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
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
149 The source of C<isl> can be obtained either as a tarball
150 or from the git repository. Both are available from
151 L<http://freshmeat.net/projects/isl/>.
152 The installation process depends on how you obtained
155 =head2 Installation from the git repository
159 =item 1 Clone or update the repository
161 The first time the source is obtained, you need to clone
164 git clone git://repo.or.cz/isl.git
166 To obtain updates, you need to pull in the latest changes
170 =item 2 Generate C<configure>
176 After performing the above steps, continue
177 with the L<Common installation instructions>.
179 =head2 Common installation instructions
183 =item 1 Obtain C<GMP>
185 Building C<isl> requires C<GMP>, including its headers files.
186 Your distribution may not provide these header files by default
187 and you may need to install a package called C<gmp-devel> or something
188 similar. Alternatively, C<GMP> can be built from
189 source, available from L<http://gmplib.org/>.
193 C<isl> uses the standard C<autoconf> C<configure> script.
198 optionally followed by some configure options.
199 A complete list of options can be obtained by running
203 Below we discuss some of the more common options.
205 C<isl> can optionally use C<piplib>, but no
206 C<piplib> functionality is currently used by default.
207 The C<--with-piplib> option can
208 be used to specify which C<piplib>
209 library to use, either an installed version (C<system>),
210 an externally built version (C<build>)
211 or no version (C<no>). The option C<build> is mostly useful
212 in C<configure> scripts of larger projects that bundle both C<isl>
219 Installation prefix for C<isl>
221 =item C<--with-gmp-prefix>
223 Installation prefix for C<GMP> (architecture-independent files).
225 =item C<--with-gmp-exec-prefix>
227 Installation prefix for C<GMP> (architecture-dependent files).
229 =item C<--with-piplib>
231 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
233 =item C<--with-piplib-prefix>
235 Installation prefix for C<system> C<piplib> (architecture-independent files).
237 =item C<--with-piplib-exec-prefix>
239 Installation prefix for C<system> C<piplib> (architecture-dependent files).
241 =item C<--with-piplib-builddir>
243 Location where C<build> C<piplib> was built.
251 =item 4 Install (optional)
259 =head2 Initialization
261 All manipulations of integer sets and relations occur within
262 the context of an C<isl_ctx>.
263 A given C<isl_ctx> can only be used within a single thread.
264 All arguments of a function are required to have been allocated
265 within the same context.
266 There are currently no functions available for moving an object
267 from one C<isl_ctx> to another C<isl_ctx>. This means that
268 there is currently no way of safely moving an object from one
269 thread to another, unless the whole C<isl_ctx> is moved.
271 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
272 freed using C<isl_ctx_free>.
273 All objects allocated within an C<isl_ctx> should be freed
274 before the C<isl_ctx> itself is freed.
276 isl_ctx *isl_ctx_alloc();
277 void isl_ctx_free(isl_ctx *ctx);
281 All operations on integers, mainly the coefficients
282 of the constraints describing the sets and relations,
283 are performed in exact integer arithmetic using C<GMP>.
284 However, to allow future versions of C<isl> to optionally
285 support fixed integer arithmetic, all calls to C<GMP>
286 are wrapped inside C<isl> specific macros.
287 The basic type is C<isl_int> and the operations below
288 are available on this type.
289 The meanings of these operations are essentially the same
290 as their C<GMP> C<mpz_> counterparts.
291 As always with C<GMP> types, C<isl_int>s need to be
292 initialized with C<isl_int_init> before they can be used
293 and they need to be released with C<isl_int_clear>
295 The user should not assume that an C<isl_int> is represented
296 as a C<mpz_t>, but should instead explicitly convert between
297 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
298 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
302 =item isl_int_init(i)
304 =item isl_int_clear(i)
306 =item isl_int_set(r,i)
308 =item isl_int_set_si(r,i)
310 =item isl_int_set_gmp(r,g)
312 =item isl_int_get_gmp(i,g)
314 =item isl_int_abs(r,i)
316 =item isl_int_neg(r,i)
318 =item isl_int_swap(i,j)
320 =item isl_int_swap_or_set(i,j)
322 =item isl_int_add_ui(r,i,j)
324 =item isl_int_sub_ui(r,i,j)
326 =item isl_int_add(r,i,j)
328 =item isl_int_sub(r,i,j)
330 =item isl_int_mul(r,i,j)
332 =item isl_int_mul_ui(r,i,j)
334 =item isl_int_addmul(r,i,j)
336 =item isl_int_submul(r,i,j)
338 =item isl_int_gcd(r,i,j)
340 =item isl_int_lcm(r,i,j)
342 =item isl_int_divexact(r,i,j)
344 =item isl_int_cdiv_q(r,i,j)
346 =item isl_int_fdiv_q(r,i,j)
348 =item isl_int_fdiv_r(r,i,j)
350 =item isl_int_fdiv_q_ui(r,i,j)
352 =item isl_int_read(r,s)
354 =item isl_int_print(out,i,width)
358 =item isl_int_cmp(i,j)
360 =item isl_int_cmp_si(i,si)
362 =item isl_int_eq(i,j)
364 =item isl_int_ne(i,j)
366 =item isl_int_lt(i,j)
368 =item isl_int_le(i,j)
370 =item isl_int_gt(i,j)
372 =item isl_int_ge(i,j)
374 =item isl_int_abs_eq(i,j)
376 =item isl_int_abs_ne(i,j)
378 =item isl_int_abs_lt(i,j)
380 =item isl_int_abs_gt(i,j)
382 =item isl_int_abs_ge(i,j)
384 =item isl_int_is_zero(i)
386 =item isl_int_is_one(i)
388 =item isl_int_is_negone(i)
390 =item isl_int_is_pos(i)
392 =item isl_int_is_neg(i)
394 =item isl_int_is_nonpos(i)
396 =item isl_int_is_nonneg(i)
398 =item isl_int_is_divisible_by(i,j)
402 =head2 Sets and Relations
404 C<isl> uses six types of objects for representing sets and relations,
405 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
406 C<isl_union_set> and C<isl_union_map>.
407 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
408 can be described as a conjunction of affine constraints, while
409 C<isl_set> and C<isl_map> represent unions of
410 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
411 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
412 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
413 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
414 where spaces are considered different if they have a different number
415 of dimensions and/or different names (see L<"Spaces">).
416 The difference between sets and relations (maps) is that sets have
417 one set of variables, while relations have two sets of variables,
418 input variables and output variables.
420 =head2 Memory Management
422 Since a high-level operation on sets and/or relations usually involves
423 several substeps and since the user is usually not interested in
424 the intermediate results, most functions that return a new object
425 will also release all the objects passed as arguments.
426 If the user still wants to use one or more of these arguments
427 after the function call, she should pass along a copy of the
428 object rather than the object itself.
429 The user is then responsible for making sure that the original
430 object gets used somewhere else or is explicitly freed.
432 The arguments and return values of all documented functions are
433 annotated to make clear which arguments are released and which
434 arguments are preserved. In particular, the following annotations
441 C<__isl_give> means that a new object is returned.
442 The user should make sure that the returned pointer is
443 used exactly once as a value for an C<__isl_take> argument.
444 In between, it can be used as a value for as many
445 C<__isl_keep> arguments as the user likes.
446 There is one exception, and that is the case where the
447 pointer returned is C<NULL>. Is this case, the user
448 is free to use it as an C<__isl_take> argument or not.
452 C<__isl_take> means that the object the argument points to
453 is taken over by the function and may no longer be used
454 by the user as an argument to any other function.
455 The pointer value must be one returned by a function
456 returning an C<__isl_give> pointer.
457 If the user passes in a C<NULL> value, then this will
458 be treated as an error in the sense that the function will
459 not perform its usual operation. However, it will still
460 make sure that all the other C<__isl_take> arguments
465 C<__isl_keep> means that the function will only use the object
466 temporarily. After the function has finished, the user
467 can still use it as an argument to other functions.
468 A C<NULL> value will be treated in the same way as
469 a C<NULL> value for an C<__isl_take> argument.
475 Identifiers are used to identify both individual dimensions
476 and tuples of dimensions. They consist of a name and an optional
477 pointer. Identifiers with the same name but different pointer values
478 are considered to be distinct.
479 Identifiers can be constructed, copied, freed, inspected and printed
480 using the following functions.
483 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
484 __isl_keep const char *name, void *user);
485 __isl_give isl_id *isl_id_copy(isl_id *id);
486 void *isl_id_free(__isl_take isl_id *id);
488 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
489 void *isl_id_get_user(__isl_keep isl_id *id);
490 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
492 __isl_give isl_printer *isl_printer_print_id(
493 __isl_take isl_printer *p, __isl_keep isl_id *id);
495 Note that C<isl_id_get_name> returns a pointer to some internal
496 data structure, so the result can only be used while the
497 corresponding C<isl_id> is alive.
501 Whenever a new set or relation is created from scratch,
502 the space in which it lives needs to be specified using an C<isl_space>.
504 #include <isl/space.h>
505 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
506 unsigned nparam, unsigned n_in, unsigned n_out);
507 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
509 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
510 unsigned nparam, unsigned dim);
511 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
512 void isl_space_free(__isl_take isl_space *space);
513 unsigned isl_space_dim(__isl_keep isl_space *space,
514 enum isl_dim_type type);
516 The space used for creating a parameter domain
517 needs to be created using C<isl_space_params_alloc>.
518 For other sets, the space
519 needs to be created using C<isl_space_set_alloc>, while
520 for a relation, the space
521 needs to be created using C<isl_space_alloc>.
522 C<isl_space_dim> can be used
523 to find out the number of dimensions of each type in
524 a space, where type may be
525 C<isl_dim_param>, C<isl_dim_in> (only for relations),
526 C<isl_dim_out> (only for relations), C<isl_dim_set>
527 (only for sets) or C<isl_dim_all>.
529 To check whether a given space is that of a set or a map
530 or whether it is a parameter space, use these functions:
532 #include <isl/space.h>
533 int isl_space_is_params(__isl_keep isl_space *space);
534 int isl_space_is_set(__isl_keep isl_space *space);
536 It is often useful to create objects that live in the
537 same space as some other object. This can be accomplished
538 by creating the new objects
539 (see L<Creating New Sets and Relations> or
540 L<Creating New (Piecewise) Quasipolynomials>) based on the space
541 of the original object.
544 __isl_give isl_space *isl_basic_set_get_space(
545 __isl_keep isl_basic_set *bset);
546 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
548 #include <isl/union_set.h>
549 __isl_give isl_space *isl_union_set_get_space(
550 __isl_keep isl_union_set *uset);
553 __isl_give isl_space *isl_basic_map_get_space(
554 __isl_keep isl_basic_map *bmap);
555 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
557 #include <isl/union_map.h>
558 __isl_give isl_space *isl_union_map_get_space(
559 __isl_keep isl_union_map *umap);
561 #include <isl/constraint.h>
562 __isl_give isl_space *isl_constraint_get_space(
563 __isl_keep isl_constraint *constraint);
565 #include <isl/polynomial.h>
566 __isl_give isl_space *isl_qpolynomial_get_domain_space(
567 __isl_keep isl_qpolynomial *qp);
568 __isl_give isl_space *isl_qpolynomial_get_space(
569 __isl_keep isl_qpolynomial *qp);
570 __isl_give isl_space *isl_qpolynomial_fold_get_space(
571 __isl_keep isl_qpolynomial_fold *fold);
572 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
573 __isl_keep isl_pw_qpolynomial *pwqp);
574 __isl_give isl_space *isl_pw_qpolynomial_get_space(
575 __isl_keep isl_pw_qpolynomial *pwqp);
576 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
577 __isl_keep isl_pw_qpolynomial_fold *pwf);
578 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
579 __isl_keep isl_pw_qpolynomial_fold *pwf);
580 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
581 __isl_keep isl_union_pw_qpolynomial *upwqp);
582 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
583 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
586 __isl_give isl_space *isl_aff_get_domain_space(
587 __isl_keep isl_aff *aff);
588 __isl_give isl_space *isl_aff_get_space(
589 __isl_keep isl_aff *aff);
590 __isl_give isl_space *isl_pw_aff_get_domain_space(
591 __isl_keep isl_pw_aff *pwaff);
592 __isl_give isl_space *isl_pw_aff_get_space(
593 __isl_keep isl_pw_aff *pwaff);
595 #include <isl/point.h>
596 __isl_give isl_space *isl_point_get_space(
597 __isl_keep isl_point *pnt);
599 The identifiers or names of the individual dimensions may be set or read off
600 using the following functions.
602 #include <isl/space.h>
603 __isl_give isl_space *isl_space_set_dim_id(
604 __isl_take isl_space *space,
605 enum isl_dim_type type, unsigned pos,
606 __isl_take isl_id *id);
607 int isl_space_has_dim_id(__isl_keep isl_space *space,
608 enum isl_dim_type type, unsigned pos);
609 __isl_give isl_id *isl_space_get_dim_id(
610 __isl_keep isl_space *space,
611 enum isl_dim_type type, unsigned pos);
612 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
613 enum isl_dim_type type, unsigned pos,
614 __isl_keep const char *name);
615 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
616 enum isl_dim_type type, unsigned pos);
618 Note that C<isl_space_get_name> returns a pointer to some internal
619 data structure, so the result can only be used while the
620 corresponding C<isl_space> is alive.
621 Also note that every function that operates on two sets or relations
622 requires that both arguments have the same parameters. This also
623 means that if one of the arguments has named parameters, then the
624 other needs to have named parameters too and the names need to match.
625 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
626 arguments may have different parameters (as long as they are named),
627 in which case the result will have as parameters the union of the parameters of
630 Given the identifier of a dimension (typically a parameter),
631 its position can be obtained from the following function.
633 #include <isl/space.h>
634 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
635 enum isl_dim_type type, __isl_keep isl_id *id);
637 The identifiers or names of entire spaces may be set or read off
638 using the following functions.
640 #include <isl/space.h>
641 __isl_give isl_space *isl_space_set_tuple_id(
642 __isl_take isl_space *space,
643 enum isl_dim_type type, __isl_take isl_id *id);
644 __isl_give isl_space *isl_space_reset_tuple_id(
645 __isl_take isl_space *space, enum isl_dim_type type);
646 int isl_space_has_tuple_id(__isl_keep isl_space *space,
647 enum isl_dim_type type);
648 __isl_give isl_id *isl_space_get_tuple_id(
649 __isl_keep isl_space *space, enum isl_dim_type type);
650 __isl_give isl_space *isl_space_set_tuple_name(
651 __isl_take isl_space *space,
652 enum isl_dim_type type, const char *s);
653 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
654 enum isl_dim_type type);
656 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
657 or C<isl_dim_set>. As with C<isl_space_get_name>,
658 the C<isl_space_get_tuple_name> function returns a pointer to some internal
660 Binary operations require the corresponding spaces of their arguments
661 to have the same name.
663 Spaces can be nested. In particular, the domain of a set or
664 the domain or range of a relation can be a nested relation.
665 The following functions can be used to construct and deconstruct
668 #include <isl/space.h>
669 int isl_space_is_wrapping(__isl_keep isl_space *space);
670 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
671 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
673 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
674 be the space of a set, while that of
675 C<isl_space_wrap> should be the space of a relation.
676 Conversely, the output of C<isl_space_unwrap> is the space
677 of a relation, while that of C<isl_space_wrap> is the space of a set.
679 Spaces can be created from other spaces
680 using the following functions.
682 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
683 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
684 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
685 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
686 __isl_give isl_space *isl_space_params(
687 __isl_take isl_space *space);
688 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
689 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
690 __isl_take isl_space *right);
691 __isl_give isl_space *isl_space_align_params(
692 __isl_take isl_space *space1, __isl_take isl_space *space2)
693 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
694 enum isl_dim_type type, unsigned pos, unsigned n);
695 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
696 enum isl_dim_type type, unsigned n);
697 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
698 enum isl_dim_type type, unsigned first, unsigned n);
699 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
700 enum isl_dim_type dst_type, unsigned dst_pos,
701 enum isl_dim_type src_type, unsigned src_pos,
703 __isl_give isl_space *isl_space_map_from_set(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
707 Note that if dimensions are added or removed from a space, then
708 the name and the internal structure are lost.
712 A local space is essentially a space with
713 zero or more existentially quantified variables.
714 The local space of a basic set or relation can be obtained
715 using the following functions.
718 __isl_give isl_local_space *isl_basic_set_get_local_space(
719 __isl_keep isl_basic_set *bset);
722 __isl_give isl_local_space *isl_basic_map_get_local_space(
723 __isl_keep isl_basic_map *bmap);
725 A new local space can be created from a space using
727 #include <isl/local_space.h>
728 __isl_give isl_local_space *isl_local_space_from_space(
729 __isl_take isl_space *space);
731 They can be inspected, copied and freed using the following functions.
733 #include <isl/local_space.h>
734 isl_ctx *isl_local_space_get_ctx(
735 __isl_keep isl_local_space *ls);
736 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
737 int isl_local_space_dim(__isl_keep isl_local_space *ls,
738 enum isl_dim_type type);
739 const char *isl_local_space_get_dim_name(
740 __isl_keep isl_local_space *ls,
741 enum isl_dim_type type, unsigned pos);
742 __isl_give isl_local_space *isl_local_space_set_dim_name(
743 __isl_take isl_local_space *ls,
744 enum isl_dim_type type, unsigned pos, const char *s);
745 __isl_give isl_space *isl_local_space_get_space(
746 __isl_keep isl_local_space *ls);
747 __isl_give isl_aff *isl_local_space_get_div(
748 __isl_keep isl_local_space *ls, int pos);
749 __isl_give isl_local_space *isl_local_space_copy(
750 __isl_keep isl_local_space *ls);
751 void *isl_local_space_free(__isl_take isl_local_space *ls);
753 Two local spaces can be compared using
755 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
756 __isl_keep isl_local_space *ls2);
758 Local spaces can be created from other local spaces
759 using the following functions.
761 __isl_give isl_local_space *isl_local_space_domain(
762 __isl_take isl_local_space *ls);
763 __isl_give isl_local_space *isl_local_space_from_domain(
764 __isl_take isl_local_space *ls);
765 __isl_give isl_local_space *isl_local_space_add_dims(
766 __isl_take isl_local_space *ls,
767 enum isl_dim_type type, unsigned n);
768 __isl_give isl_local_space *isl_local_space_insert_dims(
769 __isl_take isl_local_space *ls,
770 enum isl_dim_type type, unsigned first, unsigned n);
771 __isl_give isl_local_space *isl_local_space_drop_dims(
772 __isl_take isl_local_space *ls,
773 enum isl_dim_type type, unsigned first, unsigned n);
775 =head2 Input and Output
777 C<isl> supports its own input/output format, which is similar
778 to the C<Omega> format, but also supports the C<PolyLib> format
783 The C<isl> format is similar to that of C<Omega>, but has a different
784 syntax for describing the parameters and allows for the definition
785 of an existentially quantified variable as the integer division
786 of an affine expression.
787 For example, the set of integers C<i> between C<0> and C<n>
788 such that C<i % 10 <= 6> can be described as
790 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
793 A set or relation can have several disjuncts, separated
794 by the keyword C<or>. Each disjunct is either a conjunction
795 of constraints or a projection (C<exists>) of a conjunction
796 of constraints. The constraints are separated by the keyword
799 =head3 C<PolyLib> format
801 If the represented set is a union, then the first line
802 contains a single number representing the number of disjuncts.
803 Otherwise, a line containing the number C<1> is optional.
805 Each disjunct is represented by a matrix of constraints.
806 The first line contains two numbers representing
807 the number of rows and columns,
808 where the number of rows is equal to the number of constraints
809 and the number of columns is equal to two plus the number of variables.
810 The following lines contain the actual rows of the constraint matrix.
811 In each row, the first column indicates whether the constraint
812 is an equality (C<0>) or inequality (C<1>). The final column
813 corresponds to the constant term.
815 If the set is parametric, then the coefficients of the parameters
816 appear in the last columns before the constant column.
817 The coefficients of any existentially quantified variables appear
818 between those of the set variables and those of the parameters.
820 =head3 Extended C<PolyLib> format
822 The extended C<PolyLib> format is nearly identical to the
823 C<PolyLib> format. The only difference is that the line
824 containing the number of rows and columns of a constraint matrix
825 also contains four additional numbers:
826 the number of output dimensions, the number of input dimensions,
827 the number of local dimensions (i.e., the number of existentially
828 quantified variables) and the number of parameters.
829 For sets, the number of ``output'' dimensions is equal
830 to the number of set dimensions, while the number of ``input''
836 __isl_give isl_basic_set *isl_basic_set_read_from_file(
837 isl_ctx *ctx, FILE *input, int nparam);
838 __isl_give isl_basic_set *isl_basic_set_read_from_str(
839 isl_ctx *ctx, const char *str, int nparam);
840 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
841 FILE *input, int nparam);
842 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
843 const char *str, int nparam);
846 __isl_give isl_basic_map *isl_basic_map_read_from_file(
847 isl_ctx *ctx, FILE *input, int nparam);
848 __isl_give isl_basic_map *isl_basic_map_read_from_str(
849 isl_ctx *ctx, const char *str, int nparam);
850 __isl_give isl_map *isl_map_read_from_file(
851 isl_ctx *ctx, FILE *input, int nparam);
852 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
853 const char *str, int nparam);
855 #include <isl/union_set.h>
856 __isl_give isl_union_set *isl_union_set_read_from_file(
857 isl_ctx *ctx, FILE *input);
858 __isl_give isl_union_set *isl_union_set_read_from_str(
859 isl_ctx *ctx, const char *str);
861 #include <isl/union_map.h>
862 __isl_give isl_union_map *isl_union_map_read_from_file(
863 isl_ctx *ctx, FILE *input);
864 __isl_give isl_union_map *isl_union_map_read_from_str(
865 isl_ctx *ctx, const char *str);
867 The input format is autodetected and may be either the C<PolyLib> format
868 or the C<isl> format.
869 C<nparam> specifies how many of the final columns in
870 the C<PolyLib> format correspond to parameters.
871 If input is given in the C<isl> format, then the number
872 of parameters needs to be equal to C<nparam>.
873 If C<nparam> is negative, then any number of parameters
874 is accepted in the C<isl> format and zero parameters
875 are assumed in the C<PolyLib> format.
879 Before anything can be printed, an C<isl_printer> needs to
882 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
884 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
885 void isl_printer_free(__isl_take isl_printer *printer);
886 __isl_give char *isl_printer_get_str(
887 __isl_keep isl_printer *printer);
889 The behavior of the printer can be modified in various ways
891 __isl_give isl_printer *isl_printer_set_output_format(
892 __isl_take isl_printer *p, int output_format);
893 __isl_give isl_printer *isl_printer_set_indent(
894 __isl_take isl_printer *p, int indent);
895 __isl_give isl_printer *isl_printer_indent(
896 __isl_take isl_printer *p, int indent);
897 __isl_give isl_printer *isl_printer_set_prefix(
898 __isl_take isl_printer *p, const char *prefix);
899 __isl_give isl_printer *isl_printer_set_suffix(
900 __isl_take isl_printer *p, const char *suffix);
902 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
903 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
904 and defaults to C<ISL_FORMAT_ISL>.
905 Each line in the output is indented by C<indent> (set by
906 C<isl_printer_set_indent>) spaces
907 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
908 In the C<PolyLib> format output,
909 the coefficients of the existentially quantified variables
910 appear between those of the set variables and those
912 The function C<isl_printer_indent> increases the indentation
913 by the specified amount (which may be negative).
915 To actually print something, use
918 __isl_give isl_printer *isl_printer_print_basic_set(
919 __isl_take isl_printer *printer,
920 __isl_keep isl_basic_set *bset);
921 __isl_give isl_printer *isl_printer_print_set(
922 __isl_take isl_printer *printer,
923 __isl_keep isl_set *set);
926 __isl_give isl_printer *isl_printer_print_basic_map(
927 __isl_take isl_printer *printer,
928 __isl_keep isl_basic_map *bmap);
929 __isl_give isl_printer *isl_printer_print_map(
930 __isl_take isl_printer *printer,
931 __isl_keep isl_map *map);
933 #include <isl/union_set.h>
934 __isl_give isl_printer *isl_printer_print_union_set(
935 __isl_take isl_printer *p,
936 __isl_keep isl_union_set *uset);
938 #include <isl/union_map.h>
939 __isl_give isl_printer *isl_printer_print_union_map(
940 __isl_take isl_printer *p,
941 __isl_keep isl_union_map *umap);
943 When called on a file printer, the following function flushes
944 the file. When called on a string printer, the buffer is cleared.
946 __isl_give isl_printer *isl_printer_flush(
947 __isl_take isl_printer *p);
949 =head2 Creating New Sets and Relations
951 C<isl> has functions for creating some standard sets and relations.
955 =item * Empty sets and relations
957 __isl_give isl_basic_set *isl_basic_set_empty(
958 __isl_take isl_space *space);
959 __isl_give isl_basic_map *isl_basic_map_empty(
960 __isl_take isl_space *space);
961 __isl_give isl_set *isl_set_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_map *isl_map_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_union_set *isl_union_set_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_union_map *isl_union_map_empty(
968 __isl_take isl_space *space);
970 For C<isl_union_set>s and C<isl_union_map>s, the space
971 is only used to specify the parameters.
973 =item * Universe sets and relations
975 __isl_give isl_basic_set *isl_basic_set_universe(
976 __isl_take isl_space *space);
977 __isl_give isl_basic_map *isl_basic_map_universe(
978 __isl_take isl_space *space);
979 __isl_give isl_set *isl_set_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_map *isl_map_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_union_set *isl_union_set_universe(
984 __isl_take isl_union_set *uset);
985 __isl_give isl_union_map *isl_union_map_universe(
986 __isl_take isl_union_map *umap);
988 The sets and relations constructed by the functions above
989 contain all integer values, while those constructed by the
990 functions below only contain non-negative values.
992 __isl_give isl_basic_set *isl_basic_set_nat_universe(
993 __isl_take isl_space *space);
994 __isl_give isl_basic_map *isl_basic_map_nat_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_set *isl_set_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_map *isl_map_nat_universe(
999 __isl_take isl_space *space);
1001 =item * Identity relations
1003 __isl_give isl_basic_map *isl_basic_map_identity(
1004 __isl_take isl_space *space);
1005 __isl_give isl_map *isl_map_identity(
1006 __isl_take isl_space *space);
1008 The number of input and output dimensions in C<space> needs
1011 =item * Lexicographic order
1013 __isl_give isl_map *isl_map_lex_lt(
1014 __isl_take isl_space *set_space);
1015 __isl_give isl_map *isl_map_lex_le(
1016 __isl_take isl_space *set_space);
1017 __isl_give isl_map *isl_map_lex_gt(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_ge(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_lt_first(
1022 __isl_take isl_space *space, unsigned n);
1023 __isl_give isl_map *isl_map_lex_le_first(
1024 __isl_take isl_space *space, unsigned n);
1025 __isl_give isl_map *isl_map_lex_gt_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_ge_first(
1028 __isl_take isl_space *space, unsigned n);
1030 The first four functions take a space for a B<set>
1031 and return relations that express that the elements in the domain
1032 are lexicographically less
1033 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1034 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1035 than the elements in the range.
1036 The last four functions take a space for a map
1037 and return relations that express that the first C<n> dimensions
1038 in the domain are lexicographically less
1039 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1040 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1041 than the first C<n> dimensions in the range.
1045 A basic set or relation can be converted to a set or relation
1046 using the following functions.
1048 __isl_give isl_set *isl_set_from_basic_set(
1049 __isl_take isl_basic_set *bset);
1050 __isl_give isl_map *isl_map_from_basic_map(
1051 __isl_take isl_basic_map *bmap);
1053 Sets and relations can be converted to union sets and relations
1054 using the following functions.
1056 __isl_give isl_union_map *isl_union_map_from_map(
1057 __isl_take isl_map *map);
1058 __isl_give isl_union_set *isl_union_set_from_set(
1059 __isl_take isl_set *set);
1061 The inverse conversions below can only be used if the input
1062 union set or relation is known to contain elements in exactly one
1065 __isl_give isl_set *isl_set_from_union_set(
1066 __isl_take isl_union_set *uset);
1067 __isl_give isl_map *isl_map_from_union_map(
1068 __isl_take isl_union_map *umap);
1070 Sets and relations can be copied and freed again using the following
1073 __isl_give isl_basic_set *isl_basic_set_copy(
1074 __isl_keep isl_basic_set *bset);
1075 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1076 __isl_give isl_union_set *isl_union_set_copy(
1077 __isl_keep isl_union_set *uset);
1078 __isl_give isl_basic_map *isl_basic_map_copy(
1079 __isl_keep isl_basic_map *bmap);
1080 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1081 __isl_give isl_union_map *isl_union_map_copy(
1082 __isl_keep isl_union_map *umap);
1083 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1084 void isl_set_free(__isl_take isl_set *set);
1085 void *isl_union_set_free(__isl_take isl_union_set *uset);
1086 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1087 void isl_map_free(__isl_take isl_map *map);
1088 void *isl_union_map_free(__isl_take isl_union_map *umap);
1090 Other sets and relations can be constructed by starting
1091 from a universe set or relation, adding equality and/or
1092 inequality constraints and then projecting out the
1093 existentially quantified variables, if any.
1094 Constraints can be constructed, manipulated and
1095 added to (or removed from) (basic) sets and relations
1096 using the following functions.
1098 #include <isl/constraint.h>
1099 __isl_give isl_constraint *isl_equality_alloc(
1100 __isl_take isl_local_space *ls);
1101 __isl_give isl_constraint *isl_inequality_alloc(
1102 __isl_take isl_local_space *ls);
1103 __isl_give isl_constraint *isl_constraint_set_constant(
1104 __isl_take isl_constraint *constraint, isl_int v);
1105 __isl_give isl_constraint *isl_constraint_set_constant_si(
1106 __isl_take isl_constraint *constraint, int v);
1107 __isl_give isl_constraint *isl_constraint_set_coefficient(
1108 __isl_take isl_constraint *constraint,
1109 enum isl_dim_type type, int pos, isl_int v);
1110 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1111 __isl_take isl_constraint *constraint,
1112 enum isl_dim_type type, int pos, int v);
1113 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1114 __isl_take isl_basic_map *bmap,
1115 __isl_take isl_constraint *constraint);
1116 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1117 __isl_take isl_basic_set *bset,
1118 __isl_take isl_constraint *constraint);
1119 __isl_give isl_map *isl_map_add_constraint(
1120 __isl_take isl_map *map,
1121 __isl_take isl_constraint *constraint);
1122 __isl_give isl_set *isl_set_add_constraint(
1123 __isl_take isl_set *set,
1124 __isl_take isl_constraint *constraint);
1125 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1126 __isl_take isl_basic_set *bset,
1127 __isl_take isl_constraint *constraint);
1129 For example, to create a set containing the even integers
1130 between 10 and 42, you would use the following code.
1133 isl_local_space *ls;
1135 isl_basic_set *bset;
1137 space = isl_space_set_alloc(ctx, 0, 2);
1138 bset = isl_basic_set_universe(isl_space_copy(space));
1139 ls = isl_local_space_from_space(space);
1141 c = isl_equality_alloc(isl_local_space_copy(ls));
1142 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1143 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1144 bset = isl_basic_set_add_constraint(bset, c);
1146 c = isl_inequality_alloc(isl_local_space_copy(ls));
1147 c = isl_constraint_set_constant_si(c, -10);
1148 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1149 bset = isl_basic_set_add_constraint(bset, c);
1151 c = isl_inequality_alloc(ls);
1152 c = isl_constraint_set_constant_si(c, 42);
1153 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1154 bset = isl_basic_set_add_constraint(bset, c);
1156 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1160 isl_basic_set *bset;
1161 bset = isl_basic_set_read_from_str(ctx,
1162 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1164 A basic set or relation can also be constructed from two matrices
1165 describing the equalities and the inequalities.
1167 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1168 __isl_take isl_space *space,
1169 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1170 enum isl_dim_type c1,
1171 enum isl_dim_type c2, enum isl_dim_type c3,
1172 enum isl_dim_type c4);
1173 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1174 __isl_take isl_space *space,
1175 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1176 enum isl_dim_type c1,
1177 enum isl_dim_type c2, enum isl_dim_type c3,
1178 enum isl_dim_type c4, enum isl_dim_type c5);
1180 The C<isl_dim_type> arguments indicate the order in which
1181 different kinds of variables appear in the input matrices
1182 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1183 C<isl_dim_set> and C<isl_dim_div> for sets and
1184 of C<isl_dim_cst>, C<isl_dim_param>,
1185 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1187 A (basic) set or relation can also be constructed from a (piecewise)
1189 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1191 __isl_give isl_basic_map *isl_basic_map_from_aff(
1192 __isl_take isl_aff *aff);
1193 __isl_give isl_set *isl_set_from_pw_aff(
1194 __isl_take isl_pw_aff *pwaff);
1195 __isl_give isl_map *isl_map_from_pw_aff(
1196 __isl_take isl_pw_aff *pwaff);
1197 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1198 __isl_take isl_space *domain_space,
1199 __isl_take isl_aff_list *list);
1201 The C<domain_dim> argument describes the domain of the resulting
1202 basic relation. It is required because the C<list> may consist
1203 of zero affine expressions.
1205 =head2 Inspecting Sets and Relations
1207 Usually, the user should not have to care about the actual constraints
1208 of the sets and maps, but should instead apply the abstract operations
1209 explained in the following sections.
1210 Occasionally, however, it may be required to inspect the individual
1211 coefficients of the constraints. This section explains how to do so.
1212 In these cases, it may also be useful to have C<isl> compute
1213 an explicit representation of the existentially quantified variables.
1215 __isl_give isl_set *isl_set_compute_divs(
1216 __isl_take isl_set *set);
1217 __isl_give isl_map *isl_map_compute_divs(
1218 __isl_take isl_map *map);
1219 __isl_give isl_union_set *isl_union_set_compute_divs(
1220 __isl_take isl_union_set *uset);
1221 __isl_give isl_union_map *isl_union_map_compute_divs(
1222 __isl_take isl_union_map *umap);
1224 This explicit representation defines the existentially quantified
1225 variables as integer divisions of the other variables, possibly
1226 including earlier existentially quantified variables.
1227 An explicitly represented existentially quantified variable therefore
1228 has a unique value when the values of the other variables are known.
1229 If, furthermore, the same existentials, i.e., existentials
1230 with the same explicit representations, should appear in the
1231 same order in each of the disjuncts of a set or map, then the user should call
1232 either of the following functions.
1234 __isl_give isl_set *isl_set_align_divs(
1235 __isl_take isl_set *set);
1236 __isl_give isl_map *isl_map_align_divs(
1237 __isl_take isl_map *map);
1239 Alternatively, the existentially quantified variables can be removed
1240 using the following functions, which compute an overapproximation.
1242 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1243 __isl_take isl_basic_set *bset);
1244 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1245 __isl_take isl_basic_map *bmap);
1246 __isl_give isl_set *isl_set_remove_divs(
1247 __isl_take isl_set *set);
1248 __isl_give isl_map *isl_map_remove_divs(
1249 __isl_take isl_map *map);
1251 To iterate over all the sets or maps in a union set or map, use
1253 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1254 int (*fn)(__isl_take isl_set *set, void *user),
1256 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1257 int (*fn)(__isl_take isl_map *map, void *user),
1260 The number of sets or maps in a union set or map can be obtained
1263 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1264 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1266 To extract the set or map in a given space from a union, use
1268 __isl_give isl_set *isl_union_set_extract_set(
1269 __isl_keep isl_union_set *uset,
1270 __isl_take isl_space *space);
1271 __isl_give isl_map *isl_union_map_extract_map(
1272 __isl_keep isl_union_map *umap,
1273 __isl_take isl_space *space);
1275 To iterate over all the basic sets or maps in a set or map, use
1277 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1278 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1280 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1281 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1284 The callback function C<fn> should return 0 if successful and
1285 -1 if an error occurs. In the latter case, or if any other error
1286 occurs, the above functions will return -1.
1288 It should be noted that C<isl> does not guarantee that
1289 the basic sets or maps passed to C<fn> are disjoint.
1290 If this is required, then the user should call one of
1291 the following functions first.
1293 __isl_give isl_set *isl_set_make_disjoint(
1294 __isl_take isl_set *set);
1295 __isl_give isl_map *isl_map_make_disjoint(
1296 __isl_take isl_map *map);
1298 The number of basic sets in a set can be obtained
1301 int isl_set_n_basic_set(__isl_keep isl_set *set);
1303 To iterate over the constraints of a basic set or map, use
1305 #include <isl/constraint.h>
1307 int isl_basic_map_foreach_constraint(
1308 __isl_keep isl_basic_map *bmap,
1309 int (*fn)(__isl_take isl_constraint *c, void *user),
1311 void *isl_constraint_free(__isl_take isl_constraint *c);
1313 Again, the callback function C<fn> should return 0 if successful and
1314 -1 if an error occurs. In the latter case, or if any other error
1315 occurs, the above functions will return -1.
1316 The constraint C<c> represents either an equality or an inequality.
1317 Use the following function to find out whether a constraint
1318 represents an equality. If not, it represents an inequality.
1320 int isl_constraint_is_equality(
1321 __isl_keep isl_constraint *constraint);
1323 The coefficients of the constraints can be inspected using
1324 the following functions.
1326 void isl_constraint_get_constant(
1327 __isl_keep isl_constraint *constraint, isl_int *v);
1328 void isl_constraint_get_coefficient(
1329 __isl_keep isl_constraint *constraint,
1330 enum isl_dim_type type, int pos, isl_int *v);
1331 int isl_constraint_involves_dims(
1332 __isl_keep isl_constraint *constraint,
1333 enum isl_dim_type type, unsigned first, unsigned n);
1335 The explicit representations of the existentially quantified
1336 variables can be inspected using the following function.
1337 Note that the user is only allowed to use this function
1338 if the inspected set or map is the result of a call
1339 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1340 The existentially quantified variable is equal to the floor
1341 of the returned affine expression. The affine expression
1342 itself can be inspected using the functions in
1343 L<"Piecewise Quasi Affine Expressions">.
1345 __isl_give isl_aff *isl_constraint_get_div(
1346 __isl_keep isl_constraint *constraint, int pos);
1348 To obtain the constraints of a basic set or map in matrix
1349 form, use the following functions.
1351 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1352 __isl_keep isl_basic_set *bset,
1353 enum isl_dim_type c1, enum isl_dim_type c2,
1354 enum isl_dim_type c3, enum isl_dim_type c4);
1355 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1356 __isl_keep isl_basic_set *bset,
1357 enum isl_dim_type c1, enum isl_dim_type c2,
1358 enum isl_dim_type c3, enum isl_dim_type c4);
1359 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1360 __isl_keep isl_basic_map *bmap,
1361 enum isl_dim_type c1,
1362 enum isl_dim_type c2, enum isl_dim_type c3,
1363 enum isl_dim_type c4, enum isl_dim_type c5);
1364 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1365 __isl_keep isl_basic_map *bmap,
1366 enum isl_dim_type c1,
1367 enum isl_dim_type c2, enum isl_dim_type c3,
1368 enum isl_dim_type c4, enum isl_dim_type c5);
1370 The C<isl_dim_type> arguments dictate the order in which
1371 different kinds of variables appear in the resulting matrix
1372 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1373 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1375 The number of parameters, input, output or set dimensions can
1376 be obtained using the following functions.
1378 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1379 enum isl_dim_type type);
1380 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1381 enum isl_dim_type type);
1382 unsigned isl_set_dim(__isl_keep isl_set *set,
1383 enum isl_dim_type type);
1384 unsigned isl_map_dim(__isl_keep isl_map *map,
1385 enum isl_dim_type type);
1387 To check whether the description of a set or relation depends
1388 on one or more given dimensions, it is not necessary to iterate over all
1389 constraints. Instead the following functions can be used.
1391 int isl_basic_set_involves_dims(
1392 __isl_keep isl_basic_set *bset,
1393 enum isl_dim_type type, unsigned first, unsigned n);
1394 int isl_set_involves_dims(__isl_keep isl_set *set,
1395 enum isl_dim_type type, unsigned first, unsigned n);
1396 int isl_basic_map_involves_dims(
1397 __isl_keep isl_basic_map *bmap,
1398 enum isl_dim_type type, unsigned first, unsigned n);
1399 int isl_map_involves_dims(__isl_keep isl_map *map,
1400 enum isl_dim_type type, unsigned first, unsigned n);
1402 Similarly, the following functions can be used to check whether
1403 a given dimension is involved in any lower or upper bound.
1405 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1406 enum isl_dim_type type, unsigned pos);
1407 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1408 enum isl_dim_type type, unsigned pos);
1410 The identifiers or names of the domain and range spaces of a set
1411 or relation can be read off or set using the following functions.
1413 __isl_give isl_set *isl_set_set_tuple_id(
1414 __isl_take isl_set *set, __isl_take isl_id *id);
1415 __isl_give isl_set *isl_set_reset_tuple_id(
1416 __isl_take isl_set *set);
1417 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1418 __isl_give isl_id *isl_set_get_tuple_id(
1419 __isl_keep isl_set *set);
1420 __isl_give isl_map *isl_map_set_tuple_id(
1421 __isl_take isl_map *map, enum isl_dim_type type,
1422 __isl_take isl_id *id);
1423 __isl_give isl_map *isl_map_reset_tuple_id(
1424 __isl_take isl_map *map, enum isl_dim_type type);
1425 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1426 enum isl_dim_type type);
1427 __isl_give isl_id *isl_map_get_tuple_id(
1428 __isl_keep isl_map *map, enum isl_dim_type type);
1430 const char *isl_basic_set_get_tuple_name(
1431 __isl_keep isl_basic_set *bset);
1432 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1433 __isl_take isl_basic_set *set, const char *s);
1434 const char *isl_set_get_tuple_name(
1435 __isl_keep isl_set *set);
1436 const char *isl_basic_map_get_tuple_name(
1437 __isl_keep isl_basic_map *bmap,
1438 enum isl_dim_type type);
1439 const char *isl_map_get_tuple_name(
1440 __isl_keep isl_map *map,
1441 enum isl_dim_type type);
1443 As with C<isl_space_get_tuple_name>, the value returned points to
1444 an internal data structure.
1445 The identifiers, positions or names of individual dimensions can be
1446 read off using the following functions.
1448 __isl_give isl_set *isl_set_set_dim_id(
1449 __isl_take isl_set *set, enum isl_dim_type type,
1450 unsigned pos, __isl_take isl_id *id);
1451 int isl_set_has_dim_id(__isl_keep isl_set *set,
1452 enum isl_dim_type type, unsigned pos);
1453 __isl_give isl_id *isl_set_get_dim_id(
1454 __isl_keep isl_set *set, enum isl_dim_type type,
1456 __isl_give isl_map *isl_map_set_dim_id(
1457 __isl_take isl_map *map, enum isl_dim_type type,
1458 unsigned pos, __isl_take isl_id *id);
1459 int isl_map_has_dim_id(__isl_keep isl_map *map,
1460 enum isl_dim_type type, unsigned pos);
1461 __isl_give isl_id *isl_map_get_dim_id(
1462 __isl_keep isl_map *map, enum isl_dim_type type,
1465 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1468 enum isl_dim_type type, __isl_keep isl_id *id);
1470 const char *isl_constraint_get_dim_name(
1471 __isl_keep isl_constraint *constraint,
1472 enum isl_dim_type type, unsigned pos);
1473 const char *isl_basic_set_get_dim_name(
1474 __isl_keep isl_basic_set *bset,
1475 enum isl_dim_type type, unsigned pos);
1476 const char *isl_set_get_dim_name(
1477 __isl_keep isl_set *set,
1478 enum isl_dim_type type, unsigned pos);
1479 const char *isl_basic_map_get_dim_name(
1480 __isl_keep isl_basic_map *bmap,
1481 enum isl_dim_type type, unsigned pos);
1482 const char *isl_map_get_dim_name(
1483 __isl_keep isl_map *map,
1484 enum isl_dim_type type, unsigned pos);
1486 These functions are mostly useful to obtain the identifiers, positions
1487 or names of the parameters. Identifiers of individual dimensions are
1488 essentially only useful for printing. They are ignored by all other
1489 operations and may not be preserved across those operations.
1493 =head3 Unary Properties
1499 The following functions test whether the given set or relation
1500 contains any integer points. The ``plain'' variants do not perform
1501 any computations, but simply check if the given set or relation
1502 is already known to be empty.
1504 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1505 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1506 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1507 int isl_set_is_empty(__isl_keep isl_set *set);
1508 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1509 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1510 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1511 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1512 int isl_map_is_empty(__isl_keep isl_map *map);
1513 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1515 =item * Universality
1517 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1518 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1519 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1521 =item * Single-valuedness
1523 int isl_map_is_single_valued(__isl_keep isl_map *map);
1524 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1528 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1529 int isl_map_is_injective(__isl_keep isl_map *map);
1530 int isl_union_map_plain_is_injective(
1531 __isl_keep isl_union_map *umap);
1532 int isl_union_map_is_injective(
1533 __isl_keep isl_union_map *umap);
1537 int isl_map_is_bijective(__isl_keep isl_map *map);
1538 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1542 int isl_basic_map_plain_is_fixed(
1543 __isl_keep isl_basic_map *bmap,
1544 enum isl_dim_type type, unsigned pos,
1546 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1547 enum isl_dim_type type, unsigned pos,
1550 Check if the relation obviously lies on a hyperplane where the given dimension
1551 has a fixed value and if so, return that value in C<*val>.
1555 To check whether a set is a parameter domain, use this function:
1557 int isl_set_is_params(__isl_keep isl_set *set);
1561 The following functions check whether the domain of the given
1562 (basic) set is a wrapped relation.
1564 int isl_basic_set_is_wrapping(
1565 __isl_keep isl_basic_set *bset);
1566 int isl_set_is_wrapping(__isl_keep isl_set *set);
1568 =item * Internal Product
1570 int isl_basic_map_can_zip(
1571 __isl_keep isl_basic_map *bmap);
1572 int isl_map_can_zip(__isl_keep isl_map *map);
1574 Check whether the product of domain and range of the given relation
1576 i.e., whether both domain and range are nested relations.
1580 =head3 Binary Properties
1586 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1587 __isl_keep isl_set *set2);
1588 int isl_set_is_equal(__isl_keep isl_set *set1,
1589 __isl_keep isl_set *set2);
1590 int isl_union_set_is_equal(
1591 __isl_keep isl_union_set *uset1,
1592 __isl_keep isl_union_set *uset2);
1593 int isl_basic_map_is_equal(
1594 __isl_keep isl_basic_map *bmap1,
1595 __isl_keep isl_basic_map *bmap2);
1596 int isl_map_is_equal(__isl_keep isl_map *map1,
1597 __isl_keep isl_map *map2);
1598 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1599 __isl_keep isl_map *map2);
1600 int isl_union_map_is_equal(
1601 __isl_keep isl_union_map *umap1,
1602 __isl_keep isl_union_map *umap2);
1604 =item * Disjointness
1606 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1607 __isl_keep isl_set *set2);
1611 int isl_set_is_subset(__isl_keep isl_set *set1,
1612 __isl_keep isl_set *set2);
1613 int isl_set_is_strict_subset(
1614 __isl_keep isl_set *set1,
1615 __isl_keep isl_set *set2);
1616 int isl_union_set_is_subset(
1617 __isl_keep isl_union_set *uset1,
1618 __isl_keep isl_union_set *uset2);
1619 int isl_union_set_is_strict_subset(
1620 __isl_keep isl_union_set *uset1,
1621 __isl_keep isl_union_set *uset2);
1622 int isl_basic_map_is_subset(
1623 __isl_keep isl_basic_map *bmap1,
1624 __isl_keep isl_basic_map *bmap2);
1625 int isl_basic_map_is_strict_subset(
1626 __isl_keep isl_basic_map *bmap1,
1627 __isl_keep isl_basic_map *bmap2);
1628 int isl_map_is_subset(
1629 __isl_keep isl_map *map1,
1630 __isl_keep isl_map *map2);
1631 int isl_map_is_strict_subset(
1632 __isl_keep isl_map *map1,
1633 __isl_keep isl_map *map2);
1634 int isl_union_map_is_subset(
1635 __isl_keep isl_union_map *umap1,
1636 __isl_keep isl_union_map *umap2);
1637 int isl_union_map_is_strict_subset(
1638 __isl_keep isl_union_map *umap1,
1639 __isl_keep isl_union_map *umap2);
1643 =head2 Unary Operations
1649 __isl_give isl_set *isl_set_complement(
1650 __isl_take isl_set *set);
1654 __isl_give isl_basic_map *isl_basic_map_reverse(
1655 __isl_take isl_basic_map *bmap);
1656 __isl_give isl_map *isl_map_reverse(
1657 __isl_take isl_map *map);
1658 __isl_give isl_union_map *isl_union_map_reverse(
1659 __isl_take isl_union_map *umap);
1663 __isl_give isl_basic_set *isl_basic_set_project_out(
1664 __isl_take isl_basic_set *bset,
1665 enum isl_dim_type type, unsigned first, unsigned n);
1666 __isl_give isl_basic_map *isl_basic_map_project_out(
1667 __isl_take isl_basic_map *bmap,
1668 enum isl_dim_type type, unsigned first, unsigned n);
1669 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1670 enum isl_dim_type type, unsigned first, unsigned n);
1671 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1672 enum isl_dim_type type, unsigned first, unsigned n);
1673 __isl_give isl_basic_set *isl_basic_set_params(
1674 __isl_take isl_basic_set *bset);
1675 __isl_give isl_basic_set *isl_basic_map_domain(
1676 __isl_take isl_basic_map *bmap);
1677 __isl_give isl_basic_set *isl_basic_map_range(
1678 __isl_take isl_basic_map *bmap);
1679 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1680 __isl_give isl_set *isl_map_domain(
1681 __isl_take isl_map *bmap);
1682 __isl_give isl_set *isl_map_range(
1683 __isl_take isl_map *map);
1684 __isl_give isl_union_set *isl_union_map_domain(
1685 __isl_take isl_union_map *umap);
1686 __isl_give isl_union_set *isl_union_map_range(
1687 __isl_take isl_union_map *umap);
1689 __isl_give isl_basic_map *isl_basic_map_domain_map(
1690 __isl_take isl_basic_map *bmap);
1691 __isl_give isl_basic_map *isl_basic_map_range_map(
1692 __isl_take isl_basic_map *bmap);
1693 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1694 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1695 __isl_give isl_union_map *isl_union_map_domain_map(
1696 __isl_take isl_union_map *umap);
1697 __isl_give isl_union_map *isl_union_map_range_map(
1698 __isl_take isl_union_map *umap);
1700 The functions above construct a (basic, regular or union) relation
1701 that maps (a wrapped version of) the input relation to its domain or range.
1705 __isl_give isl_set *isl_set_eliminate(
1706 __isl_take isl_set *set, enum isl_dim_type type,
1707 unsigned first, unsigned n);
1709 Eliminate the coefficients for the given dimensions from the constraints,
1710 without removing the dimensions.
1714 __isl_give isl_basic_set *isl_basic_set_fix(
1715 __isl_take isl_basic_set *bset,
1716 enum isl_dim_type type, unsigned pos,
1718 __isl_give isl_basic_set *isl_basic_set_fix_si(
1719 __isl_take isl_basic_set *bset,
1720 enum isl_dim_type type, unsigned pos, int value);
1721 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1722 enum isl_dim_type type, unsigned pos,
1724 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1725 enum isl_dim_type type, unsigned pos, int value);
1726 __isl_give isl_basic_map *isl_basic_map_fix_si(
1727 __isl_take isl_basic_map *bmap,
1728 enum isl_dim_type type, unsigned pos, int value);
1729 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1730 enum isl_dim_type type, unsigned pos, int value);
1732 Intersect the set or relation with the hyperplane where the given
1733 dimension has the fixed given value.
1735 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1736 enum isl_dim_type type1, int pos1,
1737 enum isl_dim_type type2, int pos2);
1738 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1739 enum isl_dim_type type1, int pos1,
1740 enum isl_dim_type type2, int pos2);
1742 Intersect the set or relation with the hyperplane where the given
1743 dimensions are equal to each other.
1745 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1746 enum isl_dim_type type1, int pos1,
1747 enum isl_dim_type type2, int pos2);
1749 Intersect the relation with the hyperplane where the given
1750 dimensions have opposite values.
1754 __isl_give isl_map *isl_set_identity(
1755 __isl_take isl_set *set);
1756 __isl_give isl_union_map *isl_union_set_identity(
1757 __isl_take isl_union_set *uset);
1759 Construct an identity relation on the given (union) set.
1763 __isl_give isl_basic_set *isl_basic_map_deltas(
1764 __isl_take isl_basic_map *bmap);
1765 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1766 __isl_give isl_union_set *isl_union_map_deltas(
1767 __isl_take isl_union_map *umap);
1769 These functions return a (basic) set containing the differences
1770 between image elements and corresponding domain elements in the input.
1772 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_map *isl_map_deltas_map(
1775 __isl_take isl_map *map);
1776 __isl_give isl_union_map *isl_union_map_deltas_map(
1777 __isl_take isl_union_map *umap);
1779 The functions above construct a (basic, regular or union) relation
1780 that maps (a wrapped version of) the input relation to its delta set.
1784 Simplify the representation of a set or relation by trying
1785 to combine pairs of basic sets or relations into a single
1786 basic set or relation.
1788 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1789 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1790 __isl_give isl_union_set *isl_union_set_coalesce(
1791 __isl_take isl_union_set *uset);
1792 __isl_give isl_union_map *isl_union_map_coalesce(
1793 __isl_take isl_union_map *umap);
1795 =item * Detecting equalities
1797 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1798 __isl_take isl_basic_set *bset);
1799 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_set *isl_set_detect_equalities(
1802 __isl_take isl_set *set);
1803 __isl_give isl_map *isl_map_detect_equalities(
1804 __isl_take isl_map *map);
1805 __isl_give isl_union_set *isl_union_set_detect_equalities(
1806 __isl_take isl_union_set *uset);
1807 __isl_give isl_union_map *isl_union_map_detect_equalities(
1808 __isl_take isl_union_map *umap);
1810 Simplify the representation of a set or relation by detecting implicit
1813 =item * Removing redundant constraints
1815 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1816 __isl_take isl_basic_set *bset);
1817 __isl_give isl_set *isl_set_remove_redundancies(
1818 __isl_take isl_set *set);
1819 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1820 __isl_take isl_basic_map *bmap);
1821 __isl_give isl_map *isl_map_remove_redundancies(
1822 __isl_take isl_map *map);
1826 __isl_give isl_basic_set *isl_set_convex_hull(
1827 __isl_take isl_set *set);
1828 __isl_give isl_basic_map *isl_map_convex_hull(
1829 __isl_take isl_map *map);
1831 If the input set or relation has any existentially quantified
1832 variables, then the result of these operations is currently undefined.
1836 __isl_give isl_basic_set *isl_set_simple_hull(
1837 __isl_take isl_set *set);
1838 __isl_give isl_basic_map *isl_map_simple_hull(
1839 __isl_take isl_map *map);
1840 __isl_give isl_union_map *isl_union_map_simple_hull(
1841 __isl_take isl_union_map *umap);
1843 These functions compute a single basic set or relation
1844 that contains the whole input set or relation.
1845 In particular, the output is described by translates
1846 of the constraints describing the basic sets or relations in the input.
1850 (See \autoref{s:simple hull}.)
1856 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1857 __isl_take isl_basic_set *bset);
1858 __isl_give isl_basic_set *isl_set_affine_hull(
1859 __isl_take isl_set *set);
1860 __isl_give isl_union_set *isl_union_set_affine_hull(
1861 __isl_take isl_union_set *uset);
1862 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1863 __isl_take isl_basic_map *bmap);
1864 __isl_give isl_basic_map *isl_map_affine_hull(
1865 __isl_take isl_map *map);
1866 __isl_give isl_union_map *isl_union_map_affine_hull(
1867 __isl_take isl_union_map *umap);
1869 In case of union sets and relations, the affine hull is computed
1872 =item * Polyhedral hull
1874 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1875 __isl_take isl_set *set);
1876 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1877 __isl_take isl_map *map);
1878 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1879 __isl_take isl_union_set *uset);
1880 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1881 __isl_take isl_union_map *umap);
1883 These functions compute a single basic set or relation
1884 not involving any existentially quantified variables
1885 that contains the whole input set or relation.
1886 In case of union sets and relations, the polyhedral hull is computed
1889 =item * Optimization
1891 #include <isl/ilp.h>
1892 enum isl_lp_result isl_basic_set_max(
1893 __isl_keep isl_basic_set *bset,
1894 __isl_keep isl_aff *obj, isl_int *opt)
1895 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1896 __isl_keep isl_aff *obj, isl_int *opt);
1897 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1898 __isl_keep isl_aff *obj, isl_int *opt);
1900 Compute the minimum or maximum of the integer affine expression C<obj>
1901 over the points in C<set>, returning the result in C<opt>.
1902 The return value may be one of C<isl_lp_error>,
1903 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1905 =item * Parametric optimization
1907 __isl_give isl_pw_aff *isl_set_dim_min(
1908 __isl_take isl_set *set, int pos);
1909 __isl_give isl_pw_aff *isl_set_dim_max(
1910 __isl_take isl_set *set, int pos);
1912 Compute the minimum or maximum of the given set dimension as a function of the
1913 parameters, but independently of the other set dimensions.
1914 For lexicographic optimization, see L<"Lexicographic Optimization">.
1918 The following functions compute either the set of (rational) coefficient
1919 values of valid constraints for the given set or the set of (rational)
1920 values satisfying the constraints with coefficients from the given set.
1921 Internally, these two sets of functions perform essentially the
1922 same operations, except that the set of coefficients is assumed to
1923 be a cone, while the set of values may be any polyhedron.
1924 The current implementation is based on the Farkas lemma and
1925 Fourier-Motzkin elimination, but this may change or be made optional
1926 in future. In particular, future implementations may use different
1927 dualization algorithms or skip the elimination step.
1929 __isl_give isl_basic_set *isl_basic_set_coefficients(
1930 __isl_take isl_basic_set *bset);
1931 __isl_give isl_basic_set *isl_set_coefficients(
1932 __isl_take isl_set *set);
1933 __isl_give isl_union_set *isl_union_set_coefficients(
1934 __isl_take isl_union_set *bset);
1935 __isl_give isl_basic_set *isl_basic_set_solutions(
1936 __isl_take isl_basic_set *bset);
1937 __isl_give isl_basic_set *isl_set_solutions(
1938 __isl_take isl_set *set);
1939 __isl_give isl_union_set *isl_union_set_solutions(
1940 __isl_take isl_union_set *bset);
1944 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1946 __isl_give isl_union_map *isl_union_map_power(
1947 __isl_take isl_union_map *umap, int *exact);
1949 Compute a parametric representation for all positive powers I<k> of C<map>.
1950 The result maps I<k> to a nested relation corresponding to the
1951 I<k>th power of C<map>.
1952 The result may be an overapproximation. If the result is known to be exact,
1953 then C<*exact> is set to C<1>.
1955 =item * Transitive closure
1957 __isl_give isl_map *isl_map_transitive_closure(
1958 __isl_take isl_map *map, int *exact);
1959 __isl_give isl_union_map *isl_union_map_transitive_closure(
1960 __isl_take isl_union_map *umap, int *exact);
1962 Compute the transitive closure of C<map>.
1963 The result may be an overapproximation. If the result is known to be exact,
1964 then C<*exact> is set to C<1>.
1966 =item * Reaching path lengths
1968 __isl_give isl_map *isl_map_reaching_path_lengths(
1969 __isl_take isl_map *map, int *exact);
1971 Compute a relation that maps each element in the range of C<map>
1972 to the lengths of all paths composed of edges in C<map> that
1973 end up in the given element.
1974 The result may be an overapproximation. If the result is known to be exact,
1975 then C<*exact> is set to C<1>.
1976 To compute the I<maximal> path length, the resulting relation
1977 should be postprocessed by C<isl_map_lexmax>.
1978 In particular, if the input relation is a dependence relation
1979 (mapping sources to sinks), then the maximal path length corresponds
1980 to the free schedule.
1981 Note, however, that C<isl_map_lexmax> expects the maximum to be
1982 finite, so if the path lengths are unbounded (possibly due to
1983 the overapproximation), then you will get an error message.
1987 __isl_give isl_basic_set *isl_basic_map_wrap(
1988 __isl_take isl_basic_map *bmap);
1989 __isl_give isl_set *isl_map_wrap(
1990 __isl_take isl_map *map);
1991 __isl_give isl_union_set *isl_union_map_wrap(
1992 __isl_take isl_union_map *umap);
1993 __isl_give isl_basic_map *isl_basic_set_unwrap(
1994 __isl_take isl_basic_set *bset);
1995 __isl_give isl_map *isl_set_unwrap(
1996 __isl_take isl_set *set);
1997 __isl_give isl_union_map *isl_union_set_unwrap(
1998 __isl_take isl_union_set *uset);
2002 Remove any internal structure of domain (and range) of the given
2003 set or relation. If there is any such internal structure in the input,
2004 then the name of the space is also removed.
2006 __isl_give isl_basic_set *isl_basic_set_flatten(
2007 __isl_take isl_basic_set *bset);
2008 __isl_give isl_set *isl_set_flatten(
2009 __isl_take isl_set *set);
2010 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2011 __isl_take isl_basic_map *bmap);
2012 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2013 __isl_take isl_basic_map *bmap);
2014 __isl_give isl_map *isl_map_flatten_range(
2015 __isl_take isl_map *map);
2016 __isl_give isl_map *isl_map_flatten_domain(
2017 __isl_take isl_map *map);
2018 __isl_give isl_basic_map *isl_basic_map_flatten(
2019 __isl_take isl_basic_map *bmap);
2020 __isl_give isl_map *isl_map_flatten(
2021 __isl_take isl_map *map);
2023 __isl_give isl_map *isl_set_flatten_map(
2024 __isl_take isl_set *set);
2026 The function above constructs a relation
2027 that maps the input set to a flattened version of the set.
2031 Lift the input set to a space with extra dimensions corresponding
2032 to the existentially quantified variables in the input.
2033 In particular, the result lives in a wrapped map where the domain
2034 is the original space and the range corresponds to the original
2035 existentially quantified variables.
2037 __isl_give isl_basic_set *isl_basic_set_lift(
2038 __isl_take isl_basic_set *bset);
2039 __isl_give isl_set *isl_set_lift(
2040 __isl_take isl_set *set);
2041 __isl_give isl_union_set *isl_union_set_lift(
2042 __isl_take isl_union_set *uset);
2044 =item * Internal Product
2046 __isl_give isl_basic_map *isl_basic_map_zip(
2047 __isl_take isl_basic_map *bmap);
2048 __isl_give isl_map *isl_map_zip(
2049 __isl_take isl_map *map);
2050 __isl_give isl_union_map *isl_union_map_zip(
2051 __isl_take isl_union_map *umap);
2053 Given a relation with nested relations for domain and range,
2054 interchange the range of the domain with the domain of the range.
2056 =item * Aligning parameters
2058 __isl_give isl_set *isl_set_align_params(
2059 __isl_take isl_set *set,
2060 __isl_take isl_space *model);
2061 __isl_give isl_map *isl_map_align_params(
2062 __isl_take isl_map *map,
2063 __isl_take isl_space *model);
2065 Change the order of the parameters of the given set or relation
2066 such that the first parameters match those of C<model>.
2067 This may involve the introduction of extra parameters.
2068 All parameters need to be named.
2070 =item * Dimension manipulation
2072 __isl_give isl_set *isl_set_add_dims(
2073 __isl_take isl_set *set,
2074 enum isl_dim_type type, unsigned n);
2075 __isl_give isl_map *isl_map_add_dims(
2076 __isl_take isl_map *map,
2077 enum isl_dim_type type, unsigned n);
2078 __isl_give isl_set *isl_set_insert_dims(
2079 __isl_take isl_set *set,
2080 enum isl_dim_type type, unsigned pos, unsigned n);
2081 __isl_give isl_map *isl_map_insert_dims(
2082 __isl_take isl_map *map,
2083 enum isl_dim_type type, unsigned pos, unsigned n);
2085 It is usually not advisable to directly change the (input or output)
2086 space of a set or a relation as this removes the name and the internal
2087 structure of the space. However, the above functions can be useful
2088 to add new parameters, assuming
2089 C<isl_set_align_params> and C<isl_map_align_params>
2094 =head2 Binary Operations
2096 The two arguments of a binary operation not only need to live
2097 in the same C<isl_ctx>, they currently also need to have
2098 the same (number of) parameters.
2100 =head3 Basic Operations
2104 =item * Intersection
2106 __isl_give isl_basic_set *isl_basic_set_intersect(
2107 __isl_take isl_basic_set *bset1,
2108 __isl_take isl_basic_set *bset2);
2109 __isl_give isl_set *isl_set_intersect_params(
2110 __isl_take isl_set *set,
2111 __isl_take isl_set *params);
2112 __isl_give isl_set *isl_set_intersect(
2113 __isl_take isl_set *set1,
2114 __isl_take isl_set *set2);
2115 __isl_give isl_union_set *isl_union_set_intersect(
2116 __isl_take isl_union_set *uset1,
2117 __isl_take isl_union_set *uset2);
2118 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2119 __isl_take isl_basic_map *bmap,
2120 __isl_take isl_basic_set *bset);
2121 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2122 __isl_take isl_basic_map *bmap,
2123 __isl_take isl_basic_set *bset);
2124 __isl_give isl_basic_map *isl_basic_map_intersect(
2125 __isl_take isl_basic_map *bmap1,
2126 __isl_take isl_basic_map *bmap2);
2127 __isl_give isl_map *isl_map_intersect_params(
2128 __isl_take isl_map *map,
2129 __isl_take isl_set *params);
2130 __isl_give isl_map *isl_map_intersect_domain(
2131 __isl_take isl_map *map,
2132 __isl_take isl_set *set);
2133 __isl_give isl_map *isl_map_intersect_range(
2134 __isl_take isl_map *map,
2135 __isl_take isl_set *set);
2136 __isl_give isl_map *isl_map_intersect(
2137 __isl_take isl_map *map1,
2138 __isl_take isl_map *map2);
2139 __isl_give isl_union_map *isl_union_map_intersect_domain(
2140 __isl_take isl_union_map *umap,
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_union_map *isl_union_map_intersect_range(
2143 __isl_take isl_union_map *umap,
2144 __isl_take isl_union_set *uset);
2145 __isl_give isl_union_map *isl_union_map_intersect(
2146 __isl_take isl_union_map *umap1,
2147 __isl_take isl_union_map *umap2);
2151 __isl_give isl_set *isl_basic_set_union(
2152 __isl_take isl_basic_set *bset1,
2153 __isl_take isl_basic_set *bset2);
2154 __isl_give isl_map *isl_basic_map_union(
2155 __isl_take isl_basic_map *bmap1,
2156 __isl_take isl_basic_map *bmap2);
2157 __isl_give isl_set *isl_set_union(
2158 __isl_take isl_set *set1,
2159 __isl_take isl_set *set2);
2160 __isl_give isl_map *isl_map_union(
2161 __isl_take isl_map *map1,
2162 __isl_take isl_map *map2);
2163 __isl_give isl_union_set *isl_union_set_union(
2164 __isl_take isl_union_set *uset1,
2165 __isl_take isl_union_set *uset2);
2166 __isl_give isl_union_map *isl_union_map_union(
2167 __isl_take isl_union_map *umap1,
2168 __isl_take isl_union_map *umap2);
2170 =item * Set difference
2172 __isl_give isl_set *isl_set_subtract(
2173 __isl_take isl_set *set1,
2174 __isl_take isl_set *set2);
2175 __isl_give isl_map *isl_map_subtract(
2176 __isl_take isl_map *map1,
2177 __isl_take isl_map *map2);
2178 __isl_give isl_union_set *isl_union_set_subtract(
2179 __isl_take isl_union_set *uset1,
2180 __isl_take isl_union_set *uset2);
2181 __isl_give isl_union_map *isl_union_map_subtract(
2182 __isl_take isl_union_map *umap1,
2183 __isl_take isl_union_map *umap2);
2187 __isl_give isl_basic_set *isl_basic_set_apply(
2188 __isl_take isl_basic_set *bset,
2189 __isl_take isl_basic_map *bmap);
2190 __isl_give isl_set *isl_set_apply(
2191 __isl_take isl_set *set,
2192 __isl_take isl_map *map);
2193 __isl_give isl_union_set *isl_union_set_apply(
2194 __isl_take isl_union_set *uset,
2195 __isl_take isl_union_map *umap);
2196 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2197 __isl_take isl_basic_map *bmap1,
2198 __isl_take isl_basic_map *bmap2);
2199 __isl_give isl_basic_map *isl_basic_map_apply_range(
2200 __isl_take isl_basic_map *bmap1,
2201 __isl_take isl_basic_map *bmap2);
2202 __isl_give isl_map *isl_map_apply_domain(
2203 __isl_take isl_map *map1,
2204 __isl_take isl_map *map2);
2205 __isl_give isl_union_map *isl_union_map_apply_domain(
2206 __isl_take isl_union_map *umap1,
2207 __isl_take isl_union_map *umap2);
2208 __isl_give isl_map *isl_map_apply_range(
2209 __isl_take isl_map *map1,
2210 __isl_take isl_map *map2);
2211 __isl_give isl_union_map *isl_union_map_apply_range(
2212 __isl_take isl_union_map *umap1,
2213 __isl_take isl_union_map *umap2);
2215 =item * Cartesian Product
2217 __isl_give isl_set *isl_set_product(
2218 __isl_take isl_set *set1,
2219 __isl_take isl_set *set2);
2220 __isl_give isl_union_set *isl_union_set_product(
2221 __isl_take isl_union_set *uset1,
2222 __isl_take isl_union_set *uset2);
2223 __isl_give isl_basic_map *isl_basic_map_domain_product(
2224 __isl_take isl_basic_map *bmap1,
2225 __isl_take isl_basic_map *bmap2);
2226 __isl_give isl_basic_map *isl_basic_map_range_product(
2227 __isl_take isl_basic_map *bmap1,
2228 __isl_take isl_basic_map *bmap2);
2229 __isl_give isl_map *isl_map_domain_product(
2230 __isl_take isl_map *map1,
2231 __isl_take isl_map *map2);
2232 __isl_give isl_map *isl_map_range_product(
2233 __isl_take isl_map *map1,
2234 __isl_take isl_map *map2);
2235 __isl_give isl_union_map *isl_union_map_range_product(
2236 __isl_take isl_union_map *umap1,
2237 __isl_take isl_union_map *umap2);
2238 __isl_give isl_map *isl_map_product(
2239 __isl_take isl_map *map1,
2240 __isl_take isl_map *map2);
2241 __isl_give isl_union_map *isl_union_map_product(
2242 __isl_take isl_union_map *umap1,
2243 __isl_take isl_union_map *umap2);
2245 The above functions compute the cross product of the given
2246 sets or relations. The domains and ranges of the results
2247 are wrapped maps between domains and ranges of the inputs.
2248 To obtain a ``flat'' product, use the following functions
2251 __isl_give isl_basic_set *isl_basic_set_flat_product(
2252 __isl_take isl_basic_set *bset1,
2253 __isl_take isl_basic_set *bset2);
2254 __isl_give isl_set *isl_set_flat_product(
2255 __isl_take isl_set *set1,
2256 __isl_take isl_set *set2);
2257 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2258 __isl_take isl_basic_map *bmap1,
2259 __isl_take isl_basic_map *bmap2);
2260 __isl_give isl_map *isl_map_flat_domain_product(
2261 __isl_take isl_map *map1,
2262 __isl_take isl_map *map2);
2263 __isl_give isl_map *isl_map_flat_range_product(
2264 __isl_take isl_map *map1,
2265 __isl_take isl_map *map2);
2266 __isl_give isl_union_map *isl_union_map_flat_range_product(
2267 __isl_take isl_union_map *umap1,
2268 __isl_take isl_union_map *umap2);
2269 __isl_give isl_basic_map *isl_basic_map_flat_product(
2270 __isl_take isl_basic_map *bmap1,
2271 __isl_take isl_basic_map *bmap2);
2272 __isl_give isl_map *isl_map_flat_product(
2273 __isl_take isl_map *map1,
2274 __isl_take isl_map *map2);
2276 =item * Simplification
2278 __isl_give isl_basic_set *isl_basic_set_gist(
2279 __isl_take isl_basic_set *bset,
2280 __isl_take isl_basic_set *context);
2281 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2282 __isl_take isl_set *context);
2283 __isl_give isl_set *isl_set_gist_params(
2284 __isl_take isl_set *set,
2285 __isl_take isl_set *context);
2286 __isl_give isl_union_set *isl_union_set_gist(
2287 __isl_take isl_union_set *uset,
2288 __isl_take isl_union_set *context);
2289 __isl_give isl_basic_map *isl_basic_map_gist(
2290 __isl_take isl_basic_map *bmap,
2291 __isl_take isl_basic_map *context);
2292 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2293 __isl_take isl_map *context);
2294 __isl_give isl_map *isl_map_gist_params(
2295 __isl_take isl_map *map,
2296 __isl_take isl_set *context);
2297 __isl_give isl_union_map *isl_union_map_gist(
2298 __isl_take isl_union_map *umap,
2299 __isl_take isl_union_map *context);
2301 The gist operation returns a set or relation that has the
2302 same intersection with the context as the input set or relation.
2303 Any implicit equality in the intersection is made explicit in the result,
2304 while all inequalities that are redundant with respect to the intersection
2306 In case of union sets and relations, the gist operation is performed
2311 =head3 Lexicographic Optimization
2313 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2314 the following functions
2315 compute a set that contains the lexicographic minimum or maximum
2316 of the elements in C<set> (or C<bset>) for those values of the parameters
2317 that satisfy C<dom>.
2318 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2319 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2321 In other words, the union of the parameter values
2322 for which the result is non-empty and of C<*empty>
2325 __isl_give isl_set *isl_basic_set_partial_lexmin(
2326 __isl_take isl_basic_set *bset,
2327 __isl_take isl_basic_set *dom,
2328 __isl_give isl_set **empty);
2329 __isl_give isl_set *isl_basic_set_partial_lexmax(
2330 __isl_take isl_basic_set *bset,
2331 __isl_take isl_basic_set *dom,
2332 __isl_give isl_set **empty);
2333 __isl_give isl_set *isl_set_partial_lexmin(
2334 __isl_take isl_set *set, __isl_take isl_set *dom,
2335 __isl_give isl_set **empty);
2336 __isl_give isl_set *isl_set_partial_lexmax(
2337 __isl_take isl_set *set, __isl_take isl_set *dom,
2338 __isl_give isl_set **empty);
2340 Given a (basic) set C<set> (or C<bset>), the following functions simply
2341 return a set containing the lexicographic minimum or maximum
2342 of the elements in C<set> (or C<bset>).
2343 In case of union sets, the optimum is computed per space.
2345 __isl_give isl_set *isl_basic_set_lexmin(
2346 __isl_take isl_basic_set *bset);
2347 __isl_give isl_set *isl_basic_set_lexmax(
2348 __isl_take isl_basic_set *bset);
2349 __isl_give isl_set *isl_set_lexmin(
2350 __isl_take isl_set *set);
2351 __isl_give isl_set *isl_set_lexmax(
2352 __isl_take isl_set *set);
2353 __isl_give isl_union_set *isl_union_set_lexmin(
2354 __isl_take isl_union_set *uset);
2355 __isl_give isl_union_set *isl_union_set_lexmax(
2356 __isl_take isl_union_set *uset);
2358 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2359 the following functions
2360 compute a relation that maps each element of C<dom>
2361 to the single lexicographic minimum or maximum
2362 of the elements that are associated to that same
2363 element in C<map> (or C<bmap>).
2364 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2365 that contains the elements in C<dom> that do not map
2366 to any elements in C<map> (or C<bmap>).
2367 In other words, the union of the domain of the result and of C<*empty>
2370 __isl_give isl_map *isl_basic_map_partial_lexmax(
2371 __isl_take isl_basic_map *bmap,
2372 __isl_take isl_basic_set *dom,
2373 __isl_give isl_set **empty);
2374 __isl_give isl_map *isl_basic_map_partial_lexmin(
2375 __isl_take isl_basic_map *bmap,
2376 __isl_take isl_basic_set *dom,
2377 __isl_give isl_set **empty);
2378 __isl_give isl_map *isl_map_partial_lexmax(
2379 __isl_take isl_map *map, __isl_take isl_set *dom,
2380 __isl_give isl_set **empty);
2381 __isl_give isl_map *isl_map_partial_lexmin(
2382 __isl_take isl_map *map, __isl_take isl_set *dom,
2383 __isl_give isl_set **empty);
2385 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2386 return a map mapping each element in the domain of
2387 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2388 of all elements associated to that element.
2389 In case of union relations, the optimum is computed per space.
2391 __isl_give isl_map *isl_basic_map_lexmin(
2392 __isl_take isl_basic_map *bmap);
2393 __isl_give isl_map *isl_basic_map_lexmax(
2394 __isl_take isl_basic_map *bmap);
2395 __isl_give isl_map *isl_map_lexmin(
2396 __isl_take isl_map *map);
2397 __isl_give isl_map *isl_map_lexmax(
2398 __isl_take isl_map *map);
2399 __isl_give isl_union_map *isl_union_map_lexmin(
2400 __isl_take isl_union_map *umap);
2401 __isl_give isl_union_map *isl_union_map_lexmax(
2402 __isl_take isl_union_map *umap);
2406 Lists are defined over several element types, including
2407 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2408 Here we take lists of C<isl_set>s as an example.
2409 Lists can be created, copied and freed using the following functions.
2411 #include <isl/list.h>
2412 __isl_give isl_set_list *isl_set_list_from_set(
2413 __isl_take isl_set *el);
2414 __isl_give isl_set_list *isl_set_list_alloc(
2415 isl_ctx *ctx, int n);
2416 __isl_give isl_set_list *isl_set_list_copy(
2417 __isl_keep isl_set_list *list);
2418 __isl_give isl_set_list *isl_set_list_add(
2419 __isl_take isl_set_list *list,
2420 __isl_take isl_set *el);
2421 __isl_give isl_set_list *isl_set_list_concat(
2422 __isl_take isl_set_list *list1,
2423 __isl_take isl_set_list *list2);
2424 void *isl_set_list_free(__isl_take isl_set_list *list);
2426 C<isl_set_list_alloc> creates an empty list with a capacity for
2427 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2430 Lists can be inspected using the following functions.
2432 #include <isl/list.h>
2433 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2434 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2435 __isl_give isl_set *isl_set_list_get_set(
2436 __isl_keep isl_set_list *list, int index);
2437 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2438 int (*fn)(__isl_take isl_set *el, void *user),
2441 Lists can be printed using
2443 #include <isl/list.h>
2444 __isl_give isl_printer *isl_printer_print_set_list(
2445 __isl_take isl_printer *p,
2446 __isl_keep isl_set_list *list);
2450 Matrices can be created, copied and freed using the following functions.
2452 #include <isl/mat.h>
2453 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2454 unsigned n_row, unsigned n_col);
2455 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2456 void isl_mat_free(__isl_take isl_mat *mat);
2458 Note that the elements of a newly created matrix may have arbitrary values.
2459 The elements can be changed and inspected using the following functions.
2461 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2462 int isl_mat_rows(__isl_keep isl_mat *mat);
2463 int isl_mat_cols(__isl_keep isl_mat *mat);
2464 int isl_mat_get_element(__isl_keep isl_mat *mat,
2465 int row, int col, isl_int *v);
2466 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2467 int row, int col, isl_int v);
2468 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2469 int row, int col, int v);
2471 C<isl_mat_get_element> will return a negative value if anything went wrong.
2472 In that case, the value of C<*v> is undefined.
2474 The following function can be used to compute the (right) inverse
2475 of a matrix, i.e., a matrix such that the product of the original
2476 and the inverse (in that order) is a multiple of the identity matrix.
2477 The input matrix is assumed to be of full row-rank.
2479 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2481 The following function can be used to compute the (right) kernel
2482 (or null space) of a matrix, i.e., a matrix such that the product of
2483 the original and the kernel (in that order) is the zero matrix.
2485 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2487 =head2 Piecewise Quasi Affine Expressions
2489 The zero quasi affine expression on a given domain can be created using
2491 __isl_give isl_aff *isl_aff_zero_on_domain(
2492 __isl_take isl_local_space *ls);
2494 Note that the space in which the resulting object lives is a map space
2495 with the given space as domain and a one-dimensional range.
2497 An empty piecewise quasi affine expression (one with no cells)
2498 or a piecewise quasi affine expression with a single cell can
2499 be created using the following functions.
2501 #include <isl/aff.h>
2502 __isl_give isl_pw_aff *isl_pw_aff_empty(
2503 __isl_take isl_space *space);
2504 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2505 __isl_take isl_set *set, __isl_take isl_aff *aff);
2506 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2507 __isl_take isl_aff *aff);
2509 Quasi affine expressions can be copied and freed using
2511 #include <isl/aff.h>
2512 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2513 void *isl_aff_free(__isl_take isl_aff *aff);
2515 __isl_give isl_pw_aff *isl_pw_aff_copy(
2516 __isl_keep isl_pw_aff *pwaff);
2517 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2519 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2520 using the following function. The constraint is required to have
2521 a non-zero coefficient for the specified dimension.
2523 #include <isl/constraint.h>
2524 __isl_give isl_aff *isl_constraint_get_bound(
2525 __isl_keep isl_constraint *constraint,
2526 enum isl_dim_type type, int pos);
2528 The entire affine expression of the constraint can also be extracted
2529 using the following function.
2531 #include <isl/constraint.h>
2532 __isl_give isl_aff *isl_constraint_get_aff(
2533 __isl_keep isl_constraint *constraint);
2535 Conversely, an equality constraint equating
2536 the affine expression to zero or an inequality constraint enforcing
2537 the affine expression to be non-negative, can be constructed using
2539 __isl_give isl_constraint *isl_equality_from_aff(
2540 __isl_take isl_aff *aff);
2541 __isl_give isl_constraint *isl_inequality_from_aff(
2542 __isl_take isl_aff *aff);
2544 The expression can be inspected using
2546 #include <isl/aff.h>
2547 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2548 int isl_aff_dim(__isl_keep isl_aff *aff,
2549 enum isl_dim_type type);
2550 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2551 __isl_keep isl_aff *aff);
2552 __isl_give isl_local_space *isl_aff_get_local_space(
2553 __isl_keep isl_aff *aff);
2554 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2555 enum isl_dim_type type, unsigned pos);
2556 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2558 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2559 enum isl_dim_type type, int pos, isl_int *v);
2560 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2562 __isl_give isl_aff *isl_aff_get_div(
2563 __isl_keep isl_aff *aff, int pos);
2565 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2566 int (*fn)(__isl_take isl_set *set,
2567 __isl_take isl_aff *aff,
2568 void *user), void *user);
2570 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2571 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2573 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2574 enum isl_dim_type type, unsigned first, unsigned n);
2575 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2576 enum isl_dim_type type, unsigned first, unsigned n);
2578 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2579 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2580 enum isl_dim_type type);
2581 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2583 It can be modified using
2585 #include <isl/aff.h>
2586 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2587 __isl_take isl_pw_aff *pwaff,
2588 __isl_take isl_id *id);
2589 __isl_give isl_aff *isl_aff_set_dim_name(
2590 __isl_take isl_aff *aff, enum isl_dim_type type,
2591 unsigned pos, const char *s);
2592 __isl_give isl_aff *isl_aff_set_constant(
2593 __isl_take isl_aff *aff, isl_int v);
2594 __isl_give isl_aff *isl_aff_set_constant_si(
2595 __isl_take isl_aff *aff, int v);
2596 __isl_give isl_aff *isl_aff_set_coefficient(
2597 __isl_take isl_aff *aff,
2598 enum isl_dim_type type, int pos, isl_int v);
2599 __isl_give isl_aff *isl_aff_set_coefficient_si(
2600 __isl_take isl_aff *aff,
2601 enum isl_dim_type type, int pos, int v);
2602 __isl_give isl_aff *isl_aff_set_denominator(
2603 __isl_take isl_aff *aff, isl_int v);
2605 __isl_give isl_aff *isl_aff_add_constant(
2606 __isl_take isl_aff *aff, isl_int v);
2607 __isl_give isl_aff *isl_aff_add_constant_si(
2608 __isl_take isl_aff *aff, int v);
2609 __isl_give isl_aff *isl_aff_add_coefficient(
2610 __isl_take isl_aff *aff,
2611 enum isl_dim_type type, int pos, isl_int v);
2612 __isl_give isl_aff *isl_aff_add_coefficient_si(
2613 __isl_take isl_aff *aff,
2614 enum isl_dim_type type, int pos, int v);
2616 __isl_give isl_aff *isl_aff_insert_dims(
2617 __isl_take isl_aff *aff,
2618 enum isl_dim_type type, unsigned first, unsigned n);
2619 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2620 __isl_take isl_pw_aff *pwaff,
2621 enum isl_dim_type type, unsigned first, unsigned n);
2622 __isl_give isl_aff *isl_aff_add_dims(
2623 __isl_take isl_aff *aff,
2624 enum isl_dim_type type, unsigned n);
2625 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2626 __isl_take isl_pw_aff *pwaff,
2627 enum isl_dim_type type, unsigned n);
2628 __isl_give isl_aff *isl_aff_drop_dims(
2629 __isl_take isl_aff *aff,
2630 enum isl_dim_type type, unsigned first, unsigned n);
2631 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2632 __isl_take isl_pw_aff *pwaff,
2633 enum isl_dim_type type, unsigned first, unsigned n);
2635 Note that the C<set_constant> and C<set_coefficient> functions
2636 set the I<numerator> of the constant or coefficient, while
2637 C<add_constant> and C<add_coefficient> add an integer value to
2638 the possibly rational constant or coefficient.
2640 To check whether an affine expressions is obviously zero
2641 or obviously equal to some other affine expression, use
2643 #include <isl/aff.h>
2644 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2645 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2646 __isl_keep isl_aff *aff2);
2650 #include <isl/aff.h>
2651 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2652 __isl_take isl_aff *aff2);
2653 __isl_give isl_pw_aff *isl_pw_aff_add(
2654 __isl_take isl_pw_aff *pwaff1,
2655 __isl_take isl_pw_aff *pwaff2);
2656 __isl_give isl_pw_aff *isl_pw_aff_min(
2657 __isl_take isl_pw_aff *pwaff1,
2658 __isl_take isl_pw_aff *pwaff2);
2659 __isl_give isl_pw_aff *isl_pw_aff_max(
2660 __isl_take isl_pw_aff *pwaff1,
2661 __isl_take isl_pw_aff *pwaff2);
2662 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2663 __isl_take isl_aff *aff2);
2664 __isl_give isl_pw_aff *isl_pw_aff_sub(
2665 __isl_take isl_pw_aff *pwaff1,
2666 __isl_take isl_pw_aff *pwaff2);
2667 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2668 __isl_give isl_pw_aff *isl_pw_aff_neg(
2669 __isl_take isl_pw_aff *pwaff);
2670 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2671 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2672 __isl_take isl_pw_aff *pwaff);
2673 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2674 __isl_give isl_pw_aff *isl_pw_aff_floor(
2675 __isl_take isl_pw_aff *pwaff);
2676 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2678 __isl_give isl_pw_aff *isl_pw_aff_mod(
2679 __isl_take isl_pw_aff *pwaff, isl_int mod);
2680 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2682 __isl_give isl_pw_aff *isl_pw_aff_scale(
2683 __isl_take isl_pw_aff *pwaff, isl_int f);
2684 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2686 __isl_give isl_aff *isl_aff_scale_down_ui(
2687 __isl_take isl_aff *aff, unsigned f);
2688 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2689 __isl_take isl_pw_aff *pwaff, isl_int f);
2691 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2692 __isl_take isl_pw_aff_list *list);
2693 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2694 __isl_take isl_pw_aff_list *list);
2696 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2697 __isl_take isl_pw_aff *pwqp);
2699 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2700 __isl_take isl_pw_aff *pwaff,
2701 __isl_take isl_space *model);
2703 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2704 __isl_take isl_set *context);
2705 __isl_give isl_pw_aff *isl_pw_aff_gist(
2706 __isl_take isl_pw_aff *pwaff,
2707 __isl_take isl_set *context);
2709 __isl_give isl_set *isl_pw_aff_domain(
2710 __isl_take isl_pw_aff *pwaff);
2712 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2713 __isl_take isl_aff *aff2);
2714 __isl_give isl_pw_aff *isl_pw_aff_mul(
2715 __isl_take isl_pw_aff *pwaff1,
2716 __isl_take isl_pw_aff *pwaff2);
2718 When multiplying two affine expressions, at least one of the two needs
2721 #include <isl/aff.h>
2722 __isl_give isl_basic_set *isl_aff_le_basic_set(
2723 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2724 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2725 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2726 __isl_give isl_set *isl_pw_aff_eq_set(
2727 __isl_take isl_pw_aff *pwaff1,
2728 __isl_take isl_pw_aff *pwaff2);
2729 __isl_give isl_set *isl_pw_aff_ne_set(
2730 __isl_take isl_pw_aff *pwaff1,
2731 __isl_take isl_pw_aff *pwaff2);
2732 __isl_give isl_set *isl_pw_aff_le_set(
2733 __isl_take isl_pw_aff *pwaff1,
2734 __isl_take isl_pw_aff *pwaff2);
2735 __isl_give isl_set *isl_pw_aff_lt_set(
2736 __isl_take isl_pw_aff *pwaff1,
2737 __isl_take isl_pw_aff *pwaff2);
2738 __isl_give isl_set *isl_pw_aff_ge_set(
2739 __isl_take isl_pw_aff *pwaff1,
2740 __isl_take isl_pw_aff *pwaff2);
2741 __isl_give isl_set *isl_pw_aff_gt_set(
2742 __isl_take isl_pw_aff *pwaff1,
2743 __isl_take isl_pw_aff *pwaff2);
2745 __isl_give isl_set *isl_pw_aff_list_eq_set(
2746 __isl_take isl_pw_aff_list *list1,
2747 __isl_take isl_pw_aff_list *list2);
2748 __isl_give isl_set *isl_pw_aff_list_ne_set(
2749 __isl_take isl_pw_aff_list *list1,
2750 __isl_take isl_pw_aff_list *list2);
2751 __isl_give isl_set *isl_pw_aff_list_le_set(
2752 __isl_take isl_pw_aff_list *list1,
2753 __isl_take isl_pw_aff_list *list2);
2754 __isl_give isl_set *isl_pw_aff_list_lt_set(
2755 __isl_take isl_pw_aff_list *list1,
2756 __isl_take isl_pw_aff_list *list2);
2757 __isl_give isl_set *isl_pw_aff_list_ge_set(
2758 __isl_take isl_pw_aff_list *list1,
2759 __isl_take isl_pw_aff_list *list2);
2760 __isl_give isl_set *isl_pw_aff_list_gt_set(
2761 __isl_take isl_pw_aff_list *list1,
2762 __isl_take isl_pw_aff_list *list2);
2764 The function C<isl_aff_ge_basic_set> returns a basic set
2765 containing those elements in the shared space
2766 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2767 The function C<isl_aff_ge_set> returns a set
2768 containing those elements in the shared domain
2769 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2770 The functions operating on C<isl_pw_aff_list> apply the corresponding
2771 C<isl_pw_aff> function to each pair of elements in the two lists.
2773 #include <isl/aff.h>
2774 __isl_give isl_set *isl_pw_aff_nonneg_set(
2775 __isl_take isl_pw_aff *pwaff);
2776 __isl_give isl_set *isl_pw_aff_zero_set(
2777 __isl_take isl_pw_aff *pwaff);
2778 __isl_give isl_set *isl_pw_aff_non_zero_set(
2779 __isl_take isl_pw_aff *pwaff);
2781 The function C<isl_pw_aff_nonneg_set> returns a set
2782 containing those elements in the domain
2783 of C<pwaff> where C<pwaff> is non-negative.
2785 #include <isl/aff.h>
2786 __isl_give isl_pw_aff *isl_pw_aff_cond(
2787 __isl_take isl_set *cond,
2788 __isl_take isl_pw_aff *pwaff_true,
2789 __isl_take isl_pw_aff *pwaff_false);
2791 The function C<isl_pw_aff_cond> performs a conditional operator
2792 and returns an expression that is equal to C<pwaff_true>
2793 for elements in C<cond> and equal to C<pwaff_false> for elements
2796 #include <isl/aff.h>
2797 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2798 __isl_take isl_pw_aff *pwaff1,
2799 __isl_take isl_pw_aff *pwaff2);
2800 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2801 __isl_take isl_pw_aff *pwaff1,
2802 __isl_take isl_pw_aff *pwaff2);
2804 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2805 expression with a domain that is the union of those of C<pwaff1> and
2806 C<pwaff2> and such that on each cell, the quasi-affine expression is
2807 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2808 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2809 associated expression is the defined one.
2811 An expression can be printed using
2813 #include <isl/aff.h>
2814 __isl_give isl_printer *isl_printer_print_aff(
2815 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2817 __isl_give isl_printer *isl_printer_print_pw_aff(
2818 __isl_take isl_printer *p,
2819 __isl_keep isl_pw_aff *pwaff);
2823 Points are elements of a set. They can be used to construct
2824 simple sets (boxes) or they can be used to represent the
2825 individual elements of a set.
2826 The zero point (the origin) can be created using
2828 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2830 The coordinates of a point can be inspected, set and changed
2833 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2834 enum isl_dim_type type, int pos, isl_int *v);
2835 __isl_give isl_point *isl_point_set_coordinate(
2836 __isl_take isl_point *pnt,
2837 enum isl_dim_type type, int pos, isl_int v);
2839 __isl_give isl_point *isl_point_add_ui(
2840 __isl_take isl_point *pnt,
2841 enum isl_dim_type type, int pos, unsigned val);
2842 __isl_give isl_point *isl_point_sub_ui(
2843 __isl_take isl_point *pnt,
2844 enum isl_dim_type type, int pos, unsigned val);
2846 Other properties can be obtained using
2848 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2850 Points can be copied or freed using
2852 __isl_give isl_point *isl_point_copy(
2853 __isl_keep isl_point *pnt);
2854 void isl_point_free(__isl_take isl_point *pnt);
2856 A singleton set can be created from a point using
2858 __isl_give isl_basic_set *isl_basic_set_from_point(
2859 __isl_take isl_point *pnt);
2860 __isl_give isl_set *isl_set_from_point(
2861 __isl_take isl_point *pnt);
2863 and a box can be created from two opposite extremal points using
2865 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2866 __isl_take isl_point *pnt1,
2867 __isl_take isl_point *pnt2);
2868 __isl_give isl_set *isl_set_box_from_points(
2869 __isl_take isl_point *pnt1,
2870 __isl_take isl_point *pnt2);
2872 All elements of a B<bounded> (union) set can be enumerated using
2873 the following functions.
2875 int isl_set_foreach_point(__isl_keep isl_set *set,
2876 int (*fn)(__isl_take isl_point *pnt, void *user),
2878 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2879 int (*fn)(__isl_take isl_point *pnt, void *user),
2882 The function C<fn> is called for each integer point in
2883 C<set> with as second argument the last argument of
2884 the C<isl_set_foreach_point> call. The function C<fn>
2885 should return C<0> on success and C<-1> on failure.
2886 In the latter case, C<isl_set_foreach_point> will stop
2887 enumerating and return C<-1> as well.
2888 If the enumeration is performed successfully and to completion,
2889 then C<isl_set_foreach_point> returns C<0>.
2891 To obtain a single point of a (basic) set, use
2893 __isl_give isl_point *isl_basic_set_sample_point(
2894 __isl_take isl_basic_set *bset);
2895 __isl_give isl_point *isl_set_sample_point(
2896 __isl_take isl_set *set);
2898 If C<set> does not contain any (integer) points, then the
2899 resulting point will be ``void'', a property that can be
2902 int isl_point_is_void(__isl_keep isl_point *pnt);
2904 =head2 Piecewise Quasipolynomials
2906 A piecewise quasipolynomial is a particular kind of function that maps
2907 a parametric point to a rational value.
2908 More specifically, a quasipolynomial is a polynomial expression in greatest
2909 integer parts of affine expressions of parameters and variables.
2910 A piecewise quasipolynomial is a subdivision of a given parametric
2911 domain into disjoint cells with a quasipolynomial associated to
2912 each cell. The value of the piecewise quasipolynomial at a given
2913 point is the value of the quasipolynomial associated to the cell
2914 that contains the point. Outside of the union of cells,
2915 the value is assumed to be zero.
2916 For example, the piecewise quasipolynomial
2918 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2920 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2921 A given piecewise quasipolynomial has a fixed domain dimension.
2922 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2923 defined over different domains.
2924 Piecewise quasipolynomials are mainly used by the C<barvinok>
2925 library for representing the number of elements in a parametric set or map.
2926 For example, the piecewise quasipolynomial above represents
2927 the number of points in the map
2929 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2931 =head3 Printing (Piecewise) Quasipolynomials
2933 Quasipolynomials and piecewise quasipolynomials can be printed
2934 using the following functions.
2936 __isl_give isl_printer *isl_printer_print_qpolynomial(
2937 __isl_take isl_printer *p,
2938 __isl_keep isl_qpolynomial *qp);
2940 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2941 __isl_take isl_printer *p,
2942 __isl_keep isl_pw_qpolynomial *pwqp);
2944 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2945 __isl_take isl_printer *p,
2946 __isl_keep isl_union_pw_qpolynomial *upwqp);
2948 The output format of the printer
2949 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2950 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2952 In case of printing in C<ISL_FORMAT_C>, the user may want
2953 to set the names of all dimensions
2955 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2956 __isl_take isl_qpolynomial *qp,
2957 enum isl_dim_type type, unsigned pos,
2959 __isl_give isl_pw_qpolynomial *
2960 isl_pw_qpolynomial_set_dim_name(
2961 __isl_take isl_pw_qpolynomial *pwqp,
2962 enum isl_dim_type type, unsigned pos,
2965 =head3 Creating New (Piecewise) Quasipolynomials
2967 Some simple quasipolynomials can be created using the following functions.
2968 More complicated quasipolynomials can be created by applying
2969 operations such as addition and multiplication
2970 on the resulting quasipolynomials
2972 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2973 __isl_take isl_space *domain);
2974 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2975 __isl_take isl_space *domain);
2976 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2977 __isl_take isl_space *domain);
2978 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2979 __isl_take isl_space *domain);
2980 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2981 __isl_take isl_space *domain);
2982 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2983 __isl_take isl_space *domain,
2984 const isl_int n, const isl_int d);
2985 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2986 __isl_take isl_space *domain,
2987 enum isl_dim_type type, unsigned pos);
2988 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2989 __isl_take isl_aff *aff);
2991 Note that the space in which a quasipolynomial lives is a map space
2992 with a one-dimensional range. The C<domain> argument in some of
2993 the functions above corresponds to the domain of this map space.
2995 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2996 with a single cell can be created using the following functions.
2997 Multiple of these single cell piecewise quasipolynomials can
2998 be combined to create more complicated piecewise quasipolynomials.
3000 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3001 __isl_take isl_space *space);
3002 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3003 __isl_take isl_set *set,
3004 __isl_take isl_qpolynomial *qp);
3005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3006 __isl_take isl_qpolynomial *qp);
3007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3008 __isl_take isl_pw_aff *pwaff);
3010 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3011 __isl_take isl_space *space);
3012 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3013 __isl_take isl_pw_qpolynomial *pwqp);
3014 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3015 __isl_take isl_union_pw_qpolynomial *upwqp,
3016 __isl_take isl_pw_qpolynomial *pwqp);
3018 Quasipolynomials can be copied and freed again using the following
3021 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3022 __isl_keep isl_qpolynomial *qp);
3023 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3026 __isl_keep isl_pw_qpolynomial *pwqp);
3027 void *isl_pw_qpolynomial_free(
3028 __isl_take isl_pw_qpolynomial *pwqp);
3030 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3031 __isl_keep isl_union_pw_qpolynomial *upwqp);
3032 void isl_union_pw_qpolynomial_free(
3033 __isl_take isl_union_pw_qpolynomial *upwqp);
3035 =head3 Inspecting (Piecewise) Quasipolynomials
3037 To iterate over all piecewise quasipolynomials in a union
3038 piecewise quasipolynomial, use the following function
3040 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3041 __isl_keep isl_union_pw_qpolynomial *upwqp,
3042 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3045 To extract the piecewise quasipolynomial in a given space from a union, use
3047 __isl_give isl_pw_qpolynomial *
3048 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3049 __isl_keep isl_union_pw_qpolynomial *upwqp,
3050 __isl_take isl_space *space);
3052 To iterate over the cells in a piecewise quasipolynomial,
3053 use either of the following two functions
3055 int isl_pw_qpolynomial_foreach_piece(
3056 __isl_keep isl_pw_qpolynomial *pwqp,
3057 int (*fn)(__isl_take isl_set *set,
3058 __isl_take isl_qpolynomial *qp,
3059 void *user), void *user);
3060 int isl_pw_qpolynomial_foreach_lifted_piece(
3061 __isl_keep isl_pw_qpolynomial *pwqp,
3062 int (*fn)(__isl_take isl_set *set,
3063 __isl_take isl_qpolynomial *qp,
3064 void *user), void *user);
3066 As usual, the function C<fn> should return C<0> on success
3067 and C<-1> on failure. The difference between
3068 C<isl_pw_qpolynomial_foreach_piece> and
3069 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3070 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3071 compute unique representations for all existentially quantified
3072 variables and then turn these existentially quantified variables
3073 into extra set variables, adapting the associated quasipolynomial
3074 accordingly. This means that the C<set> passed to C<fn>
3075 will not have any existentially quantified variables, but that
3076 the dimensions of the sets may be different for different
3077 invocations of C<fn>.
3079 To iterate over all terms in a quasipolynomial,
3082 int isl_qpolynomial_foreach_term(
3083 __isl_keep isl_qpolynomial *qp,
3084 int (*fn)(__isl_take isl_term *term,
3085 void *user), void *user);
3087 The terms themselves can be inspected and freed using
3090 unsigned isl_term_dim(__isl_keep isl_term *term,
3091 enum isl_dim_type type);
3092 void isl_term_get_num(__isl_keep isl_term *term,
3094 void isl_term_get_den(__isl_keep isl_term *term,
3096 int isl_term_get_exp(__isl_keep isl_term *term,
3097 enum isl_dim_type type, unsigned pos);
3098 __isl_give isl_aff *isl_term_get_div(
3099 __isl_keep isl_term *term, unsigned pos);
3100 void isl_term_free(__isl_take isl_term *term);
3102 Each term is a product of parameters, set variables and
3103 integer divisions. The function C<isl_term_get_exp>
3104 returns the exponent of a given dimensions in the given term.
3105 The C<isl_int>s in the arguments of C<isl_term_get_num>
3106 and C<isl_term_get_den> need to have been initialized
3107 using C<isl_int_init> before calling these functions.
3109 =head3 Properties of (Piecewise) Quasipolynomials
3111 To check whether a quasipolynomial is actually a constant,
3112 use the following function.
3114 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3115 isl_int *n, isl_int *d);
3117 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3118 then the numerator and denominator of the constant
3119 are returned in C<*n> and C<*d>, respectively.
3121 =head3 Operations on (Piecewise) Quasipolynomials
3123 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3124 __isl_take isl_qpolynomial *qp, isl_int v);
3125 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3126 __isl_take isl_qpolynomial *qp);
3127 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3128 __isl_take isl_qpolynomial *qp1,
3129 __isl_take isl_qpolynomial *qp2);
3130 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3131 __isl_take isl_qpolynomial *qp1,
3132 __isl_take isl_qpolynomial *qp2);
3133 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3134 __isl_take isl_qpolynomial *qp1,
3135 __isl_take isl_qpolynomial *qp2);
3136 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3137 __isl_take isl_qpolynomial *qp, unsigned exponent);
3139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3140 __isl_take isl_pw_qpolynomial *pwqp1,
3141 __isl_take isl_pw_qpolynomial *pwqp2);
3142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3143 __isl_take isl_pw_qpolynomial *pwqp1,
3144 __isl_take isl_pw_qpolynomial *pwqp2);
3145 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3146 __isl_take isl_pw_qpolynomial *pwqp1,
3147 __isl_take isl_pw_qpolynomial *pwqp2);
3148 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3149 __isl_take isl_pw_qpolynomial *pwqp);
3150 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3151 __isl_take isl_pw_qpolynomial *pwqp1,
3152 __isl_take isl_pw_qpolynomial *pwqp2);
3153 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3154 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3157 __isl_take isl_union_pw_qpolynomial *upwqp1,
3158 __isl_take isl_union_pw_qpolynomial *upwqp2);
3159 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3160 __isl_take isl_union_pw_qpolynomial *upwqp1,
3161 __isl_take isl_union_pw_qpolynomial *upwqp2);
3162 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3163 __isl_take isl_union_pw_qpolynomial *upwqp1,
3164 __isl_take isl_union_pw_qpolynomial *upwqp2);
3166 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3167 __isl_take isl_pw_qpolynomial *pwqp,
3168 __isl_take isl_point *pnt);
3170 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3171 __isl_take isl_union_pw_qpolynomial *upwqp,
3172 __isl_take isl_point *pnt);
3174 __isl_give isl_set *isl_pw_qpolynomial_domain(
3175 __isl_take isl_pw_qpolynomial *pwqp);
3176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3177 __isl_take isl_pw_qpolynomial *pwpq,
3178 __isl_take isl_set *set);
3180 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3181 __isl_take isl_union_pw_qpolynomial *upwqp);
3182 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3183 __isl_take isl_union_pw_qpolynomial *upwpq,
3184 __isl_take isl_union_set *uset);
3186 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3187 __isl_take isl_qpolynomial *qp,
3188 __isl_take isl_space *model);
3190 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3191 __isl_take isl_qpolynomial *qp);
3192 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3193 __isl_take isl_pw_qpolynomial *pwqp);
3195 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3196 __isl_take isl_union_pw_qpolynomial *upwqp);
3198 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3199 __isl_take isl_qpolynomial *qp,
3200 __isl_take isl_set *context);
3202 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3203 __isl_take isl_pw_qpolynomial *pwqp,
3204 __isl_take isl_set *context);
3206 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3207 __isl_take isl_union_pw_qpolynomial *upwqp,
3208 __isl_take isl_union_set *context);
3210 The gist operation applies the gist operation to each of
3211 the cells in the domain of the input piecewise quasipolynomial.
3212 The context is also exploited
3213 to simplify the quasipolynomials associated to each cell.
3215 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3216 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3217 __isl_give isl_union_pw_qpolynomial *
3218 isl_union_pw_qpolynomial_to_polynomial(
3219 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3221 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3222 the polynomial will be an overapproximation. If C<sign> is negative,
3223 it will be an underapproximation. If C<sign> is zero, the approximation
3224 will lie somewhere in between.
3226 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3228 A piecewise quasipolynomial reduction is a piecewise
3229 reduction (or fold) of quasipolynomials.
3230 In particular, the reduction can be maximum or a minimum.
3231 The objects are mainly used to represent the result of
3232 an upper or lower bound on a quasipolynomial over its domain,
3233 i.e., as the result of the following function.
3235 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3236 __isl_take isl_pw_qpolynomial *pwqp,
3237 enum isl_fold type, int *tight);
3239 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3240 __isl_take isl_union_pw_qpolynomial *upwqp,
3241 enum isl_fold type, int *tight);
3243 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3244 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3245 is the returned bound is known be tight, i.e., for each value
3246 of the parameters there is at least
3247 one element in the domain that reaches the bound.
3248 If the domain of C<pwqp> is not wrapping, then the bound is computed
3249 over all elements in that domain and the result has a purely parametric
3250 domain. If the domain of C<pwqp> is wrapping, then the bound is
3251 computed over the range of the wrapped relation. The domain of the
3252 wrapped relation becomes the domain of the result.
3254 A (piecewise) quasipolynomial reduction can be copied or freed using the
3255 following functions.
3257 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3258 __isl_keep isl_qpolynomial_fold *fold);
3259 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3260 __isl_keep isl_pw_qpolynomial_fold *pwf);
3261 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3262 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3263 void isl_qpolynomial_fold_free(
3264 __isl_take isl_qpolynomial_fold *fold);
3265 void *isl_pw_qpolynomial_fold_free(
3266 __isl_take isl_pw_qpolynomial_fold *pwf);
3267 void isl_union_pw_qpolynomial_fold_free(
3268 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3270 =head3 Printing Piecewise Quasipolynomial Reductions
3272 Piecewise quasipolynomial reductions can be printed
3273 using the following function.
3275 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3276 __isl_take isl_printer *p,
3277 __isl_keep isl_pw_qpolynomial_fold *pwf);
3278 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3279 __isl_take isl_printer *p,
3280 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3282 For C<isl_printer_print_pw_qpolynomial_fold>,
3283 output format of the printer
3284 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3285 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3286 output format of the printer
3287 needs to be set to C<ISL_FORMAT_ISL>.
3288 In case of printing in C<ISL_FORMAT_C>, the user may want
3289 to set the names of all dimensions
3291 __isl_give isl_pw_qpolynomial_fold *
3292 isl_pw_qpolynomial_fold_set_dim_name(
3293 __isl_take isl_pw_qpolynomial_fold *pwf,
3294 enum isl_dim_type type, unsigned pos,
3297 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3299 To iterate over all piecewise quasipolynomial reductions in a union
3300 piecewise quasipolynomial reduction, use the following function
3302 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3303 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3304 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3305 void *user), void *user);
3307 To iterate over the cells in a piecewise quasipolynomial reduction,
3308 use either of the following two functions
3310 int isl_pw_qpolynomial_fold_foreach_piece(
3311 __isl_keep isl_pw_qpolynomial_fold *pwf,
3312 int (*fn)(__isl_take isl_set *set,
3313 __isl_take isl_qpolynomial_fold *fold,
3314 void *user), void *user);
3315 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3316 __isl_keep isl_pw_qpolynomial_fold *pwf,
3317 int (*fn)(__isl_take isl_set *set,
3318 __isl_take isl_qpolynomial_fold *fold,
3319 void *user), void *user);
3321 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3322 of the difference between these two functions.
3324 To iterate over all quasipolynomials in a reduction, use
3326 int isl_qpolynomial_fold_foreach_qpolynomial(
3327 __isl_keep isl_qpolynomial_fold *fold,
3328 int (*fn)(__isl_take isl_qpolynomial *qp,
3329 void *user), void *user);
3331 =head3 Operations on Piecewise Quasipolynomial Reductions
3333 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3334 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3336 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3337 __isl_take isl_pw_qpolynomial_fold *pwf1,
3338 __isl_take isl_pw_qpolynomial_fold *pwf2);
3340 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3341 __isl_take isl_pw_qpolynomial_fold *pwf1,
3342 __isl_take isl_pw_qpolynomial_fold *pwf2);
3344 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3345 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3346 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3348 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3349 __isl_take isl_pw_qpolynomial_fold *pwf,
3350 __isl_take isl_point *pnt);
3352 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3353 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3354 __isl_take isl_point *pnt);
3356 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3357 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3358 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3359 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3360 __isl_take isl_union_set *uset);
3362 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3363 __isl_take isl_pw_qpolynomial_fold *pwf);
3365 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3366 __isl_take isl_pw_qpolynomial_fold *pwf);
3368 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3369 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3371 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3372 __isl_take isl_pw_qpolynomial_fold *pwf,
3373 __isl_take isl_set *context);
3375 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3376 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3377 __isl_take isl_union_set *context);
3379 The gist operation applies the gist operation to each of
3380 the cells in the domain of the input piecewise quasipolynomial reduction.
3381 In future, the operation will also exploit the context
3382 to simplify the quasipolynomial reductions associated to each cell.
3384 __isl_give isl_pw_qpolynomial_fold *
3385 isl_set_apply_pw_qpolynomial_fold(
3386 __isl_take isl_set *set,
3387 __isl_take isl_pw_qpolynomial_fold *pwf,
3389 __isl_give isl_pw_qpolynomial_fold *
3390 isl_map_apply_pw_qpolynomial_fold(
3391 __isl_take isl_map *map,
3392 __isl_take isl_pw_qpolynomial_fold *pwf,
3394 __isl_give isl_union_pw_qpolynomial_fold *
3395 isl_union_set_apply_union_pw_qpolynomial_fold(
3396 __isl_take isl_union_set *uset,
3397 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3399 __isl_give isl_union_pw_qpolynomial_fold *
3400 isl_union_map_apply_union_pw_qpolynomial_fold(
3401 __isl_take isl_union_map *umap,
3402 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3405 The functions taking a map
3406 compose the given map with the given piecewise quasipolynomial reduction.
3407 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3408 over all elements in the intersection of the range of the map
3409 and the domain of the piecewise quasipolynomial reduction
3410 as a function of an element in the domain of the map.
3411 The functions taking a set compute a bound over all elements in the
3412 intersection of the set and the domain of the
3413 piecewise quasipolynomial reduction.
3415 =head2 Dependence Analysis
3417 C<isl> contains specialized functionality for performing
3418 array dataflow analysis. That is, given a I<sink> access relation
3419 and a collection of possible I<source> access relations,
3420 C<isl> can compute relations that describe
3421 for each iteration of the sink access, which iteration
3422 of which of the source access relations was the last
3423 to access the same data element before the given iteration
3425 To compute standard flow dependences, the sink should be
3426 a read, while the sources should be writes.
3427 If any of the source accesses are marked as being I<may>
3428 accesses, then there will be a dependence to the last
3429 I<must> access B<and> to any I<may> access that follows
3430 this last I<must> access.
3431 In particular, if I<all> sources are I<may> accesses,
3432 then memory based dependence analysis is performed.
3433 If, on the other hand, all sources are I<must> accesses,
3434 then value based dependence analysis is performed.
3436 #include <isl/flow.h>
3438 typedef int (*isl_access_level_before)(void *first, void *second);
3440 __isl_give isl_access_info *isl_access_info_alloc(
3441 __isl_take isl_map *sink,
3442 void *sink_user, isl_access_level_before fn,
3444 __isl_give isl_access_info *isl_access_info_add_source(
3445 __isl_take isl_access_info *acc,
3446 __isl_take isl_map *source, int must,
3448 void isl_access_info_free(__isl_take isl_access_info *acc);
3450 __isl_give isl_flow *isl_access_info_compute_flow(
3451 __isl_take isl_access_info *acc);
3453 int isl_flow_foreach(__isl_keep isl_flow *deps,
3454 int (*fn)(__isl_take isl_map *dep, int must,
3455 void *dep_user, void *user),
3457 __isl_give isl_map *isl_flow_get_no_source(
3458 __isl_keep isl_flow *deps, int must);
3459 void isl_flow_free(__isl_take isl_flow *deps);
3461 The function C<isl_access_info_compute_flow> performs the actual
3462 dependence analysis. The other functions are used to construct
3463 the input for this function or to read off the output.
3465 The input is collected in an C<isl_access_info>, which can
3466 be created through a call to C<isl_access_info_alloc>.
3467 The arguments to this functions are the sink access relation
3468 C<sink>, a token C<sink_user> used to identify the sink
3469 access to the user, a callback function for specifying the
3470 relative order of source and sink accesses, and the number
3471 of source access relations that will be added.
3472 The callback function has type C<int (*)(void *first, void *second)>.
3473 The function is called with two user supplied tokens identifying
3474 either a source or the sink and it should return the shared nesting
3475 level and the relative order of the two accesses.
3476 In particular, let I<n> be the number of loops shared by
3477 the two accesses. If C<first> precedes C<second> textually,
3478 then the function should return I<2 * n + 1>; otherwise,
3479 it should return I<2 * n>.
3480 The sources can be added to the C<isl_access_info> by performing
3481 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3482 C<must> indicates whether the source is a I<must> access
3483 or a I<may> access. Note that a multi-valued access relation
3484 should only be marked I<must> if every iteration in the domain
3485 of the relation accesses I<all> elements in its image.
3486 The C<source_user> token is again used to identify
3487 the source access. The range of the source access relation
3488 C<source> should have the same dimension as the range
3489 of the sink access relation.
3490 The C<isl_access_info_free> function should usually not be
3491 called explicitly, because it is called implicitly by
3492 C<isl_access_info_compute_flow>.
3494 The result of the dependence analysis is collected in an
3495 C<isl_flow>. There may be elements of
3496 the sink access for which no preceding source access could be
3497 found or for which all preceding sources are I<may> accesses.
3498 The relations containing these elements can be obtained through
3499 calls to C<isl_flow_get_no_source>, the first with C<must> set
3500 and the second with C<must> unset.
3501 In the case of standard flow dependence analysis,
3502 with the sink a read and the sources I<must> writes,
3503 the first relation corresponds to the reads from uninitialized
3504 array elements and the second relation is empty.
3505 The actual flow dependences can be extracted using
3506 C<isl_flow_foreach>. This function will call the user-specified
3507 callback function C<fn> for each B<non-empty> dependence between
3508 a source and the sink. The callback function is called
3509 with four arguments, the actual flow dependence relation
3510 mapping source iterations to sink iterations, a boolean that
3511 indicates whether it is a I<must> or I<may> dependence, a token
3512 identifying the source and an additional C<void *> with value
3513 equal to the third argument of the C<isl_flow_foreach> call.
3514 A dependence is marked I<must> if it originates from a I<must>
3515 source and if it is not followed by any I<may> sources.
3517 After finishing with an C<isl_flow>, the user should call
3518 C<isl_flow_free> to free all associated memory.
3520 A higher-level interface to dependence analysis is provided
3521 by the following function.
3523 #include <isl/flow.h>
3525 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3526 __isl_take isl_union_map *must_source,
3527 __isl_take isl_union_map *may_source,
3528 __isl_take isl_union_map *schedule,
3529 __isl_give isl_union_map **must_dep,
3530 __isl_give isl_union_map **may_dep,
3531 __isl_give isl_union_map **must_no_source,
3532 __isl_give isl_union_map **may_no_source);
3534 The arrays are identified by the tuple names of the ranges
3535 of the accesses. The iteration domains by the tuple names
3536 of the domains of the accesses and of the schedule.
3537 The relative order of the iteration domains is given by the
3538 schedule. The relations returned through C<must_no_source>
3539 and C<may_no_source> are subsets of C<sink>.
3540 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3541 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3542 any of the other arguments is treated as an error.
3546 B<The functionality described in this section is fairly new
3547 and may be subject to change.>
3549 The following function can be used to compute a schedule
3550 for a union of domains. The generated schedule respects
3551 all C<validity> dependences. That is, all dependence distances
3552 over these dependences in the scheduled space are lexicographically
3553 positive. The generated schedule schedule also tries to minimize
3554 the dependence distances over C<proximity> dependences.
3555 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3556 for groups of domains where the dependence distances have only
3557 non-negative values.
3558 The algorithm used to construct the schedule is similar to that
3561 #include <isl/schedule.h>
3562 __isl_give isl_schedule *isl_union_set_compute_schedule(
3563 __isl_take isl_union_set *domain,
3564 __isl_take isl_union_map *validity,
3565 __isl_take isl_union_map *proximity);
3566 void *isl_schedule_free(__isl_take isl_schedule *sched);
3568 A mapping from the domains to the scheduled space can be obtained
3569 from an C<isl_schedule> using the following function.
3571 __isl_give isl_union_map *isl_schedule_get_map(
3572 __isl_keep isl_schedule *sched);
3574 A representation of the schedule can be printed using
3576 __isl_give isl_printer *isl_printer_print_schedule(
3577 __isl_take isl_printer *p,
3578 __isl_keep isl_schedule *schedule);
3580 A representation of the schedule as a forest of bands can be obtained
3581 using the following function.
3583 __isl_give isl_band_list *isl_schedule_get_band_forest(
3584 __isl_keep isl_schedule *schedule);
3586 The list can be manipulated as explained in L<"Lists">.
3587 The bands inside the list can be copied and freed using the following
3590 #include <isl/band.h>
3591 __isl_give isl_band *isl_band_copy(
3592 __isl_keep isl_band *band);
3593 void *isl_band_free(__isl_take isl_band *band);
3595 Each band contains zero or more scheduling dimensions.
3596 These are referred to as the members of the band.
3597 The section of the schedule that corresponds to the band is
3598 referred to as the partial schedule of the band.
3599 For those nodes that participate in a band, the outer scheduling
3600 dimensions form the prefix schedule, while the inner scheduling
3601 dimensions form the suffix schedule.
3602 That is, if we take a cut of the band forest, then the union of
3603 the concatenations of the prefix, partial and suffix schedules of
3604 each band in the cut is equal to the entire schedule (modulo
3605 some possible padding at the end with zero scheduling dimensions).
3606 The properties of a band can be inspected using the following functions.
3608 #include <isl/band.h>
3609 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3611 int isl_band_has_children(__isl_keep isl_band *band);
3612 __isl_give isl_band_list *isl_band_get_children(
3613 __isl_keep isl_band *band);
3615 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3616 __isl_keep isl_band *band);
3617 __isl_give isl_union_map *isl_band_get_partial_schedule(
3618 __isl_keep isl_band *band);
3619 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3620 __isl_keep isl_band *band);
3622 int isl_band_n_member(__isl_keep isl_band *band);
3623 int isl_band_member_is_zero_distance(
3624 __isl_keep isl_band *band, int pos);
3626 Note that a scheduling dimension is considered to be ``zero
3627 distance'' if it does not carry any proximity dependences
3629 That is, if the dependence distances of the proximity
3630 dependences are all zero in that direction (for fixed
3631 iterations of outer bands).
3633 A representation of the band can be printed using
3635 #include <isl/band.h>
3636 __isl_give isl_printer *isl_printer_print_band(
3637 __isl_take isl_printer *p,
3638 __isl_keep isl_band *band);
3640 =head2 Parametric Vertex Enumeration
3642 The parametric vertex enumeration described in this section
3643 is mainly intended to be used internally and by the C<barvinok>
3646 #include <isl/vertices.h>
3647 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3648 __isl_keep isl_basic_set *bset);
3650 The function C<isl_basic_set_compute_vertices> performs the
3651 actual computation of the parametric vertices and the chamber
3652 decomposition and store the result in an C<isl_vertices> object.
3653 This information can be queried by either iterating over all
3654 the vertices or iterating over all the chambers or cells
3655 and then iterating over all vertices that are active on the chamber.
3657 int isl_vertices_foreach_vertex(
3658 __isl_keep isl_vertices *vertices,
3659 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3662 int isl_vertices_foreach_cell(
3663 __isl_keep isl_vertices *vertices,
3664 int (*fn)(__isl_take isl_cell *cell, void *user),
3666 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3667 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3670 Other operations that can be performed on an C<isl_vertices> object are
3673 isl_ctx *isl_vertices_get_ctx(
3674 __isl_keep isl_vertices *vertices);
3675 int isl_vertices_get_n_vertices(
3676 __isl_keep isl_vertices *vertices);
3677 void isl_vertices_free(__isl_take isl_vertices *vertices);
3679 Vertices can be inspected and destroyed using the following functions.
3681 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3682 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3683 __isl_give isl_basic_set *isl_vertex_get_domain(
3684 __isl_keep isl_vertex *vertex);
3685 __isl_give isl_basic_set *isl_vertex_get_expr(
3686 __isl_keep isl_vertex *vertex);
3687 void isl_vertex_free(__isl_take isl_vertex *vertex);
3689 C<isl_vertex_get_expr> returns a singleton parametric set describing
3690 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3692 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3693 B<rational> basic sets, so they should mainly be used for inspection
3694 and should not be mixed with integer sets.
3696 Chambers can be inspected and destroyed using the following functions.
3698 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3699 __isl_give isl_basic_set *isl_cell_get_domain(
3700 __isl_keep isl_cell *cell);
3701 void isl_cell_free(__isl_take isl_cell *cell);
3705 Although C<isl> is mainly meant to be used as a library,
3706 it also contains some basic applications that use some
3707 of the functionality of C<isl>.
3708 The input may be specified in either the L<isl format>
3709 or the L<PolyLib format>.
3711 =head2 C<isl_polyhedron_sample>
3713 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3714 an integer element of the polyhedron, if there is any.
3715 The first column in the output is the denominator and is always
3716 equal to 1. If the polyhedron contains no integer points,
3717 then a vector of length zero is printed.
3721 C<isl_pip> takes the same input as the C<example> program
3722 from the C<piplib> distribution, i.e., a set of constraints
3723 on the parameters, a line containing only -1 and finally a set
3724 of constraints on a parametric polyhedron.
3725 The coefficients of the parameters appear in the last columns
3726 (but before the final constant column).
3727 The output is the lexicographic minimum of the parametric polyhedron.
3728 As C<isl> currently does not have its own output format, the output
3729 is just a dump of the internal state.
3731 =head2 C<isl_polyhedron_minimize>
3733 C<isl_polyhedron_minimize> computes the minimum of some linear
3734 or affine objective function over the integer points in a polyhedron.
3735 If an affine objective function
3736 is given, then the constant should appear in the last column.
3738 =head2 C<isl_polytope_scan>
3740 Given a polytope, C<isl_polytope_scan> prints
3741 all integer points in the polytope.