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.
1113 isl_basic_set *bset;
1115 space = isl_space_set_alloc(ctx, 0, 2);
1116 bset = isl_basic_set_universe(isl_space_copy(space));
1118 c = isl_equality_alloc(isl_space_copy(space));
1119 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1120 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1121 bset = isl_basic_set_add_constraint(bset, c);
1123 c = isl_inequality_alloc(isl_space_copy(space));
1124 c = isl_constraint_set_constant_si(c, -10);
1125 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1126 bset = isl_basic_set_add_constraint(bset, c);
1128 c = isl_inequality_alloc(space);
1129 c = isl_constraint_set_constant_si(c, 42);
1130 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1131 bset = isl_basic_set_add_constraint(bset, c);
1133 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1137 isl_basic_set *bset;
1138 bset = isl_basic_set_read_from_str(ctx,
1139 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1141 A basic set or relation can also be constructed from two matrices
1142 describing the equalities and the inequalities.
1144 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1145 __isl_take isl_space *space,
1146 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1147 enum isl_dim_type c1,
1148 enum isl_dim_type c2, enum isl_dim_type c3,
1149 enum isl_dim_type c4);
1150 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1151 __isl_take isl_space *space,
1152 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1153 enum isl_dim_type c1,
1154 enum isl_dim_type c2, enum isl_dim_type c3,
1155 enum isl_dim_type c4, enum isl_dim_type c5);
1157 The C<isl_dim_type> arguments indicate the order in which
1158 different kinds of variables appear in the input matrices
1159 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1160 C<isl_dim_set> and C<isl_dim_div> for sets and
1161 of C<isl_dim_cst>, C<isl_dim_param>,
1162 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1164 A (basic) set or relation can also be constructed from a (piecewise)
1166 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1168 __isl_give isl_basic_map *isl_basic_map_from_aff(
1169 __isl_take isl_aff *aff);
1170 __isl_give isl_set *isl_set_from_pw_aff(
1171 __isl_take isl_pw_aff *pwaff);
1172 __isl_give isl_map *isl_map_from_pw_aff(
1173 __isl_take isl_pw_aff *pwaff);
1174 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1175 __isl_take isl_space *domain_space,
1176 __isl_take isl_aff_list *list);
1178 The C<domain_dim> argument describes the domain of the resulting
1179 basic relation. It is required because the C<list> may consist
1180 of zero affine expressions.
1182 =head2 Inspecting Sets and Relations
1184 Usually, the user should not have to care about the actual constraints
1185 of the sets and maps, but should instead apply the abstract operations
1186 explained in the following sections.
1187 Occasionally, however, it may be required to inspect the individual
1188 coefficients of the constraints. This section explains how to do so.
1189 In these cases, it may also be useful to have C<isl> compute
1190 an explicit representation of the existentially quantified variables.
1192 __isl_give isl_set *isl_set_compute_divs(
1193 __isl_take isl_set *set);
1194 __isl_give isl_map *isl_map_compute_divs(
1195 __isl_take isl_map *map);
1196 __isl_give isl_union_set *isl_union_set_compute_divs(
1197 __isl_take isl_union_set *uset);
1198 __isl_give isl_union_map *isl_union_map_compute_divs(
1199 __isl_take isl_union_map *umap);
1201 This explicit representation defines the existentially quantified
1202 variables as integer divisions of the other variables, possibly
1203 including earlier existentially quantified variables.
1204 An explicitly represented existentially quantified variable therefore
1205 has a unique value when the values of the other variables are known.
1206 If, furthermore, the same existentials, i.e., existentials
1207 with the same explicit representations, should appear in the
1208 same order in each of the disjuncts of a set or map, then the user should call
1209 either of the following functions.
1211 __isl_give isl_set *isl_set_align_divs(
1212 __isl_take isl_set *set);
1213 __isl_give isl_map *isl_map_align_divs(
1214 __isl_take isl_map *map);
1216 Alternatively, the existentially quantified variables can be removed
1217 using the following functions, which compute an overapproximation.
1219 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1220 __isl_take isl_basic_set *bset);
1221 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1222 __isl_take isl_basic_map *bmap);
1223 __isl_give isl_set *isl_set_remove_divs(
1224 __isl_take isl_set *set);
1225 __isl_give isl_map *isl_map_remove_divs(
1226 __isl_take isl_map *map);
1228 To iterate over all the sets or maps in a union set or map, use
1230 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1231 int (*fn)(__isl_take isl_set *set, void *user),
1233 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1234 int (*fn)(__isl_take isl_map *map, void *user),
1237 The number of sets or maps in a union set or map can be obtained
1240 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1241 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1243 To extract the set or map in a given space from a union, use
1245 __isl_give isl_set *isl_union_set_extract_set(
1246 __isl_keep isl_union_set *uset,
1247 __isl_take isl_space *space);
1248 __isl_give isl_map *isl_union_map_extract_map(
1249 __isl_keep isl_union_map *umap,
1250 __isl_take isl_space *space);
1252 To iterate over all the basic sets or maps in a set or map, use
1254 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1255 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1257 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1258 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1261 The callback function C<fn> should return 0 if successful and
1262 -1 if an error occurs. In the latter case, or if any other error
1263 occurs, the above functions will return -1.
1265 It should be noted that C<isl> does not guarantee that
1266 the basic sets or maps passed to C<fn> are disjoint.
1267 If this is required, then the user should call one of
1268 the following functions first.
1270 __isl_give isl_set *isl_set_make_disjoint(
1271 __isl_take isl_set *set);
1272 __isl_give isl_map *isl_map_make_disjoint(
1273 __isl_take isl_map *map);
1275 The number of basic sets in a set can be obtained
1278 int isl_set_n_basic_set(__isl_keep isl_set *set);
1280 To iterate over the constraints of a basic set or map, use
1282 #include <isl/constraint.h>
1284 int isl_basic_map_foreach_constraint(
1285 __isl_keep isl_basic_map *bmap,
1286 int (*fn)(__isl_take isl_constraint *c, void *user),
1288 void *isl_constraint_free(__isl_take isl_constraint *c);
1290 Again, the callback function C<fn> should return 0 if successful and
1291 -1 if an error occurs. In the latter case, or if any other error
1292 occurs, the above functions will return -1.
1293 The constraint C<c> represents either an equality or an inequality.
1294 Use the following function to find out whether a constraint
1295 represents an equality. If not, it represents an inequality.
1297 int isl_constraint_is_equality(
1298 __isl_keep isl_constraint *constraint);
1300 The coefficients of the constraints can be inspected using
1301 the following functions.
1303 void isl_constraint_get_constant(
1304 __isl_keep isl_constraint *constraint, isl_int *v);
1305 void isl_constraint_get_coefficient(
1306 __isl_keep isl_constraint *constraint,
1307 enum isl_dim_type type, int pos, isl_int *v);
1308 int isl_constraint_involves_dims(
1309 __isl_keep isl_constraint *constraint,
1310 enum isl_dim_type type, unsigned first, unsigned n);
1312 The explicit representations of the existentially quantified
1313 variables can be inspected using the following functions.
1314 Note that the user is only allowed to use these functions
1315 if the inspected set or map is the result of a call
1316 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1318 __isl_give isl_div *isl_constraint_div(
1319 __isl_keep isl_constraint *constraint, int pos);
1320 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1321 void isl_div_get_constant(__isl_keep isl_div *div,
1323 void isl_div_get_denominator(__isl_keep isl_div *div,
1325 void isl_div_get_coefficient(__isl_keep isl_div *div,
1326 enum isl_dim_type type, int pos, isl_int *v);
1328 To obtain the constraints of a basic set or map in matrix
1329 form, use the following functions.
1331 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1332 __isl_keep isl_basic_set *bset,
1333 enum isl_dim_type c1, enum isl_dim_type c2,
1334 enum isl_dim_type c3, enum isl_dim_type c4);
1335 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1336 __isl_keep isl_basic_set *bset,
1337 enum isl_dim_type c1, enum isl_dim_type c2,
1338 enum isl_dim_type c3, enum isl_dim_type c4);
1339 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1340 __isl_keep isl_basic_map *bmap,
1341 enum isl_dim_type c1,
1342 enum isl_dim_type c2, enum isl_dim_type c3,
1343 enum isl_dim_type c4, enum isl_dim_type c5);
1344 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1345 __isl_keep isl_basic_map *bmap,
1346 enum isl_dim_type c1,
1347 enum isl_dim_type c2, enum isl_dim_type c3,
1348 enum isl_dim_type c4, enum isl_dim_type c5);
1350 The C<isl_dim_type> arguments dictate the order in which
1351 different kinds of variables appear in the resulting matrix
1352 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1353 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1355 The number of parameters, input, output or set dimensions can
1356 be obtained using the following functions.
1358 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1359 enum isl_dim_type type);
1360 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1361 enum isl_dim_type type);
1362 unsigned isl_set_dim(__isl_keep isl_set *set,
1363 enum isl_dim_type type);
1364 unsigned isl_map_dim(__isl_keep isl_map *map,
1365 enum isl_dim_type type);
1367 To check whether the description of a set or relation depends
1368 on one or more given dimensions, it is not necessary to iterate over all
1369 constraints. Instead the following functions can be used.
1371 int isl_basic_set_involves_dims(
1372 __isl_keep isl_basic_set *bset,
1373 enum isl_dim_type type, unsigned first, unsigned n);
1374 int isl_set_involves_dims(__isl_keep isl_set *set,
1375 enum isl_dim_type type, unsigned first, unsigned n);
1376 int isl_basic_map_involves_dims(
1377 __isl_keep isl_basic_map *bmap,
1378 enum isl_dim_type type, unsigned first, unsigned n);
1379 int isl_map_involves_dims(__isl_keep isl_map *map,
1380 enum isl_dim_type type, unsigned first, unsigned n);
1382 Similarly, the following functions can be used to check whether
1383 a given dimension is involved in any lower or upper bound.
1385 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1386 enum isl_dim_type type, unsigned pos);
1387 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1388 enum isl_dim_type type, unsigned pos);
1390 The identifiers or names of the domain and range spaces of a set
1391 or relation can be read off or set using the following functions.
1393 __isl_give isl_set *isl_set_set_tuple_id(
1394 __isl_take isl_set *set, __isl_take isl_id *id);
1395 __isl_give isl_set *isl_set_reset_tuple_id(
1396 __isl_take isl_set *set);
1397 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1398 __isl_give isl_id *isl_set_get_tuple_id(
1399 __isl_keep isl_set *set);
1400 __isl_give isl_map *isl_map_set_tuple_id(
1401 __isl_take isl_map *map, enum isl_dim_type type,
1402 __isl_take isl_id *id);
1403 __isl_give isl_map *isl_map_reset_tuple_id(
1404 __isl_take isl_map *map, enum isl_dim_type type);
1405 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1406 enum isl_dim_type type);
1407 __isl_give isl_id *isl_map_get_tuple_id(
1408 __isl_keep isl_map *map, enum isl_dim_type type);
1410 const char *isl_basic_set_get_tuple_name(
1411 __isl_keep isl_basic_set *bset);
1412 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1413 __isl_take isl_basic_set *set, const char *s);
1414 const char *isl_set_get_tuple_name(
1415 __isl_keep isl_set *set);
1416 const char *isl_basic_map_get_tuple_name(
1417 __isl_keep isl_basic_map *bmap,
1418 enum isl_dim_type type);
1419 const char *isl_map_get_tuple_name(
1420 __isl_keep isl_map *map,
1421 enum isl_dim_type type);
1423 As with C<isl_space_get_tuple_name>, the value returned points to
1424 an internal data structure.
1425 The identifiers, positions or names of individual dimensions can be
1426 read off using the following functions.
1428 __isl_give isl_set *isl_set_set_dim_id(
1429 __isl_take isl_set *set, enum isl_dim_type type,
1430 unsigned pos, __isl_take isl_id *id);
1431 int isl_set_has_dim_id(__isl_keep isl_set *set,
1432 enum isl_dim_type type, unsigned pos);
1433 __isl_give isl_id *isl_set_get_dim_id(
1434 __isl_keep isl_set *set, enum isl_dim_type type,
1436 __isl_give isl_map *isl_map_set_dim_id(
1437 __isl_take isl_map *map, enum isl_dim_type type,
1438 unsigned pos, __isl_take isl_id *id);
1439 int isl_map_has_dim_id(__isl_keep isl_map *map,
1440 enum isl_dim_type type, unsigned pos);
1441 __isl_give isl_id *isl_map_get_dim_id(
1442 __isl_keep isl_map *map, enum isl_dim_type type,
1445 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1446 enum isl_dim_type type, __isl_keep isl_id *id);
1447 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1448 enum isl_dim_type type, __isl_keep isl_id *id);
1450 const char *isl_constraint_get_dim_name(
1451 __isl_keep isl_constraint *constraint,
1452 enum isl_dim_type type, unsigned pos);
1453 const char *isl_basic_set_get_dim_name(
1454 __isl_keep isl_basic_set *bset,
1455 enum isl_dim_type type, unsigned pos);
1456 const char *isl_set_get_dim_name(
1457 __isl_keep isl_set *set,
1458 enum isl_dim_type type, unsigned pos);
1459 const char *isl_basic_map_get_dim_name(
1460 __isl_keep isl_basic_map *bmap,
1461 enum isl_dim_type type, unsigned pos);
1462 const char *isl_map_get_dim_name(
1463 __isl_keep isl_map *map,
1464 enum isl_dim_type type, unsigned pos);
1466 These functions are mostly useful to obtain the identifiers, positions
1467 or names of the parameters. Identifiers of individual dimensions are
1468 essentially only useful for printing. They are ignored by all other
1469 operations and may not be preserved across those operations.
1473 =head3 Unary Properties
1479 The following functions test whether the given set or relation
1480 contains any integer points. The ``plain'' variants do not perform
1481 any computations, but simply check if the given set or relation
1482 is already known to be empty.
1484 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1485 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1486 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1487 int isl_set_is_empty(__isl_keep isl_set *set);
1488 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1489 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1490 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1491 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1492 int isl_map_is_empty(__isl_keep isl_map *map);
1493 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1495 =item * Universality
1497 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1498 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1499 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1501 =item * Single-valuedness
1503 int isl_map_is_single_valued(__isl_keep isl_map *map);
1504 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1508 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1509 int isl_map_is_injective(__isl_keep isl_map *map);
1510 int isl_union_map_plain_is_injective(
1511 __isl_keep isl_union_map *umap);
1512 int isl_union_map_is_injective(
1513 __isl_keep isl_union_map *umap);
1517 int isl_map_is_bijective(__isl_keep isl_map *map);
1518 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1522 int isl_basic_map_plain_is_fixed(
1523 __isl_keep isl_basic_map *bmap,
1524 enum isl_dim_type type, unsigned pos,
1526 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1527 enum isl_dim_type type, unsigned pos,
1530 Check if the relation obviously lies on a hyperplane where the given dimension
1531 has a fixed value and if so, return that value in C<*val>.
1535 To check whether a set is a parameter domain, use this function:
1537 int isl_set_is_params(__isl_keep isl_set *set);
1541 The following functions check whether the domain of the given
1542 (basic) set is a wrapped relation.
1544 int isl_basic_set_is_wrapping(
1545 __isl_keep isl_basic_set *bset);
1546 int isl_set_is_wrapping(__isl_keep isl_set *set);
1548 =item * Internal Product
1550 int isl_basic_map_can_zip(
1551 __isl_keep isl_basic_map *bmap);
1552 int isl_map_can_zip(__isl_keep isl_map *map);
1554 Check whether the product of domain and range of the given relation
1556 i.e., whether both domain and range are nested relations.
1560 =head3 Binary Properties
1566 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1567 __isl_keep isl_set *set2);
1568 int isl_set_is_equal(__isl_keep isl_set *set1,
1569 __isl_keep isl_set *set2);
1570 int isl_union_set_is_equal(
1571 __isl_keep isl_union_set *uset1,
1572 __isl_keep isl_union_set *uset2);
1573 int isl_basic_map_is_equal(
1574 __isl_keep isl_basic_map *bmap1,
1575 __isl_keep isl_basic_map *bmap2);
1576 int isl_map_is_equal(__isl_keep isl_map *map1,
1577 __isl_keep isl_map *map2);
1578 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1579 __isl_keep isl_map *map2);
1580 int isl_union_map_is_equal(
1581 __isl_keep isl_union_map *umap1,
1582 __isl_keep isl_union_map *umap2);
1584 =item * Disjointness
1586 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1587 __isl_keep isl_set *set2);
1591 int isl_set_is_subset(__isl_keep isl_set *set1,
1592 __isl_keep isl_set *set2);
1593 int isl_set_is_strict_subset(
1594 __isl_keep isl_set *set1,
1595 __isl_keep isl_set *set2);
1596 int isl_union_set_is_subset(
1597 __isl_keep isl_union_set *uset1,
1598 __isl_keep isl_union_set *uset2);
1599 int isl_union_set_is_strict_subset(
1600 __isl_keep isl_union_set *uset1,
1601 __isl_keep isl_union_set *uset2);
1602 int isl_basic_map_is_subset(
1603 __isl_keep isl_basic_map *bmap1,
1604 __isl_keep isl_basic_map *bmap2);
1605 int isl_basic_map_is_strict_subset(
1606 __isl_keep isl_basic_map *bmap1,
1607 __isl_keep isl_basic_map *bmap2);
1608 int isl_map_is_subset(
1609 __isl_keep isl_map *map1,
1610 __isl_keep isl_map *map2);
1611 int isl_map_is_strict_subset(
1612 __isl_keep isl_map *map1,
1613 __isl_keep isl_map *map2);
1614 int isl_union_map_is_subset(
1615 __isl_keep isl_union_map *umap1,
1616 __isl_keep isl_union_map *umap2);
1617 int isl_union_map_is_strict_subset(
1618 __isl_keep isl_union_map *umap1,
1619 __isl_keep isl_union_map *umap2);
1623 =head2 Unary Operations
1629 __isl_give isl_set *isl_set_complement(
1630 __isl_take isl_set *set);
1634 __isl_give isl_basic_map *isl_basic_map_reverse(
1635 __isl_take isl_basic_map *bmap);
1636 __isl_give isl_map *isl_map_reverse(
1637 __isl_take isl_map *map);
1638 __isl_give isl_union_map *isl_union_map_reverse(
1639 __isl_take isl_union_map *umap);
1643 __isl_give isl_basic_set *isl_basic_set_project_out(
1644 __isl_take isl_basic_set *bset,
1645 enum isl_dim_type type, unsigned first, unsigned n);
1646 __isl_give isl_basic_map *isl_basic_map_project_out(
1647 __isl_take isl_basic_map *bmap,
1648 enum isl_dim_type type, unsigned first, unsigned n);
1649 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1650 enum isl_dim_type type, unsigned first, unsigned n);
1651 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1652 enum isl_dim_type type, unsigned first, unsigned n);
1653 __isl_give isl_basic_set *isl_basic_set_params(
1654 __isl_take isl_basic_set *bset);
1655 __isl_give isl_basic_set *isl_basic_map_domain(
1656 __isl_take isl_basic_map *bmap);
1657 __isl_give isl_basic_set *isl_basic_map_range(
1658 __isl_take isl_basic_map *bmap);
1659 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1660 __isl_give isl_set *isl_map_domain(
1661 __isl_take isl_map *bmap);
1662 __isl_give isl_set *isl_map_range(
1663 __isl_take isl_map *map);
1664 __isl_give isl_union_set *isl_union_map_domain(
1665 __isl_take isl_union_map *umap);
1666 __isl_give isl_union_set *isl_union_map_range(
1667 __isl_take isl_union_map *umap);
1669 __isl_give isl_basic_map *isl_basic_map_domain_map(
1670 __isl_take isl_basic_map *bmap);
1671 __isl_give isl_basic_map *isl_basic_map_range_map(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1674 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1675 __isl_give isl_union_map *isl_union_map_domain_map(
1676 __isl_take isl_union_map *umap);
1677 __isl_give isl_union_map *isl_union_map_range_map(
1678 __isl_take isl_union_map *umap);
1680 The functions above construct a (basic, regular or union) relation
1681 that maps (a wrapped version of) the input relation to its domain or range.
1685 __isl_give isl_set *isl_set_eliminate(
1686 __isl_take isl_set *set, enum isl_dim_type type,
1687 unsigned first, unsigned n);
1689 Eliminate the coefficients for the given dimensions from the constraints,
1690 without removing the dimensions.
1694 __isl_give isl_basic_set *isl_basic_set_fix(
1695 __isl_take isl_basic_set *bset,
1696 enum isl_dim_type type, unsigned pos,
1698 __isl_give isl_basic_set *isl_basic_set_fix_si(
1699 __isl_take isl_basic_set *bset,
1700 enum isl_dim_type type, unsigned pos, int value);
1701 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1702 enum isl_dim_type type, unsigned pos,
1704 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1705 enum isl_dim_type type, unsigned pos, int value);
1706 __isl_give isl_basic_map *isl_basic_map_fix_si(
1707 __isl_take isl_basic_map *bmap,
1708 enum isl_dim_type type, unsigned pos, int value);
1709 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1710 enum isl_dim_type type, unsigned pos, int value);
1712 Intersect the set or relation with the hyperplane where the given
1713 dimension has the fixed given value.
1715 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1716 enum isl_dim_type type1, int pos1,
1717 enum isl_dim_type type2, int pos2);
1718 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1719 enum isl_dim_type type1, int pos1,
1720 enum isl_dim_type type2, int pos2);
1722 Intersect the set or relation with the hyperplane where the given
1723 dimensions are equal to each other.
1725 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1726 enum isl_dim_type type1, int pos1,
1727 enum isl_dim_type type2, int pos2);
1729 Intersect the relation with the hyperplane where the given
1730 dimensions have opposite values.
1734 __isl_give isl_map *isl_set_identity(
1735 __isl_take isl_set *set);
1736 __isl_give isl_union_map *isl_union_set_identity(
1737 __isl_take isl_union_set *uset);
1739 Construct an identity relation on the given (union) set.
1743 __isl_give isl_basic_set *isl_basic_map_deltas(
1744 __isl_take isl_basic_map *bmap);
1745 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1746 __isl_give isl_union_set *isl_union_map_deltas(
1747 __isl_take isl_union_map *umap);
1749 These functions return a (basic) set containing the differences
1750 between image elements and corresponding domain elements in the input.
1752 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1753 __isl_take isl_basic_map *bmap);
1754 __isl_give isl_map *isl_map_deltas_map(
1755 __isl_take isl_map *map);
1756 __isl_give isl_union_map *isl_union_map_deltas_map(
1757 __isl_take isl_union_map *umap);
1759 The functions above construct a (basic, regular or union) relation
1760 that maps (a wrapped version of) the input relation to its delta set.
1764 Simplify the representation of a set or relation by trying
1765 to combine pairs of basic sets or relations into a single
1766 basic set or relation.
1768 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1769 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1770 __isl_give isl_union_set *isl_union_set_coalesce(
1771 __isl_take isl_union_set *uset);
1772 __isl_give isl_union_map *isl_union_map_coalesce(
1773 __isl_take isl_union_map *umap);
1775 =item * Detecting equalities
1777 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1778 __isl_take isl_basic_set *bset);
1779 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1780 __isl_take isl_basic_map *bmap);
1781 __isl_give isl_set *isl_set_detect_equalities(
1782 __isl_take isl_set *set);
1783 __isl_give isl_map *isl_map_detect_equalities(
1784 __isl_take isl_map *map);
1785 __isl_give isl_union_set *isl_union_set_detect_equalities(
1786 __isl_take isl_union_set *uset);
1787 __isl_give isl_union_map *isl_union_map_detect_equalities(
1788 __isl_take isl_union_map *umap);
1790 Simplify the representation of a set or relation by detecting implicit
1793 =item * Removing redundant constraints
1795 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1796 __isl_take isl_basic_set *bset);
1797 __isl_give isl_set *isl_set_remove_redundancies(
1798 __isl_take isl_set *set);
1799 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_map *isl_map_remove_redundancies(
1802 __isl_take isl_map *map);
1806 __isl_give isl_basic_set *isl_set_convex_hull(
1807 __isl_take isl_set *set);
1808 __isl_give isl_basic_map *isl_map_convex_hull(
1809 __isl_take isl_map *map);
1811 If the input set or relation has any existentially quantified
1812 variables, then the result of these operations is currently undefined.
1816 __isl_give isl_basic_set *isl_set_simple_hull(
1817 __isl_take isl_set *set);
1818 __isl_give isl_basic_map *isl_map_simple_hull(
1819 __isl_take isl_map *map);
1820 __isl_give isl_union_map *isl_union_map_simple_hull(
1821 __isl_take isl_union_map *umap);
1823 These functions compute a single basic set or relation
1824 that contains the whole input set or relation.
1825 In particular, the output is described by translates
1826 of the constraints describing the basic sets or relations in the input.
1830 (See \autoref{s:simple hull}.)
1836 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1837 __isl_take isl_basic_set *bset);
1838 __isl_give isl_basic_set *isl_set_affine_hull(
1839 __isl_take isl_set *set);
1840 __isl_give isl_union_set *isl_union_set_affine_hull(
1841 __isl_take isl_union_set *uset);
1842 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1843 __isl_take isl_basic_map *bmap);
1844 __isl_give isl_basic_map *isl_map_affine_hull(
1845 __isl_take isl_map *map);
1846 __isl_give isl_union_map *isl_union_map_affine_hull(
1847 __isl_take isl_union_map *umap);
1849 In case of union sets and relations, the affine hull is computed
1852 =item * Polyhedral hull
1854 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1855 __isl_take isl_set *set);
1856 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1857 __isl_take isl_map *map);
1858 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1859 __isl_take isl_union_set *uset);
1860 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1861 __isl_take isl_union_map *umap);
1863 These functions compute a single basic set or relation
1864 not involving any existentially quantified variables
1865 that contains the whole input set or relation.
1866 In case of union sets and relations, the polyhedral hull is computed
1869 =item * Optimization
1871 #include <isl/ilp.h>
1872 enum isl_lp_result isl_basic_set_max(
1873 __isl_keep isl_basic_set *bset,
1874 __isl_keep isl_aff *obj, isl_int *opt)
1875 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1876 __isl_keep isl_aff *obj, isl_int *opt);
1877 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1878 __isl_keep isl_aff *obj, isl_int *opt);
1880 Compute the minimum or maximum of the integer affine expression C<obj>
1881 over the points in C<set>, returning the result in C<opt>.
1882 The return value may be one of C<isl_lp_error>,
1883 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1885 =item * Parametric optimization
1887 __isl_give isl_pw_aff *isl_set_dim_min(
1888 __isl_take isl_set *set, int pos);
1889 __isl_give isl_pw_aff *isl_set_dim_max(
1890 __isl_take isl_set *set, int pos);
1892 Compute the minimum or maximum of the given set dimension as a function of the
1893 parameters, but independently of the other set dimensions.
1894 For lexicographic optimization, see L<"Lexicographic Optimization">.
1898 The following functions compute either the set of (rational) coefficient
1899 values of valid constraints for the given set or the set of (rational)
1900 values satisfying the constraints with coefficients from the given set.
1901 Internally, these two sets of functions perform essentially the
1902 same operations, except that the set of coefficients is assumed to
1903 be a cone, while the set of values may be any polyhedron.
1904 The current implementation is based on the Farkas lemma and
1905 Fourier-Motzkin elimination, but this may change or be made optional
1906 in future. In particular, future implementations may use different
1907 dualization algorithms or skip the elimination step.
1909 __isl_give isl_basic_set *isl_basic_set_coefficients(
1910 __isl_take isl_basic_set *bset);
1911 __isl_give isl_basic_set *isl_set_coefficients(
1912 __isl_take isl_set *set);
1913 __isl_give isl_union_set *isl_union_set_coefficients(
1914 __isl_take isl_union_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_solutions(
1916 __isl_take isl_basic_set *bset);
1917 __isl_give isl_basic_set *isl_set_solutions(
1918 __isl_take isl_set *set);
1919 __isl_give isl_union_set *isl_union_set_solutions(
1920 __isl_take isl_union_set *bset);
1924 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1926 __isl_give isl_union_map *isl_union_map_power(
1927 __isl_take isl_union_map *umap, int *exact);
1929 Compute a parametric representation for all positive powers I<k> of C<map>.
1930 The result maps I<k> to a nested relation corresponding to the
1931 I<k>th power of C<map>.
1932 The result may be an overapproximation. If the result is known to be exact,
1933 then C<*exact> is set to C<1>.
1935 =item * Transitive closure
1937 __isl_give isl_map *isl_map_transitive_closure(
1938 __isl_take isl_map *map, int *exact);
1939 __isl_give isl_union_map *isl_union_map_transitive_closure(
1940 __isl_take isl_union_map *umap, int *exact);
1942 Compute the transitive closure of C<map>.
1943 The result may be an overapproximation. If the result is known to be exact,
1944 then C<*exact> is set to C<1>.
1946 =item * Reaching path lengths
1948 __isl_give isl_map *isl_map_reaching_path_lengths(
1949 __isl_take isl_map *map, int *exact);
1951 Compute a relation that maps each element in the range of C<map>
1952 to the lengths of all paths composed of edges in C<map> that
1953 end up in the given element.
1954 The result may be an overapproximation. If the result is known to be exact,
1955 then C<*exact> is set to C<1>.
1956 To compute the I<maximal> path length, the resulting relation
1957 should be postprocessed by C<isl_map_lexmax>.
1958 In particular, if the input relation is a dependence relation
1959 (mapping sources to sinks), then the maximal path length corresponds
1960 to the free schedule.
1961 Note, however, that C<isl_map_lexmax> expects the maximum to be
1962 finite, so if the path lengths are unbounded (possibly due to
1963 the overapproximation), then you will get an error message.
1967 __isl_give isl_basic_set *isl_basic_map_wrap(
1968 __isl_take isl_basic_map *bmap);
1969 __isl_give isl_set *isl_map_wrap(
1970 __isl_take isl_map *map);
1971 __isl_give isl_union_set *isl_union_map_wrap(
1972 __isl_take isl_union_map *umap);
1973 __isl_give isl_basic_map *isl_basic_set_unwrap(
1974 __isl_take isl_basic_set *bset);
1975 __isl_give isl_map *isl_set_unwrap(
1976 __isl_take isl_set *set);
1977 __isl_give isl_union_map *isl_union_set_unwrap(
1978 __isl_take isl_union_set *uset);
1982 Remove any internal structure of domain (and range) of the given
1983 set or relation. If there is any such internal structure in the input,
1984 then the name of the space is also removed.
1986 __isl_give isl_basic_set *isl_basic_set_flatten(
1987 __isl_take isl_basic_set *bset);
1988 __isl_give isl_set *isl_set_flatten(
1989 __isl_take isl_set *set);
1990 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1993 __isl_take isl_basic_map *bmap);
1994 __isl_give isl_map *isl_map_flatten_range(
1995 __isl_take isl_map *map);
1996 __isl_give isl_map *isl_map_flatten_domain(
1997 __isl_take isl_map *map);
1998 __isl_give isl_basic_map *isl_basic_map_flatten(
1999 __isl_take isl_basic_map *bmap);
2000 __isl_give isl_map *isl_map_flatten(
2001 __isl_take isl_map *map);
2003 __isl_give isl_map *isl_set_flatten_map(
2004 __isl_take isl_set *set);
2006 The function above constructs a relation
2007 that maps the input set to a flattened version of the set.
2011 Lift the input set to a space with extra dimensions corresponding
2012 to the existentially quantified variables in the input.
2013 In particular, the result lives in a wrapped map where the domain
2014 is the original space and the range corresponds to the original
2015 existentially quantified variables.
2017 __isl_give isl_basic_set *isl_basic_set_lift(
2018 __isl_take isl_basic_set *bset);
2019 __isl_give isl_set *isl_set_lift(
2020 __isl_take isl_set *set);
2021 __isl_give isl_union_set *isl_union_set_lift(
2022 __isl_take isl_union_set *uset);
2024 =item * Internal Product
2026 __isl_give isl_basic_map *isl_basic_map_zip(
2027 __isl_take isl_basic_map *bmap);
2028 __isl_give isl_map *isl_map_zip(
2029 __isl_take isl_map *map);
2030 __isl_give isl_union_map *isl_union_map_zip(
2031 __isl_take isl_union_map *umap);
2033 Given a relation with nested relations for domain and range,
2034 interchange the range of the domain with the domain of the range.
2036 =item * Aligning parameters
2038 __isl_give isl_set *isl_set_align_params(
2039 __isl_take isl_set *set,
2040 __isl_take isl_space *model);
2041 __isl_give isl_map *isl_map_align_params(
2042 __isl_take isl_map *map,
2043 __isl_take isl_space *model);
2045 Change the order of the parameters of the given set or relation
2046 such that the first parameters match those of C<model>.
2047 This may involve the introduction of extra parameters.
2048 All parameters need to be named.
2050 =item * Dimension manipulation
2052 __isl_give isl_set *isl_set_add_dims(
2053 __isl_take isl_set *set,
2054 enum isl_dim_type type, unsigned n);
2055 __isl_give isl_map *isl_map_add_dims(
2056 __isl_take isl_map *map,
2057 enum isl_dim_type type, unsigned n);
2058 __isl_give isl_set *isl_set_insert_dims(
2059 __isl_take isl_set *set,
2060 enum isl_dim_type type, unsigned pos, unsigned n);
2061 __isl_give isl_map *isl_map_insert_dims(
2062 __isl_take isl_map *map,
2063 enum isl_dim_type type, unsigned pos, unsigned n);
2065 It is usually not advisable to directly change the (input or output)
2066 space of a set or a relation as this removes the name and the internal
2067 structure of the space. However, the above functions can be useful
2068 to add new parameters, assuming
2069 C<isl_set_align_params> and C<isl_map_align_params>
2074 =head2 Binary Operations
2076 The two arguments of a binary operation not only need to live
2077 in the same C<isl_ctx>, they currently also need to have
2078 the same (number of) parameters.
2080 =head3 Basic Operations
2084 =item * Intersection
2086 __isl_give isl_basic_set *isl_basic_set_intersect(
2087 __isl_take isl_basic_set *bset1,
2088 __isl_take isl_basic_set *bset2);
2089 __isl_give isl_set *isl_set_intersect_params(
2090 __isl_take isl_set *set,
2091 __isl_take isl_set *params);
2092 __isl_give isl_set *isl_set_intersect(
2093 __isl_take isl_set *set1,
2094 __isl_take isl_set *set2);
2095 __isl_give isl_union_set *isl_union_set_intersect(
2096 __isl_take isl_union_set *uset1,
2097 __isl_take isl_union_set *uset2);
2098 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2099 __isl_take isl_basic_map *bmap,
2100 __isl_take isl_basic_set *bset);
2101 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2102 __isl_take isl_basic_map *bmap,
2103 __isl_take isl_basic_set *bset);
2104 __isl_give isl_basic_map *isl_basic_map_intersect(
2105 __isl_take isl_basic_map *bmap1,
2106 __isl_take isl_basic_map *bmap2);
2107 __isl_give isl_map *isl_map_intersect_params(
2108 __isl_take isl_map *map,
2109 __isl_take isl_set *params);
2110 __isl_give isl_map *isl_map_intersect_domain(
2111 __isl_take isl_map *map,
2112 __isl_take isl_set *set);
2113 __isl_give isl_map *isl_map_intersect_range(
2114 __isl_take isl_map *map,
2115 __isl_take isl_set *set);
2116 __isl_give isl_map *isl_map_intersect(
2117 __isl_take isl_map *map1,
2118 __isl_take isl_map *map2);
2119 __isl_give isl_union_map *isl_union_map_intersect_domain(
2120 __isl_take isl_union_map *umap,
2121 __isl_take isl_union_set *uset);
2122 __isl_give isl_union_map *isl_union_map_intersect_range(
2123 __isl_take isl_union_map *umap,
2124 __isl_take isl_union_set *uset);
2125 __isl_give isl_union_map *isl_union_map_intersect(
2126 __isl_take isl_union_map *umap1,
2127 __isl_take isl_union_map *umap2);
2131 __isl_give isl_set *isl_basic_set_union(
2132 __isl_take isl_basic_set *bset1,
2133 __isl_take isl_basic_set *bset2);
2134 __isl_give isl_map *isl_basic_map_union(
2135 __isl_take isl_basic_map *bmap1,
2136 __isl_take isl_basic_map *bmap2);
2137 __isl_give isl_set *isl_set_union(
2138 __isl_take isl_set *set1,
2139 __isl_take isl_set *set2);
2140 __isl_give isl_map *isl_map_union(
2141 __isl_take isl_map *map1,
2142 __isl_take isl_map *map2);
2143 __isl_give isl_union_set *isl_union_set_union(
2144 __isl_take isl_union_set *uset1,
2145 __isl_take isl_union_set *uset2);
2146 __isl_give isl_union_map *isl_union_map_union(
2147 __isl_take isl_union_map *umap1,
2148 __isl_take isl_union_map *umap2);
2150 =item * Set difference
2152 __isl_give isl_set *isl_set_subtract(
2153 __isl_take isl_set *set1,
2154 __isl_take isl_set *set2);
2155 __isl_give isl_map *isl_map_subtract(
2156 __isl_take isl_map *map1,
2157 __isl_take isl_map *map2);
2158 __isl_give isl_union_set *isl_union_set_subtract(
2159 __isl_take isl_union_set *uset1,
2160 __isl_take isl_union_set *uset2);
2161 __isl_give isl_union_map *isl_union_map_subtract(
2162 __isl_take isl_union_map *umap1,
2163 __isl_take isl_union_map *umap2);
2167 __isl_give isl_basic_set *isl_basic_set_apply(
2168 __isl_take isl_basic_set *bset,
2169 __isl_take isl_basic_map *bmap);
2170 __isl_give isl_set *isl_set_apply(
2171 __isl_take isl_set *set,
2172 __isl_take isl_map *map);
2173 __isl_give isl_union_set *isl_union_set_apply(
2174 __isl_take isl_union_set *uset,
2175 __isl_take isl_union_map *umap);
2176 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2177 __isl_take isl_basic_map *bmap1,
2178 __isl_take isl_basic_map *bmap2);
2179 __isl_give isl_basic_map *isl_basic_map_apply_range(
2180 __isl_take isl_basic_map *bmap1,
2181 __isl_take isl_basic_map *bmap2);
2182 __isl_give isl_map *isl_map_apply_domain(
2183 __isl_take isl_map *map1,
2184 __isl_take isl_map *map2);
2185 __isl_give isl_union_map *isl_union_map_apply_domain(
2186 __isl_take isl_union_map *umap1,
2187 __isl_take isl_union_map *umap2);
2188 __isl_give isl_map *isl_map_apply_range(
2189 __isl_take isl_map *map1,
2190 __isl_take isl_map *map2);
2191 __isl_give isl_union_map *isl_union_map_apply_range(
2192 __isl_take isl_union_map *umap1,
2193 __isl_take isl_union_map *umap2);
2195 =item * Cartesian Product
2197 __isl_give isl_set *isl_set_product(
2198 __isl_take isl_set *set1,
2199 __isl_take isl_set *set2);
2200 __isl_give isl_union_set *isl_union_set_product(
2201 __isl_take isl_union_set *uset1,
2202 __isl_take isl_union_set *uset2);
2203 __isl_give isl_basic_map *isl_basic_map_domain_product(
2204 __isl_take isl_basic_map *bmap1,
2205 __isl_take isl_basic_map *bmap2);
2206 __isl_give isl_basic_map *isl_basic_map_range_product(
2207 __isl_take isl_basic_map *bmap1,
2208 __isl_take isl_basic_map *bmap2);
2209 __isl_give isl_map *isl_map_domain_product(
2210 __isl_take isl_map *map1,
2211 __isl_take isl_map *map2);
2212 __isl_give isl_map *isl_map_range_product(
2213 __isl_take isl_map *map1,
2214 __isl_take isl_map *map2);
2215 __isl_give isl_union_map *isl_union_map_range_product(
2216 __isl_take isl_union_map *umap1,
2217 __isl_take isl_union_map *umap2);
2218 __isl_give isl_map *isl_map_product(
2219 __isl_take isl_map *map1,
2220 __isl_take isl_map *map2);
2221 __isl_give isl_union_map *isl_union_map_product(
2222 __isl_take isl_union_map *umap1,
2223 __isl_take isl_union_map *umap2);
2225 The above functions compute the cross product of the given
2226 sets or relations. The domains and ranges of the results
2227 are wrapped maps between domains and ranges of the inputs.
2228 To obtain a ``flat'' product, use the following functions
2231 __isl_give isl_basic_set *isl_basic_set_flat_product(
2232 __isl_take isl_basic_set *bset1,
2233 __isl_take isl_basic_set *bset2);
2234 __isl_give isl_set *isl_set_flat_product(
2235 __isl_take isl_set *set1,
2236 __isl_take isl_set *set2);
2237 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2238 __isl_take isl_basic_map *bmap1,
2239 __isl_take isl_basic_map *bmap2);
2240 __isl_give isl_map *isl_map_flat_domain_product(
2241 __isl_take isl_map *map1,
2242 __isl_take isl_map *map2);
2243 __isl_give isl_map *isl_map_flat_range_product(
2244 __isl_take isl_map *map1,
2245 __isl_take isl_map *map2);
2246 __isl_give isl_union_map *isl_union_map_flat_range_product(
2247 __isl_take isl_union_map *umap1,
2248 __isl_take isl_union_map *umap2);
2249 __isl_give isl_basic_map *isl_basic_map_flat_product(
2250 __isl_take isl_basic_map *bmap1,
2251 __isl_take isl_basic_map *bmap2);
2252 __isl_give isl_map *isl_map_flat_product(
2253 __isl_take isl_map *map1,
2254 __isl_take isl_map *map2);
2256 =item * Simplification
2258 __isl_give isl_basic_set *isl_basic_set_gist(
2259 __isl_take isl_basic_set *bset,
2260 __isl_take isl_basic_set *context);
2261 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2262 __isl_take isl_set *context);
2263 __isl_give isl_set *isl_set_gist_params(
2264 __isl_take isl_set *set,
2265 __isl_take isl_set *context);
2266 __isl_give isl_union_set *isl_union_set_gist(
2267 __isl_take isl_union_set *uset,
2268 __isl_take isl_union_set *context);
2269 __isl_give isl_basic_map *isl_basic_map_gist(
2270 __isl_take isl_basic_map *bmap,
2271 __isl_take isl_basic_map *context);
2272 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2273 __isl_take isl_map *context);
2274 __isl_give isl_map *isl_map_gist_params(
2275 __isl_take isl_map *map,
2276 __isl_take isl_set *context);
2277 __isl_give isl_union_map *isl_union_map_gist(
2278 __isl_take isl_union_map *umap,
2279 __isl_take isl_union_map *context);
2281 The gist operation returns a set or relation that has the
2282 same intersection with the context as the input set or relation.
2283 Any implicit equality in the intersection is made explicit in the result,
2284 while all inequalities that are redundant with respect to the intersection
2286 In case of union sets and relations, the gist operation is performed
2291 =head3 Lexicographic Optimization
2293 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2294 the following functions
2295 compute a set that contains the lexicographic minimum or maximum
2296 of the elements in C<set> (or C<bset>) for those values of the parameters
2297 that satisfy C<dom>.
2298 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2299 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2301 In other words, the union of the parameter values
2302 for which the result is non-empty and of C<*empty>
2305 __isl_give isl_set *isl_basic_set_partial_lexmin(
2306 __isl_take isl_basic_set *bset,
2307 __isl_take isl_basic_set *dom,
2308 __isl_give isl_set **empty);
2309 __isl_give isl_set *isl_basic_set_partial_lexmax(
2310 __isl_take isl_basic_set *bset,
2311 __isl_take isl_basic_set *dom,
2312 __isl_give isl_set **empty);
2313 __isl_give isl_set *isl_set_partial_lexmin(
2314 __isl_take isl_set *set, __isl_take isl_set *dom,
2315 __isl_give isl_set **empty);
2316 __isl_give isl_set *isl_set_partial_lexmax(
2317 __isl_take isl_set *set, __isl_take isl_set *dom,
2318 __isl_give isl_set **empty);
2320 Given a (basic) set C<set> (or C<bset>), the following functions simply
2321 return a set containing the lexicographic minimum or maximum
2322 of the elements in C<set> (or C<bset>).
2323 In case of union sets, the optimum is computed per space.
2325 __isl_give isl_set *isl_basic_set_lexmin(
2326 __isl_take isl_basic_set *bset);
2327 __isl_give isl_set *isl_basic_set_lexmax(
2328 __isl_take isl_basic_set *bset);
2329 __isl_give isl_set *isl_set_lexmin(
2330 __isl_take isl_set *set);
2331 __isl_give isl_set *isl_set_lexmax(
2332 __isl_take isl_set *set);
2333 __isl_give isl_union_set *isl_union_set_lexmin(
2334 __isl_take isl_union_set *uset);
2335 __isl_give isl_union_set *isl_union_set_lexmax(
2336 __isl_take isl_union_set *uset);
2338 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2339 the following functions
2340 compute a relation that maps each element of C<dom>
2341 to the single lexicographic minimum or maximum
2342 of the elements that are associated to that same
2343 element in C<map> (or C<bmap>).
2344 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2345 that contains the elements in C<dom> that do not map
2346 to any elements in C<map> (or C<bmap>).
2347 In other words, the union of the domain of the result and of C<*empty>
2350 __isl_give isl_map *isl_basic_map_partial_lexmax(
2351 __isl_take isl_basic_map *bmap,
2352 __isl_take isl_basic_set *dom,
2353 __isl_give isl_set **empty);
2354 __isl_give isl_map *isl_basic_map_partial_lexmin(
2355 __isl_take isl_basic_map *bmap,
2356 __isl_take isl_basic_set *dom,
2357 __isl_give isl_set **empty);
2358 __isl_give isl_map *isl_map_partial_lexmax(
2359 __isl_take isl_map *map, __isl_take isl_set *dom,
2360 __isl_give isl_set **empty);
2361 __isl_give isl_map *isl_map_partial_lexmin(
2362 __isl_take isl_map *map, __isl_take isl_set *dom,
2363 __isl_give isl_set **empty);
2365 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2366 return a map mapping each element in the domain of
2367 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2368 of all elements associated to that element.
2369 In case of union relations, the optimum is computed per space.
2371 __isl_give isl_map *isl_basic_map_lexmin(
2372 __isl_take isl_basic_map *bmap);
2373 __isl_give isl_map *isl_basic_map_lexmax(
2374 __isl_take isl_basic_map *bmap);
2375 __isl_give isl_map *isl_map_lexmin(
2376 __isl_take isl_map *map);
2377 __isl_give isl_map *isl_map_lexmax(
2378 __isl_take isl_map *map);
2379 __isl_give isl_union_map *isl_union_map_lexmin(
2380 __isl_take isl_union_map *umap);
2381 __isl_give isl_union_map *isl_union_map_lexmax(
2382 __isl_take isl_union_map *umap);
2386 Lists are defined over several element types, including
2387 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2388 Here we take lists of C<isl_set>s as an example.
2389 Lists can be created, copied and freed using the following functions.
2391 #include <isl/list.h>
2392 __isl_give isl_set_list *isl_set_list_from_set(
2393 __isl_take isl_set *el);
2394 __isl_give isl_set_list *isl_set_list_alloc(
2395 isl_ctx *ctx, int n);
2396 __isl_give isl_set_list *isl_set_list_copy(
2397 __isl_keep isl_set_list *list);
2398 __isl_give isl_set_list *isl_set_list_add(
2399 __isl_take isl_set_list *list,
2400 __isl_take isl_set *el);
2401 __isl_give isl_set_list *isl_set_list_concat(
2402 __isl_take isl_set_list *list1,
2403 __isl_take isl_set_list *list2);
2404 void *isl_set_list_free(__isl_take isl_set_list *list);
2406 C<isl_set_list_alloc> creates an empty list with a capacity for
2407 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2410 Lists can be inspected using the following functions.
2412 #include <isl/list.h>
2413 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2414 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2415 __isl_give isl_set *isl_set_list_get_set(
2416 __isl_keep isl_set_list *list, int index);
2417 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2418 int (*fn)(__isl_take isl_set *el, void *user),
2421 Lists can be printed using
2423 #include <isl/list.h>
2424 __isl_give isl_printer *isl_printer_print_set_list(
2425 __isl_take isl_printer *p,
2426 __isl_keep isl_set_list *list);
2430 Matrices can be created, copied and freed using the following functions.
2432 #include <isl/mat.h>
2433 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2434 unsigned n_row, unsigned n_col);
2435 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2436 void isl_mat_free(__isl_take isl_mat *mat);
2438 Note that the elements of a newly created matrix may have arbitrary values.
2439 The elements can be changed and inspected using the following functions.
2441 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2442 int isl_mat_rows(__isl_keep isl_mat *mat);
2443 int isl_mat_cols(__isl_keep isl_mat *mat);
2444 int isl_mat_get_element(__isl_keep isl_mat *mat,
2445 int row, int col, isl_int *v);
2446 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2447 int row, int col, isl_int v);
2448 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2449 int row, int col, int v);
2451 C<isl_mat_get_element> will return a negative value if anything went wrong.
2452 In that case, the value of C<*v> is undefined.
2454 The following function can be used to compute the (right) inverse
2455 of a matrix, i.e., a matrix such that the product of the original
2456 and the inverse (in that order) is a multiple of the identity matrix.
2457 The input matrix is assumed to be of full row-rank.
2459 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2461 The following function can be used to compute the (right) kernel
2462 (or null space) of a matrix, i.e., a matrix such that the product of
2463 the original and the kernel (in that order) is the zero matrix.
2465 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2467 =head2 Piecewise Quasi Affine Expressions
2469 The zero quasi affine expression on a given domain can be created using
2471 __isl_give isl_aff *isl_aff_zero_on_domain(
2472 __isl_take isl_local_space *ls);
2474 Note that the space in which the resulting object lives is a map space
2475 with the given space as domain and a one-dimensional range.
2477 A quasi affine expression can also be initialized from an C<isl_div>:
2479 #include <isl/div.h>
2480 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2482 An empty piecewise quasi affine expression (one with no cells)
2483 or a piecewise quasi affine expression with a single cell can
2484 be created using the following functions.
2486 #include <isl/aff.h>
2487 __isl_give isl_pw_aff *isl_pw_aff_empty(
2488 __isl_take isl_space *space);
2489 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2490 __isl_take isl_set *set, __isl_take isl_aff *aff);
2491 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2492 __isl_take isl_aff *aff);
2494 Quasi affine expressions can be copied and freed using
2496 #include <isl/aff.h>
2497 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2498 void *isl_aff_free(__isl_take isl_aff *aff);
2500 __isl_give isl_pw_aff *isl_pw_aff_copy(
2501 __isl_keep isl_pw_aff *pwaff);
2502 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2504 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2505 using the following function. The constraint is required to have
2506 a non-zero coefficient for the specified dimension.
2508 #include <isl/constraint.h>
2509 __isl_give isl_aff *isl_constraint_get_bound(
2510 __isl_keep isl_constraint *constraint,
2511 enum isl_dim_type type, int pos);
2513 The entire affine expression of the constraint can also be extracted
2514 using the following function.
2516 #include <isl/constraint.h>
2517 __isl_give isl_aff *isl_constraint_get_aff(
2518 __isl_keep isl_constraint *constraint);
2520 Conversely, an equality constraint equating
2521 the affine expression to zero or an inequality constraint enforcing
2522 the affine expression to be non-negative, can be constructed using
2524 __isl_give isl_constraint *isl_equality_from_aff(
2525 __isl_take isl_aff *aff);
2526 __isl_give isl_constraint *isl_inequality_from_aff(
2527 __isl_take isl_aff *aff);
2529 The expression can be inspected using
2531 #include <isl/aff.h>
2532 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2533 int isl_aff_dim(__isl_keep isl_aff *aff,
2534 enum isl_dim_type type);
2535 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2536 __isl_keep isl_aff *aff);
2537 __isl_give isl_local_space *isl_aff_get_local_space(
2538 __isl_keep isl_aff *aff);
2539 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2540 enum isl_dim_type type, unsigned pos);
2541 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2543 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2544 enum isl_dim_type type, int pos, isl_int *v);
2545 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2547 __isl_give isl_div *isl_aff_get_div(
2548 __isl_keep isl_aff *aff, int pos);
2550 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2551 int (*fn)(__isl_take isl_set *set,
2552 __isl_take isl_aff *aff,
2553 void *user), void *user);
2555 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2556 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2558 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2559 enum isl_dim_type type, unsigned first, unsigned n);
2560 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2561 enum isl_dim_type type, unsigned first, unsigned n);
2563 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2564 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2565 enum isl_dim_type type);
2566 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2568 It can be modified using
2570 #include <isl/aff.h>
2571 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2572 __isl_take isl_pw_aff *pwaff,
2573 __isl_take isl_id *id);
2574 __isl_give isl_aff *isl_aff_set_dim_name(
2575 __isl_take isl_aff *aff, enum isl_dim_type type,
2576 unsigned pos, const char *s);
2577 __isl_give isl_aff *isl_aff_set_constant(
2578 __isl_take isl_aff *aff, isl_int v);
2579 __isl_give isl_aff *isl_aff_set_constant_si(
2580 __isl_take isl_aff *aff, int v);
2581 __isl_give isl_aff *isl_aff_set_coefficient(
2582 __isl_take isl_aff *aff,
2583 enum isl_dim_type type, int pos, isl_int v);
2584 __isl_give isl_aff *isl_aff_set_coefficient_si(
2585 __isl_take isl_aff *aff,
2586 enum isl_dim_type type, int pos, int v);
2587 __isl_give isl_aff *isl_aff_set_denominator(
2588 __isl_take isl_aff *aff, isl_int v);
2590 __isl_give isl_aff *isl_aff_add_constant(
2591 __isl_take isl_aff *aff, isl_int v);
2592 __isl_give isl_aff *isl_aff_add_constant_si(
2593 __isl_take isl_aff *aff, int v);
2594 __isl_give isl_aff *isl_aff_add_coefficient(
2595 __isl_take isl_aff *aff,
2596 enum isl_dim_type type, int pos, isl_int v);
2597 __isl_give isl_aff *isl_aff_add_coefficient_si(
2598 __isl_take isl_aff *aff,
2599 enum isl_dim_type type, int pos, int v);
2601 __isl_give isl_aff *isl_aff_insert_dims(
2602 __isl_take isl_aff *aff,
2603 enum isl_dim_type type, unsigned first, unsigned n);
2604 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2605 __isl_take isl_pw_aff *pwaff,
2606 enum isl_dim_type type, unsigned first, unsigned n);
2607 __isl_give isl_aff *isl_aff_add_dims(
2608 __isl_take isl_aff *aff,
2609 enum isl_dim_type type, unsigned n);
2610 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2611 __isl_take isl_pw_aff *pwaff,
2612 enum isl_dim_type type, unsigned n);
2613 __isl_give isl_aff *isl_aff_drop_dims(
2614 __isl_take isl_aff *aff,
2615 enum isl_dim_type type, unsigned first, unsigned n);
2616 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2617 __isl_take isl_pw_aff *pwaff,
2618 enum isl_dim_type type, unsigned first, unsigned n);
2620 Note that the C<set_constant> and C<set_coefficient> functions
2621 set the I<numerator> of the constant or coefficient, while
2622 C<add_constant> and C<add_coefficient> add an integer value to
2623 the possibly rational constant or coefficient.
2625 To check whether an affine expressions is obviously zero
2626 or obviously equal to some other affine expression, use
2628 #include <isl/aff.h>
2629 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2630 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2631 __isl_keep isl_aff *aff2);
2635 #include <isl/aff.h>
2636 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2637 __isl_take isl_aff *aff2);
2638 __isl_give isl_pw_aff *isl_pw_aff_add(
2639 __isl_take isl_pw_aff *pwaff1,
2640 __isl_take isl_pw_aff *pwaff2);
2641 __isl_give isl_pw_aff *isl_pw_aff_min(
2642 __isl_take isl_pw_aff *pwaff1,
2643 __isl_take isl_pw_aff *pwaff2);
2644 __isl_give isl_pw_aff *isl_pw_aff_max(
2645 __isl_take isl_pw_aff *pwaff1,
2646 __isl_take isl_pw_aff *pwaff2);
2647 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2648 __isl_take isl_aff *aff2);
2649 __isl_give isl_pw_aff *isl_pw_aff_sub(
2650 __isl_take isl_pw_aff *pwaff1,
2651 __isl_take isl_pw_aff *pwaff2);
2652 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2653 __isl_give isl_pw_aff *isl_pw_aff_neg(
2654 __isl_take isl_pw_aff *pwaff);
2655 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2656 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2657 __isl_take isl_pw_aff *pwaff);
2658 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2659 __isl_give isl_pw_aff *isl_pw_aff_floor(
2660 __isl_take isl_pw_aff *pwaff);
2661 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2663 __isl_give isl_pw_aff *isl_pw_aff_mod(
2664 __isl_take isl_pw_aff *pwaff, isl_int mod);
2665 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2667 __isl_give isl_pw_aff *isl_pw_aff_scale(
2668 __isl_take isl_pw_aff *pwaff, isl_int f);
2669 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2671 __isl_give isl_aff *isl_aff_scale_down_ui(
2672 __isl_take isl_aff *aff, unsigned f);
2673 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2674 __isl_take isl_pw_aff *pwaff, isl_int f);
2676 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2677 __isl_take isl_pw_aff_list *list);
2678 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2679 __isl_take isl_pw_aff_list *list);
2681 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2682 __isl_take isl_pw_aff *pwqp);
2684 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2685 __isl_take isl_pw_aff *pwaff,
2686 __isl_take isl_space *model);
2688 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2689 __isl_take isl_set *context);
2690 __isl_give isl_pw_aff *isl_pw_aff_gist(
2691 __isl_take isl_pw_aff *pwaff,
2692 __isl_take isl_set *context);
2694 __isl_give isl_set *isl_pw_aff_domain(
2695 __isl_take isl_pw_aff *pwaff);
2697 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2698 __isl_take isl_aff *aff2);
2699 __isl_give isl_pw_aff *isl_pw_aff_mul(
2700 __isl_take isl_pw_aff *pwaff1,
2701 __isl_take isl_pw_aff *pwaff2);
2703 When multiplying two affine expressions, at least one of the two needs
2706 #include <isl/aff.h>
2707 __isl_give isl_basic_set *isl_aff_le_basic_set(
2708 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2709 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2710 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2711 __isl_give isl_set *isl_pw_aff_eq_set(
2712 __isl_take isl_pw_aff *pwaff1,
2713 __isl_take isl_pw_aff *pwaff2);
2714 __isl_give isl_set *isl_pw_aff_ne_set(
2715 __isl_take isl_pw_aff *pwaff1,
2716 __isl_take isl_pw_aff *pwaff2);
2717 __isl_give isl_set *isl_pw_aff_le_set(
2718 __isl_take isl_pw_aff *pwaff1,
2719 __isl_take isl_pw_aff *pwaff2);
2720 __isl_give isl_set *isl_pw_aff_lt_set(
2721 __isl_take isl_pw_aff *pwaff1,
2722 __isl_take isl_pw_aff *pwaff2);
2723 __isl_give isl_set *isl_pw_aff_ge_set(
2724 __isl_take isl_pw_aff *pwaff1,
2725 __isl_take isl_pw_aff *pwaff2);
2726 __isl_give isl_set *isl_pw_aff_gt_set(
2727 __isl_take isl_pw_aff *pwaff1,
2728 __isl_take isl_pw_aff *pwaff2);
2730 __isl_give isl_set *isl_pw_aff_list_eq_set(
2731 __isl_take isl_pw_aff_list *list1,
2732 __isl_take isl_pw_aff_list *list2);
2733 __isl_give isl_set *isl_pw_aff_list_ne_set(
2734 __isl_take isl_pw_aff_list *list1,
2735 __isl_take isl_pw_aff_list *list2);
2736 __isl_give isl_set *isl_pw_aff_list_le_set(
2737 __isl_take isl_pw_aff_list *list1,
2738 __isl_take isl_pw_aff_list *list2);
2739 __isl_give isl_set *isl_pw_aff_list_lt_set(
2740 __isl_take isl_pw_aff_list *list1,
2741 __isl_take isl_pw_aff_list *list2);
2742 __isl_give isl_set *isl_pw_aff_list_ge_set(
2743 __isl_take isl_pw_aff_list *list1,
2744 __isl_take isl_pw_aff_list *list2);
2745 __isl_give isl_set *isl_pw_aff_list_gt_set(
2746 __isl_take isl_pw_aff_list *list1,
2747 __isl_take isl_pw_aff_list *list2);
2749 The function C<isl_aff_ge_basic_set> returns a basic set
2750 containing those elements in the shared space
2751 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2752 The function C<isl_aff_ge_set> returns a set
2753 containing those elements in the shared domain
2754 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2755 The functions operating on C<isl_pw_aff_list> apply the corresponding
2756 C<isl_pw_aff> function to each pair of elements in the two lists.
2758 #include <isl/aff.h>
2759 __isl_give isl_set *isl_pw_aff_nonneg_set(
2760 __isl_take isl_pw_aff *pwaff);
2761 __isl_give isl_set *isl_pw_aff_zero_set(
2762 __isl_take isl_pw_aff *pwaff);
2763 __isl_give isl_set *isl_pw_aff_non_zero_set(
2764 __isl_take isl_pw_aff *pwaff);
2766 The function C<isl_pw_aff_nonneg_set> returns a set
2767 containing those elements in the domain
2768 of C<pwaff> where C<pwaff> is non-negative.
2770 #include <isl/aff.h>
2771 __isl_give isl_pw_aff *isl_pw_aff_cond(
2772 __isl_take isl_set *cond,
2773 __isl_take isl_pw_aff *pwaff_true,
2774 __isl_take isl_pw_aff *pwaff_false);
2776 The function C<isl_pw_aff_cond> performs a conditional operator
2777 and returns an expression that is equal to C<pwaff_true>
2778 for elements in C<cond> and equal to C<pwaff_false> for elements
2781 #include <isl/aff.h>
2782 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2783 __isl_take isl_pw_aff *pwaff1,
2784 __isl_take isl_pw_aff *pwaff2);
2785 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2786 __isl_take isl_pw_aff *pwaff1,
2787 __isl_take isl_pw_aff *pwaff2);
2789 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2790 expression with a domain that is the union of those of C<pwaff1> and
2791 C<pwaff2> and such that on each cell, the quasi-affine expression is
2792 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2793 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2794 associated expression is the defined one.
2796 An expression can be printed using
2798 #include <isl/aff.h>
2799 __isl_give isl_printer *isl_printer_print_aff(
2800 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2802 __isl_give isl_printer *isl_printer_print_pw_aff(
2803 __isl_take isl_printer *p,
2804 __isl_keep isl_pw_aff *pwaff);
2808 Points are elements of a set. They can be used to construct
2809 simple sets (boxes) or they can be used to represent the
2810 individual elements of a set.
2811 The zero point (the origin) can be created using
2813 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2815 The coordinates of a point can be inspected, set and changed
2818 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2819 enum isl_dim_type type, int pos, isl_int *v);
2820 __isl_give isl_point *isl_point_set_coordinate(
2821 __isl_take isl_point *pnt,
2822 enum isl_dim_type type, int pos, isl_int v);
2824 __isl_give isl_point *isl_point_add_ui(
2825 __isl_take isl_point *pnt,
2826 enum isl_dim_type type, int pos, unsigned val);
2827 __isl_give isl_point *isl_point_sub_ui(
2828 __isl_take isl_point *pnt,
2829 enum isl_dim_type type, int pos, unsigned val);
2831 Other properties can be obtained using
2833 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2835 Points can be copied or freed using
2837 __isl_give isl_point *isl_point_copy(
2838 __isl_keep isl_point *pnt);
2839 void isl_point_free(__isl_take isl_point *pnt);
2841 A singleton set can be created from a point using
2843 __isl_give isl_basic_set *isl_basic_set_from_point(
2844 __isl_take isl_point *pnt);
2845 __isl_give isl_set *isl_set_from_point(
2846 __isl_take isl_point *pnt);
2848 and a box can be created from two opposite extremal points using
2850 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2851 __isl_take isl_point *pnt1,
2852 __isl_take isl_point *pnt2);
2853 __isl_give isl_set *isl_set_box_from_points(
2854 __isl_take isl_point *pnt1,
2855 __isl_take isl_point *pnt2);
2857 All elements of a B<bounded> (union) set can be enumerated using
2858 the following functions.
2860 int isl_set_foreach_point(__isl_keep isl_set *set,
2861 int (*fn)(__isl_take isl_point *pnt, void *user),
2863 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2864 int (*fn)(__isl_take isl_point *pnt, void *user),
2867 The function C<fn> is called for each integer point in
2868 C<set> with as second argument the last argument of
2869 the C<isl_set_foreach_point> call. The function C<fn>
2870 should return C<0> on success and C<-1> on failure.
2871 In the latter case, C<isl_set_foreach_point> will stop
2872 enumerating and return C<-1> as well.
2873 If the enumeration is performed successfully and to completion,
2874 then C<isl_set_foreach_point> returns C<0>.
2876 To obtain a single point of a (basic) set, use
2878 __isl_give isl_point *isl_basic_set_sample_point(
2879 __isl_take isl_basic_set *bset);
2880 __isl_give isl_point *isl_set_sample_point(
2881 __isl_take isl_set *set);
2883 If C<set> does not contain any (integer) points, then the
2884 resulting point will be ``void'', a property that can be
2887 int isl_point_is_void(__isl_keep isl_point *pnt);
2889 =head2 Piecewise Quasipolynomials
2891 A piecewise quasipolynomial is a particular kind of function that maps
2892 a parametric point to a rational value.
2893 More specifically, a quasipolynomial is a polynomial expression in greatest
2894 integer parts of affine expressions of parameters and variables.
2895 A piecewise quasipolynomial is a subdivision of a given parametric
2896 domain into disjoint cells with a quasipolynomial associated to
2897 each cell. The value of the piecewise quasipolynomial at a given
2898 point is the value of the quasipolynomial associated to the cell
2899 that contains the point. Outside of the union of cells,
2900 the value is assumed to be zero.
2901 For example, the piecewise quasipolynomial
2903 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2905 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2906 A given piecewise quasipolynomial has a fixed domain dimension.
2907 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2908 defined over different domains.
2909 Piecewise quasipolynomials are mainly used by the C<barvinok>
2910 library for representing the number of elements in a parametric set or map.
2911 For example, the piecewise quasipolynomial above represents
2912 the number of points in the map
2914 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2916 =head3 Printing (Piecewise) Quasipolynomials
2918 Quasipolynomials and piecewise quasipolynomials can be printed
2919 using the following functions.
2921 __isl_give isl_printer *isl_printer_print_qpolynomial(
2922 __isl_take isl_printer *p,
2923 __isl_keep isl_qpolynomial *qp);
2925 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2926 __isl_take isl_printer *p,
2927 __isl_keep isl_pw_qpolynomial *pwqp);
2929 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2930 __isl_take isl_printer *p,
2931 __isl_keep isl_union_pw_qpolynomial *upwqp);
2933 The output format of the printer
2934 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2935 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2937 In case of printing in C<ISL_FORMAT_C>, the user may want
2938 to set the names of all dimensions
2940 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2941 __isl_take isl_qpolynomial *qp,
2942 enum isl_dim_type type, unsigned pos,
2944 __isl_give isl_pw_qpolynomial *
2945 isl_pw_qpolynomial_set_dim_name(
2946 __isl_take isl_pw_qpolynomial *pwqp,
2947 enum isl_dim_type type, unsigned pos,
2950 =head3 Creating New (Piecewise) Quasipolynomials
2952 Some simple quasipolynomials can be created using the following functions.
2953 More complicated quasipolynomials can be created by applying
2954 operations such as addition and multiplication
2955 on the resulting quasipolynomials
2957 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2958 __isl_take isl_space *domain);
2959 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2960 __isl_take isl_space *domain);
2961 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2962 __isl_take isl_space *domain);
2963 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2964 __isl_take isl_space *domain);
2965 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2966 __isl_take isl_space *domain);
2967 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2968 __isl_take isl_space *domain,
2969 const isl_int n, const isl_int d);
2970 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2971 __isl_take isl_div *div);
2972 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2973 __isl_take isl_space *domain,
2974 enum isl_dim_type type, unsigned pos);
2975 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2976 __isl_take isl_aff *aff);
2978 Note that the space in which a quasipolynomial lives is a map space
2979 with a one-dimensional range. The C<domain> argument in some of
2980 the functions above corresponds to the domain of this map space.
2982 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2983 with a single cell can be created using the following functions.
2984 Multiple of these single cell piecewise quasipolynomials can
2985 be combined to create more complicated piecewise quasipolynomials.
2987 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2988 __isl_take isl_space *space);
2989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2990 __isl_take isl_set *set,
2991 __isl_take isl_qpolynomial *qp);
2992 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2993 __isl_take isl_qpolynomial *qp);
2994 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2995 __isl_take isl_pw_aff *pwaff);
2997 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2998 __isl_take isl_space *space);
2999 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3000 __isl_take isl_pw_qpolynomial *pwqp);
3001 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3002 __isl_take isl_union_pw_qpolynomial *upwqp,
3003 __isl_take isl_pw_qpolynomial *pwqp);
3005 Quasipolynomials can be copied and freed again using the following
3008 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3009 __isl_keep isl_qpolynomial *qp);
3010 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3013 __isl_keep isl_pw_qpolynomial *pwqp);
3014 void *isl_pw_qpolynomial_free(
3015 __isl_take isl_pw_qpolynomial *pwqp);
3017 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3018 __isl_keep isl_union_pw_qpolynomial *upwqp);
3019 void isl_union_pw_qpolynomial_free(
3020 __isl_take isl_union_pw_qpolynomial *upwqp);
3022 =head3 Inspecting (Piecewise) Quasipolynomials
3024 To iterate over all piecewise quasipolynomials in a union
3025 piecewise quasipolynomial, use the following function
3027 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3028 __isl_keep isl_union_pw_qpolynomial *upwqp,
3029 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3032 To extract the piecewise quasipolynomial in a given space from a union, use
3034 __isl_give isl_pw_qpolynomial *
3035 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3036 __isl_keep isl_union_pw_qpolynomial *upwqp,
3037 __isl_take isl_space *space);
3039 To iterate over the cells in a piecewise quasipolynomial,
3040 use either of the following two functions
3042 int isl_pw_qpolynomial_foreach_piece(
3043 __isl_keep isl_pw_qpolynomial *pwqp,
3044 int (*fn)(__isl_take isl_set *set,
3045 __isl_take isl_qpolynomial *qp,
3046 void *user), void *user);
3047 int isl_pw_qpolynomial_foreach_lifted_piece(
3048 __isl_keep isl_pw_qpolynomial *pwqp,
3049 int (*fn)(__isl_take isl_set *set,
3050 __isl_take isl_qpolynomial *qp,
3051 void *user), void *user);
3053 As usual, the function C<fn> should return C<0> on success
3054 and C<-1> on failure. The difference between
3055 C<isl_pw_qpolynomial_foreach_piece> and
3056 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3057 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3058 compute unique representations for all existentially quantified
3059 variables and then turn these existentially quantified variables
3060 into extra set variables, adapting the associated quasipolynomial
3061 accordingly. This means that the C<set> passed to C<fn>
3062 will not have any existentially quantified variables, but that
3063 the dimensions of the sets may be different for different
3064 invocations of C<fn>.
3066 To iterate over all terms in a quasipolynomial,
3069 int isl_qpolynomial_foreach_term(
3070 __isl_keep isl_qpolynomial *qp,
3071 int (*fn)(__isl_take isl_term *term,
3072 void *user), void *user);
3074 The terms themselves can be inspected and freed using
3077 unsigned isl_term_dim(__isl_keep isl_term *term,
3078 enum isl_dim_type type);
3079 void isl_term_get_num(__isl_keep isl_term *term,
3081 void isl_term_get_den(__isl_keep isl_term *term,
3083 int isl_term_get_exp(__isl_keep isl_term *term,
3084 enum isl_dim_type type, unsigned pos);
3085 __isl_give isl_div *isl_term_get_div(
3086 __isl_keep isl_term *term, unsigned pos);
3087 void isl_term_free(__isl_take isl_term *term);
3089 Each term is a product of parameters, set variables and
3090 integer divisions. The function C<isl_term_get_exp>
3091 returns the exponent of a given dimensions in the given term.
3092 The C<isl_int>s in the arguments of C<isl_term_get_num>
3093 and C<isl_term_get_den> need to have been initialized
3094 using C<isl_int_init> before calling these functions.
3096 =head3 Properties of (Piecewise) Quasipolynomials
3098 To check whether a quasipolynomial is actually a constant,
3099 use the following function.
3101 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3102 isl_int *n, isl_int *d);
3104 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3105 then the numerator and denominator of the constant
3106 are returned in C<*n> and C<*d>, respectively.
3108 =head3 Operations on (Piecewise) Quasipolynomials
3110 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3111 __isl_take isl_qpolynomial *qp, isl_int v);
3112 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3113 __isl_take isl_qpolynomial *qp);
3114 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3115 __isl_take isl_qpolynomial *qp1,
3116 __isl_take isl_qpolynomial *qp2);
3117 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3118 __isl_take isl_qpolynomial *qp1,
3119 __isl_take isl_qpolynomial *qp2);
3120 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3121 __isl_take isl_qpolynomial *qp1,
3122 __isl_take isl_qpolynomial *qp2);
3123 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3124 __isl_take isl_qpolynomial *qp, unsigned exponent);
3126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3127 __isl_take isl_pw_qpolynomial *pwqp1,
3128 __isl_take isl_pw_qpolynomial *pwqp2);
3129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3130 __isl_take isl_pw_qpolynomial *pwqp1,
3131 __isl_take isl_pw_qpolynomial *pwqp2);
3132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3133 __isl_take isl_pw_qpolynomial *pwqp1,
3134 __isl_take isl_pw_qpolynomial *pwqp2);
3135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3136 __isl_take isl_pw_qpolynomial *pwqp);
3137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3138 __isl_take isl_pw_qpolynomial *pwqp1,
3139 __isl_take isl_pw_qpolynomial *pwqp2);
3140 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3141 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3143 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3144 __isl_take isl_union_pw_qpolynomial *upwqp1,
3145 __isl_take isl_union_pw_qpolynomial *upwqp2);
3146 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3147 __isl_take isl_union_pw_qpolynomial *upwqp1,
3148 __isl_take isl_union_pw_qpolynomial *upwqp2);
3149 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3150 __isl_take isl_union_pw_qpolynomial *upwqp1,
3151 __isl_take isl_union_pw_qpolynomial *upwqp2);
3153 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3154 __isl_take isl_pw_qpolynomial *pwqp,
3155 __isl_take isl_point *pnt);
3157 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3158 __isl_take isl_union_pw_qpolynomial *upwqp,
3159 __isl_take isl_point *pnt);
3161 __isl_give isl_set *isl_pw_qpolynomial_domain(
3162 __isl_take isl_pw_qpolynomial *pwqp);
3163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3164 __isl_take isl_pw_qpolynomial *pwpq,
3165 __isl_take isl_set *set);
3167 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3168 __isl_take isl_union_pw_qpolynomial *upwqp);
3169 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3170 __isl_take isl_union_pw_qpolynomial *upwpq,
3171 __isl_take isl_union_set *uset);
3173 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3174 __isl_take isl_qpolynomial *qp,
3175 __isl_take isl_space *model);
3177 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3178 __isl_take isl_qpolynomial *qp);
3179 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3180 __isl_take isl_pw_qpolynomial *pwqp);
3182 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3183 __isl_take isl_union_pw_qpolynomial *upwqp);
3185 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3186 __isl_take isl_qpolynomial *qp,
3187 __isl_take isl_set *context);
3189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3190 __isl_take isl_pw_qpolynomial *pwqp,
3191 __isl_take isl_set *context);
3193 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3194 __isl_take isl_union_pw_qpolynomial *upwqp,
3195 __isl_take isl_union_set *context);
3197 The gist operation applies the gist operation to each of
3198 the cells in the domain of the input piecewise quasipolynomial.
3199 The context is also exploited
3200 to simplify the quasipolynomials associated to each cell.
3202 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3203 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3204 __isl_give isl_union_pw_qpolynomial *
3205 isl_union_pw_qpolynomial_to_polynomial(
3206 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3208 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3209 the polynomial will be an overapproximation. If C<sign> is negative,
3210 it will be an underapproximation. If C<sign> is zero, the approximation
3211 will lie somewhere in between.
3213 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3215 A piecewise quasipolynomial reduction is a piecewise
3216 reduction (or fold) of quasipolynomials.
3217 In particular, the reduction can be maximum or a minimum.
3218 The objects are mainly used to represent the result of
3219 an upper or lower bound on a quasipolynomial over its domain,
3220 i.e., as the result of the following function.
3222 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3223 __isl_take isl_pw_qpolynomial *pwqp,
3224 enum isl_fold type, int *tight);
3226 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3227 __isl_take isl_union_pw_qpolynomial *upwqp,
3228 enum isl_fold type, int *tight);
3230 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3231 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3232 is the returned bound is known be tight, i.e., for each value
3233 of the parameters there is at least
3234 one element in the domain that reaches the bound.
3235 If the domain of C<pwqp> is not wrapping, then the bound is computed
3236 over all elements in that domain and the result has a purely parametric
3237 domain. If the domain of C<pwqp> is wrapping, then the bound is
3238 computed over the range of the wrapped relation. The domain of the
3239 wrapped relation becomes the domain of the result.
3241 A (piecewise) quasipolynomial reduction can be copied or freed using the
3242 following functions.
3244 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3245 __isl_keep isl_qpolynomial_fold *fold);
3246 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3247 __isl_keep isl_pw_qpolynomial_fold *pwf);
3248 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3249 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3250 void isl_qpolynomial_fold_free(
3251 __isl_take isl_qpolynomial_fold *fold);
3252 void *isl_pw_qpolynomial_fold_free(
3253 __isl_take isl_pw_qpolynomial_fold *pwf);
3254 void isl_union_pw_qpolynomial_fold_free(
3255 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3257 =head3 Printing Piecewise Quasipolynomial Reductions
3259 Piecewise quasipolynomial reductions can be printed
3260 using the following function.
3262 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3263 __isl_take isl_printer *p,
3264 __isl_keep isl_pw_qpolynomial_fold *pwf);
3265 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3266 __isl_take isl_printer *p,
3267 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3269 For C<isl_printer_print_pw_qpolynomial_fold>,
3270 output format of the printer
3271 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3272 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3273 output format of the printer
3274 needs to be set to C<ISL_FORMAT_ISL>.
3275 In case of printing in C<ISL_FORMAT_C>, the user may want
3276 to set the names of all dimensions
3278 __isl_give isl_pw_qpolynomial_fold *
3279 isl_pw_qpolynomial_fold_set_dim_name(
3280 __isl_take isl_pw_qpolynomial_fold *pwf,
3281 enum isl_dim_type type, unsigned pos,
3284 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3286 To iterate over all piecewise quasipolynomial reductions in a union
3287 piecewise quasipolynomial reduction, use the following function
3289 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3290 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3291 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3292 void *user), void *user);
3294 To iterate over the cells in a piecewise quasipolynomial reduction,
3295 use either of the following two functions
3297 int isl_pw_qpolynomial_fold_foreach_piece(
3298 __isl_keep isl_pw_qpolynomial_fold *pwf,
3299 int (*fn)(__isl_take isl_set *set,
3300 __isl_take isl_qpolynomial_fold *fold,
3301 void *user), void *user);
3302 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3303 __isl_keep isl_pw_qpolynomial_fold *pwf,
3304 int (*fn)(__isl_take isl_set *set,
3305 __isl_take isl_qpolynomial_fold *fold,
3306 void *user), void *user);
3308 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3309 of the difference between these two functions.
3311 To iterate over all quasipolynomials in a reduction, use
3313 int isl_qpolynomial_fold_foreach_qpolynomial(
3314 __isl_keep isl_qpolynomial_fold *fold,
3315 int (*fn)(__isl_take isl_qpolynomial *qp,
3316 void *user), void *user);
3318 =head3 Operations on Piecewise Quasipolynomial Reductions
3320 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3321 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3323 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3324 __isl_take isl_pw_qpolynomial_fold *pwf1,
3325 __isl_take isl_pw_qpolynomial_fold *pwf2);
3327 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3328 __isl_take isl_pw_qpolynomial_fold *pwf1,
3329 __isl_take isl_pw_qpolynomial_fold *pwf2);
3331 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3332 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3333 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3335 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3336 __isl_take isl_pw_qpolynomial_fold *pwf,
3337 __isl_take isl_point *pnt);
3339 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3340 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3341 __isl_take isl_point *pnt);
3343 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3344 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3345 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3346 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3347 __isl_take isl_union_set *uset);
3349 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3350 __isl_take isl_pw_qpolynomial_fold *pwf);
3352 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3353 __isl_take isl_pw_qpolynomial_fold *pwf);
3355 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3356 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3358 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3359 __isl_take isl_pw_qpolynomial_fold *pwf,
3360 __isl_take isl_set *context);
3362 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3363 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3364 __isl_take isl_union_set *context);
3366 The gist operation applies the gist operation to each of
3367 the cells in the domain of the input piecewise quasipolynomial reduction.
3368 In future, the operation will also exploit the context
3369 to simplify the quasipolynomial reductions associated to each cell.
3371 __isl_give isl_pw_qpolynomial_fold *
3372 isl_set_apply_pw_qpolynomial_fold(
3373 __isl_take isl_set *set,
3374 __isl_take isl_pw_qpolynomial_fold *pwf,
3376 __isl_give isl_pw_qpolynomial_fold *
3377 isl_map_apply_pw_qpolynomial_fold(
3378 __isl_take isl_map *map,
3379 __isl_take isl_pw_qpolynomial_fold *pwf,
3381 __isl_give isl_union_pw_qpolynomial_fold *
3382 isl_union_set_apply_union_pw_qpolynomial_fold(
3383 __isl_take isl_union_set *uset,
3384 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3386 __isl_give isl_union_pw_qpolynomial_fold *
3387 isl_union_map_apply_union_pw_qpolynomial_fold(
3388 __isl_take isl_union_map *umap,
3389 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3392 The functions taking a map
3393 compose the given map with the given piecewise quasipolynomial reduction.
3394 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3395 over all elements in the intersection of the range of the map
3396 and the domain of the piecewise quasipolynomial reduction
3397 as a function of an element in the domain of the map.
3398 The functions taking a set compute a bound over all elements in the
3399 intersection of the set and the domain of the
3400 piecewise quasipolynomial reduction.
3402 =head2 Dependence Analysis
3404 C<isl> contains specialized functionality for performing
3405 array dataflow analysis. That is, given a I<sink> access relation
3406 and a collection of possible I<source> access relations,
3407 C<isl> can compute relations that describe
3408 for each iteration of the sink access, which iteration
3409 of which of the source access relations was the last
3410 to access the same data element before the given iteration
3412 To compute standard flow dependences, the sink should be
3413 a read, while the sources should be writes.
3414 If any of the source accesses are marked as being I<may>
3415 accesses, then there will be a dependence to the last
3416 I<must> access B<and> to any I<may> access that follows
3417 this last I<must> access.
3418 In particular, if I<all> sources are I<may> accesses,
3419 then memory based dependence analysis is performed.
3420 If, on the other hand, all sources are I<must> accesses,
3421 then value based dependence analysis is performed.
3423 #include <isl/flow.h>
3425 typedef int (*isl_access_level_before)(void *first, void *second);
3427 __isl_give isl_access_info *isl_access_info_alloc(
3428 __isl_take isl_map *sink,
3429 void *sink_user, isl_access_level_before fn,
3431 __isl_give isl_access_info *isl_access_info_add_source(
3432 __isl_take isl_access_info *acc,
3433 __isl_take isl_map *source, int must,
3435 void isl_access_info_free(__isl_take isl_access_info *acc);
3437 __isl_give isl_flow *isl_access_info_compute_flow(
3438 __isl_take isl_access_info *acc);
3440 int isl_flow_foreach(__isl_keep isl_flow *deps,
3441 int (*fn)(__isl_take isl_map *dep, int must,
3442 void *dep_user, void *user),
3444 __isl_give isl_map *isl_flow_get_no_source(
3445 __isl_keep isl_flow *deps, int must);
3446 void isl_flow_free(__isl_take isl_flow *deps);
3448 The function C<isl_access_info_compute_flow> performs the actual
3449 dependence analysis. The other functions are used to construct
3450 the input for this function or to read off the output.
3452 The input is collected in an C<isl_access_info>, which can
3453 be created through a call to C<isl_access_info_alloc>.
3454 The arguments to this functions are the sink access relation
3455 C<sink>, a token C<sink_user> used to identify the sink
3456 access to the user, a callback function for specifying the
3457 relative order of source and sink accesses, and the number
3458 of source access relations that will be added.
3459 The callback function has type C<int (*)(void *first, void *second)>.
3460 The function is called with two user supplied tokens identifying
3461 either a source or the sink and it should return the shared nesting
3462 level and the relative order of the two accesses.
3463 In particular, let I<n> be the number of loops shared by
3464 the two accesses. If C<first> precedes C<second> textually,
3465 then the function should return I<2 * n + 1>; otherwise,
3466 it should return I<2 * n>.
3467 The sources can be added to the C<isl_access_info> by performing
3468 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3469 C<must> indicates whether the source is a I<must> access
3470 or a I<may> access. Note that a multi-valued access relation
3471 should only be marked I<must> if every iteration in the domain
3472 of the relation accesses I<all> elements in its image.
3473 The C<source_user> token is again used to identify
3474 the source access. The range of the source access relation
3475 C<source> should have the same dimension as the range
3476 of the sink access relation.
3477 The C<isl_access_info_free> function should usually not be
3478 called explicitly, because it is called implicitly by
3479 C<isl_access_info_compute_flow>.
3481 The result of the dependence analysis is collected in an
3482 C<isl_flow>. There may be elements of
3483 the sink access for which no preceding source access could be
3484 found or for which all preceding sources are I<may> accesses.
3485 The relations containing these elements can be obtained through
3486 calls to C<isl_flow_get_no_source>, the first with C<must> set
3487 and the second with C<must> unset.
3488 In the case of standard flow dependence analysis,
3489 with the sink a read and the sources I<must> writes,
3490 the first relation corresponds to the reads from uninitialized
3491 array elements and the second relation is empty.
3492 The actual flow dependences can be extracted using
3493 C<isl_flow_foreach>. This function will call the user-specified
3494 callback function C<fn> for each B<non-empty> dependence between
3495 a source and the sink. The callback function is called
3496 with four arguments, the actual flow dependence relation
3497 mapping source iterations to sink iterations, a boolean that
3498 indicates whether it is a I<must> or I<may> dependence, a token
3499 identifying the source and an additional C<void *> with value
3500 equal to the third argument of the C<isl_flow_foreach> call.
3501 A dependence is marked I<must> if it originates from a I<must>
3502 source and if it is not followed by any I<may> sources.
3504 After finishing with an C<isl_flow>, the user should call
3505 C<isl_flow_free> to free all associated memory.
3507 A higher-level interface to dependence analysis is provided
3508 by the following function.
3510 #include <isl/flow.h>
3512 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3513 __isl_take isl_union_map *must_source,
3514 __isl_take isl_union_map *may_source,
3515 __isl_take isl_union_map *schedule,
3516 __isl_give isl_union_map **must_dep,
3517 __isl_give isl_union_map **may_dep,
3518 __isl_give isl_union_map **must_no_source,
3519 __isl_give isl_union_map **may_no_source);
3521 The arrays are identified by the tuple names of the ranges
3522 of the accesses. The iteration domains by the tuple names
3523 of the domains of the accesses and of the schedule.
3524 The relative order of the iteration domains is given by the
3525 schedule. The relations returned through C<must_no_source>
3526 and C<may_no_source> are subsets of C<sink>.
3527 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3528 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3529 any of the other arguments is treated as an error.
3533 B<The functionality described in this section is fairly new
3534 and may be subject to change.>
3536 The following function can be used to compute a schedule
3537 for a union of domains. The generated schedule respects
3538 all C<validity> dependences. That is, all dependence distances
3539 over these dependences in the scheduled space are lexicographically
3540 positive. The generated schedule schedule also tries to minimize
3541 the dependence distances over C<proximity> dependences.
3542 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3543 for groups of domains where the dependence distances have only
3544 non-negative values.
3545 The algorithm used to construct the schedule is similar to that
3548 #include <isl/schedule.h>
3549 __isl_give isl_schedule *isl_union_set_compute_schedule(
3550 __isl_take isl_union_set *domain,
3551 __isl_take isl_union_map *validity,
3552 __isl_take isl_union_map *proximity);
3553 void *isl_schedule_free(__isl_take isl_schedule *sched);
3555 A mapping from the domains to the scheduled space can be obtained
3556 from an C<isl_schedule> using the following function.
3558 __isl_give isl_union_map *isl_schedule_get_map(
3559 __isl_keep isl_schedule *sched);
3561 A representation of the schedule can be printed using
3563 __isl_give isl_printer *isl_printer_print_schedule(
3564 __isl_take isl_printer *p,
3565 __isl_keep isl_schedule *schedule);
3567 A representation of the schedule as a forest of bands can be obtained
3568 using the following function.
3570 __isl_give isl_band_list *isl_schedule_get_band_forest(
3571 __isl_keep isl_schedule *schedule);
3573 The list can be manipulated as explained in L<"Lists">.
3574 The bands inside the list can be copied and freed using the following
3577 #include <isl/band.h>
3578 __isl_give isl_band *isl_band_copy(
3579 __isl_keep isl_band *band);
3580 void *isl_band_free(__isl_take isl_band *band);
3582 Each band contains zero or more scheduling dimensions.
3583 These are referred to as the members of the band.
3584 The section of the schedule that corresponds to the band is
3585 referred to as the partial schedule of the band.
3586 For those nodes that participate in a band, the outer scheduling
3587 dimensions form the prefix schedule, while the inner scheduling
3588 dimensions form the suffix schedule.
3589 That is, if we take a cut of the band forest, then the union of
3590 the concatenations of the prefix, partial and suffix schedules of
3591 each band in the cut is equal to the entire schedule (modulo
3592 some possible padding at the end with zero scheduling dimensions).
3593 The properties of a band can be inspected using the following functions.
3595 #include <isl/band.h>
3596 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3598 int isl_band_has_children(__isl_keep isl_band *band);
3599 __isl_give isl_band_list *isl_band_get_children(
3600 __isl_keep isl_band *band);
3602 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3603 __isl_keep isl_band *band);
3604 __isl_give isl_union_map *isl_band_get_partial_schedule(
3605 __isl_keep isl_band *band);
3606 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3607 __isl_keep isl_band *band);
3609 int isl_band_n_member(__isl_keep isl_band *band);
3610 int isl_band_member_is_zero_distance(
3611 __isl_keep isl_band *band, int pos);
3613 Note that a scheduling dimension is considered to be ``zero
3614 distance'' if it does not carry any proximity dependences
3616 That is, if the dependence distances of the proximity
3617 dependences are all zero in that direction (for fixed
3618 iterations of outer bands).
3620 A representation of the band can be printed using
3622 #include <isl/band.h>
3623 __isl_give isl_printer *isl_printer_print_band(
3624 __isl_take isl_printer *p,
3625 __isl_keep isl_band *band);
3627 =head2 Parametric Vertex Enumeration
3629 The parametric vertex enumeration described in this section
3630 is mainly intended to be used internally and by the C<barvinok>
3633 #include <isl/vertices.h>
3634 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3635 __isl_keep isl_basic_set *bset);
3637 The function C<isl_basic_set_compute_vertices> performs the
3638 actual computation of the parametric vertices and the chamber
3639 decomposition and store the result in an C<isl_vertices> object.
3640 This information can be queried by either iterating over all
3641 the vertices or iterating over all the chambers or cells
3642 and then iterating over all vertices that are active on the chamber.
3644 int isl_vertices_foreach_vertex(
3645 __isl_keep isl_vertices *vertices,
3646 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3649 int isl_vertices_foreach_cell(
3650 __isl_keep isl_vertices *vertices,
3651 int (*fn)(__isl_take isl_cell *cell, void *user),
3653 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3654 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3657 Other operations that can be performed on an C<isl_vertices> object are
3660 isl_ctx *isl_vertices_get_ctx(
3661 __isl_keep isl_vertices *vertices);
3662 int isl_vertices_get_n_vertices(
3663 __isl_keep isl_vertices *vertices);
3664 void isl_vertices_free(__isl_take isl_vertices *vertices);
3666 Vertices can be inspected and destroyed using the following functions.
3668 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3669 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3670 __isl_give isl_basic_set *isl_vertex_get_domain(
3671 __isl_keep isl_vertex *vertex);
3672 __isl_give isl_basic_set *isl_vertex_get_expr(
3673 __isl_keep isl_vertex *vertex);
3674 void isl_vertex_free(__isl_take isl_vertex *vertex);
3676 C<isl_vertex_get_expr> returns a singleton parametric set describing
3677 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3679 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3680 B<rational> basic sets, so they should mainly be used for inspection
3681 and should not be mixed with integer sets.
3683 Chambers can be inspected and destroyed using the following functions.
3685 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3686 __isl_give isl_basic_set *isl_cell_get_domain(
3687 __isl_keep isl_cell *cell);
3688 void isl_cell_free(__isl_take isl_cell *cell);
3692 Although C<isl> is mainly meant to be used as a library,
3693 it also contains some basic applications that use some
3694 of the functionality of C<isl>.
3695 The input may be specified in either the L<isl format>
3696 or the L<PolyLib format>.
3698 =head2 C<isl_polyhedron_sample>
3700 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3701 an integer element of the polyhedron, if there is any.
3702 The first column in the output is the denominator and is always
3703 equal to 1. If the polyhedron contains no integer points,
3704 then a vector of length zero is printed.
3708 C<isl_pip> takes the same input as the C<example> program
3709 from the C<piplib> distribution, i.e., a set of constraints
3710 on the parameters, a line containing only -1 and finally a set
3711 of constraints on a parametric polyhedron.
3712 The coefficients of the parameters appear in the last columns
3713 (but before the final constant column).
3714 The output is the lexicographic minimum of the parametric polyhedron.
3715 As C<isl> currently does not have its own output format, the output
3716 is just a dump of the internal state.
3718 =head2 C<isl_polyhedron_minimize>
3720 C<isl_polyhedron_minimize> computes the minimum of some linear
3721 or affine objective function over the integer points in a polyhedron.
3722 If an affine objective function
3723 is given, then the constant should appear in the last column.
3725 =head2 C<isl_polytope_scan>
3727 Given a polytope, C<isl_polytope_scan> prints
3728 all integer points in the polytope.