3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
145 =item * The C<nparam> argument has been removed from
146 C<isl_map_read_from_str> and similar functions.
147 When reading input in the original PolyLib format,
148 the result will have no parameters.
149 If parameters are expected, the caller may want to perform
150 dimension manipulation on the result.
156 The source of C<isl> can be obtained either as a tarball
157 or from the git repository. Both are available from
158 L<http://freshmeat.net/projects/isl/>.
159 The installation process depends on how you obtained
162 =head2 Installation from the git repository
166 =item 1 Clone or update the repository
168 The first time the source is obtained, you need to clone
171 git clone git://repo.or.cz/isl.git
173 To obtain updates, you need to pull in the latest changes
177 =item 2 Generate C<configure>
183 After performing the above steps, continue
184 with the L<Common installation instructions>.
186 =head2 Common installation instructions
190 =item 1 Obtain C<GMP>
192 Building C<isl> requires C<GMP>, including its headers files.
193 Your distribution may not provide these header files by default
194 and you may need to install a package called C<gmp-devel> or something
195 similar. Alternatively, C<GMP> can be built from
196 source, available from L<http://gmplib.org/>.
200 C<isl> uses the standard C<autoconf> C<configure> script.
205 optionally followed by some configure options.
206 A complete list of options can be obtained by running
210 Below we discuss some of the more common options.
212 C<isl> can optionally use C<piplib>, but no
213 C<piplib> functionality is currently used by default.
214 The C<--with-piplib> option can
215 be used to specify which C<piplib>
216 library to use, either an installed version (C<system>),
217 an externally built version (C<build>)
218 or no version (C<no>). The option C<build> is mostly useful
219 in C<configure> scripts of larger projects that bundle both C<isl>
226 Installation prefix for C<isl>
228 =item C<--with-gmp-prefix>
230 Installation prefix for C<GMP> (architecture-independent files).
232 =item C<--with-gmp-exec-prefix>
234 Installation prefix for C<GMP> (architecture-dependent files).
236 =item C<--with-piplib>
238 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
240 =item C<--with-piplib-prefix>
242 Installation prefix for C<system> C<piplib> (architecture-independent files).
244 =item C<--with-piplib-exec-prefix>
246 Installation prefix for C<system> C<piplib> (architecture-dependent files).
248 =item C<--with-piplib-builddir>
250 Location where C<build> C<piplib> was built.
258 =item 4 Install (optional)
266 =head2 Initialization
268 All manipulations of integer sets and relations occur within
269 the context of an C<isl_ctx>.
270 A given C<isl_ctx> can only be used within a single thread.
271 All arguments of a function are required to have been allocated
272 within the same context.
273 There are currently no functions available for moving an object
274 from one C<isl_ctx> to another C<isl_ctx>. This means that
275 there is currently no way of safely moving an object from one
276 thread to another, unless the whole C<isl_ctx> is moved.
278 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
279 freed using C<isl_ctx_free>.
280 All objects allocated within an C<isl_ctx> should be freed
281 before the C<isl_ctx> itself is freed.
283 isl_ctx *isl_ctx_alloc();
284 void isl_ctx_free(isl_ctx *ctx);
288 All operations on integers, mainly the coefficients
289 of the constraints describing the sets and relations,
290 are performed in exact integer arithmetic using C<GMP>.
291 However, to allow future versions of C<isl> to optionally
292 support fixed integer arithmetic, all calls to C<GMP>
293 are wrapped inside C<isl> specific macros.
294 The basic type is C<isl_int> and the operations below
295 are available on this type.
296 The meanings of these operations are essentially the same
297 as their C<GMP> C<mpz_> counterparts.
298 As always with C<GMP> types, C<isl_int>s need to be
299 initialized with C<isl_int_init> before they can be used
300 and they need to be released with C<isl_int_clear>
302 The user should not assume that an C<isl_int> is represented
303 as a C<mpz_t>, but should instead explicitly convert between
304 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
305 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
309 =item isl_int_init(i)
311 =item isl_int_clear(i)
313 =item isl_int_set(r,i)
315 =item isl_int_set_si(r,i)
317 =item isl_int_set_gmp(r,g)
319 =item isl_int_get_gmp(i,g)
321 =item isl_int_abs(r,i)
323 =item isl_int_neg(r,i)
325 =item isl_int_swap(i,j)
327 =item isl_int_swap_or_set(i,j)
329 =item isl_int_add_ui(r,i,j)
331 =item isl_int_sub_ui(r,i,j)
333 =item isl_int_add(r,i,j)
335 =item isl_int_sub(r,i,j)
337 =item isl_int_mul(r,i,j)
339 =item isl_int_mul_ui(r,i,j)
341 =item isl_int_addmul(r,i,j)
343 =item isl_int_submul(r,i,j)
345 =item isl_int_gcd(r,i,j)
347 =item isl_int_lcm(r,i,j)
349 =item isl_int_divexact(r,i,j)
351 =item isl_int_cdiv_q(r,i,j)
353 =item isl_int_fdiv_q(r,i,j)
355 =item isl_int_fdiv_r(r,i,j)
357 =item isl_int_fdiv_q_ui(r,i,j)
359 =item isl_int_read(r,s)
361 =item isl_int_print(out,i,width)
365 =item isl_int_cmp(i,j)
367 =item isl_int_cmp_si(i,si)
369 =item isl_int_eq(i,j)
371 =item isl_int_ne(i,j)
373 =item isl_int_lt(i,j)
375 =item isl_int_le(i,j)
377 =item isl_int_gt(i,j)
379 =item isl_int_ge(i,j)
381 =item isl_int_abs_eq(i,j)
383 =item isl_int_abs_ne(i,j)
385 =item isl_int_abs_lt(i,j)
387 =item isl_int_abs_gt(i,j)
389 =item isl_int_abs_ge(i,j)
391 =item isl_int_is_zero(i)
393 =item isl_int_is_one(i)
395 =item isl_int_is_negone(i)
397 =item isl_int_is_pos(i)
399 =item isl_int_is_neg(i)
401 =item isl_int_is_nonpos(i)
403 =item isl_int_is_nonneg(i)
405 =item isl_int_is_divisible_by(i,j)
409 =head2 Sets and Relations
411 C<isl> uses six types of objects for representing sets and relations,
412 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
413 C<isl_union_set> and C<isl_union_map>.
414 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
415 can be described as a conjunction of affine constraints, while
416 C<isl_set> and C<isl_map> represent unions of
417 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
418 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
419 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
420 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
421 where spaces are considered different if they have a different number
422 of dimensions and/or different names (see L<"Spaces">).
423 The difference between sets and relations (maps) is that sets have
424 one set of variables, while relations have two sets of variables,
425 input variables and output variables.
427 =head2 Memory Management
429 Since a high-level operation on sets and/or relations usually involves
430 several substeps and since the user is usually not interested in
431 the intermediate results, most functions that return a new object
432 will also release all the objects passed as arguments.
433 If the user still wants to use one or more of these arguments
434 after the function call, she should pass along a copy of the
435 object rather than the object itself.
436 The user is then responsible for making sure that the original
437 object gets used somewhere else or is explicitly freed.
439 The arguments and return values of all documented functions are
440 annotated to make clear which arguments are released and which
441 arguments are preserved. In particular, the following annotations
448 C<__isl_give> means that a new object is returned.
449 The user should make sure that the returned pointer is
450 used exactly once as a value for an C<__isl_take> argument.
451 In between, it can be used as a value for as many
452 C<__isl_keep> arguments as the user likes.
453 There is one exception, and that is the case where the
454 pointer returned is C<NULL>. Is this case, the user
455 is free to use it as an C<__isl_take> argument or not.
459 C<__isl_take> means that the object the argument points to
460 is taken over by the function and may no longer be used
461 by the user as an argument to any other function.
462 The pointer value must be one returned by a function
463 returning an C<__isl_give> pointer.
464 If the user passes in a C<NULL> value, then this will
465 be treated as an error in the sense that the function will
466 not perform its usual operation. However, it will still
467 make sure that all the other C<__isl_take> arguments
472 C<__isl_keep> means that the function will only use the object
473 temporarily. After the function has finished, the user
474 can still use it as an argument to other functions.
475 A C<NULL> value will be treated in the same way as
476 a C<NULL> value for an C<__isl_take> argument.
482 Identifiers are used to identify both individual dimensions
483 and tuples of dimensions. They consist of a name and an optional
484 pointer. Identifiers with the same name but different pointer values
485 are considered to be distinct.
486 Identifiers can be constructed, copied, freed, inspected and printed
487 using the following functions.
490 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
491 __isl_keep const char *name, void *user);
492 __isl_give isl_id *isl_id_copy(isl_id *id);
493 void *isl_id_free(__isl_take isl_id *id);
495 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
496 void *isl_id_get_user(__isl_keep isl_id *id);
497 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
499 __isl_give isl_printer *isl_printer_print_id(
500 __isl_take isl_printer *p, __isl_keep isl_id *id);
502 Note that C<isl_id_get_name> returns a pointer to some internal
503 data structure, so the result can only be used while the
504 corresponding C<isl_id> is alive.
508 Whenever a new set or relation is created from scratch,
509 the space in which it lives needs to be specified using an C<isl_space>.
511 #include <isl/space.h>
512 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
513 unsigned nparam, unsigned n_in, unsigned n_out);
514 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
516 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
517 unsigned nparam, unsigned dim);
518 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
519 void isl_space_free(__isl_take isl_space *space);
520 unsigned isl_space_dim(__isl_keep isl_space *space,
521 enum isl_dim_type type);
523 The space used for creating a parameter domain
524 needs to be created using C<isl_space_params_alloc>.
525 For other sets, the space
526 needs to be created using C<isl_space_set_alloc>, while
527 for a relation, the space
528 needs to be created using C<isl_space_alloc>.
529 C<isl_space_dim> can be used
530 to find out the number of dimensions of each type in
531 a space, where type may be
532 C<isl_dim_param>, C<isl_dim_in> (only for relations),
533 C<isl_dim_out> (only for relations), C<isl_dim_set>
534 (only for sets) or C<isl_dim_all>.
536 To check whether a given space is that of a set or a map
537 or whether it is a parameter space, use these functions:
539 #include <isl/space.h>
540 int isl_space_is_params(__isl_keep isl_space *space);
541 int isl_space_is_set(__isl_keep isl_space *space);
543 It is often useful to create objects that live in the
544 same space as some other object. This can be accomplished
545 by creating the new objects
546 (see L<Creating New Sets and Relations> or
547 L<Creating New (Piecewise) Quasipolynomials>) based on the space
548 of the original object.
551 __isl_give isl_space *isl_basic_set_get_space(
552 __isl_keep isl_basic_set *bset);
553 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
555 #include <isl/union_set.h>
556 __isl_give isl_space *isl_union_set_get_space(
557 __isl_keep isl_union_set *uset);
560 __isl_give isl_space *isl_basic_map_get_space(
561 __isl_keep isl_basic_map *bmap);
562 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
564 #include <isl/union_map.h>
565 __isl_give isl_space *isl_union_map_get_space(
566 __isl_keep isl_union_map *umap);
568 #include <isl/constraint.h>
569 __isl_give isl_space *isl_constraint_get_space(
570 __isl_keep isl_constraint *constraint);
572 #include <isl/polynomial.h>
573 __isl_give isl_space *isl_qpolynomial_get_domain_space(
574 __isl_keep isl_qpolynomial *qp);
575 __isl_give isl_space *isl_qpolynomial_get_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_fold_get_space(
578 __isl_keep isl_qpolynomial_fold *fold);
579 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
580 __isl_keep isl_pw_qpolynomial *pwqp);
581 __isl_give isl_space *isl_pw_qpolynomial_get_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
584 __isl_keep isl_pw_qpolynomial_fold *pwf);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
588 __isl_keep isl_union_pw_qpolynomial *upwqp);
589 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
590 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
593 __isl_give isl_space *isl_aff_get_domain_space(
594 __isl_keep isl_aff *aff);
595 __isl_give isl_space *isl_aff_get_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_pw_aff_get_domain_space(
598 __isl_keep isl_pw_aff *pwaff);
599 __isl_give isl_space *isl_pw_aff_get_space(
600 __isl_keep isl_pw_aff *pwaff);
602 #include <isl/point.h>
603 __isl_give isl_space *isl_point_get_space(
604 __isl_keep isl_point *pnt);
606 The identifiers or names of the individual dimensions may be set or read off
607 using the following functions.
609 #include <isl/space.h>
610 __isl_give isl_space *isl_space_set_dim_id(
611 __isl_take isl_space *space,
612 enum isl_dim_type type, unsigned pos,
613 __isl_take isl_id *id);
614 int isl_space_has_dim_id(__isl_keep isl_space *space,
615 enum isl_dim_type type, unsigned pos);
616 __isl_give isl_id *isl_space_get_dim_id(
617 __isl_keep isl_space *space,
618 enum isl_dim_type type, unsigned pos);
619 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_keep const char *name);
622 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
625 Note that C<isl_space_get_name> returns a pointer to some internal
626 data structure, so the result can only be used while the
627 corresponding C<isl_space> is alive.
628 Also note that every function that operates on two sets or relations
629 requires that both arguments have the same parameters. This also
630 means that if one of the arguments has named parameters, then the
631 other needs to have named parameters too and the names need to match.
632 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
633 arguments may have different parameters (as long as they are named),
634 in which case the result will have as parameters the union of the parameters of
637 Given the identifier or name of a dimension (typically a parameter),
638 its position can be obtained from the following function.
640 #include <isl/space.h>
641 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
642 enum isl_dim_type type, __isl_keep isl_id *id);
643 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
644 enum isl_dim_type type, const char *name);
646 The identifiers or names of entire spaces may be set or read off
647 using the following functions.
649 #include <isl/space.h>
650 __isl_give isl_space *isl_space_set_tuple_id(
651 __isl_take isl_space *space,
652 enum isl_dim_type type, __isl_take isl_id *id);
653 __isl_give isl_space *isl_space_reset_tuple_id(
654 __isl_take isl_space *space, enum isl_dim_type type);
655 int isl_space_has_tuple_id(__isl_keep isl_space *space,
656 enum isl_dim_type type);
657 __isl_give isl_id *isl_space_get_tuple_id(
658 __isl_keep isl_space *space, enum isl_dim_type type);
659 __isl_give isl_space *isl_space_set_tuple_name(
660 __isl_take isl_space *space,
661 enum isl_dim_type type, const char *s);
662 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
663 enum isl_dim_type type);
665 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
666 or C<isl_dim_set>. As with C<isl_space_get_name>,
667 the C<isl_space_get_tuple_name> function returns a pointer to some internal
669 Binary operations require the corresponding spaces of their arguments
670 to have the same name.
672 Spaces can be nested. In particular, the domain of a set or
673 the domain or range of a relation can be a nested relation.
674 The following functions can be used to construct and deconstruct
677 #include <isl/space.h>
678 int isl_space_is_wrapping(__isl_keep isl_space *space);
679 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
680 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
682 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
683 be the space of a set, while that of
684 C<isl_space_wrap> should be the space of a relation.
685 Conversely, the output of C<isl_space_unwrap> is the space
686 of a relation, while that of C<isl_space_wrap> is the space of a set.
688 Spaces can be created from other spaces
689 using the following functions.
691 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
692 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
693 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
694 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
695 __isl_give isl_space *isl_space_params(
696 __isl_take isl_space *space);
697 __isl_give isl_space *isl_space_set_from_params(
698 __isl_take isl_space *space);
699 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
701 __isl_take isl_space *right);
702 __isl_give isl_space *isl_space_align_params(
703 __isl_take isl_space *space1, __isl_take isl_space *space2)
704 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned pos, unsigned n);
706 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned n);
708 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
709 enum isl_dim_type type, unsigned first, unsigned n);
710 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
711 enum isl_dim_type dst_type, unsigned dst_pos,
712 enum isl_dim_type src_type, unsigned src_pos,
714 __isl_give isl_space *isl_space_map_from_set(
715 __isl_take isl_space *space);
716 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
718 Note that if dimensions are added or removed from a space, then
719 the name and the internal structure are lost.
723 A local space is essentially a space with
724 zero or more existentially quantified variables.
725 The local space of a basic set or relation can be obtained
726 using the following functions.
729 __isl_give isl_local_space *isl_basic_set_get_local_space(
730 __isl_keep isl_basic_set *bset);
733 __isl_give isl_local_space *isl_basic_map_get_local_space(
734 __isl_keep isl_basic_map *bmap);
736 A new local space can be created from a space using
738 #include <isl/local_space.h>
739 __isl_give isl_local_space *isl_local_space_from_space(
740 __isl_take isl_space *space);
742 They can be inspected, copied and freed using the following functions.
744 #include <isl/local_space.h>
745 isl_ctx *isl_local_space_get_ctx(
746 __isl_keep isl_local_space *ls);
747 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
748 int isl_local_space_dim(__isl_keep isl_local_space *ls,
749 enum isl_dim_type type);
750 const char *isl_local_space_get_dim_name(
751 __isl_keep isl_local_space *ls,
752 enum isl_dim_type type, unsigned pos);
753 __isl_give isl_local_space *isl_local_space_set_dim_name(
754 __isl_take isl_local_space *ls,
755 enum isl_dim_type type, unsigned pos, const char *s);
756 __isl_give isl_space *isl_local_space_get_space(
757 __isl_keep isl_local_space *ls);
758 __isl_give isl_aff *isl_local_space_get_div(
759 __isl_keep isl_local_space *ls, int pos);
760 __isl_give isl_local_space *isl_local_space_copy(
761 __isl_keep isl_local_space *ls);
762 void *isl_local_space_free(__isl_take isl_local_space *ls);
764 Two local spaces can be compared using
766 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
767 __isl_keep isl_local_space *ls2);
769 Local spaces can be created from other local spaces
770 using the following functions.
772 __isl_give isl_local_space *isl_local_space_domain(
773 __isl_take isl_local_space *ls);
774 __isl_give isl_local_space *isl_local_space_from_domain(
775 __isl_take isl_local_space *ls);
776 __isl_give isl_local_space *isl_local_space_add_dims(
777 __isl_take isl_local_space *ls,
778 enum isl_dim_type type, unsigned n);
779 __isl_give isl_local_space *isl_local_space_insert_dims(
780 __isl_take isl_local_space *ls,
781 enum isl_dim_type type, unsigned first, unsigned n);
782 __isl_give isl_local_space *isl_local_space_drop_dims(
783 __isl_take isl_local_space *ls,
784 enum isl_dim_type type, unsigned first, unsigned n);
786 =head2 Input and Output
788 C<isl> supports its own input/output format, which is similar
789 to the C<Omega> format, but also supports the C<PolyLib> format
794 The C<isl> format is similar to that of C<Omega>, but has a different
795 syntax for describing the parameters and allows for the definition
796 of an existentially quantified variable as the integer division
797 of an affine expression.
798 For example, the set of integers C<i> between C<0> and C<n>
799 such that C<i % 10 <= 6> can be described as
801 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
804 A set or relation can have several disjuncts, separated
805 by the keyword C<or>. Each disjunct is either a conjunction
806 of constraints or a projection (C<exists>) of a conjunction
807 of constraints. The constraints are separated by the keyword
810 =head3 C<PolyLib> format
812 If the represented set is a union, then the first line
813 contains a single number representing the number of disjuncts.
814 Otherwise, a line containing the number C<1> is optional.
816 Each disjunct is represented by a matrix of constraints.
817 The first line contains two numbers representing
818 the number of rows and columns,
819 where the number of rows is equal to the number of constraints
820 and the number of columns is equal to two plus the number of variables.
821 The following lines contain the actual rows of the constraint matrix.
822 In each row, the first column indicates whether the constraint
823 is an equality (C<0>) or inequality (C<1>). The final column
824 corresponds to the constant term.
826 If the set is parametric, then the coefficients of the parameters
827 appear in the last columns before the constant column.
828 The coefficients of any existentially quantified variables appear
829 between those of the set variables and those of the parameters.
831 =head3 Extended C<PolyLib> format
833 The extended C<PolyLib> format is nearly identical to the
834 C<PolyLib> format. The only difference is that the line
835 containing the number of rows and columns of a constraint matrix
836 also contains four additional numbers:
837 the number of output dimensions, the number of input dimensions,
838 the number of local dimensions (i.e., the number of existentially
839 quantified variables) and the number of parameters.
840 For sets, the number of ``output'' dimensions is equal
841 to the number of set dimensions, while the number of ``input''
847 __isl_give isl_basic_set *isl_basic_set_read_from_file(
848 isl_ctx *ctx, FILE *input);
849 __isl_give isl_basic_set *isl_basic_set_read_from_str(
850 isl_ctx *ctx, const char *str);
851 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
853 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
857 __isl_give isl_basic_map *isl_basic_map_read_from_file(
858 isl_ctx *ctx, FILE *input);
859 __isl_give isl_basic_map *isl_basic_map_read_from_str(
860 isl_ctx *ctx, const char *str);
861 __isl_give isl_map *isl_map_read_from_file(
862 isl_ctx *ctx, FILE *input);
863 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
866 #include <isl/union_set.h>
867 __isl_give isl_union_set *isl_union_set_read_from_file(
868 isl_ctx *ctx, FILE *input);
869 __isl_give isl_union_set *isl_union_set_read_from_str(
870 isl_ctx *ctx, const char *str);
872 #include <isl/union_map.h>
873 __isl_give isl_union_map *isl_union_map_read_from_file(
874 isl_ctx *ctx, FILE *input);
875 __isl_give isl_union_map *isl_union_map_read_from_str(
876 isl_ctx *ctx, const char *str);
878 The input format is autodetected and may be either the C<PolyLib> format
879 or the C<isl> format.
883 Before anything can be printed, an C<isl_printer> needs to
886 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
888 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
889 void isl_printer_free(__isl_take isl_printer *printer);
890 __isl_give char *isl_printer_get_str(
891 __isl_keep isl_printer *printer);
893 The behavior of the printer can be modified in various ways
895 __isl_give isl_printer *isl_printer_set_output_format(
896 __isl_take isl_printer *p, int output_format);
897 __isl_give isl_printer *isl_printer_set_indent(
898 __isl_take isl_printer *p, int indent);
899 __isl_give isl_printer *isl_printer_indent(
900 __isl_take isl_printer *p, int indent);
901 __isl_give isl_printer *isl_printer_set_prefix(
902 __isl_take isl_printer *p, const char *prefix);
903 __isl_give isl_printer *isl_printer_set_suffix(
904 __isl_take isl_printer *p, const char *suffix);
906 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
907 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
908 and defaults to C<ISL_FORMAT_ISL>.
909 Each line in the output is indented by C<indent> (set by
910 C<isl_printer_set_indent>) spaces
911 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
912 In the C<PolyLib> format output,
913 the coefficients of the existentially quantified variables
914 appear between those of the set variables and those
916 The function C<isl_printer_indent> increases the indentation
917 by the specified amount (which may be negative).
919 To actually print something, use
922 __isl_give isl_printer *isl_printer_print_basic_set(
923 __isl_take isl_printer *printer,
924 __isl_keep isl_basic_set *bset);
925 __isl_give isl_printer *isl_printer_print_set(
926 __isl_take isl_printer *printer,
927 __isl_keep isl_set *set);
930 __isl_give isl_printer *isl_printer_print_basic_map(
931 __isl_take isl_printer *printer,
932 __isl_keep isl_basic_map *bmap);
933 __isl_give isl_printer *isl_printer_print_map(
934 __isl_take isl_printer *printer,
935 __isl_keep isl_map *map);
937 #include <isl/union_set.h>
938 __isl_give isl_printer *isl_printer_print_union_set(
939 __isl_take isl_printer *p,
940 __isl_keep isl_union_set *uset);
942 #include <isl/union_map.h>
943 __isl_give isl_printer *isl_printer_print_union_map(
944 __isl_take isl_printer *p,
945 __isl_keep isl_union_map *umap);
947 When called on a file printer, the following function flushes
948 the file. When called on a string printer, the buffer is cleared.
950 __isl_give isl_printer *isl_printer_flush(
951 __isl_take isl_printer *p);
953 =head2 Creating New Sets and Relations
955 C<isl> has functions for creating some standard sets and relations.
959 =item * Empty sets and relations
961 __isl_give isl_basic_set *isl_basic_set_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_basic_map *isl_basic_map_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_set *isl_set_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_map *isl_map_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_union_set *isl_union_set_empty(
970 __isl_take isl_space *space);
971 __isl_give isl_union_map *isl_union_map_empty(
972 __isl_take isl_space *space);
974 For C<isl_union_set>s and C<isl_union_map>s, the space
975 is only used to specify the parameters.
977 =item * Universe sets and relations
979 __isl_give isl_basic_set *isl_basic_set_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_basic_map *isl_basic_map_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_set *isl_set_universe(
984 __isl_take isl_space *space);
985 __isl_give isl_map *isl_map_universe(
986 __isl_take isl_space *space);
987 __isl_give isl_union_set *isl_union_set_universe(
988 __isl_take isl_union_set *uset);
989 __isl_give isl_union_map *isl_union_map_universe(
990 __isl_take isl_union_map *umap);
992 The sets and relations constructed by the functions above
993 contain all integer values, while those constructed by the
994 functions below only contain non-negative values.
996 __isl_give isl_basic_set *isl_basic_set_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_basic_map *isl_basic_map_nat_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_set *isl_set_nat_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_map *isl_map_nat_universe(
1003 __isl_take isl_space *space);
1005 =item * Identity relations
1007 __isl_give isl_basic_map *isl_basic_map_identity(
1008 __isl_take isl_space *space);
1009 __isl_give isl_map *isl_map_identity(
1010 __isl_take isl_space *space);
1012 The number of input and output dimensions in C<space> needs
1015 =item * Lexicographic order
1017 __isl_give isl_map *isl_map_lex_lt(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_le(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_gt(
1022 __isl_take isl_space *set_space);
1023 __isl_give isl_map *isl_map_lex_ge(
1024 __isl_take isl_space *set_space);
1025 __isl_give isl_map *isl_map_lex_lt_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_le_first(
1028 __isl_take isl_space *space, unsigned n);
1029 __isl_give isl_map *isl_map_lex_gt_first(
1030 __isl_take isl_space *space, unsigned n);
1031 __isl_give isl_map *isl_map_lex_ge_first(
1032 __isl_take isl_space *space, unsigned n);
1034 The first four functions take a space for a B<set>
1035 and return relations that express that the elements in the domain
1036 are lexicographically less
1037 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1038 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1039 than the elements in the range.
1040 The last four functions take a space for a map
1041 and return relations that express that the first C<n> dimensions
1042 in the domain are lexicographically less
1043 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1044 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1045 than the first C<n> dimensions in the range.
1049 A basic set or relation can be converted to a set or relation
1050 using the following functions.
1052 __isl_give isl_set *isl_set_from_basic_set(
1053 __isl_take isl_basic_set *bset);
1054 __isl_give isl_map *isl_map_from_basic_map(
1055 __isl_take isl_basic_map *bmap);
1057 Sets and relations can be converted to union sets and relations
1058 using the following functions.
1060 __isl_give isl_union_map *isl_union_map_from_map(
1061 __isl_take isl_map *map);
1062 __isl_give isl_union_set *isl_union_set_from_set(
1063 __isl_take isl_set *set);
1065 The inverse conversions below can only be used if the input
1066 union set or relation is known to contain elements in exactly one
1069 __isl_give isl_set *isl_set_from_union_set(
1070 __isl_take isl_union_set *uset);
1071 __isl_give isl_map *isl_map_from_union_map(
1072 __isl_take isl_union_map *umap);
1074 A zero-dimensional set can be constructed on a given parameter domain
1075 using the following function.
1077 __isl_give isl_set *isl_set_from_params(
1078 __isl_take isl_set *set);
1080 Sets and relations can be copied and freed again using the following
1083 __isl_give isl_basic_set *isl_basic_set_copy(
1084 __isl_keep isl_basic_set *bset);
1085 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1086 __isl_give isl_union_set *isl_union_set_copy(
1087 __isl_keep isl_union_set *uset);
1088 __isl_give isl_basic_map *isl_basic_map_copy(
1089 __isl_keep isl_basic_map *bmap);
1090 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1091 __isl_give isl_union_map *isl_union_map_copy(
1092 __isl_keep isl_union_map *umap);
1093 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1094 void isl_set_free(__isl_take isl_set *set);
1095 void *isl_union_set_free(__isl_take isl_union_set *uset);
1096 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1097 void isl_map_free(__isl_take isl_map *map);
1098 void *isl_union_map_free(__isl_take isl_union_map *umap);
1100 Other sets and relations can be constructed by starting
1101 from a universe set or relation, adding equality and/or
1102 inequality constraints and then projecting out the
1103 existentially quantified variables, if any.
1104 Constraints can be constructed, manipulated and
1105 added to (or removed from) (basic) sets and relations
1106 using the following functions.
1108 #include <isl/constraint.h>
1109 __isl_give isl_constraint *isl_equality_alloc(
1110 __isl_take isl_local_space *ls);
1111 __isl_give isl_constraint *isl_inequality_alloc(
1112 __isl_take isl_local_space *ls);
1113 __isl_give isl_constraint *isl_constraint_set_constant(
1114 __isl_take isl_constraint *constraint, isl_int v);
1115 __isl_give isl_constraint *isl_constraint_set_constant_si(
1116 __isl_take isl_constraint *constraint, int v);
1117 __isl_give isl_constraint *isl_constraint_set_coefficient(
1118 __isl_take isl_constraint *constraint,
1119 enum isl_dim_type type, int pos, isl_int v);
1120 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1121 __isl_take isl_constraint *constraint,
1122 enum isl_dim_type type, int pos, int v);
1123 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1124 __isl_take isl_basic_map *bmap,
1125 __isl_take isl_constraint *constraint);
1126 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1127 __isl_take isl_basic_set *bset,
1128 __isl_take isl_constraint *constraint);
1129 __isl_give isl_map *isl_map_add_constraint(
1130 __isl_take isl_map *map,
1131 __isl_take isl_constraint *constraint);
1132 __isl_give isl_set *isl_set_add_constraint(
1133 __isl_take isl_set *set,
1134 __isl_take isl_constraint *constraint);
1135 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1136 __isl_take isl_basic_set *bset,
1137 __isl_take isl_constraint *constraint);
1139 For example, to create a set containing the even integers
1140 between 10 and 42, you would use the following code.
1143 isl_local_space *ls;
1145 isl_basic_set *bset;
1147 space = isl_space_set_alloc(ctx, 0, 2);
1148 bset = isl_basic_set_universe(isl_space_copy(space));
1149 ls = isl_local_space_from_space(space);
1151 c = isl_equality_alloc(isl_local_space_copy(ls));
1152 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1153 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1154 bset = isl_basic_set_add_constraint(bset, c);
1156 c = isl_inequality_alloc(isl_local_space_copy(ls));
1157 c = isl_constraint_set_constant_si(c, -10);
1158 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1159 bset = isl_basic_set_add_constraint(bset, c);
1161 c = isl_inequality_alloc(ls);
1162 c = isl_constraint_set_constant_si(c, 42);
1163 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1164 bset = isl_basic_set_add_constraint(bset, c);
1166 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1170 isl_basic_set *bset;
1171 bset = isl_basic_set_read_from_str(ctx,
1172 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1174 A basic set or relation can also be constructed from two matrices
1175 describing the equalities and the inequalities.
1177 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1178 __isl_take isl_space *space,
1179 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1180 enum isl_dim_type c1,
1181 enum isl_dim_type c2, enum isl_dim_type c3,
1182 enum isl_dim_type c4);
1183 __isl_give isl_basic_map *isl_basic_map_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, enum isl_dim_type c5);
1190 The C<isl_dim_type> arguments indicate the order in which
1191 different kinds of variables appear in the input matrices
1192 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1193 C<isl_dim_set> and C<isl_dim_div> for sets and
1194 of C<isl_dim_cst>, C<isl_dim_param>,
1195 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1197 A (basic) set or relation can also be constructed from a (piecewise)
1199 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1201 __isl_give isl_basic_map *isl_basic_map_from_aff(
1202 __isl_take isl_aff *aff);
1203 __isl_give isl_set *isl_set_from_pw_aff(
1204 __isl_take isl_pw_aff *pwaff);
1205 __isl_give isl_map *isl_map_from_pw_aff(
1206 __isl_take isl_pw_aff *pwaff);
1207 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1208 __isl_take isl_space *domain_space,
1209 __isl_take isl_aff_list *list);
1211 The C<domain_dim> argument describes the domain of the resulting
1212 basic relation. It is required because the C<list> may consist
1213 of zero affine expressions.
1215 =head2 Inspecting Sets and Relations
1217 Usually, the user should not have to care about the actual constraints
1218 of the sets and maps, but should instead apply the abstract operations
1219 explained in the following sections.
1220 Occasionally, however, it may be required to inspect the individual
1221 coefficients of the constraints. This section explains how to do so.
1222 In these cases, it may also be useful to have C<isl> compute
1223 an explicit representation of the existentially quantified variables.
1225 __isl_give isl_set *isl_set_compute_divs(
1226 __isl_take isl_set *set);
1227 __isl_give isl_map *isl_map_compute_divs(
1228 __isl_take isl_map *map);
1229 __isl_give isl_union_set *isl_union_set_compute_divs(
1230 __isl_take isl_union_set *uset);
1231 __isl_give isl_union_map *isl_union_map_compute_divs(
1232 __isl_take isl_union_map *umap);
1234 This explicit representation defines the existentially quantified
1235 variables as integer divisions of the other variables, possibly
1236 including earlier existentially quantified variables.
1237 An explicitly represented existentially quantified variable therefore
1238 has a unique value when the values of the other variables are known.
1239 If, furthermore, the same existentials, i.e., existentials
1240 with the same explicit representations, should appear in the
1241 same order in each of the disjuncts of a set or map, then the user should call
1242 either of the following functions.
1244 __isl_give isl_set *isl_set_align_divs(
1245 __isl_take isl_set *set);
1246 __isl_give isl_map *isl_map_align_divs(
1247 __isl_take isl_map *map);
1249 Alternatively, the existentially quantified variables can be removed
1250 using the following functions, which compute an overapproximation.
1252 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1253 __isl_take isl_basic_set *bset);
1254 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1255 __isl_take isl_basic_map *bmap);
1256 __isl_give isl_set *isl_set_remove_divs(
1257 __isl_take isl_set *set);
1258 __isl_give isl_map *isl_map_remove_divs(
1259 __isl_take isl_map *map);
1261 To iterate over all the sets or maps in a union set or map, use
1263 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1264 int (*fn)(__isl_take isl_set *set, void *user),
1266 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1267 int (*fn)(__isl_take isl_map *map, void *user),
1270 The number of sets or maps in a union set or map can be obtained
1273 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1274 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1276 To extract the set or map in a given space from a union, use
1278 __isl_give isl_set *isl_union_set_extract_set(
1279 __isl_keep isl_union_set *uset,
1280 __isl_take isl_space *space);
1281 __isl_give isl_map *isl_union_map_extract_map(
1282 __isl_keep isl_union_map *umap,
1283 __isl_take isl_space *space);
1285 To iterate over all the basic sets or maps in a set or map, use
1287 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1288 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1290 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1291 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1294 The callback function C<fn> should return 0 if successful and
1295 -1 if an error occurs. In the latter case, or if any other error
1296 occurs, the above functions will return -1.
1298 It should be noted that C<isl> does not guarantee that
1299 the basic sets or maps passed to C<fn> are disjoint.
1300 If this is required, then the user should call one of
1301 the following functions first.
1303 __isl_give isl_set *isl_set_make_disjoint(
1304 __isl_take isl_set *set);
1305 __isl_give isl_map *isl_map_make_disjoint(
1306 __isl_take isl_map *map);
1308 The number of basic sets in a set can be obtained
1311 int isl_set_n_basic_set(__isl_keep isl_set *set);
1313 To iterate over the constraints of a basic set or map, use
1315 #include <isl/constraint.h>
1317 int isl_basic_map_foreach_constraint(
1318 __isl_keep isl_basic_map *bmap,
1319 int (*fn)(__isl_take isl_constraint *c, void *user),
1321 void *isl_constraint_free(__isl_take isl_constraint *c);
1323 Again, the callback function C<fn> should return 0 if successful and
1324 -1 if an error occurs. In the latter case, or if any other error
1325 occurs, the above functions will return -1.
1326 The constraint C<c> represents either an equality or an inequality.
1327 Use the following function to find out whether a constraint
1328 represents an equality. If not, it represents an inequality.
1330 int isl_constraint_is_equality(
1331 __isl_keep isl_constraint *constraint);
1333 The coefficients of the constraints can be inspected using
1334 the following functions.
1336 void isl_constraint_get_constant(
1337 __isl_keep isl_constraint *constraint, isl_int *v);
1338 void isl_constraint_get_coefficient(
1339 __isl_keep isl_constraint *constraint,
1340 enum isl_dim_type type, int pos, isl_int *v);
1341 int isl_constraint_involves_dims(
1342 __isl_keep isl_constraint *constraint,
1343 enum isl_dim_type type, unsigned first, unsigned n);
1345 The explicit representations of the existentially quantified
1346 variables can be inspected using the following function.
1347 Note that the user is only allowed to use this function
1348 if the inspected set or map is the result of a call
1349 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1350 The existentially quantified variable is equal to the floor
1351 of the returned affine expression. The affine expression
1352 itself can be inspected using the functions in
1353 L<"Piecewise Quasi Affine Expressions">.
1355 __isl_give isl_aff *isl_constraint_get_div(
1356 __isl_keep isl_constraint *constraint, int pos);
1358 To obtain the constraints of a basic set or map in matrix
1359 form, use the following functions.
1361 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1362 __isl_keep isl_basic_set *bset,
1363 enum isl_dim_type c1, enum isl_dim_type c2,
1364 enum isl_dim_type c3, enum isl_dim_type c4);
1365 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1366 __isl_keep isl_basic_set *bset,
1367 enum isl_dim_type c1, enum isl_dim_type c2,
1368 enum isl_dim_type c3, enum isl_dim_type c4);
1369 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1370 __isl_keep isl_basic_map *bmap,
1371 enum isl_dim_type c1,
1372 enum isl_dim_type c2, enum isl_dim_type c3,
1373 enum isl_dim_type c4, enum isl_dim_type c5);
1374 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1375 __isl_keep isl_basic_map *bmap,
1376 enum isl_dim_type c1,
1377 enum isl_dim_type c2, enum isl_dim_type c3,
1378 enum isl_dim_type c4, enum isl_dim_type c5);
1380 The C<isl_dim_type> arguments dictate the order in which
1381 different kinds of variables appear in the resulting matrix
1382 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1383 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1385 The number of parameters, input, output or set dimensions can
1386 be obtained using the following functions.
1388 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1389 enum isl_dim_type type);
1390 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1391 enum isl_dim_type type);
1392 unsigned isl_set_dim(__isl_keep isl_set *set,
1393 enum isl_dim_type type);
1394 unsigned isl_map_dim(__isl_keep isl_map *map,
1395 enum isl_dim_type type);
1397 To check whether the description of a set or relation depends
1398 on one or more given dimensions, it is not necessary to iterate over all
1399 constraints. Instead the following functions can be used.
1401 int isl_basic_set_involves_dims(
1402 __isl_keep isl_basic_set *bset,
1403 enum isl_dim_type type, unsigned first, unsigned n);
1404 int isl_set_involves_dims(__isl_keep isl_set *set,
1405 enum isl_dim_type type, unsigned first, unsigned n);
1406 int isl_basic_map_involves_dims(
1407 __isl_keep isl_basic_map *bmap,
1408 enum isl_dim_type type, unsigned first, unsigned n);
1409 int isl_map_involves_dims(__isl_keep isl_map *map,
1410 enum isl_dim_type type, unsigned first, unsigned n);
1412 Similarly, the following functions can be used to check whether
1413 a given dimension is involved in any lower or upper bound.
1415 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1416 enum isl_dim_type type, unsigned pos);
1417 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1418 enum isl_dim_type type, unsigned pos);
1420 The identifiers or names of the domain and range spaces of a set
1421 or relation can be read off or set using the following functions.
1423 __isl_give isl_set *isl_set_set_tuple_id(
1424 __isl_take isl_set *set, __isl_take isl_id *id);
1425 __isl_give isl_set *isl_set_reset_tuple_id(
1426 __isl_take isl_set *set);
1427 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1428 __isl_give isl_id *isl_set_get_tuple_id(
1429 __isl_keep isl_set *set);
1430 __isl_give isl_map *isl_map_set_tuple_id(
1431 __isl_take isl_map *map, enum isl_dim_type type,
1432 __isl_take isl_id *id);
1433 __isl_give isl_map *isl_map_reset_tuple_id(
1434 __isl_take isl_map *map, enum isl_dim_type type);
1435 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1436 enum isl_dim_type type);
1437 __isl_give isl_id *isl_map_get_tuple_id(
1438 __isl_keep isl_map *map, enum isl_dim_type type);
1440 const char *isl_basic_set_get_tuple_name(
1441 __isl_keep isl_basic_set *bset);
1442 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1443 __isl_take isl_basic_set *set, const char *s);
1444 const char *isl_set_get_tuple_name(
1445 __isl_keep isl_set *set);
1446 const char *isl_basic_map_get_tuple_name(
1447 __isl_keep isl_basic_map *bmap,
1448 enum isl_dim_type type);
1449 const char *isl_map_get_tuple_name(
1450 __isl_keep isl_map *map,
1451 enum isl_dim_type type);
1453 As with C<isl_space_get_tuple_name>, the value returned points to
1454 an internal data structure.
1455 The identifiers, positions or names of individual dimensions can be
1456 read off using the following functions.
1458 __isl_give isl_set *isl_set_set_dim_id(
1459 __isl_take isl_set *set, enum isl_dim_type type,
1460 unsigned pos, __isl_take isl_id *id);
1461 int isl_set_has_dim_id(__isl_keep isl_set *set,
1462 enum isl_dim_type type, unsigned pos);
1463 __isl_give isl_id *isl_set_get_dim_id(
1464 __isl_keep isl_set *set, enum isl_dim_type type,
1466 __isl_give isl_map *isl_map_set_dim_id(
1467 __isl_take isl_map *map, enum isl_dim_type type,
1468 unsigned pos, __isl_take isl_id *id);
1469 int isl_map_has_dim_id(__isl_keep isl_map *map,
1470 enum isl_dim_type type, unsigned pos);
1471 __isl_give isl_id *isl_map_get_dim_id(
1472 __isl_keep isl_map *map, enum isl_dim_type type,
1475 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1476 enum isl_dim_type type, __isl_keep isl_id *id);
1477 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1478 enum isl_dim_type type, __isl_keep isl_id *id);
1480 const char *isl_constraint_get_dim_name(
1481 __isl_keep isl_constraint *constraint,
1482 enum isl_dim_type type, unsigned pos);
1483 const char *isl_basic_set_get_dim_name(
1484 __isl_keep isl_basic_set *bset,
1485 enum isl_dim_type type, unsigned pos);
1486 const char *isl_set_get_dim_name(
1487 __isl_keep isl_set *set,
1488 enum isl_dim_type type, unsigned pos);
1489 const char *isl_basic_map_get_dim_name(
1490 __isl_keep isl_basic_map *bmap,
1491 enum isl_dim_type type, unsigned pos);
1492 const char *isl_map_get_dim_name(
1493 __isl_keep isl_map *map,
1494 enum isl_dim_type type, unsigned pos);
1496 These functions are mostly useful to obtain the identifiers, positions
1497 or names of the parameters. Identifiers of individual dimensions are
1498 essentially only useful for printing. They are ignored by all other
1499 operations and may not be preserved across those operations.
1503 =head3 Unary Properties
1509 The following functions test whether the given set or relation
1510 contains any integer points. The ``plain'' variants do not perform
1511 any computations, but simply check if the given set or relation
1512 is already known to be empty.
1514 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1515 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1516 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1517 int isl_set_is_empty(__isl_keep isl_set *set);
1518 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1519 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1520 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1521 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1522 int isl_map_is_empty(__isl_keep isl_map *map);
1523 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1525 =item * Universality
1527 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1528 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1529 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1531 =item * Single-valuedness
1533 int isl_map_is_single_valued(__isl_keep isl_map *map);
1534 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1538 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1539 int isl_map_is_injective(__isl_keep isl_map *map);
1540 int isl_union_map_plain_is_injective(
1541 __isl_keep isl_union_map *umap);
1542 int isl_union_map_is_injective(
1543 __isl_keep isl_union_map *umap);
1547 int isl_map_is_bijective(__isl_keep isl_map *map);
1548 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1552 int isl_basic_map_plain_is_fixed(
1553 __isl_keep isl_basic_map *bmap,
1554 enum isl_dim_type type, unsigned pos,
1556 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1557 enum isl_dim_type type, unsigned pos,
1559 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1560 enum isl_dim_type type, unsigned pos,
1563 Check if the relation obviously lies on a hyperplane where the given dimension
1564 has a fixed value and if so, return that value in C<*val>.
1568 To check whether a set is a parameter domain, use this function:
1570 int isl_set_is_params(__isl_keep isl_set *set);
1574 The following functions check whether the domain of the given
1575 (basic) set is a wrapped relation.
1577 int isl_basic_set_is_wrapping(
1578 __isl_keep isl_basic_set *bset);
1579 int isl_set_is_wrapping(__isl_keep isl_set *set);
1581 =item * Internal Product
1583 int isl_basic_map_can_zip(
1584 __isl_keep isl_basic_map *bmap);
1585 int isl_map_can_zip(__isl_keep isl_map *map);
1587 Check whether the product of domain and range of the given relation
1589 i.e., whether both domain and range are nested relations.
1593 =head3 Binary Properties
1599 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1600 __isl_keep isl_set *set2);
1601 int isl_set_is_equal(__isl_keep isl_set *set1,
1602 __isl_keep isl_set *set2);
1603 int isl_union_set_is_equal(
1604 __isl_keep isl_union_set *uset1,
1605 __isl_keep isl_union_set *uset2);
1606 int isl_basic_map_is_equal(
1607 __isl_keep isl_basic_map *bmap1,
1608 __isl_keep isl_basic_map *bmap2);
1609 int isl_map_is_equal(__isl_keep isl_map *map1,
1610 __isl_keep isl_map *map2);
1611 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1612 __isl_keep isl_map *map2);
1613 int isl_union_map_is_equal(
1614 __isl_keep isl_union_map *umap1,
1615 __isl_keep isl_union_map *umap2);
1617 =item * Disjointness
1619 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1620 __isl_keep isl_set *set2);
1624 int isl_set_is_subset(__isl_keep isl_set *set1,
1625 __isl_keep isl_set *set2);
1626 int isl_set_is_strict_subset(
1627 __isl_keep isl_set *set1,
1628 __isl_keep isl_set *set2);
1629 int isl_union_set_is_subset(
1630 __isl_keep isl_union_set *uset1,
1631 __isl_keep isl_union_set *uset2);
1632 int isl_union_set_is_strict_subset(
1633 __isl_keep isl_union_set *uset1,
1634 __isl_keep isl_union_set *uset2);
1635 int isl_basic_map_is_subset(
1636 __isl_keep isl_basic_map *bmap1,
1637 __isl_keep isl_basic_map *bmap2);
1638 int isl_basic_map_is_strict_subset(
1639 __isl_keep isl_basic_map *bmap1,
1640 __isl_keep isl_basic_map *bmap2);
1641 int isl_map_is_subset(
1642 __isl_keep isl_map *map1,
1643 __isl_keep isl_map *map2);
1644 int isl_map_is_strict_subset(
1645 __isl_keep isl_map *map1,
1646 __isl_keep isl_map *map2);
1647 int isl_union_map_is_subset(
1648 __isl_keep isl_union_map *umap1,
1649 __isl_keep isl_union_map *umap2);
1650 int isl_union_map_is_strict_subset(
1651 __isl_keep isl_union_map *umap1,
1652 __isl_keep isl_union_map *umap2);
1656 =head2 Unary Operations
1662 __isl_give isl_set *isl_set_complement(
1663 __isl_take isl_set *set);
1667 __isl_give isl_basic_map *isl_basic_map_reverse(
1668 __isl_take isl_basic_map *bmap);
1669 __isl_give isl_map *isl_map_reverse(
1670 __isl_take isl_map *map);
1671 __isl_give isl_union_map *isl_union_map_reverse(
1672 __isl_take isl_union_map *umap);
1676 __isl_give isl_basic_set *isl_basic_set_project_out(
1677 __isl_take isl_basic_set *bset,
1678 enum isl_dim_type type, unsigned first, unsigned n);
1679 __isl_give isl_basic_map *isl_basic_map_project_out(
1680 __isl_take isl_basic_map *bmap,
1681 enum isl_dim_type type, unsigned first, unsigned n);
1682 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1683 enum isl_dim_type type, unsigned first, unsigned n);
1684 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1685 enum isl_dim_type type, unsigned first, unsigned n);
1686 __isl_give isl_basic_set *isl_basic_set_params(
1687 __isl_take isl_basic_set *bset);
1688 __isl_give isl_basic_set *isl_basic_map_domain(
1689 __isl_take isl_basic_map *bmap);
1690 __isl_give isl_basic_set *isl_basic_map_range(
1691 __isl_take isl_basic_map *bmap);
1692 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1693 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1694 __isl_give isl_set *isl_map_domain(
1695 __isl_take isl_map *bmap);
1696 __isl_give isl_set *isl_map_range(
1697 __isl_take isl_map *map);
1698 __isl_give isl_union_set *isl_union_map_domain(
1699 __isl_take isl_union_map *umap);
1700 __isl_give isl_union_set *isl_union_map_range(
1701 __isl_take isl_union_map *umap);
1703 __isl_give isl_basic_map *isl_basic_map_domain_map(
1704 __isl_take isl_basic_map *bmap);
1705 __isl_give isl_basic_map *isl_basic_map_range_map(
1706 __isl_take isl_basic_map *bmap);
1707 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1708 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1709 __isl_give isl_union_map *isl_union_map_domain_map(
1710 __isl_take isl_union_map *umap);
1711 __isl_give isl_union_map *isl_union_map_range_map(
1712 __isl_take isl_union_map *umap);
1714 The functions above construct a (basic, regular or union) relation
1715 that maps (a wrapped version of) the input relation to its domain or range.
1719 __isl_give isl_set *isl_set_eliminate(
1720 __isl_take isl_set *set, enum isl_dim_type type,
1721 unsigned first, unsigned n);
1723 Eliminate the coefficients for the given dimensions from the constraints,
1724 without removing the dimensions.
1728 __isl_give isl_basic_set *isl_basic_set_fix(
1729 __isl_take isl_basic_set *bset,
1730 enum isl_dim_type type, unsigned pos,
1732 __isl_give isl_basic_set *isl_basic_set_fix_si(
1733 __isl_take isl_basic_set *bset,
1734 enum isl_dim_type type, unsigned pos, int value);
1735 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1736 enum isl_dim_type type, unsigned pos,
1738 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1739 enum isl_dim_type type, unsigned pos, int value);
1740 __isl_give isl_basic_map *isl_basic_map_fix_si(
1741 __isl_take isl_basic_map *bmap,
1742 enum isl_dim_type type, unsigned pos, int value);
1743 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1744 enum isl_dim_type type, unsigned pos, int value);
1746 Intersect the set or relation with the hyperplane where the given
1747 dimension has the fixed given value.
1749 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1750 enum isl_dim_type type1, int pos1,
1751 enum isl_dim_type type2, int pos2);
1752 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1753 enum isl_dim_type type1, int pos1,
1754 enum isl_dim_type type2, int pos2);
1756 Intersect the set or relation with the hyperplane where the given
1757 dimensions are equal to each other.
1759 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1760 enum isl_dim_type type1, int pos1,
1761 enum isl_dim_type type2, int pos2);
1763 Intersect the relation with the hyperplane where the given
1764 dimensions have opposite values.
1768 __isl_give isl_map *isl_set_identity(
1769 __isl_take isl_set *set);
1770 __isl_give isl_union_map *isl_union_set_identity(
1771 __isl_take isl_union_set *uset);
1773 Construct an identity relation on the given (union) set.
1777 __isl_give isl_basic_set *isl_basic_map_deltas(
1778 __isl_take isl_basic_map *bmap);
1779 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1780 __isl_give isl_union_set *isl_union_map_deltas(
1781 __isl_take isl_union_map *umap);
1783 These functions return a (basic) set containing the differences
1784 between image elements and corresponding domain elements in the input.
1786 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1787 __isl_take isl_basic_map *bmap);
1788 __isl_give isl_map *isl_map_deltas_map(
1789 __isl_take isl_map *map);
1790 __isl_give isl_union_map *isl_union_map_deltas_map(
1791 __isl_take isl_union_map *umap);
1793 The functions above construct a (basic, regular or union) relation
1794 that maps (a wrapped version of) the input relation to its delta set.
1798 Simplify the representation of a set or relation by trying
1799 to combine pairs of basic sets or relations into a single
1800 basic set or relation.
1802 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1803 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1804 __isl_give isl_union_set *isl_union_set_coalesce(
1805 __isl_take isl_union_set *uset);
1806 __isl_give isl_union_map *isl_union_map_coalesce(
1807 __isl_take isl_union_map *umap);
1809 =item * Detecting equalities
1811 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1812 __isl_take isl_basic_set *bset);
1813 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1814 __isl_take isl_basic_map *bmap);
1815 __isl_give isl_set *isl_set_detect_equalities(
1816 __isl_take isl_set *set);
1817 __isl_give isl_map *isl_map_detect_equalities(
1818 __isl_take isl_map *map);
1819 __isl_give isl_union_set *isl_union_set_detect_equalities(
1820 __isl_take isl_union_set *uset);
1821 __isl_give isl_union_map *isl_union_map_detect_equalities(
1822 __isl_take isl_union_map *umap);
1824 Simplify the representation of a set or relation by detecting implicit
1827 =item * Removing redundant constraints
1829 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1830 __isl_take isl_basic_set *bset);
1831 __isl_give isl_set *isl_set_remove_redundancies(
1832 __isl_take isl_set *set);
1833 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1834 __isl_take isl_basic_map *bmap);
1835 __isl_give isl_map *isl_map_remove_redundancies(
1836 __isl_take isl_map *map);
1840 __isl_give isl_basic_set *isl_set_convex_hull(
1841 __isl_take isl_set *set);
1842 __isl_give isl_basic_map *isl_map_convex_hull(
1843 __isl_take isl_map *map);
1845 If the input set or relation has any existentially quantified
1846 variables, then the result of these operations is currently undefined.
1850 __isl_give isl_basic_set *isl_set_simple_hull(
1851 __isl_take isl_set *set);
1852 __isl_give isl_basic_map *isl_map_simple_hull(
1853 __isl_take isl_map *map);
1854 __isl_give isl_union_map *isl_union_map_simple_hull(
1855 __isl_take isl_union_map *umap);
1857 These functions compute a single basic set or relation
1858 that contains the whole input set or relation.
1859 In particular, the output is described by translates
1860 of the constraints describing the basic sets or relations in the input.
1864 (See \autoref{s:simple hull}.)
1870 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1871 __isl_take isl_basic_set *bset);
1872 __isl_give isl_basic_set *isl_set_affine_hull(
1873 __isl_take isl_set *set);
1874 __isl_give isl_union_set *isl_union_set_affine_hull(
1875 __isl_take isl_union_set *uset);
1876 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1877 __isl_take isl_basic_map *bmap);
1878 __isl_give isl_basic_map *isl_map_affine_hull(
1879 __isl_take isl_map *map);
1880 __isl_give isl_union_map *isl_union_map_affine_hull(
1881 __isl_take isl_union_map *umap);
1883 In case of union sets and relations, the affine hull is computed
1886 =item * Polyhedral hull
1888 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1889 __isl_take isl_set *set);
1890 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1891 __isl_take isl_map *map);
1892 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1893 __isl_take isl_union_set *uset);
1894 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1895 __isl_take isl_union_map *umap);
1897 These functions compute a single basic set or relation
1898 not involving any existentially quantified variables
1899 that contains the whole input set or relation.
1900 In case of union sets and relations, the polyhedral hull is computed
1903 =item * Optimization
1905 #include <isl/ilp.h>
1906 enum isl_lp_result isl_basic_set_max(
1907 __isl_keep isl_basic_set *bset,
1908 __isl_keep isl_aff *obj, isl_int *opt)
1909 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1910 __isl_keep isl_aff *obj, isl_int *opt);
1911 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1912 __isl_keep isl_aff *obj, isl_int *opt);
1914 Compute the minimum or maximum of the integer affine expression C<obj>
1915 over the points in C<set>, returning the result in C<opt>.
1916 The return value may be one of C<isl_lp_error>,
1917 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1919 =item * Parametric optimization
1921 __isl_give isl_pw_aff *isl_set_dim_min(
1922 __isl_take isl_set *set, int pos);
1923 __isl_give isl_pw_aff *isl_set_dim_max(
1924 __isl_take isl_set *set, int pos);
1926 Compute the minimum or maximum of the given set dimension as a function of the
1927 parameters, but independently of the other set dimensions.
1928 For lexicographic optimization, see L<"Lexicographic Optimization">.
1932 The following functions compute either the set of (rational) coefficient
1933 values of valid constraints for the given set or the set of (rational)
1934 values satisfying the constraints with coefficients from the given set.
1935 Internally, these two sets of functions perform essentially the
1936 same operations, except that the set of coefficients is assumed to
1937 be a cone, while the set of values may be any polyhedron.
1938 The current implementation is based on the Farkas lemma and
1939 Fourier-Motzkin elimination, but this may change or be made optional
1940 in future. In particular, future implementations may use different
1941 dualization algorithms or skip the elimination step.
1943 __isl_give isl_basic_set *isl_basic_set_coefficients(
1944 __isl_take isl_basic_set *bset);
1945 __isl_give isl_basic_set *isl_set_coefficients(
1946 __isl_take isl_set *set);
1947 __isl_give isl_union_set *isl_union_set_coefficients(
1948 __isl_take isl_union_set *bset);
1949 __isl_give isl_basic_set *isl_basic_set_solutions(
1950 __isl_take isl_basic_set *bset);
1951 __isl_give isl_basic_set *isl_set_solutions(
1952 __isl_take isl_set *set);
1953 __isl_give isl_union_set *isl_union_set_solutions(
1954 __isl_take isl_union_set *bset);
1958 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1960 __isl_give isl_union_map *isl_union_map_power(
1961 __isl_take isl_union_map *umap, int *exact);
1963 Compute a parametric representation for all positive powers I<k> of C<map>.
1964 The result maps I<k> to a nested relation corresponding to the
1965 I<k>th power of C<map>.
1966 The result may be an overapproximation. If the result is known to be exact,
1967 then C<*exact> is set to C<1>.
1969 =item * Transitive closure
1971 __isl_give isl_map *isl_map_transitive_closure(
1972 __isl_take isl_map *map, int *exact);
1973 __isl_give isl_union_map *isl_union_map_transitive_closure(
1974 __isl_take isl_union_map *umap, int *exact);
1976 Compute the transitive closure of C<map>.
1977 The result may be an overapproximation. If the result is known to be exact,
1978 then C<*exact> is set to C<1>.
1980 =item * Reaching path lengths
1982 __isl_give isl_map *isl_map_reaching_path_lengths(
1983 __isl_take isl_map *map, int *exact);
1985 Compute a relation that maps each element in the range of C<map>
1986 to the lengths of all paths composed of edges in C<map> that
1987 end up in the given element.
1988 The result may be an overapproximation. If the result is known to be exact,
1989 then C<*exact> is set to C<1>.
1990 To compute the I<maximal> path length, the resulting relation
1991 should be postprocessed by C<isl_map_lexmax>.
1992 In particular, if the input relation is a dependence relation
1993 (mapping sources to sinks), then the maximal path length corresponds
1994 to the free schedule.
1995 Note, however, that C<isl_map_lexmax> expects the maximum to be
1996 finite, so if the path lengths are unbounded (possibly due to
1997 the overapproximation), then you will get an error message.
2001 __isl_give isl_basic_set *isl_basic_map_wrap(
2002 __isl_take isl_basic_map *bmap);
2003 __isl_give isl_set *isl_map_wrap(
2004 __isl_take isl_map *map);
2005 __isl_give isl_union_set *isl_union_map_wrap(
2006 __isl_take isl_union_map *umap);
2007 __isl_give isl_basic_map *isl_basic_set_unwrap(
2008 __isl_take isl_basic_set *bset);
2009 __isl_give isl_map *isl_set_unwrap(
2010 __isl_take isl_set *set);
2011 __isl_give isl_union_map *isl_union_set_unwrap(
2012 __isl_take isl_union_set *uset);
2016 Remove any internal structure of domain (and range) of the given
2017 set or relation. If there is any such internal structure in the input,
2018 then the name of the space is also removed.
2020 __isl_give isl_basic_set *isl_basic_set_flatten(
2021 __isl_take isl_basic_set *bset);
2022 __isl_give isl_set *isl_set_flatten(
2023 __isl_take isl_set *set);
2024 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2025 __isl_take isl_basic_map *bmap);
2026 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2027 __isl_take isl_basic_map *bmap);
2028 __isl_give isl_map *isl_map_flatten_range(
2029 __isl_take isl_map *map);
2030 __isl_give isl_map *isl_map_flatten_domain(
2031 __isl_take isl_map *map);
2032 __isl_give isl_basic_map *isl_basic_map_flatten(
2033 __isl_take isl_basic_map *bmap);
2034 __isl_give isl_map *isl_map_flatten(
2035 __isl_take isl_map *map);
2037 __isl_give isl_map *isl_set_flatten_map(
2038 __isl_take isl_set *set);
2040 The function above constructs a relation
2041 that maps the input set to a flattened version of the set.
2045 Lift the input set to a space with extra dimensions corresponding
2046 to the existentially quantified variables in the input.
2047 In particular, the result lives in a wrapped map where the domain
2048 is the original space and the range corresponds to the original
2049 existentially quantified variables.
2051 __isl_give isl_basic_set *isl_basic_set_lift(
2052 __isl_take isl_basic_set *bset);
2053 __isl_give isl_set *isl_set_lift(
2054 __isl_take isl_set *set);
2055 __isl_give isl_union_set *isl_union_set_lift(
2056 __isl_take isl_union_set *uset);
2058 =item * Internal Product
2060 __isl_give isl_basic_map *isl_basic_map_zip(
2061 __isl_take isl_basic_map *bmap);
2062 __isl_give isl_map *isl_map_zip(
2063 __isl_take isl_map *map);
2064 __isl_give isl_union_map *isl_union_map_zip(
2065 __isl_take isl_union_map *umap);
2067 Given a relation with nested relations for domain and range,
2068 interchange the range of the domain with the domain of the range.
2070 =item * Aligning parameters
2072 __isl_give isl_set *isl_set_align_params(
2073 __isl_take isl_set *set,
2074 __isl_take isl_space *model);
2075 __isl_give isl_map *isl_map_align_params(
2076 __isl_take isl_map *map,
2077 __isl_take isl_space *model);
2079 Change the order of the parameters of the given set or relation
2080 such that the first parameters match those of C<model>.
2081 This may involve the introduction of extra parameters.
2082 All parameters need to be named.
2084 =item * Dimension manipulation
2086 __isl_give isl_set *isl_set_add_dims(
2087 __isl_take isl_set *set,
2088 enum isl_dim_type type, unsigned n);
2089 __isl_give isl_map *isl_map_add_dims(
2090 __isl_take isl_map *map,
2091 enum isl_dim_type type, unsigned n);
2092 __isl_give isl_set *isl_set_insert_dims(
2093 __isl_take isl_set *set,
2094 enum isl_dim_type type, unsigned pos, unsigned n);
2095 __isl_give isl_map *isl_map_insert_dims(
2096 __isl_take isl_map *map,
2097 enum isl_dim_type type, unsigned pos, unsigned n);
2098 __isl_give isl_basic_set *isl_basic_set_move_dims(
2099 __isl_take isl_basic_set *bset,
2100 enum isl_dim_type dst_type, unsigned dst_pos,
2101 enum isl_dim_type src_type, unsigned src_pos,
2103 __isl_give isl_basic_map *isl_basic_map_move_dims(
2104 __isl_take isl_basic_map *bmap,
2105 enum isl_dim_type dst_type, unsigned dst_pos,
2106 enum isl_dim_type src_type, unsigned src_pos,
2108 __isl_give isl_set *isl_set_move_dims(
2109 __isl_take isl_set *set,
2110 enum isl_dim_type dst_type, unsigned dst_pos,
2111 enum isl_dim_type src_type, unsigned src_pos,
2113 __isl_give isl_map *isl_map_move_dims(
2114 __isl_take isl_map *map,
2115 enum isl_dim_type dst_type, unsigned dst_pos,
2116 enum isl_dim_type src_type, unsigned src_pos,
2119 It is usually not advisable to directly change the (input or output)
2120 space of a set or a relation as this removes the name and the internal
2121 structure of the space. However, the above functions can be useful
2122 to add new parameters, assuming
2123 C<isl_set_align_params> and C<isl_map_align_params>
2128 =head2 Binary Operations
2130 The two arguments of a binary operation not only need to live
2131 in the same C<isl_ctx>, they currently also need to have
2132 the same (number of) parameters.
2134 =head3 Basic Operations
2138 =item * Intersection
2140 __isl_give isl_basic_set *isl_basic_set_intersect(
2141 __isl_take isl_basic_set *bset1,
2142 __isl_take isl_basic_set *bset2);
2143 __isl_give isl_set *isl_set_intersect_params(
2144 __isl_take isl_set *set,
2145 __isl_take isl_set *params);
2146 __isl_give isl_set *isl_set_intersect(
2147 __isl_take isl_set *set1,
2148 __isl_take isl_set *set2);
2149 __isl_give isl_union_set *isl_union_set_intersect(
2150 __isl_take isl_union_set *uset1,
2151 __isl_take isl_union_set *uset2);
2152 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2153 __isl_take isl_basic_map *bmap,
2154 __isl_take isl_basic_set *bset);
2155 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2156 __isl_take isl_basic_map *bmap,
2157 __isl_take isl_basic_set *bset);
2158 __isl_give isl_basic_map *isl_basic_map_intersect(
2159 __isl_take isl_basic_map *bmap1,
2160 __isl_take isl_basic_map *bmap2);
2161 __isl_give isl_map *isl_map_intersect_params(
2162 __isl_take isl_map *map,
2163 __isl_take isl_set *params);
2164 __isl_give isl_map *isl_map_intersect_domain(
2165 __isl_take isl_map *map,
2166 __isl_take isl_set *set);
2167 __isl_give isl_map *isl_map_intersect_range(
2168 __isl_take isl_map *map,
2169 __isl_take isl_set *set);
2170 __isl_give isl_map *isl_map_intersect(
2171 __isl_take isl_map *map1,
2172 __isl_take isl_map *map2);
2173 __isl_give isl_union_map *isl_union_map_intersect_domain(
2174 __isl_take isl_union_map *umap,
2175 __isl_take isl_union_set *uset);
2176 __isl_give isl_union_map *isl_union_map_intersect_range(
2177 __isl_take isl_union_map *umap,
2178 __isl_take isl_union_set *uset);
2179 __isl_give isl_union_map *isl_union_map_intersect(
2180 __isl_take isl_union_map *umap1,
2181 __isl_take isl_union_map *umap2);
2185 __isl_give isl_set *isl_basic_set_union(
2186 __isl_take isl_basic_set *bset1,
2187 __isl_take isl_basic_set *bset2);
2188 __isl_give isl_map *isl_basic_map_union(
2189 __isl_take isl_basic_map *bmap1,
2190 __isl_take isl_basic_map *bmap2);
2191 __isl_give isl_set *isl_set_union(
2192 __isl_take isl_set *set1,
2193 __isl_take isl_set *set2);
2194 __isl_give isl_map *isl_map_union(
2195 __isl_take isl_map *map1,
2196 __isl_take isl_map *map2);
2197 __isl_give isl_union_set *isl_union_set_union(
2198 __isl_take isl_union_set *uset1,
2199 __isl_take isl_union_set *uset2);
2200 __isl_give isl_union_map *isl_union_map_union(
2201 __isl_take isl_union_map *umap1,
2202 __isl_take isl_union_map *umap2);
2204 =item * Set difference
2206 __isl_give isl_set *isl_set_subtract(
2207 __isl_take isl_set *set1,
2208 __isl_take isl_set *set2);
2209 __isl_give isl_map *isl_map_subtract(
2210 __isl_take isl_map *map1,
2211 __isl_take isl_map *map2);
2212 __isl_give isl_union_set *isl_union_set_subtract(
2213 __isl_take isl_union_set *uset1,
2214 __isl_take isl_union_set *uset2);
2215 __isl_give isl_union_map *isl_union_map_subtract(
2216 __isl_take isl_union_map *umap1,
2217 __isl_take isl_union_map *umap2);
2221 __isl_give isl_basic_set *isl_basic_set_apply(
2222 __isl_take isl_basic_set *bset,
2223 __isl_take isl_basic_map *bmap);
2224 __isl_give isl_set *isl_set_apply(
2225 __isl_take isl_set *set,
2226 __isl_take isl_map *map);
2227 __isl_give isl_union_set *isl_union_set_apply(
2228 __isl_take isl_union_set *uset,
2229 __isl_take isl_union_map *umap);
2230 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2231 __isl_take isl_basic_map *bmap1,
2232 __isl_take isl_basic_map *bmap2);
2233 __isl_give isl_basic_map *isl_basic_map_apply_range(
2234 __isl_take isl_basic_map *bmap1,
2235 __isl_take isl_basic_map *bmap2);
2236 __isl_give isl_map *isl_map_apply_domain(
2237 __isl_take isl_map *map1,
2238 __isl_take isl_map *map2);
2239 __isl_give isl_union_map *isl_union_map_apply_domain(
2240 __isl_take isl_union_map *umap1,
2241 __isl_take isl_union_map *umap2);
2242 __isl_give isl_map *isl_map_apply_range(
2243 __isl_take isl_map *map1,
2244 __isl_take isl_map *map2);
2245 __isl_give isl_union_map *isl_union_map_apply_range(
2246 __isl_take isl_union_map *umap1,
2247 __isl_take isl_union_map *umap2);
2249 =item * Cartesian Product
2251 __isl_give isl_set *isl_set_product(
2252 __isl_take isl_set *set1,
2253 __isl_take isl_set *set2);
2254 __isl_give isl_union_set *isl_union_set_product(
2255 __isl_take isl_union_set *uset1,
2256 __isl_take isl_union_set *uset2);
2257 __isl_give isl_basic_map *isl_basic_map_domain_product(
2258 __isl_take isl_basic_map *bmap1,
2259 __isl_take isl_basic_map *bmap2);
2260 __isl_give isl_basic_map *isl_basic_map_range_product(
2261 __isl_take isl_basic_map *bmap1,
2262 __isl_take isl_basic_map *bmap2);
2263 __isl_give isl_map *isl_map_domain_product(
2264 __isl_take isl_map *map1,
2265 __isl_take isl_map *map2);
2266 __isl_give isl_map *isl_map_range_product(
2267 __isl_take isl_map *map1,
2268 __isl_take isl_map *map2);
2269 __isl_give isl_union_map *isl_union_map_range_product(
2270 __isl_take isl_union_map *umap1,
2271 __isl_take isl_union_map *umap2);
2272 __isl_give isl_map *isl_map_product(
2273 __isl_take isl_map *map1,
2274 __isl_take isl_map *map2);
2275 __isl_give isl_union_map *isl_union_map_product(
2276 __isl_take isl_union_map *umap1,
2277 __isl_take isl_union_map *umap2);
2279 The above functions compute the cross product of the given
2280 sets or relations. The domains and ranges of the results
2281 are wrapped maps between domains and ranges of the inputs.
2282 To obtain a ``flat'' product, use the following functions
2285 __isl_give isl_basic_set *isl_basic_set_flat_product(
2286 __isl_take isl_basic_set *bset1,
2287 __isl_take isl_basic_set *bset2);
2288 __isl_give isl_set *isl_set_flat_product(
2289 __isl_take isl_set *set1,
2290 __isl_take isl_set *set2);
2291 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2292 __isl_take isl_basic_map *bmap1,
2293 __isl_take isl_basic_map *bmap2);
2294 __isl_give isl_map *isl_map_flat_domain_product(
2295 __isl_take isl_map *map1,
2296 __isl_take isl_map *map2);
2297 __isl_give isl_map *isl_map_flat_range_product(
2298 __isl_take isl_map *map1,
2299 __isl_take isl_map *map2);
2300 __isl_give isl_union_map *isl_union_map_flat_range_product(
2301 __isl_take isl_union_map *umap1,
2302 __isl_take isl_union_map *umap2);
2303 __isl_give isl_basic_map *isl_basic_map_flat_product(
2304 __isl_take isl_basic_map *bmap1,
2305 __isl_take isl_basic_map *bmap2);
2306 __isl_give isl_map *isl_map_flat_product(
2307 __isl_take isl_map *map1,
2308 __isl_take isl_map *map2);
2310 =item * Simplification
2312 __isl_give isl_basic_set *isl_basic_set_gist(
2313 __isl_take isl_basic_set *bset,
2314 __isl_take isl_basic_set *context);
2315 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2316 __isl_take isl_set *context);
2317 __isl_give isl_set *isl_set_gist_params(
2318 __isl_take isl_set *set,
2319 __isl_take isl_set *context);
2320 __isl_give isl_union_set *isl_union_set_gist(
2321 __isl_take isl_union_set *uset,
2322 __isl_take isl_union_set *context);
2323 __isl_give isl_basic_map *isl_basic_map_gist(
2324 __isl_take isl_basic_map *bmap,
2325 __isl_take isl_basic_map *context);
2326 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2327 __isl_take isl_map *context);
2328 __isl_give isl_map *isl_map_gist_params(
2329 __isl_take isl_map *map,
2330 __isl_take isl_set *context);
2331 __isl_give isl_union_map *isl_union_map_gist(
2332 __isl_take isl_union_map *umap,
2333 __isl_take isl_union_map *context);
2335 The gist operation returns a set or relation that has the
2336 same intersection with the context as the input set or relation.
2337 Any implicit equality in the intersection is made explicit in the result,
2338 while all inequalities that are redundant with respect to the intersection
2340 In case of union sets and relations, the gist operation is performed
2345 =head3 Lexicographic Optimization
2347 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2348 the following functions
2349 compute a set that contains the lexicographic minimum or maximum
2350 of the elements in C<set> (or C<bset>) for those values of the parameters
2351 that satisfy C<dom>.
2352 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2353 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2355 In other words, the union of the parameter values
2356 for which the result is non-empty and of C<*empty>
2359 __isl_give isl_set *isl_basic_set_partial_lexmin(
2360 __isl_take isl_basic_set *bset,
2361 __isl_take isl_basic_set *dom,
2362 __isl_give isl_set **empty);
2363 __isl_give isl_set *isl_basic_set_partial_lexmax(
2364 __isl_take isl_basic_set *bset,
2365 __isl_take isl_basic_set *dom,
2366 __isl_give isl_set **empty);
2367 __isl_give isl_set *isl_set_partial_lexmin(
2368 __isl_take isl_set *set, __isl_take isl_set *dom,
2369 __isl_give isl_set **empty);
2370 __isl_give isl_set *isl_set_partial_lexmax(
2371 __isl_take isl_set *set, __isl_take isl_set *dom,
2372 __isl_give isl_set **empty);
2374 Given a (basic) set C<set> (or C<bset>), the following functions simply
2375 return a set containing the lexicographic minimum or maximum
2376 of the elements in C<set> (or C<bset>).
2377 In case of union sets, the optimum is computed per space.
2379 __isl_give isl_set *isl_basic_set_lexmin(
2380 __isl_take isl_basic_set *bset);
2381 __isl_give isl_set *isl_basic_set_lexmax(
2382 __isl_take isl_basic_set *bset);
2383 __isl_give isl_set *isl_set_lexmin(
2384 __isl_take isl_set *set);
2385 __isl_give isl_set *isl_set_lexmax(
2386 __isl_take isl_set *set);
2387 __isl_give isl_union_set *isl_union_set_lexmin(
2388 __isl_take isl_union_set *uset);
2389 __isl_give isl_union_set *isl_union_set_lexmax(
2390 __isl_take isl_union_set *uset);
2392 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2393 the following functions
2394 compute a relation that maps each element of C<dom>
2395 to the single lexicographic minimum or maximum
2396 of the elements that are associated to that same
2397 element in C<map> (or C<bmap>).
2398 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2399 that contains the elements in C<dom> that do not map
2400 to any elements in C<map> (or C<bmap>).
2401 In other words, the union of the domain of the result and of C<*empty>
2404 __isl_give isl_map *isl_basic_map_partial_lexmax(
2405 __isl_take isl_basic_map *bmap,
2406 __isl_take isl_basic_set *dom,
2407 __isl_give isl_set **empty);
2408 __isl_give isl_map *isl_basic_map_partial_lexmin(
2409 __isl_take isl_basic_map *bmap,
2410 __isl_take isl_basic_set *dom,
2411 __isl_give isl_set **empty);
2412 __isl_give isl_map *isl_map_partial_lexmax(
2413 __isl_take isl_map *map, __isl_take isl_set *dom,
2414 __isl_give isl_set **empty);
2415 __isl_give isl_map *isl_map_partial_lexmin(
2416 __isl_take isl_map *map, __isl_take isl_set *dom,
2417 __isl_give isl_set **empty);
2419 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2420 return a map mapping each element in the domain of
2421 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2422 of all elements associated to that element.
2423 In case of union relations, the optimum is computed per space.
2425 __isl_give isl_map *isl_basic_map_lexmin(
2426 __isl_take isl_basic_map *bmap);
2427 __isl_give isl_map *isl_basic_map_lexmax(
2428 __isl_take isl_basic_map *bmap);
2429 __isl_give isl_map *isl_map_lexmin(
2430 __isl_take isl_map *map);
2431 __isl_give isl_map *isl_map_lexmax(
2432 __isl_take isl_map *map);
2433 __isl_give isl_union_map *isl_union_map_lexmin(
2434 __isl_take isl_union_map *umap);
2435 __isl_give isl_union_map *isl_union_map_lexmax(
2436 __isl_take isl_union_map *umap);
2440 Lists are defined over several element types, including
2441 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2442 Here we take lists of C<isl_set>s as an example.
2443 Lists can be created, copied and freed using the following functions.
2445 #include <isl/list.h>
2446 __isl_give isl_set_list *isl_set_list_from_set(
2447 __isl_take isl_set *el);
2448 __isl_give isl_set_list *isl_set_list_alloc(
2449 isl_ctx *ctx, int n);
2450 __isl_give isl_set_list *isl_set_list_copy(
2451 __isl_keep isl_set_list *list);
2452 __isl_give isl_set_list *isl_set_list_add(
2453 __isl_take isl_set_list *list,
2454 __isl_take isl_set *el);
2455 __isl_give isl_set_list *isl_set_list_concat(
2456 __isl_take isl_set_list *list1,
2457 __isl_take isl_set_list *list2);
2458 void *isl_set_list_free(__isl_take isl_set_list *list);
2460 C<isl_set_list_alloc> creates an empty list with a capacity for
2461 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2464 Lists can be inspected using the following functions.
2466 #include <isl/list.h>
2467 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2468 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2469 __isl_give isl_set *isl_set_list_get_set(
2470 __isl_keep isl_set_list *list, int index);
2471 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2472 int (*fn)(__isl_take isl_set *el, void *user),
2475 Lists can be printed using
2477 #include <isl/list.h>
2478 __isl_give isl_printer *isl_printer_print_set_list(
2479 __isl_take isl_printer *p,
2480 __isl_keep isl_set_list *list);
2484 Matrices can be created, copied and freed using the following functions.
2486 #include <isl/mat.h>
2487 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2488 unsigned n_row, unsigned n_col);
2489 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2490 void isl_mat_free(__isl_take isl_mat *mat);
2492 Note that the elements of a newly created matrix may have arbitrary values.
2493 The elements can be changed and inspected using the following functions.
2495 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2496 int isl_mat_rows(__isl_keep isl_mat *mat);
2497 int isl_mat_cols(__isl_keep isl_mat *mat);
2498 int isl_mat_get_element(__isl_keep isl_mat *mat,
2499 int row, int col, isl_int *v);
2500 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2501 int row, int col, isl_int v);
2502 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2503 int row, int col, int v);
2505 C<isl_mat_get_element> will return a negative value if anything went wrong.
2506 In that case, the value of C<*v> is undefined.
2508 The following function can be used to compute the (right) inverse
2509 of a matrix, i.e., a matrix such that the product of the original
2510 and the inverse (in that order) is a multiple of the identity matrix.
2511 The input matrix is assumed to be of full row-rank.
2513 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2515 The following function can be used to compute the (right) kernel
2516 (or null space) of a matrix, i.e., a matrix such that the product of
2517 the original and the kernel (in that order) is the zero matrix.
2519 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2521 =head2 Piecewise Quasi Affine Expressions
2523 The zero quasi affine expression on a given domain can be created using
2525 __isl_give isl_aff *isl_aff_zero_on_domain(
2526 __isl_take isl_local_space *ls);
2528 Note that the space in which the resulting object lives is a map space
2529 with the given space as domain and a one-dimensional range.
2531 An empty piecewise quasi affine expression (one with no cells)
2532 or a piecewise quasi affine expression with a single cell can
2533 be created using the following functions.
2535 #include <isl/aff.h>
2536 __isl_give isl_pw_aff *isl_pw_aff_empty(
2537 __isl_take isl_space *space);
2538 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2539 __isl_take isl_set *set, __isl_take isl_aff *aff);
2540 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2541 __isl_take isl_aff *aff);
2543 Quasi affine expressions can be copied and freed using
2545 #include <isl/aff.h>
2546 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2547 void *isl_aff_free(__isl_take isl_aff *aff);
2549 __isl_give isl_pw_aff *isl_pw_aff_copy(
2550 __isl_keep isl_pw_aff *pwaff);
2551 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2553 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2554 using the following function. The constraint is required to have
2555 a non-zero coefficient for the specified dimension.
2557 #include <isl/constraint.h>
2558 __isl_give isl_aff *isl_constraint_get_bound(
2559 __isl_keep isl_constraint *constraint,
2560 enum isl_dim_type type, int pos);
2562 The entire affine expression of the constraint can also be extracted
2563 using the following function.
2565 #include <isl/constraint.h>
2566 __isl_give isl_aff *isl_constraint_get_aff(
2567 __isl_keep isl_constraint *constraint);
2569 Conversely, an equality constraint equating
2570 the affine expression to zero or an inequality constraint enforcing
2571 the affine expression to be non-negative, can be constructed using
2573 __isl_give isl_constraint *isl_equality_from_aff(
2574 __isl_take isl_aff *aff);
2575 __isl_give isl_constraint *isl_inequality_from_aff(
2576 __isl_take isl_aff *aff);
2578 The expression can be inspected using
2580 #include <isl/aff.h>
2581 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2582 int isl_aff_dim(__isl_keep isl_aff *aff,
2583 enum isl_dim_type type);
2584 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2585 __isl_keep isl_aff *aff);
2586 __isl_give isl_local_space *isl_aff_get_local_space(
2587 __isl_keep isl_aff *aff);
2588 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2589 enum isl_dim_type type, unsigned pos);
2590 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2592 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2593 enum isl_dim_type type, int pos, isl_int *v);
2594 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2596 __isl_give isl_aff *isl_aff_get_div(
2597 __isl_keep isl_aff *aff, int pos);
2599 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2600 int (*fn)(__isl_take isl_set *set,
2601 __isl_take isl_aff *aff,
2602 void *user), void *user);
2604 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2605 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2607 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2608 enum isl_dim_type type, unsigned first, unsigned n);
2609 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2610 enum isl_dim_type type, unsigned first, unsigned n);
2612 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2613 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2614 enum isl_dim_type type);
2615 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2617 It can be modified using
2619 #include <isl/aff.h>
2620 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2621 __isl_take isl_pw_aff *pwaff,
2622 enum isl_dim_type type, __isl_take isl_id *id);
2623 __isl_give isl_aff *isl_aff_set_dim_name(
2624 __isl_take isl_aff *aff, enum isl_dim_type type,
2625 unsigned pos, const char *s);
2626 __isl_give isl_aff *isl_aff_set_constant(
2627 __isl_take isl_aff *aff, isl_int v);
2628 __isl_give isl_aff *isl_aff_set_constant_si(
2629 __isl_take isl_aff *aff, int v);
2630 __isl_give isl_aff *isl_aff_set_coefficient(
2631 __isl_take isl_aff *aff,
2632 enum isl_dim_type type, int pos, isl_int v);
2633 __isl_give isl_aff *isl_aff_set_coefficient_si(
2634 __isl_take isl_aff *aff,
2635 enum isl_dim_type type, int pos, int v);
2636 __isl_give isl_aff *isl_aff_set_denominator(
2637 __isl_take isl_aff *aff, isl_int v);
2639 __isl_give isl_aff *isl_aff_add_constant(
2640 __isl_take isl_aff *aff, isl_int v);
2641 __isl_give isl_aff *isl_aff_add_constant_si(
2642 __isl_take isl_aff *aff, int v);
2643 __isl_give isl_aff *isl_aff_add_coefficient(
2644 __isl_take isl_aff *aff,
2645 enum isl_dim_type type, int pos, isl_int v);
2646 __isl_give isl_aff *isl_aff_add_coefficient_si(
2647 __isl_take isl_aff *aff,
2648 enum isl_dim_type type, int pos, int v);
2650 __isl_give isl_aff *isl_aff_insert_dims(
2651 __isl_take isl_aff *aff,
2652 enum isl_dim_type type, unsigned first, unsigned n);
2653 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2654 __isl_take isl_pw_aff *pwaff,
2655 enum isl_dim_type type, unsigned first, unsigned n);
2656 __isl_give isl_aff *isl_aff_add_dims(
2657 __isl_take isl_aff *aff,
2658 enum isl_dim_type type, unsigned n);
2659 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2660 __isl_take isl_pw_aff *pwaff,
2661 enum isl_dim_type type, unsigned n);
2662 __isl_give isl_aff *isl_aff_drop_dims(
2663 __isl_take isl_aff *aff,
2664 enum isl_dim_type type, unsigned first, unsigned n);
2665 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2666 __isl_take isl_pw_aff *pwaff,
2667 enum isl_dim_type type, unsigned first, unsigned n);
2669 Note that the C<set_constant> and C<set_coefficient> functions
2670 set the I<numerator> of the constant or coefficient, while
2671 C<add_constant> and C<add_coefficient> add an integer value to
2672 the possibly rational constant or coefficient.
2674 To check whether an affine expressions is obviously zero
2675 or obviously equal to some other affine expression, use
2677 #include <isl/aff.h>
2678 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2679 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2680 __isl_keep isl_aff *aff2);
2681 int isl_pw_aff_plain_is_equal(
2682 __isl_keep isl_pw_aff *pwaff1,
2683 __isl_keep isl_pw_aff *pwaff2);
2687 #include <isl/aff.h>
2688 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2689 __isl_take isl_aff *aff2);
2690 __isl_give isl_pw_aff *isl_pw_aff_add(
2691 __isl_take isl_pw_aff *pwaff1,
2692 __isl_take isl_pw_aff *pwaff2);
2693 __isl_give isl_pw_aff *isl_pw_aff_min(
2694 __isl_take isl_pw_aff *pwaff1,
2695 __isl_take isl_pw_aff *pwaff2);
2696 __isl_give isl_pw_aff *isl_pw_aff_max(
2697 __isl_take isl_pw_aff *pwaff1,
2698 __isl_take isl_pw_aff *pwaff2);
2699 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2700 __isl_take isl_aff *aff2);
2701 __isl_give isl_pw_aff *isl_pw_aff_sub(
2702 __isl_take isl_pw_aff *pwaff1,
2703 __isl_take isl_pw_aff *pwaff2);
2704 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2705 __isl_give isl_pw_aff *isl_pw_aff_neg(
2706 __isl_take isl_pw_aff *pwaff);
2707 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2708 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2709 __isl_take isl_pw_aff *pwaff);
2710 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2711 __isl_give isl_pw_aff *isl_pw_aff_floor(
2712 __isl_take isl_pw_aff *pwaff);
2713 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2715 __isl_give isl_pw_aff *isl_pw_aff_mod(
2716 __isl_take isl_pw_aff *pwaff, isl_int mod);
2717 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2719 __isl_give isl_pw_aff *isl_pw_aff_scale(
2720 __isl_take isl_pw_aff *pwaff, isl_int f);
2721 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2723 __isl_give isl_aff *isl_aff_scale_down_ui(
2724 __isl_take isl_aff *aff, unsigned f);
2725 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2726 __isl_take isl_pw_aff *pwaff, isl_int f);
2728 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2729 __isl_take isl_pw_aff_list *list);
2730 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2731 __isl_take isl_pw_aff_list *list);
2733 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2734 __isl_take isl_pw_aff *pwqp);
2736 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2737 __isl_take isl_pw_aff *pwaff,
2738 __isl_take isl_space *model);
2740 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2741 __isl_take isl_set *context);
2742 __isl_give isl_pw_aff *isl_pw_aff_gist(
2743 __isl_take isl_pw_aff *pwaff,
2744 __isl_take isl_set *context);
2746 __isl_give isl_set *isl_pw_aff_domain(
2747 __isl_take isl_pw_aff *pwaff);
2748 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2749 __isl_take isl_pw_aff *pa,
2750 __isl_take isl_set *set);
2752 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2753 __isl_take isl_aff *aff2);
2754 __isl_give isl_pw_aff *isl_pw_aff_mul(
2755 __isl_take isl_pw_aff *pwaff1,
2756 __isl_take isl_pw_aff *pwaff2);
2758 When multiplying two affine expressions, at least one of the two needs
2761 #include <isl/aff.h>
2762 __isl_give isl_basic_set *isl_aff_le_basic_set(
2763 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2764 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2765 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2766 __isl_give isl_set *isl_pw_aff_eq_set(
2767 __isl_take isl_pw_aff *pwaff1,
2768 __isl_take isl_pw_aff *pwaff2);
2769 __isl_give isl_set *isl_pw_aff_ne_set(
2770 __isl_take isl_pw_aff *pwaff1,
2771 __isl_take isl_pw_aff *pwaff2);
2772 __isl_give isl_set *isl_pw_aff_le_set(
2773 __isl_take isl_pw_aff *pwaff1,
2774 __isl_take isl_pw_aff *pwaff2);
2775 __isl_give isl_set *isl_pw_aff_lt_set(
2776 __isl_take isl_pw_aff *pwaff1,
2777 __isl_take isl_pw_aff *pwaff2);
2778 __isl_give isl_set *isl_pw_aff_ge_set(
2779 __isl_take isl_pw_aff *pwaff1,
2780 __isl_take isl_pw_aff *pwaff2);
2781 __isl_give isl_set *isl_pw_aff_gt_set(
2782 __isl_take isl_pw_aff *pwaff1,
2783 __isl_take isl_pw_aff *pwaff2);
2785 __isl_give isl_set *isl_pw_aff_list_eq_set(
2786 __isl_take isl_pw_aff_list *list1,
2787 __isl_take isl_pw_aff_list *list2);
2788 __isl_give isl_set *isl_pw_aff_list_ne_set(
2789 __isl_take isl_pw_aff_list *list1,
2790 __isl_take isl_pw_aff_list *list2);
2791 __isl_give isl_set *isl_pw_aff_list_le_set(
2792 __isl_take isl_pw_aff_list *list1,
2793 __isl_take isl_pw_aff_list *list2);
2794 __isl_give isl_set *isl_pw_aff_list_lt_set(
2795 __isl_take isl_pw_aff_list *list1,
2796 __isl_take isl_pw_aff_list *list2);
2797 __isl_give isl_set *isl_pw_aff_list_ge_set(
2798 __isl_take isl_pw_aff_list *list1,
2799 __isl_take isl_pw_aff_list *list2);
2800 __isl_give isl_set *isl_pw_aff_list_gt_set(
2801 __isl_take isl_pw_aff_list *list1,
2802 __isl_take isl_pw_aff_list *list2);
2804 The function C<isl_aff_ge_basic_set> returns a basic set
2805 containing those elements in the shared space
2806 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2807 The function C<isl_aff_ge_set> returns a set
2808 containing those elements in the shared domain
2809 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2810 The functions operating on C<isl_pw_aff_list> apply the corresponding
2811 C<isl_pw_aff> function to each pair of elements in the two lists.
2813 #include <isl/aff.h>
2814 __isl_give isl_set *isl_pw_aff_nonneg_set(
2815 __isl_take isl_pw_aff *pwaff);
2816 __isl_give isl_set *isl_pw_aff_zero_set(
2817 __isl_take isl_pw_aff *pwaff);
2818 __isl_give isl_set *isl_pw_aff_non_zero_set(
2819 __isl_take isl_pw_aff *pwaff);
2821 The function C<isl_pw_aff_nonneg_set> returns a set
2822 containing those elements in the domain
2823 of C<pwaff> where C<pwaff> is non-negative.
2825 #include <isl/aff.h>
2826 __isl_give isl_pw_aff *isl_pw_aff_cond(
2827 __isl_take isl_set *cond,
2828 __isl_take isl_pw_aff *pwaff_true,
2829 __isl_take isl_pw_aff *pwaff_false);
2831 The function C<isl_pw_aff_cond> performs a conditional operator
2832 and returns an expression that is equal to C<pwaff_true>
2833 for elements in C<cond> and equal to C<pwaff_false> for elements
2836 #include <isl/aff.h>
2837 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2838 __isl_take isl_pw_aff *pwaff1,
2839 __isl_take isl_pw_aff *pwaff2);
2840 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2841 __isl_take isl_pw_aff *pwaff1,
2842 __isl_take isl_pw_aff *pwaff2);
2844 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2845 expression with a domain that is the union of those of C<pwaff1> and
2846 C<pwaff2> and such that on each cell, the quasi-affine expression is
2847 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2848 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2849 associated expression is the defined one.
2851 An expression can be printed using
2853 #include <isl/aff.h>
2854 __isl_give isl_printer *isl_printer_print_aff(
2855 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2857 __isl_give isl_printer *isl_printer_print_pw_aff(
2858 __isl_take isl_printer *p,
2859 __isl_keep isl_pw_aff *pwaff);
2863 Points are elements of a set. They can be used to construct
2864 simple sets (boxes) or they can be used to represent the
2865 individual elements of a set.
2866 The zero point (the origin) can be created using
2868 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2870 The coordinates of a point can be inspected, set and changed
2873 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2874 enum isl_dim_type type, int pos, isl_int *v);
2875 __isl_give isl_point *isl_point_set_coordinate(
2876 __isl_take isl_point *pnt,
2877 enum isl_dim_type type, int pos, isl_int v);
2879 __isl_give isl_point *isl_point_add_ui(
2880 __isl_take isl_point *pnt,
2881 enum isl_dim_type type, int pos, unsigned val);
2882 __isl_give isl_point *isl_point_sub_ui(
2883 __isl_take isl_point *pnt,
2884 enum isl_dim_type type, int pos, unsigned val);
2886 Other properties can be obtained using
2888 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2890 Points can be copied or freed using
2892 __isl_give isl_point *isl_point_copy(
2893 __isl_keep isl_point *pnt);
2894 void isl_point_free(__isl_take isl_point *pnt);
2896 A singleton set can be created from a point using
2898 __isl_give isl_basic_set *isl_basic_set_from_point(
2899 __isl_take isl_point *pnt);
2900 __isl_give isl_set *isl_set_from_point(
2901 __isl_take isl_point *pnt);
2903 and a box can be created from two opposite extremal points using
2905 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2906 __isl_take isl_point *pnt1,
2907 __isl_take isl_point *pnt2);
2908 __isl_give isl_set *isl_set_box_from_points(
2909 __isl_take isl_point *pnt1,
2910 __isl_take isl_point *pnt2);
2912 All elements of a B<bounded> (union) set can be enumerated using
2913 the following functions.
2915 int isl_set_foreach_point(__isl_keep isl_set *set,
2916 int (*fn)(__isl_take isl_point *pnt, void *user),
2918 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2919 int (*fn)(__isl_take isl_point *pnt, void *user),
2922 The function C<fn> is called for each integer point in
2923 C<set> with as second argument the last argument of
2924 the C<isl_set_foreach_point> call. The function C<fn>
2925 should return C<0> on success and C<-1> on failure.
2926 In the latter case, C<isl_set_foreach_point> will stop
2927 enumerating and return C<-1> as well.
2928 If the enumeration is performed successfully and to completion,
2929 then C<isl_set_foreach_point> returns C<0>.
2931 To obtain a single point of a (basic) set, use
2933 __isl_give isl_point *isl_basic_set_sample_point(
2934 __isl_take isl_basic_set *bset);
2935 __isl_give isl_point *isl_set_sample_point(
2936 __isl_take isl_set *set);
2938 If C<set> does not contain any (integer) points, then the
2939 resulting point will be ``void'', a property that can be
2942 int isl_point_is_void(__isl_keep isl_point *pnt);
2944 =head2 Piecewise Quasipolynomials
2946 A piecewise quasipolynomial is a particular kind of function that maps
2947 a parametric point to a rational value.
2948 More specifically, a quasipolynomial is a polynomial expression in greatest
2949 integer parts of affine expressions of parameters and variables.
2950 A piecewise quasipolynomial is a subdivision of a given parametric
2951 domain into disjoint cells with a quasipolynomial associated to
2952 each cell. The value of the piecewise quasipolynomial at a given
2953 point is the value of the quasipolynomial associated to the cell
2954 that contains the point. Outside of the union of cells,
2955 the value is assumed to be zero.
2956 For example, the piecewise quasipolynomial
2958 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2960 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2961 A given piecewise quasipolynomial has a fixed domain dimension.
2962 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2963 defined over different domains.
2964 Piecewise quasipolynomials are mainly used by the C<barvinok>
2965 library for representing the number of elements in a parametric set or map.
2966 For example, the piecewise quasipolynomial above represents
2967 the number of points in the map
2969 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2971 =head3 Printing (Piecewise) Quasipolynomials
2973 Quasipolynomials and piecewise quasipolynomials can be printed
2974 using the following functions.
2976 __isl_give isl_printer *isl_printer_print_qpolynomial(
2977 __isl_take isl_printer *p,
2978 __isl_keep isl_qpolynomial *qp);
2980 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2981 __isl_take isl_printer *p,
2982 __isl_keep isl_pw_qpolynomial *pwqp);
2984 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2985 __isl_take isl_printer *p,
2986 __isl_keep isl_union_pw_qpolynomial *upwqp);
2988 The output format of the printer
2989 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2990 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2992 In case of printing in C<ISL_FORMAT_C>, the user may want
2993 to set the names of all dimensions
2995 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2996 __isl_take isl_qpolynomial *qp,
2997 enum isl_dim_type type, unsigned pos,
2999 __isl_give isl_pw_qpolynomial *
3000 isl_pw_qpolynomial_set_dim_name(
3001 __isl_take isl_pw_qpolynomial *pwqp,
3002 enum isl_dim_type type, unsigned pos,
3005 =head3 Creating New (Piecewise) Quasipolynomials
3007 Some simple quasipolynomials can be created using the following functions.
3008 More complicated quasipolynomials can be created by applying
3009 operations such as addition and multiplication
3010 on the resulting quasipolynomials
3012 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3013 __isl_take isl_space *domain);
3014 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3015 __isl_take isl_space *domain);
3016 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3017 __isl_take isl_space *domain);
3018 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3019 __isl_take isl_space *domain);
3020 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3021 __isl_take isl_space *domain);
3022 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3023 __isl_take isl_space *domain,
3024 const isl_int n, const isl_int d);
3025 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3026 __isl_take isl_space *domain,
3027 enum isl_dim_type type, unsigned pos);
3028 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3029 __isl_take isl_aff *aff);
3031 Note that the space in which a quasipolynomial lives is a map space
3032 with a one-dimensional range. The C<domain> argument in some of
3033 the functions above corresponds to the domain of this map space.
3035 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3036 with a single cell can be created using the following functions.
3037 Multiple of these single cell piecewise quasipolynomials can
3038 be combined to create more complicated piecewise quasipolynomials.
3040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3041 __isl_take isl_space *space);
3042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3043 __isl_take isl_set *set,
3044 __isl_take isl_qpolynomial *qp);
3045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3046 __isl_take isl_qpolynomial *qp);
3047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3048 __isl_take isl_pw_aff *pwaff);
3050 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3051 __isl_take isl_space *space);
3052 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3053 __isl_take isl_pw_qpolynomial *pwqp);
3054 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3055 __isl_take isl_union_pw_qpolynomial *upwqp,
3056 __isl_take isl_pw_qpolynomial *pwqp);
3058 Quasipolynomials can be copied and freed again using the following
3061 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3062 __isl_keep isl_qpolynomial *qp);
3063 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3066 __isl_keep isl_pw_qpolynomial *pwqp);
3067 void *isl_pw_qpolynomial_free(
3068 __isl_take isl_pw_qpolynomial *pwqp);
3070 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3071 __isl_keep isl_union_pw_qpolynomial *upwqp);
3072 void isl_union_pw_qpolynomial_free(
3073 __isl_take isl_union_pw_qpolynomial *upwqp);
3075 =head3 Inspecting (Piecewise) Quasipolynomials
3077 To iterate over all piecewise quasipolynomials in a union
3078 piecewise quasipolynomial, use the following function
3080 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3081 __isl_keep isl_union_pw_qpolynomial *upwqp,
3082 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3085 To extract the piecewise quasipolynomial in a given space from a union, use
3087 __isl_give isl_pw_qpolynomial *
3088 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3089 __isl_keep isl_union_pw_qpolynomial *upwqp,
3090 __isl_take isl_space *space);
3092 To iterate over the cells in a piecewise quasipolynomial,
3093 use either of the following two functions
3095 int isl_pw_qpolynomial_foreach_piece(
3096 __isl_keep isl_pw_qpolynomial *pwqp,
3097 int (*fn)(__isl_take isl_set *set,
3098 __isl_take isl_qpolynomial *qp,
3099 void *user), void *user);
3100 int isl_pw_qpolynomial_foreach_lifted_piece(
3101 __isl_keep isl_pw_qpolynomial *pwqp,
3102 int (*fn)(__isl_take isl_set *set,
3103 __isl_take isl_qpolynomial *qp,
3104 void *user), void *user);
3106 As usual, the function C<fn> should return C<0> on success
3107 and C<-1> on failure. The difference between
3108 C<isl_pw_qpolynomial_foreach_piece> and
3109 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3110 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3111 compute unique representations for all existentially quantified
3112 variables and then turn these existentially quantified variables
3113 into extra set variables, adapting the associated quasipolynomial
3114 accordingly. This means that the C<set> passed to C<fn>
3115 will not have any existentially quantified variables, but that
3116 the dimensions of the sets may be different for different
3117 invocations of C<fn>.
3119 To iterate over all terms in a quasipolynomial,
3122 int isl_qpolynomial_foreach_term(
3123 __isl_keep isl_qpolynomial *qp,
3124 int (*fn)(__isl_take isl_term *term,
3125 void *user), void *user);
3127 The terms themselves can be inspected and freed using
3130 unsigned isl_term_dim(__isl_keep isl_term *term,
3131 enum isl_dim_type type);
3132 void isl_term_get_num(__isl_keep isl_term *term,
3134 void isl_term_get_den(__isl_keep isl_term *term,
3136 int isl_term_get_exp(__isl_keep isl_term *term,
3137 enum isl_dim_type type, unsigned pos);
3138 __isl_give isl_aff *isl_term_get_div(
3139 __isl_keep isl_term *term, unsigned pos);
3140 void isl_term_free(__isl_take isl_term *term);
3142 Each term is a product of parameters, set variables and
3143 integer divisions. The function C<isl_term_get_exp>
3144 returns the exponent of a given dimensions in the given term.
3145 The C<isl_int>s in the arguments of C<isl_term_get_num>
3146 and C<isl_term_get_den> need to have been initialized
3147 using C<isl_int_init> before calling these functions.
3149 =head3 Properties of (Piecewise) Quasipolynomials
3151 To check whether a quasipolynomial is actually a constant,
3152 use the following function.
3154 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3155 isl_int *n, isl_int *d);
3157 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3158 then the numerator and denominator of the constant
3159 are returned in C<*n> and C<*d>, respectively.
3161 To check whether two union piecewise quasipolynomials are
3162 obviously equal, use
3164 int isl_union_pw_qpolynomial_plain_is_equal(
3165 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3166 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3168 =head3 Operations on (Piecewise) Quasipolynomials
3170 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3171 __isl_take isl_qpolynomial *qp, isl_int v);
3172 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3173 __isl_take isl_qpolynomial *qp);
3174 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3175 __isl_take isl_qpolynomial *qp1,
3176 __isl_take isl_qpolynomial *qp2);
3177 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3178 __isl_take isl_qpolynomial *qp1,
3179 __isl_take isl_qpolynomial *qp2);
3180 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3181 __isl_take isl_qpolynomial *qp1,
3182 __isl_take isl_qpolynomial *qp2);
3183 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3184 __isl_take isl_qpolynomial *qp, unsigned exponent);
3186 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3187 __isl_take isl_pw_qpolynomial *pwqp1,
3188 __isl_take isl_pw_qpolynomial *pwqp2);
3189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3190 __isl_take isl_pw_qpolynomial *pwqp1,
3191 __isl_take isl_pw_qpolynomial *pwqp2);
3192 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3193 __isl_take isl_pw_qpolynomial *pwqp1,
3194 __isl_take isl_pw_qpolynomial *pwqp2);
3195 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3196 __isl_take isl_pw_qpolynomial *pwqp);
3197 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3198 __isl_take isl_pw_qpolynomial *pwqp1,
3199 __isl_take isl_pw_qpolynomial *pwqp2);
3200 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3201 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3203 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3204 __isl_take isl_union_pw_qpolynomial *upwqp1,
3205 __isl_take isl_union_pw_qpolynomial *upwqp2);
3206 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3207 __isl_take isl_union_pw_qpolynomial *upwqp1,
3208 __isl_take isl_union_pw_qpolynomial *upwqp2);
3209 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3210 __isl_take isl_union_pw_qpolynomial *upwqp1,
3211 __isl_take isl_union_pw_qpolynomial *upwqp2);
3213 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3214 __isl_take isl_pw_qpolynomial *pwqp,
3215 __isl_take isl_point *pnt);
3217 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3218 __isl_take isl_union_pw_qpolynomial *upwqp,
3219 __isl_take isl_point *pnt);
3221 __isl_give isl_set *isl_pw_qpolynomial_domain(
3222 __isl_take isl_pw_qpolynomial *pwqp);
3223 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3224 __isl_take isl_pw_qpolynomial *pwpq,
3225 __isl_take isl_set *set);
3227 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3228 __isl_take isl_union_pw_qpolynomial *upwqp);
3229 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3230 __isl_take isl_union_pw_qpolynomial *upwpq,
3231 __isl_take isl_union_set *uset);
3233 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3234 __isl_take isl_qpolynomial *qp,
3235 __isl_take isl_space *model);
3237 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3238 __isl_take isl_qpolynomial *qp);
3239 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3240 __isl_take isl_pw_qpolynomial *pwqp);
3242 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3243 __isl_take isl_union_pw_qpolynomial *upwqp);
3245 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3246 __isl_take isl_qpolynomial *qp,
3247 __isl_take isl_set *context);
3249 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3250 __isl_take isl_pw_qpolynomial *pwqp,
3251 __isl_take isl_set *context);
3253 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3254 __isl_take isl_union_pw_qpolynomial *upwqp,
3255 __isl_take isl_union_set *context);
3257 The gist operation applies the gist operation to each of
3258 the cells in the domain of the input piecewise quasipolynomial.
3259 The context is also exploited
3260 to simplify the quasipolynomials associated to each cell.
3262 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3263 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3264 __isl_give isl_union_pw_qpolynomial *
3265 isl_union_pw_qpolynomial_to_polynomial(
3266 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3268 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3269 the polynomial will be an overapproximation. If C<sign> is negative,
3270 it will be an underapproximation. If C<sign> is zero, the approximation
3271 will lie somewhere in between.
3273 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3275 A piecewise quasipolynomial reduction is a piecewise
3276 reduction (or fold) of quasipolynomials.
3277 In particular, the reduction can be maximum or a minimum.
3278 The objects are mainly used to represent the result of
3279 an upper or lower bound on a quasipolynomial over its domain,
3280 i.e., as the result of the following function.
3282 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3283 __isl_take isl_pw_qpolynomial *pwqp,
3284 enum isl_fold type, int *tight);
3286 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3287 __isl_take isl_union_pw_qpolynomial *upwqp,
3288 enum isl_fold type, int *tight);
3290 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3291 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3292 is the returned bound is known be tight, i.e., for each value
3293 of the parameters there is at least
3294 one element in the domain that reaches the bound.
3295 If the domain of C<pwqp> is not wrapping, then the bound is computed
3296 over all elements in that domain and the result has a purely parametric
3297 domain. If the domain of C<pwqp> is wrapping, then the bound is
3298 computed over the range of the wrapped relation. The domain of the
3299 wrapped relation becomes the domain of the result.
3301 A (piecewise) quasipolynomial reduction can be copied or freed using the
3302 following functions.
3304 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3305 __isl_keep isl_qpolynomial_fold *fold);
3306 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3307 __isl_keep isl_pw_qpolynomial_fold *pwf);
3308 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3309 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3310 void isl_qpolynomial_fold_free(
3311 __isl_take isl_qpolynomial_fold *fold);
3312 void *isl_pw_qpolynomial_fold_free(
3313 __isl_take isl_pw_qpolynomial_fold *pwf);
3314 void isl_union_pw_qpolynomial_fold_free(
3315 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3317 =head3 Printing Piecewise Quasipolynomial Reductions
3319 Piecewise quasipolynomial reductions can be printed
3320 using the following function.
3322 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3323 __isl_take isl_printer *p,
3324 __isl_keep isl_pw_qpolynomial_fold *pwf);
3325 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3326 __isl_take isl_printer *p,
3327 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3329 For C<isl_printer_print_pw_qpolynomial_fold>,
3330 output format of the printer
3331 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3332 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3333 output format of the printer
3334 needs to be set to C<ISL_FORMAT_ISL>.
3335 In case of printing in C<ISL_FORMAT_C>, the user may want
3336 to set the names of all dimensions
3338 __isl_give isl_pw_qpolynomial_fold *
3339 isl_pw_qpolynomial_fold_set_dim_name(
3340 __isl_take isl_pw_qpolynomial_fold *pwf,
3341 enum isl_dim_type type, unsigned pos,
3344 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3346 To iterate over all piecewise quasipolynomial reductions in a union
3347 piecewise quasipolynomial reduction, use the following function
3349 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3350 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3351 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3352 void *user), void *user);
3354 To iterate over the cells in a piecewise quasipolynomial reduction,
3355 use either of the following two functions
3357 int isl_pw_qpolynomial_fold_foreach_piece(
3358 __isl_keep isl_pw_qpolynomial_fold *pwf,
3359 int (*fn)(__isl_take isl_set *set,
3360 __isl_take isl_qpolynomial_fold *fold,
3361 void *user), void *user);
3362 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3363 __isl_keep isl_pw_qpolynomial_fold *pwf,
3364 int (*fn)(__isl_take isl_set *set,
3365 __isl_take isl_qpolynomial_fold *fold,
3366 void *user), void *user);
3368 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3369 of the difference between these two functions.
3371 To iterate over all quasipolynomials in a reduction, use
3373 int isl_qpolynomial_fold_foreach_qpolynomial(
3374 __isl_keep isl_qpolynomial_fold *fold,
3375 int (*fn)(__isl_take isl_qpolynomial *qp,
3376 void *user), void *user);
3378 =head3 Properties of Piecewise Quasipolynomial Reductions
3380 To check whether two union piecewise quasipolynomial reductions are
3381 obviously equal, use
3383 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3384 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3385 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3387 =head3 Operations on Piecewise Quasipolynomial Reductions
3389 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3390 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3392 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3393 __isl_take isl_pw_qpolynomial_fold *pwf1,
3394 __isl_take isl_pw_qpolynomial_fold *pwf2);
3396 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3397 __isl_take isl_pw_qpolynomial_fold *pwf1,
3398 __isl_take isl_pw_qpolynomial_fold *pwf2);
3400 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3401 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3402 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3404 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3405 __isl_take isl_pw_qpolynomial_fold *pwf,
3406 __isl_take isl_point *pnt);
3408 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3409 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3410 __isl_take isl_point *pnt);
3412 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3413 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3414 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3415 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3416 __isl_take isl_union_set *uset);
3418 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3419 __isl_take isl_pw_qpolynomial_fold *pwf);
3421 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3422 __isl_take isl_pw_qpolynomial_fold *pwf);
3424 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3425 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3427 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3428 __isl_take isl_pw_qpolynomial_fold *pwf,
3429 __isl_take isl_set *context);
3431 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3432 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3433 __isl_take isl_union_set *context);
3435 The gist operation applies the gist operation to each of
3436 the cells in the domain of the input piecewise quasipolynomial reduction.
3437 In future, the operation will also exploit the context
3438 to simplify the quasipolynomial reductions associated to each cell.
3440 __isl_give isl_pw_qpolynomial_fold *
3441 isl_set_apply_pw_qpolynomial_fold(
3442 __isl_take isl_set *set,
3443 __isl_take isl_pw_qpolynomial_fold *pwf,
3445 __isl_give isl_pw_qpolynomial_fold *
3446 isl_map_apply_pw_qpolynomial_fold(
3447 __isl_take isl_map *map,
3448 __isl_take isl_pw_qpolynomial_fold *pwf,
3450 __isl_give isl_union_pw_qpolynomial_fold *
3451 isl_union_set_apply_union_pw_qpolynomial_fold(
3452 __isl_take isl_union_set *uset,
3453 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3455 __isl_give isl_union_pw_qpolynomial_fold *
3456 isl_union_map_apply_union_pw_qpolynomial_fold(
3457 __isl_take isl_union_map *umap,
3458 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3461 The functions taking a map
3462 compose the given map with the given piecewise quasipolynomial reduction.
3463 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3464 over all elements in the intersection of the range of the map
3465 and the domain of the piecewise quasipolynomial reduction
3466 as a function of an element in the domain of the map.
3467 The functions taking a set compute a bound over all elements in the
3468 intersection of the set and the domain of the
3469 piecewise quasipolynomial reduction.
3471 =head2 Dependence Analysis
3473 C<isl> contains specialized functionality for performing
3474 array dataflow analysis. That is, given a I<sink> access relation
3475 and a collection of possible I<source> access relations,
3476 C<isl> can compute relations that describe
3477 for each iteration of the sink access, which iteration
3478 of which of the source access relations was the last
3479 to access the same data element before the given iteration
3481 To compute standard flow dependences, the sink should be
3482 a read, while the sources should be writes.
3483 If any of the source accesses are marked as being I<may>
3484 accesses, then there will be a dependence to the last
3485 I<must> access B<and> to any I<may> access that follows
3486 this last I<must> access.
3487 In particular, if I<all> sources are I<may> accesses,
3488 then memory based dependence analysis is performed.
3489 If, on the other hand, all sources are I<must> accesses,
3490 then value based dependence analysis is performed.
3492 #include <isl/flow.h>
3494 typedef int (*isl_access_level_before)(void *first, void *second);
3496 __isl_give isl_access_info *isl_access_info_alloc(
3497 __isl_take isl_map *sink,
3498 void *sink_user, isl_access_level_before fn,
3500 __isl_give isl_access_info *isl_access_info_add_source(
3501 __isl_take isl_access_info *acc,
3502 __isl_take isl_map *source, int must,
3504 void isl_access_info_free(__isl_take isl_access_info *acc);
3506 __isl_give isl_flow *isl_access_info_compute_flow(
3507 __isl_take isl_access_info *acc);
3509 int isl_flow_foreach(__isl_keep isl_flow *deps,
3510 int (*fn)(__isl_take isl_map *dep, int must,
3511 void *dep_user, void *user),
3513 __isl_give isl_map *isl_flow_get_no_source(
3514 __isl_keep isl_flow *deps, int must);
3515 void isl_flow_free(__isl_take isl_flow *deps);
3517 The function C<isl_access_info_compute_flow> performs the actual
3518 dependence analysis. The other functions are used to construct
3519 the input for this function or to read off the output.
3521 The input is collected in an C<isl_access_info>, which can
3522 be created through a call to C<isl_access_info_alloc>.
3523 The arguments to this functions are the sink access relation
3524 C<sink>, a token C<sink_user> used to identify the sink
3525 access to the user, a callback function for specifying the
3526 relative order of source and sink accesses, and the number
3527 of source access relations that will be added.
3528 The callback function has type C<int (*)(void *first, void *second)>.
3529 The function is called with two user supplied tokens identifying
3530 either a source or the sink and it should return the shared nesting
3531 level and the relative order of the two accesses.
3532 In particular, let I<n> be the number of loops shared by
3533 the two accesses. If C<first> precedes C<second> textually,
3534 then the function should return I<2 * n + 1>; otherwise,
3535 it should return I<2 * n>.
3536 The sources can be added to the C<isl_access_info> by performing
3537 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3538 C<must> indicates whether the source is a I<must> access
3539 or a I<may> access. Note that a multi-valued access relation
3540 should only be marked I<must> if every iteration in the domain
3541 of the relation accesses I<all> elements in its image.
3542 The C<source_user> token is again used to identify
3543 the source access. The range of the source access relation
3544 C<source> should have the same dimension as the range
3545 of the sink access relation.
3546 The C<isl_access_info_free> function should usually not be
3547 called explicitly, because it is called implicitly by
3548 C<isl_access_info_compute_flow>.
3550 The result of the dependence analysis is collected in an
3551 C<isl_flow>. There may be elements of
3552 the sink access for which no preceding source access could be
3553 found or for which all preceding sources are I<may> accesses.
3554 The relations containing these elements can be obtained through
3555 calls to C<isl_flow_get_no_source>, the first with C<must> set
3556 and the second with C<must> unset.
3557 In the case of standard flow dependence analysis,
3558 with the sink a read and the sources I<must> writes,
3559 the first relation corresponds to the reads from uninitialized
3560 array elements and the second relation is empty.
3561 The actual flow dependences can be extracted using
3562 C<isl_flow_foreach>. This function will call the user-specified
3563 callback function C<fn> for each B<non-empty> dependence between
3564 a source and the sink. The callback function is called
3565 with four arguments, the actual flow dependence relation
3566 mapping source iterations to sink iterations, a boolean that
3567 indicates whether it is a I<must> or I<may> dependence, a token
3568 identifying the source and an additional C<void *> with value
3569 equal to the third argument of the C<isl_flow_foreach> call.
3570 A dependence is marked I<must> if it originates from a I<must>
3571 source and if it is not followed by any I<may> sources.
3573 After finishing with an C<isl_flow>, the user should call
3574 C<isl_flow_free> to free all associated memory.
3576 A higher-level interface to dependence analysis is provided
3577 by the following function.
3579 #include <isl/flow.h>
3581 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3582 __isl_take isl_union_map *must_source,
3583 __isl_take isl_union_map *may_source,
3584 __isl_take isl_union_map *schedule,
3585 __isl_give isl_union_map **must_dep,
3586 __isl_give isl_union_map **may_dep,
3587 __isl_give isl_union_map **must_no_source,
3588 __isl_give isl_union_map **may_no_source);
3590 The arrays are identified by the tuple names of the ranges
3591 of the accesses. The iteration domains by the tuple names
3592 of the domains of the accesses and of the schedule.
3593 The relative order of the iteration domains is given by the
3594 schedule. The relations returned through C<must_no_source>
3595 and C<may_no_source> are subsets of C<sink>.
3596 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3597 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3598 any of the other arguments is treated as an error.
3602 B<The functionality described in this section is fairly new
3603 and may be subject to change.>
3605 The following function can be used to compute a schedule
3606 for a union of domains. The generated schedule respects
3607 all C<validity> dependences. That is, all dependence distances
3608 over these dependences in the scheduled space are lexicographically
3609 positive. The generated schedule schedule also tries to minimize
3610 the dependence distances over C<proximity> dependences.
3611 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3612 for groups of domains where the dependence distances have only
3613 non-negative values.
3614 The algorithm used to construct the schedule is similar to that
3617 #include <isl/schedule.h>
3618 __isl_give isl_schedule *isl_union_set_compute_schedule(
3619 __isl_take isl_union_set *domain,
3620 __isl_take isl_union_map *validity,
3621 __isl_take isl_union_map *proximity);
3622 void *isl_schedule_free(__isl_take isl_schedule *sched);
3624 A mapping from the domains to the scheduled space can be obtained
3625 from an C<isl_schedule> using the following function.
3627 __isl_give isl_union_map *isl_schedule_get_map(
3628 __isl_keep isl_schedule *sched);
3630 A representation of the schedule can be printed using
3632 __isl_give isl_printer *isl_printer_print_schedule(
3633 __isl_take isl_printer *p,
3634 __isl_keep isl_schedule *schedule);
3636 A representation of the schedule as a forest of bands can be obtained
3637 using the following function.
3639 __isl_give isl_band_list *isl_schedule_get_band_forest(
3640 __isl_keep isl_schedule *schedule);
3642 The list can be manipulated as explained in L<"Lists">.
3643 The bands inside the list can be copied and freed using the following
3646 #include <isl/band.h>
3647 __isl_give isl_band *isl_band_copy(
3648 __isl_keep isl_band *band);
3649 void *isl_band_free(__isl_take isl_band *band);
3651 Each band contains zero or more scheduling dimensions.
3652 These are referred to as the members of the band.
3653 The section of the schedule that corresponds to the band is
3654 referred to as the partial schedule of the band.
3655 For those nodes that participate in a band, the outer scheduling
3656 dimensions form the prefix schedule, while the inner scheduling
3657 dimensions form the suffix schedule.
3658 That is, if we take a cut of the band forest, then the union of
3659 the concatenations of the prefix, partial and suffix schedules of
3660 each band in the cut is equal to the entire schedule (modulo
3661 some possible padding at the end with zero scheduling dimensions).
3662 The properties of a band can be inspected using the following functions.
3664 #include <isl/band.h>
3665 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3667 int isl_band_has_children(__isl_keep isl_band *band);
3668 __isl_give isl_band_list *isl_band_get_children(
3669 __isl_keep isl_band *band);
3671 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3672 __isl_keep isl_band *band);
3673 __isl_give isl_union_map *isl_band_get_partial_schedule(
3674 __isl_keep isl_band *band);
3675 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3676 __isl_keep isl_band *band);
3678 int isl_band_n_member(__isl_keep isl_band *band);
3679 int isl_band_member_is_zero_distance(
3680 __isl_keep isl_band *band, int pos);
3682 Note that a scheduling dimension is considered to be ``zero
3683 distance'' if it does not carry any proximity dependences
3685 That is, if the dependence distances of the proximity
3686 dependences are all zero in that direction (for fixed
3687 iterations of outer bands).
3689 A representation of the band can be printed using
3691 #include <isl/band.h>
3692 __isl_give isl_printer *isl_printer_print_band(
3693 __isl_take isl_printer *p,
3694 __isl_keep isl_band *band);
3696 =head2 Parametric Vertex Enumeration
3698 The parametric vertex enumeration described in this section
3699 is mainly intended to be used internally and by the C<barvinok>
3702 #include <isl/vertices.h>
3703 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3704 __isl_keep isl_basic_set *bset);
3706 The function C<isl_basic_set_compute_vertices> performs the
3707 actual computation of the parametric vertices and the chamber
3708 decomposition and store the result in an C<isl_vertices> object.
3709 This information can be queried by either iterating over all
3710 the vertices or iterating over all the chambers or cells
3711 and then iterating over all vertices that are active on the chamber.
3713 int isl_vertices_foreach_vertex(
3714 __isl_keep isl_vertices *vertices,
3715 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3718 int isl_vertices_foreach_cell(
3719 __isl_keep isl_vertices *vertices,
3720 int (*fn)(__isl_take isl_cell *cell, void *user),
3722 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3723 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3726 Other operations that can be performed on an C<isl_vertices> object are
3729 isl_ctx *isl_vertices_get_ctx(
3730 __isl_keep isl_vertices *vertices);
3731 int isl_vertices_get_n_vertices(
3732 __isl_keep isl_vertices *vertices);
3733 void isl_vertices_free(__isl_take isl_vertices *vertices);
3735 Vertices can be inspected and destroyed using the following functions.
3737 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3738 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3739 __isl_give isl_basic_set *isl_vertex_get_domain(
3740 __isl_keep isl_vertex *vertex);
3741 __isl_give isl_basic_set *isl_vertex_get_expr(
3742 __isl_keep isl_vertex *vertex);
3743 void isl_vertex_free(__isl_take isl_vertex *vertex);
3745 C<isl_vertex_get_expr> returns a singleton parametric set describing
3746 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3748 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3749 B<rational> basic sets, so they should mainly be used for inspection
3750 and should not be mixed with integer sets.
3752 Chambers can be inspected and destroyed using the following functions.
3754 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3755 __isl_give isl_basic_set *isl_cell_get_domain(
3756 __isl_keep isl_cell *cell);
3757 void isl_cell_free(__isl_take isl_cell *cell);
3761 Although C<isl> is mainly meant to be used as a library,
3762 it also contains some basic applications that use some
3763 of the functionality of C<isl>.
3764 The input may be specified in either the L<isl format>
3765 or the L<PolyLib format>.
3767 =head2 C<isl_polyhedron_sample>
3769 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3770 an integer element of the polyhedron, if there is any.
3771 The first column in the output is the denominator and is always
3772 equal to 1. If the polyhedron contains no integer points,
3773 then a vector of length zero is printed.
3777 C<isl_pip> takes the same input as the C<example> program
3778 from the C<piplib> distribution, i.e., a set of constraints
3779 on the parameters, a line containing only -1 and finally a set
3780 of constraints on a parametric polyhedron.
3781 The coefficients of the parameters appear in the last columns
3782 (but before the final constant column).
3783 The output is the lexicographic minimum of the parametric polyhedron.
3784 As C<isl> currently does not have its own output format, the output
3785 is just a dump of the internal state.
3787 =head2 C<isl_polyhedron_minimize>
3789 C<isl_polyhedron_minimize> computes the minimum of some linear
3790 or affine objective function over the integer points in a polyhedron.
3791 If an affine objective function
3792 is given, then the constant should appear in the last column.
3794 =head2 C<isl_polytope_scan>
3796 Given a polytope, C<isl_polytope_scan> prints
3797 all integer points in the polytope.