynomial_fold *
3350 isl_map_apply_pw_qpolynomial_fold(
3351 __isl_take isl_map *map,
3352 __isl_take isl_pw_qpolynomial_fold *pwf,
3354 __isl_give isl_union_pw_qpolynomial_fold *
3355 isl_union_set_apply_union_pw_qpolynomial_fold(
3356 __isl_take isl_union_set *uset,
3357 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3359 __isl_give isl_union_pw_qpolynomial_fold *
3360 isl_union_map_apply_union_pw_qpolynomial_fold(
3361 __isl_take isl_union_map *umap,
3362 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3365 The functions taking a map
3366 compose the given map with the given piecewise quasipolynomial reduction.
3367 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3368 over all elements in the intersection of the range of the map
3369 and the domain of the piecewise quasipolynomial reduction
3370 as a function of an element in the domain of the map.
3371 The functions taking a set compute a bound over all elements in the
3372 intersection of the set and the domain of the
3373 piecewise quasipolynomial reduction.
3375 =head2 Dependence Analysis
3377 C<isl> contains specialized functionality for performing
3378 array dataflow analysis. That is, given a I<sink> access relation
3379 and a collection of possible I<source> access relations,
3380 C<isl> can compute relations that describe
3381 for each iteration of the sink access, which iteration
3382 of which of the source access relations was the last
3383 to access the same data element before the given iteration
3385 To compute standard flow dependences, the sink should be
3386 a read, while the sources should be writes.
3387 If any of the source accesses are marked as being I<may>
3388 accesses, then there will be a dependence to the last
3389 I<must> access B<and> to any I<may> access that follows
3390 this last I<must> access.
3391 In particular, if I<all> sources are I<may> accesses,
3392 then memory based dependence analysis is performed.
3393 If, on the other hand, all sources are I<must> accesses,
3394 then value based dependence analysis is performed.
3396 #include <isl/flow.h>
3398 typedef int (*isl_access_level_before)(void *first, void *second);
3400 __isl_give isl_access_info *isl_access_info_alloc(
3401 __isl_take isl_map *sink,
3402 void *sink_user, isl_access_level_before fn,
3404 __isl_give isl_access_info *isl_access_info_add_source(
3405 __isl_take isl_access_info *acc,
3406 __isl_take isl_map *source, int must,
3408 void isl_access_info_free(__isl_take isl_access_info *acc);
3410 __isl_give isl_flow *isl_access_info_compute_flow(
3411 __isl_take isl_access_info *acc);
3413 int isl_flow_foreach(__isl_keep isl_flow *deps,
3414 int (*fn)(__isl_take isl_map *dep, int must,
3415 void *dep_user, void *user),
3417 __isl_give isl_map *isl_flow_get_no_source(
3418 __isl_keep isl_flow *deps, int must);
3419 void isl_flow_free(__isl_take isl_flow *deps);
3421 The function C<isl_access_info_compute_flow> performs the actual
3422 dependence analysis. The other functions are used to construct
3423 the input for this function or to read off the output.
3425 The input is collected in an C<isl_access_info>, which can
3426 be created through a call to C<isl_access_info_alloc>.
3427 The arguments to this functions are the sink access relation
3428 C<sink>, a token C<sink_user> used to identify the sink
3429 access to the user, a callback function for specifying the
3430 relative order of source and sink accesses, and the number
3431 of source access relations that will be added.
3432 The callback function has type C<int (*)(void *first, void *second)>.
3433 The function is called with two user supplied tokens identifying
3434 either a source or the sink and it should return the shared nesting
3435 level and the relative order of the two accesses.
3436 In particular, let I<n> be the number of loops shared by
3437 the two accesses. If C<first> precedes C<second> textually,
3438 then the function should return I<2 * n + 1>; otherwise,
3439 it should return I<2 * n>.
3440 The sources can be added to the C<isl_access_info> by performing
3441 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3442 C<must> indicates whether the source is a I<must> access
3443 or a I<may> access. Note that a multi-valued access relation
3444 should only be marked I<must> if every iteration in the domain
3445 of the relation accesses I<all> elements in its image.
3446 The C<source_user> token is again used to identify
3447 the source access. The range of the source access relation
3448 C<source> should have the same dimension as the range
3449 of the sink access relation.
3450 The C<isl_access_info_free> function should usually not be
3451 called explicitly, because it is called implicitly by
3452 C<isl_access_info_compute_flow>.
3454 The result of the dependence analysis is collected in an
3455 C<isl_flow>. There may be elements of
3456 the sink access for which no preceding source access could be
3457 found or for which all preceding sources are I<may> accesses.
3458 The relations containing these elements can be obtained through
3459 calls to C<isl_flow_get_no_source>, the first with C<must> set
3460 and the second with C<must> unset.
3461 In the case of standard flow dependence analysis,
3462 with the sink a read and the sources I<must> writes,
3463 the first relation corresponds to the reads from uninitialized
3464 array elements and the second relation is empty.
3465 The actual flow dependences can be extracted using
3466 C<isl_flow_foreach>. This function will call the user-specified
3467 callback function C<fn> for each B<non-empty> dependence between
3468 a source and the sink. The callback function is called
3469 with four arguments, the actual flow dependence relation
3470 mapping source iterations to sink iterations, a boolean that
3471 indicates whether it is a I<must> or I<may> dependence, a token
3472 identifying the source and an additional C<void *> with value
3473 equal to the third argument of the C<isl_flow_foreach> call.
3474 A dependence is marked I<must> if it originates from a I<must>
3475 source and if it is not followed by any I<may> sources.
3477 After finishing with an C<isl_flow>, the user should call
3478 C<isl_flow_free> to free all associated memory.
3480 A higher-level interface to dependence analysis is provided
3481 by the following function.
3483 #include <isl/flow.h>
3485 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3486 __isl_take isl_union_map *must_source,
3487 __isl_take isl_union_map *may_source,
3488 __isl_take isl_union_map *schedule,
3489 __isl_give isl_union_map **must_dep,
3490 __isl_give isl_union_map **may_dep,
3491 __isl_give isl_union_map **must_no_source,
3492 __isl_give isl_union_map **may_no_source);
3494 The arrays are identified by the tuple names of the ranges
3495 of the accesses. The iteration domains by the tuple names
3496 of the domains of the accesses and of the schedule.
3497 The relative order of the iteration domains is given by the
3498 schedule. The relations returned through C<must_no_source>
3499 and C<may_no_source> are subsets of C<sink>.
3500 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3501 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3502 any of the other arguments is treated as an error.
3506 B<The functionality described in this section is fairly new
3507 and may be subject to change.>
3509 The following function can be used to compute a schedule
3510 for a union of domains. The generated schedule respects
3511 all C<validity> dependences. That is, all dependence distances
3512 over these dependences in the scheduled space are lexicographically
3513 positive. The generated schedule schedule also tries to minimize
3514 the dependence distances over C<proximity> dependences.
3515 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3516 for groups of domains where the dependence distances have only
3517 non-negative values.
3518 The algorithm used to construct the schedule is similar to that
3521 #include <isl/schedule.h>
3522 __isl_give isl_schedule *isl_union_set_compute_schedule(
3523 __isl_take isl_union_set *domain,
3524 __isl_take isl_union_map *validity,
3525 __isl_take isl_union_map *proximity);
3526 void *isl_schedule_free(__isl_take isl_schedule *sched);
3528 A mapping from the domains to the scheduled space can be obtained
3529 from an C<isl_schedule> using the following function.
3531 __isl_give isl_union_map *isl_schedule_get_map(
3532 __isl_keep isl_schedule *sched);
3534 A representation of the schedule can be printed using
3536 __isl_give isl_printer *isl_printer_print_schedule(
3537 __isl_take isl_printer *p,
3538 __isl_keep isl_schedule *schedule);
3540 A representation of the schedule as a forest of bands can be obtained
3541 using the following function.
3543 __isl_give isl_band_list *isl_schedule_get_band_forest(
3544 __isl_keep isl_schedule *schedule);
3546 The list can be manipulated as explained in L<"Lists">.
3547 The bands inside the list can be copied and freed using the following
3550 #include <isl/band.h>
3551 __isl_give isl_band *isl_band_copy(
3552 __isl_keep isl_band *band);
3553 void *isl_band_free(__isl_take isl_band *band);
3555 Each band contains zero or more scheduling dimensions.
3556 These are referred to as the members of the band.
3557 The section of the schedule that corresponds to the band is
3558 referred to as the partial schedule of the band.
3559 For those nodes that participate in a band, the outer scheduling
3560 dimensions form the prefix schedule, while the inner scheduling
3561 dimensions form the suffix schedule.
3562 That is, if we take a cut of the band forest, then the union of
3563 the concatenations of the prefix, partial and suffix schedules of
3564 each band in the cut is equal to the entire schedule (modulo
3565 some possible padding at the end with zero scheduling dimensions).
3566 The properties of a band can be inspected using the following functions.
3568 #include <isl/band.h>
3569 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3571 int isl_band_has_children(__isl_keep isl_band *band);
3572 __isl_give isl_band_list *isl_band_get_children(
3573 __isl_keep isl_band *band);
3575 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3576 __isl_keep isl_band *band);
3577 __isl_give isl_union_map *isl_band_get_partial_schedule(
3578 __isl_keep isl_band *band);
3579 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3580 __isl_keep isl_band *band);
3582 int isl_band_n_member(__isl_keep isl_band *band);
3583 int isl_band_member_is_zero_distance(
3584 __isl_keep isl_band *band, int pos);
3586 Note that a scheduling dimension is considered to be ``zero
3587 distance'' if it does not carry any proximity dependences
3589 That is, if the dependence distances of the proximity
3590 dependences are all zero in that direction (for fixed
3591 iterations of outer bands).
3593 A representation of the band can be printed using
3595 #include <isl/band.h>
3596 __isl_give isl_printer *isl_printer_print_band(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_band *band);
3600 =head2 Parametric Vertex Enumeration
3602 The parametric vertex enumeration described in this section
3603 is mainly intended to be used internally and by the C<barvinok>
3606 #include <isl/vertices.h>
3607 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3608 __isl_keep isl_basic_set *bset);
3610 The function C<isl_basic_set_compute_vertices> performs the
3611 actual computation of the parametric vertices and the chamber
3612 decomposition and store the result in an C<isl_vertices> object.
3613 This information can be queried by either iterating over all
3614 the vertices or iterating over all the chambers or cells
3615 and then iterating over all vertices that are active on the chamber.
3617 int isl_vertices_foreach_vertex(
3618 __isl_keep isl_vertices *vertices,
3619 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3622 int isl_vertices_foreach_cell(
3623 __isl_keep isl_vertices *vertices,
3624 int (*fn)(__isl_take isl_cell *cell, void *user),
3626 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3627 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3630 Other operations that can be performed on an C<isl_vertices> object are
3633 isl_ctx *isl_vertices_get_ctx(
3634 __isl_keep isl_vertices *vertices);
3635 int isl_vertices_get_n_vertices(
3636 __isl_keep isl_vertices *vertices);
3637 void isl_vertices_free(__isl_take isl_vertices *vertices);
3639 Vertices can be inspected and destroyed using the following functions.
3641 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3642 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3643 __isl_give isl_basic_set *isl_vertex_get_domain(
3644 __isl_keep isl_vertex *vertex);
3645 __isl_give isl_basic_set *isl_vertex_get_expr(
3646 __isl_keep isl_vertex *vertex);
3647 void isl_vertex_free(__isl_take isl_vertex *vertex);
3649 C<isl_vertex_get_expr> returns a singleton parametric set describing
3650 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3652 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3653 B<rational> basic sets, so they should mainly be used for inspection
3654 and should not be mixed with integer sets.
3656 Chambers can be inspected and destroyed using the following functions.
3658 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3659 __isl_give isl_basic_set *isl_cell_get_domain(
3660 __isl_keep isl_cell *cell);
3661 void isl_cell_free(__isl_take isl_cell *cell);
3665 Although C<isl> is mainly meant to be used as a library,
3666 it also contains some basic applications that use some
3667 of the functionality of C<isl>.
3668 The input may be specified in either the L<isl format>
3669 or the L<PolyLib format>.
3671 =head2 C<isl_polyhedron_sample>
3673 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3674 an integer element of the polyhedron, if there is any.
3675 The first column in the output is the denominator and is always
3676 equal to 1. If the polyhedron contains no integer points,
3677 then a vector of length zero is printed.
3681 C<isl_pip> takes the same input as the C<example> program
3682 from the C<piplib> distribution, i.e., a set of constraints
3683 on the parameters, a line containing only -1 and finally a set
3684 of constraints on a parametric polyhedron.
3685 The coefficients of the parameters appear in the last columns
3686 (but before the final constant column).
3687 The output is the lexicographic minimum of the parametric polyhedron.
3688 As C<isl> currently does not have its own output format, the output
3689 is just a dump of the internal state.
3691 =head2 C<isl_polyhedron_minimize>
3693 C<isl_polyhedron_minimize> computes the minimum of some linear
3694 or affine objective function over the integer points in a polyhedron.
3695 If an affine objective function
3696 is given, then the constant should appear in the last column.
3698 =head2 C<isl_polytope_scan>
3700 Given a polytope, C<isl_polytope_scan> prints
3701 all integer points in the polytope.