3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
145 =item * The C<nparam> argument has been removed from
146 C<isl_map_read_from_str> and similar functions.
147 When reading input in the original PolyLib format,
148 the result will have no parameters.
149 If parameters are expected, the caller may want to perform
150 dimension manipulation on the result.
156 The source of C<isl> can be obtained either as a tarball
157 or from the git repository. Both are available from
158 L<http://freshmeat.net/projects/isl/>.
159 The installation process depends on how you obtained
162 =head2 Installation from the git repository
166 =item 1 Clone or update the repository
168 The first time the source is obtained, you need to clone
171 git clone git://repo.or.cz/isl.git
173 To obtain updates, you need to pull in the latest changes
177 =item 2 Generate C<configure>
183 After performing the above steps, continue
184 with the L<Common installation instructions>.
186 =head2 Common installation instructions
190 =item 1 Obtain C<GMP>
192 Building C<isl> requires C<GMP>, including its headers files.
193 Your distribution may not provide these header files by default
194 and you may need to install a package called C<gmp-devel> or something
195 similar. Alternatively, C<GMP> can be built from
196 source, available from L<http://gmplib.org/>.
200 C<isl> uses the standard C<autoconf> C<configure> script.
205 optionally followed by some configure options.
206 A complete list of options can be obtained by running
210 Below we discuss some of the more common options.
212 C<isl> can optionally use C<piplib>, but no
213 C<piplib> functionality is currently used by default.
214 The C<--with-piplib> option can
215 be used to specify which C<piplib>
216 library to use, either an installed version (C<system>),
217 an externally built version (C<build>)
218 or no version (C<no>). The option C<build> is mostly useful
219 in C<configure> scripts of larger projects that bundle both C<isl>
226 Installation prefix for C<isl>
228 =item C<--with-gmp-prefix>
230 Installation prefix for C<GMP> (architecture-independent files).
232 =item C<--with-gmp-exec-prefix>
234 Installation prefix for C<GMP> (architecture-dependent files).
236 =item C<--with-piplib>
238 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
240 =item C<--with-piplib-prefix>
242 Installation prefix for C<system> C<piplib> (architecture-independent files).
244 =item C<--with-piplib-exec-prefix>
246 Installation prefix for C<system> C<piplib> (architecture-dependent files).
248 =item C<--with-piplib-builddir>
250 Location where C<build> C<piplib> was built.
258 =item 4 Install (optional)
266 =head2 Initialization
268 All manipulations of integer sets and relations occur within
269 the context of an C<isl_ctx>.
270 A given C<isl_ctx> can only be used within a single thread.
271 All arguments of a function are required to have been allocated
272 within the same context.
273 There are currently no functions available for moving an object
274 from one C<isl_ctx> to another C<isl_ctx>. This means that
275 there is currently no way of safely moving an object from one
276 thread to another, unless the whole C<isl_ctx> is moved.
278 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
279 freed using C<isl_ctx_free>.
280 All objects allocated within an C<isl_ctx> should be freed
281 before the C<isl_ctx> itself is freed.
283 isl_ctx *isl_ctx_alloc();
284 void isl_ctx_free(isl_ctx *ctx);
288 All operations on integers, mainly the coefficients
289 of the constraints describing the sets and relations,
290 are performed in exact integer arithmetic using C<GMP>.
291 However, to allow future versions of C<isl> to optionally
292 support fixed integer arithmetic, all calls to C<GMP>
293 are wrapped inside C<isl> specific macros.
294 The basic type is C<isl_int> and the operations below
295 are available on this type.
296 The meanings of these operations are essentially the same
297 as their C<GMP> C<mpz_> counterparts.
298 As always with C<GMP> types, C<isl_int>s need to be
299 initialized with C<isl_int_init> before they can be used
300 and they need to be released with C<isl_int_clear>
302 The user should not assume that an C<isl_int> is represented
303 as a C<mpz_t>, but should instead explicitly convert between
304 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
305 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
309 =item isl_int_init(i)
311 =item isl_int_clear(i)
313 =item isl_int_set(r,i)
315 =item isl_int_set_si(r,i)
317 =item isl_int_set_gmp(r,g)
319 =item isl_int_get_gmp(i,g)
321 =item isl_int_abs(r,i)
323 =item isl_int_neg(r,i)
325 =item isl_int_swap(i,j)
327 =item isl_int_swap_or_set(i,j)
329 =item isl_int_add_ui(r,i,j)
331 =item isl_int_sub_ui(r,i,j)
333 =item isl_int_add(r,i,j)
335 =item isl_int_sub(r,i,j)
337 =item isl_int_mul(r,i,j)
339 =item isl_int_mul_ui(r,i,j)
341 =item isl_int_addmul(r,i,j)
343 =item isl_int_submul(r,i,j)
345 =item isl_int_gcd(r,i,j)
347 =item isl_int_lcm(r,i,j)
349 =item isl_int_divexact(r,i,j)
351 =item isl_int_cdiv_q(r,i,j)
353 =item isl_int_fdiv_q(r,i,j)
355 =item isl_int_fdiv_r(r,i,j)
357 =item isl_int_fdiv_q_ui(r,i,j)
359 =item isl_int_read(r,s)
361 =item isl_int_print(out,i,width)
365 =item isl_int_cmp(i,j)
367 =item isl_int_cmp_si(i,si)
369 =item isl_int_eq(i,j)
371 =item isl_int_ne(i,j)
373 =item isl_int_lt(i,j)
375 =item isl_int_le(i,j)
377 =item isl_int_gt(i,j)
379 =item isl_int_ge(i,j)
381 =item isl_int_abs_eq(i,j)
383 =item isl_int_abs_ne(i,j)
385 =item isl_int_abs_lt(i,j)
387 =item isl_int_abs_gt(i,j)
389 =item isl_int_abs_ge(i,j)
391 =item isl_int_is_zero(i)
393 =item isl_int_is_one(i)
395 =item isl_int_is_negone(i)
397 =item isl_int_is_pos(i)
399 =item isl_int_is_neg(i)
401 =item isl_int_is_nonpos(i)
403 =item isl_int_is_nonneg(i)
405 =item isl_int_is_divisible_by(i,j)
409 =head2 Sets and Relations
411 C<isl> uses six types of objects for representing sets and relations,
412 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
413 C<isl_union_set> and C<isl_union_map>.
414 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
415 can be described as a conjunction of affine constraints, while
416 C<isl_set> and C<isl_map> represent unions of
417 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
418 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
419 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
420 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
421 where spaces are considered different if they have a different number
422 of dimensions and/or different names (see L<"Spaces">).
423 The difference between sets and relations (maps) is that sets have
424 one set of variables, while relations have two sets of variables,
425 input variables and output variables.
427 =head2 Memory Management
429 Since a high-level operation on sets and/or relations usually involves
430 several substeps and since the user is usually not interested in
431 the intermediate results, most functions that return a new object
432 will also release all the objects passed as arguments.
433 If the user still wants to use one or more of these arguments
434 after the function call, she should pass along a copy of the
435 object rather than the object itself.
436 The user is then responsible for making sure that the original
437 object gets used somewhere else or is explicitly freed.
439 The arguments and return values of all documented functions are
440 annotated to make clear which arguments are released and which
441 arguments are preserved. In particular, the following annotations
448 C<__isl_give> means that a new object is returned.
449 The user should make sure that the returned pointer is
450 used exactly once as a value for an C<__isl_take> argument.
451 In between, it can be used as a value for as many
452 C<__isl_keep> arguments as the user likes.
453 There is one exception, and that is the case where the
454 pointer returned is C<NULL>. Is this case, the user
455 is free to use it as an C<__isl_take> argument or not.
459 C<__isl_take> means that the object the argument points to
460 is taken over by the function and may no longer be used
461 by the user as an argument to any other function.
462 The pointer value must be one returned by a function
463 returning an C<__isl_give> pointer.
464 If the user passes in a C<NULL> value, then this will
465 be treated as an error in the sense that the function will
466 not perform its usual operation. However, it will still
467 make sure that all the other C<__isl_take> arguments
472 C<__isl_keep> means that the function will only use the object
473 temporarily. After the function has finished, the user
474 can still use it as an argument to other functions.
475 A C<NULL> value will be treated in the same way as
476 a C<NULL> value for an C<__isl_take> argument.
482 Identifiers are used to identify both individual dimensions
483 and tuples of dimensions. They consist of a name and an optional
484 pointer. Identifiers with the same name but different pointer values
485 are considered to be distinct.
486 Identifiers can be constructed, copied, freed, inspected and printed
487 using the following functions.
490 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
491 __isl_keep const char *name, void *user);
492 __isl_give isl_id *isl_id_copy(isl_id *id);
493 void *isl_id_free(__isl_take isl_id *id);
495 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
496 void *isl_id_get_user(__isl_keep isl_id *id);
497 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
499 __isl_give isl_printer *isl_printer_print_id(
500 __isl_take isl_printer *p, __isl_keep isl_id *id);
502 Note that C<isl_id_get_name> returns a pointer to some internal
503 data structure, so the result can only be used while the
504 corresponding C<isl_id> is alive.
508 Whenever a new set or relation is created from scratch,
509 the space in which it lives needs to be specified using an C<isl_space>.
511 #include <isl/space.h>
512 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
513 unsigned nparam, unsigned n_in, unsigned n_out);
514 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
516 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
517 unsigned nparam, unsigned dim);
518 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
519 void isl_space_free(__isl_take isl_space *space);
520 unsigned isl_space_dim(__isl_keep isl_space *space,
521 enum isl_dim_type type);
523 The space used for creating a parameter domain
524 needs to be created using C<isl_space_params_alloc>.
525 For other sets, the space
526 needs to be created using C<isl_space_set_alloc>, while
527 for a relation, the space
528 needs to be created using C<isl_space_alloc>.
529 C<isl_space_dim> can be used
530 to find out the number of dimensions of each type in
531 a space, where type may be
532 C<isl_dim_param>, C<isl_dim_in> (only for relations),
533 C<isl_dim_out> (only for relations), C<isl_dim_set>
534 (only for sets) or C<isl_dim_all>.
536 To check whether a given space is that of a set or a map
537 or whether it is a parameter space, use these functions:
539 #include <isl/space.h>
540 int isl_space_is_params(__isl_keep isl_space *space);
541 int isl_space_is_set(__isl_keep isl_space *space);
543 It is often useful to create objects that live in the
544 same space as some other object. This can be accomplished
545 by creating the new objects
546 (see L<Creating New Sets and Relations> or
547 L<Creating New (Piecewise) Quasipolynomials>) based on the space
548 of the original object.
551 __isl_give isl_space *isl_basic_set_get_space(
552 __isl_keep isl_basic_set *bset);
553 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
555 #include <isl/union_set.h>
556 __isl_give isl_space *isl_union_set_get_space(
557 __isl_keep isl_union_set *uset);
560 __isl_give isl_space *isl_basic_map_get_space(
561 __isl_keep isl_basic_map *bmap);
562 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
564 #include <isl/union_map.h>
565 __isl_give isl_space *isl_union_map_get_space(
566 __isl_keep isl_union_map *umap);
568 #include <isl/constraint.h>
569 __isl_give isl_space *isl_constraint_get_space(
570 __isl_keep isl_constraint *constraint);
572 #include <isl/polynomial.h>
573 __isl_give isl_space *isl_qpolynomial_get_domain_space(
574 __isl_keep isl_qpolynomial *qp);
575 __isl_give isl_space *isl_qpolynomial_get_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_fold_get_space(
578 __isl_keep isl_qpolynomial_fold *fold);
579 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
580 __isl_keep isl_pw_qpolynomial *pwqp);
581 __isl_give isl_space *isl_pw_qpolynomial_get_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
584 __isl_keep isl_pw_qpolynomial_fold *pwf);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
588 __isl_keep isl_union_pw_qpolynomial *upwqp);
589 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
590 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
593 __isl_give isl_space *isl_aff_get_domain_space(
594 __isl_keep isl_aff *aff);
595 __isl_give isl_space *isl_aff_get_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_pw_aff_get_domain_space(
598 __isl_keep isl_pw_aff *pwaff);
599 __isl_give isl_space *isl_pw_aff_get_space(
600 __isl_keep isl_pw_aff *pwaff);
602 #include <isl/point.h>
603 __isl_give isl_space *isl_point_get_space(
604 __isl_keep isl_point *pnt);
606 The identifiers or names of the individual dimensions may be set or read off
607 using the following functions.
609 #include <isl/space.h>
610 __isl_give isl_space *isl_space_set_dim_id(
611 __isl_take isl_space *space,
612 enum isl_dim_type type, unsigned pos,
613 __isl_take isl_id *id);
614 int isl_space_has_dim_id(__isl_keep isl_space *space,
615 enum isl_dim_type type, unsigned pos);
616 __isl_give isl_id *isl_space_get_dim_id(
617 __isl_keep isl_space *space,
618 enum isl_dim_type type, unsigned pos);
619 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_keep const char *name);
622 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
625 Note that C<isl_space_get_name> returns a pointer to some internal
626 data structure, so the result can only be used while the
627 corresponding C<isl_space> is alive.
628 Also note that every function that operates on two sets or relations
629 requires that both arguments have the same parameters. This also
630 means that if one of the arguments has named parameters, then the
631 other needs to have named parameters too and the names need to match.
632 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
633 arguments may have different parameters (as long as they are named),
634 in which case the result will have as parameters the union of the parameters of
637 Given the identifier of a dimension (typically a parameter),
638 its position can be obtained from the following function.
640 #include <isl/space.h>
641 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
642 enum isl_dim_type type, __isl_keep isl_id *id);
644 The identifiers or names of entire spaces may be set or read off
645 using the following functions.
647 #include <isl/space.h>
648 __isl_give isl_space *isl_space_set_tuple_id(
649 __isl_take isl_space *space,
650 enum isl_dim_type type, __isl_take isl_id *id);
651 __isl_give isl_space *isl_space_reset_tuple_id(
652 __isl_take isl_space *space, enum isl_dim_type type);
653 int isl_space_has_tuple_id(__isl_keep isl_space *space,
654 enum isl_dim_type type);
655 __isl_give isl_id *isl_space_get_tuple_id(
656 __isl_keep isl_space *space, enum isl_dim_type type);
657 __isl_give isl_space *isl_space_set_tuple_name(
658 __isl_take isl_space *space,
659 enum isl_dim_type type, const char *s);
660 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
661 enum isl_dim_type type);
663 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
664 or C<isl_dim_set>. As with C<isl_space_get_name>,
665 the C<isl_space_get_tuple_name> function returns a pointer to some internal
667 Binary operations require the corresponding spaces of their arguments
668 to have the same name.
670 Spaces can be nested. In particular, the domain of a set or
671 the domain or range of a relation can be a nested relation.
672 The following functions can be used to construct and deconstruct
675 #include <isl/space.h>
676 int isl_space_is_wrapping(__isl_keep isl_space *space);
677 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
678 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
680 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
681 be the space of a set, while that of
682 C<isl_space_wrap> should be the space of a relation.
683 Conversely, the output of C<isl_space_unwrap> is the space
684 of a relation, while that of C<isl_space_wrap> is the space of a set.
686 Spaces can be created from other spaces
687 using the following functions.
689 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
690 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
691 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
692 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
693 __isl_give isl_space *isl_space_params(
694 __isl_take isl_space *space);
695 __isl_give isl_space *isl_space_set_from_params(
696 __isl_take isl_space *space);
697 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
698 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
699 __isl_take isl_space *right);
700 __isl_give isl_space *isl_space_align_params(
701 __isl_take isl_space *space1, __isl_take isl_space *space2)
702 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
703 enum isl_dim_type type, unsigned pos, unsigned n);
704 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned n);
706 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned first, unsigned n);
708 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
709 enum isl_dim_type dst_type, unsigned dst_pos,
710 enum isl_dim_type src_type, unsigned src_pos,
712 __isl_give isl_space *isl_space_map_from_set(
713 __isl_take isl_space *space);
714 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
716 Note that if dimensions are added or removed from a space, then
717 the name and the internal structure are lost.
721 A local space is essentially a space with
722 zero or more existentially quantified variables.
723 The local space of a basic set or relation can be obtained
724 using the following functions.
727 __isl_give isl_local_space *isl_basic_set_get_local_space(
728 __isl_keep isl_basic_set *bset);
731 __isl_give isl_local_space *isl_basic_map_get_local_space(
732 __isl_keep isl_basic_map *bmap);
734 A new local space can be created from a space using
736 #include <isl/local_space.h>
737 __isl_give isl_local_space *isl_local_space_from_space(
738 __isl_take isl_space *space);
740 They can be inspected, copied and freed using the following functions.
742 #include <isl/local_space.h>
743 isl_ctx *isl_local_space_get_ctx(
744 __isl_keep isl_local_space *ls);
745 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
746 int isl_local_space_dim(__isl_keep isl_local_space *ls,
747 enum isl_dim_type type);
748 const char *isl_local_space_get_dim_name(
749 __isl_keep isl_local_space *ls,
750 enum isl_dim_type type, unsigned pos);
751 __isl_give isl_local_space *isl_local_space_set_dim_name(
752 __isl_take isl_local_space *ls,
753 enum isl_dim_type type, unsigned pos, const char *s);
754 __isl_give isl_space *isl_local_space_get_space(
755 __isl_keep isl_local_space *ls);
756 __isl_give isl_aff *isl_local_space_get_div(
757 __isl_keep isl_local_space *ls, int pos);
758 __isl_give isl_local_space *isl_local_space_copy(
759 __isl_keep isl_local_space *ls);
760 void *isl_local_space_free(__isl_take isl_local_space *ls);
762 Two local spaces can be compared using
764 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
765 __isl_keep isl_local_space *ls2);
767 Local spaces can be created from other local spaces
768 using the following functions.
770 __isl_give isl_local_space *isl_local_space_domain(
771 __isl_take isl_local_space *ls);
772 __isl_give isl_local_space *isl_local_space_from_domain(
773 __isl_take isl_local_space *ls);
774 __isl_give isl_local_space *isl_local_space_add_dims(
775 __isl_take isl_local_space *ls,
776 enum isl_dim_type type, unsigned n);
777 __isl_give isl_local_space *isl_local_space_insert_dims(
778 __isl_take isl_local_space *ls,
779 enum isl_dim_type type, unsigned first, unsigned n);
780 __isl_give isl_local_space *isl_local_space_drop_dims(
781 __isl_take isl_local_space *ls,
782 enum isl_dim_type type, unsigned first, unsigned n);
784 =head2 Input and Output
786 C<isl> supports its own input/output format, which is similar
787 to the C<Omega> format, but also supports the C<PolyLib> format
792 The C<isl> format is similar to that of C<Omega>, but has a different
793 syntax for describing the parameters and allows for the definition
794 of an existentially quantified variable as the integer division
795 of an affine expression.
796 For example, the set of integers C<i> between C<0> and C<n>
797 such that C<i % 10 <= 6> can be described as
799 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
802 A set or relation can have several disjuncts, separated
803 by the keyword C<or>. Each disjunct is either a conjunction
804 of constraints or a projection (C<exists>) of a conjunction
805 of constraints. The constraints are separated by the keyword
808 =head3 C<PolyLib> format
810 If the represented set is a union, then the first line
811 contains a single number representing the number of disjuncts.
812 Otherwise, a line containing the number C<1> is optional.
814 Each disjunct is represented by a matrix of constraints.
815 The first line contains two numbers representing
816 the number of rows and columns,
817 where the number of rows is equal to the number of constraints
818 and the number of columns is equal to two plus the number of variables.
819 The following lines contain the actual rows of the constraint matrix.
820 In each row, the first column indicates whether the constraint
821 is an equality (C<0>) or inequality (C<1>). The final column
822 corresponds to the constant term.
824 If the set is parametric, then the coefficients of the parameters
825 appear in the last columns before the constant column.
826 The coefficients of any existentially quantified variables appear
827 between those of the set variables and those of the parameters.
829 =head3 Extended C<PolyLib> format
831 The extended C<PolyLib> format is nearly identical to the
832 C<PolyLib> format. The only difference is that the line
833 containing the number of rows and columns of a constraint matrix
834 also contains four additional numbers:
835 the number of output dimensions, the number of input dimensions,
836 the number of local dimensions (i.e., the number of existentially
837 quantified variables) and the number of parameters.
838 For sets, the number of ``output'' dimensions is equal
839 to the number of set dimensions, while the number of ``input''
845 __isl_give isl_basic_set *isl_basic_set_read_from_file(
846 isl_ctx *ctx, FILE *input);
847 __isl_give isl_basic_set *isl_basic_set_read_from_str(
848 isl_ctx *ctx, const char *str);
849 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
851 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
855 __isl_give isl_basic_map *isl_basic_map_read_from_file(
856 isl_ctx *ctx, FILE *input);
857 __isl_give isl_basic_map *isl_basic_map_read_from_str(
858 isl_ctx *ctx, const char *str);
859 __isl_give isl_map *isl_map_read_from_file(
860 isl_ctx *ctx, FILE *input);
861 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
864 #include <isl/union_set.h>
865 __isl_give isl_union_set *isl_union_set_read_from_file(
866 isl_ctx *ctx, FILE *input);
867 __isl_give isl_union_set *isl_union_set_read_from_str(
868 isl_ctx *ctx, const char *str);
870 #include <isl/union_map.h>
871 __isl_give isl_union_map *isl_union_map_read_from_file(
872 isl_ctx *ctx, FILE *input);
873 __isl_give isl_union_map *isl_union_map_read_from_str(
874 isl_ctx *ctx, const char *str);
876 The input format is autodetected and may be either the C<PolyLib> format
877 or the C<isl> format.
881 Before anything can be printed, an C<isl_printer> needs to
884 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
886 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
887 void isl_printer_free(__isl_take isl_printer *printer);
888 __isl_give char *isl_printer_get_str(
889 __isl_keep isl_printer *printer);
891 The behavior of the printer can be modified in various ways
893 __isl_give isl_printer *isl_printer_set_output_format(
894 __isl_take isl_printer *p, int output_format);
895 __isl_give isl_printer *isl_printer_set_indent(
896 __isl_take isl_printer *p, int indent);
897 __isl_give isl_printer *isl_printer_indent(
898 __isl_take isl_printer *p, int indent);
899 __isl_give isl_printer *isl_printer_set_prefix(
900 __isl_take isl_printer *p, const char *prefix);
901 __isl_give isl_printer *isl_printer_set_suffix(
902 __isl_take isl_printer *p, const char *suffix);
904 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
905 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
906 and defaults to C<ISL_FORMAT_ISL>.
907 Each line in the output is indented by C<indent> (set by
908 C<isl_printer_set_indent>) spaces
909 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
910 In the C<PolyLib> format output,
911 the coefficients of the existentially quantified variables
912 appear between those of the set variables and those
914 The function C<isl_printer_indent> increases the indentation
915 by the specified amount (which may be negative).
917 To actually print something, use
920 __isl_give isl_printer *isl_printer_print_basic_set(
921 __isl_take isl_printer *printer,
922 __isl_keep isl_basic_set *bset);
923 __isl_give isl_printer *isl_printer_print_set(
924 __isl_take isl_printer *printer,
925 __isl_keep isl_set *set);
928 __isl_give isl_printer *isl_printer_print_basic_map(
929 __isl_take isl_printer *printer,
930 __isl_keep isl_basic_map *bmap);
931 __isl_give isl_printer *isl_printer_print_map(
932 __isl_take isl_printer *printer,
933 __isl_keep isl_map *map);
935 #include <isl/union_set.h>
936 __isl_give isl_printer *isl_printer_print_union_set(
937 __isl_take isl_printer *p,
938 __isl_keep isl_union_set *uset);
940 #include <isl/union_map.h>
941 __isl_give isl_printer *isl_printer_print_union_map(
942 __isl_take isl_printer *p,
943 __isl_keep isl_union_map *umap);
945 When called on a file printer, the following function flushes
946 the file. When called on a string printer, the buffer is cleared.
948 __isl_give isl_printer *isl_printer_flush(
949 __isl_take isl_printer *p);
951 =head2 Creating New Sets and Relations
953 C<isl> has functions for creating some standard sets and relations.
957 =item * Empty sets and relations
959 __isl_give isl_basic_set *isl_basic_set_empty(
960 __isl_take isl_space *space);
961 __isl_give isl_basic_map *isl_basic_map_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_set *isl_set_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_map *isl_map_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_union_set *isl_union_set_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_union_map *isl_union_map_empty(
970 __isl_take isl_space *space);
972 For C<isl_union_set>s and C<isl_union_map>s, the space
973 is only used to specify the parameters.
975 =item * Universe sets and relations
977 __isl_give isl_basic_set *isl_basic_set_universe(
978 __isl_take isl_space *space);
979 __isl_give isl_basic_map *isl_basic_map_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_set *isl_set_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_map *isl_map_universe(
984 __isl_take isl_space *space);
985 __isl_give isl_union_set *isl_union_set_universe(
986 __isl_take isl_union_set *uset);
987 __isl_give isl_union_map *isl_union_map_universe(
988 __isl_take isl_union_map *umap);
990 The sets and relations constructed by the functions above
991 contain all integer values, while those constructed by the
992 functions below only contain non-negative values.
994 __isl_give isl_basic_set *isl_basic_set_nat_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_nat_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_nat_universe(
1001 __isl_take isl_space *space);
1003 =item * Identity relations
1005 __isl_give isl_basic_map *isl_basic_map_identity(
1006 __isl_take isl_space *space);
1007 __isl_give isl_map *isl_map_identity(
1008 __isl_take isl_space *space);
1010 The number of input and output dimensions in C<space> needs
1013 =item * Lexicographic order
1015 __isl_give isl_map *isl_map_lex_lt(
1016 __isl_take isl_space *set_space);
1017 __isl_give isl_map *isl_map_lex_le(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_gt(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_ge(
1022 __isl_take isl_space *set_space);
1023 __isl_give isl_map *isl_map_lex_lt_first(
1024 __isl_take isl_space *space, unsigned n);
1025 __isl_give isl_map *isl_map_lex_le_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_gt_first(
1028 __isl_take isl_space *space, unsigned n);
1029 __isl_give isl_map *isl_map_lex_ge_first(
1030 __isl_take isl_space *space, unsigned n);
1032 The first four functions take a space for a B<set>
1033 and return relations that express that the elements in the domain
1034 are lexicographically less
1035 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1036 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1037 than the elements in the range.
1038 The last four functions take a space for a map
1039 and return relations that express that the first C<n> dimensions
1040 in the domain are lexicographically less
1041 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1042 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1043 than the first C<n> dimensions in the range.
1047 A basic set or relation can be converted to a set or relation
1048 using the following functions.
1050 __isl_give isl_set *isl_set_from_basic_set(
1051 __isl_take isl_basic_set *bset);
1052 __isl_give isl_map *isl_map_from_basic_map(
1053 __isl_take isl_basic_map *bmap);
1055 Sets and relations can be converted to union sets and relations
1056 using the following functions.
1058 __isl_give isl_union_map *isl_union_map_from_map(
1059 __isl_take isl_map *map);
1060 __isl_give isl_union_set *isl_union_set_from_set(
1061 __isl_take isl_set *set);
1063 The inverse conversions below can only be used if the input
1064 union set or relation is known to contain elements in exactly one
1067 __isl_give isl_set *isl_set_from_union_set(
1068 __isl_take isl_union_set *uset);
1069 __isl_give isl_map *isl_map_from_union_map(
1070 __isl_take isl_union_map *umap);
1072 A zero-dimensional set can be constructed on a given parameter domain
1073 using the following function.
1075 __isl_give isl_set *isl_set_from_params(
1076 __isl_take isl_set *set);
1078 Sets and relations can be copied and freed again using the following
1081 __isl_give isl_basic_set *isl_basic_set_copy(
1082 __isl_keep isl_basic_set *bset);
1083 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1084 __isl_give isl_union_set *isl_union_set_copy(
1085 __isl_keep isl_union_set *uset);
1086 __isl_give isl_basic_map *isl_basic_map_copy(
1087 __isl_keep isl_basic_map *bmap);
1088 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1089 __isl_give isl_union_map *isl_union_map_copy(
1090 __isl_keep isl_union_map *umap);
1091 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1092 void isl_set_free(__isl_take isl_set *set);
1093 void *isl_union_set_free(__isl_take isl_union_set *uset);
1094 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1095 void isl_map_free(__isl_take isl_map *map);
1096 void *isl_union_map_free(__isl_take isl_union_map *umap);
1098 Other sets and relations can be constructed by starting
1099 from a universe set or relation, adding equality and/or
1100 inequality constraints and then projecting out the
1101 existentially quantified variables, if any.
1102 Constraints can be constructed, manipulated and
1103 added to (or removed from) (basic) sets and relations
1104 using the following functions.
1106 #include <isl/constraint.h>
1107 __isl_give isl_constraint *isl_equality_alloc(
1108 __isl_take isl_local_space *ls);
1109 __isl_give isl_constraint *isl_inequality_alloc(
1110 __isl_take isl_local_space *ls);
1111 __isl_give isl_constraint *isl_constraint_set_constant(
1112 __isl_take isl_constraint *constraint, isl_int v);
1113 __isl_give isl_constraint *isl_constraint_set_constant_si(
1114 __isl_take isl_constraint *constraint, int v);
1115 __isl_give isl_constraint *isl_constraint_set_coefficient(
1116 __isl_take isl_constraint *constraint,
1117 enum isl_dim_type type, int pos, isl_int v);
1118 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1119 __isl_take isl_constraint *constraint,
1120 enum isl_dim_type type, int pos, int v);
1121 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1122 __isl_take isl_basic_map *bmap,
1123 __isl_take isl_constraint *constraint);
1124 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1125 __isl_take isl_basic_set *bset,
1126 __isl_take isl_constraint *constraint);
1127 __isl_give isl_map *isl_map_add_constraint(
1128 __isl_take isl_map *map,
1129 __isl_take isl_constraint *constraint);
1130 __isl_give isl_set *isl_set_add_constraint(
1131 __isl_take isl_set *set,
1132 __isl_take isl_constraint *constraint);
1133 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1134 __isl_take isl_basic_set *bset,
1135 __isl_take isl_constraint *constraint);
1137 For example, to create a set containing the even integers
1138 between 10 and 42, you would use the following code.
1141 isl_local_space *ls;
1143 isl_basic_set *bset;
1145 space = isl_space_set_alloc(ctx, 0, 2);
1146 bset = isl_basic_set_universe(isl_space_copy(space));
1147 ls = isl_local_space_from_space(space);
1149 c = isl_equality_alloc(isl_local_space_copy(ls));
1150 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1151 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1152 bset = isl_basic_set_add_constraint(bset, c);
1154 c = isl_inequality_alloc(isl_local_space_copy(ls));
1155 c = isl_constraint_set_constant_si(c, -10);
1156 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1157 bset = isl_basic_set_add_constraint(bset, c);
1159 c = isl_inequality_alloc(ls);
1160 c = isl_constraint_set_constant_si(c, 42);
1161 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1162 bset = isl_basic_set_add_constraint(bset, c);
1164 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1168 isl_basic_set *bset;
1169 bset = isl_basic_set_read_from_str(ctx,
1170 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1172 A basic set or relation can also be constructed from two matrices
1173 describing the equalities and the inequalities.
1175 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1176 __isl_take isl_space *space,
1177 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1178 enum isl_dim_type c1,
1179 enum isl_dim_type c2, enum isl_dim_type c3,
1180 enum isl_dim_type c4);
1181 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1182 __isl_take isl_space *space,
1183 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1184 enum isl_dim_type c1,
1185 enum isl_dim_type c2, enum isl_dim_type c3,
1186 enum isl_dim_type c4, enum isl_dim_type c5);
1188 The C<isl_dim_type> arguments indicate the order in which
1189 different kinds of variables appear in the input matrices
1190 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1191 C<isl_dim_set> and C<isl_dim_div> for sets and
1192 of C<isl_dim_cst>, C<isl_dim_param>,
1193 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1195 A (basic) set or relation can also be constructed from a (piecewise)
1197 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1199 __isl_give isl_basic_map *isl_basic_map_from_aff(
1200 __isl_take isl_aff *aff);
1201 __isl_give isl_set *isl_set_from_pw_aff(
1202 __isl_take isl_pw_aff *pwaff);
1203 __isl_give isl_map *isl_map_from_pw_aff(
1204 __isl_take isl_pw_aff *pwaff);
1205 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1206 __isl_take isl_space *domain_space,
1207 __isl_take isl_aff_list *list);
1209 The C<domain_dim> argument describes the domain of the resulting
1210 basic relation. It is required because the C<list> may consist
1211 of zero affine expressions.
1213 =head2 Inspecting Sets and Relations
1215 Usually, the user should not have to care about the actual constraints
1216 of the sets and maps, but should instead apply the abstract operations
1217 explained in the following sections.
1218 Occasionally, however, it may be required to inspect the individual
1219 coefficients of the constraints. This section explains how to do so.
1220 In these cases, it may also be useful to have C<isl> compute
1221 an explicit representation of the existentially quantified variables.
1223 __isl_give isl_set *isl_set_compute_divs(
1224 __isl_take isl_set *set);
1225 __isl_give isl_map *isl_map_compute_divs(
1226 __isl_take isl_map *map);
1227 __isl_give isl_union_set *isl_union_set_compute_divs(
1228 __isl_take isl_union_set *uset);
1229 __isl_give isl_union_map *isl_union_map_compute_divs(
1230 __isl_take isl_union_map *umap);
1232 This explicit representation defines the existentially quantified
1233 variables as integer divisions of the other variables, possibly
1234 including earlier existentially quantified variables.
1235 An explicitly represented existentially quantified variable therefore
1236 has a unique value when the values of the other variables are known.
1237 If, furthermore, the same existentials, i.e., existentials
1238 with the same explicit representations, should appear in the
1239 same order in each of the disjuncts of a set or map, then the user should call
1240 either of the following functions.
1242 __isl_give isl_set *isl_set_align_divs(
1243 __isl_take isl_set *set);
1244 __isl_give isl_map *isl_map_align_divs(
1245 __isl_take isl_map *map);
1247 Alternatively, the existentially quantified variables can be removed
1248 using the following functions, which compute an overapproximation.
1250 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1251 __isl_take isl_basic_set *bset);
1252 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1253 __isl_take isl_basic_map *bmap);
1254 __isl_give isl_set *isl_set_remove_divs(
1255 __isl_take isl_set *set);
1256 __isl_give isl_map *isl_map_remove_divs(
1257 __isl_take isl_map *map);
1259 To iterate over all the sets or maps in a union set or map, use
1261 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1262 int (*fn)(__isl_take isl_set *set, void *user),
1264 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1265 int (*fn)(__isl_take isl_map *map, void *user),
1268 The number of sets or maps in a union set or map can be obtained
1271 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1272 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1274 To extract the set or map in a given space from a union, use
1276 __isl_give isl_set *isl_union_set_extract_set(
1277 __isl_keep isl_union_set *uset,
1278 __isl_take isl_space *space);
1279 __isl_give isl_map *isl_union_map_extract_map(
1280 __isl_keep isl_union_map *umap,
1281 __isl_take isl_space *space);
1283 To iterate over all the basic sets or maps in a set or map, use
1285 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1286 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1288 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1289 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1292 The callback function C<fn> should return 0 if successful and
1293 -1 if an error occurs. In the latter case, or if any other error
1294 occurs, the above functions will return -1.
1296 It should be noted that C<isl> does not guarantee that
1297 the basic sets or maps passed to C<fn> are disjoint.
1298 If this is required, then the user should call one of
1299 the following functions first.
1301 __isl_give isl_set *isl_set_make_disjoint(
1302 __isl_take isl_set *set);
1303 __isl_give isl_map *isl_map_make_disjoint(
1304 __isl_take isl_map *map);
1306 The number of basic sets in a set can be obtained
1309 int isl_set_n_basic_set(__isl_keep isl_set *set);
1311 To iterate over the constraints of a basic set or map, use
1313 #include <isl/constraint.h>
1315 int isl_basic_map_foreach_constraint(
1316 __isl_keep isl_basic_map *bmap,
1317 int (*fn)(__isl_take isl_constraint *c, void *user),
1319 void *isl_constraint_free(__isl_take isl_constraint *c);
1321 Again, the callback function C<fn> should return 0 if successful and
1322 -1 if an error occurs. In the latter case, or if any other error
1323 occurs, the above functions will return -1.
1324 The constraint C<c> represents either an equality or an inequality.
1325 Use the following function to find out whether a constraint
1326 represents an equality. If not, it represents an inequality.
1328 int isl_constraint_is_equality(
1329 __isl_keep isl_constraint *constraint);
1331 The coefficients of the constraints can be inspected using
1332 the following functions.
1334 void isl_constraint_get_constant(
1335 __isl_keep isl_constraint *constraint, isl_int *v);
1336 void isl_constraint_get_coefficient(
1337 __isl_keep isl_constraint *constraint,
1338 enum isl_dim_type type, int pos, isl_int *v);
1339 int isl_constraint_involves_dims(
1340 __isl_keep isl_constraint *constraint,
1341 enum isl_dim_type type, unsigned first, unsigned n);
1343 The explicit representations of the existentially quantified
1344 variables can be inspected using the following function.
1345 Note that the user is only allowed to use this function
1346 if the inspected set or map is the result of a call
1347 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1348 The existentially quantified variable is equal to the floor
1349 of the returned affine expression. The affine expression
1350 itself can be inspected using the functions in
1351 L<"Piecewise Quasi Affine Expressions">.
1353 __isl_give isl_aff *isl_constraint_get_div(
1354 __isl_keep isl_constraint *constraint, int pos);
1356 To obtain the constraints of a basic set or map in matrix
1357 form, use the following functions.
1359 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1360 __isl_keep isl_basic_set *bset,
1361 enum isl_dim_type c1, enum isl_dim_type c2,
1362 enum isl_dim_type c3, enum isl_dim_type c4);
1363 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1364 __isl_keep isl_basic_set *bset,
1365 enum isl_dim_type c1, enum isl_dim_type c2,
1366 enum isl_dim_type c3, enum isl_dim_type c4);
1367 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1368 __isl_keep isl_basic_map *bmap,
1369 enum isl_dim_type c1,
1370 enum isl_dim_type c2, enum isl_dim_type c3,
1371 enum isl_dim_type c4, enum isl_dim_type c5);
1372 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1373 __isl_keep isl_basic_map *bmap,
1374 enum isl_dim_type c1,
1375 enum isl_dim_type c2, enum isl_dim_type c3,
1376 enum isl_dim_type c4, enum isl_dim_type c5);
1378 The C<isl_dim_type> arguments dictate the order in which
1379 different kinds of variables appear in the resulting matrix
1380 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1381 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1383 The number of parameters, input, output or set dimensions can
1384 be obtained using the following functions.
1386 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1387 enum isl_dim_type type);
1388 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1389 enum isl_dim_type type);
1390 unsigned isl_set_dim(__isl_keep isl_set *set,
1391 enum isl_dim_type type);
1392 unsigned isl_map_dim(__isl_keep isl_map *map,
1393 enum isl_dim_type type);
1395 To check whether the description of a set or relation depends
1396 on one or more given dimensions, it is not necessary to iterate over all
1397 constraints. Instead the following functions can be used.
1399 int isl_basic_set_involves_dims(
1400 __isl_keep isl_basic_set *bset,
1401 enum isl_dim_type type, unsigned first, unsigned n);
1402 int isl_set_involves_dims(__isl_keep isl_set *set,
1403 enum isl_dim_type type, unsigned first, unsigned n);
1404 int isl_basic_map_involves_dims(
1405 __isl_keep isl_basic_map *bmap,
1406 enum isl_dim_type type, unsigned first, unsigned n);
1407 int isl_map_involves_dims(__isl_keep isl_map *map,
1408 enum isl_dim_type type, unsigned first, unsigned n);
1410 Similarly, the following functions can be used to check whether
1411 a given dimension is involved in any lower or upper bound.
1413 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1414 enum isl_dim_type type, unsigned pos);
1415 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1416 enum isl_dim_type type, unsigned pos);
1418 The identifiers or names of the domain and range spaces of a set
1419 or relation can be read off or set using the following functions.
1421 __isl_give isl_set *isl_set_set_tuple_id(
1422 __isl_take isl_set *set, __isl_take isl_id *id);
1423 __isl_give isl_set *isl_set_reset_tuple_id(
1424 __isl_take isl_set *set);
1425 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1426 __isl_give isl_id *isl_set_get_tuple_id(
1427 __isl_keep isl_set *set);
1428 __isl_give isl_map *isl_map_set_tuple_id(
1429 __isl_take isl_map *map, enum isl_dim_type type,
1430 __isl_take isl_id *id);
1431 __isl_give isl_map *isl_map_reset_tuple_id(
1432 __isl_take isl_map *map, enum isl_dim_type type);
1433 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1434 enum isl_dim_type type);
1435 __isl_give isl_id *isl_map_get_tuple_id(
1436 __isl_keep isl_map *map, enum isl_dim_type type);
1438 const char *isl_basic_set_get_tuple_name(
1439 __isl_keep isl_basic_set *bset);
1440 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1441 __isl_take isl_basic_set *set, const char *s);
1442 const char *isl_set_get_tuple_name(
1443 __isl_keep isl_set *set);
1444 const char *isl_basic_map_get_tuple_name(
1445 __isl_keep isl_basic_map *bmap,
1446 enum isl_dim_type type);
1447 const char *isl_map_get_tuple_name(
1448 __isl_keep isl_map *map,
1449 enum isl_dim_type type);
1451 As with C<isl_space_get_tuple_name>, the value returned points to
1452 an internal data structure.
1453 The identifiers, positions or names of individual dimensions can be
1454 read off using the following functions.
1456 __isl_give isl_set *isl_set_set_dim_id(
1457 __isl_take isl_set *set, enum isl_dim_type type,
1458 unsigned pos, __isl_take isl_id *id);
1459 int isl_set_has_dim_id(__isl_keep isl_set *set,
1460 enum isl_dim_type type, unsigned pos);
1461 __isl_give isl_id *isl_set_get_dim_id(
1462 __isl_keep isl_set *set, enum isl_dim_type type,
1464 __isl_give isl_map *isl_map_set_dim_id(
1465 __isl_take isl_map *map, enum isl_dim_type type,
1466 unsigned pos, __isl_take isl_id *id);
1467 int isl_map_has_dim_id(__isl_keep isl_map *map,
1468 enum isl_dim_type type, unsigned pos);
1469 __isl_give isl_id *isl_map_get_dim_id(
1470 __isl_keep isl_map *map, enum isl_dim_type type,
1473 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1474 enum isl_dim_type type, __isl_keep isl_id *id);
1475 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1476 enum isl_dim_type type, __isl_keep isl_id *id);
1478 const char *isl_constraint_get_dim_name(
1479 __isl_keep isl_constraint *constraint,
1480 enum isl_dim_type type, unsigned pos);
1481 const char *isl_basic_set_get_dim_name(
1482 __isl_keep isl_basic_set *bset,
1483 enum isl_dim_type type, unsigned pos);
1484 const char *isl_set_get_dim_name(
1485 __isl_keep isl_set *set,
1486 enum isl_dim_type type, unsigned pos);
1487 const char *isl_basic_map_get_dim_name(
1488 __isl_keep isl_basic_map *bmap,
1489 enum isl_dim_type type, unsigned pos);
1490 const char *isl_map_get_dim_name(
1491 __isl_keep isl_map *map,
1492 enum isl_dim_type type, unsigned pos);
1494 These functions are mostly useful to obtain the identifiers, positions
1495 or names of the parameters. Identifiers of individual dimensions are
1496 essentially only useful for printing. They are ignored by all other
1497 operations and may not be preserved across those operations.
1501 =head3 Unary Properties
1507 The following functions test whether the given set or relation
1508 contains any integer points. The ``plain'' variants do not perform
1509 any computations, but simply check if the given set or relation
1510 is already known to be empty.
1512 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1513 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1514 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1515 int isl_set_is_empty(__isl_keep isl_set *set);
1516 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1517 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1518 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1519 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1520 int isl_map_is_empty(__isl_keep isl_map *map);
1521 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1523 =item * Universality
1525 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1526 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1527 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1529 =item * Single-valuedness
1531 int isl_map_is_single_valued(__isl_keep isl_map *map);
1532 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1536 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1537 int isl_map_is_injective(__isl_keep isl_map *map);
1538 int isl_union_map_plain_is_injective(
1539 __isl_keep isl_union_map *umap);
1540 int isl_union_map_is_injective(
1541 __isl_keep isl_union_map *umap);
1545 int isl_map_is_bijective(__isl_keep isl_map *map);
1546 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1550 int isl_basic_map_plain_is_fixed(
1551 __isl_keep isl_basic_map *bmap,
1552 enum isl_dim_type type, unsigned pos,
1554 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1555 enum isl_dim_type type, unsigned pos,
1557 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1558 enum isl_dim_type type, unsigned pos,
1561 Check if the relation obviously lies on a hyperplane where the given dimension
1562 has a fixed value and if so, return that value in C<*val>.
1566 To check whether a set is a parameter domain, use this function:
1568 int isl_set_is_params(__isl_keep isl_set *set);
1572 The following functions check whether the domain of the given
1573 (basic) set is a wrapped relation.
1575 int isl_basic_set_is_wrapping(
1576 __isl_keep isl_basic_set *bset);
1577 int isl_set_is_wrapping(__isl_keep isl_set *set);
1579 =item * Internal Product
1581 int isl_basic_map_can_zip(
1582 __isl_keep isl_basic_map *bmap);
1583 int isl_map_can_zip(__isl_keep isl_map *map);
1585 Check whether the product of domain and range of the given relation
1587 i.e., whether both domain and range are nested relations.
1591 =head3 Binary Properties
1597 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1598 __isl_keep isl_set *set2);
1599 int isl_set_is_equal(__isl_keep isl_set *set1,
1600 __isl_keep isl_set *set2);
1601 int isl_union_set_is_equal(
1602 __isl_keep isl_union_set *uset1,
1603 __isl_keep isl_union_set *uset2);
1604 int isl_basic_map_is_equal(
1605 __isl_keep isl_basic_map *bmap1,
1606 __isl_keep isl_basic_map *bmap2);
1607 int isl_map_is_equal(__isl_keep isl_map *map1,
1608 __isl_keep isl_map *map2);
1609 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1610 __isl_keep isl_map *map2);
1611 int isl_union_map_is_equal(
1612 __isl_keep isl_union_map *umap1,
1613 __isl_keep isl_union_map *umap2);
1615 =item * Disjointness
1617 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1618 __isl_keep isl_set *set2);
1622 int isl_set_is_subset(__isl_keep isl_set *set1,
1623 __isl_keep isl_set *set2);
1624 int isl_set_is_strict_subset(
1625 __isl_keep isl_set *set1,
1626 __isl_keep isl_set *set2);
1627 int isl_union_set_is_subset(
1628 __isl_keep isl_union_set *uset1,
1629 __isl_keep isl_union_set *uset2);
1630 int isl_union_set_is_strict_subset(
1631 __isl_keep isl_union_set *uset1,
1632 __isl_keep isl_union_set *uset2);
1633 int isl_basic_map_is_subset(
1634 __isl_keep isl_basic_map *bmap1,
1635 __isl_keep isl_basic_map *bmap2);
1636 int isl_basic_map_is_strict_subset(
1637 __isl_keep isl_basic_map *bmap1,
1638 __isl_keep isl_basic_map *bmap2);
1639 int isl_map_is_subset(
1640 __isl_keep isl_map *map1,
1641 __isl_keep isl_map *map2);
1642 int isl_map_is_strict_subset(
1643 __isl_keep isl_map *map1,
1644 __isl_keep isl_map *map2);
1645 int isl_union_map_is_subset(
1646 __isl_keep isl_union_map *umap1,
1647 __isl_keep isl_union_map *umap2);
1648 int isl_union_map_is_strict_subset(
1649 __isl_keep isl_union_map *umap1,
1650 __isl_keep isl_union_map *umap2);
1654 =head2 Unary Operations
1660 __isl_give isl_set *isl_set_complement(
1661 __isl_take isl_set *set);
1665 __isl_give isl_basic_map *isl_basic_map_reverse(
1666 __isl_take isl_basic_map *bmap);
1667 __isl_give isl_map *isl_map_reverse(
1668 __isl_take isl_map *map);
1669 __isl_give isl_union_map *isl_union_map_reverse(
1670 __isl_take isl_union_map *umap);
1674 __isl_give isl_basic_set *isl_basic_set_project_out(
1675 __isl_take isl_basic_set *bset,
1676 enum isl_dim_type type, unsigned first, unsigned n);
1677 __isl_give isl_basic_map *isl_basic_map_project_out(
1678 __isl_take isl_basic_map *bmap,
1679 enum isl_dim_type type, unsigned first, unsigned n);
1680 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1681 enum isl_dim_type type, unsigned first, unsigned n);
1682 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1683 enum isl_dim_type type, unsigned first, unsigned n);
1684 __isl_give isl_basic_set *isl_basic_set_params(
1685 __isl_take isl_basic_set *bset);
1686 __isl_give isl_basic_set *isl_basic_map_domain(
1687 __isl_take isl_basic_map *bmap);
1688 __isl_give isl_basic_set *isl_basic_map_range(
1689 __isl_take isl_basic_map *bmap);
1690 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1691 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1692 __isl_give isl_set *isl_map_domain(
1693 __isl_take isl_map *bmap);
1694 __isl_give isl_set *isl_map_range(
1695 __isl_take isl_map *map);
1696 __isl_give isl_union_set *isl_union_map_domain(
1697 __isl_take isl_union_map *umap);
1698 __isl_give isl_union_set *isl_union_map_range(
1699 __isl_take isl_union_map *umap);
1701 __isl_give isl_basic_map *isl_basic_map_domain_map(
1702 __isl_take isl_basic_map *bmap);
1703 __isl_give isl_basic_map *isl_basic_map_range_map(
1704 __isl_take isl_basic_map *bmap);
1705 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1706 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1707 __isl_give isl_union_map *isl_union_map_domain_map(
1708 __isl_take isl_union_map *umap);
1709 __isl_give isl_union_map *isl_union_map_range_map(
1710 __isl_take isl_union_map *umap);
1712 The functions above construct a (basic, regular or union) relation
1713 that maps (a wrapped version of) the input relation to its domain or range.
1717 __isl_give isl_set *isl_set_eliminate(
1718 __isl_take isl_set *set, enum isl_dim_type type,
1719 unsigned first, unsigned n);
1721 Eliminate the coefficients for the given dimensions from the constraints,
1722 without removing the dimensions.
1726 __isl_give isl_basic_set *isl_basic_set_fix(
1727 __isl_take isl_basic_set *bset,
1728 enum isl_dim_type type, unsigned pos,
1730 __isl_give isl_basic_set *isl_basic_set_fix_si(
1731 __isl_take isl_basic_set *bset,
1732 enum isl_dim_type type, unsigned pos, int value);
1733 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1734 enum isl_dim_type type, unsigned pos,
1736 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1737 enum isl_dim_type type, unsigned pos, int value);
1738 __isl_give isl_basic_map *isl_basic_map_fix_si(
1739 __isl_take isl_basic_map *bmap,
1740 enum isl_dim_type type, unsigned pos, int value);
1741 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1742 enum isl_dim_type type, unsigned pos, int value);
1744 Intersect the set or relation with the hyperplane where the given
1745 dimension has the fixed given value.
1747 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1748 enum isl_dim_type type1, int pos1,
1749 enum isl_dim_type type2, int pos2);
1750 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1751 enum isl_dim_type type1, int pos1,
1752 enum isl_dim_type type2, int pos2);
1754 Intersect the set or relation with the hyperplane where the given
1755 dimensions are equal to each other.
1757 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1758 enum isl_dim_type type1, int pos1,
1759 enum isl_dim_type type2, int pos2);
1761 Intersect the relation with the hyperplane where the given
1762 dimensions have opposite values.
1766 __isl_give isl_map *isl_set_identity(
1767 __isl_take isl_set *set);
1768 __isl_give isl_union_map *isl_union_set_identity(
1769 __isl_take isl_union_set *uset);
1771 Construct an identity relation on the given (union) set.
1775 __isl_give isl_basic_set *isl_basic_map_deltas(
1776 __isl_take isl_basic_map *bmap);
1777 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1778 __isl_give isl_union_set *isl_union_map_deltas(
1779 __isl_take isl_union_map *umap);
1781 These functions return a (basic) set containing the differences
1782 between image elements and corresponding domain elements in the input.
1784 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1785 __isl_take isl_basic_map *bmap);
1786 __isl_give isl_map *isl_map_deltas_map(
1787 __isl_take isl_map *map);
1788 __isl_give isl_union_map *isl_union_map_deltas_map(
1789 __isl_take isl_union_map *umap);
1791 The functions above construct a (basic, regular or union) relation
1792 that maps (a wrapped version of) the input relation to its delta set.
1796 Simplify the representation of a set or relation by trying
1797 to combine pairs of basic sets or relations into a single
1798 basic set or relation.
1800 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1801 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1802 __isl_give isl_union_set *isl_union_set_coalesce(
1803 __isl_take isl_union_set *uset);
1804 __isl_give isl_union_map *isl_union_map_coalesce(
1805 __isl_take isl_union_map *umap);
1807 =item * Detecting equalities
1809 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1810 __isl_take isl_basic_set *bset);
1811 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1812 __isl_take isl_basic_map *bmap);
1813 __isl_give isl_set *isl_set_detect_equalities(
1814 __isl_take isl_set *set);
1815 __isl_give isl_map *isl_map_detect_equalities(
1816 __isl_take isl_map *map);
1817 __isl_give isl_union_set *isl_union_set_detect_equalities(
1818 __isl_take isl_union_set *uset);
1819 __isl_give isl_union_map *isl_union_map_detect_equalities(
1820 __isl_take isl_union_map *umap);
1822 Simplify the representation of a set or relation by detecting implicit
1825 =item * Removing redundant constraints
1827 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1828 __isl_take isl_basic_set *bset);
1829 __isl_give isl_set *isl_set_remove_redundancies(
1830 __isl_take isl_set *set);
1831 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1832 __isl_take isl_basic_map *bmap);
1833 __isl_give isl_map *isl_map_remove_redundancies(
1834 __isl_take isl_map *map);
1838 __isl_give isl_basic_set *isl_set_convex_hull(
1839 __isl_take isl_set *set);
1840 __isl_give isl_basic_map *isl_map_convex_hull(
1841 __isl_take isl_map *map);
1843 If the input set or relation has any existentially quantified
1844 variables, then the result of these operations is currently undefined.
1848 __isl_give isl_basic_set *isl_set_simple_hull(
1849 __isl_take isl_set *set);
1850 __isl_give isl_basic_map *isl_map_simple_hull(
1851 __isl_take isl_map *map);
1852 __isl_give isl_union_map *isl_union_map_simple_hull(
1853 __isl_take isl_union_map *umap);
1855 These functions compute a single basic set or relation
1856 that contains the whole input set or relation.
1857 In particular, the output is described by translates
1858 of the constraints describing the basic sets or relations in the input.
1862 (See \autoref{s:simple hull}.)
1868 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1869 __isl_take isl_basic_set *bset);
1870 __isl_give isl_basic_set *isl_set_affine_hull(
1871 __isl_take isl_set *set);
1872 __isl_give isl_union_set *isl_union_set_affine_hull(
1873 __isl_take isl_union_set *uset);
1874 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1875 __isl_take isl_basic_map *bmap);
1876 __isl_give isl_basic_map *isl_map_affine_hull(
1877 __isl_take isl_map *map);
1878 __isl_give isl_union_map *isl_union_map_affine_hull(
1879 __isl_take isl_union_map *umap);
1881 In case of union sets and relations, the affine hull is computed
1884 =item * Polyhedral hull
1886 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1887 __isl_take isl_set *set);
1888 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1889 __isl_take isl_map *map);
1890 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1891 __isl_take isl_union_set *uset);
1892 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1893 __isl_take isl_union_map *umap);
1895 These functions compute a single basic set or relation
1896 not involving any existentially quantified variables
1897 that contains the whole input set or relation.
1898 In case of union sets and relations, the polyhedral hull is computed
1901 =item * Optimization
1903 #include <isl/ilp.h>
1904 enum isl_lp_result isl_basic_set_max(
1905 __isl_keep isl_basic_set *bset,
1906 __isl_keep isl_aff *obj, isl_int *opt)
1907 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1908 __isl_keep isl_aff *obj, isl_int *opt);
1909 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1910 __isl_keep isl_aff *obj, isl_int *opt);
1912 Compute the minimum or maximum of the integer affine expression C<obj>
1913 over the points in C<set>, returning the result in C<opt>.
1914 The return value may be one of C<isl_lp_error>,
1915 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1917 =item * Parametric optimization
1919 __isl_give isl_pw_aff *isl_set_dim_min(
1920 __isl_take isl_set *set, int pos);
1921 __isl_give isl_pw_aff *isl_set_dim_max(
1922 __isl_take isl_set *set, int pos);
1924 Compute the minimum or maximum of the given set dimension as a function of the
1925 parameters, but independently of the other set dimensions.
1926 For lexicographic optimization, see L<"Lexicographic Optimization">.
1930 The following functions compute either the set of (rational) coefficient
1931 values of valid constraints for the given set or the set of (rational)
1932 values satisfying the constraints with coefficients from the given set.
1933 Internally, these two sets of functions perform essentially the
1934 same operations, except that the set of coefficients is assumed to
1935 be a cone, while the set of values may be any polyhedron.
1936 The current implementation is based on the Farkas lemma and
1937 Fourier-Motzkin elimination, but this may change or be made optional
1938 in future. In particular, future implementations may use different
1939 dualization algorithms or skip the elimination step.
1941 __isl_give isl_basic_set *isl_basic_set_coefficients(
1942 __isl_take isl_basic_set *bset);
1943 __isl_give isl_basic_set *isl_set_coefficients(
1944 __isl_take isl_set *set);
1945 __isl_give isl_union_set *isl_union_set_coefficients(
1946 __isl_take isl_union_set *bset);
1947 __isl_give isl_basic_set *isl_basic_set_solutions(
1948 __isl_take isl_basic_set *bset);
1949 __isl_give isl_basic_set *isl_set_solutions(
1950 __isl_take isl_set *set);
1951 __isl_give isl_union_set *isl_union_set_solutions(
1952 __isl_take isl_union_set *bset);
1956 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1958 __isl_give isl_union_map *isl_union_map_power(
1959 __isl_take isl_union_map *umap, int *exact);
1961 Compute a parametric representation for all positive powers I<k> of C<map>.
1962 The result maps I<k> to a nested relation corresponding to the
1963 I<k>th power of C<map>.
1964 The result may be an overapproximation. If the result is known to be exact,
1965 then C<*exact> is set to C<1>.
1967 =item * Transitive closure
1969 __isl_give isl_map *isl_map_transitive_closure(
1970 __isl_take isl_map *map, int *exact);
1971 __isl_give isl_union_map *isl_union_map_transitive_closure(
1972 __isl_take isl_union_map *umap, int *exact);
1974 Compute the transitive closure of C<map>.
1975 The result may be an overapproximation. If the result is known to be exact,
1976 then C<*exact> is set to C<1>.
1978 =item * Reaching path lengths
1980 __isl_give isl_map *isl_map_reaching_path_lengths(
1981 __isl_take isl_map *map, int *exact);
1983 Compute a relation that maps each element in the range of C<map>
1984 to the lengths of all paths composed of edges in C<map> that
1985 end up in the given element.
1986 The result may be an overapproximation. If the result is known to be exact,
1987 then C<*exact> is set to C<1>.
1988 To compute the I<maximal> path length, the resulting relation
1989 should be postprocessed by C<isl_map_lexmax>.
1990 In particular, if the input relation is a dependence relation
1991 (mapping sources to sinks), then the maximal path length corresponds
1992 to the free schedule.
1993 Note, however, that C<isl_map_lexmax> expects the maximum to be
1994 finite, so if the path lengths are unbounded (possibly due to
1995 the overapproximation), then you will get an error message.
1999 __isl_give isl_basic_set *isl_basic_map_wrap(
2000 __isl_take isl_basic_map *bmap);
2001 __isl_give isl_set *isl_map_wrap(
2002 __isl_take isl_map *map);
2003 __isl_give isl_union_set *isl_union_map_wrap(
2004 __isl_take isl_union_map *umap);
2005 __isl_give isl_basic_map *isl_basic_set_unwrap(
2006 __isl_take isl_basic_set *bset);
2007 __isl_give isl_map *isl_set_unwrap(
2008 __isl_take isl_set *set);
2009 __isl_give isl_union_map *isl_union_set_unwrap(
2010 __isl_take isl_union_set *uset);
2014 Remove any internal structure of domain (and range) of the given
2015 set or relation. If there is any such internal structure in the input,
2016 then the name of the space is also removed.
2018 __isl_give isl_basic_set *isl_basic_set_flatten(
2019 __isl_take isl_basic_set *bset);
2020 __isl_give isl_set *isl_set_flatten(
2021 __isl_take isl_set *set);
2022 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2023 __isl_take isl_basic_map *bmap);
2024 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2025 __isl_take isl_basic_map *bmap);
2026 __isl_give isl_map *isl_map_flatten_range(
2027 __isl_take isl_map *map);
2028 __isl_give isl_map *isl_map_flatten_domain(
2029 __isl_take isl_map *map);
2030 __isl_give isl_basic_map *isl_basic_map_flatten(
2031 __isl_take isl_basic_map *bmap);
2032 __isl_give isl_map *isl_map_flatten(
2033 __isl_take isl_map *map);
2035 __isl_give isl_map *isl_set_flatten_map(
2036 __isl_take isl_set *set);
2038 The function above constructs a relation
2039 that maps the input set to a flattened version of the set.
2043 Lift the input set to a space with extra dimensions corresponding
2044 to the existentially quantified variables in the input.
2045 In particular, the result lives in a wrapped map where the domain
2046 is the original space and the range corresponds to the original
2047 existentially quantified variables.
2049 __isl_give isl_basic_set *isl_basic_set_lift(
2050 __isl_take isl_basic_set *bset);
2051 __isl_give isl_set *isl_set_lift(
2052 __isl_take isl_set *set);
2053 __isl_give isl_union_set *isl_union_set_lift(
2054 __isl_take isl_union_set *uset);
2056 =item * Internal Product
2058 __isl_give isl_basic_map *isl_basic_map_zip(
2059 __isl_take isl_basic_map *bmap);
2060 __isl_give isl_map *isl_map_zip(
2061 __isl_take isl_map *map);
2062 __isl_give isl_union_map *isl_union_map_zip(
2063 __isl_take isl_union_map *umap);
2065 Given a relation with nested relations for domain and range,
2066 interchange the range of the domain with the domain of the range.
2068 =item * Aligning parameters
2070 __isl_give isl_set *isl_set_align_params(
2071 __isl_take isl_set *set,
2072 __isl_take isl_space *model);
2073 __isl_give isl_map *isl_map_align_params(
2074 __isl_take isl_map *map,
2075 __isl_take isl_space *model);
2077 Change the order of the parameters of the given set or relation
2078 such that the first parameters match those of C<model>.
2079 This may involve the introduction of extra parameters.
2080 All parameters need to be named.
2082 =item * Dimension manipulation
2084 __isl_give isl_set *isl_set_add_dims(
2085 __isl_take isl_set *set,
2086 enum isl_dim_type type, unsigned n);
2087 __isl_give isl_map *isl_map_add_dims(
2088 __isl_take isl_map *map,
2089 enum isl_dim_type type, unsigned n);
2090 __isl_give isl_set *isl_set_insert_dims(
2091 __isl_take isl_set *set,
2092 enum isl_dim_type type, unsigned pos, unsigned n);
2093 __isl_give isl_map *isl_map_insert_dims(
2094 __isl_take isl_map *map,
2095 enum isl_dim_type type, unsigned pos, unsigned n);
2096 __isl_give isl_basic_set *isl_basic_set_move_dims(
2097 __isl_take isl_basic_set *bset,
2098 enum isl_dim_type dst_type, unsigned dst_pos,
2099 enum isl_dim_type src_type, unsigned src_pos,
2101 __isl_give isl_basic_map *isl_basic_map_move_dims(
2102 __isl_take isl_basic_map *bmap,
2103 enum isl_dim_type dst_type, unsigned dst_pos,
2104 enum isl_dim_type src_type, unsigned src_pos,
2106 __isl_give isl_set *isl_set_move_dims(
2107 __isl_take isl_set *set,
2108 enum isl_dim_type dst_type, unsigned dst_pos,
2109 enum isl_dim_type src_type, unsigned src_pos,
2111 __isl_give isl_map *isl_map_move_dims(
2112 __isl_take isl_map *map,
2113 enum isl_dim_type dst_type, unsigned dst_pos,
2114 enum isl_dim_type src_type, unsigned src_pos,
2117 It is usually not advisable to directly change the (input or output)
2118 space of a set or a relation as this removes the name and the internal
2119 structure of the space. However, the above functions can be useful
2120 to add new parameters, assuming
2121 C<isl_set_align_params> and C<isl_map_align_params>
2126 =head2 Binary Operations
2128 The two arguments of a binary operation not only need to live
2129 in the same C<isl_ctx>, they currently also need to have
2130 the same (number of) parameters.
2132 =head3 Basic Operations
2136 =item * Intersection
2138 __isl_give isl_basic_set *isl_basic_set_intersect(
2139 __isl_take isl_basic_set *bset1,
2140 __isl_take isl_basic_set *bset2);
2141 __isl_give isl_set *isl_set_intersect_params(
2142 __isl_take isl_set *set,
2143 __isl_take isl_set *params);
2144 __isl_give isl_set *isl_set_intersect(
2145 __isl_take isl_set *set1,
2146 __isl_take isl_set *set2);
2147 __isl_give isl_union_set *isl_union_set_intersect(
2148 __isl_take isl_union_set *uset1,
2149 __isl_take isl_union_set *uset2);
2150 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2151 __isl_take isl_basic_map *bmap,
2152 __isl_take isl_basic_set *bset);
2153 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2154 __isl_take isl_basic_map *bmap,
2155 __isl_take isl_basic_set *bset);
2156 __isl_give isl_basic_map *isl_basic_map_intersect(
2157 __isl_take isl_basic_map *bmap1,
2158 __isl_take isl_basic_map *bmap2);
2159 __isl_give isl_map *isl_map_intersect_params(
2160 __isl_take isl_map *map,
2161 __isl_take isl_set *params);
2162 __isl_give isl_map *isl_map_intersect_domain(
2163 __isl_take isl_map *map,
2164 __isl_take isl_set *set);
2165 __isl_give isl_map *isl_map_intersect_range(
2166 __isl_take isl_map *map,
2167 __isl_take isl_set *set);
2168 __isl_give isl_map *isl_map_intersect(
2169 __isl_take isl_map *map1,
2170 __isl_take isl_map *map2);
2171 __isl_give isl_union_map *isl_union_map_intersect_domain(
2172 __isl_take isl_union_map *umap,
2173 __isl_take isl_union_set *uset);
2174 __isl_give isl_union_map *isl_union_map_intersect_range(
2175 __isl_take isl_union_map *umap,
2176 __isl_take isl_union_set *uset);
2177 __isl_give isl_union_map *isl_union_map_intersect(
2178 __isl_take isl_union_map *umap1,
2179 __isl_take isl_union_map *umap2);
2183 __isl_give isl_set *isl_basic_set_union(
2184 __isl_take isl_basic_set *bset1,
2185 __isl_take isl_basic_set *bset2);
2186 __isl_give isl_map *isl_basic_map_union(
2187 __isl_take isl_basic_map *bmap1,
2188 __isl_take isl_basic_map *bmap2);
2189 __isl_give isl_set *isl_set_union(
2190 __isl_take isl_set *set1,
2191 __isl_take isl_set *set2);
2192 __isl_give isl_map *isl_map_union(
2193 __isl_take isl_map *map1,
2194 __isl_take isl_map *map2);
2195 __isl_give isl_union_set *isl_union_set_union(
2196 __isl_take isl_union_set *uset1,
2197 __isl_take isl_union_set *uset2);
2198 __isl_give isl_union_map *isl_union_map_union(
2199 __isl_take isl_union_map *umap1,
2200 __isl_take isl_union_map *umap2);
2202 =item * Set difference
2204 __isl_give isl_set *isl_set_subtract(
2205 __isl_take isl_set *set1,
2206 __isl_take isl_set *set2);
2207 __isl_give isl_map *isl_map_subtract(
2208 __isl_take isl_map *map1,
2209 __isl_take isl_map *map2);
2210 __isl_give isl_union_set *isl_union_set_subtract(
2211 __isl_take isl_union_set *uset1,
2212 __isl_take isl_union_set *uset2);
2213 __isl_give isl_union_map *isl_union_map_subtract(
2214 __isl_take isl_union_map *umap1,
2215 __isl_take isl_union_map *umap2);
2219 __isl_give isl_basic_set *isl_basic_set_apply(
2220 __isl_take isl_basic_set *bset,
2221 __isl_take isl_basic_map *bmap);
2222 __isl_give isl_set *isl_set_apply(
2223 __isl_take isl_set *set,
2224 __isl_take isl_map *map);
2225 __isl_give isl_union_set *isl_union_set_apply(
2226 __isl_take isl_union_set *uset,
2227 __isl_take isl_union_map *umap);
2228 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2229 __isl_take isl_basic_map *bmap1,
2230 __isl_take isl_basic_map *bmap2);
2231 __isl_give isl_basic_map *isl_basic_map_apply_range(
2232 __isl_take isl_basic_map *bmap1,
2233 __isl_take isl_basic_map *bmap2);
2234 __isl_give isl_map *isl_map_apply_domain(
2235 __isl_take isl_map *map1,
2236 __isl_take isl_map *map2);
2237 __isl_give isl_union_map *isl_union_map_apply_domain(
2238 __isl_take isl_union_map *umap1,
2239 __isl_take isl_union_map *umap2);
2240 __isl_give isl_map *isl_map_apply_range(
2241 __isl_take isl_map *map1,
2242 __isl_take isl_map *map2);
2243 __isl_give isl_union_map *isl_union_map_apply_range(
2244 __isl_take isl_union_map *umap1,
2245 __isl_take isl_union_map *umap2);
2247 =item * Cartesian Product
2249 __isl_give isl_set *isl_set_product(
2250 __isl_take isl_set *set1,
2251 __isl_take isl_set *set2);
2252 __isl_give isl_union_set *isl_union_set_product(
2253 __isl_take isl_union_set *uset1,
2254 __isl_take isl_union_set *uset2);
2255 __isl_give isl_basic_map *isl_basic_map_domain_product(
2256 __isl_take isl_basic_map *bmap1,
2257 __isl_take isl_basic_map *bmap2);
2258 __isl_give isl_basic_map *isl_basic_map_range_product(
2259 __isl_take isl_basic_map *bmap1,
2260 __isl_take isl_basic_map *bmap2);
2261 __isl_give isl_map *isl_map_domain_product(
2262 __isl_take isl_map *map1,
2263 __isl_take isl_map *map2);
2264 __isl_give isl_map *isl_map_range_product(
2265 __isl_take isl_map *map1,
2266 __isl_take isl_map *map2);
2267 __isl_give isl_union_map *isl_union_map_range_product(
2268 __isl_take isl_union_map *umap1,
2269 __isl_take isl_union_map *umap2);
2270 __isl_give isl_map *isl_map_product(
2271 __isl_take isl_map *map1,
2272 __isl_take isl_map *map2);
2273 __isl_give isl_union_map *isl_union_map_product(
2274 __isl_take isl_union_map *umap1,
2275 __isl_take isl_union_map *umap2);
2277 The above functions compute the cross product of the given
2278 sets or relations. The domains and ranges of the results
2279 are wrapped maps between domains and ranges of the inputs.
2280 To obtain a ``flat'' product, use the following functions
2283 __isl_give isl_basic_set *isl_basic_set_flat_product(
2284 __isl_take isl_basic_set *bset1,
2285 __isl_take isl_basic_set *bset2);
2286 __isl_give isl_set *isl_set_flat_product(
2287 __isl_take isl_set *set1,
2288 __isl_take isl_set *set2);
2289 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2290 __isl_take isl_basic_map *bmap1,
2291 __isl_take isl_basic_map *bmap2);
2292 __isl_give isl_map *isl_map_flat_domain_product(
2293 __isl_take isl_map *map1,
2294 __isl_take isl_map *map2);
2295 __isl_give isl_map *isl_map_flat_range_product(
2296 __isl_take isl_map *map1,
2297 __isl_take isl_map *map2);
2298 __isl_give isl_union_map *isl_union_map_flat_range_product(
2299 __isl_take isl_union_map *umap1,
2300 __isl_take isl_union_map *umap2);
2301 __isl_give isl_basic_map *isl_basic_map_flat_product(
2302 __isl_take isl_basic_map *bmap1,
2303 __isl_take isl_basic_map *bmap2);
2304 __isl_give isl_map *isl_map_flat_product(
2305 __isl_take isl_map *map1,
2306 __isl_take isl_map *map2);
2308 =item * Simplification
2310 __isl_give isl_basic_set *isl_basic_set_gist(
2311 __isl_take isl_basic_set *bset,
2312 __isl_take isl_basic_set *context);
2313 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2314 __isl_take isl_set *context);
2315 __isl_give isl_set *isl_set_gist_params(
2316 __isl_take isl_set *set,
2317 __isl_take isl_set *context);
2318 __isl_give isl_union_set *isl_union_set_gist(
2319 __isl_take isl_union_set *uset,
2320 __isl_take isl_union_set *context);
2321 __isl_give isl_basic_map *isl_basic_map_gist(
2322 __isl_take isl_basic_map *bmap,
2323 __isl_take isl_basic_map *context);
2324 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2325 __isl_take isl_map *context);
2326 __isl_give isl_map *isl_map_gist_params(
2327 __isl_take isl_map *map,
2328 __isl_take isl_set *context);
2329 __isl_give isl_union_map *isl_union_map_gist(
2330 __isl_take isl_union_map *umap,
2331 __isl_take isl_union_map *context);
2333 The gist operation returns a set or relation that has the
2334 same intersection with the context as the input set or relation.
2335 Any implicit equality in the intersection is made explicit in the result,
2336 while all inequalities that are redundant with respect to the intersection
2338 In case of union sets and relations, the gist operation is performed
2343 =head3 Lexicographic Optimization
2345 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2346 the following functions
2347 compute a set that contains the lexicographic minimum or maximum
2348 of the elements in C<set> (or C<bset>) for those values of the parameters
2349 that satisfy C<dom>.
2350 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2351 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2353 In other words, the union of the parameter values
2354 for which the result is non-empty and of C<*empty>
2357 __isl_give isl_set *isl_basic_set_partial_lexmin(
2358 __isl_take isl_basic_set *bset,
2359 __isl_take isl_basic_set *dom,
2360 __isl_give isl_set **empty);
2361 __isl_give isl_set *isl_basic_set_partial_lexmax(
2362 __isl_take isl_basic_set *bset,
2363 __isl_take isl_basic_set *dom,
2364 __isl_give isl_set **empty);
2365 __isl_give isl_set *isl_set_partial_lexmin(
2366 __isl_take isl_set *set, __isl_take isl_set *dom,
2367 __isl_give isl_set **empty);
2368 __isl_give isl_set *isl_set_partial_lexmax(
2369 __isl_take isl_set *set, __isl_take isl_set *dom,
2370 __isl_give isl_set **empty);
2372 Given a (basic) set C<set> (or C<bset>), the following functions simply
2373 return a set containing the lexicographic minimum or maximum
2374 of the elements in C<set> (or C<bset>).
2375 In case of union sets, the optimum is computed per space.
2377 __isl_give isl_set *isl_basic_set_lexmin(
2378 __isl_take isl_basic_set *bset);
2379 __isl_give isl_set *isl_basic_set_lexmax(
2380 __isl_take isl_basic_set *bset);
2381 __isl_give isl_set *isl_set_lexmin(
2382 __isl_take isl_set *set);
2383 __isl_give isl_set *isl_set_lexmax(
2384 __isl_take isl_set *set);
2385 __isl_give isl_union_set *isl_union_set_lexmin(
2386 __isl_take isl_union_set *uset);
2387 __isl_give isl_union_set *isl_union_set_lexmax(
2388 __isl_take isl_union_set *uset);
2390 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2391 the following functions
2392 compute a relation that maps each element of C<dom>
2393 to the single lexicographic minimum or maximum
2394 of the elements that are associated to that same
2395 element in C<map> (or C<bmap>).
2396 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2397 that contains the elements in C<dom> that do not map
2398 to any elements in C<map> (or C<bmap>).
2399 In other words, the union of the domain of the result and of C<*empty>
2402 __isl_give isl_map *isl_basic_map_partial_lexmax(
2403 __isl_take isl_basic_map *bmap,
2404 __isl_take isl_basic_set *dom,
2405 __isl_give isl_set **empty);
2406 __isl_give isl_map *isl_basic_map_partial_lexmin(
2407 __isl_take isl_basic_map *bmap,
2408 __isl_take isl_basic_set *dom,
2409 __isl_give isl_set **empty);
2410 __isl_give isl_map *isl_map_partial_lexmax(
2411 __isl_take isl_map *map, __isl_take isl_set *dom,
2412 __isl_give isl_set **empty);
2413 __isl_give isl_map *isl_map_partial_lexmin(
2414 __isl_take isl_map *map, __isl_take isl_set *dom,
2415 __isl_give isl_set **empty);
2417 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2418 return a map mapping each element in the domain of
2419 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2420 of all elements associated to that element.
2421 In case of union relations, the optimum is computed per space.
2423 __isl_give isl_map *isl_basic_map_lexmin(
2424 __isl_take isl_basic_map *bmap);
2425 __isl_give isl_map *isl_basic_map_lexmax(
2426 __isl_take isl_basic_map *bmap);
2427 __isl_give isl_map *isl_map_lexmin(
2428 __isl_take isl_map *map);
2429 __isl_give isl_map *isl_map_lexmax(
2430 __isl_take isl_map *map);
2431 __isl_give isl_union_map *isl_union_map_lexmin(
2432 __isl_take isl_union_map *umap);
2433 __isl_give isl_union_map *isl_union_map_lexmax(
2434 __isl_take isl_union_map *umap);
2438 Lists are defined over several element types, including
2439 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2440 Here we take lists of C<isl_set>s as an example.
2441 Lists can be created, copied and freed using the following functions.
2443 #include <isl/list.h>
2444 __isl_give isl_set_list *isl_set_list_from_set(
2445 __isl_take isl_set *el);
2446 __isl_give isl_set_list *isl_set_list_alloc(
2447 isl_ctx *ctx, int n);
2448 __isl_give isl_set_list *isl_set_list_copy(
2449 __isl_keep isl_set_list *list);
2450 __isl_give isl_set_list *isl_set_list_add(
2451 __isl_take isl_set_list *list,
2452 __isl_take isl_set *el);
2453 __isl_give isl_set_list *isl_set_list_concat(
2454 __isl_take isl_set_list *list1,
2455 __isl_take isl_set_list *list2);
2456 void *isl_set_list_free(__isl_take isl_set_list *list);
2458 C<isl_set_list_alloc> creates an empty list with a capacity for
2459 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2462 Lists can be inspected using the following functions.
2464 #include <isl/list.h>
2465 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2466 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2467 __isl_give isl_set *isl_set_list_get_set(
2468 __isl_keep isl_set_list *list, int index);
2469 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2470 int (*fn)(__isl_take isl_set *el, void *user),
2473 Lists can be printed using
2475 #include <isl/list.h>
2476 __isl_give isl_printer *isl_printer_print_set_list(
2477 __isl_take isl_printer *p,
2478 __isl_keep isl_set_list *list);
2482 Matrices can be created, copied and freed using the following functions.
2484 #include <isl/mat.h>
2485 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2486 unsigned n_row, unsigned n_col);
2487 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2488 void isl_mat_free(__isl_take isl_mat *mat);
2490 Note that the elements of a newly created matrix may have arbitrary values.
2491 The elements can be changed and inspected using the following functions.
2493 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2494 int isl_mat_rows(__isl_keep isl_mat *mat);
2495 int isl_mat_cols(__isl_keep isl_mat *mat);
2496 int isl_mat_get_element(__isl_keep isl_mat *mat,
2497 int row, int col, isl_int *v);
2498 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2499 int row, int col, isl_int v);
2500 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2501 int row, int col, int v);
2503 C<isl_mat_get_element> will return a negative value if anything went wrong.
2504 In that case, the value of C<*v> is undefined.
2506 The following function can be used to compute the (right) inverse
2507 of a matrix, i.e., a matrix such that the product of the original
2508 and the inverse (in that order) is a multiple of the identity matrix.
2509 The input matrix is assumed to be of full row-rank.
2511 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2513 The following function can be used to compute the (right) kernel
2514 (or null space) of a matrix, i.e., a matrix such that the product of
2515 the original and the kernel (in that order) is the zero matrix.
2517 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2519 =head2 Piecewise Quasi Affine Expressions
2521 The zero quasi affine expression on a given domain can be created using
2523 __isl_give isl_aff *isl_aff_zero_on_domain(
2524 __isl_take isl_local_space *ls);
2526 Note that the space in which the resulting object lives is a map space
2527 with the given space as domain and a one-dimensional range.
2529 An empty piecewise quasi affine expression (one with no cells)
2530 or a piecewise quasi affine expression with a single cell can
2531 be created using the following functions.
2533 #include <isl/aff.h>
2534 __isl_give isl_pw_aff *isl_pw_aff_empty(
2535 __isl_take isl_space *space);
2536 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2537 __isl_take isl_set *set, __isl_take isl_aff *aff);
2538 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2539 __isl_take isl_aff *aff);
2541 Quasi affine expressions can be copied and freed using
2543 #include <isl/aff.h>
2544 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2545 void *isl_aff_free(__isl_take isl_aff *aff);
2547 __isl_give isl_pw_aff *isl_pw_aff_copy(
2548 __isl_keep isl_pw_aff *pwaff);
2549 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2551 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2552 using the following function. The constraint is required to have
2553 a non-zero coefficient for the specified dimension.
2555 #include <isl/constraint.h>
2556 __isl_give isl_aff *isl_constraint_get_bound(
2557 __isl_keep isl_constraint *constraint,
2558 enum isl_dim_type type, int pos);
2560 The entire affine expression of the constraint can also be extracted
2561 using the following function.
2563 #include <isl/constraint.h>
2564 __isl_give isl_aff *isl_constraint_get_aff(
2565 __isl_keep isl_constraint *constraint);
2567 Conversely, an equality constraint equating
2568 the affine expression to zero or an inequality constraint enforcing
2569 the affine expression to be non-negative, can be constructed using
2571 __isl_give isl_constraint *isl_equality_from_aff(
2572 __isl_take isl_aff *aff);
2573 __isl_give isl_constraint *isl_inequality_from_aff(
2574 __isl_take isl_aff *aff);
2576 The expression can be inspected using
2578 #include <isl/aff.h>
2579 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2580 int isl_aff_dim(__isl_keep isl_aff *aff,
2581 enum isl_dim_type type);
2582 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2583 __isl_keep isl_aff *aff);
2584 __isl_give isl_local_space *isl_aff_get_local_space(
2585 __isl_keep isl_aff *aff);
2586 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2587 enum isl_dim_type type, unsigned pos);
2588 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2590 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2591 enum isl_dim_type type, int pos, isl_int *v);
2592 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2594 __isl_give isl_aff *isl_aff_get_div(
2595 __isl_keep isl_aff *aff, int pos);
2597 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2598 int (*fn)(__isl_take isl_set *set,
2599 __isl_take isl_aff *aff,
2600 void *user), void *user);
2602 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2603 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2605 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2606 enum isl_dim_type type, unsigned first, unsigned n);
2607 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2608 enum isl_dim_type type, unsigned first, unsigned n);
2610 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2611 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2612 enum isl_dim_type type);
2613 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2615 It can be modified using
2617 #include <isl/aff.h>
2618 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2619 __isl_take isl_pw_aff *pwaff,
2620 enum isl_dim_type type, __isl_take isl_id *id);
2621 __isl_give isl_aff *isl_aff_set_dim_name(
2622 __isl_take isl_aff *aff, enum isl_dim_type type,
2623 unsigned pos, const char *s);
2624 __isl_give isl_aff *isl_aff_set_constant(
2625 __isl_take isl_aff *aff, isl_int v);
2626 __isl_give isl_aff *isl_aff_set_constant_si(
2627 __isl_take isl_aff *aff, int v);
2628 __isl_give isl_aff *isl_aff_set_coefficient(
2629 __isl_take isl_aff *aff,
2630 enum isl_dim_type type, int pos, isl_int v);
2631 __isl_give isl_aff *isl_aff_set_coefficient_si(
2632 __isl_take isl_aff *aff,
2633 enum isl_dim_type type, int pos, int v);
2634 __isl_give isl_aff *isl_aff_set_denominator(
2635 __isl_take isl_aff *aff, isl_int v);
2637 __isl_give isl_aff *isl_aff_add_constant(
2638 __isl_take isl_aff *aff, isl_int v);
2639 __isl_give isl_aff *isl_aff_add_constant_si(
2640 __isl_take isl_aff *aff, int v);
2641 __isl_give isl_aff *isl_aff_add_coefficient(
2642 __isl_take isl_aff *aff,
2643 enum isl_dim_type type, int pos, isl_int v);
2644 __isl_give isl_aff *isl_aff_add_coefficient_si(
2645 __isl_take isl_aff *aff,
2646 enum isl_dim_type type, int pos, int v);
2648 __isl_give isl_aff *isl_aff_insert_dims(
2649 __isl_take isl_aff *aff,
2650 enum isl_dim_type type, unsigned first, unsigned n);
2651 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2652 __isl_take isl_pw_aff *pwaff,
2653 enum isl_dim_type type, unsigned first, unsigned n);
2654 __isl_give isl_aff *isl_aff_add_dims(
2655 __isl_take isl_aff *aff,
2656 enum isl_dim_type type, unsigned n);
2657 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2658 __isl_take isl_pw_aff *pwaff,
2659 enum isl_dim_type type, unsigned n);
2660 __isl_give isl_aff *isl_aff_drop_dims(
2661 __isl_take isl_aff *aff,
2662 enum isl_dim_type type, unsigned first, unsigned n);
2663 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2664 __isl_take isl_pw_aff *pwaff,
2665 enum isl_dim_type type, unsigned first, unsigned n);
2667 Note that the C<set_constant> and C<set_coefficient> functions
2668 set the I<numerator> of the constant or coefficient, while
2669 C<add_constant> and C<add_coefficient> add an integer value to
2670 the possibly rational constant or coefficient.
2672 To check whether an affine expressions is obviously zero
2673 or obviously equal to some other affine expression, use
2675 #include <isl/aff.h>
2676 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2677 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2678 __isl_keep isl_aff *aff2);
2679 int isl_pw_aff_plain_is_equal(
2680 __isl_keep isl_pw_aff *pwaff1,
2681 __isl_keep isl_pw_aff *pwaff2);
2685 #include <isl/aff.h>
2686 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2687 __isl_take isl_aff *aff2);
2688 __isl_give isl_pw_aff *isl_pw_aff_add(
2689 __isl_take isl_pw_aff *pwaff1,
2690 __isl_take isl_pw_aff *pwaff2);
2691 __isl_give isl_pw_aff *isl_pw_aff_min(
2692 __isl_take isl_pw_aff *pwaff1,
2693 __isl_take isl_pw_aff *pwaff2);
2694 __isl_give isl_pw_aff *isl_pw_aff_max(
2695 __isl_take isl_pw_aff *pwaff1,
2696 __isl_take isl_pw_aff *pwaff2);
2697 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2698 __isl_take isl_aff *aff2);
2699 __isl_give isl_pw_aff *isl_pw_aff_sub(
2700 __isl_take isl_pw_aff *pwaff1,
2701 __isl_take isl_pw_aff *pwaff2);
2702 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2703 __isl_give isl_pw_aff *isl_pw_aff_neg(
2704 __isl_take isl_pw_aff *pwaff);
2705 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2706 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2707 __isl_take isl_pw_aff *pwaff);
2708 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2709 __isl_give isl_pw_aff *isl_pw_aff_floor(
2710 __isl_take isl_pw_aff *pwaff);
2711 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2713 __isl_give isl_pw_aff *isl_pw_aff_mod(
2714 __isl_take isl_pw_aff *pwaff, isl_int mod);
2715 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2717 __isl_give isl_pw_aff *isl_pw_aff_scale(
2718 __isl_take isl_pw_aff *pwaff, isl_int f);
2719 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2721 __isl_give isl_aff *isl_aff_scale_down_ui(
2722 __isl_take isl_aff *aff, unsigned f);
2723 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2724 __isl_take isl_pw_aff *pwaff, isl_int f);
2726 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2727 __isl_take isl_pw_aff_list *list);
2728 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2729 __isl_take isl_pw_aff_list *list);
2731 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2732 __isl_take isl_pw_aff *pwqp);
2734 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2735 __isl_take isl_pw_aff *pwaff,
2736 __isl_take isl_space *model);
2738 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2739 __isl_take isl_set *context);
2740 __isl_give isl_pw_aff *isl_pw_aff_gist(
2741 __isl_take isl_pw_aff *pwaff,
2742 __isl_take isl_set *context);
2744 __isl_give isl_set *isl_pw_aff_domain(
2745 __isl_take isl_pw_aff *pwaff);
2746 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2747 __isl_take isl_pw_aff *pa,
2748 __isl_take isl_set *set);
2750 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2751 __isl_take isl_aff *aff2);
2752 __isl_give isl_pw_aff *isl_pw_aff_mul(
2753 __isl_take isl_pw_aff *pwaff1,
2754 __isl_take isl_pw_aff *pwaff2);
2756 When multiplying two affine expressions, at least one of the two needs
2759 #include <isl/aff.h>
2760 __isl_give isl_basic_set *isl_aff_le_basic_set(
2761 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2762 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2763 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2764 __isl_give isl_set *isl_pw_aff_eq_set(
2765 __isl_take isl_pw_aff *pwaff1,
2766 __isl_take isl_pw_aff *pwaff2);
2767 __isl_give isl_set *isl_pw_aff_ne_set(
2768 __isl_take isl_pw_aff *pwaff1,
2769 __isl_take isl_pw_aff *pwaff2);
2770 __isl_give isl_set *isl_pw_aff_le_set(
2771 __isl_take isl_pw_aff *pwaff1,
2772 __isl_take isl_pw_aff *pwaff2);
2773 __isl_give isl_set *isl_pw_aff_lt_set(
2774 __isl_take isl_pw_aff *pwaff1,
2775 __isl_take isl_pw_aff *pwaff2);
2776 __isl_give isl_set *isl_pw_aff_ge_set(
2777 __isl_take isl_pw_aff *pwaff1,
2778 __isl_take isl_pw_aff *pwaff2);
2779 __isl_give isl_set *isl_pw_aff_gt_set(
2780 __isl_take isl_pw_aff *pwaff1,
2781 __isl_take isl_pw_aff *pwaff2);
2783 __isl_give isl_set *isl_pw_aff_list_eq_set(
2784 __isl_take isl_pw_aff_list *list1,
2785 __isl_take isl_pw_aff_list *list2);
2786 __isl_give isl_set *isl_pw_aff_list_ne_set(
2787 __isl_take isl_pw_aff_list *list1,
2788 __isl_take isl_pw_aff_list *list2);
2789 __isl_give isl_set *isl_pw_aff_list_le_set(
2790 __isl_take isl_pw_aff_list *list1,
2791 __isl_take isl_pw_aff_list *list2);
2792 __isl_give isl_set *isl_pw_aff_list_lt_set(
2793 __isl_take isl_pw_aff_list *list1,
2794 __isl_take isl_pw_aff_list *list2);
2795 __isl_give isl_set *isl_pw_aff_list_ge_set(
2796 __isl_take isl_pw_aff_list *list1,
2797 __isl_take isl_pw_aff_list *list2);
2798 __isl_give isl_set *isl_pw_aff_list_gt_set(
2799 __isl_take isl_pw_aff_list *list1,
2800 __isl_take isl_pw_aff_list *list2);
2802 The function C<isl_aff_ge_basic_set> returns a basic set
2803 containing those elements in the shared space
2804 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2805 The function C<isl_aff_ge_set> returns a set
2806 containing those elements in the shared domain
2807 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2808 The functions operating on C<isl_pw_aff_list> apply the corresponding
2809 C<isl_pw_aff> function to each pair of elements in the two lists.
2811 #include <isl/aff.h>
2812 __isl_give isl_set *isl_pw_aff_nonneg_set(
2813 __isl_take isl_pw_aff *pwaff);
2814 __isl_give isl_set *isl_pw_aff_zero_set(
2815 __isl_take isl_pw_aff *pwaff);
2816 __isl_give isl_set *isl_pw_aff_non_zero_set(
2817 __isl_take isl_pw_aff *pwaff);
2819 The function C<isl_pw_aff_nonneg_set> returns a set
2820 containing those elements in the domain
2821 of C<pwaff> where C<pwaff> is non-negative.
2823 #include <isl/aff.h>
2824 __isl_give isl_pw_aff *isl_pw_aff_cond(
2825 __isl_take isl_set *cond,
2826 __isl_take isl_pw_aff *pwaff_true,
2827 __isl_take isl_pw_aff *pwaff_false);
2829 The function C<isl_pw_aff_cond> performs a conditional operator
2830 and returns an expression that is equal to C<pwaff_true>
2831 for elements in C<cond> and equal to C<pwaff_false> for elements
2834 #include <isl/aff.h>
2835 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2836 __isl_take isl_pw_aff *pwaff1,
2837 __isl_take isl_pw_aff *pwaff2);
2838 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2839 __isl_take isl_pw_aff *pwaff1,
2840 __isl_take isl_pw_aff *pwaff2);
2842 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2843 expression with a domain that is the union of those of C<pwaff1> and
2844 C<pwaff2> and such that on each cell, the quasi-affine expression is
2845 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2846 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2847 associated expression is the defined one.
2849 An expression can be printed using
2851 #include <isl/aff.h>
2852 __isl_give isl_printer *isl_printer_print_aff(
2853 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2855 __isl_give isl_printer *isl_printer_print_pw_aff(
2856 __isl_take isl_printer *p,
2857 __isl_keep isl_pw_aff *pwaff);
2861 Points are elements of a set. They can be used to construct
2862 simple sets (boxes) or they can be used to represent the
2863 individual elements of a set.
2864 The zero point (the origin) can be created using
2866 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2868 The coordinates of a point can be inspected, set and changed
2871 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2872 enum isl_dim_type type, int pos, isl_int *v);
2873 __isl_give isl_point *isl_point_set_coordinate(
2874 __isl_take isl_point *pnt,
2875 enum isl_dim_type type, int pos, isl_int v);
2877 __isl_give isl_point *isl_point_add_ui(
2878 __isl_take isl_point *pnt,
2879 enum isl_dim_type type, int pos, unsigned val);
2880 __isl_give isl_point *isl_point_sub_ui(
2881 __isl_take isl_point *pnt,
2882 enum isl_dim_type type, int pos, unsigned val);
2884 Other properties can be obtained using
2886 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2888 Points can be copied or freed using
2890 __isl_give isl_point *isl_point_copy(
2891 __isl_keep isl_point *pnt);
2892 void isl_point_free(__isl_take isl_point *pnt);
2894 A singleton set can be created from a point using
2896 __isl_give isl_basic_set *isl_basic_set_from_point(
2897 __isl_take isl_point *pnt);
2898 __isl_give isl_set *isl_set_from_point(
2899 __isl_take isl_point *pnt);
2901 and a box can be created from two opposite extremal points using
2903 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2904 __isl_take isl_point *pnt1,
2905 __isl_take isl_point *pnt2);
2906 __isl_give isl_set *isl_set_box_from_points(
2907 __isl_take isl_point *pnt1,
2908 __isl_take isl_point *pnt2);
2910 All elements of a B<bounded> (union) set can be enumerated using
2911 the following functions.
2913 int isl_set_foreach_point(__isl_keep isl_set *set,
2914 int (*fn)(__isl_take isl_point *pnt, void *user),
2916 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2917 int (*fn)(__isl_take isl_point *pnt, void *user),
2920 The function C<fn> is called for each integer point in
2921 C<set> with as second argument the last argument of
2922 the C<isl_set_foreach_point> call. The function C<fn>
2923 should return C<0> on success and C<-1> on failure.
2924 In the latter case, C<isl_set_foreach_point> will stop
2925 enumerating and return C<-1> as well.
2926 If the enumeration is performed successfully and to completion,
2927 then C<isl_set_foreach_point> returns C<0>.
2929 To obtain a single point of a (basic) set, use
2931 __isl_give isl_point *isl_basic_set_sample_point(
2932 __isl_take isl_basic_set *bset);
2933 __isl_give isl_point *isl_set_sample_point(
2934 __isl_take isl_set *set);
2936 If C<set> does not contain any (integer) points, then the
2937 resulting point will be ``void'', a property that can be
2940 int isl_point_is_void(__isl_keep isl_point *pnt);
2942 =head2 Piecewise Quasipolynomials
2944 A piecewise quasipolynomial is a particular kind of function that maps
2945 a parametric point to a rational value.
2946 More specifically, a quasipolynomial is a polynomial expression in greatest
2947 integer parts of affine expressions of parameters and variables.
2948 A piecewise quasipolynomial is a subdivision of a given parametric
2949 domain into disjoint cells with a quasipolynomial associated to
2950 each cell. The value of the piecewise quasipolynomial at a given
2951 point is the value of the quasipolynomial associated to the cell
2952 that contains the point. Outside of the union of cells,
2953 the value is assumed to be zero.
2954 For example, the piecewise quasipolynomial
2956 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2958 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2959 A given piecewise quasipolynomial has a fixed domain dimension.
2960 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2961 defined over different domains.
2962 Piecewise quasipolynomials are mainly used by the C<barvinok>
2963 library for representing the number of elements in a parametric set or map.
2964 For example, the piecewise quasipolynomial above represents
2965 the number of points in the map
2967 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2969 =head3 Printing (Piecewise) Quasipolynomials
2971 Quasipolynomials and piecewise quasipolynomials can be printed
2972 using the following functions.
2974 __isl_give isl_printer *isl_printer_print_qpolynomial(
2975 __isl_take isl_printer *p,
2976 __isl_keep isl_qpolynomial *qp);
2978 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2979 __isl_take isl_printer *p,
2980 __isl_keep isl_pw_qpolynomial *pwqp);
2982 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2983 __isl_take isl_printer *p,
2984 __isl_keep isl_union_pw_qpolynomial *upwqp);
2986 The output format of the printer
2987 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2988 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2990 In case of printing in C<ISL_FORMAT_C>, the user may want
2991 to set the names of all dimensions
2993 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2994 __isl_take isl_qpolynomial *qp,
2995 enum isl_dim_type type, unsigned pos,
2997 __isl_give isl_pw_qpolynomial *
2998 isl_pw_qpolynomial_set_dim_name(
2999 __isl_take isl_pw_qpolynomial *pwqp,
3000 enum isl_dim_type type, unsigned pos,
3003 =head3 Creating New (Piecewise) Quasipolynomials
3005 Some simple quasipolynomials can be created using the following functions.
3006 More complicated quasipolynomials can be created by applying
3007 operations such as addition and multiplication
3008 on the resulting quasipolynomials
3010 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3011 __isl_take isl_space *domain);
3012 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3013 __isl_take isl_space *domain);
3014 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3015 __isl_take isl_space *domain);
3016 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3017 __isl_take isl_space *domain);
3018 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3019 __isl_take isl_space *domain);
3020 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3021 __isl_take isl_space *domain,
3022 const isl_int n, const isl_int d);
3023 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3024 __isl_take isl_space *domain,
3025 enum isl_dim_type type, unsigned pos);
3026 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3027 __isl_take isl_aff *aff);
3029 Note that the space in which a quasipolynomial lives is a map space
3030 with a one-dimensional range. The C<domain> argument in some of
3031 the functions above corresponds to the domain of this map space.
3033 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3034 with a single cell can be created using the following functions.
3035 Multiple of these single cell piecewise quasipolynomials can
3036 be combined to create more complicated piecewise quasipolynomials.
3038 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3039 __isl_take isl_space *space);
3040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3041 __isl_take isl_set *set,
3042 __isl_take isl_qpolynomial *qp);
3043 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3044 __isl_take isl_qpolynomial *qp);
3045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3046 __isl_take isl_pw_aff *pwaff);
3048 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3049 __isl_take isl_space *space);
3050 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3051 __isl_take isl_pw_qpolynomial *pwqp);
3052 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3053 __isl_take isl_union_pw_qpolynomial *upwqp,
3054 __isl_take isl_pw_qpolynomial *pwqp);
3056 Quasipolynomials can be copied and freed again using the following
3059 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3060 __isl_keep isl_qpolynomial *qp);
3061 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3064 __isl_keep isl_pw_qpolynomial *pwqp);
3065 void *isl_pw_qpolynomial_free(
3066 __isl_take isl_pw_qpolynomial *pwqp);
3068 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3069 __isl_keep isl_union_pw_qpolynomial *upwqp);
3070 void isl_union_pw_qpolynomial_free(
3071 __isl_take isl_union_pw_qpolynomial *upwqp);
3073 =head3 Inspecting (Piecewise) Quasipolynomials
3075 To iterate over all piecewise quasipolynomials in a union
3076 piecewise quasipolynomial, use the following function
3078 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3079 __isl_keep isl_union_pw_qpolynomial *upwqp,
3080 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3083 To extract the piecewise quasipolynomial in a given space from a union, use
3085 __isl_give isl_pw_qpolynomial *
3086 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3087 __isl_keep isl_union_pw_qpolynomial *upwqp,
3088 __isl_take isl_space *space);
3090 To iterate over the cells in a piecewise quasipolynomial,
3091 use either of the following two functions
3093 int isl_pw_qpolynomial_foreach_piece(
3094 __isl_keep isl_pw_qpolynomial *pwqp,
3095 int (*fn)(__isl_take isl_set *set,
3096 __isl_take isl_qpolynomial *qp,
3097 void *user), void *user);
3098 int isl_pw_qpolynomial_foreach_lifted_piece(
3099 __isl_keep isl_pw_qpolynomial *pwqp,
3100 int (*fn)(__isl_take isl_set *set,
3101 __isl_take isl_qpolynomial *qp,
3102 void *user), void *user);
3104 As usual, the function C<fn> should return C<0> on success
3105 and C<-1> on failure. The difference between
3106 C<isl_pw_qpolynomial_foreach_piece> and
3107 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3108 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3109 compute unique representations for all existentially quantified
3110 variables and then turn these existentially quantified variables
3111 into extra set variables, adapting the associated quasipolynomial
3112 accordingly. This means that the C<set> passed to C<fn>
3113 will not have any existentially quantified variables, but that
3114 the dimensions of the sets may be different for different
3115 invocations of C<fn>.
3117 To iterate over all terms in a quasipolynomial,
3120 int isl_qpolynomial_foreach_term(
3121 __isl_keep isl_qpolynomial *qp,
3122 int (*fn)(__isl_take isl_term *term,
3123 void *user), void *user);
3125 The terms themselves can be inspected and freed using
3128 unsigned isl_term_dim(__isl_keep isl_term *term,
3129 enum isl_dim_type type);
3130 void isl_term_get_num(__isl_keep isl_term *term,
3132 void isl_term_get_den(__isl_keep isl_term *term,
3134 int isl_term_get_exp(__isl_keep isl_term *term,
3135 enum isl_dim_type type, unsigned pos);
3136 __isl_give isl_aff *isl_term_get_div(
3137 __isl_keep isl_term *term, unsigned pos);
3138 void isl_term_free(__isl_take isl_term *term);
3140 Each term is a product of parameters, set variables and
3141 integer divisions. The function C<isl_term_get_exp>
3142 returns the exponent of a given dimensions in the given term.
3143 The C<isl_int>s in the arguments of C<isl_term_get_num>
3144 and C<isl_term_get_den> need to have been initialized
3145 using C<isl_int_init> before calling these functions.
3147 =head3 Properties of (Piecewise) Quasipolynomials
3149 To check whether a quasipolynomial is actually a constant,
3150 use the following function.
3152 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3153 isl_int *n, isl_int *d);
3155 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3156 then the numerator and denominator of the constant
3157 are returned in C<*n> and C<*d>, respectively.
3159 To check whether two union piecewise quasipolynomials are
3160 obviously equal, use
3162 int isl_union_pw_qpolynomial_plain_is_equal(
3163 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3164 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3166 =head3 Operations on (Piecewise) Quasipolynomials
3168 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3169 __isl_take isl_qpolynomial *qp, isl_int v);
3170 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3171 __isl_take isl_qpolynomial *qp);
3172 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3173 __isl_take isl_qpolynomial *qp1,
3174 __isl_take isl_qpolynomial *qp2);
3175 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3176 __isl_take isl_qpolynomial *qp1,
3177 __isl_take isl_qpolynomial *qp2);
3178 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3179 __isl_take isl_qpolynomial *qp1,
3180 __isl_take isl_qpolynomial *qp2);
3181 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3182 __isl_take isl_qpolynomial *qp, unsigned exponent);
3184 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3185 __isl_take isl_pw_qpolynomial *pwqp1,
3186 __isl_take isl_pw_qpolynomial *pwqp2);
3187 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3188 __isl_take isl_pw_qpolynomial *pwqp1,
3189 __isl_take isl_pw_qpolynomial *pwqp2);
3190 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3191 __isl_take isl_pw_qpolynomial *pwqp1,
3192 __isl_take isl_pw_qpolynomial *pwqp2);
3193 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3194 __isl_take isl_pw_qpolynomial *pwqp);
3195 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3196 __isl_take isl_pw_qpolynomial *pwqp1,
3197 __isl_take isl_pw_qpolynomial *pwqp2);
3198 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3199 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3201 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3202 __isl_take isl_union_pw_qpolynomial *upwqp1,
3203 __isl_take isl_union_pw_qpolynomial *upwqp2);
3204 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3205 __isl_take isl_union_pw_qpolynomial *upwqp1,
3206 __isl_take isl_union_pw_qpolynomial *upwqp2);
3207 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3208 __isl_take isl_union_pw_qpolynomial *upwqp1,
3209 __isl_take isl_union_pw_qpolynomial *upwqp2);
3211 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3212 __isl_take isl_pw_qpolynomial *pwqp,
3213 __isl_take isl_point *pnt);
3215 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3216 __isl_take isl_union_pw_qpolynomial *upwqp,
3217 __isl_take isl_point *pnt);
3219 __isl_give isl_set *isl_pw_qpolynomial_domain(
3220 __isl_take isl_pw_qpolynomial *pwqp);
3221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3222 __isl_take isl_pw_qpolynomial *pwpq,
3223 __isl_take isl_set *set);
3225 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3226 __isl_take isl_union_pw_qpolynomial *upwqp);
3227 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3228 __isl_take isl_union_pw_qpolynomial *upwpq,
3229 __isl_take isl_union_set *uset);
3231 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3232 __isl_take isl_qpolynomial *qp,
3233 __isl_take isl_space *model);
3235 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3236 __isl_take isl_qpolynomial *qp);
3237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3238 __isl_take isl_pw_qpolynomial *pwqp);
3240 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3241 __isl_take isl_union_pw_qpolynomial *upwqp);
3243 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3244 __isl_take isl_qpolynomial *qp,
3245 __isl_take isl_set *context);
3247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3248 __isl_take isl_pw_qpolynomial *pwqp,
3249 __isl_take isl_set *context);
3251 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3252 __isl_take isl_union_pw_qpolynomial *upwqp,
3253 __isl_take isl_union_set *context);
3255 The gist operation applies the gist operation to each of
3256 the cells in the domain of the input piecewise quasipolynomial.
3257 The context is also exploited
3258 to simplify the quasipolynomials associated to each cell.
3260 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3261 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3262 __isl_give isl_union_pw_qpolynomial *
3263 isl_union_pw_qpolynomial_to_polynomial(
3264 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3266 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3267 the polynomial will be an overapproximation. If C<sign> is negative,
3268 it will be an underapproximation. If C<sign> is zero, the approximation
3269 will lie somewhere in between.
3271 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3273 A piecewise quasipolynomial reduction is a piecewise
3274 reduction (or fold) of quasipolynomials.
3275 In particular, the reduction can be maximum or a minimum.
3276 The objects are mainly used to represent the result of
3277 an upper or lower bound on a quasipolynomial over its domain,
3278 i.e., as the result of the following function.
3280 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3281 __isl_take isl_pw_qpolynomial *pwqp,
3282 enum isl_fold type, int *tight);
3284 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3285 __isl_take isl_union_pw_qpolynomial *upwqp,
3286 enum isl_fold type, int *tight);
3288 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3289 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3290 is the returned bound is known be tight, i.e., for each value
3291 of the parameters there is at least
3292 one element in the domain that reaches the bound.
3293 If the domain of C<pwqp> is not wrapping, then the bound is computed
3294 over all elements in that domain and the result has a purely parametric
3295 domain. If the domain of C<pwqp> is wrapping, then the bound is
3296 computed over the range of the wrapped relation. The domain of the
3297 wrapped relation becomes the domain of the result.
3299 A (piecewise) quasipolynomial reduction can be copied or freed using the
3300 following functions.
3302 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3303 __isl_keep isl_qpolynomial_fold *fold);
3304 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3305 __isl_keep isl_pw_qpolynomial_fold *pwf);
3306 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3307 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3308 void isl_qpolynomial_fold_free(
3309 __isl_take isl_qpolynomial_fold *fold);
3310 void *isl_pw_qpolynomial_fold_free(
3311 __isl_take isl_pw_qpolynomial_fold *pwf);
3312 void isl_union_pw_qpolynomial_fold_free(
3313 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3315 =head3 Printing Piecewise Quasipolynomial Reductions
3317 Piecewise quasipolynomial reductions can be printed
3318 using the following function.
3320 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3321 __isl_take isl_printer *p,
3322 __isl_keep isl_pw_qpolynomial_fold *pwf);
3323 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3324 __isl_take isl_printer *p,
3325 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3327 For C<isl_printer_print_pw_qpolynomial_fold>,
3328 output format of the printer
3329 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3330 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3331 output format of the printer
3332 needs to be set to C<ISL_FORMAT_ISL>.
3333 In case of printing in C<ISL_FORMAT_C>, the user may want
3334 to set the names of all dimensions
3336 __isl_give isl_pw_qpolynomial_fold *
3337 isl_pw_qpolynomial_fold_set_dim_name(
3338 __isl_take isl_pw_qpolynomial_fold *pwf,
3339 enum isl_dim_type type, unsigned pos,
3342 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3344 To iterate over all piecewise quasipolynomial reductions in a union
3345 piecewise quasipolynomial reduction, use the following function
3347 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3348 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3349 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3350 void *user), void *user);
3352 To iterate over the cells in a piecewise quasipolynomial reduction,
3353 use either of the following two functions
3355 int isl_pw_qpolynomial_fold_foreach_piece(
3356 __isl_keep isl_pw_qpolynomial_fold *pwf,
3357 int (*fn)(__isl_take isl_set *set,
3358 __isl_take isl_qpolynomial_fold *fold,
3359 void *user), void *user);
3360 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3361 __isl_keep isl_pw_qpolynomial_fold *pwf,
3362 int (*fn)(__isl_take isl_set *set,
3363 __isl_take isl_qpolynomial_fold *fold,
3364 void *user), void *user);
3366 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3367 of the difference between these two functions.
3369 To iterate over all quasipolynomials in a reduction, use
3371 int isl_qpolynomial_fold_foreach_qpolynomial(
3372 __isl_keep isl_qpolynomial_fold *fold,
3373 int (*fn)(__isl_take isl_qpolynomial *qp,
3374 void *user), void *user);
3376 =head3 Properties of Piecewise Quasipolynomial Reductions
3378 To check whether two union piecewise quasipolynomial reductions are
3379 obviously equal, use
3381 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3382 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3383 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3385 =head3 Operations on Piecewise Quasipolynomial Reductions
3387 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3388 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3390 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3391 __isl_take isl_pw_qpolynomial_fold *pwf1,
3392 __isl_take isl_pw_qpolynomial_fold *pwf2);
3394 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3395 __isl_take isl_pw_qpolynomial_fold *pwf1,
3396 __isl_take isl_pw_qpolynomial_fold *pwf2);
3398 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3399 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3400 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3402 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3403 __isl_take isl_pw_qpolynomial_fold *pwf,
3404 __isl_take isl_point *pnt);
3406 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3407 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3408 __isl_take isl_point *pnt);
3410 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3411 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3412 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3413 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3414 __isl_take isl_union_set *uset);
3416 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3417 __isl_take isl_pw_qpolynomial_fold *pwf);
3419 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3420 __isl_take isl_pw_qpolynomial_fold *pwf);
3422 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3423 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3425 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3426 __isl_take isl_pw_qpolynomial_fold *pwf,
3427 __isl_take isl_set *context);
3429 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3430 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3431 __isl_take isl_union_set *context);
3433 The gist operation applies the gist operation to each of
3434 the cells in the domain of the input piecewise quasipolynomial reduction.
3435 In future, the operation will also exploit the context
3436 to simplify the quasipolynomial reductions associated to each cell.
3438 __isl_give isl_pw_qpolynomial_fold *
3439 isl_set_apply_pw_qpolynomial_fold(
3440 __isl_take isl_set *set,
3441 __isl_take isl_pw_qpolynomial_fold *pwf,
3443 __isl_give isl_pw_qpolynomial_fold *
3444 isl_map_apply_pw_qpolynomial_fold(
3445 __isl_take isl_map *map,
3446 __isl_take isl_pw_qpolynomial_fold *pwf,
3448 __isl_give isl_union_pw_qpolynomial_fold *
3449 isl_union_set_apply_union_pw_qpolynomial_fold(
3450 __isl_take isl_union_set *uset,
3451 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3453 __isl_give isl_union_pw_qpolynomial_fold *
3454 isl_union_map_apply_union_pw_qpolynomial_fold(
3455 __isl_take isl_union_map *umap,
3456 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3459 The functions taking a map
3460 compose the given map with the given piecewise quasipolynomial reduction.
3461 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3462 over all elements in the intersection of the range of the map
3463 and the domain of the piecewise quasipolynomial reduction
3464 as a function of an element in the domain of the map.
3465 The functions taking a set compute a bound over all elements in the
3466 intersection of the set and the domain of the
3467 piecewise quasipolynomial reduction.
3469 =head2 Dependence Analysis
3471 C<isl> contains specialized functionality for performing
3472 array dataflow analysis. That is, given a I<sink> access relation
3473 and a collection of possible I<source> access relations,
3474 C<isl> can compute relations that describe
3475 for each iteration of the sink access, which iteration
3476 of which of the source access relations was the last
3477 to access the same data element before the given iteration
3479 To compute standard flow dependences, the sink should be
3480 a read, while the sources should be writes.
3481 If any of the source accesses are marked as being I<may>
3482 accesses, then there will be a dependence to the last
3483 I<must> access B<and> to any I<may> access that follows
3484 this last I<must> access.
3485 In particular, if I<all> sources are I<may> accesses,
3486 then memory based dependence analysis is performed.
3487 If, on the other hand, all sources are I<must> accesses,
3488 then value based dependence analysis is performed.
3490 #include <isl/flow.h>
3492 typedef int (*isl_access_level_before)(void *first, void *second);
3494 __isl_give isl_access_info *isl_access_info_alloc(
3495 __isl_take isl_map *sink,
3496 void *sink_user, isl_access_level_before fn,
3498 __isl_give isl_access_info *isl_access_info_add_source(
3499 __isl_take isl_access_info *acc,
3500 __isl_take isl_map *source, int must,
3502 void isl_access_info_free(__isl_take isl_access_info *acc);
3504 __isl_give isl_flow *isl_access_info_compute_flow(
3505 __isl_take isl_access_info *acc);
3507 int isl_flow_foreach(__isl_keep isl_flow *deps,
3508 int (*fn)(__isl_take isl_map *dep, int must,
3509 void *dep_user, void *user),
3511 __isl_give isl_map *isl_flow_get_no_source(
3512 __isl_keep isl_flow *deps, int must);
3513 void isl_flow_free(__isl_take isl_flow *deps);
3515 The function C<isl_access_info_compute_flow> performs the actual
3516 dependence analysis. The other functions are used to construct
3517 the input for this function or to read off the output.
3519 The input is collected in an C<isl_access_info>, which can
3520 be created through a call to C<isl_access_info_alloc>.
3521 The arguments to this functions are the sink access relation
3522 C<sink>, a token C<sink_user> used to identify the sink
3523 access to the user, a callback function for specifying the
3524 relative order of source and sink accesses, and the number
3525 of source access relations that will be added.
3526 The callback function has type C<int (*)(void *first, void *second)>.
3527 The function is called with two user supplied tokens identifying
3528 either a source or the sink and it should return the shared nesting
3529 level and the relative order of the two accesses.
3530 In particular, let I<n> be the number of loops shared by
3531 the two accesses. If C<first> precedes C<second> textually,
3532 then the function should return I<2 * n + 1>; otherwise,
3533 it should return I<2 * n>.
3534 The sources can be added to the C<isl_access_info> by performing
3535 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3536 C<must> indicates whether the source is a I<must> access
3537 or a I<may> access. Note that a multi-valued access relation
3538 should only be marked I<must> if every iteration in the domain
3539 of the relation accesses I<all> elements in its image.
3540 The C<source_user> token is again used to identify
3541 the source access. The range of the source access relation
3542 C<source> should have the same dimension as the range
3543 of the sink access relation.
3544 The C<isl_access_info_free> function should usually not be
3545 called explicitly, because it is called implicitly by
3546 C<isl_access_info_compute_flow>.
3548 The result of the dependence analysis is collected in an
3549 C<isl_flow>. There may be elements of
3550 the sink access for which no preceding source access could be
3551 found or for which all preceding sources are I<may> accesses.
3552 The relations containing these elements can be obtained through
3553 calls to C<isl_flow_get_no_source>, the first with C<must> set
3554 and the second with C<must> unset.
3555 In the case of standard flow dependence analysis,
3556 with the sink a read and the sources I<must> writes,
3557 the first relation corresponds to the reads from uninitialized
3558 array elements and the second relation is empty.
3559 The actual flow dependences can be extracted using
3560 C<isl_flow_foreach>. This function will call the user-specified
3561 callback function C<fn> for each B<non-empty> dependence between
3562 a source and the sink. The callback function is called
3563 with four arguments, the actual flow dependence relation
3564 mapping source iterations to sink iterations, a boolean that
3565 indicates whether it is a I<must> or I<may> dependence, a token
3566 identifying the source and an additional C<void *> with value
3567 equal to the third argument of the C<isl_flow_foreach> call.
3568 A dependence is marked I<must> if it originates from a I<must>
3569 source and if it is not followed by any I<may> sources.
3571 After finishing with an C<isl_flow>, the user should call
3572 C<isl_flow_free> to free all associated memory.
3574 A higher-level interface to dependence analysis is provided
3575 by the following function.
3577 #include <isl/flow.h>
3579 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3580 __isl_take isl_union_map *must_source,
3581 __isl_take isl_union_map *may_source,
3582 __isl_take isl_union_map *schedule,
3583 __isl_give isl_union_map **must_dep,
3584 __isl_give isl_union_map **may_dep,
3585 __isl_give isl_union_map **must_no_source,
3586 __isl_give isl_union_map **may_no_source);
3588 The arrays are identified by the tuple names of the ranges
3589 of the accesses. The iteration domains by the tuple names
3590 of the domains of the accesses and of the schedule.
3591 The relative order of the iteration domains is given by the
3592 schedule. The relations returned through C<must_no_source>
3593 and C<may_no_source> are subsets of C<sink>.
3594 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3595 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3596 any of the other arguments is treated as an error.
3600 B<The functionality described in this section is fairly new
3601 and may be subject to change.>
3603 The following function can be used to compute a schedule
3604 for a union of domains. The generated schedule respects
3605 all C<validity> dependences. That is, all dependence distances
3606 over these dependences in the scheduled space are lexicographically
3607 positive. The generated schedule schedule also tries to minimize
3608 the dependence distances over C<proximity> dependences.
3609 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3610 for groups of domains where the dependence distances have only
3611 non-negative values.
3612 The algorithm used to construct the schedule is similar to that
3615 #include <isl/schedule.h>
3616 __isl_give isl_schedule *isl_union_set_compute_schedule(
3617 __isl_take isl_union_set *domain,
3618 __isl_take isl_union_map *validity,
3619 __isl_take isl_union_map *proximity);
3620 void *isl_schedule_free(__isl_take isl_schedule *sched);
3622 A mapping from the domains to the scheduled space can be obtained
3623 from an C<isl_schedule> using the following function.
3625 __isl_give isl_union_map *isl_schedule_get_map(
3626 __isl_keep isl_schedule *sched);
3628 A representation of the schedule can be printed using
3630 __isl_give isl_printer *isl_printer_print_schedule(
3631 __isl_take isl_printer *p,
3632 __isl_keep isl_schedule *schedule);
3634 A representation of the schedule as a forest of bands can be obtained
3635 using the following function.
3637 __isl_give isl_band_list *isl_schedule_get_band_forest(
3638 __isl_keep isl_schedule *schedule);
3640 The list can be manipulated as explained in L<"Lists">.
3641 The bands inside the list can be copied and freed using the following
3644 #include <isl/band.h>
3645 __isl_give isl_band *isl_band_copy(
3646 __isl_keep isl_band *band);
3647 void *isl_band_free(__isl_take isl_band *band);
3649 Each band contains zero or more scheduling dimensions.
3650 These are referred to as the members of the band.
3651 The section of the schedule that corresponds to the band is
3652 referred to as the partial schedule of the band.
3653 For those nodes that participate in a band, the outer scheduling
3654 dimensions form the prefix schedule, while the inner scheduling
3655 dimensions form the suffix schedule.
3656 That is, if we take a cut of the band forest, then the union of
3657 the concatenations of the prefix, partial and suffix schedules of
3658 each band in the cut is equal to the entire schedule (modulo
3659 some possible padding at the end with zero scheduling dimensions).
3660 The properties of a band can be inspected using the following functions.
3662 #include <isl/band.h>
3663 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3665 int isl_band_has_children(__isl_keep isl_band *band);
3666 __isl_give isl_band_list *isl_band_get_children(
3667 __isl_keep isl_band *band);
3669 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3670 __isl_keep isl_band *band);
3671 __isl_give isl_union_map *isl_band_get_partial_schedule(
3672 __isl_keep isl_band *band);
3673 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3674 __isl_keep isl_band *band);
3676 int isl_band_n_member(__isl_keep isl_band *band);
3677 int isl_band_member_is_zero_distance(
3678 __isl_keep isl_band *band, int pos);
3680 Note that a scheduling dimension is considered to be ``zero
3681 distance'' if it does not carry any proximity dependences
3683 That is, if the dependence distances of the proximity
3684 dependences are all zero in that direction (for fixed
3685 iterations of outer bands).
3687 A representation of the band can be printed using
3689 #include <isl/band.h>
3690 __isl_give isl_printer *isl_printer_print_band(
3691 __isl_take isl_printer *p,
3692 __isl_keep isl_band *band);
3694 =head2 Parametric Vertex Enumeration
3696 The parametric vertex enumeration described in this section
3697 is mainly intended to be used internally and by the C<barvinok>
3700 #include <isl/vertices.h>
3701 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3702 __isl_keep isl_basic_set *bset);
3704 The function C<isl_basic_set_compute_vertices> performs the
3705 actual computation of the parametric vertices and the chamber
3706 decomposition and store the result in an C<isl_vertices> object.
3707 This information can be queried by either iterating over all
3708 the vertices or iterating over all the chambers or cells
3709 and then iterating over all vertices that are active on the chamber.
3711 int isl_vertices_foreach_vertex(
3712 __isl_keep isl_vertices *vertices,
3713 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3716 int isl_vertices_foreach_cell(
3717 __isl_keep isl_vertices *vertices,
3718 int (*fn)(__isl_take isl_cell *cell, void *user),
3720 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3721 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3724 Other operations that can be performed on an C<isl_vertices> object are
3727 isl_ctx *isl_vertices_get_ctx(
3728 __isl_keep isl_vertices *vertices);
3729 int isl_vertices_get_n_vertices(
3730 __isl_keep isl_vertices *vertices);
3731 void isl_vertices_free(__isl_take isl_vertices *vertices);
3733 Vertices can be inspected and destroyed using the following functions.
3735 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3736 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3737 __isl_give isl_basic_set *isl_vertex_get_domain(
3738 __isl_keep isl_vertex *vertex);
3739 __isl_give isl_basic_set *isl_vertex_get_expr(
3740 __isl_keep isl_vertex *vertex);
3741 void isl_vertex_free(__isl_take isl_vertex *vertex);
3743 C<isl_vertex_get_expr> returns a singleton parametric set describing
3744 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3746 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3747 B<rational> basic sets, so they should mainly be used for inspection
3748 and should not be mixed with integer sets.
3750 Chambers can be inspected and destroyed using the following functions.
3752 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3753 __isl_give isl_basic_set *isl_cell_get_domain(
3754 __isl_keep isl_cell *cell);
3755 void isl_cell_free(__isl_take isl_cell *cell);
3759 Although C<isl> is mainly meant to be used as a library,
3760 it also contains some basic applications that use some
3761 of the functionality of C<isl>.
3762 The input may be specified in either the L<isl format>
3763 or the L<PolyLib format>.
3765 =head2 C<isl_polyhedron_sample>
3767 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3768 an integer element of the polyhedron, if there is any.
3769 The first column in the output is the denominator and is always
3770 equal to 1. If the polyhedron contains no integer points,
3771 then a vector of length zero is printed.
3775 C<isl_pip> takes the same input as the C<example> program
3776 from the C<piplib> distribution, i.e., a set of constraints
3777 on the parameters, a line containing only -1 and finally a set
3778 of constraints on a parametric polyhedron.
3779 The coefficients of the parameters appear in the last columns
3780 (but before the final constant column).
3781 The output is the lexicographic minimum of the parametric polyhedron.
3782 As C<isl> currently does not have its own output format, the output
3783 is just a dump of the internal state.
3785 =head2 C<isl_polyhedron_minimize>
3787 C<isl_polyhedron_minimize> computes the minimum of some linear
3788 or affine objective function over the integer points in a polyhedron.
3789 If an affine objective function
3790 is given, then the constant should appear in the last column.
3792 =head2 C<isl_polytope_scan>
3794 Given a polytope, C<isl_polytope_scan> prints
3795 all integer points in the polytope.