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);
601 __isl_give isl_space *isl_multi_aff_get_space(
602 __isl_keep isl_multi_aff *maff);
604 #include <isl/point.h>
605 __isl_give isl_space *isl_point_get_space(
606 __isl_keep isl_point *pnt);
608 The identifiers or names of the individual dimensions may be set or read off
609 using the following functions.
611 #include <isl/space.h>
612 __isl_give isl_space *isl_space_set_dim_id(
613 __isl_take isl_space *space,
614 enum isl_dim_type type, unsigned pos,
615 __isl_take isl_id *id);
616 int isl_space_has_dim_id(__isl_keep isl_space *space,
617 enum isl_dim_type type, unsigned pos);
618 __isl_give isl_id *isl_space_get_dim_id(
619 __isl_keep isl_space *space,
620 enum isl_dim_type type, unsigned pos);
621 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
622 enum isl_dim_type type, unsigned pos,
623 __isl_keep const char *name);
624 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
625 enum isl_dim_type type, unsigned pos);
627 Note that C<isl_space_get_name> returns a pointer to some internal
628 data structure, so the result can only be used while the
629 corresponding C<isl_space> is alive.
630 Also note that every function that operates on two sets or relations
631 requires that both arguments have the same parameters. This also
632 means that if one of the arguments has named parameters, then the
633 other needs to have named parameters too and the names need to match.
634 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
635 arguments may have different parameters (as long as they are named),
636 in which case the result will have as parameters the union of the parameters of
639 Given the identifier or name of a dimension (typically a parameter),
640 its position can be obtained from the following function.
642 #include <isl/space.h>
643 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
644 enum isl_dim_type type, __isl_keep isl_id *id);
645 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
646 enum isl_dim_type type, const char *name);
648 The identifiers or names of entire spaces may be set or read off
649 using the following functions.
651 #include <isl/space.h>
652 __isl_give isl_space *isl_space_set_tuple_id(
653 __isl_take isl_space *space,
654 enum isl_dim_type type, __isl_take isl_id *id);
655 __isl_give isl_space *isl_space_reset_tuple_id(
656 __isl_take isl_space *space, enum isl_dim_type type);
657 int isl_space_has_tuple_id(__isl_keep isl_space *space,
658 enum isl_dim_type type);
659 __isl_give isl_id *isl_space_get_tuple_id(
660 __isl_keep isl_space *space, enum isl_dim_type type);
661 __isl_give isl_space *isl_space_set_tuple_name(
662 __isl_take isl_space *space,
663 enum isl_dim_type type, const char *s);
664 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
665 enum isl_dim_type type);
667 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
668 or C<isl_dim_set>. As with C<isl_space_get_name>,
669 the C<isl_space_get_tuple_name> function returns a pointer to some internal
671 Binary operations require the corresponding spaces of their arguments
672 to have the same name.
674 Spaces can be nested. In particular, the domain of a set or
675 the domain or range of a relation can be a nested relation.
676 The following functions can be used to construct and deconstruct
679 #include <isl/space.h>
680 int isl_space_is_wrapping(__isl_keep isl_space *space);
681 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
682 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
684 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
685 be the space of a set, while that of
686 C<isl_space_wrap> should be the space of a relation.
687 Conversely, the output of C<isl_space_unwrap> is the space
688 of a relation, while that of C<isl_space_wrap> is the space of a set.
690 Spaces can be created from other spaces
691 using the following functions.
693 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
694 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
695 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
696 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
697 __isl_give isl_space *isl_space_params(
698 __isl_take isl_space *space);
699 __isl_give isl_space *isl_space_set_from_params(
700 __isl_take isl_space *space);
701 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
702 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
703 __isl_take isl_space *right);
704 __isl_give isl_space *isl_space_align_params(
705 __isl_take isl_space *space1, __isl_take isl_space *space2)
706 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned pos, unsigned n);
708 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
709 enum isl_dim_type type, unsigned n);
710 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
711 enum isl_dim_type type, unsigned first, unsigned n);
712 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
713 enum isl_dim_type dst_type, unsigned dst_pos,
714 enum isl_dim_type src_type, unsigned src_pos,
716 __isl_give isl_space *isl_space_map_from_set(
717 __isl_take isl_space *space);
718 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
720 Note that if dimensions are added or removed from a space, then
721 the name and the internal structure are lost.
725 A local space is essentially a space with
726 zero or more existentially quantified variables.
727 The local space of a basic set or relation can be obtained
728 using the following functions.
731 __isl_give isl_local_space *isl_basic_set_get_local_space(
732 __isl_keep isl_basic_set *bset);
735 __isl_give isl_local_space *isl_basic_map_get_local_space(
736 __isl_keep isl_basic_map *bmap);
738 A new local space can be created from a space using
740 #include <isl/local_space.h>
741 __isl_give isl_local_space *isl_local_space_from_space(
742 __isl_take isl_space *space);
744 They can be inspected, modified, copied and freed using the following functions.
746 #include <isl/local_space.h>
747 isl_ctx *isl_local_space_get_ctx(
748 __isl_keep isl_local_space *ls);
749 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
750 int isl_local_space_dim(__isl_keep isl_local_space *ls,
751 enum isl_dim_type type);
752 const char *isl_local_space_get_dim_name(
753 __isl_keep isl_local_space *ls,
754 enum isl_dim_type type, unsigned pos);
755 __isl_give isl_local_space *isl_local_space_set_dim_name(
756 __isl_take isl_local_space *ls,
757 enum isl_dim_type type, unsigned pos, const char *s);
758 __isl_give isl_local_space *isl_local_space_set_dim_id(
759 __isl_take isl_local_space *ls,
760 enum isl_dim_type type, unsigned pos,
761 __isl_take isl_id *id);
762 __isl_give isl_space *isl_local_space_get_space(
763 __isl_keep isl_local_space *ls);
764 __isl_give isl_aff *isl_local_space_get_div(
765 __isl_keep isl_local_space *ls, int pos);
766 __isl_give isl_local_space *isl_local_space_copy(
767 __isl_keep isl_local_space *ls);
768 void *isl_local_space_free(__isl_take isl_local_space *ls);
770 Two local spaces can be compared using
772 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
773 __isl_keep isl_local_space *ls2);
775 Local spaces can be created from other local spaces
776 using the following functions.
778 __isl_give isl_local_space *isl_local_space_domain(
779 __isl_take isl_local_space *ls);
780 __isl_give isl_local_space *isl_local_space_from_domain(
781 __isl_take isl_local_space *ls);
782 __isl_give isl_local_space *isl_local_space_add_dims(
783 __isl_take isl_local_space *ls,
784 enum isl_dim_type type, unsigned n);
785 __isl_give isl_local_space *isl_local_space_insert_dims(
786 __isl_take isl_local_space *ls,
787 enum isl_dim_type type, unsigned first, unsigned n);
788 __isl_give isl_local_space *isl_local_space_drop_dims(
789 __isl_take isl_local_space *ls,
790 enum isl_dim_type type, unsigned first, unsigned n);
792 =head2 Input and Output
794 C<isl> supports its own input/output format, which is similar
795 to the C<Omega> format, but also supports the C<PolyLib> format
800 The C<isl> format is similar to that of C<Omega>, but has a different
801 syntax for describing the parameters and allows for the definition
802 of an existentially quantified variable as the integer division
803 of an affine expression.
804 For example, the set of integers C<i> between C<0> and C<n>
805 such that C<i % 10 <= 6> can be described as
807 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
810 A set or relation can have several disjuncts, separated
811 by the keyword C<or>. Each disjunct is either a conjunction
812 of constraints or a projection (C<exists>) of a conjunction
813 of constraints. The constraints are separated by the keyword
816 =head3 C<PolyLib> format
818 If the represented set is a union, then the first line
819 contains a single number representing the number of disjuncts.
820 Otherwise, a line containing the number C<1> is optional.
822 Each disjunct is represented by a matrix of constraints.
823 The first line contains two numbers representing
824 the number of rows and columns,
825 where the number of rows is equal to the number of constraints
826 and the number of columns is equal to two plus the number of variables.
827 The following lines contain the actual rows of the constraint matrix.
828 In each row, the first column indicates whether the constraint
829 is an equality (C<0>) or inequality (C<1>). The final column
830 corresponds to the constant term.
832 If the set is parametric, then the coefficients of the parameters
833 appear in the last columns before the constant column.
834 The coefficients of any existentially quantified variables appear
835 between those of the set variables and those of the parameters.
837 =head3 Extended C<PolyLib> format
839 The extended C<PolyLib> format is nearly identical to the
840 C<PolyLib> format. The only difference is that the line
841 containing the number of rows and columns of a constraint matrix
842 also contains four additional numbers:
843 the number of output dimensions, the number of input dimensions,
844 the number of local dimensions (i.e., the number of existentially
845 quantified variables) and the number of parameters.
846 For sets, the number of ``output'' dimensions is equal
847 to the number of set dimensions, while the number of ``input''
853 __isl_give isl_basic_set *isl_basic_set_read_from_file(
854 isl_ctx *ctx, FILE *input);
855 __isl_give isl_basic_set *isl_basic_set_read_from_str(
856 isl_ctx *ctx, const char *str);
857 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
859 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
863 __isl_give isl_basic_map *isl_basic_map_read_from_file(
864 isl_ctx *ctx, FILE *input);
865 __isl_give isl_basic_map *isl_basic_map_read_from_str(
866 isl_ctx *ctx, const char *str);
867 __isl_give isl_map *isl_map_read_from_file(
868 isl_ctx *ctx, FILE *input);
869 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
872 #include <isl/union_set.h>
873 __isl_give isl_union_set *isl_union_set_read_from_file(
874 isl_ctx *ctx, FILE *input);
875 __isl_give isl_union_set *isl_union_set_read_from_str(
876 isl_ctx *ctx, const char *str);
878 #include <isl/union_map.h>
879 __isl_give isl_union_map *isl_union_map_read_from_file(
880 isl_ctx *ctx, FILE *input);
881 __isl_give isl_union_map *isl_union_map_read_from_str(
882 isl_ctx *ctx, const char *str);
884 The input format is autodetected and may be either the C<PolyLib> format
885 or the C<isl> format.
889 Before anything can be printed, an C<isl_printer> needs to
892 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
894 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
895 void isl_printer_free(__isl_take isl_printer *printer);
896 __isl_give char *isl_printer_get_str(
897 __isl_keep isl_printer *printer);
899 The behavior of the printer can be modified in various ways
901 __isl_give isl_printer *isl_printer_set_output_format(
902 __isl_take isl_printer *p, int output_format);
903 __isl_give isl_printer *isl_printer_set_indent(
904 __isl_take isl_printer *p, int indent);
905 __isl_give isl_printer *isl_printer_indent(
906 __isl_take isl_printer *p, int indent);
907 __isl_give isl_printer *isl_printer_set_prefix(
908 __isl_take isl_printer *p, const char *prefix);
909 __isl_give isl_printer *isl_printer_set_suffix(
910 __isl_take isl_printer *p, const char *suffix);
912 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
913 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
914 and defaults to C<ISL_FORMAT_ISL>.
915 Each line in the output is indented by C<indent> (set by
916 C<isl_printer_set_indent>) spaces
917 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
918 In the C<PolyLib> format output,
919 the coefficients of the existentially quantified variables
920 appear between those of the set variables and those
922 The function C<isl_printer_indent> increases the indentation
923 by the specified amount (which may be negative).
925 To actually print something, use
928 __isl_give isl_printer *isl_printer_print_basic_set(
929 __isl_take isl_printer *printer,
930 __isl_keep isl_basic_set *bset);
931 __isl_give isl_printer *isl_printer_print_set(
932 __isl_take isl_printer *printer,
933 __isl_keep isl_set *set);
936 __isl_give isl_printer *isl_printer_print_basic_map(
937 __isl_take isl_printer *printer,
938 __isl_keep isl_basic_map *bmap);
939 __isl_give isl_printer *isl_printer_print_map(
940 __isl_take isl_printer *printer,
941 __isl_keep isl_map *map);
943 #include <isl/union_set.h>
944 __isl_give isl_printer *isl_printer_print_union_set(
945 __isl_take isl_printer *p,
946 __isl_keep isl_union_set *uset);
948 #include <isl/union_map.h>
949 __isl_give isl_printer *isl_printer_print_union_map(
950 __isl_take isl_printer *p,
951 __isl_keep isl_union_map *umap);
953 When called on a file printer, the following function flushes
954 the file. When called on a string printer, the buffer is cleared.
956 __isl_give isl_printer *isl_printer_flush(
957 __isl_take isl_printer *p);
959 =head2 Creating New Sets and Relations
961 C<isl> has functions for creating some standard sets and relations.
965 =item * Empty sets and relations
967 __isl_give isl_basic_set *isl_basic_set_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_basic_map *isl_basic_map_empty(
970 __isl_take isl_space *space);
971 __isl_give isl_set *isl_set_empty(
972 __isl_take isl_space *space);
973 __isl_give isl_map *isl_map_empty(
974 __isl_take isl_space *space);
975 __isl_give isl_union_set *isl_union_set_empty(
976 __isl_take isl_space *space);
977 __isl_give isl_union_map *isl_union_map_empty(
978 __isl_take isl_space *space);
980 For C<isl_union_set>s and C<isl_union_map>s, the space
981 is only used to specify the parameters.
983 =item * Universe sets and relations
985 __isl_give isl_basic_set *isl_basic_set_universe(
986 __isl_take isl_space *space);
987 __isl_give isl_basic_map *isl_basic_map_universe(
988 __isl_take isl_space *space);
989 __isl_give isl_set *isl_set_universe(
990 __isl_take isl_space *space);
991 __isl_give isl_map *isl_map_universe(
992 __isl_take isl_space *space);
993 __isl_give isl_union_set *isl_union_set_universe(
994 __isl_take isl_union_set *uset);
995 __isl_give isl_union_map *isl_union_map_universe(
996 __isl_take isl_union_map *umap);
998 The sets and relations constructed by the functions above
999 contain all integer values, while those constructed by the
1000 functions below only contain non-negative values.
1002 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1003 __isl_take isl_space *space);
1004 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1005 __isl_take isl_space *space);
1006 __isl_give isl_set *isl_set_nat_universe(
1007 __isl_take isl_space *space);
1008 __isl_give isl_map *isl_map_nat_universe(
1009 __isl_take isl_space *space);
1011 =item * Identity relations
1013 __isl_give isl_basic_map *isl_basic_map_identity(
1014 __isl_take isl_space *space);
1015 __isl_give isl_map *isl_map_identity(
1016 __isl_take isl_space *space);
1018 The number of input and output dimensions in C<space> needs
1021 =item * Lexicographic order
1023 __isl_give isl_map *isl_map_lex_lt(
1024 __isl_take isl_space *set_space);
1025 __isl_give isl_map *isl_map_lex_le(
1026 __isl_take isl_space *set_space);
1027 __isl_give isl_map *isl_map_lex_gt(
1028 __isl_take isl_space *set_space);
1029 __isl_give isl_map *isl_map_lex_ge(
1030 __isl_take isl_space *set_space);
1031 __isl_give isl_map *isl_map_lex_lt_first(
1032 __isl_take isl_space *space, unsigned n);
1033 __isl_give isl_map *isl_map_lex_le_first(
1034 __isl_take isl_space *space, unsigned n);
1035 __isl_give isl_map *isl_map_lex_gt_first(
1036 __isl_take isl_space *space, unsigned n);
1037 __isl_give isl_map *isl_map_lex_ge_first(
1038 __isl_take isl_space *space, unsigned n);
1040 The first four functions take a space for a B<set>
1041 and return relations that express that the elements in the domain
1042 are lexicographically less
1043 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1044 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1045 than the elements in the range.
1046 The last four functions take a space for a map
1047 and return relations that express that the first C<n> dimensions
1048 in the domain are lexicographically less
1049 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1050 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1051 than the first C<n> dimensions in the range.
1055 A basic set or relation can be converted to a set or relation
1056 using the following functions.
1058 __isl_give isl_set *isl_set_from_basic_set(
1059 __isl_take isl_basic_set *bset);
1060 __isl_give isl_map *isl_map_from_basic_map(
1061 __isl_take isl_basic_map *bmap);
1063 Sets and relations can be converted to union sets and relations
1064 using the following functions.
1066 __isl_give isl_union_map *isl_union_map_from_map(
1067 __isl_take isl_map *map);
1068 __isl_give isl_union_set *isl_union_set_from_set(
1069 __isl_take isl_set *set);
1071 The inverse conversions below can only be used if the input
1072 union set or relation is known to contain elements in exactly one
1075 __isl_give isl_set *isl_set_from_union_set(
1076 __isl_take isl_union_set *uset);
1077 __isl_give isl_map *isl_map_from_union_map(
1078 __isl_take isl_union_map *umap);
1080 A zero-dimensional set can be constructed on a given parameter domain
1081 using the following function.
1083 __isl_give isl_set *isl_set_from_params(
1084 __isl_take isl_set *set);
1086 Sets and relations can be copied and freed again using the following
1089 __isl_give isl_basic_set *isl_basic_set_copy(
1090 __isl_keep isl_basic_set *bset);
1091 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1092 __isl_give isl_union_set *isl_union_set_copy(
1093 __isl_keep isl_union_set *uset);
1094 __isl_give isl_basic_map *isl_basic_map_copy(
1095 __isl_keep isl_basic_map *bmap);
1096 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1097 __isl_give isl_union_map *isl_union_map_copy(
1098 __isl_keep isl_union_map *umap);
1099 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1100 void isl_set_free(__isl_take isl_set *set);
1101 void *isl_union_set_free(__isl_take isl_union_set *uset);
1102 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1103 void isl_map_free(__isl_take isl_map *map);
1104 void *isl_union_map_free(__isl_take isl_union_map *umap);
1106 Other sets and relations can be constructed by starting
1107 from a universe set or relation, adding equality and/or
1108 inequality constraints and then projecting out the
1109 existentially quantified variables, if any.
1110 Constraints can be constructed, manipulated and
1111 added to (or removed from) (basic) sets and relations
1112 using the following functions.
1114 #include <isl/constraint.h>
1115 __isl_give isl_constraint *isl_equality_alloc(
1116 __isl_take isl_local_space *ls);
1117 __isl_give isl_constraint *isl_inequality_alloc(
1118 __isl_take isl_local_space *ls);
1119 __isl_give isl_constraint *isl_constraint_set_constant(
1120 __isl_take isl_constraint *constraint, isl_int v);
1121 __isl_give isl_constraint *isl_constraint_set_constant_si(
1122 __isl_take isl_constraint *constraint, int v);
1123 __isl_give isl_constraint *isl_constraint_set_coefficient(
1124 __isl_take isl_constraint *constraint,
1125 enum isl_dim_type type, int pos, isl_int v);
1126 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1127 __isl_take isl_constraint *constraint,
1128 enum isl_dim_type type, int pos, int v);
1129 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1130 __isl_take isl_basic_map *bmap,
1131 __isl_take isl_constraint *constraint);
1132 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1133 __isl_take isl_basic_set *bset,
1134 __isl_take isl_constraint *constraint);
1135 __isl_give isl_map *isl_map_add_constraint(
1136 __isl_take isl_map *map,
1137 __isl_take isl_constraint *constraint);
1138 __isl_give isl_set *isl_set_add_constraint(
1139 __isl_take isl_set *set,
1140 __isl_take isl_constraint *constraint);
1141 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1142 __isl_take isl_basic_set *bset,
1143 __isl_take isl_constraint *constraint);
1145 For example, to create a set containing the even integers
1146 between 10 and 42, you would use the following code.
1149 isl_local_space *ls;
1151 isl_basic_set *bset;
1153 space = isl_space_set_alloc(ctx, 0, 2);
1154 bset = isl_basic_set_universe(isl_space_copy(space));
1155 ls = isl_local_space_from_space(space);
1157 c = isl_equality_alloc(isl_local_space_copy(ls));
1158 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1159 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1160 bset = isl_basic_set_add_constraint(bset, c);
1162 c = isl_inequality_alloc(isl_local_space_copy(ls));
1163 c = isl_constraint_set_constant_si(c, -10);
1164 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1165 bset = isl_basic_set_add_constraint(bset, c);
1167 c = isl_inequality_alloc(ls);
1168 c = isl_constraint_set_constant_si(c, 42);
1169 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1170 bset = isl_basic_set_add_constraint(bset, c);
1172 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1176 isl_basic_set *bset;
1177 bset = isl_basic_set_read_from_str(ctx,
1178 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1180 A basic set or relation can also be constructed from two matrices
1181 describing the equalities and the inequalities.
1183 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1184 __isl_take isl_space *space,
1185 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1186 enum isl_dim_type c1,
1187 enum isl_dim_type c2, enum isl_dim_type c3,
1188 enum isl_dim_type c4);
1189 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1190 __isl_take isl_space *space,
1191 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1192 enum isl_dim_type c1,
1193 enum isl_dim_type c2, enum isl_dim_type c3,
1194 enum isl_dim_type c4, enum isl_dim_type c5);
1196 The C<isl_dim_type> arguments indicate the order in which
1197 different kinds of variables appear in the input matrices
1198 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1199 C<isl_dim_set> and C<isl_dim_div> for sets and
1200 of C<isl_dim_cst>, C<isl_dim_param>,
1201 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1203 A (basic) set or relation can also be constructed from a (piecewise)
1204 (multiple) affine expression
1205 or a list of affine expressions
1206 (See L<"Piecewise Quasi Affine Expressions"> and
1207 L<"Multiple Quasi Affine Expressions">).
1209 __isl_give isl_basic_map *isl_basic_map_from_aff(
1210 __isl_take isl_aff *aff);
1211 __isl_give isl_set *isl_set_from_pw_aff(
1212 __isl_take isl_pw_aff *pwaff);
1213 __isl_give isl_map *isl_map_from_pw_aff(
1214 __isl_take isl_pw_aff *pwaff);
1215 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1216 __isl_take isl_space *domain_space,
1217 __isl_take isl_aff_list *list);
1218 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1219 __isl_take isl_multi_aff *maff)
1221 The C<domain_dim> argument describes the domain of the resulting
1222 basic relation. It is required because the C<list> may consist
1223 of zero affine expressions.
1225 =head2 Inspecting Sets and Relations
1227 Usually, the user should not have to care about the actual constraints
1228 of the sets and maps, but should instead apply the abstract operations
1229 explained in the following sections.
1230 Occasionally, however, it may be required to inspect the individual
1231 coefficients of the constraints. This section explains how to do so.
1232 In these cases, it may also be useful to have C<isl> compute
1233 an explicit representation of the existentially quantified variables.
1235 __isl_give isl_set *isl_set_compute_divs(
1236 __isl_take isl_set *set);
1237 __isl_give isl_map *isl_map_compute_divs(
1238 __isl_take isl_map *map);
1239 __isl_give isl_union_set *isl_union_set_compute_divs(
1240 __isl_take isl_union_set *uset);
1241 __isl_give isl_union_map *isl_union_map_compute_divs(
1242 __isl_take isl_union_map *umap);
1244 This explicit representation defines the existentially quantified
1245 variables as integer divisions of the other variables, possibly
1246 including earlier existentially quantified variables.
1247 An explicitly represented existentially quantified variable therefore
1248 has a unique value when the values of the other variables are known.
1249 If, furthermore, the same existentials, i.e., existentials
1250 with the same explicit representations, should appear in the
1251 same order in each of the disjuncts of a set or map, then the user should call
1252 either of the following functions.
1254 __isl_give isl_set *isl_set_align_divs(
1255 __isl_take isl_set *set);
1256 __isl_give isl_map *isl_map_align_divs(
1257 __isl_take isl_map *map);
1259 Alternatively, the existentially quantified variables can be removed
1260 using the following functions, which compute an overapproximation.
1262 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1263 __isl_take isl_basic_set *bset);
1264 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1265 __isl_take isl_basic_map *bmap);
1266 __isl_give isl_set *isl_set_remove_divs(
1267 __isl_take isl_set *set);
1268 __isl_give isl_map *isl_map_remove_divs(
1269 __isl_take isl_map *map);
1271 To iterate over all the sets or maps in a union set or map, use
1273 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1274 int (*fn)(__isl_take isl_set *set, void *user),
1276 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1277 int (*fn)(__isl_take isl_map *map, void *user),
1280 The number of sets or maps in a union set or map can be obtained
1283 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1284 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1286 To extract the set or map in a given space from a union, use
1288 __isl_give isl_set *isl_union_set_extract_set(
1289 __isl_keep isl_union_set *uset,
1290 __isl_take isl_space *space);
1291 __isl_give isl_map *isl_union_map_extract_map(
1292 __isl_keep isl_union_map *umap,
1293 __isl_take isl_space *space);
1295 To iterate over all the basic sets or maps in a set or map, use
1297 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1298 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1300 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1301 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1304 The callback function C<fn> should return 0 if successful and
1305 -1 if an error occurs. In the latter case, or if any other error
1306 occurs, the above functions will return -1.
1308 It should be noted that C<isl> does not guarantee that
1309 the basic sets or maps passed to C<fn> are disjoint.
1310 If this is required, then the user should call one of
1311 the following functions first.
1313 __isl_give isl_set *isl_set_make_disjoint(
1314 __isl_take isl_set *set);
1315 __isl_give isl_map *isl_map_make_disjoint(
1316 __isl_take isl_map *map);
1318 The number of basic sets in a set can be obtained
1321 int isl_set_n_basic_set(__isl_keep isl_set *set);
1323 To iterate over the constraints of a basic set or map, use
1325 #include <isl/constraint.h>
1327 int isl_basic_map_foreach_constraint(
1328 __isl_keep isl_basic_map *bmap,
1329 int (*fn)(__isl_take isl_constraint *c, void *user),
1331 void *isl_constraint_free(__isl_take isl_constraint *c);
1333 Again, the callback function C<fn> should return 0 if successful and
1334 -1 if an error occurs. In the latter case, or if any other error
1335 occurs, the above functions will return -1.
1336 The constraint C<c> represents either an equality or an inequality.
1337 Use the following function to find out whether a constraint
1338 represents an equality. If not, it represents an inequality.
1340 int isl_constraint_is_equality(
1341 __isl_keep isl_constraint *constraint);
1343 The coefficients of the constraints can be inspected using
1344 the following functions.
1346 void isl_constraint_get_constant(
1347 __isl_keep isl_constraint *constraint, isl_int *v);
1348 void isl_constraint_get_coefficient(
1349 __isl_keep isl_constraint *constraint,
1350 enum isl_dim_type type, int pos, isl_int *v);
1351 int isl_constraint_involves_dims(
1352 __isl_keep isl_constraint *constraint,
1353 enum isl_dim_type type, unsigned first, unsigned n);
1355 The explicit representations of the existentially quantified
1356 variables can be inspected using the following function.
1357 Note that the user is only allowed to use this function
1358 if the inspected set or map is the result of a call
1359 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1360 The existentially quantified variable is equal to the floor
1361 of the returned affine expression. The affine expression
1362 itself can be inspected using the functions in
1363 L<"Piecewise Quasi Affine Expressions">.
1365 __isl_give isl_aff *isl_constraint_get_div(
1366 __isl_keep isl_constraint *constraint, int pos);
1368 To obtain the constraints of a basic set or map in matrix
1369 form, use the following functions.
1371 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1372 __isl_keep isl_basic_set *bset,
1373 enum isl_dim_type c1, enum isl_dim_type c2,
1374 enum isl_dim_type c3, enum isl_dim_type c4);
1375 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1376 __isl_keep isl_basic_set *bset,
1377 enum isl_dim_type c1, enum isl_dim_type c2,
1378 enum isl_dim_type c3, enum isl_dim_type c4);
1379 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1380 __isl_keep isl_basic_map *bmap,
1381 enum isl_dim_type c1,
1382 enum isl_dim_type c2, enum isl_dim_type c3,
1383 enum isl_dim_type c4, enum isl_dim_type c5);
1384 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1385 __isl_keep isl_basic_map *bmap,
1386 enum isl_dim_type c1,
1387 enum isl_dim_type c2, enum isl_dim_type c3,
1388 enum isl_dim_type c4, enum isl_dim_type c5);
1390 The C<isl_dim_type> arguments dictate the order in which
1391 different kinds of variables appear in the resulting matrix
1392 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1393 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1395 The number of parameters, input, output or set dimensions can
1396 be obtained using the following functions.
1398 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1399 enum isl_dim_type type);
1400 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1401 enum isl_dim_type type);
1402 unsigned isl_set_dim(__isl_keep isl_set *set,
1403 enum isl_dim_type type);
1404 unsigned isl_map_dim(__isl_keep isl_map *map,
1405 enum isl_dim_type type);
1407 To check whether the description of a set or relation depends
1408 on one or more given dimensions, it is not necessary to iterate over all
1409 constraints. Instead the following functions can be used.
1411 int isl_basic_set_involves_dims(
1412 __isl_keep isl_basic_set *bset,
1413 enum isl_dim_type type, unsigned first, unsigned n);
1414 int isl_set_involves_dims(__isl_keep isl_set *set,
1415 enum isl_dim_type type, unsigned first, unsigned n);
1416 int isl_basic_map_involves_dims(
1417 __isl_keep isl_basic_map *bmap,
1418 enum isl_dim_type type, unsigned first, unsigned n);
1419 int isl_map_involves_dims(__isl_keep isl_map *map,
1420 enum isl_dim_type type, unsigned first, unsigned n);
1422 Similarly, the following functions can be used to check whether
1423 a given dimension is involved in any lower or upper bound.
1425 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1426 enum isl_dim_type type, unsigned pos);
1427 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1428 enum isl_dim_type type, unsigned pos);
1430 The identifiers or names of the domain and range spaces of a set
1431 or relation can be read off or set using the following functions.
1433 __isl_give isl_set *isl_set_set_tuple_id(
1434 __isl_take isl_set *set, __isl_take isl_id *id);
1435 __isl_give isl_set *isl_set_reset_tuple_id(
1436 __isl_take isl_set *set);
1437 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1438 __isl_give isl_id *isl_set_get_tuple_id(
1439 __isl_keep isl_set *set);
1440 __isl_give isl_map *isl_map_set_tuple_id(
1441 __isl_take isl_map *map, enum isl_dim_type type,
1442 __isl_take isl_id *id);
1443 __isl_give isl_map *isl_map_reset_tuple_id(
1444 __isl_take isl_map *map, enum isl_dim_type type);
1445 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1446 enum isl_dim_type type);
1447 __isl_give isl_id *isl_map_get_tuple_id(
1448 __isl_keep isl_map *map, enum isl_dim_type type);
1450 const char *isl_basic_set_get_tuple_name(
1451 __isl_keep isl_basic_set *bset);
1452 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1453 __isl_take isl_basic_set *set, const char *s);
1454 const char *isl_set_get_tuple_name(
1455 __isl_keep isl_set *set);
1456 const char *isl_basic_map_get_tuple_name(
1457 __isl_keep isl_basic_map *bmap,
1458 enum isl_dim_type type);
1459 const char *isl_map_get_tuple_name(
1460 __isl_keep isl_map *map,
1461 enum isl_dim_type type);
1463 As with C<isl_space_get_tuple_name>, the value returned points to
1464 an internal data structure.
1465 The identifiers, positions or names of individual dimensions can be
1466 read off using the following functions.
1468 __isl_give isl_set *isl_set_set_dim_id(
1469 __isl_take isl_set *set, enum isl_dim_type type,
1470 unsigned pos, __isl_take isl_id *id);
1471 int isl_set_has_dim_id(__isl_keep isl_set *set,
1472 enum isl_dim_type type, unsigned pos);
1473 __isl_give isl_id *isl_set_get_dim_id(
1474 __isl_keep isl_set *set, enum isl_dim_type type,
1476 int isl_basic_map_has_dim_id(
1477 __isl_keep isl_basic_map *bmap,
1478 enum isl_dim_type type, unsigned pos);
1479 __isl_give isl_map *isl_map_set_dim_id(
1480 __isl_take isl_map *map, enum isl_dim_type type,
1481 unsigned pos, __isl_take isl_id *id);
1482 int isl_map_has_dim_id(__isl_keep isl_map *map,
1483 enum isl_dim_type type, unsigned pos);
1484 __isl_give isl_id *isl_map_get_dim_id(
1485 __isl_keep isl_map *map, enum isl_dim_type type,
1488 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1489 enum isl_dim_type type, __isl_keep isl_id *id);
1490 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1491 enum isl_dim_type type, __isl_keep isl_id *id);
1492 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1493 enum isl_dim_type type, const char *name);
1495 const char *isl_constraint_get_dim_name(
1496 __isl_keep isl_constraint *constraint,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_basic_set_get_dim_name(
1499 __isl_keep isl_basic_set *bset,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_set_get_dim_name(
1502 __isl_keep isl_set *set,
1503 enum isl_dim_type type, unsigned pos);
1504 const char *isl_basic_map_get_dim_name(
1505 __isl_keep isl_basic_map *bmap,
1506 enum isl_dim_type type, unsigned pos);
1507 const char *isl_map_get_dim_name(
1508 __isl_keep isl_map *map,
1509 enum isl_dim_type type, unsigned pos);
1511 These functions are mostly useful to obtain the identifiers, positions
1512 or names of the parameters. Identifiers of individual dimensions are
1513 essentially only useful for printing. They are ignored by all other
1514 operations and may not be preserved across those operations.
1518 =head3 Unary Properties
1524 The following functions test whether the given set or relation
1525 contains any integer points. The ``plain'' variants do not perform
1526 any computations, but simply check if the given set or relation
1527 is already known to be empty.
1529 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1530 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1531 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1532 int isl_set_is_empty(__isl_keep isl_set *set);
1533 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1534 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1535 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1536 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1537 int isl_map_is_empty(__isl_keep isl_map *map);
1538 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1540 =item * Universality
1542 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1543 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1544 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1546 =item * Single-valuedness
1548 int isl_map_is_single_valued(__isl_keep isl_map *map);
1549 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1553 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1554 int isl_map_is_injective(__isl_keep isl_map *map);
1555 int isl_union_map_plain_is_injective(
1556 __isl_keep isl_union_map *umap);
1557 int isl_union_map_is_injective(
1558 __isl_keep isl_union_map *umap);
1562 int isl_map_is_bijective(__isl_keep isl_map *map);
1563 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1567 int isl_basic_map_plain_is_fixed(
1568 __isl_keep isl_basic_map *bmap,
1569 enum isl_dim_type type, unsigned pos,
1571 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1572 enum isl_dim_type type, unsigned pos,
1574 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1575 enum isl_dim_type type, unsigned pos,
1578 Check if the relation obviously lies on a hyperplane where the given dimension
1579 has a fixed value and if so, return that value in C<*val>.
1583 To check whether a set is a parameter domain, use this function:
1585 int isl_set_is_params(__isl_keep isl_set *set);
1589 The following functions check whether the domain of the given
1590 (basic) set is a wrapped relation.
1592 int isl_basic_set_is_wrapping(
1593 __isl_keep isl_basic_set *bset);
1594 int isl_set_is_wrapping(__isl_keep isl_set *set);
1596 =item * Internal Product
1598 int isl_basic_map_can_zip(
1599 __isl_keep isl_basic_map *bmap);
1600 int isl_map_can_zip(__isl_keep isl_map *map);
1602 Check whether the product of domain and range of the given relation
1604 i.e., whether both domain and range are nested relations.
1608 =head3 Binary Properties
1614 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1615 __isl_keep isl_set *set2);
1616 int isl_set_is_equal(__isl_keep isl_set *set1,
1617 __isl_keep isl_set *set2);
1618 int isl_union_set_is_equal(
1619 __isl_keep isl_union_set *uset1,
1620 __isl_keep isl_union_set *uset2);
1621 int isl_basic_map_is_equal(
1622 __isl_keep isl_basic_map *bmap1,
1623 __isl_keep isl_basic_map *bmap2);
1624 int isl_map_is_equal(__isl_keep isl_map *map1,
1625 __isl_keep isl_map *map2);
1626 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1627 __isl_keep isl_map *map2);
1628 int isl_union_map_is_equal(
1629 __isl_keep isl_union_map *umap1,
1630 __isl_keep isl_union_map *umap2);
1632 =item * Disjointness
1634 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1635 __isl_keep isl_set *set2);
1639 int isl_set_is_subset(__isl_keep isl_set *set1,
1640 __isl_keep isl_set *set2);
1641 int isl_set_is_strict_subset(
1642 __isl_keep isl_set *set1,
1643 __isl_keep isl_set *set2);
1644 int isl_union_set_is_subset(
1645 __isl_keep isl_union_set *uset1,
1646 __isl_keep isl_union_set *uset2);
1647 int isl_union_set_is_strict_subset(
1648 __isl_keep isl_union_set *uset1,
1649 __isl_keep isl_union_set *uset2);
1650 int isl_basic_map_is_subset(
1651 __isl_keep isl_basic_map *bmap1,
1652 __isl_keep isl_basic_map *bmap2);
1653 int isl_basic_map_is_strict_subset(
1654 __isl_keep isl_basic_map *bmap1,
1655 __isl_keep isl_basic_map *bmap2);
1656 int isl_map_is_subset(
1657 __isl_keep isl_map *map1,
1658 __isl_keep isl_map *map2);
1659 int isl_map_is_strict_subset(
1660 __isl_keep isl_map *map1,
1661 __isl_keep isl_map *map2);
1662 int isl_union_map_is_subset(
1663 __isl_keep isl_union_map *umap1,
1664 __isl_keep isl_union_map *umap2);
1665 int isl_union_map_is_strict_subset(
1666 __isl_keep isl_union_map *umap1,
1667 __isl_keep isl_union_map *umap2);
1671 =head2 Unary Operations
1677 __isl_give isl_set *isl_set_complement(
1678 __isl_take isl_set *set);
1682 __isl_give isl_basic_map *isl_basic_map_reverse(
1683 __isl_take isl_basic_map *bmap);
1684 __isl_give isl_map *isl_map_reverse(
1685 __isl_take isl_map *map);
1686 __isl_give isl_union_map *isl_union_map_reverse(
1687 __isl_take isl_union_map *umap);
1691 __isl_give isl_basic_set *isl_basic_set_project_out(
1692 __isl_take isl_basic_set *bset,
1693 enum isl_dim_type type, unsigned first, unsigned n);
1694 __isl_give isl_basic_map *isl_basic_map_project_out(
1695 __isl_take isl_basic_map *bmap,
1696 enum isl_dim_type type, unsigned first, unsigned n);
1697 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1698 enum isl_dim_type type, unsigned first, unsigned n);
1699 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1700 enum isl_dim_type type, unsigned first, unsigned n);
1701 __isl_give isl_basic_set *isl_basic_set_params(
1702 __isl_take isl_basic_set *bset);
1703 __isl_give isl_basic_set *isl_basic_map_domain(
1704 __isl_take isl_basic_map *bmap);
1705 __isl_give isl_basic_set *isl_basic_map_range(
1706 __isl_take isl_basic_map *bmap);
1707 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1708 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1709 __isl_give isl_set *isl_map_domain(
1710 __isl_take isl_map *bmap);
1711 __isl_give isl_set *isl_map_range(
1712 __isl_take isl_map *map);
1713 __isl_give isl_union_set *isl_union_map_domain(
1714 __isl_take isl_union_map *umap);
1715 __isl_give isl_union_set *isl_union_map_range(
1716 __isl_take isl_union_map *umap);
1718 __isl_give isl_basic_map *isl_basic_map_domain_map(
1719 __isl_take isl_basic_map *bmap);
1720 __isl_give isl_basic_map *isl_basic_map_range_map(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1723 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1724 __isl_give isl_union_map *isl_union_map_domain_map(
1725 __isl_take isl_union_map *umap);
1726 __isl_give isl_union_map *isl_union_map_range_map(
1727 __isl_take isl_union_map *umap);
1729 The functions above construct a (basic, regular or union) relation
1730 that maps (a wrapped version of) the input relation to its domain or range.
1734 __isl_give isl_set *isl_set_eliminate(
1735 __isl_take isl_set *set, enum isl_dim_type type,
1736 unsigned first, unsigned n);
1737 __isl_give isl_basic_map *isl_basic_map_eliminate(
1738 __isl_take isl_basic_map *bmap,
1739 enum isl_dim_type type,
1740 unsigned first, unsigned n);
1742 Eliminate the coefficients for the given dimensions from the constraints,
1743 without removing the dimensions.
1747 __isl_give isl_basic_set *isl_basic_set_fix(
1748 __isl_take isl_basic_set *bset,
1749 enum isl_dim_type type, unsigned pos,
1751 __isl_give isl_basic_set *isl_basic_set_fix_si(
1752 __isl_take isl_basic_set *bset,
1753 enum isl_dim_type type, unsigned pos, int value);
1754 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1755 enum isl_dim_type type, unsigned pos,
1757 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1758 enum isl_dim_type type, unsigned pos, int value);
1759 __isl_give isl_basic_map *isl_basic_map_fix_si(
1760 __isl_take isl_basic_map *bmap,
1761 enum isl_dim_type type, unsigned pos, int value);
1762 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1763 enum isl_dim_type type, unsigned pos, int value);
1765 Intersect the set or relation with the hyperplane where the given
1766 dimension has the fixed given value.
1768 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1769 enum isl_dim_type type1, int pos1,
1770 enum isl_dim_type type2, int pos2);
1771 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1772 enum isl_dim_type type1, int pos1,
1773 enum isl_dim_type type2, int pos2);
1775 Intersect the set or relation with the hyperplane where the given
1776 dimensions are equal to each other.
1778 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1779 enum isl_dim_type type1, int pos1,
1780 enum isl_dim_type type2, int pos2);
1782 Intersect the relation with the hyperplane where the given
1783 dimensions have opposite values.
1787 __isl_give isl_map *isl_set_identity(
1788 __isl_take isl_set *set);
1789 __isl_give isl_union_map *isl_union_set_identity(
1790 __isl_take isl_union_set *uset);
1792 Construct an identity relation on the given (union) set.
1796 __isl_give isl_basic_set *isl_basic_map_deltas(
1797 __isl_take isl_basic_map *bmap);
1798 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1799 __isl_give isl_union_set *isl_union_map_deltas(
1800 __isl_take isl_union_map *umap);
1802 These functions return a (basic) set containing the differences
1803 between image elements and corresponding domain elements in the input.
1805 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1806 __isl_take isl_basic_map *bmap);
1807 __isl_give isl_map *isl_map_deltas_map(
1808 __isl_take isl_map *map);
1809 __isl_give isl_union_map *isl_union_map_deltas_map(
1810 __isl_take isl_union_map *umap);
1812 The functions above construct a (basic, regular or union) relation
1813 that maps (a wrapped version of) the input relation to its delta set.
1817 Simplify the representation of a set or relation by trying
1818 to combine pairs of basic sets or relations into a single
1819 basic set or relation.
1821 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1822 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1823 __isl_give isl_union_set *isl_union_set_coalesce(
1824 __isl_take isl_union_set *uset);
1825 __isl_give isl_union_map *isl_union_map_coalesce(
1826 __isl_take isl_union_map *umap);
1828 =item * Detecting equalities
1830 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1831 __isl_take isl_basic_set *bset);
1832 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1833 __isl_take isl_basic_map *bmap);
1834 __isl_give isl_set *isl_set_detect_equalities(
1835 __isl_take isl_set *set);
1836 __isl_give isl_map *isl_map_detect_equalities(
1837 __isl_take isl_map *map);
1838 __isl_give isl_union_set *isl_union_set_detect_equalities(
1839 __isl_take isl_union_set *uset);
1840 __isl_give isl_union_map *isl_union_map_detect_equalities(
1841 __isl_take isl_union_map *umap);
1843 Simplify the representation of a set or relation by detecting implicit
1846 =item * Removing redundant constraints
1848 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1849 __isl_take isl_basic_set *bset);
1850 __isl_give isl_set *isl_set_remove_redundancies(
1851 __isl_take isl_set *set);
1852 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1853 __isl_take isl_basic_map *bmap);
1854 __isl_give isl_map *isl_map_remove_redundancies(
1855 __isl_take isl_map *map);
1859 __isl_give isl_basic_set *isl_set_convex_hull(
1860 __isl_take isl_set *set);
1861 __isl_give isl_basic_map *isl_map_convex_hull(
1862 __isl_take isl_map *map);
1864 If the input set or relation has any existentially quantified
1865 variables, then the result of these operations is currently undefined.
1869 __isl_give isl_basic_set *isl_set_simple_hull(
1870 __isl_take isl_set *set);
1871 __isl_give isl_basic_map *isl_map_simple_hull(
1872 __isl_take isl_map *map);
1873 __isl_give isl_union_map *isl_union_map_simple_hull(
1874 __isl_take isl_union_map *umap);
1876 These functions compute a single basic set or relation
1877 that contains the whole input set or relation.
1878 In particular, the output is described by translates
1879 of the constraints describing the basic sets or relations in the input.
1883 (See \autoref{s:simple hull}.)
1889 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1890 __isl_take isl_basic_set *bset);
1891 __isl_give isl_basic_set *isl_set_affine_hull(
1892 __isl_take isl_set *set);
1893 __isl_give isl_union_set *isl_union_set_affine_hull(
1894 __isl_take isl_union_set *uset);
1895 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1896 __isl_take isl_basic_map *bmap);
1897 __isl_give isl_basic_map *isl_map_affine_hull(
1898 __isl_take isl_map *map);
1899 __isl_give isl_union_map *isl_union_map_affine_hull(
1900 __isl_take isl_union_map *umap);
1902 In case of union sets and relations, the affine hull is computed
1905 =item * Polyhedral hull
1907 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1908 __isl_take isl_set *set);
1909 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1910 __isl_take isl_map *map);
1911 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1912 __isl_take isl_union_set *uset);
1913 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1914 __isl_take isl_union_map *umap);
1916 These functions compute a single basic set or relation
1917 not involving any existentially quantified variables
1918 that contains the whole input set or relation.
1919 In case of union sets and relations, the polyhedral hull is computed
1922 =item * Optimization
1924 #include <isl/ilp.h>
1925 enum isl_lp_result isl_basic_set_max(
1926 __isl_keep isl_basic_set *bset,
1927 __isl_keep isl_aff *obj, isl_int *opt)
1928 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1929 __isl_keep isl_aff *obj, isl_int *opt);
1930 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1931 __isl_keep isl_aff *obj, isl_int *opt);
1933 Compute the minimum or maximum of the integer affine expression C<obj>
1934 over the points in C<set>, returning the result in C<opt>.
1935 The return value may be one of C<isl_lp_error>,
1936 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1938 =item * Parametric optimization
1940 __isl_give isl_pw_aff *isl_set_dim_min(
1941 __isl_take isl_set *set, int pos);
1942 __isl_give isl_pw_aff *isl_set_dim_max(
1943 __isl_take isl_set *set, int pos);
1944 __isl_give isl_pw_aff *isl_map_dim_max(
1945 __isl_take isl_map *map, int pos);
1947 Compute the minimum or maximum of the given set or output dimension
1948 as a function of the parameters (and input dimensions), but independently
1949 of the other set or output dimensions.
1950 For lexicographic optimization, see L<"Lexicographic Optimization">.
1954 The following functions compute either the set of (rational) coefficient
1955 values of valid constraints for the given set or the set of (rational)
1956 values satisfying the constraints with coefficients from the given set.
1957 Internally, these two sets of functions perform essentially the
1958 same operations, except that the set of coefficients is assumed to
1959 be a cone, while the set of values may be any polyhedron.
1960 The current implementation is based on the Farkas lemma and
1961 Fourier-Motzkin elimination, but this may change or be made optional
1962 in future. In particular, future implementations may use different
1963 dualization algorithms or skip the elimination step.
1965 __isl_give isl_basic_set *isl_basic_set_coefficients(
1966 __isl_take isl_basic_set *bset);
1967 __isl_give isl_basic_set *isl_set_coefficients(
1968 __isl_take isl_set *set);
1969 __isl_give isl_union_set *isl_union_set_coefficients(
1970 __isl_take isl_union_set *bset);
1971 __isl_give isl_basic_set *isl_basic_set_solutions(
1972 __isl_take isl_basic_set *bset);
1973 __isl_give isl_basic_set *isl_set_solutions(
1974 __isl_take isl_set *set);
1975 __isl_give isl_union_set *isl_union_set_solutions(
1976 __isl_take isl_union_set *bset);
1980 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1982 __isl_give isl_union_map *isl_union_map_power(
1983 __isl_take isl_union_map *umap, int *exact);
1985 Compute a parametric representation for all positive powers I<k> of C<map>.
1986 The result maps I<k> to a nested relation corresponding to the
1987 I<k>th power of C<map>.
1988 The result may be an overapproximation. If the result is known to be exact,
1989 then C<*exact> is set to C<1>.
1991 =item * Transitive closure
1993 __isl_give isl_map *isl_map_transitive_closure(
1994 __isl_take isl_map *map, int *exact);
1995 __isl_give isl_union_map *isl_union_map_transitive_closure(
1996 __isl_take isl_union_map *umap, int *exact);
1998 Compute the transitive closure of C<map>.
1999 The result may be an overapproximation. If the result is known to be exact,
2000 then C<*exact> is set to C<1>.
2002 =item * Reaching path lengths
2004 __isl_give isl_map *isl_map_reaching_path_lengths(
2005 __isl_take isl_map *map, int *exact);
2007 Compute a relation that maps each element in the range of C<map>
2008 to the lengths of all paths composed of edges in C<map> that
2009 end up in the given element.
2010 The result may be an overapproximation. If the result is known to be exact,
2011 then C<*exact> is set to C<1>.
2012 To compute the I<maximal> path length, the resulting relation
2013 should be postprocessed by C<isl_map_lexmax>.
2014 In particular, if the input relation is a dependence relation
2015 (mapping sources to sinks), then the maximal path length corresponds
2016 to the free schedule.
2017 Note, however, that C<isl_map_lexmax> expects the maximum to be
2018 finite, so if the path lengths are unbounded (possibly due to
2019 the overapproximation), then you will get an error message.
2023 __isl_give isl_basic_set *isl_basic_map_wrap(
2024 __isl_take isl_basic_map *bmap);
2025 __isl_give isl_set *isl_map_wrap(
2026 __isl_take isl_map *map);
2027 __isl_give isl_union_set *isl_union_map_wrap(
2028 __isl_take isl_union_map *umap);
2029 __isl_give isl_basic_map *isl_basic_set_unwrap(
2030 __isl_take isl_basic_set *bset);
2031 __isl_give isl_map *isl_set_unwrap(
2032 __isl_take isl_set *set);
2033 __isl_give isl_union_map *isl_union_set_unwrap(
2034 __isl_take isl_union_set *uset);
2038 Remove any internal structure of domain (and range) of the given
2039 set or relation. If there is any such internal structure in the input,
2040 then the name of the space is also removed.
2042 __isl_give isl_basic_set *isl_basic_set_flatten(
2043 __isl_take isl_basic_set *bset);
2044 __isl_give isl_set *isl_set_flatten(
2045 __isl_take isl_set *set);
2046 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2047 __isl_take isl_basic_map *bmap);
2048 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2049 __isl_take isl_basic_map *bmap);
2050 __isl_give isl_map *isl_map_flatten_range(
2051 __isl_take isl_map *map);
2052 __isl_give isl_map *isl_map_flatten_domain(
2053 __isl_take isl_map *map);
2054 __isl_give isl_basic_map *isl_basic_map_flatten(
2055 __isl_take isl_basic_map *bmap);
2056 __isl_give isl_map *isl_map_flatten(
2057 __isl_take isl_map *map);
2059 __isl_give isl_map *isl_set_flatten_map(
2060 __isl_take isl_set *set);
2062 The function above constructs a relation
2063 that maps the input set to a flattened version of the set.
2067 Lift the input set to a space with extra dimensions corresponding
2068 to the existentially quantified variables in the input.
2069 In particular, the result lives in a wrapped map where the domain
2070 is the original space and the range corresponds to the original
2071 existentially quantified variables.
2073 __isl_give isl_basic_set *isl_basic_set_lift(
2074 __isl_take isl_basic_set *bset);
2075 __isl_give isl_set *isl_set_lift(
2076 __isl_take isl_set *set);
2077 __isl_give isl_union_set *isl_union_set_lift(
2078 __isl_take isl_union_set *uset);
2080 =item * Internal Product
2082 __isl_give isl_basic_map *isl_basic_map_zip(
2083 __isl_take isl_basic_map *bmap);
2084 __isl_give isl_map *isl_map_zip(
2085 __isl_take isl_map *map);
2086 __isl_give isl_union_map *isl_union_map_zip(
2087 __isl_take isl_union_map *umap);
2089 Given a relation with nested relations for domain and range,
2090 interchange the range of the domain with the domain of the range.
2092 =item * Aligning parameters
2094 __isl_give isl_set *isl_set_align_params(
2095 __isl_take isl_set *set,
2096 __isl_take isl_space *model);
2097 __isl_give isl_map *isl_map_align_params(
2098 __isl_take isl_map *map,
2099 __isl_take isl_space *model);
2101 Change the order of the parameters of the given set or relation
2102 such that the first parameters match those of C<model>.
2103 This may involve the introduction of extra parameters.
2104 All parameters need to be named.
2106 =item * Dimension manipulation
2108 __isl_give isl_set *isl_set_add_dims(
2109 __isl_take isl_set *set,
2110 enum isl_dim_type type, unsigned n);
2111 __isl_give isl_map *isl_map_add_dims(
2112 __isl_take isl_map *map,
2113 enum isl_dim_type type, unsigned n);
2114 __isl_give isl_set *isl_set_insert_dims(
2115 __isl_take isl_set *set,
2116 enum isl_dim_type type, unsigned pos, unsigned n);
2117 __isl_give isl_map *isl_map_insert_dims(
2118 __isl_take isl_map *map,
2119 enum isl_dim_type type, unsigned pos, unsigned n);
2120 __isl_give isl_basic_set *isl_basic_set_move_dims(
2121 __isl_take isl_basic_set *bset,
2122 enum isl_dim_type dst_type, unsigned dst_pos,
2123 enum isl_dim_type src_type, unsigned src_pos,
2125 __isl_give isl_basic_map *isl_basic_map_move_dims(
2126 __isl_take isl_basic_map *bmap,
2127 enum isl_dim_type dst_type, unsigned dst_pos,
2128 enum isl_dim_type src_type, unsigned src_pos,
2130 __isl_give isl_set *isl_set_move_dims(
2131 __isl_take isl_set *set,
2132 enum isl_dim_type dst_type, unsigned dst_pos,
2133 enum isl_dim_type src_type, unsigned src_pos,
2135 __isl_give isl_map *isl_map_move_dims(
2136 __isl_take isl_map *map,
2137 enum isl_dim_type dst_type, unsigned dst_pos,
2138 enum isl_dim_type src_type, unsigned src_pos,
2141 It is usually not advisable to directly change the (input or output)
2142 space of a set or a relation as this removes the name and the internal
2143 structure of the space. However, the above functions can be useful
2144 to add new parameters, assuming
2145 C<isl_set_align_params> and C<isl_map_align_params>
2150 =head2 Binary Operations
2152 The two arguments of a binary operation not only need to live
2153 in the same C<isl_ctx>, they currently also need to have
2154 the same (number of) parameters.
2156 =head3 Basic Operations
2160 =item * Intersection
2162 __isl_give isl_basic_set *isl_basic_set_intersect(
2163 __isl_take isl_basic_set *bset1,
2164 __isl_take isl_basic_set *bset2);
2165 __isl_give isl_set *isl_set_intersect_params(
2166 __isl_take isl_set *set,
2167 __isl_take isl_set *params);
2168 __isl_give isl_set *isl_set_intersect(
2169 __isl_take isl_set *set1,
2170 __isl_take isl_set *set2);
2171 __isl_give isl_union_set *isl_union_set_intersect(
2172 __isl_take isl_union_set *uset1,
2173 __isl_take isl_union_set *uset2);
2174 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2175 __isl_take isl_basic_map *bmap,
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2178 __isl_take isl_basic_map *bmap,
2179 __isl_take isl_basic_set *bset);
2180 __isl_give isl_basic_map *isl_basic_map_intersect(
2181 __isl_take isl_basic_map *bmap1,
2182 __isl_take isl_basic_map *bmap2);
2183 __isl_give isl_map *isl_map_intersect_params(
2184 __isl_take isl_map *map,
2185 __isl_take isl_set *params);
2186 __isl_give isl_map *isl_map_intersect_domain(
2187 __isl_take isl_map *map,
2188 __isl_take isl_set *set);
2189 __isl_give isl_map *isl_map_intersect_range(
2190 __isl_take isl_map *map,
2191 __isl_take isl_set *set);
2192 __isl_give isl_map *isl_map_intersect(
2193 __isl_take isl_map *map1,
2194 __isl_take isl_map *map2);
2195 __isl_give isl_union_map *isl_union_map_intersect_domain(
2196 __isl_take isl_union_map *umap,
2197 __isl_take isl_union_set *uset);
2198 __isl_give isl_union_map *isl_union_map_intersect_range(
2199 __isl_take isl_union_map *umap,
2200 __isl_take isl_union_set *uset);
2201 __isl_give isl_union_map *isl_union_map_intersect(
2202 __isl_take isl_union_map *umap1,
2203 __isl_take isl_union_map *umap2);
2207 __isl_give isl_set *isl_basic_set_union(
2208 __isl_take isl_basic_set *bset1,
2209 __isl_take isl_basic_set *bset2);
2210 __isl_give isl_map *isl_basic_map_union(
2211 __isl_take isl_basic_map *bmap1,
2212 __isl_take isl_basic_map *bmap2);
2213 __isl_give isl_set *isl_set_union(
2214 __isl_take isl_set *set1,
2215 __isl_take isl_set *set2);
2216 __isl_give isl_map *isl_map_union(
2217 __isl_take isl_map *map1,
2218 __isl_take isl_map *map2);
2219 __isl_give isl_union_set *isl_union_set_union(
2220 __isl_take isl_union_set *uset1,
2221 __isl_take isl_union_set *uset2);
2222 __isl_give isl_union_map *isl_union_map_union(
2223 __isl_take isl_union_map *umap1,
2224 __isl_take isl_union_map *umap2);
2226 =item * Set difference
2228 __isl_give isl_set *isl_set_subtract(
2229 __isl_take isl_set *set1,
2230 __isl_take isl_set *set2);
2231 __isl_give isl_map *isl_map_subtract(
2232 __isl_take isl_map *map1,
2233 __isl_take isl_map *map2);
2234 __isl_give isl_union_set *isl_union_set_subtract(
2235 __isl_take isl_union_set *uset1,
2236 __isl_take isl_union_set *uset2);
2237 __isl_give isl_union_map *isl_union_map_subtract(
2238 __isl_take isl_union_map *umap1,
2239 __isl_take isl_union_map *umap2);
2243 __isl_give isl_basic_set *isl_basic_set_apply(
2244 __isl_take isl_basic_set *bset,
2245 __isl_take isl_basic_map *bmap);
2246 __isl_give isl_set *isl_set_apply(
2247 __isl_take isl_set *set,
2248 __isl_take isl_map *map);
2249 __isl_give isl_union_set *isl_union_set_apply(
2250 __isl_take isl_union_set *uset,
2251 __isl_take isl_union_map *umap);
2252 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2253 __isl_take isl_basic_map *bmap1,
2254 __isl_take isl_basic_map *bmap2);
2255 __isl_give isl_basic_map *isl_basic_map_apply_range(
2256 __isl_take isl_basic_map *bmap1,
2257 __isl_take isl_basic_map *bmap2);
2258 __isl_give isl_map *isl_map_apply_domain(
2259 __isl_take isl_map *map1,
2260 __isl_take isl_map *map2);
2261 __isl_give isl_union_map *isl_union_map_apply_domain(
2262 __isl_take isl_union_map *umap1,
2263 __isl_take isl_union_map *umap2);
2264 __isl_give isl_map *isl_map_apply_range(
2265 __isl_take isl_map *map1,
2266 __isl_take isl_map *map2);
2267 __isl_give isl_union_map *isl_union_map_apply_range(
2268 __isl_take isl_union_map *umap1,
2269 __isl_take isl_union_map *umap2);
2271 =item * Cartesian Product
2273 __isl_give isl_set *isl_set_product(
2274 __isl_take isl_set *set1,
2275 __isl_take isl_set *set2);
2276 __isl_give isl_union_set *isl_union_set_product(
2277 __isl_take isl_union_set *uset1,
2278 __isl_take isl_union_set *uset2);
2279 __isl_give isl_basic_map *isl_basic_map_domain_product(
2280 __isl_take isl_basic_map *bmap1,
2281 __isl_take isl_basic_map *bmap2);
2282 __isl_give isl_basic_map *isl_basic_map_range_product(
2283 __isl_take isl_basic_map *bmap1,
2284 __isl_take isl_basic_map *bmap2);
2285 __isl_give isl_map *isl_map_domain_product(
2286 __isl_take isl_map *map1,
2287 __isl_take isl_map *map2);
2288 __isl_give isl_map *isl_map_range_product(
2289 __isl_take isl_map *map1,
2290 __isl_take isl_map *map2);
2291 __isl_give isl_union_map *isl_union_map_range_product(
2292 __isl_take isl_union_map *umap1,
2293 __isl_take isl_union_map *umap2);
2294 __isl_give isl_map *isl_map_product(
2295 __isl_take isl_map *map1,
2296 __isl_take isl_map *map2);
2297 __isl_give isl_union_map *isl_union_map_product(
2298 __isl_take isl_union_map *umap1,
2299 __isl_take isl_union_map *umap2);
2301 The above functions compute the cross product of the given
2302 sets or relations. The domains and ranges of the results
2303 are wrapped maps between domains and ranges of the inputs.
2304 To obtain a ``flat'' product, use the following functions
2307 __isl_give isl_basic_set *isl_basic_set_flat_product(
2308 __isl_take isl_basic_set *bset1,
2309 __isl_take isl_basic_set *bset2);
2310 __isl_give isl_set *isl_set_flat_product(
2311 __isl_take isl_set *set1,
2312 __isl_take isl_set *set2);
2313 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2314 __isl_take isl_basic_map *bmap1,
2315 __isl_take isl_basic_map *bmap2);
2316 __isl_give isl_map *isl_map_flat_domain_product(
2317 __isl_take isl_map *map1,
2318 __isl_take isl_map *map2);
2319 __isl_give isl_map *isl_map_flat_range_product(
2320 __isl_take isl_map *map1,
2321 __isl_take isl_map *map2);
2322 __isl_give isl_union_map *isl_union_map_flat_range_product(
2323 __isl_take isl_union_map *umap1,
2324 __isl_take isl_union_map *umap2);
2325 __isl_give isl_basic_map *isl_basic_map_flat_product(
2326 __isl_take isl_basic_map *bmap1,
2327 __isl_take isl_basic_map *bmap2);
2328 __isl_give isl_map *isl_map_flat_product(
2329 __isl_take isl_map *map1,
2330 __isl_take isl_map *map2);
2332 =item * Simplification
2334 __isl_give isl_basic_set *isl_basic_set_gist(
2335 __isl_take isl_basic_set *bset,
2336 __isl_take isl_basic_set *context);
2337 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2338 __isl_take isl_set *context);
2339 __isl_give isl_set *isl_set_gist_params(
2340 __isl_take isl_set *set,
2341 __isl_take isl_set *context);
2342 __isl_give isl_union_set *isl_union_set_gist(
2343 __isl_take isl_union_set *uset,
2344 __isl_take isl_union_set *context);
2345 __isl_give isl_basic_map *isl_basic_map_gist(
2346 __isl_take isl_basic_map *bmap,
2347 __isl_take isl_basic_map *context);
2348 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2349 __isl_take isl_map *context);
2350 __isl_give isl_map *isl_map_gist_params(
2351 __isl_take isl_map *map,
2352 __isl_take isl_set *context);
2353 __isl_give isl_union_map *isl_union_map_gist(
2354 __isl_take isl_union_map *umap,
2355 __isl_take isl_union_map *context);
2357 The gist operation returns a set or relation that has the
2358 same intersection with the context as the input set or relation.
2359 Any implicit equality in the intersection is made explicit in the result,
2360 while all inequalities that are redundant with respect to the intersection
2362 In case of union sets and relations, the gist operation is performed
2367 =head3 Lexicographic Optimization
2369 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2370 the following functions
2371 compute a set that contains the lexicographic minimum or maximum
2372 of the elements in C<set> (or C<bset>) for those values of the parameters
2373 that satisfy C<dom>.
2374 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2375 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2377 In other words, the union of the parameter values
2378 for which the result is non-empty and of C<*empty>
2381 __isl_give isl_set *isl_basic_set_partial_lexmin(
2382 __isl_take isl_basic_set *bset,
2383 __isl_take isl_basic_set *dom,
2384 __isl_give isl_set **empty);
2385 __isl_give isl_set *isl_basic_set_partial_lexmax(
2386 __isl_take isl_basic_set *bset,
2387 __isl_take isl_basic_set *dom,
2388 __isl_give isl_set **empty);
2389 __isl_give isl_set *isl_set_partial_lexmin(
2390 __isl_take isl_set *set, __isl_take isl_set *dom,
2391 __isl_give isl_set **empty);
2392 __isl_give isl_set *isl_set_partial_lexmax(
2393 __isl_take isl_set *set, __isl_take isl_set *dom,
2394 __isl_give isl_set **empty);
2396 Given a (basic) set C<set> (or C<bset>), the following functions simply
2397 return a set containing the lexicographic minimum or maximum
2398 of the elements in C<set> (or C<bset>).
2399 In case of union sets, the optimum is computed per space.
2401 __isl_give isl_set *isl_basic_set_lexmin(
2402 __isl_take isl_basic_set *bset);
2403 __isl_give isl_set *isl_basic_set_lexmax(
2404 __isl_take isl_basic_set *bset);
2405 __isl_give isl_set *isl_set_lexmin(
2406 __isl_take isl_set *set);
2407 __isl_give isl_set *isl_set_lexmax(
2408 __isl_take isl_set *set);
2409 __isl_give isl_union_set *isl_union_set_lexmin(
2410 __isl_take isl_union_set *uset);
2411 __isl_give isl_union_set *isl_union_set_lexmax(
2412 __isl_take isl_union_set *uset);
2414 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2415 the following functions
2416 compute a relation that maps each element of C<dom>
2417 to the single lexicographic minimum or maximum
2418 of the elements that are associated to that same
2419 element in C<map> (or C<bmap>).
2420 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2421 that contains the elements in C<dom> that do not map
2422 to any elements in C<map> (or C<bmap>).
2423 In other words, the union of the domain of the result and of C<*empty>
2426 __isl_give isl_map *isl_basic_map_partial_lexmax(
2427 __isl_take isl_basic_map *bmap,
2428 __isl_take isl_basic_set *dom,
2429 __isl_give isl_set **empty);
2430 __isl_give isl_map *isl_basic_map_partial_lexmin(
2431 __isl_take isl_basic_map *bmap,
2432 __isl_take isl_basic_set *dom,
2433 __isl_give isl_set **empty);
2434 __isl_give isl_map *isl_map_partial_lexmax(
2435 __isl_take isl_map *map, __isl_take isl_set *dom,
2436 __isl_give isl_set **empty);
2437 __isl_give isl_map *isl_map_partial_lexmin(
2438 __isl_take isl_map *map, __isl_take isl_set *dom,
2439 __isl_give isl_set **empty);
2441 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2442 return a map mapping each element in the domain of
2443 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2444 of all elements associated to that element.
2445 In case of union relations, the optimum is computed per space.
2447 __isl_give isl_map *isl_basic_map_lexmin(
2448 __isl_take isl_basic_map *bmap);
2449 __isl_give isl_map *isl_basic_map_lexmax(
2450 __isl_take isl_basic_map *bmap);
2451 __isl_give isl_map *isl_map_lexmin(
2452 __isl_take isl_map *map);
2453 __isl_give isl_map *isl_map_lexmax(
2454 __isl_take isl_map *map);
2455 __isl_give isl_union_map *isl_union_map_lexmin(
2456 __isl_take isl_union_map *umap);
2457 __isl_give isl_union_map *isl_union_map_lexmax(
2458 __isl_take isl_union_map *umap);
2462 Lists are defined over several element types, including
2463 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2464 Here we take lists of C<isl_set>s as an example.
2465 Lists can be created, copied and freed using the following functions.
2467 #include <isl/list.h>
2468 __isl_give isl_set_list *isl_set_list_from_set(
2469 __isl_take isl_set *el);
2470 __isl_give isl_set_list *isl_set_list_alloc(
2471 isl_ctx *ctx, int n);
2472 __isl_give isl_set_list *isl_set_list_copy(
2473 __isl_keep isl_set_list *list);
2474 __isl_give isl_set_list *isl_set_list_add(
2475 __isl_take isl_set_list *list,
2476 __isl_take isl_set *el);
2477 __isl_give isl_set_list *isl_set_list_concat(
2478 __isl_take isl_set_list *list1,
2479 __isl_take isl_set_list *list2);
2480 void *isl_set_list_free(__isl_take isl_set_list *list);
2482 C<isl_set_list_alloc> creates an empty list with a capacity for
2483 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2486 Lists can be inspected using the following functions.
2488 #include <isl/list.h>
2489 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2490 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2491 __isl_give isl_set *isl_set_list_get_set(
2492 __isl_keep isl_set_list *list, int index);
2493 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2494 int (*fn)(__isl_take isl_set *el, void *user),
2497 Lists can be printed using
2499 #include <isl/list.h>
2500 __isl_give isl_printer *isl_printer_print_set_list(
2501 __isl_take isl_printer *p,
2502 __isl_keep isl_set_list *list);
2506 Matrices can be created, copied and freed using the following functions.
2508 #include <isl/mat.h>
2509 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2510 unsigned n_row, unsigned n_col);
2511 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2512 void isl_mat_free(__isl_take isl_mat *mat);
2514 Note that the elements of a newly created matrix may have arbitrary values.
2515 The elements can be changed and inspected using the following functions.
2517 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2518 int isl_mat_rows(__isl_keep isl_mat *mat);
2519 int isl_mat_cols(__isl_keep isl_mat *mat);
2520 int isl_mat_get_element(__isl_keep isl_mat *mat,
2521 int row, int col, isl_int *v);
2522 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2523 int row, int col, isl_int v);
2524 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2525 int row, int col, int v);
2527 C<isl_mat_get_element> will return a negative value if anything went wrong.
2528 In that case, the value of C<*v> is undefined.
2530 The following function can be used to compute the (right) inverse
2531 of a matrix, i.e., a matrix such that the product of the original
2532 and the inverse (in that order) is a multiple of the identity matrix.
2533 The input matrix is assumed to be of full row-rank.
2535 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2537 The following function can be used to compute the (right) kernel
2538 (or null space) of a matrix, i.e., a matrix such that the product of
2539 the original and the kernel (in that order) is the zero matrix.
2541 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2543 =head2 Piecewise Quasi Affine Expressions
2545 The zero quasi affine expression on a given domain can be created using
2547 __isl_give isl_aff *isl_aff_zero_on_domain(
2548 __isl_take isl_local_space *ls);
2550 Note that the space in which the resulting object lives is a map space
2551 with the given space as domain and a one-dimensional range.
2553 An empty piecewise quasi affine expression (one with no cells)
2554 or a piecewise quasi affine expression with a single cell can
2555 be created using the following functions.
2557 #include <isl/aff.h>
2558 __isl_give isl_pw_aff *isl_pw_aff_empty(
2559 __isl_take isl_space *space);
2560 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2561 __isl_take isl_set *set, __isl_take isl_aff *aff);
2562 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2563 __isl_take isl_aff *aff);
2565 Quasi affine expressions can be copied and freed using
2567 #include <isl/aff.h>
2568 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2569 void *isl_aff_free(__isl_take isl_aff *aff);
2571 __isl_give isl_pw_aff *isl_pw_aff_copy(
2572 __isl_keep isl_pw_aff *pwaff);
2573 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2575 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2576 using the following function. The constraint is required to have
2577 a non-zero coefficient for the specified dimension.
2579 #include <isl/constraint.h>
2580 __isl_give isl_aff *isl_constraint_get_bound(
2581 __isl_keep isl_constraint *constraint,
2582 enum isl_dim_type type, int pos);
2584 The entire affine expression of the constraint can also be extracted
2585 using the following function.
2587 #include <isl/constraint.h>
2588 __isl_give isl_aff *isl_constraint_get_aff(
2589 __isl_keep isl_constraint *constraint);
2591 Conversely, an equality constraint equating
2592 the affine expression to zero or an inequality constraint enforcing
2593 the affine expression to be non-negative, can be constructed using
2595 __isl_give isl_constraint *isl_equality_from_aff(
2596 __isl_take isl_aff *aff);
2597 __isl_give isl_constraint *isl_inequality_from_aff(
2598 __isl_take isl_aff *aff);
2600 The expression can be inspected using
2602 #include <isl/aff.h>
2603 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2604 int isl_aff_dim(__isl_keep isl_aff *aff,
2605 enum isl_dim_type type);
2606 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2607 __isl_keep isl_aff *aff);
2608 __isl_give isl_local_space *isl_aff_get_local_space(
2609 __isl_keep isl_aff *aff);
2610 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2611 enum isl_dim_type type, unsigned pos);
2612 const char *isl_pw_aff_get_dim_name(
2613 __isl_keep isl_pw_aff *pa,
2614 enum isl_dim_type type, unsigned pos);
2615 __isl_give isl_id *isl_pw_aff_get_dim_id(
2616 __isl_keep isl_pw_aff *pa,
2617 enum isl_dim_type type, unsigned pos);
2618 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2620 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2621 enum isl_dim_type type, int pos, isl_int *v);
2622 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2624 __isl_give isl_aff *isl_aff_get_div(
2625 __isl_keep isl_aff *aff, int pos);
2627 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2628 int (*fn)(__isl_take isl_set *set,
2629 __isl_take isl_aff *aff,
2630 void *user), void *user);
2632 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2633 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2635 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2636 enum isl_dim_type type, unsigned first, unsigned n);
2637 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2638 enum isl_dim_type type, unsigned first, unsigned n);
2640 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2641 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2642 enum isl_dim_type type);
2643 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2645 It can be modified using
2647 #include <isl/aff.h>
2648 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2649 __isl_take isl_pw_aff *pwaff,
2650 enum isl_dim_type type, __isl_take isl_id *id);
2651 __isl_give isl_aff *isl_aff_set_dim_name(
2652 __isl_take isl_aff *aff, enum isl_dim_type type,
2653 unsigned pos, const char *s);
2654 __isl_give isl_aff *isl_aff_set_dim_id(
2655 __isl_take isl_aff *aff, enum isl_dim_type type,
2656 unsigned pos, __isl_take isl_id *id);
2657 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2658 __isl_take isl_pw_aff *pma,
2659 enum isl_dim_type type, unsigned pos,
2660 __isl_take isl_id *id);
2661 __isl_give isl_aff *isl_aff_set_constant(
2662 __isl_take isl_aff *aff, isl_int v);
2663 __isl_give isl_aff *isl_aff_set_constant_si(
2664 __isl_take isl_aff *aff, int v);
2665 __isl_give isl_aff *isl_aff_set_coefficient(
2666 __isl_take isl_aff *aff,
2667 enum isl_dim_type type, int pos, isl_int v);
2668 __isl_give isl_aff *isl_aff_set_coefficient_si(
2669 __isl_take isl_aff *aff,
2670 enum isl_dim_type type, int pos, int v);
2671 __isl_give isl_aff *isl_aff_set_denominator(
2672 __isl_take isl_aff *aff, isl_int v);
2674 __isl_give isl_aff *isl_aff_add_constant(
2675 __isl_take isl_aff *aff, isl_int v);
2676 __isl_give isl_aff *isl_aff_add_constant_si(
2677 __isl_take isl_aff *aff, int v);
2678 __isl_give isl_aff *isl_aff_add_coefficient(
2679 __isl_take isl_aff *aff,
2680 enum isl_dim_type type, int pos, isl_int v);
2681 __isl_give isl_aff *isl_aff_add_coefficient_si(
2682 __isl_take isl_aff *aff,
2683 enum isl_dim_type type, int pos, int v);
2685 __isl_give isl_aff *isl_aff_insert_dims(
2686 __isl_take isl_aff *aff,
2687 enum isl_dim_type type, unsigned first, unsigned n);
2688 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2689 __isl_take isl_pw_aff *pwaff,
2690 enum isl_dim_type type, unsigned first, unsigned n);
2691 __isl_give isl_aff *isl_aff_add_dims(
2692 __isl_take isl_aff *aff,
2693 enum isl_dim_type type, unsigned n);
2694 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2695 __isl_take isl_pw_aff *pwaff,
2696 enum isl_dim_type type, unsigned n);
2697 __isl_give isl_aff *isl_aff_drop_dims(
2698 __isl_take isl_aff *aff,
2699 enum isl_dim_type type, unsigned first, unsigned n);
2700 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2701 __isl_take isl_pw_aff *pwaff,
2702 enum isl_dim_type type, unsigned first, unsigned n);
2704 Note that the C<set_constant> and C<set_coefficient> functions
2705 set the I<numerator> of the constant or coefficient, while
2706 C<add_constant> and C<add_coefficient> add an integer value to
2707 the possibly rational constant or coefficient.
2709 To check whether an affine expressions is obviously zero
2710 or obviously equal to some other affine expression, use
2712 #include <isl/aff.h>
2713 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2714 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2715 __isl_keep isl_aff *aff2);
2716 int isl_pw_aff_plain_is_equal(
2717 __isl_keep isl_pw_aff *pwaff1,
2718 __isl_keep isl_pw_aff *pwaff2);
2722 #include <isl/aff.h>
2723 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2724 __isl_take isl_aff *aff2);
2725 __isl_give isl_pw_aff *isl_pw_aff_add(
2726 __isl_take isl_pw_aff *pwaff1,
2727 __isl_take isl_pw_aff *pwaff2);
2728 __isl_give isl_pw_aff *isl_pw_aff_min(
2729 __isl_take isl_pw_aff *pwaff1,
2730 __isl_take isl_pw_aff *pwaff2);
2731 __isl_give isl_pw_aff *isl_pw_aff_max(
2732 __isl_take isl_pw_aff *pwaff1,
2733 __isl_take isl_pw_aff *pwaff2);
2734 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2735 __isl_take isl_aff *aff2);
2736 __isl_give isl_pw_aff *isl_pw_aff_sub(
2737 __isl_take isl_pw_aff *pwaff1,
2738 __isl_take isl_pw_aff *pwaff2);
2739 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2740 __isl_give isl_pw_aff *isl_pw_aff_neg(
2741 __isl_take isl_pw_aff *pwaff);
2742 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2743 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2744 __isl_take isl_pw_aff *pwaff);
2745 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2746 __isl_give isl_pw_aff *isl_pw_aff_floor(
2747 __isl_take isl_pw_aff *pwaff);
2748 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2750 __isl_give isl_pw_aff *isl_pw_aff_mod(
2751 __isl_take isl_pw_aff *pwaff, isl_int mod);
2752 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2754 __isl_give isl_pw_aff *isl_pw_aff_scale(
2755 __isl_take isl_pw_aff *pwaff, isl_int f);
2756 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2758 __isl_give isl_aff *isl_aff_scale_down_ui(
2759 __isl_take isl_aff *aff, unsigned f);
2760 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2761 __isl_take isl_pw_aff *pwaff, isl_int f);
2763 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2764 __isl_take isl_pw_aff_list *list);
2765 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2766 __isl_take isl_pw_aff_list *list);
2768 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2769 __isl_take isl_pw_aff *pwqp);
2771 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2772 __isl_take isl_pw_aff *pwaff,
2773 __isl_take isl_space *model);
2775 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2776 __isl_take isl_set *context);
2777 __isl_give isl_pw_aff *isl_pw_aff_gist(
2778 __isl_take isl_pw_aff *pwaff,
2779 __isl_take isl_set *context);
2781 __isl_give isl_set *isl_pw_aff_domain(
2782 __isl_take isl_pw_aff *pwaff);
2783 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2784 __isl_take isl_pw_aff *pa,
2785 __isl_take isl_set *set);
2787 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2788 __isl_take isl_aff *aff2);
2789 __isl_give isl_pw_aff *isl_pw_aff_mul(
2790 __isl_take isl_pw_aff *pwaff1,
2791 __isl_take isl_pw_aff *pwaff2);
2793 When multiplying two affine expressions, at least one of the two needs
2796 #include <isl/aff.h>
2797 __isl_give isl_basic_set *isl_aff_le_basic_set(
2798 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2799 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2800 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2801 __isl_give isl_set *isl_pw_aff_eq_set(
2802 __isl_take isl_pw_aff *pwaff1,
2803 __isl_take isl_pw_aff *pwaff2);
2804 __isl_give isl_set *isl_pw_aff_ne_set(
2805 __isl_take isl_pw_aff *pwaff1,
2806 __isl_take isl_pw_aff *pwaff2);
2807 __isl_give isl_set *isl_pw_aff_le_set(
2808 __isl_take isl_pw_aff *pwaff1,
2809 __isl_take isl_pw_aff *pwaff2);
2810 __isl_give isl_set *isl_pw_aff_lt_set(
2811 __isl_take isl_pw_aff *pwaff1,
2812 __isl_take isl_pw_aff *pwaff2);
2813 __isl_give isl_set *isl_pw_aff_ge_set(
2814 __isl_take isl_pw_aff *pwaff1,
2815 __isl_take isl_pw_aff *pwaff2);
2816 __isl_give isl_set *isl_pw_aff_gt_set(
2817 __isl_take isl_pw_aff *pwaff1,
2818 __isl_take isl_pw_aff *pwaff2);
2820 __isl_give isl_set *isl_pw_aff_list_eq_set(
2821 __isl_take isl_pw_aff_list *list1,
2822 __isl_take isl_pw_aff_list *list2);
2823 __isl_give isl_set *isl_pw_aff_list_ne_set(
2824 __isl_take isl_pw_aff_list *list1,
2825 __isl_take isl_pw_aff_list *list2);
2826 __isl_give isl_set *isl_pw_aff_list_le_set(
2827 __isl_take isl_pw_aff_list *list1,
2828 __isl_take isl_pw_aff_list *list2);
2829 __isl_give isl_set *isl_pw_aff_list_lt_set(
2830 __isl_take isl_pw_aff_list *list1,
2831 __isl_take isl_pw_aff_list *list2);
2832 __isl_give isl_set *isl_pw_aff_list_ge_set(
2833 __isl_take isl_pw_aff_list *list1,
2834 __isl_take isl_pw_aff_list *list2);
2835 __isl_give isl_set *isl_pw_aff_list_gt_set(
2836 __isl_take isl_pw_aff_list *list1,
2837 __isl_take isl_pw_aff_list *list2);
2839 The function C<isl_aff_ge_basic_set> returns a basic set
2840 containing those elements in the shared space
2841 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2842 The function C<isl_aff_ge_set> returns a set
2843 containing those elements in the shared domain
2844 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2845 The functions operating on C<isl_pw_aff_list> apply the corresponding
2846 C<isl_pw_aff> function to each pair of elements in the two lists.
2848 #include <isl/aff.h>
2849 __isl_give isl_set *isl_pw_aff_nonneg_set(
2850 __isl_take isl_pw_aff *pwaff);
2851 __isl_give isl_set *isl_pw_aff_zero_set(
2852 __isl_take isl_pw_aff *pwaff);
2853 __isl_give isl_set *isl_pw_aff_non_zero_set(
2854 __isl_take isl_pw_aff *pwaff);
2856 The function C<isl_pw_aff_nonneg_set> returns a set
2857 containing those elements in the domain
2858 of C<pwaff> where C<pwaff> is non-negative.
2860 #include <isl/aff.h>
2861 __isl_give isl_pw_aff *isl_pw_aff_cond(
2862 __isl_take isl_set *cond,
2863 __isl_take isl_pw_aff *pwaff_true,
2864 __isl_take isl_pw_aff *pwaff_false);
2866 The function C<isl_pw_aff_cond> performs a conditional operator
2867 and returns an expression that is equal to C<pwaff_true>
2868 for elements in C<cond> and equal to C<pwaff_false> for elements
2871 #include <isl/aff.h>
2872 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2873 __isl_take isl_pw_aff *pwaff1,
2874 __isl_take isl_pw_aff *pwaff2);
2875 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2876 __isl_take isl_pw_aff *pwaff1,
2877 __isl_take isl_pw_aff *pwaff2);
2879 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2880 expression with a domain that is the union of those of C<pwaff1> and
2881 C<pwaff2> and such that on each cell, the quasi-affine expression is
2882 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2883 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2884 associated expression is the defined one.
2886 An expression can be printed using
2888 #include <isl/aff.h>
2889 __isl_give isl_printer *isl_printer_print_aff(
2890 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2892 __isl_give isl_printer *isl_printer_print_pw_aff(
2893 __isl_take isl_printer *p,
2894 __isl_keep isl_pw_aff *pwaff);
2896 =head2 Multiple Quasi Affine Expressions
2898 An C<isl_multi_aff> object represents a sequence of
2899 zero or more affine expressions, all defined on the same domain space.
2901 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
2904 #include <isl/aff.h>
2905 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2906 __isl_take isl_space *space,
2907 __isl_take isl_aff_list *list);
2909 Multiple quasi affine expressions can be copied and freed using
2911 #include <isl/aff.h>
2912 __isl_give isl_multi_aff *isl_multi_aff_copy(
2913 __isl_keep isl_multi_aff *maff);
2914 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
2916 The expression can be inspected using
2918 #include <isl/aff.h>
2919 isl_ctx *isl_multi_aff_get_ctx(
2920 __isl_keep isl_multi_aff *maff);
2921 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
2922 enum isl_dim_type type);
2923 __isl_give isl_aff *isl_multi_aff_get_aff(
2924 __isl_keep isl_multi_aff *multi, int pos);
2925 const char *isl_multi_aff_get_tuple_name(
2926 __isl_keep isl_multi_aff *multi,
2927 enum isl_dim_type type);
2929 It can be modified using
2931 #include <isl/aff.h>
2932 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
2933 __isl_take isl_multi_aff *maff,
2934 enum isl_dim_type type, unsigned pos, const char *s);
2936 To check whether two multiple affine expressions are
2937 obviously equal to each other, use
2939 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2940 __isl_keep isl_multi_aff *maff2);
2944 #include <isl/aff.h>
2945 __isl_give isl_multi_aff *isl_multi_aff_add(
2946 __isl_take isl_multi_aff *maff1,
2947 __isl_take isl_multi_aff *maff2);
2948 __isl_give isl_multi_aff *isl_multi_aff_scale(
2949 __isl_take isl_multi_aff *maff,
2951 __isl_give isl_multi_aff *isl_multi_aff_gist(
2952 __isl_take isl_multi_aff *maff,
2953 __isl_take isl_set *context);
2955 An expression can be printed using
2957 #include <isl/aff.h>
2958 __isl_give isl_printer *isl_printer_print_multi_aff(
2959 __isl_take isl_printer *p,
2960 __isl_keep isl_multi_aff *maff);
2964 Points are elements of a set. They can be used to construct
2965 simple sets (boxes) or they can be used to represent the
2966 individual elements of a set.
2967 The zero point (the origin) can be created using
2969 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2971 The coordinates of a point can be inspected, set and changed
2974 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2975 enum isl_dim_type type, int pos, isl_int *v);
2976 __isl_give isl_point *isl_point_set_coordinate(
2977 __isl_take isl_point *pnt,
2978 enum isl_dim_type type, int pos, isl_int v);
2980 __isl_give isl_point *isl_point_add_ui(
2981 __isl_take isl_point *pnt,
2982 enum isl_dim_type type, int pos, unsigned val);
2983 __isl_give isl_point *isl_point_sub_ui(
2984 __isl_take isl_point *pnt,
2985 enum isl_dim_type type, int pos, unsigned val);
2987 Other properties can be obtained using
2989 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2991 Points can be copied or freed using
2993 __isl_give isl_point *isl_point_copy(
2994 __isl_keep isl_point *pnt);
2995 void isl_point_free(__isl_take isl_point *pnt);
2997 A singleton set can be created from a point using
2999 __isl_give isl_basic_set *isl_basic_set_from_point(
3000 __isl_take isl_point *pnt);
3001 __isl_give isl_set *isl_set_from_point(
3002 __isl_take isl_point *pnt);
3004 and a box can be created from two opposite extremal points using
3006 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3007 __isl_take isl_point *pnt1,
3008 __isl_take isl_point *pnt2);
3009 __isl_give isl_set *isl_set_box_from_points(
3010 __isl_take isl_point *pnt1,
3011 __isl_take isl_point *pnt2);
3013 All elements of a B<bounded> (union) set can be enumerated using
3014 the following functions.
3016 int isl_set_foreach_point(__isl_keep isl_set *set,
3017 int (*fn)(__isl_take isl_point *pnt, void *user),
3019 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3020 int (*fn)(__isl_take isl_point *pnt, void *user),
3023 The function C<fn> is called for each integer point in
3024 C<set> with as second argument the last argument of
3025 the C<isl_set_foreach_point> call. The function C<fn>
3026 should return C<0> on success and C<-1> on failure.
3027 In the latter case, C<isl_set_foreach_point> will stop
3028 enumerating and return C<-1> as well.
3029 If the enumeration is performed successfully and to completion,
3030 then C<isl_set_foreach_point> returns C<0>.
3032 To obtain a single point of a (basic) set, use
3034 __isl_give isl_point *isl_basic_set_sample_point(
3035 __isl_take isl_basic_set *bset);
3036 __isl_give isl_point *isl_set_sample_point(
3037 __isl_take isl_set *set);
3039 If C<set> does not contain any (integer) points, then the
3040 resulting point will be ``void'', a property that can be
3043 int isl_point_is_void(__isl_keep isl_point *pnt);
3045 =head2 Piecewise Quasipolynomials
3047 A piecewise quasipolynomial is a particular kind of function that maps
3048 a parametric point to a rational value.
3049 More specifically, a quasipolynomial is a polynomial expression in greatest
3050 integer parts of affine expressions of parameters and variables.
3051 A piecewise quasipolynomial is a subdivision of a given parametric
3052 domain into disjoint cells with a quasipolynomial associated to
3053 each cell. The value of the piecewise quasipolynomial at a given
3054 point is the value of the quasipolynomial associated to the cell
3055 that contains the point. Outside of the union of cells,
3056 the value is assumed to be zero.
3057 For example, the piecewise quasipolynomial
3059 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3061 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3062 A given piecewise quasipolynomial has a fixed domain dimension.
3063 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3064 defined over different domains.
3065 Piecewise quasipolynomials are mainly used by the C<barvinok>
3066 library for representing the number of elements in a parametric set or map.
3067 For example, the piecewise quasipolynomial above represents
3068 the number of points in the map
3070 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3072 =head3 Printing (Piecewise) Quasipolynomials
3074 Quasipolynomials and piecewise quasipolynomials can be printed
3075 using the following functions.
3077 __isl_give isl_printer *isl_printer_print_qpolynomial(
3078 __isl_take isl_printer *p,
3079 __isl_keep isl_qpolynomial *qp);
3081 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3082 __isl_take isl_printer *p,
3083 __isl_keep isl_pw_qpolynomial *pwqp);
3085 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3086 __isl_take isl_printer *p,
3087 __isl_keep isl_union_pw_qpolynomial *upwqp);
3089 The output format of the printer
3090 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3091 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3093 In case of printing in C<ISL_FORMAT_C>, the user may want
3094 to set the names of all dimensions
3096 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3097 __isl_take isl_qpolynomial *qp,
3098 enum isl_dim_type type, unsigned pos,
3100 __isl_give isl_pw_qpolynomial *
3101 isl_pw_qpolynomial_set_dim_name(
3102 __isl_take isl_pw_qpolynomial *pwqp,
3103 enum isl_dim_type type, unsigned pos,
3106 =head3 Creating New (Piecewise) Quasipolynomials
3108 Some simple quasipolynomials can be created using the following functions.
3109 More complicated quasipolynomials can be created by applying
3110 operations such as addition and multiplication
3111 on the resulting quasipolynomials
3113 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3114 __isl_take isl_space *domain);
3115 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3116 __isl_take isl_space *domain);
3117 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3118 __isl_take isl_space *domain);
3119 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3120 __isl_take isl_space *domain);
3121 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3122 __isl_take isl_space *domain);
3123 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3124 __isl_take isl_space *domain,
3125 const isl_int n, const isl_int d);
3126 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3127 __isl_take isl_space *domain,
3128 enum isl_dim_type type, unsigned pos);
3129 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3130 __isl_take isl_aff *aff);
3132 Note that the space in which a quasipolynomial lives is a map space
3133 with a one-dimensional range. The C<domain> argument in some of
3134 the functions above corresponds to the domain of this map space.
3136 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3137 with a single cell can be created using the following functions.
3138 Multiple of these single cell piecewise quasipolynomials can
3139 be combined to create more complicated piecewise quasipolynomials.
3141 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3142 __isl_take isl_space *space);
3143 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3144 __isl_take isl_set *set,
3145 __isl_take isl_qpolynomial *qp);
3146 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3147 __isl_take isl_qpolynomial *qp);
3148 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3149 __isl_take isl_pw_aff *pwaff);
3151 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3152 __isl_take isl_space *space);
3153 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3154 __isl_take isl_pw_qpolynomial *pwqp);
3155 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3156 __isl_take isl_union_pw_qpolynomial *upwqp,
3157 __isl_take isl_pw_qpolynomial *pwqp);
3159 Quasipolynomials can be copied and freed again using the following
3162 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3163 __isl_keep isl_qpolynomial *qp);
3164 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3166 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3167 __isl_keep isl_pw_qpolynomial *pwqp);
3168 void *isl_pw_qpolynomial_free(
3169 __isl_take isl_pw_qpolynomial *pwqp);
3171 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3172 __isl_keep isl_union_pw_qpolynomial *upwqp);
3173 void isl_union_pw_qpolynomial_free(
3174 __isl_take isl_union_pw_qpolynomial *upwqp);
3176 =head3 Inspecting (Piecewise) Quasipolynomials
3178 To iterate over all piecewise quasipolynomials in a union
3179 piecewise quasipolynomial, use the following function
3181 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3182 __isl_keep isl_union_pw_qpolynomial *upwqp,
3183 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3186 To extract the piecewise quasipolynomial in a given space from a union, use
3188 __isl_give isl_pw_qpolynomial *
3189 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3190 __isl_keep isl_union_pw_qpolynomial *upwqp,
3191 __isl_take isl_space *space);
3193 To iterate over the cells in a piecewise quasipolynomial,
3194 use either of the following two functions
3196 int isl_pw_qpolynomial_foreach_piece(
3197 __isl_keep isl_pw_qpolynomial *pwqp,
3198 int (*fn)(__isl_take isl_set *set,
3199 __isl_take isl_qpolynomial *qp,
3200 void *user), void *user);
3201 int isl_pw_qpolynomial_foreach_lifted_piece(
3202 __isl_keep isl_pw_qpolynomial *pwqp,
3203 int (*fn)(__isl_take isl_set *set,
3204 __isl_take isl_qpolynomial *qp,
3205 void *user), void *user);
3207 As usual, the function C<fn> should return C<0> on success
3208 and C<-1> on failure. The difference between
3209 C<isl_pw_qpolynomial_foreach_piece> and
3210 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3211 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3212 compute unique representations for all existentially quantified
3213 variables and then turn these existentially quantified variables
3214 into extra set variables, adapting the associated quasipolynomial
3215 accordingly. This means that the C<set> passed to C<fn>
3216 will not have any existentially quantified variables, but that
3217 the dimensions of the sets may be different for different
3218 invocations of C<fn>.
3220 To iterate over all terms in a quasipolynomial,
3223 int isl_qpolynomial_foreach_term(
3224 __isl_keep isl_qpolynomial *qp,
3225 int (*fn)(__isl_take isl_term *term,
3226 void *user), void *user);
3228 The terms themselves can be inspected and freed using
3231 unsigned isl_term_dim(__isl_keep isl_term *term,
3232 enum isl_dim_type type);
3233 void isl_term_get_num(__isl_keep isl_term *term,
3235 void isl_term_get_den(__isl_keep isl_term *term,
3237 int isl_term_get_exp(__isl_keep isl_term *term,
3238 enum isl_dim_type type, unsigned pos);
3239 __isl_give isl_aff *isl_term_get_div(
3240 __isl_keep isl_term *term, unsigned pos);
3241 void isl_term_free(__isl_take isl_term *term);
3243 Each term is a product of parameters, set variables and
3244 integer divisions. The function C<isl_term_get_exp>
3245 returns the exponent of a given dimensions in the given term.
3246 The C<isl_int>s in the arguments of C<isl_term_get_num>
3247 and C<isl_term_get_den> need to have been initialized
3248 using C<isl_int_init> before calling these functions.
3250 =head3 Properties of (Piecewise) Quasipolynomials
3252 To check whether a quasipolynomial is actually a constant,
3253 use the following function.
3255 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3256 isl_int *n, isl_int *d);
3258 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3259 then the numerator and denominator of the constant
3260 are returned in C<*n> and C<*d>, respectively.
3262 To check whether two union piecewise quasipolynomials are
3263 obviously equal, use
3265 int isl_union_pw_qpolynomial_plain_is_equal(
3266 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3267 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3269 =head3 Operations on (Piecewise) Quasipolynomials
3271 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3272 __isl_take isl_qpolynomial *qp, isl_int v);
3273 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3274 __isl_take isl_qpolynomial *qp);
3275 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3276 __isl_take isl_qpolynomial *qp1,
3277 __isl_take isl_qpolynomial *qp2);
3278 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3279 __isl_take isl_qpolynomial *qp1,
3280 __isl_take isl_qpolynomial *qp2);
3281 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3282 __isl_take isl_qpolynomial *qp1,
3283 __isl_take isl_qpolynomial *qp2);
3284 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3285 __isl_take isl_qpolynomial *qp, unsigned exponent);
3287 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3288 __isl_take isl_pw_qpolynomial *pwqp1,
3289 __isl_take isl_pw_qpolynomial *pwqp2);
3290 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3291 __isl_take isl_pw_qpolynomial *pwqp1,
3292 __isl_take isl_pw_qpolynomial *pwqp2);
3293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3294 __isl_take isl_pw_qpolynomial *pwqp1,
3295 __isl_take isl_pw_qpolynomial *pwqp2);
3296 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3297 __isl_take isl_pw_qpolynomial *pwqp);
3298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3299 __isl_take isl_pw_qpolynomial *pwqp1,
3300 __isl_take isl_pw_qpolynomial *pwqp2);
3301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3302 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3304 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3305 __isl_take isl_union_pw_qpolynomial *upwqp1,
3306 __isl_take isl_union_pw_qpolynomial *upwqp2);
3307 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3308 __isl_take isl_union_pw_qpolynomial *upwqp1,
3309 __isl_take isl_union_pw_qpolynomial *upwqp2);
3310 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3311 __isl_take isl_union_pw_qpolynomial *upwqp1,
3312 __isl_take isl_union_pw_qpolynomial *upwqp2);
3314 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3315 __isl_take isl_pw_qpolynomial *pwqp,
3316 __isl_take isl_point *pnt);
3318 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3319 __isl_take isl_union_pw_qpolynomial *upwqp,
3320 __isl_take isl_point *pnt);
3322 __isl_give isl_set *isl_pw_qpolynomial_domain(
3323 __isl_take isl_pw_qpolynomial *pwqp);
3324 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3325 __isl_take isl_pw_qpolynomial *pwpq,
3326 __isl_take isl_set *set);
3328 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3329 __isl_take isl_union_pw_qpolynomial *upwqp);
3330 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3331 __isl_take isl_union_pw_qpolynomial *upwpq,
3332 __isl_take isl_union_set *uset);
3334 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3335 __isl_take isl_qpolynomial *qp,
3336 __isl_take isl_space *model);
3338 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3339 __isl_take isl_qpolynomial *qp);
3340 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3341 __isl_take isl_pw_qpolynomial *pwqp);
3343 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3344 __isl_take isl_union_pw_qpolynomial *upwqp);
3346 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3347 __isl_take isl_qpolynomial *qp,
3348 __isl_take isl_set *context);
3350 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3351 __isl_take isl_pw_qpolynomial *pwqp,
3352 __isl_take isl_set *context);
3354 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3355 __isl_take isl_union_pw_qpolynomial *upwqp,
3356 __isl_take isl_union_set *context);
3358 The gist operation applies the gist operation to each of
3359 the cells in the domain of the input piecewise quasipolynomial.
3360 The context is also exploited
3361 to simplify the quasipolynomials associated to each cell.
3363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3364 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3365 __isl_give isl_union_pw_qpolynomial *
3366 isl_union_pw_qpolynomial_to_polynomial(
3367 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3369 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3370 the polynomial will be an overapproximation. If C<sign> is negative,
3371 it will be an underapproximation. If C<sign> is zero, the approximation
3372 will lie somewhere in between.
3374 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3376 A piecewise quasipolynomial reduction is a piecewise
3377 reduction (or fold) of quasipolynomials.
3378 In particular, the reduction can be maximum or a minimum.
3379 The objects are mainly used to represent the result of
3380 an upper or lower bound on a quasipolynomial over its domain,
3381 i.e., as the result of the following function.
3383 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3384 __isl_take isl_pw_qpolynomial *pwqp,
3385 enum isl_fold type, int *tight);
3387 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3388 __isl_take isl_union_pw_qpolynomial *upwqp,
3389 enum isl_fold type, int *tight);
3391 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3392 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3393 is the returned bound is known be tight, i.e., for each value
3394 of the parameters there is at least
3395 one element in the domain that reaches the bound.
3396 If the domain of C<pwqp> is not wrapping, then the bound is computed
3397 over all elements in that domain and the result has a purely parametric
3398 domain. If the domain of C<pwqp> is wrapping, then the bound is
3399 computed over the range of the wrapped relation. The domain of the
3400 wrapped relation becomes the domain of the result.
3402 A (piecewise) quasipolynomial reduction can be copied or freed using the
3403 following functions.
3405 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3406 __isl_keep isl_qpolynomial_fold *fold);
3407 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3408 __isl_keep isl_pw_qpolynomial_fold *pwf);
3409 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3410 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3411 void isl_qpolynomial_fold_free(
3412 __isl_take isl_qpolynomial_fold *fold);
3413 void *isl_pw_qpolynomial_fold_free(
3414 __isl_take isl_pw_qpolynomial_fold *pwf);
3415 void isl_union_pw_qpolynomial_fold_free(
3416 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3418 =head3 Printing Piecewise Quasipolynomial Reductions
3420 Piecewise quasipolynomial reductions can be printed
3421 using the following function.
3423 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3424 __isl_take isl_printer *p,
3425 __isl_keep isl_pw_qpolynomial_fold *pwf);
3426 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3427 __isl_take isl_printer *p,
3428 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3430 For C<isl_printer_print_pw_qpolynomial_fold>,
3431 output format of the printer
3432 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3433 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3434 output format of the printer
3435 needs to be set to C<ISL_FORMAT_ISL>.
3436 In case of printing in C<ISL_FORMAT_C>, the user may want
3437 to set the names of all dimensions
3439 __isl_give isl_pw_qpolynomial_fold *
3440 isl_pw_qpolynomial_fold_set_dim_name(
3441 __isl_take isl_pw_qpolynomial_fold *pwf,
3442 enum isl_dim_type type, unsigned pos,
3445 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3447 To iterate over all piecewise quasipolynomial reductions in a union
3448 piecewise quasipolynomial reduction, use the following function
3450 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3451 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3452 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3453 void *user), void *user);
3455 To iterate over the cells in a piecewise quasipolynomial reduction,
3456 use either of the following two functions
3458 int isl_pw_qpolynomial_fold_foreach_piece(
3459 __isl_keep isl_pw_qpolynomial_fold *pwf,
3460 int (*fn)(__isl_take isl_set *set,
3461 __isl_take isl_qpolynomial_fold *fold,
3462 void *user), void *user);
3463 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3464 __isl_keep isl_pw_qpolynomial_fold *pwf,
3465 int (*fn)(__isl_take isl_set *set,
3466 __isl_take isl_qpolynomial_fold *fold,
3467 void *user), void *user);
3469 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3470 of the difference between these two functions.
3472 To iterate over all quasipolynomials in a reduction, use
3474 int isl_qpolynomial_fold_foreach_qpolynomial(
3475 __isl_keep isl_qpolynomial_fold *fold,
3476 int (*fn)(__isl_take isl_qpolynomial *qp,
3477 void *user), void *user);
3479 =head3 Properties of Piecewise Quasipolynomial Reductions
3481 To check whether two union piecewise quasipolynomial reductions are
3482 obviously equal, use
3484 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3485 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3486 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3488 =head3 Operations on Piecewise Quasipolynomial Reductions
3490 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3491 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3493 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3494 __isl_take isl_pw_qpolynomial_fold *pwf1,
3495 __isl_take isl_pw_qpolynomial_fold *pwf2);
3497 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3498 __isl_take isl_pw_qpolynomial_fold *pwf1,
3499 __isl_take isl_pw_qpolynomial_fold *pwf2);
3501 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3502 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3503 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3505 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3506 __isl_take isl_pw_qpolynomial_fold *pwf,
3507 __isl_take isl_point *pnt);
3509 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3510 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3511 __isl_take isl_point *pnt);
3513 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3514 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3515 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3516 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3517 __isl_take isl_union_set *uset);
3519 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3520 __isl_take isl_pw_qpolynomial_fold *pwf);
3522 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3523 __isl_take isl_pw_qpolynomial_fold *pwf);
3525 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3526 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3528 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3529 __isl_take isl_pw_qpolynomial_fold *pwf,
3530 __isl_take isl_set *context);
3532 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3533 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3534 __isl_take isl_union_set *context);
3536 The gist operation applies the gist operation to each of
3537 the cells in the domain of the input piecewise quasipolynomial reduction.
3538 In future, the operation will also exploit the context
3539 to simplify the quasipolynomial reductions associated to each cell.
3541 __isl_give isl_pw_qpolynomial_fold *
3542 isl_set_apply_pw_qpolynomial_fold(
3543 __isl_take isl_set *set,
3544 __isl_take isl_pw_qpolynomial_fold *pwf,
3546 __isl_give isl_pw_qpolynomial_fold *
3547 isl_map_apply_pw_qpolynomial_fold(
3548 __isl_take isl_map *map,
3549 __isl_take isl_pw_qpolynomial_fold *pwf,
3551 __isl_give isl_union_pw_qpolynomial_fold *
3552 isl_union_set_apply_union_pw_qpolynomial_fold(
3553 __isl_take isl_union_set *uset,
3554 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3556 __isl_give isl_union_pw_qpolynomial_fold *
3557 isl_union_map_apply_union_pw_qpolynomial_fold(
3558 __isl_take isl_union_map *umap,
3559 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3562 The functions taking a map
3563 compose the given map with the given piecewise quasipolynomial reduction.
3564 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3565 over all elements in the intersection of the range of the map
3566 and the domain of the piecewise quasipolynomial reduction
3567 as a function of an element in the domain of the map.
3568 The functions taking a set compute a bound over all elements in the
3569 intersection of the set and the domain of the
3570 piecewise quasipolynomial reduction.
3572 =head2 Dependence Analysis
3574 C<isl> contains specialized functionality for performing
3575 array dataflow analysis. That is, given a I<sink> access relation
3576 and a collection of possible I<source> access relations,
3577 C<isl> can compute relations that describe
3578 for each iteration of the sink access, which iteration
3579 of which of the source access relations was the last
3580 to access the same data element before the given iteration
3582 To compute standard flow dependences, the sink should be
3583 a read, while the sources should be writes.
3584 If any of the source accesses are marked as being I<may>
3585 accesses, then there will be a dependence to the last
3586 I<must> access B<and> to any I<may> access that follows
3587 this last I<must> access.
3588 In particular, if I<all> sources are I<may> accesses,
3589 then memory based dependence analysis is performed.
3590 If, on the other hand, all sources are I<must> accesses,
3591 then value based dependence analysis is performed.
3593 #include <isl/flow.h>
3595 typedef int (*isl_access_level_before)(void *first, void *second);
3597 __isl_give isl_access_info *isl_access_info_alloc(
3598 __isl_take isl_map *sink,
3599 void *sink_user, isl_access_level_before fn,
3601 __isl_give isl_access_info *isl_access_info_add_source(
3602 __isl_take isl_access_info *acc,
3603 __isl_take isl_map *source, int must,
3605 void isl_access_info_free(__isl_take isl_access_info *acc);
3607 __isl_give isl_flow *isl_access_info_compute_flow(
3608 __isl_take isl_access_info *acc);
3610 int isl_flow_foreach(__isl_keep isl_flow *deps,
3611 int (*fn)(__isl_take isl_map *dep, int must,
3612 void *dep_user, void *user),
3614 __isl_give isl_map *isl_flow_get_no_source(
3615 __isl_keep isl_flow *deps, int must);
3616 void isl_flow_free(__isl_take isl_flow *deps);
3618 The function C<isl_access_info_compute_flow> performs the actual
3619 dependence analysis. The other functions are used to construct
3620 the input for this function or to read off the output.
3622 The input is collected in an C<isl_access_info>, which can
3623 be created through a call to C<isl_access_info_alloc>.
3624 The arguments to this functions are the sink access relation
3625 C<sink>, a token C<sink_user> used to identify the sink
3626 access to the user, a callback function for specifying the
3627 relative order of source and sink accesses, and the number
3628 of source access relations that will be added.
3629 The callback function has type C<int (*)(void *first, void *second)>.
3630 The function is called with two user supplied tokens identifying
3631 either a source or the sink and it should return the shared nesting
3632 level and the relative order of the two accesses.
3633 In particular, let I<n> be the number of loops shared by
3634 the two accesses. If C<first> precedes C<second> textually,
3635 then the function should return I<2 * n + 1>; otherwise,
3636 it should return I<2 * n>.
3637 The sources can be added to the C<isl_access_info> by performing
3638 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3639 C<must> indicates whether the source is a I<must> access
3640 or a I<may> access. Note that a multi-valued access relation
3641 should only be marked I<must> if every iteration in the domain
3642 of the relation accesses I<all> elements in its image.
3643 The C<source_user> token is again used to identify
3644 the source access. The range of the source access relation
3645 C<source> should have the same dimension as the range
3646 of the sink access relation.
3647 The C<isl_access_info_free> function should usually not be
3648 called explicitly, because it is called implicitly by
3649 C<isl_access_info_compute_flow>.
3651 The result of the dependence analysis is collected in an
3652 C<isl_flow>. There may be elements of
3653 the sink access for which no preceding source access could be
3654 found or for which all preceding sources are I<may> accesses.
3655 The relations containing these elements can be obtained through
3656 calls to C<isl_flow_get_no_source>, the first with C<must> set
3657 and the second with C<must> unset.
3658 In the case of standard flow dependence analysis,
3659 with the sink a read and the sources I<must> writes,
3660 the first relation corresponds to the reads from uninitialized
3661 array elements and the second relation is empty.
3662 The actual flow dependences can be extracted using
3663 C<isl_flow_foreach>. This function will call the user-specified
3664 callback function C<fn> for each B<non-empty> dependence between
3665 a source and the sink. The callback function is called
3666 with four arguments, the actual flow dependence relation
3667 mapping source iterations to sink iterations, a boolean that
3668 indicates whether it is a I<must> or I<may> dependence, a token
3669 identifying the source and an additional C<void *> with value
3670 equal to the third argument of the C<isl_flow_foreach> call.
3671 A dependence is marked I<must> if it originates from a I<must>
3672 source and if it is not followed by any I<may> sources.
3674 After finishing with an C<isl_flow>, the user should call
3675 C<isl_flow_free> to free all associated memory.
3677 A higher-level interface to dependence analysis is provided
3678 by the following function.
3680 #include <isl/flow.h>
3682 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3683 __isl_take isl_union_map *must_source,
3684 __isl_take isl_union_map *may_source,
3685 __isl_take isl_union_map *schedule,
3686 __isl_give isl_union_map **must_dep,
3687 __isl_give isl_union_map **may_dep,
3688 __isl_give isl_union_map **must_no_source,
3689 __isl_give isl_union_map **may_no_source);
3691 The arrays are identified by the tuple names of the ranges
3692 of the accesses. The iteration domains by the tuple names
3693 of the domains of the accesses and of the schedule.
3694 The relative order of the iteration domains is given by the
3695 schedule. The relations returned through C<must_no_source>
3696 and C<may_no_source> are subsets of C<sink>.
3697 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3698 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3699 any of the other arguments is treated as an error.
3703 B<The functionality described in this section is fairly new
3704 and may be subject to change.>
3706 The following function can be used to compute a schedule
3707 for a union of domains. The generated schedule respects
3708 all C<validity> dependences. That is, all dependence distances
3709 over these dependences in the scheduled space are lexicographically
3710 positive. The generated schedule schedule also tries to minimize
3711 the dependence distances over C<proximity> dependences.
3712 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3713 for groups of domains where the dependence distances have only
3714 non-negative values.
3715 The algorithm used to construct the schedule is similar to that
3718 #include <isl/schedule.h>
3719 __isl_give isl_schedule *isl_union_set_compute_schedule(
3720 __isl_take isl_union_set *domain,
3721 __isl_take isl_union_map *validity,
3722 __isl_take isl_union_map *proximity);
3723 void *isl_schedule_free(__isl_take isl_schedule *sched);
3725 A mapping from the domains to the scheduled space can be obtained
3726 from an C<isl_schedule> using the following function.
3728 __isl_give isl_union_map *isl_schedule_get_map(
3729 __isl_keep isl_schedule *sched);
3731 A representation of the schedule can be printed using
3733 __isl_give isl_printer *isl_printer_print_schedule(
3734 __isl_take isl_printer *p,
3735 __isl_keep isl_schedule *schedule);
3737 A representation of the schedule as a forest of bands can be obtained
3738 using the following function.
3740 __isl_give isl_band_list *isl_schedule_get_band_forest(
3741 __isl_keep isl_schedule *schedule);
3743 The list can be manipulated as explained in L<"Lists">.
3744 The bands inside the list can be copied and freed using the following
3747 #include <isl/band.h>
3748 __isl_give isl_band *isl_band_copy(
3749 __isl_keep isl_band *band);
3750 void *isl_band_free(__isl_take isl_band *band);
3752 Each band contains zero or more scheduling dimensions.
3753 These are referred to as the members of the band.
3754 The section of the schedule that corresponds to the band is
3755 referred to as the partial schedule of the band.
3756 For those nodes that participate in a band, the outer scheduling
3757 dimensions form the prefix schedule, while the inner scheduling
3758 dimensions form the suffix schedule.
3759 That is, if we take a cut of the band forest, then the union of
3760 the concatenations of the prefix, partial and suffix schedules of
3761 each band in the cut is equal to the entire schedule (modulo
3762 some possible padding at the end with zero scheduling dimensions).
3763 The properties of a band can be inspected using the following functions.
3765 #include <isl/band.h>
3766 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3768 int isl_band_has_children(__isl_keep isl_band *band);
3769 __isl_give isl_band_list *isl_band_get_children(
3770 __isl_keep isl_band *band);
3772 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3773 __isl_keep isl_band *band);
3774 __isl_give isl_union_map *isl_band_get_partial_schedule(
3775 __isl_keep isl_band *band);
3776 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3777 __isl_keep isl_band *band);
3779 int isl_band_n_member(__isl_keep isl_band *band);
3780 int isl_band_member_is_zero_distance(
3781 __isl_keep isl_band *band, int pos);
3783 Note that a scheduling dimension is considered to be ``zero
3784 distance'' if it does not carry any proximity dependences
3786 That is, if the dependence distances of the proximity
3787 dependences are all zero in that direction (for fixed
3788 iterations of outer bands).
3790 A representation of the band can be printed using
3792 #include <isl/band.h>
3793 __isl_give isl_printer *isl_printer_print_band(
3794 __isl_take isl_printer *p,
3795 __isl_keep isl_band *band);
3797 =head2 Parametric Vertex Enumeration
3799 The parametric vertex enumeration described in this section
3800 is mainly intended to be used internally and by the C<barvinok>
3803 #include <isl/vertices.h>
3804 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3805 __isl_keep isl_basic_set *bset);
3807 The function C<isl_basic_set_compute_vertices> performs the
3808 actual computation of the parametric vertices and the chamber
3809 decomposition and store the result in an C<isl_vertices> object.
3810 This information can be queried by either iterating over all
3811 the vertices or iterating over all the chambers or cells
3812 and then iterating over all vertices that are active on the chamber.
3814 int isl_vertices_foreach_vertex(
3815 __isl_keep isl_vertices *vertices,
3816 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3819 int isl_vertices_foreach_cell(
3820 __isl_keep isl_vertices *vertices,
3821 int (*fn)(__isl_take isl_cell *cell, void *user),
3823 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3824 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3827 Other operations that can be performed on an C<isl_vertices> object are
3830 isl_ctx *isl_vertices_get_ctx(
3831 __isl_keep isl_vertices *vertices);
3832 int isl_vertices_get_n_vertices(
3833 __isl_keep isl_vertices *vertices);
3834 void isl_vertices_free(__isl_take isl_vertices *vertices);
3836 Vertices can be inspected and destroyed using the following functions.
3838 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3839 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3840 __isl_give isl_basic_set *isl_vertex_get_domain(
3841 __isl_keep isl_vertex *vertex);
3842 __isl_give isl_basic_set *isl_vertex_get_expr(
3843 __isl_keep isl_vertex *vertex);
3844 void isl_vertex_free(__isl_take isl_vertex *vertex);
3846 C<isl_vertex_get_expr> returns a singleton parametric set describing
3847 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3849 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3850 B<rational> basic sets, so they should mainly be used for inspection
3851 and should not be mixed with integer sets.
3853 Chambers can be inspected and destroyed using the following functions.
3855 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3856 __isl_give isl_basic_set *isl_cell_get_domain(
3857 __isl_keep isl_cell *cell);
3858 void isl_cell_free(__isl_take isl_cell *cell);
3862 Although C<isl> is mainly meant to be used as a library,
3863 it also contains some basic applications that use some
3864 of the functionality of C<isl>.
3865 The input may be specified in either the L<isl format>
3866 or the L<PolyLib format>.
3868 =head2 C<isl_polyhedron_sample>
3870 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3871 an integer element of the polyhedron, if there is any.
3872 The first column in the output is the denominator and is always
3873 equal to 1. If the polyhedron contains no integer points,
3874 then a vector of length zero is printed.
3878 C<isl_pip> takes the same input as the C<example> program
3879 from the C<piplib> distribution, i.e., a set of constraints
3880 on the parameters, a line containing only -1 and finally a set
3881 of constraints on a parametric polyhedron.
3882 The coefficients of the parameters appear in the last columns
3883 (but before the final constant column).
3884 The output is the lexicographic minimum of the parametric polyhedron.
3885 As C<isl> currently does not have its own output format, the output
3886 is just a dump of the internal state.
3888 =head2 C<isl_polyhedron_minimize>
3890 C<isl_polyhedron_minimize> computes the minimum of some linear
3891 or affine objective function over the integer points in a polyhedron.
3892 If an affine objective function
3893 is given, then the constant should appear in the last column.
3895 =head2 C<isl_polytope_scan>
3897 Given a polytope, C<isl_polytope_scan> prints
3898 all integer points in the polytope.