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.
128 The source of C<isl> can be obtained either as a tarball
129 or from the git repository. Both are available from
130 L<http://freshmeat.net/projects/isl/>.
131 The installation process depends on how you obtained
134 =head2 Installation from the git repository
138 =item 1 Clone or update the repository
140 The first time the source is obtained, you need to clone
143 git clone git://repo.or.cz/isl.git
145 To obtain updates, you need to pull in the latest changes
149 =item 2 Generate C<configure>
155 After performing the above steps, continue
156 with the L<Common installation instructions>.
158 =head2 Common installation instructions
162 =item 1 Obtain C<GMP>
164 Building C<isl> requires C<GMP>, including its headers files.
165 Your distribution may not provide these header files by default
166 and you may need to install a package called C<gmp-devel> or something
167 similar. Alternatively, C<GMP> can be built from
168 source, available from L<http://gmplib.org/>.
172 C<isl> uses the standard C<autoconf> C<configure> script.
177 optionally followed by some configure options.
178 A complete list of options can be obtained by running
182 Below we discuss some of the more common options.
184 C<isl> can optionally use C<piplib>, but no
185 C<piplib> functionality is currently used by default.
186 The C<--with-piplib> option can
187 be used to specify which C<piplib>
188 library to use, either an installed version (C<system>),
189 an externally built version (C<build>)
190 or no version (C<no>). The option C<build> is mostly useful
191 in C<configure> scripts of larger projects that bundle both C<isl>
198 Installation prefix for C<isl>
200 =item C<--with-gmp-prefix>
202 Installation prefix for C<GMP> (architecture-independent files).
204 =item C<--with-gmp-exec-prefix>
206 Installation prefix for C<GMP> (architecture-dependent files).
208 =item C<--with-piplib>
210 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
212 =item C<--with-piplib-prefix>
214 Installation prefix for C<system> C<piplib> (architecture-independent files).
216 =item C<--with-piplib-exec-prefix>
218 Installation prefix for C<system> C<piplib> (architecture-dependent files).
220 =item C<--with-piplib-builddir>
222 Location where C<build> C<piplib> was built.
230 =item 4 Install (optional)
238 =head2 Initialization
240 All manipulations of integer sets and relations occur within
241 the context of an C<isl_ctx>.
242 A given C<isl_ctx> can only be used within a single thread.
243 All arguments of a function are required to have been allocated
244 within the same context.
245 There are currently no functions available for moving an object
246 from one C<isl_ctx> to another C<isl_ctx>. This means that
247 there is currently no way of safely moving an object from one
248 thread to another, unless the whole C<isl_ctx> is moved.
250 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
251 freed using C<isl_ctx_free>.
252 All objects allocated within an C<isl_ctx> should be freed
253 before the C<isl_ctx> itself is freed.
255 isl_ctx *isl_ctx_alloc();
256 void isl_ctx_free(isl_ctx *ctx);
260 All operations on integers, mainly the coefficients
261 of the constraints describing the sets and relations,
262 are performed in exact integer arithmetic using C<GMP>.
263 However, to allow future versions of C<isl> to optionally
264 support fixed integer arithmetic, all calls to C<GMP>
265 are wrapped inside C<isl> specific macros.
266 The basic type is C<isl_int> and the operations below
267 are available on this type.
268 The meanings of these operations are essentially the same
269 as their C<GMP> C<mpz_> counterparts.
270 As always with C<GMP> types, C<isl_int>s need to be
271 initialized with C<isl_int_init> before they can be used
272 and they need to be released with C<isl_int_clear>
274 The user should not assume that an C<isl_int> is represented
275 as a C<mpz_t>, but should instead explicitly convert between
276 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
277 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
281 =item isl_int_init(i)
283 =item isl_int_clear(i)
285 =item isl_int_set(r,i)
287 =item isl_int_set_si(r,i)
289 =item isl_int_set_gmp(r,g)
291 =item isl_int_get_gmp(i,g)
293 =item isl_int_abs(r,i)
295 =item isl_int_neg(r,i)
297 =item isl_int_swap(i,j)
299 =item isl_int_swap_or_set(i,j)
301 =item isl_int_add_ui(r,i,j)
303 =item isl_int_sub_ui(r,i,j)
305 =item isl_int_add(r,i,j)
307 =item isl_int_sub(r,i,j)
309 =item isl_int_mul(r,i,j)
311 =item isl_int_mul_ui(r,i,j)
313 =item isl_int_addmul(r,i,j)
315 =item isl_int_submul(r,i,j)
317 =item isl_int_gcd(r,i,j)
319 =item isl_int_lcm(r,i,j)
321 =item isl_int_divexact(r,i,j)
323 =item isl_int_cdiv_q(r,i,j)
325 =item isl_int_fdiv_q(r,i,j)
327 =item isl_int_fdiv_r(r,i,j)
329 =item isl_int_fdiv_q_ui(r,i,j)
331 =item isl_int_read(r,s)
333 =item isl_int_print(out,i,width)
337 =item isl_int_cmp(i,j)
339 =item isl_int_cmp_si(i,si)
341 =item isl_int_eq(i,j)
343 =item isl_int_ne(i,j)
345 =item isl_int_lt(i,j)
347 =item isl_int_le(i,j)
349 =item isl_int_gt(i,j)
351 =item isl_int_ge(i,j)
353 =item isl_int_abs_eq(i,j)
355 =item isl_int_abs_ne(i,j)
357 =item isl_int_abs_lt(i,j)
359 =item isl_int_abs_gt(i,j)
361 =item isl_int_abs_ge(i,j)
363 =item isl_int_is_zero(i)
365 =item isl_int_is_one(i)
367 =item isl_int_is_negone(i)
369 =item isl_int_is_pos(i)
371 =item isl_int_is_neg(i)
373 =item isl_int_is_nonpos(i)
375 =item isl_int_is_nonneg(i)
377 =item isl_int_is_divisible_by(i,j)
381 =head2 Sets and Relations
383 C<isl> uses six types of objects for representing sets and relations,
384 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
385 C<isl_union_set> and C<isl_union_map>.
386 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
387 can be described as a conjunction of affine constraints, while
388 C<isl_set> and C<isl_map> represent unions of
389 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
390 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
391 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
392 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
393 where spaces are considered different if they have a different number
394 of dimensions and/or different names (see L<"Spaces">).
395 The difference between sets and relations (maps) is that sets have
396 one set of variables, while relations have two sets of variables,
397 input variables and output variables.
399 =head2 Memory Management
401 Since a high-level operation on sets and/or relations usually involves
402 several substeps and since the user is usually not interested in
403 the intermediate results, most functions that return a new object
404 will also release all the objects passed as arguments.
405 If the user still wants to use one or more of these arguments
406 after the function call, she should pass along a copy of the
407 object rather than the object itself.
408 The user is then responsible for making sure that the original
409 object gets used somewhere else or is explicitly freed.
411 The arguments and return values of all documented functions are
412 annotated to make clear which arguments are released and which
413 arguments are preserved. In particular, the following annotations
420 C<__isl_give> means that a new object is returned.
421 The user should make sure that the returned pointer is
422 used exactly once as a value for an C<__isl_take> argument.
423 In between, it can be used as a value for as many
424 C<__isl_keep> arguments as the user likes.
425 There is one exception, and that is the case where the
426 pointer returned is C<NULL>. Is this case, the user
427 is free to use it as an C<__isl_take> argument or not.
431 C<__isl_take> means that the object the argument points to
432 is taken over by the function and may no longer be used
433 by the user as an argument to any other function.
434 The pointer value must be one returned by a function
435 returning an C<__isl_give> pointer.
436 If the user passes in a C<NULL> value, then this will
437 be treated as an error in the sense that the function will
438 not perform its usual operation. However, it will still
439 make sure that all the other C<__isl_take> arguments
444 C<__isl_keep> means that the function will only use the object
445 temporarily. After the function has finished, the user
446 can still use it as an argument to other functions.
447 A C<NULL> value will be treated in the same way as
448 a C<NULL> value for an C<__isl_take> argument.
454 Identifiers are used to identify both individual dimensions
455 and tuples of dimensions. They consist of a name and an optional
456 pointer. Identifiers with the same name but different pointer values
457 are considered to be distinct.
458 Identifiers can be constructed, copied, freed, inspected and printed
459 using the following functions.
462 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
463 __isl_keep const char *name, void *user);
464 __isl_give isl_id *isl_id_copy(isl_id *id);
465 void *isl_id_free(__isl_take isl_id *id);
467 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
468 void *isl_id_get_user(__isl_keep isl_id *id);
469 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
471 __isl_give isl_printer *isl_printer_print_id(
472 __isl_take isl_printer *p, __isl_keep isl_id *id);
474 Note that C<isl_id_get_name> returns a pointer to some internal
475 data structure, so the result can only be used while the
476 corresponding C<isl_id> is alive.
480 Whenever a new set or relation is created from scratch,
481 the space in which it lives needs to be specified using an C<isl_space>.
483 #include <isl/space.h>
484 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
485 unsigned nparam, unsigned n_in, unsigned n_out);
486 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
488 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
489 unsigned nparam, unsigned dim);
490 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
491 void isl_space_free(__isl_take isl_space *space);
492 unsigned isl_space_dim(__isl_keep isl_space *space,
493 enum isl_dim_type type);
495 The space used for creating a parameter domain
496 needs to be created using C<isl_space_params_alloc>.
497 For other sets, the space
498 needs to be created using C<isl_space_set_alloc>, while
499 for a relation, the space
500 needs to be created using C<isl_space_alloc>.
501 C<isl_space_dim> can be used
502 to find out the number of dimensions of each type in
503 a space, where type may be
504 C<isl_dim_param>, C<isl_dim_in> (only for relations),
505 C<isl_dim_out> (only for relations), C<isl_dim_set>
506 (only for sets) or C<isl_dim_all>.
508 To check whether a given space is that of a set or a map
509 or whether it is a parameter space, use these functions:
511 #include <isl/space.h>
512 int isl_space_is_params(__isl_keep isl_space *space);
513 int isl_space_is_set(__isl_keep isl_space *space);
515 It is often useful to create objects that live in the
516 same space as some other object. This can be accomplished
517 by creating the new objects
518 (see L<Creating New Sets and Relations> or
519 L<Creating New (Piecewise) Quasipolynomials>) based on the space
520 of the original object.
523 __isl_give isl_space *isl_basic_set_get_space(
524 __isl_keep isl_basic_set *bset);
525 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
527 #include <isl/union_set.h>
528 __isl_give isl_space *isl_union_set_get_space(
529 __isl_keep isl_union_set *uset);
532 __isl_give isl_space *isl_basic_map_get_space(
533 __isl_keep isl_basic_map *bmap);
534 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
536 #include <isl/union_map.h>
537 __isl_give isl_space *isl_union_map_get_space(
538 __isl_keep isl_union_map *umap);
540 #include <isl/constraint.h>
541 __isl_give isl_space *isl_constraint_get_space(
542 __isl_keep isl_constraint *constraint);
544 #include <isl/polynomial.h>
545 __isl_give isl_space *isl_qpolynomial_get_domain_space(
546 __isl_keep isl_qpolynomial *qp);
547 __isl_give isl_space *isl_qpolynomial_get_space(
548 __isl_keep isl_qpolynomial *qp);
549 __isl_give isl_space *isl_qpolynomial_fold_get_space(
550 __isl_keep isl_qpolynomial_fold *fold);
551 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
552 __isl_keep isl_pw_qpolynomial *pwqp);
553 __isl_give isl_space *isl_pw_qpolynomial_get_space(
554 __isl_keep isl_pw_qpolynomial *pwqp);
555 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
556 __isl_keep isl_pw_qpolynomial_fold *pwf);
557 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
558 __isl_keep isl_pw_qpolynomial_fold *pwf);
559 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
560 __isl_keep isl_union_pw_qpolynomial *upwqp);
561 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
562 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
565 __isl_give isl_space *isl_aff_get_domain_space(
566 __isl_keep isl_aff *aff);
567 __isl_give isl_space *isl_aff_get_space(
568 __isl_keep isl_aff *aff);
569 __isl_give isl_space *isl_pw_aff_get_domain_space(
570 __isl_keep isl_pw_aff *pwaff);
571 __isl_give isl_space *isl_pw_aff_get_space(
572 __isl_keep isl_pw_aff *pwaff);
574 #include <isl/point.h>
575 __isl_give isl_space *isl_point_get_space(
576 __isl_keep isl_point *pnt);
578 The identifiers or names of the individual dimensions may be set or read off
579 using the following functions.
581 #include <isl/space.h>
582 __isl_give isl_space *isl_space_set_dim_id(
583 __isl_take isl_space *space,
584 enum isl_dim_type type, unsigned pos,
585 __isl_take isl_id *id);
586 int isl_space_has_dim_id(__isl_keep isl_space *space,
587 enum isl_dim_type type, unsigned pos);
588 __isl_give isl_id *isl_space_get_dim_id(
589 __isl_keep isl_space *space,
590 enum isl_dim_type type, unsigned pos);
591 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
592 enum isl_dim_type type, unsigned pos,
593 __isl_keep const char *name);
594 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
595 enum isl_dim_type type, unsigned pos);
597 Note that C<isl_space_get_name> returns a pointer to some internal
598 data structure, so the result can only be used while the
599 corresponding C<isl_space> is alive.
600 Also note that every function that operates on two sets or relations
601 requires that both arguments have the same parameters. This also
602 means that if one of the arguments has named parameters, then the
603 other needs to have named parameters too and the names need to match.
604 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
605 arguments may have different parameters (as long as they are named),
606 in which case the result will have as parameters the union of the parameters of
609 Given the identifier of a dimension (typically a parameter),
610 its position can be obtained from the following function.
612 #include <isl/space.h>
613 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
614 enum isl_dim_type type, __isl_keep isl_id *id);
616 The identifiers or names of entire spaces may be set or read off
617 using the following functions.
619 #include <isl/space.h>
620 __isl_give isl_space *isl_space_set_tuple_id(
621 __isl_take isl_space *space,
622 enum isl_dim_type type, __isl_take isl_id *id);
623 __isl_give isl_space *isl_space_reset_tuple_id(
624 __isl_take isl_space *space, enum isl_dim_type type);
625 int isl_space_has_tuple_id(__isl_keep isl_space *space,
626 enum isl_dim_type type);
627 __isl_give isl_id *isl_space_get_tuple_id(
628 __isl_keep isl_space *space, enum isl_dim_type type);
629 __isl_give isl_space *isl_space_set_tuple_name(
630 __isl_take isl_space *space,
631 enum isl_dim_type type, const char *s);
632 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
633 enum isl_dim_type type);
635 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
636 or C<isl_dim_set>. As with C<isl_space_get_name>,
637 the C<isl_space_get_tuple_name> function returns a pointer to some internal
639 Binary operations require the corresponding spaces of their arguments
640 to have the same name.
642 Spaces can be nested. In particular, the domain of a set or
643 the domain or range of a relation can be a nested relation.
644 The following functions can be used to construct and deconstruct
647 #include <isl/space.h>
648 int isl_space_is_wrapping(__isl_keep isl_space *space);
649 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
650 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
652 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
653 be the space of a set, while that of
654 C<isl_space_wrap> should be the space of a relation.
655 Conversely, the output of C<isl_space_unwrap> is the space
656 of a relation, while that of C<isl_space_wrap> is the space of a set.
658 Spaces can be created from other spaces
659 using the following functions.
661 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
662 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
663 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
664 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
665 __isl_give isl_space *isl_space_params(
666 __isl_take isl_space *space);
667 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
668 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
669 __isl_take isl_space *right);
670 __isl_give isl_space *isl_space_align_params(
671 __isl_take isl_space *space1, __isl_take isl_space *space2)
672 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
673 enum isl_dim_type type, unsigned pos, unsigned n);
674 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
675 enum isl_dim_type type, unsigned n);
676 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
677 enum isl_dim_type type, unsigned first, unsigned n);
678 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
679 enum isl_dim_type dst_type, unsigned dst_pos,
680 enum isl_dim_type src_type, unsigned src_pos,
682 __isl_give isl_space *isl_space_map_from_set(
683 __isl_take isl_space *space);
684 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
686 Note that if dimensions are added or removed from a space, then
687 the name and the internal structure are lost.
691 A local space is essentially a space with
692 zero or more existentially quantified variables.
693 The local space of a basic set or relation can be obtained
694 using the following functions.
697 __isl_give isl_local_space *isl_basic_set_get_local_space(
698 __isl_keep isl_basic_set *bset);
701 __isl_give isl_local_space *isl_basic_map_get_local_space(
702 __isl_keep isl_basic_map *bmap);
704 A new local space can be created from a space using
706 #include <isl/local_space.h>
707 __isl_give isl_local_space *isl_local_space_from_space(
708 __isl_take isl_space *space);
710 They can be inspected, copied and freed using the following functions.
712 #include <isl/local_space.h>
713 isl_ctx *isl_local_space_get_ctx(
714 __isl_keep isl_local_space *ls);
715 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
716 int isl_local_space_dim(__isl_keep isl_local_space *ls,
717 enum isl_dim_type type);
718 const char *isl_local_space_get_dim_name(
719 __isl_keep isl_local_space *ls,
720 enum isl_dim_type type, unsigned pos);
721 __isl_give isl_local_space *isl_local_space_set_dim_name(
722 __isl_take isl_local_space *ls,
723 enum isl_dim_type type, unsigned pos, const char *s);
724 __isl_give isl_space *isl_local_space_get_space(
725 __isl_keep isl_local_space *ls);
726 __isl_give isl_div *isl_local_space_get_div(
727 __isl_keep isl_local_space *ls, int pos);
728 __isl_give isl_local_space *isl_local_space_copy(
729 __isl_keep isl_local_space *ls);
730 void *isl_local_space_free(__isl_take isl_local_space *ls);
732 Two local spaces can be compared using
734 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
735 __isl_keep isl_local_space *ls2);
737 Local spaces can be created from other local spaces
738 using the following functions.
740 __isl_give isl_local_space *isl_local_space_domain(
741 __isl_take isl_local_space *ls);
742 __isl_give isl_local_space *isl_local_space_from_domain(
743 __isl_take isl_local_space *ls);
744 __isl_give isl_local_space *isl_local_space_add_dims(
745 __isl_take isl_local_space *ls,
746 enum isl_dim_type type, unsigned n);
747 __isl_give isl_local_space *isl_local_space_insert_dims(
748 __isl_take isl_local_space *ls,
749 enum isl_dim_type type, unsigned first, unsigned n);
750 __isl_give isl_local_space *isl_local_space_drop_dims(
751 __isl_take isl_local_space *ls,
752 enum isl_dim_type type, unsigned first, unsigned n);
754 =head2 Input and Output
756 C<isl> supports its own input/output format, which is similar
757 to the C<Omega> format, but also supports the C<PolyLib> format
762 The C<isl> format is similar to that of C<Omega>, but has a different
763 syntax for describing the parameters and allows for the definition
764 of an existentially quantified variable as the integer division
765 of an affine expression.
766 For example, the set of integers C<i> between C<0> and C<n>
767 such that C<i % 10 <= 6> can be described as
769 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
772 A set or relation can have several disjuncts, separated
773 by the keyword C<or>. Each disjunct is either a conjunction
774 of constraints or a projection (C<exists>) of a conjunction
775 of constraints. The constraints are separated by the keyword
778 =head3 C<PolyLib> format
780 If the represented set is a union, then the first line
781 contains a single number representing the number of disjuncts.
782 Otherwise, a line containing the number C<1> is optional.
784 Each disjunct is represented by a matrix of constraints.
785 The first line contains two numbers representing
786 the number of rows and columns,
787 where the number of rows is equal to the number of constraints
788 and the number of columns is equal to two plus the number of variables.
789 The following lines contain the actual rows of the constraint matrix.
790 In each row, the first column indicates whether the constraint
791 is an equality (C<0>) or inequality (C<1>). The final column
792 corresponds to the constant term.
794 If the set is parametric, then the coefficients of the parameters
795 appear in the last columns before the constant column.
796 The coefficients of any existentially quantified variables appear
797 between those of the set variables and those of the parameters.
799 =head3 Extended C<PolyLib> format
801 The extended C<PolyLib> format is nearly identical to the
802 C<PolyLib> format. The only difference is that the line
803 containing the number of rows and columns of a constraint matrix
804 also contains four additional numbers:
805 the number of output dimensions, the number of input dimensions,
806 the number of local dimensions (i.e., the number of existentially
807 quantified variables) and the number of parameters.
808 For sets, the number of ``output'' dimensions is equal
809 to the number of set dimensions, while the number of ``input''
815 __isl_give isl_basic_set *isl_basic_set_read_from_file(
816 isl_ctx *ctx, FILE *input, int nparam);
817 __isl_give isl_basic_set *isl_basic_set_read_from_str(
818 isl_ctx *ctx, const char *str, int nparam);
819 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
820 FILE *input, int nparam);
821 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
822 const char *str, int nparam);
825 __isl_give isl_basic_map *isl_basic_map_read_from_file(
826 isl_ctx *ctx, FILE *input, int nparam);
827 __isl_give isl_basic_map *isl_basic_map_read_from_str(
828 isl_ctx *ctx, const char *str, int nparam);
829 __isl_give isl_map *isl_map_read_from_file(
830 isl_ctx *ctx, FILE *input, int nparam);
831 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
832 const char *str, int nparam);
834 #include <isl/union_set.h>
835 __isl_give isl_union_set *isl_union_set_read_from_file(
836 isl_ctx *ctx, FILE *input);
837 __isl_give isl_union_set *isl_union_set_read_from_str(
838 isl_ctx *ctx, const char *str);
840 #include <isl/union_map.h>
841 __isl_give isl_union_map *isl_union_map_read_from_file(
842 isl_ctx *ctx, FILE *input);
843 __isl_give isl_union_map *isl_union_map_read_from_str(
844 isl_ctx *ctx, const char *str);
846 The input format is autodetected and may be either the C<PolyLib> format
847 or the C<isl> format.
848 C<nparam> specifies how many of the final columns in
849 the C<PolyLib> format correspond to parameters.
850 If input is given in the C<isl> format, then the number
851 of parameters needs to be equal to C<nparam>.
852 If C<nparam> is negative, then any number of parameters
853 is accepted in the C<isl> format and zero parameters
854 are assumed in the C<PolyLib> format.
858 Before anything can be printed, an C<isl_printer> needs to
861 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
863 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
864 void isl_printer_free(__isl_take isl_printer *printer);
865 __isl_give char *isl_printer_get_str(
866 __isl_keep isl_printer *printer);
868 The behavior of the printer can be modified in various ways
870 __isl_give isl_printer *isl_printer_set_output_format(
871 __isl_take isl_printer *p, int output_format);
872 __isl_give isl_printer *isl_printer_set_indent(
873 __isl_take isl_printer *p, int indent);
874 __isl_give isl_printer *isl_printer_indent(
875 __isl_take isl_printer *p, int indent);
876 __isl_give isl_printer *isl_printer_set_prefix(
877 __isl_take isl_printer *p, const char *prefix);
878 __isl_give isl_printer *isl_printer_set_suffix(
879 __isl_take isl_printer *p, const char *suffix);
881 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
882 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
883 and defaults to C<ISL_FORMAT_ISL>.
884 Each line in the output is indented by C<indent> (set by
885 C<isl_printer_set_indent>) spaces
886 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
887 In the C<PolyLib> format output,
888 the coefficients of the existentially quantified variables
889 appear between those of the set variables and those
891 The function C<isl_printer_indent> increases the indentation
892 by the specified amount (which may be negative).
894 To actually print something, use
897 __isl_give isl_printer *isl_printer_print_basic_set(
898 __isl_take isl_printer *printer,
899 __isl_keep isl_basic_set *bset);
900 __isl_give isl_printer *isl_printer_print_set(
901 __isl_take isl_printer *printer,
902 __isl_keep isl_set *set);
905 __isl_give isl_printer *isl_printer_print_basic_map(
906 __isl_take isl_printer *printer,
907 __isl_keep isl_basic_map *bmap);
908 __isl_give isl_printer *isl_printer_print_map(
909 __isl_take isl_printer *printer,
910 __isl_keep isl_map *map);
912 #include <isl/union_set.h>
913 __isl_give isl_printer *isl_printer_print_union_set(
914 __isl_take isl_printer *p,
915 __isl_keep isl_union_set *uset);
917 #include <isl/union_map.h>
918 __isl_give isl_printer *isl_printer_print_union_map(
919 __isl_take isl_printer *p,
920 __isl_keep isl_union_map *umap);
922 When called on a file printer, the following function flushes
923 the file. When called on a string printer, the buffer is cleared.
925 __isl_give isl_printer *isl_printer_flush(
926 __isl_take isl_printer *p);
928 =head2 Creating New Sets and Relations
930 C<isl> has functions for creating some standard sets and relations.
934 =item * Empty sets and relations
936 __isl_give isl_basic_set *isl_basic_set_empty(
937 __isl_take isl_space *space);
938 __isl_give isl_basic_map *isl_basic_map_empty(
939 __isl_take isl_space *space);
940 __isl_give isl_set *isl_set_empty(
941 __isl_take isl_space *space);
942 __isl_give isl_map *isl_map_empty(
943 __isl_take isl_space *space);
944 __isl_give isl_union_set *isl_union_set_empty(
945 __isl_take isl_space *space);
946 __isl_give isl_union_map *isl_union_map_empty(
947 __isl_take isl_space *space);
949 For C<isl_union_set>s and C<isl_union_map>s, the space
950 is only used to specify the parameters.
952 =item * Universe sets and relations
954 __isl_give isl_basic_set *isl_basic_set_universe(
955 __isl_take isl_space *space);
956 __isl_give isl_basic_map *isl_basic_map_universe(
957 __isl_take isl_space *space);
958 __isl_give isl_set *isl_set_universe(
959 __isl_take isl_space *space);
960 __isl_give isl_map *isl_map_universe(
961 __isl_take isl_space *space);
962 __isl_give isl_union_set *isl_union_set_universe(
963 __isl_take isl_union_set *uset);
964 __isl_give isl_union_map *isl_union_map_universe(
965 __isl_take isl_union_map *umap);
967 The sets and relations constructed by the functions above
968 contain all integer values, while those constructed by the
969 functions below only contain non-negative values.
971 __isl_give isl_basic_set *isl_basic_set_nat_universe(
972 __isl_take isl_space *space);
973 __isl_give isl_basic_map *isl_basic_map_nat_universe(
974 __isl_take isl_space *space);
975 __isl_give isl_set *isl_set_nat_universe(
976 __isl_take isl_space *space);
977 __isl_give isl_map *isl_map_nat_universe(
978 __isl_take isl_space *space);
980 =item * Identity relations
982 __isl_give isl_basic_map *isl_basic_map_identity(
983 __isl_take isl_space *space);
984 __isl_give isl_map *isl_map_identity(
985 __isl_take isl_space *space);
987 The number of input and output dimensions in C<space> needs
990 =item * Lexicographic order
992 __isl_give isl_map *isl_map_lex_lt(
993 __isl_take isl_space *set_space);
994 __isl_give isl_map *isl_map_lex_le(
995 __isl_take isl_space *set_space);
996 __isl_give isl_map *isl_map_lex_gt(
997 __isl_take isl_space *set_space);
998 __isl_give isl_map *isl_map_lex_ge(
999 __isl_take isl_space *set_space);
1000 __isl_give isl_map *isl_map_lex_lt_first(
1001 __isl_take isl_space *space, unsigned n);
1002 __isl_give isl_map *isl_map_lex_le_first(
1003 __isl_take isl_space *space, unsigned n);
1004 __isl_give isl_map *isl_map_lex_gt_first(
1005 __isl_take isl_space *space, unsigned n);
1006 __isl_give isl_map *isl_map_lex_ge_first(
1007 __isl_take isl_space *space, unsigned n);
1009 The first four functions take a space for a B<set>
1010 and return relations that express that the elements in the domain
1011 are lexicographically less
1012 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1013 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1014 than the elements in the range.
1015 The last four functions take a space for a map
1016 and return relations that express that the first C<n> dimensions
1017 in the domain are lexicographically less
1018 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1019 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1020 than the first C<n> dimensions in the range.
1024 A basic set or relation can be converted to a set or relation
1025 using the following functions.
1027 __isl_give isl_set *isl_set_from_basic_set(
1028 __isl_take isl_basic_set *bset);
1029 __isl_give isl_map *isl_map_from_basic_map(
1030 __isl_take isl_basic_map *bmap);
1032 Sets and relations can be converted to union sets and relations
1033 using the following functions.
1035 __isl_give isl_union_map *isl_union_map_from_map(
1036 __isl_take isl_map *map);
1037 __isl_give isl_union_set *isl_union_set_from_set(
1038 __isl_take isl_set *set);
1040 The inverse conversions below can only be used if the input
1041 union set or relation is known to contain elements in exactly one
1044 __isl_give isl_set *isl_set_from_union_set(
1045 __isl_take isl_union_set *uset);
1046 __isl_give isl_map *isl_map_from_union_map(
1047 __isl_take isl_union_map *umap);
1049 Sets and relations can be copied and freed again using the following
1052 __isl_give isl_basic_set *isl_basic_set_copy(
1053 __isl_keep isl_basic_set *bset);
1054 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1055 __isl_give isl_union_set *isl_union_set_copy(
1056 __isl_keep isl_union_set *uset);
1057 __isl_give isl_basic_map *isl_basic_map_copy(
1058 __isl_keep isl_basic_map *bmap);
1059 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1060 __isl_give isl_union_map *isl_union_map_copy(
1061 __isl_keep isl_union_map *umap);
1062 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1063 void isl_set_free(__isl_take isl_set *set);
1064 void *isl_union_set_free(__isl_take isl_union_set *uset);
1065 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1066 void isl_map_free(__isl_take isl_map *map);
1067 void *isl_union_map_free(__isl_take isl_union_map *umap);
1069 Other sets and relations can be constructed by starting
1070 from a universe set or relation, adding equality and/or
1071 inequality constraints and then projecting out the
1072 existentially quantified variables, if any.
1073 Constraints can be constructed, manipulated and
1074 added to (or removed from) (basic) sets and relations
1075 using the following functions.
1077 #include <isl/constraint.h>
1078 __isl_give isl_constraint *isl_equality_alloc(
1079 __isl_take isl_space *space);
1080 __isl_give isl_constraint *isl_inequality_alloc(
1081 __isl_take isl_space *space);
1082 __isl_give isl_constraint *isl_constraint_set_constant(
1083 __isl_take isl_constraint *constraint, isl_int v);
1084 __isl_give isl_constraint *isl_constraint_set_constant_si(
1085 __isl_take isl_constraint *constraint, int v);
1086 __isl_give isl_constraint *isl_constraint_set_coefficient(
1087 __isl_take isl_constraint *constraint,
1088 enum isl_dim_type type, int pos, isl_int v);
1089 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1090 __isl_take isl_constraint *constraint,
1091 enum isl_dim_type type, int pos, int v);
1092 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1093 __isl_take isl_basic_map *bmap,
1094 __isl_take isl_constraint *constraint);
1095 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1096 __isl_take isl_basic_set *bset,
1097 __isl_take isl_constraint *constraint);
1098 __isl_give isl_map *isl_map_add_constraint(
1099 __isl_take isl_map *map,
1100 __isl_take isl_constraint *constraint);
1101 __isl_give isl_set *isl_set_add_constraint(
1102 __isl_take isl_set *set,
1103 __isl_take isl_constraint *constraint);
1104 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1105 __isl_take isl_basic_set *bset,
1106 __isl_take isl_constraint *constraint);
1108 For example, to create a set containing the even integers
1109 between 10 and 42, you would use the following code.
1114 isl_basic_set *bset;
1117 space = isl_space_set_alloc(ctx, 0, 2);
1118 bset = isl_basic_set_universe(isl_space_copy(space));
1120 c = isl_equality_alloc(isl_space_copy(space));
1121 isl_int_set_si(v, -1);
1122 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1123 isl_int_set_si(v, 2);
1124 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1125 bset = isl_basic_set_add_constraint(bset, c);
1127 c = isl_inequality_alloc(isl_space_copy(space));
1128 isl_int_set_si(v, -10);
1129 isl_constraint_set_constant(c, v);
1130 isl_int_set_si(v, 1);
1131 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1132 bset = isl_basic_set_add_constraint(bset, c);
1134 c = isl_inequality_alloc(space);
1135 isl_int_set_si(v, 42);
1136 isl_constraint_set_constant(c, v);
1137 isl_int_set_si(v, -1);
1138 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1139 bset = isl_basic_set_add_constraint(bset, c);
1141 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1147 isl_basic_set *bset;
1148 bset = isl_basic_set_read_from_str(ctx,
1149 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1151 A basic set or relation can also be constructed from two matrices
1152 describing the equalities and the inequalities.
1154 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1155 __isl_take isl_space *space,
1156 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1157 enum isl_dim_type c1,
1158 enum isl_dim_type c2, enum isl_dim_type c3,
1159 enum isl_dim_type c4);
1160 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1161 __isl_take isl_space *space,
1162 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1163 enum isl_dim_type c1,
1164 enum isl_dim_type c2, enum isl_dim_type c3,
1165 enum isl_dim_type c4, enum isl_dim_type c5);
1167 The C<isl_dim_type> arguments indicate the order in which
1168 different kinds of variables appear in the input matrices
1169 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1170 C<isl_dim_set> and C<isl_dim_div> for sets and
1171 of C<isl_dim_cst>, C<isl_dim_param>,
1172 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1174 A (basic) set or relation can also be constructed from a (piecewise)
1176 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1178 __isl_give isl_basic_map *isl_basic_map_from_aff(
1179 __isl_take isl_aff *aff);
1180 __isl_give isl_set *isl_set_from_pw_aff(
1181 __isl_take isl_pw_aff *pwaff);
1182 __isl_give isl_map *isl_map_from_pw_aff(
1183 __isl_take isl_pw_aff *pwaff);
1184 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1185 __isl_take isl_space *domain_space,
1186 __isl_take isl_aff_list *list);
1188 The C<domain_dim> argument describes the domain of the resulting
1189 basic relation. It is required because the C<list> may consist
1190 of zero affine expressions.
1192 =head2 Inspecting Sets and Relations
1194 Usually, the user should not have to care about the actual constraints
1195 of the sets and maps, but should instead apply the abstract operations
1196 explained in the following sections.
1197 Occasionally, however, it may be required to inspect the individual
1198 coefficients of the constraints. This section explains how to do so.
1199 In these cases, it may also be useful to have C<isl> compute
1200 an explicit representation of the existentially quantified variables.
1202 __isl_give isl_set *isl_set_compute_divs(
1203 __isl_take isl_set *set);
1204 __isl_give isl_map *isl_map_compute_divs(
1205 __isl_take isl_map *map);
1206 __isl_give isl_union_set *isl_union_set_compute_divs(
1207 __isl_take isl_union_set *uset);
1208 __isl_give isl_union_map *isl_union_map_compute_divs(
1209 __isl_take isl_union_map *umap);
1211 This explicit representation defines the existentially quantified
1212 variables as integer divisions of the other variables, possibly
1213 including earlier existentially quantified variables.
1214 An explicitly represented existentially quantified variable therefore
1215 has a unique value when the values of the other variables are known.
1216 If, furthermore, the same existentials, i.e., existentials
1217 with the same explicit representations, should appear in the
1218 same order in each of the disjuncts of a set or map, then the user should call
1219 either of the following functions.
1221 __isl_give isl_set *isl_set_align_divs(
1222 __isl_take isl_set *set);
1223 __isl_give isl_map *isl_map_align_divs(
1224 __isl_take isl_map *map);
1226 Alternatively, the existentially quantified variables can be removed
1227 using the following functions, which compute an overapproximation.
1229 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1230 __isl_take isl_basic_set *bset);
1231 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1232 __isl_take isl_basic_map *bmap);
1233 __isl_give isl_set *isl_set_remove_divs(
1234 __isl_take isl_set *set);
1235 __isl_give isl_map *isl_map_remove_divs(
1236 __isl_take isl_map *map);
1238 To iterate over all the sets or maps in a union set or map, use
1240 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1241 int (*fn)(__isl_take isl_set *set, void *user),
1243 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1244 int (*fn)(__isl_take isl_map *map, void *user),
1247 The number of sets or maps in a union set or map can be obtained
1250 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1251 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1253 To extract the set or map in a given space from a union, use
1255 __isl_give isl_set *isl_union_set_extract_set(
1256 __isl_keep isl_union_set *uset,
1257 __isl_take isl_space *space);
1258 __isl_give isl_map *isl_union_map_extract_map(
1259 __isl_keep isl_union_map *umap,
1260 __isl_take isl_space *space);
1262 To iterate over all the basic sets or maps in a set or map, use
1264 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1265 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1267 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1268 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1271 The callback function C<fn> should return 0 if successful and
1272 -1 if an error occurs. In the latter case, or if any other error
1273 occurs, the above functions will return -1.
1275 It should be noted that C<isl> does not guarantee that
1276 the basic sets or maps passed to C<fn> are disjoint.
1277 If this is required, then the user should call one of
1278 the following functions first.
1280 __isl_give isl_set *isl_set_make_disjoint(
1281 __isl_take isl_set *set);
1282 __isl_give isl_map *isl_map_make_disjoint(
1283 __isl_take isl_map *map);
1285 The number of basic sets in a set can be obtained
1288 int isl_set_n_basic_set(__isl_keep isl_set *set);
1290 To iterate over the constraints of a basic set or map, use
1292 #include <isl/constraint.h>
1294 int isl_basic_map_foreach_constraint(
1295 __isl_keep isl_basic_map *bmap,
1296 int (*fn)(__isl_take isl_constraint *c, void *user),
1298 void *isl_constraint_free(__isl_take isl_constraint *c);
1300 Again, the callback function C<fn> should return 0 if successful and
1301 -1 if an error occurs. In the latter case, or if any other error
1302 occurs, the above functions will return -1.
1303 The constraint C<c> represents either an equality or an inequality.
1304 Use the following function to find out whether a constraint
1305 represents an equality. If not, it represents an inequality.
1307 int isl_constraint_is_equality(
1308 __isl_keep isl_constraint *constraint);
1310 The coefficients of the constraints can be inspected using
1311 the following functions.
1313 void isl_constraint_get_constant(
1314 __isl_keep isl_constraint *constraint, isl_int *v);
1315 void isl_constraint_get_coefficient(
1316 __isl_keep isl_constraint *constraint,
1317 enum isl_dim_type type, int pos, isl_int *v);
1318 int isl_constraint_involves_dims(
1319 __isl_keep isl_constraint *constraint,
1320 enum isl_dim_type type, unsigned first, unsigned n);
1322 The explicit representations of the existentially quantified
1323 variables can be inspected using the following functions.
1324 Note that the user is only allowed to use these functions
1325 if the inspected set or map is the result of a call
1326 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1328 __isl_give isl_div *isl_constraint_div(
1329 __isl_keep isl_constraint *constraint, int pos);
1330 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1331 void isl_div_get_constant(__isl_keep isl_div *div,
1333 void isl_div_get_denominator(__isl_keep isl_div *div,
1335 void isl_div_get_coefficient(__isl_keep isl_div *div,
1336 enum isl_dim_type type, int pos, isl_int *v);
1338 To obtain the constraints of a basic set or map in matrix
1339 form, use the following functions.
1341 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1342 __isl_keep isl_basic_set *bset,
1343 enum isl_dim_type c1, enum isl_dim_type c2,
1344 enum isl_dim_type c3, enum isl_dim_type c4);
1345 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1346 __isl_keep isl_basic_set *bset,
1347 enum isl_dim_type c1, enum isl_dim_type c2,
1348 enum isl_dim_type c3, enum isl_dim_type c4);
1349 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1350 __isl_keep isl_basic_map *bmap,
1351 enum isl_dim_type c1,
1352 enum isl_dim_type c2, enum isl_dim_type c3,
1353 enum isl_dim_type c4, enum isl_dim_type c5);
1354 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1355 __isl_keep isl_basic_map *bmap,
1356 enum isl_dim_type c1,
1357 enum isl_dim_type c2, enum isl_dim_type c3,
1358 enum isl_dim_type c4, enum isl_dim_type c5);
1360 The C<isl_dim_type> arguments dictate the order in which
1361 different kinds of variables appear in the resulting matrix
1362 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1363 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1365 The number of parameters, input, output or set dimensions can
1366 be obtained using the following functions.
1368 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1369 enum isl_dim_type type);
1370 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1371 enum isl_dim_type type);
1372 unsigned isl_set_dim(__isl_keep isl_set *set,
1373 enum isl_dim_type type);
1374 unsigned isl_map_dim(__isl_keep isl_map *map,
1375 enum isl_dim_type type);
1377 To check whether the description of a set or relation depends
1378 on one or more given dimensions, it is not necessary to iterate over all
1379 constraints. Instead the following functions can be used.
1381 int isl_basic_set_involves_dims(
1382 __isl_keep isl_basic_set *bset,
1383 enum isl_dim_type type, unsigned first, unsigned n);
1384 int isl_set_involves_dims(__isl_keep isl_set *set,
1385 enum isl_dim_type type, unsigned first, unsigned n);
1386 int isl_basic_map_involves_dims(
1387 __isl_keep isl_basic_map *bmap,
1388 enum isl_dim_type type, unsigned first, unsigned n);
1389 int isl_map_involves_dims(__isl_keep isl_map *map,
1390 enum isl_dim_type type, unsigned first, unsigned n);
1392 Similarly, the following functions can be used to check whether
1393 a given dimension is involved in any lower or upper bound.
1395 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1396 enum isl_dim_type type, unsigned pos);
1397 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1398 enum isl_dim_type type, unsigned pos);
1400 The identifiers or names of the domain and range spaces of a set
1401 or relation can be read off or set using the following functions.
1403 __isl_give isl_set *isl_set_set_tuple_id(
1404 __isl_take isl_set *set, __isl_take isl_id *id);
1405 __isl_give isl_set *isl_set_reset_tuple_id(
1406 __isl_take isl_set *set);
1407 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1408 __isl_give isl_id *isl_set_get_tuple_id(
1409 __isl_keep isl_set *set);
1410 __isl_give isl_map *isl_map_set_tuple_id(
1411 __isl_take isl_map *map, enum isl_dim_type type,
1412 __isl_take isl_id *id);
1413 __isl_give isl_map *isl_map_reset_tuple_id(
1414 __isl_take isl_map *map, enum isl_dim_type type);
1415 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1416 enum isl_dim_type type);
1417 __isl_give isl_id *isl_map_get_tuple_id(
1418 __isl_keep isl_map *map, enum isl_dim_type type);
1420 const char *isl_basic_set_get_tuple_name(
1421 __isl_keep isl_basic_set *bset);
1422 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1423 __isl_take isl_basic_set *set, const char *s);
1424 const char *isl_set_get_tuple_name(
1425 __isl_keep isl_set *set);
1426 const char *isl_basic_map_get_tuple_name(
1427 __isl_keep isl_basic_map *bmap,
1428 enum isl_dim_type type);
1429 const char *isl_map_get_tuple_name(
1430 __isl_keep isl_map *map,
1431 enum isl_dim_type type);
1433 As with C<isl_space_get_tuple_name>, the value returned points to
1434 an internal data structure.
1435 The identifiers, positions or names of individual dimensions can be
1436 read off using the following functions.
1438 __isl_give isl_set *isl_set_set_dim_id(
1439 __isl_take isl_set *set, enum isl_dim_type type,
1440 unsigned pos, __isl_take isl_id *id);
1441 int isl_set_has_dim_id(__isl_keep isl_set *set,
1442 enum isl_dim_type type, unsigned pos);
1443 __isl_give isl_id *isl_set_get_dim_id(
1444 __isl_keep isl_set *set, enum isl_dim_type type,
1446 __isl_give isl_map *isl_map_set_dim_id(
1447 __isl_take isl_map *map, enum isl_dim_type type,
1448 unsigned pos, __isl_take isl_id *id);
1449 int isl_map_has_dim_id(__isl_keep isl_map *map,
1450 enum isl_dim_type type, unsigned pos);
1451 __isl_give isl_id *isl_map_get_dim_id(
1452 __isl_keep isl_map *map, enum isl_dim_type type,
1455 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1456 enum isl_dim_type type, __isl_keep isl_id *id);
1457 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1458 enum isl_dim_type type, __isl_keep isl_id *id);
1460 const char *isl_constraint_get_dim_name(
1461 __isl_keep isl_constraint *constraint,
1462 enum isl_dim_type type, unsigned pos);
1463 const char *isl_basic_set_get_dim_name(
1464 __isl_keep isl_basic_set *bset,
1465 enum isl_dim_type type, unsigned pos);
1466 const char *isl_set_get_dim_name(
1467 __isl_keep isl_set *set,
1468 enum isl_dim_type type, unsigned pos);
1469 const char *isl_basic_map_get_dim_name(
1470 __isl_keep isl_basic_map *bmap,
1471 enum isl_dim_type type, unsigned pos);
1472 const char *isl_map_get_dim_name(
1473 __isl_keep isl_map *map,
1474 enum isl_dim_type type, unsigned pos);
1476 These functions are mostly useful to obtain the identifiers, positions
1477 or names of the parameters. Identifiers of individual dimensions are
1478 essentially only useful for printing. They are ignored by all other
1479 operations and may not be preserved across those operations.
1483 =head3 Unary Properties
1489 The following functions test whether the given set or relation
1490 contains any integer points. The ``plain'' variants do not perform
1491 any computations, but simply check if the given set or relation
1492 is already known to be empty.
1494 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1495 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1496 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1497 int isl_set_is_empty(__isl_keep isl_set *set);
1498 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1499 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1500 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1501 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1502 int isl_map_is_empty(__isl_keep isl_map *map);
1503 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1505 =item * Universality
1507 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1508 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1509 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1511 =item * Single-valuedness
1513 int isl_map_is_single_valued(__isl_keep isl_map *map);
1514 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1518 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1519 int isl_map_is_injective(__isl_keep isl_map *map);
1520 int isl_union_map_plain_is_injective(
1521 __isl_keep isl_union_map *umap);
1522 int isl_union_map_is_injective(
1523 __isl_keep isl_union_map *umap);
1527 int isl_map_is_bijective(__isl_keep isl_map *map);
1528 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1532 int isl_basic_map_plain_is_fixed(
1533 __isl_keep isl_basic_map *bmap,
1534 enum isl_dim_type type, unsigned pos,
1536 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1537 enum isl_dim_type type, unsigned pos,
1540 Check if the relation obviously lies on a hyperplane where the given dimension
1541 has a fixed value and if so, return that value in C<*val>.
1545 To check whether a set is a parameter domain, use this function:
1547 int isl_set_is_params(__isl_keep isl_set *set);
1551 The following functions check whether the domain of the given
1552 (basic) set is a wrapped relation.
1554 int isl_basic_set_is_wrapping(
1555 __isl_keep isl_basic_set *bset);
1556 int isl_set_is_wrapping(__isl_keep isl_set *set);
1558 =item * Internal Product
1560 int isl_basic_map_can_zip(
1561 __isl_keep isl_basic_map *bmap);
1562 int isl_map_can_zip(__isl_keep isl_map *map);
1564 Check whether the product of domain and range of the given relation
1566 i.e., whether both domain and range are nested relations.
1570 =head3 Binary Properties
1576 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1577 __isl_keep isl_set *set2);
1578 int isl_set_is_equal(__isl_keep isl_set *set1,
1579 __isl_keep isl_set *set2);
1580 int isl_union_set_is_equal(
1581 __isl_keep isl_union_set *uset1,
1582 __isl_keep isl_union_set *uset2);
1583 int isl_basic_map_is_equal(
1584 __isl_keep isl_basic_map *bmap1,
1585 __isl_keep isl_basic_map *bmap2);
1586 int isl_map_is_equal(__isl_keep isl_map *map1,
1587 __isl_keep isl_map *map2);
1588 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1589 __isl_keep isl_map *map2);
1590 int isl_union_map_is_equal(
1591 __isl_keep isl_union_map *umap1,
1592 __isl_keep isl_union_map *umap2);
1594 =item * Disjointness
1596 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1597 __isl_keep isl_set *set2);
1601 int isl_set_is_subset(__isl_keep isl_set *set1,
1602 __isl_keep isl_set *set2);
1603 int isl_set_is_strict_subset(
1604 __isl_keep isl_set *set1,
1605 __isl_keep isl_set *set2);
1606 int isl_union_set_is_subset(
1607 __isl_keep isl_union_set *uset1,
1608 __isl_keep isl_union_set *uset2);
1609 int isl_union_set_is_strict_subset(
1610 __isl_keep isl_union_set *uset1,
1611 __isl_keep isl_union_set *uset2);
1612 int isl_basic_map_is_subset(
1613 __isl_keep isl_basic_map *bmap1,
1614 __isl_keep isl_basic_map *bmap2);
1615 int isl_basic_map_is_strict_subset(
1616 __isl_keep isl_basic_map *bmap1,
1617 __isl_keep isl_basic_map *bmap2);
1618 int isl_map_is_subset(
1619 __isl_keep isl_map *map1,
1620 __isl_keep isl_map *map2);
1621 int isl_map_is_strict_subset(
1622 __isl_keep isl_map *map1,
1623 __isl_keep isl_map *map2);
1624 int isl_union_map_is_subset(
1625 __isl_keep isl_union_map *umap1,
1626 __isl_keep isl_union_map *umap2);
1627 int isl_union_map_is_strict_subset(
1628 __isl_keep isl_union_map *umap1,
1629 __isl_keep isl_union_map *umap2);
1633 =head2 Unary Operations
1639 __isl_give isl_set *isl_set_complement(
1640 __isl_take isl_set *set);
1644 __isl_give isl_basic_map *isl_basic_map_reverse(
1645 __isl_take isl_basic_map *bmap);
1646 __isl_give isl_map *isl_map_reverse(
1647 __isl_take isl_map *map);
1648 __isl_give isl_union_map *isl_union_map_reverse(
1649 __isl_take isl_union_map *umap);
1653 __isl_give isl_basic_set *isl_basic_set_project_out(
1654 __isl_take isl_basic_set *bset,
1655 enum isl_dim_type type, unsigned first, unsigned n);
1656 __isl_give isl_basic_map *isl_basic_map_project_out(
1657 __isl_take isl_basic_map *bmap,
1658 enum isl_dim_type type, unsigned first, unsigned n);
1659 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1660 enum isl_dim_type type, unsigned first, unsigned n);
1661 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1662 enum isl_dim_type type, unsigned first, unsigned n);
1663 __isl_give isl_basic_set *isl_basic_set_params(
1664 __isl_take isl_basic_set *bset);
1665 __isl_give isl_basic_set *isl_basic_map_domain(
1666 __isl_take isl_basic_map *bmap);
1667 __isl_give isl_basic_set *isl_basic_map_range(
1668 __isl_take isl_basic_map *bmap);
1669 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1670 __isl_give isl_set *isl_map_domain(
1671 __isl_take isl_map *bmap);
1672 __isl_give isl_set *isl_map_range(
1673 __isl_take isl_map *map);
1674 __isl_give isl_union_set *isl_union_map_domain(
1675 __isl_take isl_union_map *umap);
1676 __isl_give isl_union_set *isl_union_map_range(
1677 __isl_take isl_union_map *umap);
1679 __isl_give isl_basic_map *isl_basic_map_domain_map(
1680 __isl_take isl_basic_map *bmap);
1681 __isl_give isl_basic_map *isl_basic_map_range_map(
1682 __isl_take isl_basic_map *bmap);
1683 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1684 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1685 __isl_give isl_union_map *isl_union_map_domain_map(
1686 __isl_take isl_union_map *umap);
1687 __isl_give isl_union_map *isl_union_map_range_map(
1688 __isl_take isl_union_map *umap);
1690 The functions above construct a (basic, regular or union) relation
1691 that maps (a wrapped version of) the input relation to its domain or range.
1695 __isl_give isl_set *isl_set_eliminate(
1696 __isl_take isl_set *set, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 Eliminate the coefficients for the given dimensions from the constraints,
1700 without removing the dimensions.
1704 __isl_give isl_basic_set *isl_basic_set_fix(
1705 __isl_take isl_basic_set *bset,
1706 enum isl_dim_type type, unsigned pos,
1708 __isl_give isl_basic_set *isl_basic_set_fix_si(
1709 __isl_take isl_basic_set *bset,
1710 enum isl_dim_type type, unsigned pos, int value);
1711 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1712 enum isl_dim_type type, unsigned pos,
1714 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1715 enum isl_dim_type type, unsigned pos, int value);
1716 __isl_give isl_basic_map *isl_basic_map_fix_si(
1717 __isl_take isl_basic_map *bmap,
1718 enum isl_dim_type type, unsigned pos, int value);
1719 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1720 enum isl_dim_type type, unsigned pos, int value);
1722 Intersect the set or relation with the hyperplane where the given
1723 dimension has the fixed given value.
1725 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1726 enum isl_dim_type type1, int pos1,
1727 enum isl_dim_type type2, int pos2);
1728 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1729 enum isl_dim_type type1, int pos1,
1730 enum isl_dim_type type2, int pos2);
1732 Intersect the set or relation with the hyperplane where the given
1733 dimensions are equal to each other.
1735 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1736 enum isl_dim_type type1, int pos1,
1737 enum isl_dim_type type2, int pos2);
1739 Intersect the relation with the hyperplane where the given
1740 dimensions have opposite values.
1744 __isl_give isl_map *isl_set_identity(
1745 __isl_take isl_set *set);
1746 __isl_give isl_union_map *isl_union_set_identity(
1747 __isl_take isl_union_set *uset);
1749 Construct an identity relation on the given (union) set.
1753 __isl_give isl_basic_set *isl_basic_map_deltas(
1754 __isl_take isl_basic_map *bmap);
1755 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1756 __isl_give isl_union_set *isl_union_map_deltas(
1757 __isl_take isl_union_map *umap);
1759 These functions return a (basic) set containing the differences
1760 between image elements and corresponding domain elements in the input.
1762 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1763 __isl_take isl_basic_map *bmap);
1764 __isl_give isl_map *isl_map_deltas_map(
1765 __isl_take isl_map *map);
1766 __isl_give isl_union_map *isl_union_map_deltas_map(
1767 __isl_take isl_union_map *umap);
1769 The functions above construct a (basic, regular or union) relation
1770 that maps (a wrapped version of) the input relation to its delta set.
1774 Simplify the representation of a set or relation by trying
1775 to combine pairs of basic sets or relations into a single
1776 basic set or relation.
1778 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1779 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1780 __isl_give isl_union_set *isl_union_set_coalesce(
1781 __isl_take isl_union_set *uset);
1782 __isl_give isl_union_map *isl_union_map_coalesce(
1783 __isl_take isl_union_map *umap);
1785 =item * Detecting equalities
1787 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1788 __isl_take isl_basic_set *bset);
1789 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1790 __isl_take isl_basic_map *bmap);
1791 __isl_give isl_set *isl_set_detect_equalities(
1792 __isl_take isl_set *set);
1793 __isl_give isl_map *isl_map_detect_equalities(
1794 __isl_take isl_map *map);
1795 __isl_give isl_union_set *isl_union_set_detect_equalities(
1796 __isl_take isl_union_set *uset);
1797 __isl_give isl_union_map *isl_union_map_detect_equalities(
1798 __isl_take isl_union_map *umap);
1800 Simplify the representation of a set or relation by detecting implicit
1803 =item * Removing redundant constraints
1805 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1806 __isl_take isl_basic_set *bset);
1807 __isl_give isl_set *isl_set_remove_redundancies(
1808 __isl_take isl_set *set);
1809 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1810 __isl_take isl_basic_map *bmap);
1811 __isl_give isl_map *isl_map_remove_redundancies(
1812 __isl_take isl_map *map);
1816 __isl_give isl_basic_set *isl_set_convex_hull(
1817 __isl_take isl_set *set);
1818 __isl_give isl_basic_map *isl_map_convex_hull(
1819 __isl_take isl_map *map);
1821 If the input set or relation has any existentially quantified
1822 variables, then the result of these operations is currently undefined.
1826 __isl_give isl_basic_set *isl_set_simple_hull(
1827 __isl_take isl_set *set);
1828 __isl_give isl_basic_map *isl_map_simple_hull(
1829 __isl_take isl_map *map);
1830 __isl_give isl_union_map *isl_union_map_simple_hull(
1831 __isl_take isl_union_map *umap);
1833 These functions compute a single basic set or relation
1834 that contains the whole input set or relation.
1835 In particular, the output is described by translates
1836 of the constraints describing the basic sets or relations in the input.
1840 (See \autoref{s:simple hull}.)
1846 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1847 __isl_take isl_basic_set *bset);
1848 __isl_give isl_basic_set *isl_set_affine_hull(
1849 __isl_take isl_set *set);
1850 __isl_give isl_union_set *isl_union_set_affine_hull(
1851 __isl_take isl_union_set *uset);
1852 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1853 __isl_take isl_basic_map *bmap);
1854 __isl_give isl_basic_map *isl_map_affine_hull(
1855 __isl_take isl_map *map);
1856 __isl_give isl_union_map *isl_union_map_affine_hull(
1857 __isl_take isl_union_map *umap);
1859 In case of union sets and relations, the affine hull is computed
1862 =item * Polyhedral hull
1864 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1865 __isl_take isl_set *set);
1866 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1867 __isl_take isl_map *map);
1868 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1869 __isl_take isl_union_set *uset);
1870 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1871 __isl_take isl_union_map *umap);
1873 These functions compute a single basic set or relation
1874 not involving any existentially quantified variables
1875 that contains the whole input set or relation.
1876 In case of union sets and relations, the polyhedral hull is computed
1879 =item * Optimization
1881 #include <isl/ilp.h>
1882 enum isl_lp_result isl_basic_set_max(
1883 __isl_keep isl_basic_set *bset,
1884 __isl_keep isl_aff *obj, isl_int *opt)
1885 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1886 __isl_keep isl_aff *obj, isl_int *opt);
1887 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1888 __isl_keep isl_aff *obj, isl_int *opt);
1890 Compute the minimum or maximum of the integer affine expression C<obj>
1891 over the points in C<set>, returning the result in C<opt>.
1892 The return value may be one of C<isl_lp_error>,
1893 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1895 =item * Parametric optimization
1897 __isl_give isl_pw_aff *isl_set_dim_min(
1898 __isl_take isl_set *set, int pos);
1899 __isl_give isl_pw_aff *isl_set_dim_max(
1900 __isl_take isl_set *set, int pos);
1902 Compute the minimum or maximum of the given set dimension as a function of the
1903 parameters, but independently of the other set dimensions.
1904 For lexicographic optimization, see L<"Lexicographic Optimization">.
1908 The following functions compute either the set of (rational) coefficient
1909 values of valid constraints for the given set or the set of (rational)
1910 values satisfying the constraints with coefficients from the given set.
1911 Internally, these two sets of functions perform essentially the
1912 same operations, except that the set of coefficients is assumed to
1913 be a cone, while the set of values may be any polyhedron.
1914 The current implementation is based on the Farkas lemma and
1915 Fourier-Motzkin elimination, but this may change or be made optional
1916 in future. In particular, future implementations may use different
1917 dualization algorithms or skip the elimination step.
1919 __isl_give isl_basic_set *isl_basic_set_coefficients(
1920 __isl_take isl_basic_set *bset);
1921 __isl_give isl_basic_set *isl_set_coefficients(
1922 __isl_take isl_set *set);
1923 __isl_give isl_union_set *isl_union_set_coefficients(
1924 __isl_take isl_union_set *bset);
1925 __isl_give isl_basic_set *isl_basic_set_solutions(
1926 __isl_take isl_basic_set *bset);
1927 __isl_give isl_basic_set *isl_set_solutions(
1928 __isl_take isl_set *set);
1929 __isl_give isl_union_set *isl_union_set_solutions(
1930 __isl_take isl_union_set *bset);
1934 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1936 __isl_give isl_union_map *isl_union_map_power(
1937 __isl_take isl_union_map *umap, int *exact);
1939 Compute a parametric representation for all positive powers I<k> of C<map>.
1940 The result maps I<k> to a nested relation corresponding to the
1941 I<k>th power of C<map>.
1942 The result may be an overapproximation. If the result is known to be exact,
1943 then C<*exact> is set to C<1>.
1945 =item * Transitive closure
1947 __isl_give isl_map *isl_map_transitive_closure(
1948 __isl_take isl_map *map, int *exact);
1949 __isl_give isl_union_map *isl_union_map_transitive_closure(
1950 __isl_take isl_union_map *umap, int *exact);
1952 Compute the transitive closure of C<map>.
1953 The result may be an overapproximation. If the result is known to be exact,
1954 then C<*exact> is set to C<1>.
1956 =item * Reaching path lengths
1958 __isl_give isl_map *isl_map_reaching_path_lengths(
1959 __isl_take isl_map *map, int *exact);
1961 Compute a relation that maps each element in the range of C<map>
1962 to the lengths of all paths composed of edges in C<map> that
1963 end up in the given element.
1964 The result may be an overapproximation. If the result is known to be exact,
1965 then C<*exact> is set to C<1>.
1966 To compute the I<maximal> path length, the resulting relation
1967 should be postprocessed by C<isl_map_lexmax>.
1968 In particular, if the input relation is a dependence relation
1969 (mapping sources to sinks), then the maximal path length corresponds
1970 to the free schedule.
1971 Note, however, that C<isl_map_lexmax> expects the maximum to be
1972 finite, so if the path lengths are unbounded (possibly due to
1973 the overapproximation), then you will get an error message.
1977 __isl_give isl_basic_set *isl_basic_map_wrap(
1978 __isl_take isl_basic_map *bmap);
1979 __isl_give isl_set *isl_map_wrap(
1980 __isl_take isl_map *map);
1981 __isl_give isl_union_set *isl_union_map_wrap(
1982 __isl_take isl_union_map *umap);
1983 __isl_give isl_basic_map *isl_basic_set_unwrap(
1984 __isl_take isl_basic_set *bset);
1985 __isl_give isl_map *isl_set_unwrap(
1986 __isl_take isl_set *set);
1987 __isl_give isl_union_map *isl_union_set_unwrap(
1988 __isl_take isl_union_set *uset);
1992 Remove any internal structure of domain (and range) of the given
1993 set or relation. If there is any such internal structure in the input,
1994 then the name of the space is also removed.
1996 __isl_give isl_basic_set *isl_basic_set_flatten(
1997 __isl_take isl_basic_set *bset);
1998 __isl_give isl_set *isl_set_flatten(
1999 __isl_take isl_set *set);
2000 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2001 __isl_take isl_basic_map *bmap);
2002 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2003 __isl_take isl_basic_map *bmap);
2004 __isl_give isl_map *isl_map_flatten_range(
2005 __isl_take isl_map *map);
2006 __isl_give isl_map *isl_map_flatten_domain(
2007 __isl_take isl_map *map);
2008 __isl_give isl_basic_map *isl_basic_map_flatten(
2009 __isl_take isl_basic_map *bmap);
2010 __isl_give isl_map *isl_map_flatten(
2011 __isl_take isl_map *map);
2013 __isl_give isl_map *isl_set_flatten_map(
2014 __isl_take isl_set *set);
2016 The function above constructs a relation
2017 that maps the input set to a flattened version of the set.
2021 Lift the input set to a space with extra dimensions corresponding
2022 to the existentially quantified variables in the input.
2023 In particular, the result lives in a wrapped map where the domain
2024 is the original space and the range corresponds to the original
2025 existentially quantified variables.
2027 __isl_give isl_basic_set *isl_basic_set_lift(
2028 __isl_take isl_basic_set *bset);
2029 __isl_give isl_set *isl_set_lift(
2030 __isl_take isl_set *set);
2031 __isl_give isl_union_set *isl_union_set_lift(
2032 __isl_take isl_union_set *uset);
2034 =item * Internal Product
2036 __isl_give isl_basic_map *isl_basic_map_zip(
2037 __isl_take isl_basic_map *bmap);
2038 __isl_give isl_map *isl_map_zip(
2039 __isl_take isl_map *map);
2040 __isl_give isl_union_map *isl_union_map_zip(
2041 __isl_take isl_union_map *umap);
2043 Given a relation with nested relations for domain and range,
2044 interchange the range of the domain with the domain of the range.
2046 =item * Aligning parameters
2048 __isl_give isl_set *isl_set_align_params(
2049 __isl_take isl_set *set,
2050 __isl_take isl_space *model);
2051 __isl_give isl_map *isl_map_align_params(
2052 __isl_take isl_map *map,
2053 __isl_take isl_space *model);
2055 Change the order of the parameters of the given set or relation
2056 such that the first parameters match those of C<model>.
2057 This may involve the introduction of extra parameters.
2058 All parameters need to be named.
2060 =item * Dimension manipulation
2062 __isl_give isl_set *isl_set_add_dims(
2063 __isl_take isl_set *set,
2064 enum isl_dim_type type, unsigned n);
2065 __isl_give isl_map *isl_map_add_dims(
2066 __isl_take isl_map *map,
2067 enum isl_dim_type type, unsigned n);
2068 __isl_give isl_set *isl_set_insert_dims(
2069 __isl_take isl_set *set,
2070 enum isl_dim_type type, unsigned pos, unsigned n);
2071 __isl_give isl_map *isl_map_insert_dims(
2072 __isl_take isl_map *map,
2073 enum isl_dim_type type, unsigned pos, unsigned n);
2075 It is usually not advisable to directly change the (input or output)
2076 space of a set or a relation as this removes the name and the internal
2077 structure of the space. However, the above functions can be useful
2078 to add new parameters, assuming
2079 C<isl_set_align_params> and C<isl_map_align_params>
2084 =head2 Binary Operations
2086 The two arguments of a binary operation not only need to live
2087 in the same C<isl_ctx>, they currently also need to have
2088 the same (number of) parameters.
2090 =head3 Basic Operations
2094 =item * Intersection
2096 __isl_give isl_basic_set *isl_basic_set_intersect(
2097 __isl_take isl_basic_set *bset1,
2098 __isl_take isl_basic_set *bset2);
2099 __isl_give isl_set *isl_set_intersect_params(
2100 __isl_take isl_set *set,
2101 __isl_take isl_set *params);
2102 __isl_give isl_set *isl_set_intersect(
2103 __isl_take isl_set *set1,
2104 __isl_take isl_set *set2);
2105 __isl_give isl_union_set *isl_union_set_intersect(
2106 __isl_take isl_union_set *uset1,
2107 __isl_take isl_union_set *uset2);
2108 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2109 __isl_take isl_basic_map *bmap,
2110 __isl_take isl_basic_set *bset);
2111 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2112 __isl_take isl_basic_map *bmap,
2113 __isl_take isl_basic_set *bset);
2114 __isl_give isl_basic_map *isl_basic_map_intersect(
2115 __isl_take isl_basic_map *bmap1,
2116 __isl_take isl_basic_map *bmap2);
2117 __isl_give isl_map *isl_map_intersect_params(
2118 __isl_take isl_map *map,
2119 __isl_take isl_set *params);
2120 __isl_give isl_map *isl_map_intersect_domain(
2121 __isl_take isl_map *map,
2122 __isl_take isl_set *set);
2123 __isl_give isl_map *isl_map_intersect_range(
2124 __isl_take isl_map *map,
2125 __isl_take isl_set *set);
2126 __isl_give isl_map *isl_map_intersect(
2127 __isl_take isl_map *map1,
2128 __isl_take isl_map *map2);
2129 __isl_give isl_union_map *isl_union_map_intersect_domain(
2130 __isl_take isl_union_map *umap,
2131 __isl_take isl_union_set *uset);
2132 __isl_give isl_union_map *isl_union_map_intersect_range(
2133 __isl_take isl_union_map *umap,
2134 __isl_take isl_union_set *uset);
2135 __isl_give isl_union_map *isl_union_map_intersect(
2136 __isl_take isl_union_map *umap1,
2137 __isl_take isl_union_map *umap2);
2141 __isl_give isl_set *isl_basic_set_union(
2142 __isl_take isl_basic_set *bset1,
2143 __isl_take isl_basic_set *bset2);
2144 __isl_give isl_map *isl_basic_map_union(
2145 __isl_take isl_basic_map *bmap1,
2146 __isl_take isl_basic_map *bmap2);
2147 __isl_give isl_set *isl_set_union(
2148 __isl_take isl_set *set1,
2149 __isl_take isl_set *set2);
2150 __isl_give isl_map *isl_map_union(
2151 __isl_take isl_map *map1,
2152 __isl_take isl_map *map2);
2153 __isl_give isl_union_set *isl_union_set_union(
2154 __isl_take isl_union_set *uset1,
2155 __isl_take isl_union_set *uset2);
2156 __isl_give isl_union_map *isl_union_map_union(
2157 __isl_take isl_union_map *umap1,
2158 __isl_take isl_union_map *umap2);
2160 =item * Set difference
2162 __isl_give isl_set *isl_set_subtract(
2163 __isl_take isl_set *set1,
2164 __isl_take isl_set *set2);
2165 __isl_give isl_map *isl_map_subtract(
2166 __isl_take isl_map *map1,
2167 __isl_take isl_map *map2);
2168 __isl_give isl_union_set *isl_union_set_subtract(
2169 __isl_take isl_union_set *uset1,
2170 __isl_take isl_union_set *uset2);
2171 __isl_give isl_union_map *isl_union_map_subtract(
2172 __isl_take isl_union_map *umap1,
2173 __isl_take isl_union_map *umap2);
2177 __isl_give isl_basic_set *isl_basic_set_apply(
2178 __isl_take isl_basic_set *bset,
2179 __isl_take isl_basic_map *bmap);
2180 __isl_give isl_set *isl_set_apply(
2181 __isl_take isl_set *set,
2182 __isl_take isl_map *map);
2183 __isl_give isl_union_set *isl_union_set_apply(
2184 __isl_take isl_union_set *uset,
2185 __isl_take isl_union_map *umap);
2186 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2187 __isl_take isl_basic_map *bmap1,
2188 __isl_take isl_basic_map *bmap2);
2189 __isl_give isl_basic_map *isl_basic_map_apply_range(
2190 __isl_take isl_basic_map *bmap1,
2191 __isl_take isl_basic_map *bmap2);
2192 __isl_give isl_map *isl_map_apply_domain(
2193 __isl_take isl_map *map1,
2194 __isl_take isl_map *map2);
2195 __isl_give isl_union_map *isl_union_map_apply_domain(
2196 __isl_take isl_union_map *umap1,
2197 __isl_take isl_union_map *umap2);
2198 __isl_give isl_map *isl_map_apply_range(
2199 __isl_take isl_map *map1,
2200 __isl_take isl_map *map2);
2201 __isl_give isl_union_map *isl_union_map_apply_range(
2202 __isl_take isl_union_map *umap1,
2203 __isl_take isl_union_map *umap2);
2205 =item * Cartesian Product
2207 __isl_give isl_set *isl_set_product(
2208 __isl_take isl_set *set1,
2209 __isl_take isl_set *set2);
2210 __isl_give isl_union_set *isl_union_set_product(
2211 __isl_take isl_union_set *uset1,
2212 __isl_take isl_union_set *uset2);
2213 __isl_give isl_basic_map *isl_basic_map_domain_product(
2214 __isl_take isl_basic_map *bmap1,
2215 __isl_take isl_basic_map *bmap2);
2216 __isl_give isl_basic_map *isl_basic_map_range_product(
2217 __isl_take isl_basic_map *bmap1,
2218 __isl_take isl_basic_map *bmap2);
2219 __isl_give isl_map *isl_map_domain_product(
2220 __isl_take isl_map *map1,
2221 __isl_take isl_map *map2);
2222 __isl_give isl_map *isl_map_range_product(
2223 __isl_take isl_map *map1,
2224 __isl_take isl_map *map2);
2225 __isl_give isl_union_map *isl_union_map_range_product(
2226 __isl_take isl_union_map *umap1,
2227 __isl_take isl_union_map *umap2);
2228 __isl_give isl_map *isl_map_product(
2229 __isl_take isl_map *map1,
2230 __isl_take isl_map *map2);
2231 __isl_give isl_union_map *isl_union_map_product(
2232 __isl_take isl_union_map *umap1,
2233 __isl_take isl_union_map *umap2);
2235 The above functions compute the cross product of the given
2236 sets or relations. The domains and ranges of the results
2237 are wrapped maps between domains and ranges of the inputs.
2238 To obtain a ``flat'' product, use the following functions
2241 __isl_give isl_basic_set *isl_basic_set_flat_product(
2242 __isl_take isl_basic_set *bset1,
2243 __isl_take isl_basic_set *bset2);
2244 __isl_give isl_set *isl_set_flat_product(
2245 __isl_take isl_set *set1,
2246 __isl_take isl_set *set2);
2247 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2248 __isl_take isl_basic_map *bmap1,
2249 __isl_take isl_basic_map *bmap2);
2250 __isl_give isl_map *isl_map_flat_domain_product(
2251 __isl_take isl_map *map1,
2252 __isl_take isl_map *map2);
2253 __isl_give isl_map *isl_map_flat_range_product(
2254 __isl_take isl_map *map1,
2255 __isl_take isl_map *map2);
2256 __isl_give isl_union_map *isl_union_map_flat_range_product(
2257 __isl_take isl_union_map *umap1,
2258 __isl_take isl_union_map *umap2);
2259 __isl_give isl_basic_map *isl_basic_map_flat_product(
2260 __isl_take isl_basic_map *bmap1,
2261 __isl_take isl_basic_map *bmap2);
2262 __isl_give isl_map *isl_map_flat_product(
2263 __isl_take isl_map *map1,
2264 __isl_take isl_map *map2);
2266 =item * Simplification
2268 __isl_give isl_basic_set *isl_basic_set_gist(
2269 __isl_take isl_basic_set *bset,
2270 __isl_take isl_basic_set *context);
2271 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2272 __isl_take isl_set *context);
2273 __isl_give isl_set *isl_set_gist_params(
2274 __isl_take isl_set *set,
2275 __isl_take isl_set *context);
2276 __isl_give isl_union_set *isl_union_set_gist(
2277 __isl_take isl_union_set *uset,
2278 __isl_take isl_union_set *context);
2279 __isl_give isl_basic_map *isl_basic_map_gist(
2280 __isl_take isl_basic_map *bmap,
2281 __isl_take isl_basic_map *context);
2282 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2283 __isl_take isl_map *context);
2284 __isl_give isl_map *isl_map_gist_params(
2285 __isl_take isl_map *map,
2286 __isl_take isl_set *context);
2287 __isl_give isl_union_map *isl_union_map_gist(
2288 __isl_take isl_union_map *umap,
2289 __isl_take isl_union_map *context);
2291 The gist operation returns a set or relation that has the
2292 same intersection with the context as the input set or relation.
2293 Any implicit equality in the intersection is made explicit in the result,
2294 while all inequalities that are redundant with respect to the intersection
2296 In case of union sets and relations, the gist operation is performed
2301 =head3 Lexicographic Optimization
2303 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2304 the following functions
2305 compute a set that contains the lexicographic minimum or maximum
2306 of the elements in C<set> (or C<bset>) for those values of the parameters
2307 that satisfy C<dom>.
2308 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2309 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2311 In other words, the union of the parameter values
2312 for which the result is non-empty and of C<*empty>
2315 __isl_give isl_set *isl_basic_set_partial_lexmin(
2316 __isl_take isl_basic_set *bset,
2317 __isl_take isl_basic_set *dom,
2318 __isl_give isl_set **empty);
2319 __isl_give isl_set *isl_basic_set_partial_lexmax(
2320 __isl_take isl_basic_set *bset,
2321 __isl_take isl_basic_set *dom,
2322 __isl_give isl_set **empty);
2323 __isl_give isl_set *isl_set_partial_lexmin(
2324 __isl_take isl_set *set, __isl_take isl_set *dom,
2325 __isl_give isl_set **empty);
2326 __isl_give isl_set *isl_set_partial_lexmax(
2327 __isl_take isl_set *set, __isl_take isl_set *dom,
2328 __isl_give isl_set **empty);
2330 Given a (basic) set C<set> (or C<bset>), the following functions simply
2331 return a set containing the lexicographic minimum or maximum
2332 of the elements in C<set> (or C<bset>).
2333 In case of union sets, the optimum is computed per space.
2335 __isl_give isl_set *isl_basic_set_lexmin(
2336 __isl_take isl_basic_set *bset);
2337 __isl_give isl_set *isl_basic_set_lexmax(
2338 __isl_take isl_basic_set *bset);
2339 __isl_give isl_set *isl_set_lexmin(
2340 __isl_take isl_set *set);
2341 __isl_give isl_set *isl_set_lexmax(
2342 __isl_take isl_set *set);
2343 __isl_give isl_union_set *isl_union_set_lexmin(
2344 __isl_take isl_union_set *uset);
2345 __isl_give isl_union_set *isl_union_set_lexmax(
2346 __isl_take isl_union_set *uset);
2348 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2349 the following functions
2350 compute a relation that maps each element of C<dom>
2351 to the single lexicographic minimum or maximum
2352 of the elements that are associated to that same
2353 element in C<map> (or C<bmap>).
2354 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2355 that contains the elements in C<dom> that do not map
2356 to any elements in C<map> (or C<bmap>).
2357 In other words, the union of the domain of the result and of C<*empty>
2360 __isl_give isl_map *isl_basic_map_partial_lexmax(
2361 __isl_take isl_basic_map *bmap,
2362 __isl_take isl_basic_set *dom,
2363 __isl_give isl_set **empty);
2364 __isl_give isl_map *isl_basic_map_partial_lexmin(
2365 __isl_take isl_basic_map *bmap,
2366 __isl_take isl_basic_set *dom,
2367 __isl_give isl_set **empty);
2368 __isl_give isl_map *isl_map_partial_lexmax(
2369 __isl_take isl_map *map, __isl_take isl_set *dom,
2370 __isl_give isl_set **empty);
2371 __isl_give isl_map *isl_map_partial_lexmin(
2372 __isl_take isl_map *map, __isl_take isl_set *dom,
2373 __isl_give isl_set **empty);
2375 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2376 return a map mapping each element in the domain of
2377 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2378 of all elements associated to that element.
2379 In case of union relations, the optimum is computed per space.
2381 __isl_give isl_map *isl_basic_map_lexmin(
2382 __isl_take isl_basic_map *bmap);
2383 __isl_give isl_map *isl_basic_map_lexmax(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_map *isl_map_lexmin(
2386 __isl_take isl_map *map);
2387 __isl_give isl_map *isl_map_lexmax(
2388 __isl_take isl_map *map);
2389 __isl_give isl_union_map *isl_union_map_lexmin(
2390 __isl_take isl_union_map *umap);
2391 __isl_give isl_union_map *isl_union_map_lexmax(
2392 __isl_take isl_union_map *umap);
2396 Lists are defined over several element types, including
2397 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2398 Here we take lists of C<isl_set>s as an example.
2399 Lists can be created, copied and freed using the following functions.
2401 #include <isl/list.h>
2402 __isl_give isl_set_list *isl_set_list_from_set(
2403 __isl_take isl_set *el);
2404 __isl_give isl_set_list *isl_set_list_alloc(
2405 isl_ctx *ctx, int n);
2406 __isl_give isl_set_list *isl_set_list_copy(
2407 __isl_keep isl_set_list *list);
2408 __isl_give isl_set_list *isl_set_list_add(
2409 __isl_take isl_set_list *list,
2410 __isl_take isl_set *el);
2411 __isl_give isl_set_list *isl_set_list_concat(
2412 __isl_take isl_set_list *list1,
2413 __isl_take isl_set_list *list2);
2414 void *isl_set_list_free(__isl_take isl_set_list *list);
2416 C<isl_set_list_alloc> creates an empty list with a capacity for
2417 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2420 Lists can be inspected using the following functions.
2422 #include <isl/list.h>
2423 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2424 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2425 __isl_give isl_set *isl_set_list_get_set(
2426 __isl_keep isl_set_list *list, int index);
2427 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2428 int (*fn)(__isl_take isl_set *el, void *user),
2431 Lists can be printed using
2433 #include <isl/list.h>
2434 __isl_give isl_printer *isl_printer_print_set_list(
2435 __isl_take isl_printer *p,
2436 __isl_keep isl_set_list *list);
2440 Matrices can be created, copied and freed using the following functions.
2442 #include <isl/mat.h>
2443 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2444 unsigned n_row, unsigned n_col);
2445 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2446 void isl_mat_free(__isl_take isl_mat *mat);
2448 Note that the elements of a newly created matrix may have arbitrary values.
2449 The elements can be changed and inspected using the following functions.
2451 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2452 int isl_mat_rows(__isl_keep isl_mat *mat);
2453 int isl_mat_cols(__isl_keep isl_mat *mat);
2454 int isl_mat_get_element(__isl_keep isl_mat *mat,
2455 int row, int col, isl_int *v);
2456 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2457 int row, int col, isl_int v);
2458 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2459 int row, int col, int v);
2461 C<isl_mat_get_element> will return a negative value if anything went wrong.
2462 In that case, the value of C<*v> is undefined.
2464 The following function can be used to compute the (right) inverse
2465 of a matrix, i.e., a matrix such that the product of the original
2466 and the inverse (in that order) is a multiple of the identity matrix.
2467 The input matrix is assumed to be of full row-rank.
2469 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2471 The following function can be used to compute the (right) kernel
2472 (or null space) of a matrix, i.e., a matrix such that the product of
2473 the original and the kernel (in that order) is the zero matrix.
2475 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2477 =head2 Piecewise Quasi Affine Expressions
2479 The zero quasi affine expression on a given domain can be created using
2481 __isl_give isl_aff *isl_aff_zero_on_domain(
2482 __isl_take isl_local_space *ls);
2484 Note that the space in which the resulting object lives is a map space
2485 with the given space as domain and a one-dimensional range.
2487 A quasi affine expression can also be initialized from an C<isl_div>:
2489 #include <isl/div.h>
2490 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2492 An empty piecewise quasi affine expression (one with no cells)
2493 or a piecewise quasi affine expression with a single cell can
2494 be created using the following functions.
2496 #include <isl/aff.h>
2497 __isl_give isl_pw_aff *isl_pw_aff_empty(
2498 __isl_take isl_space *space);
2499 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2500 __isl_take isl_set *set, __isl_take isl_aff *aff);
2501 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2502 __isl_take isl_aff *aff);
2504 Quasi affine expressions can be copied and freed using
2506 #include <isl/aff.h>
2507 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2508 void *isl_aff_free(__isl_take isl_aff *aff);
2510 __isl_give isl_pw_aff *isl_pw_aff_copy(
2511 __isl_keep isl_pw_aff *pwaff);
2512 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2514 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2515 using the following function. The constraint is required to have
2516 a non-zero coefficient for the specified dimension.
2518 #include <isl/constraint.h>
2519 __isl_give isl_aff *isl_constraint_get_bound(
2520 __isl_keep isl_constraint *constraint,
2521 enum isl_dim_type type, int pos);
2523 The entire affine expression of the constraint can also be extracted
2524 using the following function.
2526 #include <isl/constraint.h>
2527 __isl_give isl_aff *isl_constraint_get_aff(
2528 __isl_keep isl_constraint *constraint);
2530 Conversely, an equality constraint equating
2531 the affine expression to zero or an inequality constraint enforcing
2532 the affine expression to be non-negative, can be constructed using
2534 __isl_give isl_constraint *isl_equality_from_aff(
2535 __isl_take isl_aff *aff);
2536 __isl_give isl_constraint *isl_inequality_from_aff(
2537 __isl_take isl_aff *aff);
2539 The expression can be inspected using
2541 #include <isl/aff.h>
2542 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2543 int isl_aff_dim(__isl_keep isl_aff *aff,
2544 enum isl_dim_type type);
2545 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2546 __isl_keep isl_aff *aff);
2547 __isl_give isl_local_space *isl_aff_get_local_space(
2548 __isl_keep isl_aff *aff);
2549 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2550 enum isl_dim_type type, unsigned pos);
2551 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2553 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2554 enum isl_dim_type type, int pos, isl_int *v);
2555 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2557 __isl_give isl_div *isl_aff_get_div(
2558 __isl_keep isl_aff *aff, int pos);
2560 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2561 int (*fn)(__isl_take isl_set *set,
2562 __isl_take isl_aff *aff,
2563 void *user), void *user);
2565 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2566 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2568 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2569 enum isl_dim_type type, unsigned first, unsigned n);
2570 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2571 enum isl_dim_type type, unsigned first, unsigned n);
2573 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2574 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2575 enum isl_dim_type type);
2576 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2578 It can be modified using
2580 #include <isl/aff.h>
2581 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2582 __isl_take isl_pw_aff *pwaff,
2583 __isl_take isl_id *id);
2584 __isl_give isl_aff *isl_aff_set_dim_name(
2585 __isl_take isl_aff *aff, enum isl_dim_type type,
2586 unsigned pos, const char *s);
2587 __isl_give isl_aff *isl_aff_set_constant(
2588 __isl_take isl_aff *aff, isl_int v);
2589 __isl_give isl_aff *isl_aff_set_constant_si(
2590 __isl_take isl_aff *aff, int v);
2591 __isl_give isl_aff *isl_aff_set_coefficient(
2592 __isl_take isl_aff *aff,
2593 enum isl_dim_type type, int pos, isl_int v);
2594 __isl_give isl_aff *isl_aff_set_coefficient_si(
2595 __isl_take isl_aff *aff,
2596 enum isl_dim_type type, int pos, int v);
2597 __isl_give isl_aff *isl_aff_set_denominator(
2598 __isl_take isl_aff *aff, isl_int v);
2600 __isl_give isl_aff *isl_aff_add_constant(
2601 __isl_take isl_aff *aff, isl_int v);
2602 __isl_give isl_aff *isl_aff_add_constant_si(
2603 __isl_take isl_aff *aff, int v);
2604 __isl_give isl_aff *isl_aff_add_coefficient(
2605 __isl_take isl_aff *aff,
2606 enum isl_dim_type type, int pos, isl_int v);
2607 __isl_give isl_aff *isl_aff_add_coefficient_si(
2608 __isl_take isl_aff *aff,
2609 enum isl_dim_type type, int pos, int v);
2611 __isl_give isl_aff *isl_aff_insert_dims(
2612 __isl_take isl_aff *aff,
2613 enum isl_dim_type type, unsigned first, unsigned n);
2614 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2615 __isl_take isl_pw_aff *pwaff,
2616 enum isl_dim_type type, unsigned first, unsigned n);
2617 __isl_give isl_aff *isl_aff_add_dims(
2618 __isl_take isl_aff *aff,
2619 enum isl_dim_type type, unsigned n);
2620 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2621 __isl_take isl_pw_aff *pwaff,
2622 enum isl_dim_type type, unsigned n);
2623 __isl_give isl_aff *isl_aff_drop_dims(
2624 __isl_take isl_aff *aff,
2625 enum isl_dim_type type, unsigned first, unsigned n);
2626 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2627 __isl_take isl_pw_aff *pwaff,
2628 enum isl_dim_type type, unsigned first, unsigned n);
2630 Note that the C<set_constant> and C<set_coefficient> functions
2631 set the I<numerator> of the constant or coefficient, while
2632 C<add_constant> and C<add_coefficient> add an integer value to
2633 the possibly rational constant or coefficient.
2635 To check whether an affine expressions is obviously zero
2636 or obviously equal to some other affine expression, use
2638 #include <isl/aff.h>
2639 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2640 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2641 __isl_keep isl_aff *aff2);
2645 #include <isl/aff.h>
2646 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2647 __isl_take isl_aff *aff2);
2648 __isl_give isl_pw_aff *isl_pw_aff_add(
2649 __isl_take isl_pw_aff *pwaff1,
2650 __isl_take isl_pw_aff *pwaff2);
2651 __isl_give isl_pw_aff *isl_pw_aff_min(
2652 __isl_take isl_pw_aff *pwaff1,
2653 __isl_take isl_pw_aff *pwaff2);
2654 __isl_give isl_pw_aff *isl_pw_aff_max(
2655 __isl_take isl_pw_aff *pwaff1,
2656 __isl_take isl_pw_aff *pwaff2);
2657 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2658 __isl_take isl_aff *aff2);
2659 __isl_give isl_pw_aff *isl_pw_aff_sub(
2660 __isl_take isl_pw_aff *pwaff1,
2661 __isl_take isl_pw_aff *pwaff2);
2662 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2663 __isl_give isl_pw_aff *isl_pw_aff_neg(
2664 __isl_take isl_pw_aff *pwaff);
2665 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2666 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2667 __isl_take isl_pw_aff *pwaff);
2668 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2669 __isl_give isl_pw_aff *isl_pw_aff_floor(
2670 __isl_take isl_pw_aff *pwaff);
2671 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2673 __isl_give isl_pw_aff *isl_pw_aff_mod(
2674 __isl_take isl_pw_aff *pwaff, isl_int mod);
2675 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2677 __isl_give isl_pw_aff *isl_pw_aff_scale(
2678 __isl_take isl_pw_aff *pwaff, isl_int f);
2679 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2681 __isl_give isl_aff *isl_aff_scale_down_ui(
2682 __isl_take isl_aff *aff, unsigned f);
2683 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2684 __isl_take isl_pw_aff *pwaff, isl_int f);
2686 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2687 __isl_take isl_pw_aff_list *list);
2688 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2689 __isl_take isl_pw_aff_list *list);
2691 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2692 __isl_take isl_pw_aff *pwqp);
2694 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2695 __isl_take isl_pw_aff *pwaff,
2696 __isl_take isl_space *model);
2698 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2699 __isl_take isl_set *context);
2700 __isl_give isl_pw_aff *isl_pw_aff_gist(
2701 __isl_take isl_pw_aff *pwaff,
2702 __isl_take isl_set *context);
2704 __isl_give isl_set *isl_pw_aff_domain(
2705 __isl_take isl_pw_aff *pwaff);
2707 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2708 __isl_take isl_aff *aff2);
2709 __isl_give isl_pw_aff *isl_pw_aff_mul(
2710 __isl_take isl_pw_aff *pwaff1,
2711 __isl_take isl_pw_aff *pwaff2);
2713 When multiplying two affine expressions, at least one of the two needs
2716 #include <isl/aff.h>
2717 __isl_give isl_basic_set *isl_aff_le_basic_set(
2718 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2719 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2720 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2721 __isl_give isl_set *isl_pw_aff_eq_set(
2722 __isl_take isl_pw_aff *pwaff1,
2723 __isl_take isl_pw_aff *pwaff2);
2724 __isl_give isl_set *isl_pw_aff_ne_set(
2725 __isl_take isl_pw_aff *pwaff1,
2726 __isl_take isl_pw_aff *pwaff2);
2727 __isl_give isl_set *isl_pw_aff_le_set(
2728 __isl_take isl_pw_aff *pwaff1,
2729 __isl_take isl_pw_aff *pwaff2);
2730 __isl_give isl_set *isl_pw_aff_lt_set(
2731 __isl_take isl_pw_aff *pwaff1,
2732 __isl_take isl_pw_aff *pwaff2);
2733 __isl_give isl_set *isl_pw_aff_ge_set(
2734 __isl_take isl_pw_aff *pwaff1,
2735 __isl_take isl_pw_aff *pwaff2);
2736 __isl_give isl_set *isl_pw_aff_gt_set(
2737 __isl_take isl_pw_aff *pwaff1,
2738 __isl_take isl_pw_aff *pwaff2);
2740 __isl_give isl_set *isl_pw_aff_list_eq_set(
2741 __isl_take isl_pw_aff_list *list1,
2742 __isl_take isl_pw_aff_list *list2);
2743 __isl_give isl_set *isl_pw_aff_list_ne_set(
2744 __isl_take isl_pw_aff_list *list1,
2745 __isl_take isl_pw_aff_list *list2);
2746 __isl_give isl_set *isl_pw_aff_list_le_set(
2747 __isl_take isl_pw_aff_list *list1,
2748 __isl_take isl_pw_aff_list *list2);
2749 __isl_give isl_set *isl_pw_aff_list_lt_set(
2750 __isl_take isl_pw_aff_list *list1,
2751 __isl_take isl_pw_aff_list *list2);
2752 __isl_give isl_set *isl_pw_aff_list_ge_set(
2753 __isl_take isl_pw_aff_list *list1,
2754 __isl_take isl_pw_aff_list *list2);
2755 __isl_give isl_set *isl_pw_aff_list_gt_set(
2756 __isl_take isl_pw_aff_list *list1,
2757 __isl_take isl_pw_aff_list *list2);
2759 The function C<isl_aff_ge_basic_set> returns a basic set
2760 containing those elements in the shared space
2761 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2762 The function C<isl_aff_ge_set> returns a set
2763 containing those elements in the shared domain
2764 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2765 The functions operating on C<isl_pw_aff_list> apply the corresponding
2766 C<isl_pw_aff> function to each pair of elements in the two lists.
2768 #include <isl/aff.h>
2769 __isl_give isl_set *isl_pw_aff_nonneg_set(
2770 __isl_take isl_pw_aff *pwaff);
2771 __isl_give isl_set *isl_pw_aff_zero_set(
2772 __isl_take isl_pw_aff *pwaff);
2773 __isl_give isl_set *isl_pw_aff_non_zero_set(
2774 __isl_take isl_pw_aff *pwaff);
2776 The function C<isl_pw_aff_nonneg_set> returns a set
2777 containing those elements in the domain
2778 of C<pwaff> where C<pwaff> is non-negative.
2780 #include <isl/aff.h>
2781 __isl_give isl_pw_aff *isl_pw_aff_cond(
2782 __isl_take isl_set *cond,
2783 __isl_take isl_pw_aff *pwaff_true,
2784 __isl_take isl_pw_aff *pwaff_false);
2786 The function C<isl_pw_aff_cond> performs a conditional operator
2787 and returns an expression that is equal to C<pwaff_true>
2788 for elements in C<cond> and equal to C<pwaff_false> for elements
2791 #include <isl/aff.h>
2792 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2793 __isl_take isl_pw_aff *pwaff1,
2794 __isl_take isl_pw_aff *pwaff2);
2795 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2796 __isl_take isl_pw_aff *pwaff1,
2797 __isl_take isl_pw_aff *pwaff2);
2799 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2800 expression with a domain that is the union of those of C<pwaff1> and
2801 C<pwaff2> and such that on each cell, the quasi-affine expression is
2802 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2803 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2804 associated expression is the defined one.
2806 An expression can be printed using
2808 #include <isl/aff.h>
2809 __isl_give isl_printer *isl_printer_print_aff(
2810 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2812 __isl_give isl_printer *isl_printer_print_pw_aff(
2813 __isl_take isl_printer *p,
2814 __isl_keep isl_pw_aff *pwaff);
2818 Points are elements of a set. They can be used to construct
2819 simple sets (boxes) or they can be used to represent the
2820 individual elements of a set.
2821 The zero point (the origin) can be created using
2823 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2825 The coordinates of a point can be inspected, set and changed
2828 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2829 enum isl_dim_type type, int pos, isl_int *v);
2830 __isl_give isl_point *isl_point_set_coordinate(
2831 __isl_take isl_point *pnt,
2832 enum isl_dim_type type, int pos, isl_int v);
2834 __isl_give isl_point *isl_point_add_ui(
2835 __isl_take isl_point *pnt,
2836 enum isl_dim_type type, int pos, unsigned val);
2837 __isl_give isl_point *isl_point_sub_ui(
2838 __isl_take isl_point *pnt,
2839 enum isl_dim_type type, int pos, unsigned val);
2841 Other properties can be obtained using
2843 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2845 Points can be copied or freed using
2847 __isl_give isl_point *isl_point_copy(
2848 __isl_keep isl_point *pnt);
2849 void isl_point_free(__isl_take isl_point *pnt);
2851 A singleton set can be created from a point using
2853 __isl_give isl_basic_set *isl_basic_set_from_point(
2854 __isl_take isl_point *pnt);
2855 __isl_give isl_set *isl_set_from_point(
2856 __isl_take isl_point *pnt);
2858 and a box can be created from two opposite extremal points using
2860 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2861 __isl_take isl_point *pnt1,
2862 __isl_take isl_point *pnt2);
2863 __isl_give isl_set *isl_set_box_from_points(
2864 __isl_take isl_point *pnt1,
2865 __isl_take isl_point *pnt2);
2867 All elements of a B<bounded> (union) set can be enumerated using
2868 the following functions.
2870 int isl_set_foreach_point(__isl_keep isl_set *set,
2871 int (*fn)(__isl_take isl_point *pnt, void *user),
2873 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2874 int (*fn)(__isl_take isl_point *pnt, void *user),
2877 The function C<fn> is called for each integer point in
2878 C<set> with as second argument the last argument of
2879 the C<isl_set_foreach_point> call. The function C<fn>
2880 should return C<0> on success and C<-1> on failure.
2881 In the latter case, C<isl_set_foreach_point> will stop
2882 enumerating and return C<-1> as well.
2883 If the enumeration is performed successfully and to completion,
2884 then C<isl_set_foreach_point> returns C<0>.
2886 To obtain a single point of a (basic) set, use
2888 __isl_give isl_point *isl_basic_set_sample_point(
2889 __isl_take isl_basic_set *bset);
2890 __isl_give isl_point *isl_set_sample_point(
2891 __isl_take isl_set *set);
2893 If C<set> does not contain any (integer) points, then the
2894 resulting point will be ``void'', a property that can be
2897 int isl_point_is_void(__isl_keep isl_point *pnt);
2899 =head2 Piecewise Quasipolynomials
2901 A piecewise quasipolynomial is a particular kind of function that maps
2902 a parametric point to a rational value.
2903 More specifically, a quasipolynomial is a polynomial expression in greatest
2904 integer parts of affine expressions of parameters and variables.
2905 A piecewise quasipolynomial is a subdivision of a given parametric
2906 domain into disjoint cells with a quasipolynomial associated to
2907 each cell. The value of the piecewise quasipolynomial at a given
2908 point is the value of the quasipolynomial associated to the cell
2909 that contains the point. Outside of the union of cells,
2910 the value is assumed to be zero.
2911 For example, the piecewise quasipolynomial
2913 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2915 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2916 A given piecewise quasipolynomial has a fixed domain dimension.
2917 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2918 defined over different domains.
2919 Piecewise quasipolynomials are mainly used by the C<barvinok>
2920 library for representing the number of elements in a parametric set or map.
2921 For example, the piecewise quasipolynomial above represents
2922 the number of points in the map
2924 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2926 =head3 Printing (Piecewise) Quasipolynomials
2928 Quasipolynomials and piecewise quasipolynomials can be printed
2929 using the following functions.
2931 __isl_give isl_printer *isl_printer_print_qpolynomial(
2932 __isl_take isl_printer *p,
2933 __isl_keep isl_qpolynomial *qp);
2935 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2936 __isl_take isl_printer *p,
2937 __isl_keep isl_pw_qpolynomial *pwqp);
2939 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2940 __isl_take isl_printer *p,
2941 __isl_keep isl_union_pw_qpolynomial *upwqp);
2943 The output format of the printer
2944 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2945 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2947 In case of printing in C<ISL_FORMAT_C>, the user may want
2948 to set the names of all dimensions
2950 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2951 __isl_take isl_qpolynomial *qp,
2952 enum isl_dim_type type, unsigned pos,
2954 __isl_give isl_pw_qpolynomial *
2955 isl_pw_qpolynomial_set_dim_name(
2956 __isl_take isl_pw_qpolynomial *pwqp,
2957 enum isl_dim_type type, unsigned pos,
2960 =head3 Creating New (Piecewise) Quasipolynomials
2962 Some simple quasipolynomials can be created using the following functions.
2963 More complicated quasipolynomials can be created by applying
2964 operations such as addition and multiplication
2965 on the resulting quasipolynomials
2967 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2968 __isl_take isl_space *domain);
2969 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2970 __isl_take isl_space *domain);
2971 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2972 __isl_take isl_space *domain);
2973 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2974 __isl_take isl_space *domain);
2975 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2976 __isl_take isl_space *domain);
2977 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2978 __isl_take isl_space *domain,
2979 const isl_int n, const isl_int d);
2980 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2981 __isl_take isl_div *div);
2982 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2983 __isl_take isl_space *domain,
2984 enum isl_dim_type type, unsigned pos);
2985 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2986 __isl_take isl_aff *aff);
2988 Note that the space in which a quasipolynomial lives is a map space
2989 with a one-dimensional range. The C<domain> argument in some of
2990 the functions above corresponds to the domain of this map space.
2992 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2993 with a single cell can be created using the following functions.
2994 Multiple of these single cell piecewise quasipolynomials can
2995 be combined to create more complicated piecewise quasipolynomials.
2997 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2998 __isl_take isl_space *space);
2999 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3000 __isl_take isl_set *set,
3001 __isl_take isl_qpolynomial *qp);
3002 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3003 __isl_take isl_qpolynomial *qp);
3004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3005 __isl_take isl_pw_aff *pwaff);
3007 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3008 __isl_take isl_space *space);
3009 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3010 __isl_take isl_pw_qpolynomial *pwqp);
3011 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3012 __isl_take isl_union_pw_qpolynomial *upwqp,
3013 __isl_take isl_pw_qpolynomial *pwqp);
3015 Quasipolynomials can be copied and freed again using the following
3018 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3019 __isl_keep isl_qpolynomial *qp);
3020 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3023 __isl_keep isl_pw_qpolynomial *pwqp);
3024 void *isl_pw_qpolynomial_free(
3025 __isl_take isl_pw_qpolynomial *pwqp);
3027 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3028 __isl_keep isl_union_pw_qpolynomial *upwqp);
3029 void isl_union_pw_qpolynomial_free(
3030 __isl_take isl_union_pw_qpolynomial *upwqp);
3032 =head3 Inspecting (Piecewise) Quasipolynomials
3034 To iterate over all piecewise quasipolynomials in a union
3035 piecewise quasipolynomial, use the following function
3037 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3038 __isl_keep isl_union_pw_qpolynomial *upwqp,
3039 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3042 To extract the piecewise quasipolynomial in a given space from a union, use
3044 __isl_give isl_pw_qpolynomial *
3045 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3046 __isl_keep isl_union_pw_qpolynomial *upwqp,
3047 __isl_take isl_space *space);
3049 To iterate over the cells in a piecewise quasipolynomial,
3050 use either of the following two functions
3052 int isl_pw_qpolynomial_foreach_piece(
3053 __isl_keep isl_pw_qpolynomial *pwqp,
3054 int (*fn)(__isl_take isl_set *set,
3055 __isl_take isl_qpolynomial *qp,
3056 void *user), void *user);
3057 int isl_pw_qpolynomial_foreach_lifted_piece(
3058 __isl_keep isl_pw_qpolynomial *pwqp,
3059 int (*fn)(__isl_take isl_set *set,
3060 __isl_take isl_qpolynomial *qp,
3061 void *user), void *user);
3063 As usual, the function C<fn> should return C<0> on success
3064 and C<-1> on failure. The difference between
3065 C<isl_pw_qpolynomial_foreach_piece> and
3066 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3067 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3068 compute unique representations for all existentially quantified
3069 variables and then turn these existentially quantified variables
3070 into extra set variables, adapting the associated quasipolynomial
3071 accordingly. This means that the C<set> passed to C<fn>
3072 will not have any existentially quantified variables, but that
3073 the dimensions of the sets may be different for different
3074 invocations of C<fn>.
3076 To iterate over all terms in a quasipolynomial,
3079 int isl_qpolynomial_foreach_term(
3080 __isl_keep isl_qpolynomial *qp,
3081 int (*fn)(__isl_take isl_term *term,
3082 void *user), void *user);
3084 The terms themselves can be inspected and freed using
3087 unsigned isl_term_dim(__isl_keep isl_term *term,
3088 enum isl_dim_type type);
3089 void isl_term_get_num(__isl_keep isl_term *term,
3091 void isl_term_get_den(__isl_keep isl_term *term,
3093 int isl_term_get_exp(__isl_keep isl_term *term,
3094 enum isl_dim_type type, unsigned pos);
3095 __isl_give isl_div *isl_term_get_div(
3096 __isl_keep isl_term *term, unsigned pos);
3097 void isl_term_free(__isl_take isl_term *term);
3099 Each term is a product of parameters, set variables and
3100 integer divisions. The function C<isl_term_get_exp>
3101 returns the exponent of a given dimensions in the given term.
3102 The C<isl_int>s in the arguments of C<isl_term_get_num>
3103 and C<isl_term_get_den> need to have been initialized
3104 using C<isl_int_init> before calling these functions.
3106 =head3 Properties of (Piecewise) Quasipolynomials
3108 To check whether a quasipolynomial is actually a constant,
3109 use the following function.
3111 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3112 isl_int *n, isl_int *d);
3114 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3115 then the numerator and denominator of the constant
3116 are returned in C<*n> and C<*d>, respectively.
3118 =head3 Operations on (Piecewise) Quasipolynomials
3120 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3121 __isl_take isl_qpolynomial *qp, isl_int v);
3122 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3123 __isl_take isl_qpolynomial *qp);
3124 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3125 __isl_take isl_qpolynomial *qp1,
3126 __isl_take isl_qpolynomial *qp2);
3127 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3128 __isl_take isl_qpolynomial *qp1,
3129 __isl_take isl_qpolynomial *qp2);
3130 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3131 __isl_take isl_qpolynomial *qp1,
3132 __isl_take isl_qpolynomial *qp2);
3133 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3134 __isl_take isl_qpolynomial *qp, unsigned exponent);
3136 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3137 __isl_take isl_pw_qpolynomial *pwqp1,
3138 __isl_take isl_pw_qpolynomial *pwqp2);
3139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3140 __isl_take isl_pw_qpolynomial *pwqp1,
3141 __isl_take isl_pw_qpolynomial *pwqp2);
3142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3143 __isl_take isl_pw_qpolynomial *pwqp1,
3144 __isl_take isl_pw_qpolynomial *pwqp2);
3145 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3146 __isl_take isl_pw_qpolynomial *pwqp);
3147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3148 __isl_take isl_pw_qpolynomial *pwqp1,
3149 __isl_take isl_pw_qpolynomial *pwqp2);
3150 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3151 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3153 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3154 __isl_take isl_union_pw_qpolynomial *upwqp1,
3155 __isl_take isl_union_pw_qpolynomial *upwqp2);
3156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
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_mul(
3160 __isl_take isl_union_pw_qpolynomial *upwqp1,
3161 __isl_take isl_union_pw_qpolynomial *upwqp2);
3163 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3164 __isl_take isl_pw_qpolynomial *pwqp,
3165 __isl_take isl_point *pnt);
3167 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3168 __isl_take isl_union_pw_qpolynomial *upwqp,
3169 __isl_take isl_point *pnt);
3171 __isl_give isl_set *isl_pw_qpolynomial_domain(
3172 __isl_take isl_pw_qpolynomial *pwqp);
3173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3174 __isl_take isl_pw_qpolynomial *pwpq,
3175 __isl_take isl_set *set);
3177 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3178 __isl_take isl_union_pw_qpolynomial *upwqp);
3179 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3180 __isl_take isl_union_pw_qpolynomial *upwpq,
3181 __isl_take isl_union_set *uset);
3183 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3184 __isl_take isl_qpolynomial *qp,
3185 __isl_take isl_space *model);
3187 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3188 __isl_take isl_qpolynomial *qp);
3189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3190 __isl_take isl_pw_qpolynomial *pwqp);
3192 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3193 __isl_take isl_union_pw_qpolynomial *upwqp);
3195 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3196 __isl_take isl_qpolynomial *qp,
3197 __isl_take isl_set *context);
3199 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3200 __isl_take isl_pw_qpolynomial *pwqp,
3201 __isl_take isl_set *context);
3203 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3204 __isl_take isl_union_pw_qpolynomial *upwqp,
3205 __isl_take isl_union_set *context);
3207 The gist operation applies the gist operation to each of
3208 the cells in the domain of the input piecewise quasipolynomial.
3209 The context is also exploited
3210 to simplify the quasipolynomials associated to each cell.
3212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3213 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3214 __isl_give isl_union_pw_qpolynomial *
3215 isl_union_pw_qpolynomial_to_polynomial(
3216 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3218 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3219 the polynomial will be an overapproximation. If C<sign> is negative,
3220 it will be an underapproximation. If C<sign> is zero, the approximation
3221 will lie somewhere in between.
3223 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3225 A piecewise quasipolynomial reduction is a piecewise
3226 reduction (or fold) of quasipolynomials.
3227 In particular, the reduction can be maximum or a minimum.
3228 The objects are mainly used to represent the result of
3229 an upper or lower bound on a quasipolynomial over its domain,
3230 i.e., as the result of the following function.
3232 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3233 __isl_take isl_pw_qpolynomial *pwqp,
3234 enum isl_fold type, int *tight);
3236 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3237 __isl_take isl_union_pw_qpolynomial *upwqp,
3238 enum isl_fold type, int *tight);
3240 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3241 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3242 is the returned bound is known be tight, i.e., for each value
3243 of the parameters there is at least
3244 one element in the domain that reaches the bound.
3245 If the domain of C<pwqp> is not wrapping, then the bound is computed
3246 over all elements in that domain and the result has a purely parametric
3247 domain. If the domain of C<pwqp> is wrapping, then the bound is
3248 computed over the range of the wrapped relation. The domain of the
3249 wrapped relation becomes the domain of the result.
3251 A (piecewise) quasipolynomial reduction can be copied or freed using the
3252 following functions.
3254 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3255 __isl_keep isl_qpolynomial_fold *fold);
3256 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3257 __isl_keep isl_pw_qpolynomial_fold *pwf);
3258 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3259 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3260 void isl_qpolynomial_fold_free(
3261 __isl_take isl_qpolynomial_fold *fold);
3262 void *isl_pw_qpolynomial_fold_free(
3263 __isl_take isl_pw_qpolynomial_fold *pwf);
3264 void isl_union_pw_qpolynomial_fold_free(
3265 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3267 =head3 Printing Piecewise Quasipolynomial Reductions
3269 Piecewise quasipolynomial reductions can be printed
3270 using the following function.
3272 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3273 __isl_take isl_printer *p,
3274 __isl_keep isl_pw_qpolynomial_fold *pwf);
3275 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3276 __isl_take isl_printer *p,
3277 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3279 For C<isl_printer_print_pw_qpolynomial_fold>,
3280 output format of the printer
3281 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3282 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3283 output format of the printer
3284 needs to be set to C<ISL_FORMAT_ISL>.
3285 In case of printing in C<ISL_FORMAT_C>, the user may want
3286 to set the names of all dimensions
3288 __isl_give isl_pw_qpolynomial_fold *
3289 isl_pw_qpolynomial_fold_set_dim_name(
3290 __isl_take isl_pw_qpolynomial_fold *pwf,
3291 enum isl_dim_type type, unsigned pos,
3294 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3296 To iterate over all piecewise quasipolynomial reductions in a union
3297 piecewise quasipolynomial reduction, use the following function
3299 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3300 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3301 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3302 void *user), void *user);
3304 To iterate over the cells in a piecewise quasipolynomial reduction,
3305 use either of the following two functions
3307 int isl_pw_qpolynomial_fold_foreach_piece(
3308 __isl_keep isl_pw_qpolynomial_fold *pwf,
3309 int (*fn)(__isl_take isl_set *set,
3310 __isl_take isl_qpolynomial_fold *fold,
3311 void *user), void *user);
3312 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3313 __isl_keep isl_pw_qpolynomial_fold *pwf,
3314 int (*fn)(__isl_take isl_set *set,
3315 __isl_take isl_qpolynomial_fold *fold,
3316 void *user), void *user);
3318 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3319 of the difference between these two functions.
3321 To iterate over all quasipolynomials in a reduction, use
3323 int isl_qpolynomial_fold_foreach_qpolynomial(
3324 __isl_keep isl_qpolynomial_fold *fold,
3325 int (*fn)(__isl_take isl_qpolynomial *qp,
3326 void *user), void *user);
3328 =head3 Operations on Piecewise Quasipolynomial Reductions
3330 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3331 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3333 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3334 __isl_take isl_pw_qpolynomial_fold *pwf1,
3335 __isl_take isl_pw_qpolynomial_fold *pwf2);
3337 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3338 __isl_take isl_pw_qpolynomial_fold *pwf1,
3339 __isl_take isl_pw_qpolynomial_fold *pwf2);
3341 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3342 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3343 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3345 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3346 __isl_take isl_pw_qpolynomial_fold *pwf,
3347 __isl_take isl_point *pnt);
3349 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3350 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3351 __isl_take isl_point *pnt);
3353 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3354 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3355 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3356 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3357 __isl_take isl_union_set *uset);
3359 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3360 __isl_take isl_pw_qpolynomial_fold *pwf);
3362 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3363 __isl_take isl_pw_qpolynomial_fold *pwf);
3365 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3366 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3368 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3369 __isl_take isl_pw_qpolynomial_fold *pwf,
3370 __isl_take isl_set *context);
3372 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3373 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3374 __isl_take isl_union_set *context);
3376 The gist operation applies the gist operation to each of
3377 the cells in the domain of the input piecewise quasipolynomial reduction.
3378 In future, the operation will also exploit the context
3379 to simplify the quasipolynomial reductions associated to each cell.
3381 __isl_give isl_pw_qpolynomial_fold *
3382 isl_set_apply_pw_qpolynomial_fold(
3383 __isl_take isl_set *set,
3384 __isl_take isl_pw_qpolynomial_fold *pwf,
3386 __isl_give isl_pw_qpolynomial_fold *
3387 isl_map_apply_pw_qpolynomial_fold(
3388 __isl_take isl_map *map,
3389 __isl_take isl_pw_qpolynomial_fold *pwf,
3391 __isl_give isl_union_pw_qpolynomial_fold *
3392 isl_union_set_apply_union_pw_qpolynomial_fold(
3393 __isl_take isl_union_set *uset,
3394 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3396 __isl_give isl_union_pw_qpolynomial_fold *
3397 isl_union_map_apply_union_pw_qpolynomial_fold(
3398 __isl_take isl_union_map *umap,
3399 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3402 The functions taking a map
3403 compose the given map with the given piecewise quasipolynomial reduction.
3404 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3405 over all elements in the intersection of the range of the map
3406 and the domain of the piecewise quasipolynomial reduction
3407 as a function of an element in the domain of the map.
3408 The functions taking a set compute a bound over all elements in the
3409 intersection of the set and the domain of the
3410 piecewise quasipolynomial reduction.
3412 =head2 Dependence Analysis
3414 C<isl> contains specialized functionality for performing
3415 array dataflow analysis. That is, given a I<sink> access relation
3416 and a collection of possible I<source> access relations,
3417 C<isl> can compute relations that describe
3418 for each iteration of the sink access, which iteration
3419 of which of the source access relations was the last
3420 to access the same data element before the given iteration
3422 To compute standard flow dependences, the sink should be
3423 a read, while the sources should be writes.
3424 If any of the source accesses are marked as being I<may>
3425 accesses, then there will be a dependence to the last
3426 I<must> access B<and> to any I<may> access that follows
3427 this last I<must> access.
3428 In particular, if I<all> sources are I<may> accesses,
3429 then memory based dependence analysis is performed.
3430 If, on the other hand, all sources are I<must> accesses,
3431 then value based dependence analysis is performed.
3433 #include <isl/flow.h>
3435 typedef int (*isl_access_level_before)(void *first, void *second);
3437 __isl_give isl_access_info *isl_access_info_alloc(
3438 __isl_take isl_map *sink,
3439 void *sink_user, isl_access_level_before fn,
3441 __isl_give isl_access_info *isl_access_info_add_source(
3442 __isl_take isl_access_info *acc,
3443 __isl_take isl_map *source, int must,
3445 void isl_access_info_free(__isl_take isl_access_info *acc);
3447 __isl_give isl_flow *isl_access_info_compute_flow(
3448 __isl_take isl_access_info *acc);
3450 int isl_flow_foreach(__isl_keep isl_flow *deps,
3451 int (*fn)(__isl_take isl_map *dep, int must,
3452 void *dep_user, void *user),
3454 __isl_give isl_map *isl_flow_get_no_source(
3455 __isl_keep isl_flow *deps, int must);
3456 void isl_flow_free(__isl_take isl_flow *deps);
3458 The function C<isl_access_info_compute_flow> performs the actual
3459 dependence analysis. The other functions are used to construct
3460 the input for this function or to read off the output.
3462 The input is collected in an C<isl_access_info>, which can
3463 be created through a call to C<isl_access_info_alloc>.
3464 The arguments to this functions are the sink access relation
3465 C<sink>, a token C<sink_user> used to identify the sink
3466 access to the user, a callback function for specifying the
3467 relative order of source and sink accesses, and the number
3468 of source access relations that will be added.
3469 The callback function has type C<int (*)(void *first, void *second)>.
3470 The function is called with two user supplied tokens identifying
3471 either a source or the sink and it should return the shared nesting
3472 level and the relative order of the two accesses.
3473 In particular, let I<n> be the number of loops shared by
3474 the two accesses. If C<first> precedes C<second> textually,
3475 then the function should return I<2 * n + 1>; otherwise,
3476 it should return I<2 * n>.
3477 The sources can be added to the C<isl_access_info> by performing
3478 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3479 C<must> indicates whether the source is a I<must> access
3480 or a I<may> access. Note that a multi-valued access relation
3481 should only be marked I<must> if every iteration in the domain
3482 of the relation accesses I<all> elements in its image.
3483 The C<source_user> token is again used to identify
3484 the source access. The range of the source access relation
3485 C<source> should have the same dimension as the range
3486 of the sink access relation.
3487 The C<isl_access_info_free> function should usually not be
3488 called explicitly, because it is called implicitly by
3489 C<isl_access_info_compute_flow>.
3491 The result of the dependence analysis is collected in an
3492 C<isl_flow>. There may be elements of
3493 the sink access for which no preceding source access could be
3494 found or for which all preceding sources are I<may> accesses.
3495 The relations containing these elements can be obtained through
3496 calls to C<isl_flow_get_no_source>, the first with C<must> set
3497 and the second with C<must> unset.
3498 In the case of standard flow dependence analysis,
3499 with the sink a read and the sources I<must> writes,
3500 the first relation corresponds to the reads from uninitialized
3501 array elements and the second relation is empty.
3502 The actual flow dependences can be extracted using
3503 C<isl_flow_foreach>. This function will call the user-specified
3504 callback function C<fn> for each B<non-empty> dependence between
3505 a source and the sink. The callback function is called
3506 with four arguments, the actual flow dependence relation
3507 mapping source iterations to sink iterations, a boolean that
3508 indicates whether it is a I<must> or I<may> dependence, a token
3509 identifying the source and an additional C<void *> with value
3510 equal to the third argument of the C<isl_flow_foreach> call.
3511 A dependence is marked I<must> if it originates from a I<must>
3512 source and if it is not followed by any I<may> sources.
3514 After finishing with an C<isl_flow>, the user should call
3515 C<isl_flow_free> to free all associated memory.
3517 A higher-level interface to dependence analysis is provided
3518 by the following function.
3520 #include <isl/flow.h>
3522 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3523 __isl_take isl_union_map *must_source,
3524 __isl_take isl_union_map *may_source,
3525 __isl_take isl_union_map *schedule,
3526 __isl_give isl_union_map **must_dep,
3527 __isl_give isl_union_map **may_dep,
3528 __isl_give isl_union_map **must_no_source,
3529 __isl_give isl_union_map **may_no_source);
3531 The arrays are identified by the tuple names of the ranges
3532 of the accesses. The iteration domains by the tuple names
3533 of the domains of the accesses and of the schedule.
3534 The relative order of the iteration domains is given by the
3535 schedule. The relations returned through C<must_no_source>
3536 and C<may_no_source> are subsets of C<sink>.
3537 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3538 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3539 any of the other arguments is treated as an error.
3543 B<The functionality described in this section is fairly new
3544 and may be subject to change.>
3546 The following function can be used to compute a schedule
3547 for a union of domains. The generated schedule respects
3548 all C<validity> dependences. That is, all dependence distances
3549 over these dependences in the scheduled space are lexicographically
3550 positive. The generated schedule schedule also tries to minimize
3551 the dependence distances over C<proximity> dependences.
3552 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3553 for groups of domains where the dependence distances have only
3554 non-negative values.
3555 The algorithm used to construct the schedule is similar to that
3558 #include <isl/schedule.h>
3559 __isl_give isl_schedule *isl_union_set_compute_schedule(
3560 __isl_take isl_union_set *domain,
3561 __isl_take isl_union_map *validity,
3562 __isl_take isl_union_map *proximity);
3563 void *isl_schedule_free(__isl_take isl_schedule *sched);
3565 A mapping from the domains to the scheduled space can be obtained
3566 from an C<isl_schedule> using the following function.
3568 __isl_give isl_union_map *isl_schedule_get_map(
3569 __isl_keep isl_schedule *sched);
3571 A representation of the schedule can be printed using
3573 __isl_give isl_printer *isl_printer_print_schedule(
3574 __isl_take isl_printer *p,
3575 __isl_keep isl_schedule *schedule);
3577 A representation of the schedule as a forest of bands can be obtained
3578 using the following function.
3580 __isl_give isl_band_list *isl_schedule_get_band_forest(
3581 __isl_keep isl_schedule *schedule);
3583 The list can be manipulated as explained in L<"Lists">.
3584 The bands inside the list can be copied and freed using the following
3587 #include <isl/band.h>
3588 __isl_give isl_band *isl_band_copy(
3589 __isl_keep isl_band *band);
3590 void *isl_band_free(__isl_take isl_band *band);
3592 Each band contains zero or more scheduling dimensions.
3593 These are referred to as the members of the band.
3594 The section of the schedule that corresponds to the band is
3595 referred to as the partial schedule of the band.
3596 For those nodes that participate in a band, the outer scheduling
3597 dimensions form the prefix schedule, while the inner scheduling
3598 dimensions form the suffix schedule.
3599 That is, if we take a cut of the band forest, then the union of
3600 the concatenations of the prefix, partial and suffix schedules of
3601 each band in the cut is equal to the entire schedule (modulo
3602 some possible padding at the end with zero scheduling dimensions).
3603 The properties of a band can be inspected using the following functions.
3605 #include <isl/band.h>
3606 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3608 int isl_band_has_children(__isl_keep isl_band *band);
3609 __isl_give isl_band_list *isl_band_get_children(
3610 __isl_keep isl_band *band);
3612 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3613 __isl_keep isl_band *band);
3614 __isl_give isl_union_map *isl_band_get_partial_schedule(
3615 __isl_keep isl_band *band);
3616 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3617 __isl_keep isl_band *band);
3619 int isl_band_n_member(__isl_keep isl_band *band);
3620 int isl_band_member_is_zero_distance(
3621 __isl_keep isl_band *band, int pos);
3623 Note that a scheduling dimension is considered to be ``zero
3624 distance'' if it does not carry any proximity dependences
3626 That is, if the dependence distances of the proximity
3627 dependences are all zero in that direction (for fixed
3628 iterations of outer bands).
3630 A representation of the band can be printed using
3632 #include <isl/band.h>
3633 __isl_give isl_printer *isl_printer_print_band(
3634 __isl_take isl_printer *p,
3635 __isl_keep isl_band *band);
3637 =head2 Parametric Vertex Enumeration
3639 The parametric vertex enumeration described in this section
3640 is mainly intended to be used internally and by the C<barvinok>
3643 #include <isl/vertices.h>
3644 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3645 __isl_keep isl_basic_set *bset);
3647 The function C<isl_basic_set_compute_vertices> performs the
3648 actual computation of the parametric vertices and the chamber
3649 decomposition and store the result in an C<isl_vertices> object.
3650 This information can be queried by either iterating over all
3651 the vertices or iterating over all the chambers or cells
3652 and then iterating over all vertices that are active on the chamber.
3654 int isl_vertices_foreach_vertex(
3655 __isl_keep isl_vertices *vertices,
3656 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3659 int isl_vertices_foreach_cell(
3660 __isl_keep isl_vertices *vertices,
3661 int (*fn)(__isl_take isl_cell *cell, void *user),
3663 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3664 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3667 Other operations that can be performed on an C<isl_vertices> object are
3670 isl_ctx *isl_vertices_get_ctx(
3671 __isl_keep isl_vertices *vertices);
3672 int isl_vertices_get_n_vertices(
3673 __isl_keep isl_vertices *vertices);
3674 void isl_vertices_free(__isl_take isl_vertices *vertices);
3676 Vertices can be inspected and destroyed using the following functions.
3678 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3679 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3680 __isl_give isl_basic_set *isl_vertex_get_domain(
3681 __isl_keep isl_vertex *vertex);
3682 __isl_give isl_basic_set *isl_vertex_get_expr(
3683 __isl_keep isl_vertex *vertex);
3684 void isl_vertex_free(__isl_take isl_vertex *vertex);
3686 C<isl_vertex_get_expr> returns a singleton parametric set describing
3687 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3689 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3690 B<rational> basic sets, so they should mainly be used for inspection
3691 and should not be mixed with integer sets.
3693 Chambers can be inspected and destroyed using the following functions.
3695 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3696 __isl_give isl_basic_set *isl_cell_get_domain(
3697 __isl_keep isl_cell *cell);
3698 void isl_cell_free(__isl_take isl_cell *cell);
3702 Although C<isl> is mainly meant to be used as a library,
3703 it also contains some basic applications that use some
3704 of the functionality of C<isl>.
3705 The input may be specified in either the L<isl format>
3706 or the L<PolyLib format>.
3708 =head2 C<isl_polyhedron_sample>
3710 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3711 an integer element of the polyhedron, if there is any.
3712 The first column in the output is the denominator and is always
3713 equal to 1. If the polyhedron contains no integer points,
3714 then a vector of length zero is printed.
3718 C<isl_pip> takes the same input as the C<example> program
3719 from the C<piplib> distribution, i.e., a set of constraints
3720 on the parameters, a line containing only -1 and finally a set
3721 of constraints on a parametric polyhedron.
3722 The coefficients of the parameters appear in the last columns
3723 (but before the final constant column).
3724 The output is the lexicographic minimum of the parametric polyhedron.
3725 As C<isl> currently does not have its own output format, the output
3726 is just a dump of the internal state.
3728 =head2 C<isl_polyhedron_minimize>
3730 C<isl_polyhedron_minimize> computes the minimum of some linear
3731 or affine objective function over the integer points in a polyhedron.
3732 If an affine objective function
3733 is given, then the constant should appear in the last column.
3735 =head2 C<isl_polytope_scan>
3737 Given a polytope, C<isl_polytope_scan> prints
3738 all integer points in the polytope.