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_from_domain(
719 __isl_take isl_local_space *ls);
720 __isl_give isl_local_space *isl_local_space_add_dims(
721 __isl_take isl_local_space *ls,
722 enum isl_dim_type type, unsigned n);
723 __isl_give isl_local_space *isl_local_space_insert_dims(
724 __isl_take isl_local_space *ls,
725 enum isl_dim_type type, unsigned first, unsigned n);
726 __isl_give isl_local_space *isl_local_space_drop_dims(
727 __isl_take isl_local_space *ls,
728 enum isl_dim_type type, unsigned first, unsigned n);
730 =head2 Input and Output
732 C<isl> supports its own input/output format, which is similar
733 to the C<Omega> format, but also supports the C<PolyLib> format
738 The C<isl> format is similar to that of C<Omega>, but has a different
739 syntax for describing the parameters and allows for the definition
740 of an existentially quantified variable as the integer division
741 of an affine expression.
742 For example, the set of integers C<i> between C<0> and C<n>
743 such that C<i % 10 <= 6> can be described as
745 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
748 A set or relation can have several disjuncts, separated
749 by the keyword C<or>. Each disjunct is either a conjunction
750 of constraints or a projection (C<exists>) of a conjunction
751 of constraints. The constraints are separated by the keyword
754 =head3 C<PolyLib> format
756 If the represented set is a union, then the first line
757 contains a single number representing the number of disjuncts.
758 Otherwise, a line containing the number C<1> is optional.
760 Each disjunct is represented by a matrix of constraints.
761 The first line contains two numbers representing
762 the number of rows and columns,
763 where the number of rows is equal to the number of constraints
764 and the number of columns is equal to two plus the number of variables.
765 The following lines contain the actual rows of the constraint matrix.
766 In each row, the first column indicates whether the constraint
767 is an equality (C<0>) or inequality (C<1>). The final column
768 corresponds to the constant term.
770 If the set is parametric, then the coefficients of the parameters
771 appear in the last columns before the constant column.
772 The coefficients of any existentially quantified variables appear
773 between those of the set variables and those of the parameters.
775 =head3 Extended C<PolyLib> format
777 The extended C<PolyLib> format is nearly identical to the
778 C<PolyLib> format. The only difference is that the line
779 containing the number of rows and columns of a constraint matrix
780 also contains four additional numbers:
781 the number of output dimensions, the number of input dimensions,
782 the number of local dimensions (i.e., the number of existentially
783 quantified variables) and the number of parameters.
784 For sets, the number of ``output'' dimensions is equal
785 to the number of set dimensions, while the number of ``input''
791 __isl_give isl_basic_set *isl_basic_set_read_from_file(
792 isl_ctx *ctx, FILE *input, int nparam);
793 __isl_give isl_basic_set *isl_basic_set_read_from_str(
794 isl_ctx *ctx, const char *str, int nparam);
795 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
796 FILE *input, int nparam);
797 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
798 const char *str, int nparam);
801 __isl_give isl_basic_map *isl_basic_map_read_from_file(
802 isl_ctx *ctx, FILE *input, int nparam);
803 __isl_give isl_basic_map *isl_basic_map_read_from_str(
804 isl_ctx *ctx, const char *str, int nparam);
805 __isl_give isl_map *isl_map_read_from_file(
806 isl_ctx *ctx, FILE *input, int nparam);
807 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
808 const char *str, int nparam);
810 #include <isl/union_set.h>
811 __isl_give isl_union_set *isl_union_set_read_from_file(
812 isl_ctx *ctx, FILE *input);
813 __isl_give isl_union_set *isl_union_set_read_from_str(
814 isl_ctx *ctx, const char *str);
816 #include <isl/union_map.h>
817 __isl_give isl_union_map *isl_union_map_read_from_file(
818 isl_ctx *ctx, FILE *input);
819 __isl_give isl_union_map *isl_union_map_read_from_str(
820 isl_ctx *ctx, const char *str);
822 The input format is autodetected and may be either the C<PolyLib> format
823 or the C<isl> format.
824 C<nparam> specifies how many of the final columns in
825 the C<PolyLib> format correspond to parameters.
826 If input is given in the C<isl> format, then the number
827 of parameters needs to be equal to C<nparam>.
828 If C<nparam> is negative, then any number of parameters
829 is accepted in the C<isl> format and zero parameters
830 are assumed in the C<PolyLib> format.
834 Before anything can be printed, an C<isl_printer> needs to
837 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
839 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
840 void isl_printer_free(__isl_take isl_printer *printer);
841 __isl_give char *isl_printer_get_str(
842 __isl_keep isl_printer *printer);
844 The behavior of the printer can be modified in various ways
846 __isl_give isl_printer *isl_printer_set_output_format(
847 __isl_take isl_printer *p, int output_format);
848 __isl_give isl_printer *isl_printer_set_indent(
849 __isl_take isl_printer *p, int indent);
850 __isl_give isl_printer *isl_printer_indent(
851 __isl_take isl_printer *p, int indent);
852 __isl_give isl_printer *isl_printer_set_prefix(
853 __isl_take isl_printer *p, const char *prefix);
854 __isl_give isl_printer *isl_printer_set_suffix(
855 __isl_take isl_printer *p, const char *suffix);
857 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
858 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
859 and defaults to C<ISL_FORMAT_ISL>.
860 Each line in the output is indented by C<indent> (set by
861 C<isl_printer_set_indent>) spaces
862 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
863 In the C<PolyLib> format output,
864 the coefficients of the existentially quantified variables
865 appear between those of the set variables and those
867 The function C<isl_printer_indent> increases the indentation
868 by the specified amount (which may be negative).
870 To actually print something, use
873 __isl_give isl_printer *isl_printer_print_basic_set(
874 __isl_take isl_printer *printer,
875 __isl_keep isl_basic_set *bset);
876 __isl_give isl_printer *isl_printer_print_set(
877 __isl_take isl_printer *printer,
878 __isl_keep isl_set *set);
881 __isl_give isl_printer *isl_printer_print_basic_map(
882 __isl_take isl_printer *printer,
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_printer *isl_printer_print_map(
885 __isl_take isl_printer *printer,
886 __isl_keep isl_map *map);
888 #include <isl/union_set.h>
889 __isl_give isl_printer *isl_printer_print_union_set(
890 __isl_take isl_printer *p,
891 __isl_keep isl_union_set *uset);
893 #include <isl/union_map.h>
894 __isl_give isl_printer *isl_printer_print_union_map(
895 __isl_take isl_printer *p,
896 __isl_keep isl_union_map *umap);
898 When called on a file printer, the following function flushes
899 the file. When called on a string printer, the buffer is cleared.
901 __isl_give isl_printer *isl_printer_flush(
902 __isl_take isl_printer *p);
904 =head2 Creating New Sets and Relations
906 C<isl> has functions for creating some standard sets and relations.
910 =item * Empty sets and relations
912 __isl_give isl_basic_set *isl_basic_set_empty(
913 __isl_take isl_space *space);
914 __isl_give isl_basic_map *isl_basic_map_empty(
915 __isl_take isl_space *space);
916 __isl_give isl_set *isl_set_empty(
917 __isl_take isl_space *space);
918 __isl_give isl_map *isl_map_empty(
919 __isl_take isl_space *space);
920 __isl_give isl_union_set *isl_union_set_empty(
921 __isl_take isl_space *space);
922 __isl_give isl_union_map *isl_union_map_empty(
923 __isl_take isl_space *space);
925 For C<isl_union_set>s and C<isl_union_map>s, the space
926 is only used to specify the parameters.
928 =item * Universe sets and relations
930 __isl_give isl_basic_set *isl_basic_set_universe(
931 __isl_take isl_space *space);
932 __isl_give isl_basic_map *isl_basic_map_universe(
933 __isl_take isl_space *space);
934 __isl_give isl_set *isl_set_universe(
935 __isl_take isl_space *space);
936 __isl_give isl_map *isl_map_universe(
937 __isl_take isl_space *space);
938 __isl_give isl_union_set *isl_union_set_universe(
939 __isl_take isl_union_set *uset);
940 __isl_give isl_union_map *isl_union_map_universe(
941 __isl_take isl_union_map *umap);
943 The sets and relations constructed by the functions above
944 contain all integer values, while those constructed by the
945 functions below only contain non-negative values.
947 __isl_give isl_basic_set *isl_basic_set_nat_universe(
948 __isl_take isl_space *space);
949 __isl_give isl_basic_map *isl_basic_map_nat_universe(
950 __isl_take isl_space *space);
951 __isl_give isl_set *isl_set_nat_universe(
952 __isl_take isl_space *space);
953 __isl_give isl_map *isl_map_nat_universe(
954 __isl_take isl_space *space);
956 =item * Identity relations
958 __isl_give isl_basic_map *isl_basic_map_identity(
959 __isl_take isl_space *space);
960 __isl_give isl_map *isl_map_identity(
961 __isl_take isl_space *space);
963 The number of input and output dimensions in C<space> needs
966 =item * Lexicographic order
968 __isl_give isl_map *isl_map_lex_lt(
969 __isl_take isl_space *set_space);
970 __isl_give isl_map *isl_map_lex_le(
971 __isl_take isl_space *set_space);
972 __isl_give isl_map *isl_map_lex_gt(
973 __isl_take isl_space *set_space);
974 __isl_give isl_map *isl_map_lex_ge(
975 __isl_take isl_space *set_space);
976 __isl_give isl_map *isl_map_lex_lt_first(
977 __isl_take isl_space *space, unsigned n);
978 __isl_give isl_map *isl_map_lex_le_first(
979 __isl_take isl_space *space, unsigned n);
980 __isl_give isl_map *isl_map_lex_gt_first(
981 __isl_take isl_space *space, unsigned n);
982 __isl_give isl_map *isl_map_lex_ge_first(
983 __isl_take isl_space *space, unsigned n);
985 The first four functions take a space for a B<set>
986 and return relations that express that the elements in the domain
987 are lexicographically less
988 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
989 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
990 than the elements in the range.
991 The last four functions take a space for a map
992 and return relations that express that the first C<n> dimensions
993 in the domain are lexicographically less
994 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
995 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
996 than the first C<n> dimensions in the range.
1000 A basic set or relation can be converted to a set or relation
1001 using the following functions.
1003 __isl_give isl_set *isl_set_from_basic_set(
1004 __isl_take isl_basic_set *bset);
1005 __isl_give isl_map *isl_map_from_basic_map(
1006 __isl_take isl_basic_map *bmap);
1008 Sets and relations can be converted to union sets and relations
1009 using the following functions.
1011 __isl_give isl_union_map *isl_union_map_from_map(
1012 __isl_take isl_map *map);
1013 __isl_give isl_union_set *isl_union_set_from_set(
1014 __isl_take isl_set *set);
1016 The inverse conversions below can only be used if the input
1017 union set or relation is known to contain elements in exactly one
1020 __isl_give isl_set *isl_set_from_union_set(
1021 __isl_take isl_union_set *uset);
1022 __isl_give isl_map *isl_map_from_union_map(
1023 __isl_take isl_union_map *umap);
1025 Sets and relations can be copied and freed again using the following
1028 __isl_give isl_basic_set *isl_basic_set_copy(
1029 __isl_keep isl_basic_set *bset);
1030 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1031 __isl_give isl_union_set *isl_union_set_copy(
1032 __isl_keep isl_union_set *uset);
1033 __isl_give isl_basic_map *isl_basic_map_copy(
1034 __isl_keep isl_basic_map *bmap);
1035 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1036 __isl_give isl_union_map *isl_union_map_copy(
1037 __isl_keep isl_union_map *umap);
1038 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1039 void isl_set_free(__isl_take isl_set *set);
1040 void *isl_union_set_free(__isl_take isl_union_set *uset);
1041 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1042 void isl_map_free(__isl_take isl_map *map);
1043 void *isl_union_map_free(__isl_take isl_union_map *umap);
1045 Other sets and relations can be constructed by starting
1046 from a universe set or relation, adding equality and/or
1047 inequality constraints and then projecting out the
1048 existentially quantified variables, if any.
1049 Constraints can be constructed, manipulated and
1050 added to (or removed from) (basic) sets and relations
1051 using the following functions.
1053 #include <isl/constraint.h>
1054 __isl_give isl_constraint *isl_equality_alloc(
1055 __isl_take isl_space *space);
1056 __isl_give isl_constraint *isl_inequality_alloc(
1057 __isl_take isl_space *space);
1058 __isl_give isl_constraint *isl_constraint_set_constant(
1059 __isl_take isl_constraint *constraint, isl_int v);
1060 __isl_give isl_constraint *isl_constraint_set_constant_si(
1061 __isl_take isl_constraint *constraint, int v);
1062 __isl_give isl_constraint *isl_constraint_set_coefficient(
1063 __isl_take isl_constraint *constraint,
1064 enum isl_dim_type type, int pos, isl_int v);
1065 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1066 __isl_take isl_constraint *constraint,
1067 enum isl_dim_type type, int pos, int v);
1068 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1069 __isl_take isl_basic_map *bmap,
1070 __isl_take isl_constraint *constraint);
1071 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1072 __isl_take isl_basic_set *bset,
1073 __isl_take isl_constraint *constraint);
1074 __isl_give isl_map *isl_map_add_constraint(
1075 __isl_take isl_map *map,
1076 __isl_take isl_constraint *constraint);
1077 __isl_give isl_set *isl_set_add_constraint(
1078 __isl_take isl_set *set,
1079 __isl_take isl_constraint *constraint);
1080 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1081 __isl_take isl_basic_set *bset,
1082 __isl_take isl_constraint *constraint);
1084 For example, to create a set containing the even integers
1085 between 10 and 42, you would use the following code.
1090 isl_basic_set *bset;
1093 space = isl_space_set_alloc(ctx, 0, 2);
1094 bset = isl_basic_set_universe(isl_space_copy(space));
1096 c = isl_equality_alloc(isl_space_copy(space));
1097 isl_int_set_si(v, -1);
1098 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1099 isl_int_set_si(v, 2);
1100 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1101 bset = isl_basic_set_add_constraint(bset, c);
1103 c = isl_inequality_alloc(isl_space_copy(space));
1104 isl_int_set_si(v, -10);
1105 isl_constraint_set_constant(c, v);
1106 isl_int_set_si(v, 1);
1107 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1108 bset = isl_basic_set_add_constraint(bset, c);
1110 c = isl_inequality_alloc(space);
1111 isl_int_set_si(v, 42);
1112 isl_constraint_set_constant(c, v);
1113 isl_int_set_si(v, -1);
1114 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1115 bset = isl_basic_set_add_constraint(bset, c);
1117 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1123 isl_basic_set *bset;
1124 bset = isl_basic_set_read_from_str(ctx,
1125 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1127 A basic set or relation can also be constructed from two matrices
1128 describing the equalities and the inequalities.
1130 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1131 __isl_take isl_space *space,
1132 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1133 enum isl_dim_type c1,
1134 enum isl_dim_type c2, enum isl_dim_type c3,
1135 enum isl_dim_type c4);
1136 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1137 __isl_take isl_space *space,
1138 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1139 enum isl_dim_type c1,
1140 enum isl_dim_type c2, enum isl_dim_type c3,
1141 enum isl_dim_type c4, enum isl_dim_type c5);
1143 The C<isl_dim_type> arguments indicate the order in which
1144 different kinds of variables appear in the input matrices
1145 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1146 C<isl_dim_set> and C<isl_dim_div> for sets and
1147 of C<isl_dim_cst>, C<isl_dim_param>,
1148 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1150 A (basic) set or relation can also be constructed from a (piecewise)
1152 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1154 __isl_give isl_basic_map *isl_basic_map_from_aff(
1155 __isl_take isl_aff *aff);
1156 __isl_give isl_set *isl_set_from_pw_aff(
1157 __isl_take isl_pw_aff *pwaff);
1158 __isl_give isl_map *isl_map_from_pw_aff(
1159 __isl_take isl_pw_aff *pwaff);
1160 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1161 __isl_take isl_space *domain_space,
1162 __isl_take isl_aff_list *list);
1164 The C<domain_dim> argument describes the domain of the resulting
1165 basic relation. It is required because the C<list> may consist
1166 of zero affine expressions.
1168 =head2 Inspecting Sets and Relations
1170 Usually, the user should not have to care about the actual constraints
1171 of the sets and maps, but should instead apply the abstract operations
1172 explained in the following sections.
1173 Occasionally, however, it may be required to inspect the individual
1174 coefficients of the constraints. This section explains how to do so.
1175 In these cases, it may also be useful to have C<isl> compute
1176 an explicit representation of the existentially quantified variables.
1178 __isl_give isl_set *isl_set_compute_divs(
1179 __isl_take isl_set *set);
1180 __isl_give isl_map *isl_map_compute_divs(
1181 __isl_take isl_map *map);
1182 __isl_give isl_union_set *isl_union_set_compute_divs(
1183 __isl_take isl_union_set *uset);
1184 __isl_give isl_union_map *isl_union_map_compute_divs(
1185 __isl_take isl_union_map *umap);
1187 This explicit representation defines the existentially quantified
1188 variables as integer divisions of the other variables, possibly
1189 including earlier existentially quantified variables.
1190 An explicitly represented existentially quantified variable therefore
1191 has a unique value when the values of the other variables are known.
1192 If, furthermore, the same existentials, i.e., existentials
1193 with the same explicit representations, should appear in the
1194 same order in each of the disjuncts of a set or map, then the user should call
1195 either of the following functions.
1197 __isl_give isl_set *isl_set_align_divs(
1198 __isl_take isl_set *set);
1199 __isl_give isl_map *isl_map_align_divs(
1200 __isl_take isl_map *map);
1202 Alternatively, the existentially quantified variables can be removed
1203 using the following functions, which compute an overapproximation.
1205 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1206 __isl_take isl_basic_set *bset);
1207 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1208 __isl_take isl_basic_map *bmap);
1209 __isl_give isl_set *isl_set_remove_divs(
1210 __isl_take isl_set *set);
1211 __isl_give isl_map *isl_map_remove_divs(
1212 __isl_take isl_map *map);
1214 To iterate over all the sets or maps in a union set or map, use
1216 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1217 int (*fn)(__isl_take isl_set *set, void *user),
1219 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1220 int (*fn)(__isl_take isl_map *map, void *user),
1223 The number of sets or maps in a union set or map can be obtained
1226 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1227 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1229 To extract the set or map in a given space from a union, use
1231 __isl_give isl_set *isl_union_set_extract_set(
1232 __isl_keep isl_union_set *uset,
1233 __isl_take isl_space *space);
1234 __isl_give isl_map *isl_union_map_extract_map(
1235 __isl_keep isl_union_map *umap,
1236 __isl_take isl_space *space);
1238 To iterate over all the basic sets or maps in a set or map, use
1240 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1241 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1243 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1244 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1247 The callback function C<fn> should return 0 if successful and
1248 -1 if an error occurs. In the latter case, or if any other error
1249 occurs, the above functions will return -1.
1251 It should be noted that C<isl> does not guarantee that
1252 the basic sets or maps passed to C<fn> are disjoint.
1253 If this is required, then the user should call one of
1254 the following functions first.
1256 __isl_give isl_set *isl_set_make_disjoint(
1257 __isl_take isl_set *set);
1258 __isl_give isl_map *isl_map_make_disjoint(
1259 __isl_take isl_map *map);
1261 The number of basic sets in a set can be obtained
1264 int isl_set_n_basic_set(__isl_keep isl_set *set);
1266 To iterate over the constraints of a basic set or map, use
1268 #include <isl/constraint.h>
1270 int isl_basic_map_foreach_constraint(
1271 __isl_keep isl_basic_map *bmap,
1272 int (*fn)(__isl_take isl_constraint *c, void *user),
1274 void *isl_constraint_free(__isl_take isl_constraint *c);
1276 Again, the callback function C<fn> should return 0 if successful and
1277 -1 if an error occurs. In the latter case, or if any other error
1278 occurs, the above functions will return -1.
1279 The constraint C<c> represents either an equality or an inequality.
1280 Use the following function to find out whether a constraint
1281 represents an equality. If not, it represents an inequality.
1283 int isl_constraint_is_equality(
1284 __isl_keep isl_constraint *constraint);
1286 The coefficients of the constraints can be inspected using
1287 the following functions.
1289 void isl_constraint_get_constant(
1290 __isl_keep isl_constraint *constraint, isl_int *v);
1291 void isl_constraint_get_coefficient(
1292 __isl_keep isl_constraint *constraint,
1293 enum isl_dim_type type, int pos, isl_int *v);
1294 int isl_constraint_involves_dims(
1295 __isl_keep isl_constraint *constraint,
1296 enum isl_dim_type type, unsigned first, unsigned n);
1298 The explicit representations of the existentially quantified
1299 variables can be inspected using the following functions.
1300 Note that the user is only allowed to use these functions
1301 if the inspected set or map is the result of a call
1302 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1304 __isl_give isl_div *isl_constraint_div(
1305 __isl_keep isl_constraint *constraint, int pos);
1306 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1307 void isl_div_get_constant(__isl_keep isl_div *div,
1309 void isl_div_get_denominator(__isl_keep isl_div *div,
1311 void isl_div_get_coefficient(__isl_keep isl_div *div,
1312 enum isl_dim_type type, int pos, isl_int *v);
1314 To obtain the constraints of a basic set or map in matrix
1315 form, use the following functions.
1317 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1318 __isl_keep isl_basic_set *bset,
1319 enum isl_dim_type c1, enum isl_dim_type c2,
1320 enum isl_dim_type c3, enum isl_dim_type c4);
1321 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1322 __isl_keep isl_basic_set *bset,
1323 enum isl_dim_type c1, enum isl_dim_type c2,
1324 enum isl_dim_type c3, enum isl_dim_type c4);
1325 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1326 __isl_keep isl_basic_map *bmap,
1327 enum isl_dim_type c1,
1328 enum isl_dim_type c2, enum isl_dim_type c3,
1329 enum isl_dim_type c4, enum isl_dim_type c5);
1330 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1331 __isl_keep isl_basic_map *bmap,
1332 enum isl_dim_type c1,
1333 enum isl_dim_type c2, enum isl_dim_type c3,
1334 enum isl_dim_type c4, enum isl_dim_type c5);
1336 The C<isl_dim_type> arguments dictate the order in which
1337 different kinds of variables appear in the resulting matrix
1338 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1339 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1341 The number of parameters, input, output or set dimensions can
1342 be obtained using the following functions.
1344 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1345 enum isl_dim_type type);
1346 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1347 enum isl_dim_type type);
1348 unsigned isl_set_dim(__isl_keep isl_set *set,
1349 enum isl_dim_type type);
1350 unsigned isl_map_dim(__isl_keep isl_map *map,
1351 enum isl_dim_type type);
1353 To check whether the description of a set or relation depends
1354 on one or more given dimensions, it is not necessary to iterate over all
1355 constraints. Instead the following functions can be used.
1357 int isl_basic_set_involves_dims(
1358 __isl_keep isl_basic_set *bset,
1359 enum isl_dim_type type, unsigned first, unsigned n);
1360 int isl_set_involves_dims(__isl_keep isl_set *set,
1361 enum isl_dim_type type, unsigned first, unsigned n);
1362 int isl_basic_map_involves_dims(
1363 __isl_keep isl_basic_map *bmap,
1364 enum isl_dim_type type, unsigned first, unsigned n);
1365 int isl_map_involves_dims(__isl_keep isl_map *map,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1368 Similarly, the following functions can be used to check whether
1369 a given dimension is involved in any lower or upper bound.
1371 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1372 enum isl_dim_type type, unsigned pos);
1373 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1374 enum isl_dim_type type, unsigned pos);
1376 The identifiers or names of the domain and range spaces of a set
1377 or relation can be read off or set using the following functions.
1379 __isl_give isl_set *isl_set_set_tuple_id(
1380 __isl_take isl_set *set, __isl_take isl_id *id);
1381 __isl_give isl_set *isl_set_reset_tuple_id(
1382 __isl_take isl_set *set);
1383 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1384 __isl_give isl_id *isl_set_get_tuple_id(
1385 __isl_keep isl_set *set);
1386 __isl_give isl_map *isl_map_set_tuple_id(
1387 __isl_take isl_map *map, enum isl_dim_type type,
1388 __isl_take isl_id *id);
1389 __isl_give isl_map *isl_map_reset_tuple_id(
1390 __isl_take isl_map *map, enum isl_dim_type type);
1391 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1392 enum isl_dim_type type);
1393 __isl_give isl_id *isl_map_get_tuple_id(
1394 __isl_keep isl_map *map, enum isl_dim_type type);
1396 const char *isl_basic_set_get_tuple_name(
1397 __isl_keep isl_basic_set *bset);
1398 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1399 __isl_take isl_basic_set *set, const char *s);
1400 const char *isl_set_get_tuple_name(
1401 __isl_keep isl_set *set);
1402 const char *isl_basic_map_get_tuple_name(
1403 __isl_keep isl_basic_map *bmap,
1404 enum isl_dim_type type);
1405 const char *isl_map_get_tuple_name(
1406 __isl_keep isl_map *map,
1407 enum isl_dim_type type);
1409 As with C<isl_space_get_tuple_name>, the value returned points to
1410 an internal data structure.
1411 The identifiers, positions or names of individual dimensions can be
1412 read off using the following functions.
1414 __isl_give isl_set *isl_set_set_dim_id(
1415 __isl_take isl_set *set, enum isl_dim_type type,
1416 unsigned pos, __isl_take isl_id *id);
1417 int isl_set_has_dim_id(__isl_keep isl_set *set,
1418 enum isl_dim_type type, unsigned pos);
1419 __isl_give isl_id *isl_set_get_dim_id(
1420 __isl_keep isl_set *set, enum isl_dim_type type,
1422 __isl_give isl_map *isl_map_set_dim_id(
1423 __isl_take isl_map *map, enum isl_dim_type type,
1424 unsigned pos, __isl_take isl_id *id);
1425 int isl_map_has_dim_id(__isl_keep isl_map *map,
1426 enum isl_dim_type type, unsigned pos);
1427 __isl_give isl_id *isl_map_get_dim_id(
1428 __isl_keep isl_map *map, enum isl_dim_type type,
1431 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1432 enum isl_dim_type type, __isl_keep isl_id *id);
1433 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1434 enum isl_dim_type type, __isl_keep isl_id *id);
1436 const char *isl_constraint_get_dim_name(
1437 __isl_keep isl_constraint *constraint,
1438 enum isl_dim_type type, unsigned pos);
1439 const char *isl_basic_set_get_dim_name(
1440 __isl_keep isl_basic_set *bset,
1441 enum isl_dim_type type, unsigned pos);
1442 const char *isl_set_get_dim_name(
1443 __isl_keep isl_set *set,
1444 enum isl_dim_type type, unsigned pos);
1445 const char *isl_basic_map_get_dim_name(
1446 __isl_keep isl_basic_map *bmap,
1447 enum isl_dim_type type, unsigned pos);
1448 const char *isl_map_get_dim_name(
1449 __isl_keep isl_map *map,
1450 enum isl_dim_type type, unsigned pos);
1452 These functions are mostly useful to obtain the identifiers, positions
1453 or names of the parameters. Identifiers of individual dimensions are
1454 essentially only useful for printing. They are ignored by all other
1455 operations and may not be preserved across those operations.
1459 =head3 Unary Properties
1465 The following functions test whether the given set or relation
1466 contains any integer points. The ``plain'' variants do not perform
1467 any computations, but simply check if the given set or relation
1468 is already known to be empty.
1470 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1471 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1472 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1473 int isl_set_is_empty(__isl_keep isl_set *set);
1474 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1475 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1476 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1477 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1478 int isl_map_is_empty(__isl_keep isl_map *map);
1479 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1481 =item * Universality
1483 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1484 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1485 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1487 =item * Single-valuedness
1489 int isl_map_is_single_valued(__isl_keep isl_map *map);
1490 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1494 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1495 int isl_map_is_injective(__isl_keep isl_map *map);
1496 int isl_union_map_plain_is_injective(
1497 __isl_keep isl_union_map *umap);
1498 int isl_union_map_is_injective(
1499 __isl_keep isl_union_map *umap);
1503 int isl_map_is_bijective(__isl_keep isl_map *map);
1504 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1508 int isl_basic_map_plain_is_fixed(
1509 __isl_keep isl_basic_map *bmap,
1510 enum isl_dim_type type, unsigned pos,
1512 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1513 enum isl_dim_type type, unsigned pos,
1516 Check if the relation obviously lies on a hyperplane where the given dimension
1517 has a fixed value and if so, return that value in C<*val>.
1521 To check whether a set is a parameter domain, use this function:
1523 int isl_set_is_params(__isl_keep isl_set *set);
1527 The following functions check whether the domain of the given
1528 (basic) set is a wrapped relation.
1530 int isl_basic_set_is_wrapping(
1531 __isl_keep isl_basic_set *bset);
1532 int isl_set_is_wrapping(__isl_keep isl_set *set);
1534 =item * Internal Product
1536 int isl_basic_map_can_zip(
1537 __isl_keep isl_basic_map *bmap);
1538 int isl_map_can_zip(__isl_keep isl_map *map);
1540 Check whether the product of domain and range of the given relation
1542 i.e., whether both domain and range are nested relations.
1546 =head3 Binary Properties
1552 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1553 __isl_keep isl_set *set2);
1554 int isl_set_is_equal(__isl_keep isl_set *set1,
1555 __isl_keep isl_set *set2);
1556 int isl_union_set_is_equal(
1557 __isl_keep isl_union_set *uset1,
1558 __isl_keep isl_union_set *uset2);
1559 int isl_basic_map_is_equal(
1560 __isl_keep isl_basic_map *bmap1,
1561 __isl_keep isl_basic_map *bmap2);
1562 int isl_map_is_equal(__isl_keep isl_map *map1,
1563 __isl_keep isl_map *map2);
1564 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1565 __isl_keep isl_map *map2);
1566 int isl_union_map_is_equal(
1567 __isl_keep isl_union_map *umap1,
1568 __isl_keep isl_union_map *umap2);
1570 =item * Disjointness
1572 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1573 __isl_keep isl_set *set2);
1577 int isl_set_is_subset(__isl_keep isl_set *set1,
1578 __isl_keep isl_set *set2);
1579 int isl_set_is_strict_subset(
1580 __isl_keep isl_set *set1,
1581 __isl_keep isl_set *set2);
1582 int isl_union_set_is_subset(
1583 __isl_keep isl_union_set *uset1,
1584 __isl_keep isl_union_set *uset2);
1585 int isl_union_set_is_strict_subset(
1586 __isl_keep isl_union_set *uset1,
1587 __isl_keep isl_union_set *uset2);
1588 int isl_basic_map_is_subset(
1589 __isl_keep isl_basic_map *bmap1,
1590 __isl_keep isl_basic_map *bmap2);
1591 int isl_basic_map_is_strict_subset(
1592 __isl_keep isl_basic_map *bmap1,
1593 __isl_keep isl_basic_map *bmap2);
1594 int isl_map_is_subset(
1595 __isl_keep isl_map *map1,
1596 __isl_keep isl_map *map2);
1597 int isl_map_is_strict_subset(
1598 __isl_keep isl_map *map1,
1599 __isl_keep isl_map *map2);
1600 int isl_union_map_is_subset(
1601 __isl_keep isl_union_map *umap1,
1602 __isl_keep isl_union_map *umap2);
1603 int isl_union_map_is_strict_subset(
1604 __isl_keep isl_union_map *umap1,
1605 __isl_keep isl_union_map *umap2);
1609 =head2 Unary Operations
1615 __isl_give isl_set *isl_set_complement(
1616 __isl_take isl_set *set);
1620 __isl_give isl_basic_map *isl_basic_map_reverse(
1621 __isl_take isl_basic_map *bmap);
1622 __isl_give isl_map *isl_map_reverse(
1623 __isl_take isl_map *map);
1624 __isl_give isl_union_map *isl_union_map_reverse(
1625 __isl_take isl_union_map *umap);
1629 __isl_give isl_basic_set *isl_basic_set_project_out(
1630 __isl_take isl_basic_set *bset,
1631 enum isl_dim_type type, unsigned first, unsigned n);
1632 __isl_give isl_basic_map *isl_basic_map_project_out(
1633 __isl_take isl_basic_map *bmap,
1634 enum isl_dim_type type, unsigned first, unsigned n);
1635 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1636 enum isl_dim_type type, unsigned first, unsigned n);
1637 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1638 enum isl_dim_type type, unsigned first, unsigned n);
1639 __isl_give isl_basic_set *isl_basic_set_params(
1640 __isl_take isl_basic_set *bset);
1641 __isl_give isl_basic_set *isl_basic_map_domain(
1642 __isl_take isl_basic_map *bmap);
1643 __isl_give isl_basic_set *isl_basic_map_range(
1644 __isl_take isl_basic_map *bmap);
1645 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1646 __isl_give isl_set *isl_map_domain(
1647 __isl_take isl_map *bmap);
1648 __isl_give isl_set *isl_map_range(
1649 __isl_take isl_map *map);
1650 __isl_give isl_union_set *isl_union_map_domain(
1651 __isl_take isl_union_map *umap);
1652 __isl_give isl_union_set *isl_union_map_range(
1653 __isl_take isl_union_map *umap);
1655 __isl_give isl_basic_map *isl_basic_map_domain_map(
1656 __isl_take isl_basic_map *bmap);
1657 __isl_give isl_basic_map *isl_basic_map_range_map(
1658 __isl_take isl_basic_map *bmap);
1659 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1660 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1661 __isl_give isl_union_map *isl_union_map_domain_map(
1662 __isl_take isl_union_map *umap);
1663 __isl_give isl_union_map *isl_union_map_range_map(
1664 __isl_take isl_union_map *umap);
1666 The functions above construct a (basic, regular or union) relation
1667 that maps (a wrapped version of) the input relation to its domain or range.
1671 __isl_give isl_set *isl_set_eliminate(
1672 __isl_take isl_set *set, enum isl_dim_type type,
1673 unsigned first, unsigned n);
1675 Eliminate the coefficients for the given dimensions from the constraints,
1676 without removing the dimensions.
1680 __isl_give isl_basic_set *isl_basic_set_fix(
1681 __isl_take isl_basic_set *bset,
1682 enum isl_dim_type type, unsigned pos,
1684 __isl_give isl_basic_set *isl_basic_set_fix_si(
1685 __isl_take isl_basic_set *bset,
1686 enum isl_dim_type type, unsigned pos, int value);
1687 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1688 enum isl_dim_type type, unsigned pos,
1690 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1691 enum isl_dim_type type, unsigned pos, int value);
1692 __isl_give isl_basic_map *isl_basic_map_fix_si(
1693 __isl_take isl_basic_map *bmap,
1694 enum isl_dim_type type, unsigned pos, int value);
1695 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1696 enum isl_dim_type type, unsigned pos, int value);
1698 Intersect the set or relation with the hyperplane where the given
1699 dimension has the fixed given value.
1701 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1702 enum isl_dim_type type1, int pos1,
1703 enum isl_dim_type type2, int pos2);
1704 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1705 enum isl_dim_type type1, int pos1,
1706 enum isl_dim_type type2, int pos2);
1708 Intersect the set or relation with the hyperplane where the given
1709 dimensions are equal to each other.
1711 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1712 enum isl_dim_type type1, int pos1,
1713 enum isl_dim_type type2, int pos2);
1715 Intersect the relation with the hyperplane where the given
1716 dimensions have opposite values.
1720 __isl_give isl_map *isl_set_identity(
1721 __isl_take isl_set *set);
1722 __isl_give isl_union_map *isl_union_set_identity(
1723 __isl_take isl_union_set *uset);
1725 Construct an identity relation on the given (union) set.
1729 __isl_give isl_basic_set *isl_basic_map_deltas(
1730 __isl_take isl_basic_map *bmap);
1731 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1732 __isl_give isl_union_set *isl_union_map_deltas(
1733 __isl_take isl_union_map *umap);
1735 These functions return a (basic) set containing the differences
1736 between image elements and corresponding domain elements in the input.
1738 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1739 __isl_take isl_basic_map *bmap);
1740 __isl_give isl_map *isl_map_deltas_map(
1741 __isl_take isl_map *map);
1742 __isl_give isl_union_map *isl_union_map_deltas_map(
1743 __isl_take isl_union_map *umap);
1745 The functions above construct a (basic, regular or union) relation
1746 that maps (a wrapped version of) the input relation to its delta set.
1750 Simplify the representation of a set or relation by trying
1751 to combine pairs of basic sets or relations into a single
1752 basic set or relation.
1754 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1755 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1756 __isl_give isl_union_set *isl_union_set_coalesce(
1757 __isl_take isl_union_set *uset);
1758 __isl_give isl_union_map *isl_union_map_coalesce(
1759 __isl_take isl_union_map *umap);
1761 =item * Detecting equalities
1763 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1764 __isl_take isl_basic_set *bset);
1765 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1766 __isl_take isl_basic_map *bmap);
1767 __isl_give isl_set *isl_set_detect_equalities(
1768 __isl_take isl_set *set);
1769 __isl_give isl_map *isl_map_detect_equalities(
1770 __isl_take isl_map *map);
1771 __isl_give isl_union_set *isl_union_set_detect_equalities(
1772 __isl_take isl_union_set *uset);
1773 __isl_give isl_union_map *isl_union_map_detect_equalities(
1774 __isl_take isl_union_map *umap);
1776 Simplify the representation of a set or relation by detecting implicit
1779 =item * Removing redundant constraints
1781 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1782 __isl_take isl_basic_set *bset);
1783 __isl_give isl_set *isl_set_remove_redundancies(
1784 __isl_take isl_set *set);
1785 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1786 __isl_take isl_basic_map *bmap);
1787 __isl_give isl_map *isl_map_remove_redundancies(
1788 __isl_take isl_map *map);
1792 __isl_give isl_basic_set *isl_set_convex_hull(
1793 __isl_take isl_set *set);
1794 __isl_give isl_basic_map *isl_map_convex_hull(
1795 __isl_take isl_map *map);
1797 If the input set or relation has any existentially quantified
1798 variables, then the result of these operations is currently undefined.
1802 __isl_give isl_basic_set *isl_set_simple_hull(
1803 __isl_take isl_set *set);
1804 __isl_give isl_basic_map *isl_map_simple_hull(
1805 __isl_take isl_map *map);
1806 __isl_give isl_union_map *isl_union_map_simple_hull(
1807 __isl_take isl_union_map *umap);
1809 These functions compute a single basic set or relation
1810 that contains the whole input set or relation.
1811 In particular, the output is described by translates
1812 of the constraints describing the basic sets or relations in the input.
1816 (See \autoref{s:simple hull}.)
1822 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1823 __isl_take isl_basic_set *bset);
1824 __isl_give isl_basic_set *isl_set_affine_hull(
1825 __isl_take isl_set *set);
1826 __isl_give isl_union_set *isl_union_set_affine_hull(
1827 __isl_take isl_union_set *uset);
1828 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_give isl_basic_map *isl_map_affine_hull(
1831 __isl_take isl_map *map);
1832 __isl_give isl_union_map *isl_union_map_affine_hull(
1833 __isl_take isl_union_map *umap);
1835 In case of union sets and relations, the affine hull is computed
1838 =item * Polyhedral hull
1840 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1841 __isl_take isl_set *set);
1842 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1843 __isl_take isl_map *map);
1844 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1845 __isl_take isl_union_set *uset);
1846 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1847 __isl_take isl_union_map *umap);
1849 These functions compute a single basic set or relation
1850 not involving any existentially quantified variables
1851 that contains the whole input set or relation.
1852 In case of union sets and relations, the polyhedral hull is computed
1855 =item * Optimization
1857 #include <isl/ilp.h>
1858 enum isl_lp_result isl_basic_set_max(
1859 __isl_keep isl_basic_set *bset,
1860 __isl_keep isl_aff *obj, isl_int *opt)
1861 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1862 __isl_keep isl_aff *obj, isl_int *opt);
1863 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1864 __isl_keep isl_aff *obj, isl_int *opt);
1866 Compute the minimum or maximum of the integer affine expression C<obj>
1867 over the points in C<set>, returning the result in C<opt>.
1868 The return value may be one of C<isl_lp_error>,
1869 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1871 =item * Parametric optimization
1873 __isl_give isl_pw_aff *isl_set_dim_min(
1874 __isl_take isl_set *set, int pos);
1875 __isl_give isl_pw_aff *isl_set_dim_max(
1876 __isl_take isl_set *set, int pos);
1878 Compute the minimum or maximum of the given set dimension as a function of the
1879 parameters, but independently of the other set dimensions.
1880 For lexicographic optimization, see L<"Lexicographic Optimization">.
1884 The following functions compute either the set of (rational) coefficient
1885 values of valid constraints for the given set or the set of (rational)
1886 values satisfying the constraints with coefficients from the given set.
1887 Internally, these two sets of functions perform essentially the
1888 same operations, except that the set of coefficients is assumed to
1889 be a cone, while the set of values may be any polyhedron.
1890 The current implementation is based on the Farkas lemma and
1891 Fourier-Motzkin elimination, but this may change or be made optional
1892 in future. In particular, future implementations may use different
1893 dualization algorithms or skip the elimination step.
1895 __isl_give isl_basic_set *isl_basic_set_coefficients(
1896 __isl_take isl_basic_set *bset);
1897 __isl_give isl_basic_set *isl_set_coefficients(
1898 __isl_take isl_set *set);
1899 __isl_give isl_union_set *isl_union_set_coefficients(
1900 __isl_take isl_union_set *bset);
1901 __isl_give isl_basic_set *isl_basic_set_solutions(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_basic_set *isl_set_solutions(
1904 __isl_take isl_set *set);
1905 __isl_give isl_union_set *isl_union_set_solutions(
1906 __isl_take isl_union_set *bset);
1910 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1912 __isl_give isl_union_map *isl_union_map_power(
1913 __isl_take isl_union_map *umap, int *exact);
1915 Compute a parametric representation for all positive powers I<k> of C<map>.
1916 The result maps I<k> to a nested relation corresponding to the
1917 I<k>th power of C<map>.
1918 The result may be an overapproximation. If the result is known to be exact,
1919 then C<*exact> is set to C<1>.
1921 =item * Transitive closure
1923 __isl_give isl_map *isl_map_transitive_closure(
1924 __isl_take isl_map *map, int *exact);
1925 __isl_give isl_union_map *isl_union_map_transitive_closure(
1926 __isl_take isl_union_map *umap, int *exact);
1928 Compute the transitive closure of C<map>.
1929 The result may be an overapproximation. If the result is known to be exact,
1930 then C<*exact> is set to C<1>.
1932 =item * Reaching path lengths
1934 __isl_give isl_map *isl_map_reaching_path_lengths(
1935 __isl_take isl_map *map, int *exact);
1937 Compute a relation that maps each element in the range of C<map>
1938 to the lengths of all paths composed of edges in C<map> that
1939 end up in the given element.
1940 The result may be an overapproximation. If the result is known to be exact,
1941 then C<*exact> is set to C<1>.
1942 To compute the I<maximal> path length, the resulting relation
1943 should be postprocessed by C<isl_map_lexmax>.
1944 In particular, if the input relation is a dependence relation
1945 (mapping sources to sinks), then the maximal path length corresponds
1946 to the free schedule.
1947 Note, however, that C<isl_map_lexmax> expects the maximum to be
1948 finite, so if the path lengths are unbounded (possibly due to
1949 the overapproximation), then you will get an error message.
1953 __isl_give isl_basic_set *isl_basic_map_wrap(
1954 __isl_take isl_basic_map *bmap);
1955 __isl_give isl_set *isl_map_wrap(
1956 __isl_take isl_map *map);
1957 __isl_give isl_union_set *isl_union_map_wrap(
1958 __isl_take isl_union_map *umap);
1959 __isl_give isl_basic_map *isl_basic_set_unwrap(
1960 __isl_take isl_basic_set *bset);
1961 __isl_give isl_map *isl_set_unwrap(
1962 __isl_take isl_set *set);
1963 __isl_give isl_union_map *isl_union_set_unwrap(
1964 __isl_take isl_union_set *uset);
1968 Remove any internal structure of domain (and range) of the given
1969 set or relation. If there is any such internal structure in the input,
1970 then the name of the space is also removed.
1972 __isl_give isl_basic_set *isl_basic_set_flatten(
1973 __isl_take isl_basic_set *bset);
1974 __isl_give isl_set *isl_set_flatten(
1975 __isl_take isl_set *set);
1976 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1977 __isl_take isl_basic_map *bmap);
1978 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_give isl_map *isl_map_flatten_range(
1981 __isl_take isl_map *map);
1982 __isl_give isl_map *isl_map_flatten_domain(
1983 __isl_take isl_map *map);
1984 __isl_give isl_basic_map *isl_basic_map_flatten(
1985 __isl_take isl_basic_map *bmap);
1986 __isl_give isl_map *isl_map_flatten(
1987 __isl_take isl_map *map);
1989 __isl_give isl_map *isl_set_flatten_map(
1990 __isl_take isl_set *set);
1992 The function above constructs a relation
1993 that maps the input set to a flattened version of the set.
1997 Lift the input set to a space with extra dimensions corresponding
1998 to the existentially quantified variables in the input.
1999 In particular, the result lives in a wrapped map where the domain
2000 is the original space and the range corresponds to the original
2001 existentially quantified variables.
2003 __isl_give isl_basic_set *isl_basic_set_lift(
2004 __isl_take isl_basic_set *bset);
2005 __isl_give isl_set *isl_set_lift(
2006 __isl_take isl_set *set);
2007 __isl_give isl_union_set *isl_union_set_lift(
2008 __isl_take isl_union_set *uset);
2010 =item * Internal Product
2012 __isl_give isl_basic_map *isl_basic_map_zip(
2013 __isl_take isl_basic_map *bmap);
2014 __isl_give isl_map *isl_map_zip(
2015 __isl_take isl_map *map);
2016 __isl_give isl_union_map *isl_union_map_zip(
2017 __isl_take isl_union_map *umap);
2019 Given a relation with nested relations for domain and range,
2020 interchange the range of the domain with the domain of the range.
2022 =item * Aligning parameters
2024 __isl_give isl_set *isl_set_align_params(
2025 __isl_take isl_set *set,
2026 __isl_take isl_space *model);
2027 __isl_give isl_map *isl_map_align_params(
2028 __isl_take isl_map *map,
2029 __isl_take isl_space *model);
2031 Change the order of the parameters of the given set or relation
2032 such that the first parameters match those of C<model>.
2033 This may involve the introduction of extra parameters.
2034 All parameters need to be named.
2036 =item * Dimension manipulation
2038 __isl_give isl_set *isl_set_add_dims(
2039 __isl_take isl_set *set,
2040 enum isl_dim_type type, unsigned n);
2041 __isl_give isl_map *isl_map_add_dims(
2042 __isl_take isl_map *map,
2043 enum isl_dim_type type, unsigned n);
2044 __isl_give isl_set *isl_set_insert_dims(
2045 __isl_take isl_set *set,
2046 enum isl_dim_type type, unsigned pos, unsigned n);
2047 __isl_give isl_map *isl_map_insert_dims(
2048 __isl_take isl_map *map,
2049 enum isl_dim_type type, unsigned pos, unsigned n);
2051 It is usually not advisable to directly change the (input or output)
2052 space of a set or a relation as this removes the name and the internal
2053 structure of the space. However, the above functions can be useful
2054 to add new parameters, assuming
2055 C<isl_set_align_params> and C<isl_map_align_params>
2060 =head2 Binary Operations
2062 The two arguments of a binary operation not only need to live
2063 in the same C<isl_ctx>, they currently also need to have
2064 the same (number of) parameters.
2066 =head3 Basic Operations
2070 =item * Intersection
2072 __isl_give isl_basic_set *isl_basic_set_intersect(
2073 __isl_take isl_basic_set *bset1,
2074 __isl_take isl_basic_set *bset2);
2075 __isl_give isl_set *isl_set_intersect_params(
2076 __isl_take isl_set *set,
2077 __isl_take isl_set *params);
2078 __isl_give isl_set *isl_set_intersect(
2079 __isl_take isl_set *set1,
2080 __isl_take isl_set *set2);
2081 __isl_give isl_union_set *isl_union_set_intersect(
2082 __isl_take isl_union_set *uset1,
2083 __isl_take isl_union_set *uset2);
2084 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2085 __isl_take isl_basic_map *bmap,
2086 __isl_take isl_basic_set *bset);
2087 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2088 __isl_take isl_basic_map *bmap,
2089 __isl_take isl_basic_set *bset);
2090 __isl_give isl_basic_map *isl_basic_map_intersect(
2091 __isl_take isl_basic_map *bmap1,
2092 __isl_take isl_basic_map *bmap2);
2093 __isl_give isl_map *isl_map_intersect_params(
2094 __isl_take isl_map *map,
2095 __isl_take isl_set *params);
2096 __isl_give isl_map *isl_map_intersect_domain(
2097 __isl_take isl_map *map,
2098 __isl_take isl_set *set);
2099 __isl_give isl_map *isl_map_intersect_range(
2100 __isl_take isl_map *map,
2101 __isl_take isl_set *set);
2102 __isl_give isl_map *isl_map_intersect(
2103 __isl_take isl_map *map1,
2104 __isl_take isl_map *map2);
2105 __isl_give isl_union_map *isl_union_map_intersect_domain(
2106 __isl_take isl_union_map *umap,
2107 __isl_take isl_union_set *uset);
2108 __isl_give isl_union_map *isl_union_map_intersect_range(
2109 __isl_take isl_union_map *umap,
2110 __isl_take isl_union_set *uset);
2111 __isl_give isl_union_map *isl_union_map_intersect(
2112 __isl_take isl_union_map *umap1,
2113 __isl_take isl_union_map *umap2);
2117 __isl_give isl_set *isl_basic_set_union(
2118 __isl_take isl_basic_set *bset1,
2119 __isl_take isl_basic_set *bset2);
2120 __isl_give isl_map *isl_basic_map_union(
2121 __isl_take isl_basic_map *bmap1,
2122 __isl_take isl_basic_map *bmap2);
2123 __isl_give isl_set *isl_set_union(
2124 __isl_take isl_set *set1,
2125 __isl_take isl_set *set2);
2126 __isl_give isl_map *isl_map_union(
2127 __isl_take isl_map *map1,
2128 __isl_take isl_map *map2);
2129 __isl_give isl_union_set *isl_union_set_union(
2130 __isl_take isl_union_set *uset1,
2131 __isl_take isl_union_set *uset2);
2132 __isl_give isl_union_map *isl_union_map_union(
2133 __isl_take isl_union_map *umap1,
2134 __isl_take isl_union_map *umap2);
2136 =item * Set difference
2138 __isl_give isl_set *isl_set_subtract(
2139 __isl_take isl_set *set1,
2140 __isl_take isl_set *set2);
2141 __isl_give isl_map *isl_map_subtract(
2142 __isl_take isl_map *map1,
2143 __isl_take isl_map *map2);
2144 __isl_give isl_union_set *isl_union_set_subtract(
2145 __isl_take isl_union_set *uset1,
2146 __isl_take isl_union_set *uset2);
2147 __isl_give isl_union_map *isl_union_map_subtract(
2148 __isl_take isl_union_map *umap1,
2149 __isl_take isl_union_map *umap2);
2153 __isl_give isl_basic_set *isl_basic_set_apply(
2154 __isl_take isl_basic_set *bset,
2155 __isl_take isl_basic_map *bmap);
2156 __isl_give isl_set *isl_set_apply(
2157 __isl_take isl_set *set,
2158 __isl_take isl_map *map);
2159 __isl_give isl_union_set *isl_union_set_apply(
2160 __isl_take isl_union_set *uset,
2161 __isl_take isl_union_map *umap);
2162 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2163 __isl_take isl_basic_map *bmap1,
2164 __isl_take isl_basic_map *bmap2);
2165 __isl_give isl_basic_map *isl_basic_map_apply_range(
2166 __isl_take isl_basic_map *bmap1,
2167 __isl_take isl_basic_map *bmap2);
2168 __isl_give isl_map *isl_map_apply_domain(
2169 __isl_take isl_map *map1,
2170 __isl_take isl_map *map2);
2171 __isl_give isl_union_map *isl_union_map_apply_domain(
2172 __isl_take isl_union_map *umap1,
2173 __isl_take isl_union_map *umap2);
2174 __isl_give isl_map *isl_map_apply_range(
2175 __isl_take isl_map *map1,
2176 __isl_take isl_map *map2);
2177 __isl_give isl_union_map *isl_union_map_apply_range(
2178 __isl_take isl_union_map *umap1,
2179 __isl_take isl_union_map *umap2);
2181 =item * Cartesian Product
2183 __isl_give isl_set *isl_set_product(
2184 __isl_take isl_set *set1,
2185 __isl_take isl_set *set2);
2186 __isl_give isl_union_set *isl_union_set_product(
2187 __isl_take isl_union_set *uset1,
2188 __isl_take isl_union_set *uset2);
2189 __isl_give isl_basic_map *isl_basic_map_domain_product(
2190 __isl_take isl_basic_map *bmap1,
2191 __isl_take isl_basic_map *bmap2);
2192 __isl_give isl_basic_map *isl_basic_map_range_product(
2193 __isl_take isl_basic_map *bmap1,
2194 __isl_take isl_basic_map *bmap2);
2195 __isl_give isl_map *isl_map_domain_product(
2196 __isl_take isl_map *map1,
2197 __isl_take isl_map *map2);
2198 __isl_give isl_map *isl_map_range_product(
2199 __isl_take isl_map *map1,
2200 __isl_take isl_map *map2);
2201 __isl_give isl_union_map *isl_union_map_range_product(
2202 __isl_take isl_union_map *umap1,
2203 __isl_take isl_union_map *umap2);
2204 __isl_give isl_map *isl_map_product(
2205 __isl_take isl_map *map1,
2206 __isl_take isl_map *map2);
2207 __isl_give isl_union_map *isl_union_map_product(
2208 __isl_take isl_union_map *umap1,
2209 __isl_take isl_union_map *umap2);
2211 The above functions compute the cross product of the given
2212 sets or relations. The domains and ranges of the results
2213 are wrapped maps between domains and ranges of the inputs.
2214 To obtain a ``flat'' product, use the following functions
2217 __isl_give isl_basic_set *isl_basic_set_flat_product(
2218 __isl_take isl_basic_set *bset1,
2219 __isl_take isl_basic_set *bset2);
2220 __isl_give isl_set *isl_set_flat_product(
2221 __isl_take isl_set *set1,
2222 __isl_take isl_set *set2);
2223 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2224 __isl_take isl_basic_map *bmap1,
2225 __isl_take isl_basic_map *bmap2);
2226 __isl_give isl_map *isl_map_flat_domain_product(
2227 __isl_take isl_map *map1,
2228 __isl_take isl_map *map2);
2229 __isl_give isl_map *isl_map_flat_range_product(
2230 __isl_take isl_map *map1,
2231 __isl_take isl_map *map2);
2232 __isl_give isl_union_map *isl_union_map_flat_range_product(
2233 __isl_take isl_union_map *umap1,
2234 __isl_take isl_union_map *umap2);
2235 __isl_give isl_basic_map *isl_basic_map_flat_product(
2236 __isl_take isl_basic_map *bmap1,
2237 __isl_take isl_basic_map *bmap2);
2238 __isl_give isl_map *isl_map_flat_product(
2239 __isl_take isl_map *map1,
2240 __isl_take isl_map *map2);
2242 =item * Simplification
2244 __isl_give isl_basic_set *isl_basic_set_gist(
2245 __isl_take isl_basic_set *bset,
2246 __isl_take isl_basic_set *context);
2247 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2248 __isl_take isl_set *context);
2249 __isl_give isl_union_set *isl_union_set_gist(
2250 __isl_take isl_union_set *uset,
2251 __isl_take isl_union_set *context);
2252 __isl_give isl_basic_map *isl_basic_map_gist(
2253 __isl_take isl_basic_map *bmap,
2254 __isl_take isl_basic_map *context);
2255 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2256 __isl_take isl_map *context);
2257 __isl_give isl_union_map *isl_union_map_gist(
2258 __isl_take isl_union_map *umap,
2259 __isl_take isl_union_map *context);
2261 The gist operation returns a set or relation that has the
2262 same intersection with the context as the input set or relation.
2263 Any implicit equality in the intersection is made explicit in the result,
2264 while all inequalities that are redundant with respect to the intersection
2266 In case of union sets and relations, the gist operation is performed
2271 =head3 Lexicographic Optimization
2273 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2274 the following functions
2275 compute a set that contains the lexicographic minimum or maximum
2276 of the elements in C<set> (or C<bset>) for those values of the parameters
2277 that satisfy C<dom>.
2278 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2279 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2281 In other words, the union of the parameter values
2282 for which the result is non-empty and of C<*empty>
2285 __isl_give isl_set *isl_basic_set_partial_lexmin(
2286 __isl_take isl_basic_set *bset,
2287 __isl_take isl_basic_set *dom,
2288 __isl_give isl_set **empty);
2289 __isl_give isl_set *isl_basic_set_partial_lexmax(
2290 __isl_take isl_basic_set *bset,
2291 __isl_take isl_basic_set *dom,
2292 __isl_give isl_set **empty);
2293 __isl_give isl_set *isl_set_partial_lexmin(
2294 __isl_take isl_set *set, __isl_take isl_set *dom,
2295 __isl_give isl_set **empty);
2296 __isl_give isl_set *isl_set_partial_lexmax(
2297 __isl_take isl_set *set, __isl_take isl_set *dom,
2298 __isl_give isl_set **empty);
2300 Given a (basic) set C<set> (or C<bset>), the following functions simply
2301 return a set containing the lexicographic minimum or maximum
2302 of the elements in C<set> (or C<bset>).
2303 In case of union sets, the optimum is computed per space.
2305 __isl_give isl_set *isl_basic_set_lexmin(
2306 __isl_take isl_basic_set *bset);
2307 __isl_give isl_set *isl_basic_set_lexmax(
2308 __isl_take isl_basic_set *bset);
2309 __isl_give isl_set *isl_set_lexmin(
2310 __isl_take isl_set *set);
2311 __isl_give isl_set *isl_set_lexmax(
2312 __isl_take isl_set *set);
2313 __isl_give isl_union_set *isl_union_set_lexmin(
2314 __isl_take isl_union_set *uset);
2315 __isl_give isl_union_set *isl_union_set_lexmax(
2316 __isl_take isl_union_set *uset);
2318 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2319 the following functions
2320 compute a relation that maps each element of C<dom>
2321 to the single lexicographic minimum or maximum
2322 of the elements that are associated to that same
2323 element in C<map> (or C<bmap>).
2324 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2325 that contains the elements in C<dom> that do not map
2326 to any elements in C<map> (or C<bmap>).
2327 In other words, the union of the domain of the result and of C<*empty>
2330 __isl_give isl_map *isl_basic_map_partial_lexmax(
2331 __isl_take isl_basic_map *bmap,
2332 __isl_take isl_basic_set *dom,
2333 __isl_give isl_set **empty);
2334 __isl_give isl_map *isl_basic_map_partial_lexmin(
2335 __isl_take isl_basic_map *bmap,
2336 __isl_take isl_basic_set *dom,
2337 __isl_give isl_set **empty);
2338 __isl_give isl_map *isl_map_partial_lexmax(
2339 __isl_take isl_map *map, __isl_take isl_set *dom,
2340 __isl_give isl_set **empty);
2341 __isl_give isl_map *isl_map_partial_lexmin(
2342 __isl_take isl_map *map, __isl_take isl_set *dom,
2343 __isl_give isl_set **empty);
2345 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2346 return a map mapping each element in the domain of
2347 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2348 of all elements associated to that element.
2349 In case of union relations, the optimum is computed per space.
2351 __isl_give isl_map *isl_basic_map_lexmin(
2352 __isl_take isl_basic_map *bmap);
2353 __isl_give isl_map *isl_basic_map_lexmax(
2354 __isl_take isl_basic_map *bmap);
2355 __isl_give isl_map *isl_map_lexmin(
2356 __isl_take isl_map *map);
2357 __isl_give isl_map *isl_map_lexmax(
2358 __isl_take isl_map *map);
2359 __isl_give isl_union_map *isl_union_map_lexmin(
2360 __isl_take isl_union_map *umap);
2361 __isl_give isl_union_map *isl_union_map_lexmax(
2362 __isl_take isl_union_map *umap);
2366 Lists are defined over several element types, including
2367 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2368 Here we take lists of C<isl_set>s as an example.
2369 Lists can be created, copied and freed using the following functions.
2371 #include <isl/list.h>
2372 __isl_give isl_set_list *isl_set_list_from_set(
2373 __isl_take isl_set *el);
2374 __isl_give isl_set_list *isl_set_list_alloc(
2375 isl_ctx *ctx, int n);
2376 __isl_give isl_set_list *isl_set_list_copy(
2377 __isl_keep isl_set_list *list);
2378 __isl_give isl_set_list *isl_set_list_add(
2379 __isl_take isl_set_list *list,
2380 __isl_take isl_set *el);
2381 __isl_give isl_set_list *isl_set_list_concat(
2382 __isl_take isl_set_list *list1,
2383 __isl_take isl_set_list *list2);
2384 void *isl_set_list_free(__isl_take isl_set_list *list);
2386 C<isl_set_list_alloc> creates an empty list with a capacity for
2387 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2390 Lists can be inspected using the following functions.
2392 #include <isl/list.h>
2393 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2394 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2395 __isl_give isl_set *isl_set_list_get_set(
2396 __isl_keep isl_set_list *list, int index);
2397 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2398 int (*fn)(__isl_take isl_set *el, void *user),
2401 Lists can be printed using
2403 #include <isl/list.h>
2404 __isl_give isl_printer *isl_printer_print_set_list(
2405 __isl_take isl_printer *p,
2406 __isl_keep isl_set_list *list);
2410 Matrices can be created, copied and freed using the following functions.
2412 #include <isl/mat.h>
2413 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2414 unsigned n_row, unsigned n_col);
2415 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2416 void isl_mat_free(__isl_take isl_mat *mat);
2418 Note that the elements of a newly created matrix may have arbitrary values.
2419 The elements can be changed and inspected using the following functions.
2421 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2422 int isl_mat_rows(__isl_keep isl_mat *mat);
2423 int isl_mat_cols(__isl_keep isl_mat *mat);
2424 int isl_mat_get_element(__isl_keep isl_mat *mat,
2425 int row, int col, isl_int *v);
2426 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2427 int row, int col, isl_int v);
2428 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2429 int row, int col, int v);
2431 C<isl_mat_get_element> will return a negative value if anything went wrong.
2432 In that case, the value of C<*v> is undefined.
2434 The following function can be used to compute the (right) inverse
2435 of a matrix, i.e., a matrix such that the product of the original
2436 and the inverse (in that order) is a multiple of the identity matrix.
2437 The input matrix is assumed to be of full row-rank.
2439 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2441 The following function can be used to compute the (right) kernel
2442 (or null space) of a matrix, i.e., a matrix such that the product of
2443 the original and the kernel (in that order) is the zero matrix.
2445 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2447 =head2 Piecewise Quasi Affine Expressions
2449 The zero quasi affine expression can be created using
2451 __isl_give isl_aff *isl_aff_zero(
2452 __isl_take isl_local_space *ls);
2454 A quasi affine expression can also be initialized from an C<isl_div>:
2456 #include <isl/div.h>
2457 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2459 An empty piecewise quasi affine expression (one with no cells)
2460 or a piecewise quasi affine expression with a single cell can
2461 be created using the following functions.
2463 #include <isl/aff.h>
2464 __isl_give isl_pw_aff *isl_pw_aff_empty(
2465 __isl_take isl_space *space);
2466 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2467 __isl_take isl_set *set, __isl_take isl_aff *aff);
2468 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2469 __isl_take isl_aff *aff);
2471 Quasi affine expressions can be copied and freed using
2473 #include <isl/aff.h>
2474 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2475 void *isl_aff_free(__isl_take isl_aff *aff);
2477 __isl_give isl_pw_aff *isl_pw_aff_copy(
2478 __isl_keep isl_pw_aff *pwaff);
2479 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2481 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2482 using the following function. The constraint is required to have
2483 a non-zero coefficient for the specified dimension.
2485 #include <isl/constraint.h>
2486 __isl_give isl_aff *isl_constraint_get_bound(
2487 __isl_keep isl_constraint *constraint,
2488 enum isl_dim_type type, int pos);
2490 The entire affine expression of the constraint can also be extracted
2491 using the following function.
2493 #include <isl/constraint.h>
2494 __isl_give isl_aff *isl_constraint_get_aff(
2495 __isl_keep isl_constraint *constraint);
2497 Conversely, an equality constraint equating
2498 the affine expression to zero or an inequality constraint enforcing
2499 the affine expression to be non-negative, can be constructed using
2501 __isl_give isl_constraint *isl_equality_from_aff(
2502 __isl_take isl_aff *aff);
2503 __isl_give isl_constraint *isl_inequality_from_aff(
2504 __isl_take isl_aff *aff);
2506 The expression can be inspected using
2508 #include <isl/aff.h>
2509 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2510 int isl_aff_dim(__isl_keep isl_aff *aff,
2511 enum isl_dim_type type);
2512 __isl_give isl_local_space *isl_aff_get_local_space(
2513 __isl_keep isl_aff *aff);
2514 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2515 enum isl_dim_type type, unsigned pos);
2516 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2518 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2519 enum isl_dim_type type, int pos, isl_int *v);
2520 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2522 __isl_give isl_div *isl_aff_get_div(
2523 __isl_keep isl_aff *aff, int pos);
2525 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2526 int (*fn)(__isl_take isl_set *set,
2527 __isl_take isl_aff *aff,
2528 void *user), void *user);
2530 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2531 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2533 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2534 enum isl_dim_type type, unsigned first, unsigned n);
2535 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2536 enum isl_dim_type type, unsigned first, unsigned n);
2538 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2539 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2540 enum isl_dim_type type);
2541 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2543 It can be modified using
2545 #include <isl/aff.h>
2546 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2547 __isl_take isl_pw_aff *pwaff,
2548 __isl_take isl_id *id);
2549 __isl_give isl_aff *isl_aff_set_dim_name(
2550 __isl_take isl_aff *aff, enum isl_dim_type type,
2551 unsigned pos, const char *s);
2552 __isl_give isl_aff *isl_aff_set_constant(
2553 __isl_take isl_aff *aff, isl_int v);
2554 __isl_give isl_aff *isl_aff_set_constant_si(
2555 __isl_take isl_aff *aff, int v);
2556 __isl_give isl_aff *isl_aff_set_coefficient(
2557 __isl_take isl_aff *aff,
2558 enum isl_dim_type type, int pos, isl_int v);
2559 __isl_give isl_aff *isl_aff_set_coefficient_si(
2560 __isl_take isl_aff *aff,
2561 enum isl_dim_type type, int pos, int v);
2562 __isl_give isl_aff *isl_aff_set_denominator(
2563 __isl_take isl_aff *aff, isl_int v);
2565 __isl_give isl_aff *isl_aff_add_constant(
2566 __isl_take isl_aff *aff, isl_int v);
2567 __isl_give isl_aff *isl_aff_add_constant_si(
2568 __isl_take isl_aff *aff, int v);
2569 __isl_give isl_aff *isl_aff_add_coefficient(
2570 __isl_take isl_aff *aff,
2571 enum isl_dim_type type, int pos, isl_int v);
2572 __isl_give isl_aff *isl_aff_add_coefficient_si(
2573 __isl_take isl_aff *aff,
2574 enum isl_dim_type type, int pos, int v);
2576 __isl_give isl_aff *isl_aff_insert_dims(
2577 __isl_take isl_aff *aff,
2578 enum isl_dim_type type, unsigned first, unsigned n);
2579 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2580 __isl_take isl_pw_aff *pwaff,
2581 enum isl_dim_type type, unsigned first, unsigned n);
2582 __isl_give isl_aff *isl_aff_add_dims(
2583 __isl_take isl_aff *aff,
2584 enum isl_dim_type type, unsigned n);
2585 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2586 __isl_take isl_pw_aff *pwaff,
2587 enum isl_dim_type type, unsigned n);
2588 __isl_give isl_aff *isl_aff_drop_dims(
2589 __isl_take isl_aff *aff,
2590 enum isl_dim_type type, unsigned first, unsigned n);
2591 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2592 __isl_take isl_pw_aff *pwaff,
2593 enum isl_dim_type type, unsigned first, unsigned n);
2595 Note that the C<set_constant> and C<set_coefficient> functions
2596 set the I<numerator> of the constant or coefficient, while
2597 C<add_constant> and C<add_coefficient> add an integer value to
2598 the possibly rational constant or coefficient.
2600 To check whether an affine expressions is obviously zero
2601 or obviously equal to some other affine expression, use
2603 #include <isl/aff.h>
2604 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2605 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2606 __isl_keep isl_aff *aff2);
2610 #include <isl/aff.h>
2611 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2612 __isl_take isl_aff *aff2);
2613 __isl_give isl_pw_aff *isl_pw_aff_add(
2614 __isl_take isl_pw_aff *pwaff1,
2615 __isl_take isl_pw_aff *pwaff2);
2616 __isl_give isl_pw_aff *isl_pw_aff_min(
2617 __isl_take isl_pw_aff *pwaff1,
2618 __isl_take isl_pw_aff *pwaff2);
2619 __isl_give isl_pw_aff *isl_pw_aff_max(
2620 __isl_take isl_pw_aff *pwaff1,
2621 __isl_take isl_pw_aff *pwaff2);
2622 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2623 __isl_take isl_aff *aff2);
2624 __isl_give isl_pw_aff *isl_pw_aff_sub(
2625 __isl_take isl_pw_aff *pwaff1,
2626 __isl_take isl_pw_aff *pwaff2);
2627 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2628 __isl_give isl_pw_aff *isl_pw_aff_neg(
2629 __isl_take isl_pw_aff *pwaff);
2630 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2631 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2632 __isl_take isl_pw_aff *pwaff);
2633 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2634 __isl_give isl_pw_aff *isl_pw_aff_floor(
2635 __isl_take isl_pw_aff *pwaff);
2636 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2638 __isl_give isl_pw_aff *isl_pw_aff_mod(
2639 __isl_take isl_pw_aff *pwaff, isl_int mod);
2640 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2642 __isl_give isl_pw_aff *isl_pw_aff_scale(
2643 __isl_take isl_pw_aff *pwaff, isl_int f);
2644 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2646 __isl_give isl_aff *isl_aff_scale_down_ui(
2647 __isl_take isl_aff *aff, unsigned f);
2648 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2649 __isl_take isl_pw_aff *pwaff, isl_int f);
2651 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2652 __isl_take isl_pw_aff_list *list);
2653 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2654 __isl_take isl_pw_aff_list *list);
2656 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2657 __isl_take isl_pw_aff *pwqp);
2659 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2660 __isl_take isl_pw_aff *pwaff,
2661 __isl_take isl_space *model);
2663 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2664 __isl_take isl_set *context);
2665 __isl_give isl_pw_aff *isl_pw_aff_gist(
2666 __isl_take isl_pw_aff *pwaff,
2667 __isl_take isl_set *context);
2669 __isl_give isl_set *isl_pw_aff_domain(
2670 __isl_take isl_pw_aff *pwaff);
2672 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2673 __isl_take isl_aff *aff2);
2674 __isl_give isl_pw_aff *isl_pw_aff_mul(
2675 __isl_take isl_pw_aff *pwaff1,
2676 __isl_take isl_pw_aff *pwaff2);
2678 When multiplying two affine expressions, at least one of the two needs
2681 #include <isl/aff.h>
2682 __isl_give isl_basic_set *isl_aff_le_basic_set(
2683 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2684 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2685 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2686 __isl_give isl_set *isl_pw_aff_eq_set(
2687 __isl_take isl_pw_aff *pwaff1,
2688 __isl_take isl_pw_aff *pwaff2);
2689 __isl_give isl_set *isl_pw_aff_ne_set(
2690 __isl_take isl_pw_aff *pwaff1,
2691 __isl_take isl_pw_aff *pwaff2);
2692 __isl_give isl_set *isl_pw_aff_le_set(
2693 __isl_take isl_pw_aff *pwaff1,
2694 __isl_take isl_pw_aff *pwaff2);
2695 __isl_give isl_set *isl_pw_aff_lt_set(
2696 __isl_take isl_pw_aff *pwaff1,
2697 __isl_take isl_pw_aff *pwaff2);
2698 __isl_give isl_set *isl_pw_aff_ge_set(
2699 __isl_take isl_pw_aff *pwaff1,
2700 __isl_take isl_pw_aff *pwaff2);
2701 __isl_give isl_set *isl_pw_aff_gt_set(
2702 __isl_take isl_pw_aff *pwaff1,
2703 __isl_take isl_pw_aff *pwaff2);
2705 __isl_give isl_set *isl_pw_aff_list_eq_set(
2706 __isl_take isl_pw_aff_list *list1,
2707 __isl_take isl_pw_aff_list *list2);
2708 __isl_give isl_set *isl_pw_aff_list_ne_set(
2709 __isl_take isl_pw_aff_list *list1,
2710 __isl_take isl_pw_aff_list *list2);
2711 __isl_give isl_set *isl_pw_aff_list_le_set(
2712 __isl_take isl_pw_aff_list *list1,
2713 __isl_take isl_pw_aff_list *list2);
2714 __isl_give isl_set *isl_pw_aff_list_lt_set(
2715 __isl_take isl_pw_aff_list *list1,
2716 __isl_take isl_pw_aff_list *list2);
2717 __isl_give isl_set *isl_pw_aff_list_ge_set(
2718 __isl_take isl_pw_aff_list *list1,
2719 __isl_take isl_pw_aff_list *list2);
2720 __isl_give isl_set *isl_pw_aff_list_gt_set(
2721 __isl_take isl_pw_aff_list *list1,
2722 __isl_take isl_pw_aff_list *list2);
2724 The function C<isl_aff_ge_basic_set> returns a basic set
2725 containing those elements in the shared space
2726 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2727 The function C<isl_aff_ge_set> returns a set
2728 containing those elements in the shared domain
2729 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2730 The functions operating on C<isl_pw_aff_list> apply the corresponding
2731 C<isl_pw_aff> function to each pair of elements in the two lists.
2733 #include <isl/aff.h>
2734 __isl_give isl_set *isl_pw_aff_nonneg_set(
2735 __isl_take isl_pw_aff *pwaff);
2736 __isl_give isl_set *isl_pw_aff_zero_set(
2737 __isl_take isl_pw_aff *pwaff);
2738 __isl_give isl_set *isl_pw_aff_non_zero_set(
2739 __isl_take isl_pw_aff *pwaff);
2741 The function C<isl_pw_aff_nonneg_set> returns a set
2742 containing those elements in the domain
2743 of C<pwaff> where C<pwaff> is non-negative.
2745 #include <isl/aff.h>
2746 __isl_give isl_pw_aff *isl_pw_aff_cond(
2747 __isl_take isl_set *cond,
2748 __isl_take isl_pw_aff *pwaff_true,
2749 __isl_take isl_pw_aff *pwaff_false);
2751 The function C<isl_pw_aff_cond> performs a conditional operator
2752 and returns an expression that is equal to C<pwaff_true>
2753 for elements in C<cond> and equal to C<pwaff_false> for elements
2756 #include <isl/aff.h>
2757 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2758 __isl_take isl_pw_aff *pwaff1,
2759 __isl_take isl_pw_aff *pwaff2);
2760 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2761 __isl_take isl_pw_aff *pwaff1,
2762 __isl_take isl_pw_aff *pwaff2);
2764 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2765 expression with a domain that is the union of those of C<pwaff1> and
2766 C<pwaff2> and such that on each cell, the quasi-affine expression is
2767 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2768 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2769 associated expression is the defined one.
2771 An expression can be printed using
2773 #include <isl/aff.h>
2774 __isl_give isl_printer *isl_printer_print_aff(
2775 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2777 __isl_give isl_printer *isl_printer_print_pw_aff(
2778 __isl_take isl_printer *p,
2779 __isl_keep isl_pw_aff *pwaff);
2783 Points are elements of a set. They can be used to construct
2784 simple sets (boxes) or they can be used to represent the
2785 individual elements of a set.
2786 The zero point (the origin) can be created using
2788 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2790 The coordinates of a point can be inspected, set and changed
2793 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2794 enum isl_dim_type type, int pos, isl_int *v);
2795 __isl_give isl_point *isl_point_set_coordinate(
2796 __isl_take isl_point *pnt,
2797 enum isl_dim_type type, int pos, isl_int v);
2799 __isl_give isl_point *isl_point_add_ui(
2800 __isl_take isl_point *pnt,
2801 enum isl_dim_type type, int pos, unsigned val);
2802 __isl_give isl_point *isl_point_sub_ui(
2803 __isl_take isl_point *pnt,
2804 enum isl_dim_type type, int pos, unsigned val);
2806 Other properties can be obtained using
2808 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2810 Points can be copied or freed using
2812 __isl_give isl_point *isl_point_copy(
2813 __isl_keep isl_point *pnt);
2814 void isl_point_free(__isl_take isl_point *pnt);
2816 A singleton set can be created from a point using
2818 __isl_give isl_basic_set *isl_basic_set_from_point(
2819 __isl_take isl_point *pnt);
2820 __isl_give isl_set *isl_set_from_point(
2821 __isl_take isl_point *pnt);
2823 and a box can be created from two opposite extremal points using
2825 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2826 __isl_take isl_point *pnt1,
2827 __isl_take isl_point *pnt2);
2828 __isl_give isl_set *isl_set_box_from_points(
2829 __isl_take isl_point *pnt1,
2830 __isl_take isl_point *pnt2);
2832 All elements of a B<bounded> (union) set can be enumerated using
2833 the following functions.
2835 int isl_set_foreach_point(__isl_keep isl_set *set,
2836 int (*fn)(__isl_take isl_point *pnt, void *user),
2838 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2839 int (*fn)(__isl_take isl_point *pnt, void *user),
2842 The function C<fn> is called for each integer point in
2843 C<set> with as second argument the last argument of
2844 the C<isl_set_foreach_point> call. The function C<fn>
2845 should return C<0> on success and C<-1> on failure.
2846 In the latter case, C<isl_set_foreach_point> will stop
2847 enumerating and return C<-1> as well.
2848 If the enumeration is performed successfully and to completion,
2849 then C<isl_set_foreach_point> returns C<0>.
2851 To obtain a single point of a (basic) set, use
2853 __isl_give isl_point *isl_basic_set_sample_point(
2854 __isl_take isl_basic_set *bset);
2855 __isl_give isl_point *isl_set_sample_point(
2856 __isl_take isl_set *set);
2858 If C<set> does not contain any (integer) points, then the
2859 resulting point will be ``void'', a property that can be
2862 int isl_point_is_void(__isl_keep isl_point *pnt);
2864 =head2 Piecewise Quasipolynomials
2866 A piecewise quasipolynomial is a particular kind of function that maps
2867 a parametric point to a rational value.
2868 More specifically, a quasipolynomial is a polynomial expression in greatest
2869 integer parts of affine expressions of parameters and variables.
2870 A piecewise quasipolynomial is a subdivision of a given parametric
2871 domain into disjoint cells with a quasipolynomial associated to
2872 each cell. The value of the piecewise quasipolynomial at a given
2873 point is the value of the quasipolynomial associated to the cell
2874 that contains the point. Outside of the union of cells,
2875 the value is assumed to be zero.
2876 For example, the piecewise quasipolynomial
2878 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2880 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2881 A given piecewise quasipolynomial has a fixed domain dimension.
2882 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2883 defined over different domains.
2884 Piecewise quasipolynomials are mainly used by the C<barvinok>
2885 library for representing the number of elements in a parametric set or map.
2886 For example, the piecewise quasipolynomial above represents
2887 the number of points in the map
2889 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2891 =head3 Printing (Piecewise) Quasipolynomials
2893 Quasipolynomials and piecewise quasipolynomials can be printed
2894 using the following functions.
2896 __isl_give isl_printer *isl_printer_print_qpolynomial(
2897 __isl_take isl_printer *p,
2898 __isl_keep isl_qpolynomial *qp);
2900 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2901 __isl_take isl_printer *p,
2902 __isl_keep isl_pw_qpolynomial *pwqp);
2904 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2905 __isl_take isl_printer *p,
2906 __isl_keep isl_union_pw_qpolynomial *upwqp);
2908 The output format of the printer
2909 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2910 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2912 In case of printing in C<ISL_FORMAT_C>, the user may want
2913 to set the names of all dimensions
2915 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2916 __isl_take isl_qpolynomial *qp,
2917 enum isl_dim_type type, unsigned pos,
2919 __isl_give isl_pw_qpolynomial *
2920 isl_pw_qpolynomial_set_dim_name(
2921 __isl_take isl_pw_qpolynomial *pwqp,
2922 enum isl_dim_type type, unsigned pos,
2925 =head3 Creating New (Piecewise) Quasipolynomials
2927 Some simple quasipolynomials can be created using the following functions.
2928 More complicated quasipolynomials can be created by applying
2929 operations such as addition and multiplication
2930 on the resulting quasipolynomials
2932 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2933 __isl_take isl_space *dim);
2934 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2935 __isl_take isl_space *dim);
2936 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2937 __isl_take isl_space *dim);
2938 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2939 __isl_take isl_space *dim);
2940 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2941 __isl_take isl_space *dim);
2942 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2943 __isl_take isl_space *dim,
2944 const isl_int n, const isl_int d);
2945 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2946 __isl_take isl_div *div);
2947 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2948 __isl_take isl_space *dim,
2949 enum isl_dim_type type, unsigned pos);
2950 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2951 __isl_take isl_aff *aff);
2953 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2954 with a single cell can be created using the following functions.
2955 Multiple of these single cell piecewise quasipolynomials can
2956 be combined to create more complicated piecewise quasipolynomials.
2958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2959 __isl_take isl_space *space);
2960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2961 __isl_take isl_set *set,
2962 __isl_take isl_qpolynomial *qp);
2963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2964 __isl_take isl_qpolynomial *qp);
2965 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2966 __isl_take isl_pw_aff *pwaff);
2968 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2969 __isl_take isl_space *space);
2970 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2971 __isl_take isl_pw_qpolynomial *pwqp);
2972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2973 __isl_take isl_union_pw_qpolynomial *upwqp,
2974 __isl_take isl_pw_qpolynomial *pwqp);
2976 Quasipolynomials can be copied and freed again using the following
2979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2980 __isl_keep isl_qpolynomial *qp);
2981 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2984 __isl_keep isl_pw_qpolynomial *pwqp);
2985 void *isl_pw_qpolynomial_free(
2986 __isl_take isl_pw_qpolynomial *pwqp);
2988 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2989 __isl_keep isl_union_pw_qpolynomial *upwqp);
2990 void isl_union_pw_qpolynomial_free(
2991 __isl_take isl_union_pw_qpolynomial *upwqp);
2993 =head3 Inspecting (Piecewise) Quasipolynomials
2995 To iterate over all piecewise quasipolynomials in a union
2996 piecewise quasipolynomial, use the following function
2998 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2999 __isl_keep isl_union_pw_qpolynomial *upwqp,
3000 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3003 To extract the piecewise quasipolynomial in a given space from a union, use
3005 __isl_give isl_pw_qpolynomial *
3006 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3007 __isl_keep isl_union_pw_qpolynomial *upwqp,
3008 __isl_take isl_space *space);
3010 To iterate over the cells in a piecewise quasipolynomial,
3011 use either of the following two functions
3013 int isl_pw_qpolynomial_foreach_piece(
3014 __isl_keep isl_pw_qpolynomial *pwqp,
3015 int (*fn)(__isl_take isl_set *set,
3016 __isl_take isl_qpolynomial *qp,
3017 void *user), void *user);
3018 int isl_pw_qpolynomial_foreach_lifted_piece(
3019 __isl_keep isl_pw_qpolynomial *pwqp,
3020 int (*fn)(__isl_take isl_set *set,
3021 __isl_take isl_qpolynomial *qp,
3022 void *user), void *user);
3024 As usual, the function C<fn> should return C<0> on success
3025 and C<-1> on failure. The difference between
3026 C<isl_pw_qpolynomial_foreach_piece> and
3027 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3028 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3029 compute unique representations for all existentially quantified
3030 variables and then turn these existentially quantified variables
3031 into extra set variables, adapting the associated quasipolynomial
3032 accordingly. This means that the C<set> passed to C<fn>
3033 will not have any existentially quantified variables, but that
3034 the dimensions of the sets may be different for different
3035 invocations of C<fn>.
3037 To iterate over all terms in a quasipolynomial,
3040 int isl_qpolynomial_foreach_term(
3041 __isl_keep isl_qpolynomial *qp,
3042 int (*fn)(__isl_take isl_term *term,
3043 void *user), void *user);
3045 The terms themselves can be inspected and freed using
3048 unsigned isl_term_dim(__isl_keep isl_term *term,
3049 enum isl_dim_type type);
3050 void isl_term_get_num(__isl_keep isl_term *term,
3052 void isl_term_get_den(__isl_keep isl_term *term,
3054 int isl_term_get_exp(__isl_keep isl_term *term,
3055 enum isl_dim_type type, unsigned pos);
3056 __isl_give isl_div *isl_term_get_div(
3057 __isl_keep isl_term *term, unsigned pos);
3058 void isl_term_free(__isl_take isl_term *term);
3060 Each term is a product of parameters, set variables and
3061 integer divisions. The function C<isl_term_get_exp>
3062 returns the exponent of a given dimensions in the given term.
3063 The C<isl_int>s in the arguments of C<isl_term_get_num>
3064 and C<isl_term_get_den> need to have been initialized
3065 using C<isl_int_init> before calling these functions.
3067 =head3 Properties of (Piecewise) Quasipolynomials
3069 To check whether a quasipolynomial is actually a constant,
3070 use the following function.
3072 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3073 isl_int *n, isl_int *d);
3075 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3076 then the numerator and denominator of the constant
3077 are returned in C<*n> and C<*d>, respectively.
3079 =head3 Operations on (Piecewise) Quasipolynomials
3081 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3082 __isl_take isl_qpolynomial *qp, isl_int v);
3083 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3084 __isl_take isl_qpolynomial *qp);
3085 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3086 __isl_take isl_qpolynomial *qp1,
3087 __isl_take isl_qpolynomial *qp2);
3088 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3089 __isl_take isl_qpolynomial *qp1,
3090 __isl_take isl_qpolynomial *qp2);
3091 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3092 __isl_take isl_qpolynomial *qp1,
3093 __isl_take isl_qpolynomial *qp2);
3094 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3095 __isl_take isl_qpolynomial *qp, unsigned exponent);
3097 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3098 __isl_take isl_pw_qpolynomial *pwqp1,
3099 __isl_take isl_pw_qpolynomial *pwqp2);
3100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3101 __isl_take isl_pw_qpolynomial *pwqp1,
3102 __isl_take isl_pw_qpolynomial *pwqp2);
3103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3104 __isl_take isl_pw_qpolynomial *pwqp1,
3105 __isl_take isl_pw_qpolynomial *pwqp2);
3106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3107 __isl_take isl_pw_qpolynomial *pwqp);
3108 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3109 __isl_take isl_pw_qpolynomial *pwqp1,
3110 __isl_take isl_pw_qpolynomial *pwqp2);
3111 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3112 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3114 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3115 __isl_take isl_union_pw_qpolynomial *upwqp1,
3116 __isl_take isl_union_pw_qpolynomial *upwqp2);
3117 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3118 __isl_take isl_union_pw_qpolynomial *upwqp1,
3119 __isl_take isl_union_pw_qpolynomial *upwqp2);
3120 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3121 __isl_take isl_union_pw_qpolynomial *upwqp1,
3122 __isl_take isl_union_pw_qpolynomial *upwqp2);
3124 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3125 __isl_take isl_pw_qpolynomial *pwqp,
3126 __isl_take isl_point *pnt);
3128 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3129 __isl_take isl_union_pw_qpolynomial *upwqp,
3130 __isl_take isl_point *pnt);
3132 __isl_give isl_set *isl_pw_qpolynomial_domain(
3133 __isl_take isl_pw_qpolynomial *pwqp);
3134 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3135 __isl_take isl_pw_qpolynomial *pwpq,
3136 __isl_take isl_set *set);
3138 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3139 __isl_take isl_union_pw_qpolynomial *upwqp);
3140 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3141 __isl_take isl_union_pw_qpolynomial *upwpq,
3142 __isl_take isl_union_set *uset);
3144 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3145 __isl_take isl_qpolynomial *qp,
3146 __isl_take isl_space *model);
3148 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3149 __isl_take isl_qpolynomial *qp);
3150 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3151 __isl_take isl_pw_qpolynomial *pwqp);
3153 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3154 __isl_take isl_union_pw_qpolynomial *upwqp);
3156 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3157 __isl_take isl_qpolynomial *qp,
3158 __isl_take isl_set *context);
3160 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3161 __isl_take isl_pw_qpolynomial *pwqp,
3162 __isl_take isl_set *context);
3164 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3165 __isl_take isl_union_pw_qpolynomial *upwqp,
3166 __isl_take isl_union_set *context);
3168 The gist operation applies the gist operation to each of
3169 the cells in the domain of the input piecewise quasipolynomial.
3170 The context is also exploited
3171 to simplify the quasipolynomials associated to each cell.
3173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3174 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3175 __isl_give isl_union_pw_qpolynomial *
3176 isl_union_pw_qpolynomial_to_polynomial(
3177 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3179 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3180 the polynomial will be an overapproximation. If C<sign> is negative,
3181 it will be an underapproximation. If C<sign> is zero, the approximation
3182 will lie somewhere in between.
3184 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3186 A piecewise quasipolynomial reduction is a piecewise
3187 reduction (or fold) of quasipolynomials.
3188 In particular, the reduction can be maximum or a minimum.
3189 The objects are mainly used to represent the result of
3190 an upper or lower bound on a quasipolynomial over its domain,
3191 i.e., as the result of the following function.
3193 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3194 __isl_take isl_pw_qpolynomial *pwqp,
3195 enum isl_fold type, int *tight);
3197 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3198 __isl_take isl_union_pw_qpolynomial *upwqp,
3199 enum isl_fold type, int *tight);
3201 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3202 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3203 is the returned bound is known be tight, i.e., for each value
3204 of the parameters there is at least
3205 one element in the domain that reaches the bound.
3206 If the domain of C<pwqp> is not wrapping, then the bound is computed
3207 over all elements in that domain and the result has a purely parametric
3208 domain. If the domain of C<pwqp> is wrapping, then the bound is
3209 computed over the range of the wrapped relation. The domain of the
3210 wrapped relation becomes the domain of the result.
3212 A (piecewise) quasipolynomial reduction can be copied or freed using the
3213 following functions.
3215 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3216 __isl_keep isl_qpolynomial_fold *fold);
3217 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3218 __isl_keep isl_pw_qpolynomial_fold *pwf);
3219 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3220 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3221 void isl_qpolynomial_fold_free(
3222 __isl_take isl_qpolynomial_fold *fold);
3223 void *isl_pw_qpolynomial_fold_free(
3224 __isl_take isl_pw_qpolynomial_fold *pwf);
3225 void isl_union_pw_qpolynomial_fold_free(
3226 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3228 =head3 Printing Piecewise Quasipolynomial Reductions
3230 Piecewise quasipolynomial reductions can be printed
3231 using the following function.
3233 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3234 __isl_take isl_printer *p,
3235 __isl_keep isl_pw_qpolynomial_fold *pwf);
3236 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3237 __isl_take isl_printer *p,
3238 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3240 For C<isl_printer_print_pw_qpolynomial_fold>,
3241 output format of the printer
3242 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3243 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3244 output format of the printer
3245 needs to be set to C<ISL_FORMAT_ISL>.
3246 In case of printing in C<ISL_FORMAT_C>, the user may want
3247 to set the names of all dimensions
3249 __isl_give isl_pw_qpolynomial_fold *
3250 isl_pw_qpolynomial_fold_set_dim_name(
3251 __isl_take isl_pw_qpolynomial_fold *pwf,
3252 enum isl_dim_type type, unsigned pos,
3255 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3257 To iterate over all piecewise quasipolynomial reductions in a union
3258 piecewise quasipolynomial reduction, use the following function
3260 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3261 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3262 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3263 void *user), void *user);
3265 To iterate over the cells in a piecewise quasipolynomial reduction,
3266 use either of the following two functions
3268 int isl_pw_qpolynomial_fold_foreach_piece(
3269 __isl_keep isl_pw_qpolynomial_fold *pwf,
3270 int (*fn)(__isl_take isl_set *set,
3271 __isl_take isl_qpolynomial_fold *fold,
3272 void *user), void *user);
3273 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3274 __isl_keep isl_pw_qpolynomial_fold *pwf,
3275 int (*fn)(__isl_take isl_set *set,
3276 __isl_take isl_qpolynomial_fold *fold,
3277 void *user), void *user);
3279 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3280 of the difference between these two functions.
3282 To iterate over all quasipolynomials in a reduction, use
3284 int isl_qpolynomial_fold_foreach_qpolynomial(
3285 __isl_keep isl_qpolynomial_fold *fold,
3286 int (*fn)(__isl_take isl_qpolynomial *qp,
3287 void *user), void *user);
3289 =head3 Operations on Piecewise Quasipolynomial Reductions
3291 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3292 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3294 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3295 __isl_take isl_pw_qpolynomial_fold *pwf1,
3296 __isl_take isl_pw_qpolynomial_fold *pwf2);
3298 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3299 __isl_take isl_pw_qpolynomial_fold *pwf1,
3300 __isl_take isl_pw_qpolynomial_fold *pwf2);
3302 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3303 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3304 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3306 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3307 __isl_take isl_pw_qpolynomial_fold *pwf,
3308 __isl_take isl_point *pnt);
3310 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3311 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3312 __isl_take isl_point *pnt);
3314 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3315 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3316 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3317 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3318 __isl_take isl_union_set *uset);
3320 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3321 __isl_take isl_pw_qpolynomial_fold *pwf);
3323 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3324 __isl_take isl_pw_qpolynomial_fold *pwf);
3326 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3327 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3329 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3330 __isl_take isl_pw_qpolynomial_fold *pwf,
3331 __isl_take isl_set *context);
3333 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3334 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3335 __isl_take isl_union_set *context);
3337 The gist operation applies the gist operation to each of
3338 the cells in the domain of the input piecewise quasipolynomial reduction.
3339 In future, the operation will also exploit the context
3340 to simplify the quasipolynomial reductions associated to each cell.
3342 __isl_give isl_pw_qpolynomial_fold *
3343 isl_set_apply_pw_qpolynomial_fold(
3344 __isl_take isl_set *set,
3345 __isl_take isl_pw_qpolynomial_fold *pwf,
3347 __isl_give isl_pw_qpolynomial_fold *
3348 isl_map_apply_pw_qpolynomial_fold(
3349 __isl_take isl_map *map,
3350 __isl_take isl_pw_qpolynomial_fold *pwf,
3352 __isl_give isl_union_pw_qpolynomial_fold *
3353 isl_union_set_apply_union_pw_qpolynomial_fold(
3354 __isl_take isl_union_set *uset,
3355 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3357 __isl_give isl_union_pw_qpolynomial_fold *
3358 isl_union_map_apply_union_pw_qpolynomial_fold(
3359 __isl_take isl_union_map *umap,
3360 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3363 The functions taking a map
3364 compose the given map with the given piecewise quasipolynomial reduction.
3365 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3366 over all elements in the intersection of the range of the map
3367 and the domain of the piecewise quasipolynomial reduction
3368 as a function of an element in the domain of the map.
3369 The functions taking a set compute a bound over all elements in the
3370 intersection of the set and the domain of the
3371 piecewise quasipolynomial reduction.
3373 =head2 Dependence Analysis
3375 C<isl> contains specialized functionality for performing
3376 array dataflow analysis. That is, given a I<sink> access relation
3377 and a collection of possible I<source> access relations,
3378 C<isl> can compute relations that describe
3379 for each iteration of the sink access, which iteration
3380 of which of the source access relations was the last
3381 to access the same data element before the given iteration
3383 To compute standard flow dependences, the sink should be
3384 a read, while the sources should be writes.
3385 If any of the source accesses are marked as being I<may>
3386 accesses, then there will be a dependence to the last
3387 I<must> access B<and> to any I<may> access that follows
3388 this last I<must> access.
3389 In particular, if I<all> sources are I<may> accesses,
3390 then memory based dependence analysis is performed.
3391 If, on the other hand, all sources are I<must> accesses,
3392 then value based dependence analysis is performed.
3394 #include <isl/flow.h>
3396 typedef int (*isl_access_level_before)(void *first, void *second);
3398 __isl_give isl_access_info *isl_access_info_alloc(
3399 __isl_take isl_map *sink,
3400 void *sink_user, isl_access_level_before fn,
3402 __isl_give isl_access_info *isl_access_info_add_source(
3403 __isl_take isl_access_info *acc,
3404 __isl_take isl_map *source, int must,
3406 void isl_access_info_free(__isl_take isl_access_info *acc);
3408 __isl_give isl_flow *isl_access_info_compute_flow(
3409 __isl_take isl_access_info *acc);
3411 int isl_flow_foreach(__isl_keep isl_flow *deps,
3412 int (*fn)(__isl_take isl_map *dep, int must,
3413 void *dep_user, void *user),
3415 __isl_give isl_map *isl_flow_get_no_source(
3416 __isl_keep isl_flow *deps, int must);
3417 void isl_flow_free(__isl_take isl_flow *deps);
3419 The function C<isl_access_info_compute_flow> performs the actual
3420 dependence analysis. The other functions are used to construct
3421 the input for this function or to read off the output.
3423 The input is collected in an C<isl_access_info>, which can
3424 be created through a call to C<isl_access_info_alloc>.
3425 The arguments to this functions are the sink access relation
3426 C<sink>, a token C<sink_user> used to identify the sink
3427 access to the user, a callback function for specifying the
3428 relative order of source and sink accesses, and the number
3429 of source access relations that will be added.
3430 The callback function has type C<int (*)(void *first, void *second)>.
3431 The function is called with two user supplied tokens identifying
3432 either a source or the sink and it should return the shared nesting
3433 level and the relative order of the two accesses.
3434 In particular, let I<n> be the number of loops shared by
3435 the two accesses. If C<first> precedes C<second> textually,
3436 then the function should return I<2 * n + 1>; otherwise,
3437 it should return I<2 * n>.
3438 The sources can be added to the C<isl_access_info> by performing
3439 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3440 C<must> indicates whether the source is a I<must> access
3441 or a I<may> access. Note that a multi-valued access relation
3442 should only be marked I<must> if every iteration in the domain
3443 of the relation accesses I<all> elements in its image.
3444 The C<source_user> token is again used to identify
3445 the source access. The range of the source access relation
3446 C<source> should have the same dimension as the range
3447 of the sink access relation.
3448 The C<isl_access_info_free> function should usually not be
3449 called explicitly, because it is called implicitly by
3450 C<isl_access_info_compute_flow>.
3452 The result of the dependence analysis is collected in an
3453 C<isl_flow>. There may be elements of
3454 the sink access for which no preceding source access could be
3455 found or for which all preceding sources are I<may> accesses.
3456 The relations containing these elements can be obtained through
3457 calls to C<isl_flow_get_no_source>, the first with C<must> set
3458 and the second with C<must> unset.
3459 In the case of standard flow dependence analysis,
3460 with the sink a read and the sources I<must> writes,
3461 the first relation corresponds to the reads from uninitialized
3462 array elements and the second relation is empty.
3463 The actual flow dependences can be extracted using
3464 C<isl_flow_foreach>. This function will call the user-specified
3465 callback function C<fn> for each B<non-empty> dependence between
3466 a source and the sink. The callback function is called
3467 with four arguments, the actual flow dependence relation
3468 mapping source iterations to sink iterations, a boolean that
3469 indicates whether it is a I<must> or I<may> dependence, a token
3470 identifying the source and an additional C<void *> with value
3471 equal to the third argument of the C<isl_flow_foreach> call.
3472 A dependence is marked I<must> if it originates from a I<must>
3473 source and if it is not followed by any I<may> sources.
3475 After finishing with an C<isl_flow>, the user should call
3476 C<isl_flow_free> to free all associated memory.
3478 A higher-level interface to dependence analysis is provided
3479 by the following function.
3481 #include <isl/flow.h>
3483 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3484 __isl_take isl_union_map *must_source,
3485 __isl_take isl_union_map *may_source,
3486 __isl_take isl_union_map *schedule,
3487 __isl_give isl_union_map **must_dep,
3488 __isl_give isl_union_map **may_dep,
3489 __isl_give isl_union_map **must_no_source,
3490 __isl_give isl_union_map **may_no_source);
3492 The arrays are identified by the tuple names of the ranges
3493 of the accesses. The iteration domains by the tuple names
3494 of the domains of the accesses and of the schedule.
3495 The relative order of the iteration domains is given by the
3496 schedule. The relations returned through C<must_no_source>
3497 and C<may_no_source> are subsets of C<sink>.
3498 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3499 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3500 any of the other arguments is treated as an error.
3504 B<The functionality described in this section is fairly new
3505 and may be subject to change.>
3507 The following function can be used to compute a schedule
3508 for a union of domains. The generated schedule respects
3509 all C<validity> dependences. That is, all dependence distances
3510 over these dependences in the scheduled space are lexicographically
3511 positive. The generated schedule schedule also tries to minimize
3512 the dependence distances over C<proximity> dependences.
3513 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3514 for groups of domains where the dependence distances have only
3515 non-negative values.
3516 The algorithm used to construct the schedule is similar to that
3519 #include <isl/schedule.h>
3520 __isl_give isl_schedule *isl_union_set_compute_schedule(
3521 __isl_take isl_union_set *domain,
3522 __isl_take isl_union_map *validity,
3523 __isl_take isl_union_map *proximity);
3524 void *isl_schedule_free(__isl_take isl_schedule *sched);
3526 A mapping from the domains to the scheduled space can be obtained
3527 from an C<isl_schedule> using the following function.
3529 __isl_give isl_union_map *isl_schedule_get_map(
3530 __isl_keep isl_schedule *sched);
3532 A representation of the schedule can be printed using
3534 __isl_give isl_printer *isl_printer_print_schedule(
3535 __isl_take isl_printer *p,
3536 __isl_keep isl_schedule *schedule);
3538 A representation of the schedule as a forest of bands can be obtained
3539 using the following function.
3541 __isl_give isl_band_list *isl_schedule_get_band_forest(
3542 __isl_keep isl_schedule *schedule);
3544 The list can be manipulated as explained in L<"Lists">.
3545 The bands inside the list can be copied and freed using the following
3548 #include <isl/band.h>
3549 __isl_give isl_band *isl_band_copy(
3550 __isl_keep isl_band *band);
3551 void *isl_band_free(__isl_take isl_band *band);
3553 Each band contains zero or more scheduling dimensions.
3554 These are referred to as the members of the band.
3555 The section of the schedule that corresponds to the band is
3556 referred to as the partial schedule of the band.
3557 For those nodes that participate in a band, the outer scheduling
3558 dimensions form the prefix schedule, while the inner scheduling
3559 dimensions form the suffix schedule.
3560 That is, if we take a cut of the band forest, then the union of
3561 the concatenations of the prefix, partial and suffix schedules of
3562 each band in the cut is equal to the entire schedule (modulo
3563 some possible padding at the end with zero scheduling dimensions).
3564 The properties of a band can be inspected using the following functions.
3566 #include <isl/band.h>
3567 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3569 int isl_band_has_children(__isl_keep isl_band *band);
3570 __isl_give isl_band_list *isl_band_get_children(
3571 __isl_keep isl_band *band);
3573 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3574 __isl_keep isl_band *band);
3575 __isl_give isl_union_map *isl_band_get_partial_schedule(
3576 __isl_keep isl_band *band);
3577 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3578 __isl_keep isl_band *band);
3580 int isl_band_n_member(__isl_keep isl_band *band);
3581 int isl_band_member_is_zero_distance(
3582 __isl_keep isl_band *band, int pos);
3584 Note that a scheduling dimension is considered to be ``zero
3585 distance'' if it does not carry any proximity dependences
3587 That is, if the dependence distances of the proximity
3588 dependences are all zero in that direction (for fixed
3589 iterations of outer bands).
3591 A representation of the band can be printed using
3593 #include <isl/band.h>
3594 __isl_give isl_printer *isl_printer_print_band(
3595 __isl_take isl_printer *p,
3596 __isl_keep isl_band *band);
3598 =head2 Parametric Vertex Enumeration
3600 The parametric vertex enumeration described in this section
3601 is mainly intended to be used internally and by the C<barvinok>
3604 #include <isl/vertices.h>
3605 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3606 __isl_keep isl_basic_set *bset);
3608 The function C<isl_basic_set_compute_vertices> performs the
3609 actual computation of the parametric vertices and the chamber
3610 decomposition and store the result in an C<isl_vertices> object.
3611 This information can be queried by either iterating over all
3612 the vertices or iterating over all the chambers or cells
3613 and then iterating over all vertices that are active on the chamber.
3615 int isl_vertices_foreach_vertex(
3616 __isl_keep isl_vertices *vertices,
3617 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3620 int isl_vertices_foreach_cell(
3621 __isl_keep isl_vertices *vertices,
3622 int (*fn)(__isl_take isl_cell *cell, void *user),
3624 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3625 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3628 Other operations that can be performed on an C<isl_vertices> object are
3631 isl_ctx *isl_vertices_get_ctx(
3632 __isl_keep isl_vertices *vertices);
3633 int isl_vertices_get_n_vertices(
3634 __isl_keep isl_vertices *vertices);
3635 void isl_vertices_free(__isl_take isl_vertices *vertices);
3637 Vertices can be inspected and destroyed using the following functions.
3639 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3640 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3641 __isl_give isl_basic_set *isl_vertex_get_domain(
3642 __isl_keep isl_vertex *vertex);
3643 __isl_give isl_basic_set *isl_vertex_get_expr(
3644 __isl_keep isl_vertex *vertex);
3645 void isl_vertex_free(__isl_take isl_vertex *vertex);
3647 C<isl_vertex_get_expr> returns a singleton parametric set describing
3648 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3650 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3651 B<rational> basic sets, so they should mainly be used for inspection
3652 and should not be mixed with integer sets.
3654 Chambers can be inspected and destroyed using the following functions.
3656 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3657 __isl_give isl_basic_set *isl_cell_get_domain(
3658 __isl_keep isl_cell *cell);
3659 void isl_cell_free(__isl_take isl_cell *cell);
3663 Although C<isl> is mainly meant to be used as a library,
3664 it also contains some basic applications that use some
3665 of the functionality of C<isl>.
3666 The input may be specified in either the L<isl format>
3667 or the L<PolyLib format>.
3669 =head2 C<isl_polyhedron_sample>
3671 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3672 an integer element of the polyhedron, if there is any.
3673 The first column in the output is the denominator and is always
3674 equal to 1. If the polyhedron contains no integer points,
3675 then a vector of length zero is printed.
3679 C<isl_pip> takes the same input as the C<example> program
3680 from the C<piplib> distribution, i.e., a set of constraints
3681 on the parameters, a line containing only -1 and finally a set
3682 of constraints on a parametric polyhedron.
3683 The coefficients of the parameters appear in the last columns
3684 (but before the final constant column).
3685 The output is the lexicographic minimum of the parametric polyhedron.
3686 As C<isl> currently does not have its own output format, the output
3687 is just a dump of the internal state.
3689 =head2 C<isl_polyhedron_minimize>
3691 C<isl_polyhedron_minimize> computes the minimum of some linear
3692 or affine objective function over the integer points in a polyhedron.
3693 If an affine objective function
3694 is given, then the constant should appear in the last column.
3696 =head2 C<isl_polytope_scan>
3698 Given a polytope, C<isl_polytope_scan> prints
3699 all integer points in the polytope.