3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
145 =item * The C<nparam> argument has been removed from
146 C<isl_map_read_from_str> and similar functions.
147 When reading input in the original PolyLib format,
148 the result will have no parameters.
149 If parameters are expected, the caller may want to perform
150 dimension manipulation on the result.
156 The source of C<isl> can be obtained either as a tarball
157 or from the git repository. Both are available from
158 L<http://freshmeat.net/projects/isl/>.
159 The installation process depends on how you obtained
162 =head2 Installation from the git repository
166 =item 1 Clone or update the repository
168 The first time the source is obtained, you need to clone
171 git clone git://repo.or.cz/isl.git
173 To obtain updates, you need to pull in the latest changes
177 =item 2 Generate C<configure>
183 After performing the above steps, continue
184 with the L<Common installation instructions>.
186 =head2 Common installation instructions
190 =item 1 Obtain C<GMP>
192 Building C<isl> requires C<GMP>, including its headers files.
193 Your distribution may not provide these header files by default
194 and you may need to install a package called C<gmp-devel> or something
195 similar. Alternatively, C<GMP> can be built from
196 source, available from L<http://gmplib.org/>.
200 C<isl> uses the standard C<autoconf> C<configure> script.
205 optionally followed by some configure options.
206 A complete list of options can be obtained by running
210 Below we discuss some of the more common options.
212 C<isl> can optionally use C<piplib>, but no
213 C<piplib> functionality is currently used by default.
214 The C<--with-piplib> option can
215 be used to specify which C<piplib>
216 library to use, either an installed version (C<system>),
217 an externally built version (C<build>)
218 or no version (C<no>). The option C<build> is mostly useful
219 in C<configure> scripts of larger projects that bundle both C<isl>
226 Installation prefix for C<isl>
228 =item C<--with-gmp-prefix>
230 Installation prefix for C<GMP> (architecture-independent files).
232 =item C<--with-gmp-exec-prefix>
234 Installation prefix for C<GMP> (architecture-dependent files).
236 =item C<--with-piplib>
238 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
240 =item C<--with-piplib-prefix>
242 Installation prefix for C<system> C<piplib> (architecture-independent files).
244 =item C<--with-piplib-exec-prefix>
246 Installation prefix for C<system> C<piplib> (architecture-dependent files).
248 =item C<--with-piplib-builddir>
250 Location where C<build> C<piplib> was built.
258 =item 4 Install (optional)
266 =head2 Initialization
268 All manipulations of integer sets and relations occur within
269 the context of an C<isl_ctx>.
270 A given C<isl_ctx> can only be used within a single thread.
271 All arguments of a function are required to have been allocated
272 within the same context.
273 There are currently no functions available for moving an object
274 from one C<isl_ctx> to another C<isl_ctx>. This means that
275 there is currently no way of safely moving an object from one
276 thread to another, unless the whole C<isl_ctx> is moved.
278 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
279 freed using C<isl_ctx_free>.
280 All objects allocated within an C<isl_ctx> should be freed
281 before the C<isl_ctx> itself is freed.
283 isl_ctx *isl_ctx_alloc();
284 void isl_ctx_free(isl_ctx *ctx);
288 All operations on integers, mainly the coefficients
289 of the constraints describing the sets and relations,
290 are performed in exact integer arithmetic using C<GMP>.
291 However, to allow future versions of C<isl> to optionally
292 support fixed integer arithmetic, all calls to C<GMP>
293 are wrapped inside C<isl> specific macros.
294 The basic type is C<isl_int> and the operations below
295 are available on this type.
296 The meanings of these operations are essentially the same
297 as their C<GMP> C<mpz_> counterparts.
298 As always with C<GMP> types, C<isl_int>s need to be
299 initialized with C<isl_int_init> before they can be used
300 and they need to be released with C<isl_int_clear>
302 The user should not assume that an C<isl_int> is represented
303 as a C<mpz_t>, but should instead explicitly convert between
304 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
305 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
309 =item isl_int_init(i)
311 =item isl_int_clear(i)
313 =item isl_int_set(r,i)
315 =item isl_int_set_si(r,i)
317 =item isl_int_set_gmp(r,g)
319 =item isl_int_get_gmp(i,g)
321 =item isl_int_abs(r,i)
323 =item isl_int_neg(r,i)
325 =item isl_int_swap(i,j)
327 =item isl_int_swap_or_set(i,j)
329 =item isl_int_add_ui(r,i,j)
331 =item isl_int_sub_ui(r,i,j)
333 =item isl_int_add(r,i,j)
335 =item isl_int_sub(r,i,j)
337 =item isl_int_mul(r,i,j)
339 =item isl_int_mul_ui(r,i,j)
341 =item isl_int_addmul(r,i,j)
343 =item isl_int_submul(r,i,j)
345 =item isl_int_gcd(r,i,j)
347 =item isl_int_lcm(r,i,j)
349 =item isl_int_divexact(r,i,j)
351 =item isl_int_cdiv_q(r,i,j)
353 =item isl_int_fdiv_q(r,i,j)
355 =item isl_int_fdiv_r(r,i,j)
357 =item isl_int_fdiv_q_ui(r,i,j)
359 =item isl_int_read(r,s)
361 =item isl_int_print(out,i,width)
365 =item isl_int_cmp(i,j)
367 =item isl_int_cmp_si(i,si)
369 =item isl_int_eq(i,j)
371 =item isl_int_ne(i,j)
373 =item isl_int_lt(i,j)
375 =item isl_int_le(i,j)
377 =item isl_int_gt(i,j)
379 =item isl_int_ge(i,j)
381 =item isl_int_abs_eq(i,j)
383 =item isl_int_abs_ne(i,j)
385 =item isl_int_abs_lt(i,j)
387 =item isl_int_abs_gt(i,j)
389 =item isl_int_abs_ge(i,j)
391 =item isl_int_is_zero(i)
393 =item isl_int_is_one(i)
395 =item isl_int_is_negone(i)
397 =item isl_int_is_pos(i)
399 =item isl_int_is_neg(i)
401 =item isl_int_is_nonpos(i)
403 =item isl_int_is_nonneg(i)
405 =item isl_int_is_divisible_by(i,j)
409 =head2 Sets and Relations
411 C<isl> uses six types of objects for representing sets and relations,
412 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
413 C<isl_union_set> and C<isl_union_map>.
414 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
415 can be described as a conjunction of affine constraints, while
416 C<isl_set> and C<isl_map> represent unions of
417 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
418 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
419 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
420 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
421 where spaces are considered different if they have a different number
422 of dimensions and/or different names (see L<"Spaces">).
423 The difference between sets and relations (maps) is that sets have
424 one set of variables, while relations have two sets of variables,
425 input variables and output variables.
427 =head2 Memory Management
429 Since a high-level operation on sets and/or relations usually involves
430 several substeps and since the user is usually not interested in
431 the intermediate results, most functions that return a new object
432 will also release all the objects passed as arguments.
433 If the user still wants to use one or more of these arguments
434 after the function call, she should pass along a copy of the
435 object rather than the object itself.
436 The user is then responsible for making sure that the original
437 object gets used somewhere else or is explicitly freed.
439 The arguments and return values of all documented functions are
440 annotated to make clear which arguments are released and which
441 arguments are preserved. In particular, the following annotations
448 C<__isl_give> means that a new object is returned.
449 The user should make sure that the returned pointer is
450 used exactly once as a value for an C<__isl_take> argument.
451 In between, it can be used as a value for as many
452 C<__isl_keep> arguments as the user likes.
453 There is one exception, and that is the case where the
454 pointer returned is C<NULL>. Is this case, the user
455 is free to use it as an C<__isl_take> argument or not.
459 C<__isl_take> means that the object the argument points to
460 is taken over by the function and may no longer be used
461 by the user as an argument to any other function.
462 The pointer value must be one returned by a function
463 returning an C<__isl_give> pointer.
464 If the user passes in a C<NULL> value, then this will
465 be treated as an error in the sense that the function will
466 not perform its usual operation. However, it will still
467 make sure that all the other C<__isl_take> arguments
472 C<__isl_keep> means that the function will only use the object
473 temporarily. After the function has finished, the user
474 can still use it as an argument to other functions.
475 A C<NULL> value will be treated in the same way as
476 a C<NULL> value for an C<__isl_take> argument.
482 Identifiers are used to identify both individual dimensions
483 and tuples of dimensions. They consist of a name and an optional
484 pointer. Identifiers with the same name but different pointer values
485 are considered to be distinct.
486 Identifiers can be constructed, copied, freed, inspected and printed
487 using the following functions.
490 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
491 __isl_keep const char *name, void *user);
492 __isl_give isl_id *isl_id_copy(isl_id *id);
493 void *isl_id_free(__isl_take isl_id *id);
495 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
496 void *isl_id_get_user(__isl_keep isl_id *id);
497 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
499 __isl_give isl_printer *isl_printer_print_id(
500 __isl_take isl_printer *p, __isl_keep isl_id *id);
502 Note that C<isl_id_get_name> returns a pointer to some internal
503 data structure, so the result can only be used while the
504 corresponding C<isl_id> is alive.
508 Whenever a new set or relation is created from scratch,
509 the space in which it lives needs to be specified using an C<isl_space>.
511 #include <isl/space.h>
512 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
513 unsigned nparam, unsigned n_in, unsigned n_out);
514 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
516 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
517 unsigned nparam, unsigned dim);
518 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
519 void isl_space_free(__isl_take isl_space *space);
520 unsigned isl_space_dim(__isl_keep isl_space *space,
521 enum isl_dim_type type);
523 The space used for creating a parameter domain
524 needs to be created using C<isl_space_params_alloc>.
525 For other sets, the space
526 needs to be created using C<isl_space_set_alloc>, while
527 for a relation, the space
528 needs to be created using C<isl_space_alloc>.
529 C<isl_space_dim> can be used
530 to find out the number of dimensions of each type in
531 a space, where type may be
532 C<isl_dim_param>, C<isl_dim_in> (only for relations),
533 C<isl_dim_out> (only for relations), C<isl_dim_set>
534 (only for sets) or C<isl_dim_all>.
536 To check whether a given space is that of a set or a map
537 or whether it is a parameter space, use these functions:
539 #include <isl/space.h>
540 int isl_space_is_params(__isl_keep isl_space *space);
541 int isl_space_is_set(__isl_keep isl_space *space);
543 It is often useful to create objects that live in the
544 same space as some other object. This can be accomplished
545 by creating the new objects
546 (see L<Creating New Sets and Relations> or
547 L<Creating New (Piecewise) Quasipolynomials>) based on the space
548 of the original object.
551 __isl_give isl_space *isl_basic_set_get_space(
552 __isl_keep isl_basic_set *bset);
553 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
555 #include <isl/union_set.h>
556 __isl_give isl_space *isl_union_set_get_space(
557 __isl_keep isl_union_set *uset);
560 __isl_give isl_space *isl_basic_map_get_space(
561 __isl_keep isl_basic_map *bmap);
562 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
564 #include <isl/union_map.h>
565 __isl_give isl_space *isl_union_map_get_space(
566 __isl_keep isl_union_map *umap);
568 #include <isl/constraint.h>
569 __isl_give isl_space *isl_constraint_get_space(
570 __isl_keep isl_constraint *constraint);
572 #include <isl/polynomial.h>
573 __isl_give isl_space *isl_qpolynomial_get_domain_space(
574 __isl_keep isl_qpolynomial *qp);
575 __isl_give isl_space *isl_qpolynomial_get_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_fold_get_space(
578 __isl_keep isl_qpolynomial_fold *fold);
579 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
580 __isl_keep isl_pw_qpolynomial *pwqp);
581 __isl_give isl_space *isl_pw_qpolynomial_get_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
584 __isl_keep isl_pw_qpolynomial_fold *pwf);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
588 __isl_keep isl_union_pw_qpolynomial *upwqp);
589 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
590 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
593 __isl_give isl_space *isl_aff_get_domain_space(
594 __isl_keep isl_aff *aff);
595 __isl_give isl_space *isl_aff_get_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_pw_aff_get_domain_space(
598 __isl_keep isl_pw_aff *pwaff);
599 __isl_give isl_space *isl_pw_aff_get_space(
600 __isl_keep isl_pw_aff *pwaff);
602 #include <isl/point.h>
603 __isl_give isl_space *isl_point_get_space(
604 __isl_keep isl_point *pnt);
606 The identifiers or names of the individual dimensions may be set or read off
607 using the following functions.
609 #include <isl/space.h>
610 __isl_give isl_space *isl_space_set_dim_id(
611 __isl_take isl_space *space,
612 enum isl_dim_type type, unsigned pos,
613 __isl_take isl_id *id);
614 int isl_space_has_dim_id(__isl_keep isl_space *space,
615 enum isl_dim_type type, unsigned pos);
616 __isl_give isl_id *isl_space_get_dim_id(
617 __isl_keep isl_space *space,
618 enum isl_dim_type type, unsigned pos);
619 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_keep const char *name);
622 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
625 Note that C<isl_space_get_name> returns a pointer to some internal
626 data structure, so the result can only be used while the
627 corresponding C<isl_space> is alive.
628 Also note that every function that operates on two sets or relations
629 requires that both arguments have the same parameters. This also
630 means that if one of the arguments has named parameters, then the
631 other needs to have named parameters too and the names need to match.
632 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
633 arguments may have different parameters (as long as they are named),
634 in which case the result will have as parameters the union of the parameters of
637 Given the identifier of a dimension (typically a parameter),
638 its position can be obtained from the following function.
640 #include <isl/space.h>
641 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
642 enum isl_dim_type type, __isl_keep isl_id *id);
644 The identifiers or names of entire spaces may be set or read off
645 using the following functions.
647 #include <isl/space.h>
648 __isl_give isl_space *isl_space_set_tuple_id(
649 __isl_take isl_space *space,
650 enum isl_dim_type type, __isl_take isl_id *id);
651 __isl_give isl_space *isl_space_reset_tuple_id(
652 __isl_take isl_space *space, enum isl_dim_type type);
653 int isl_space_has_tuple_id(__isl_keep isl_space *space,
654 enum isl_dim_type type);
655 __isl_give isl_id *isl_space_get_tuple_id(
656 __isl_keep isl_space *space, enum isl_dim_type type);
657 __isl_give isl_space *isl_space_set_tuple_name(
658 __isl_take isl_space *space,
659 enum isl_dim_type type, const char *s);
660 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
661 enum isl_dim_type type);
663 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
664 or C<isl_dim_set>. As with C<isl_space_get_name>,
665 the C<isl_space_get_tuple_name> function returns a pointer to some internal
667 Binary operations require the corresponding spaces of their arguments
668 to have the same name.
670 Spaces can be nested. In particular, the domain of a set or
671 the domain or range of a relation can be a nested relation.
672 The following functions can be used to construct and deconstruct
675 #include <isl/space.h>
676 int isl_space_is_wrapping(__isl_keep isl_space *space);
677 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
678 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
680 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
681 be the space of a set, while that of
682 C<isl_space_wrap> should be the space of a relation.
683 Conversely, the output of C<isl_space_unwrap> is the space
684 of a relation, while that of C<isl_space_wrap> is the space of a set.
686 Spaces can be created from other spaces
687 using the following functions.
689 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
690 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
691 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
692 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
693 __isl_give isl_space *isl_space_params(
694 __isl_take isl_space *space);
695 __isl_give isl_space *isl_space_set_from_params(
696 __isl_take isl_space *space);
697 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
698 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
699 __isl_take isl_space *right);
700 __isl_give isl_space *isl_space_align_params(
701 __isl_take isl_space *space1, __isl_take isl_space *space2)
702 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
703 enum isl_dim_type type, unsigned pos, unsigned n);
704 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned n);
706 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned first, unsigned n);
708 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
709 enum isl_dim_type dst_type, unsigned dst_pos,
710 enum isl_dim_type src_type, unsigned src_pos,
712 __isl_give isl_space *isl_space_map_from_set(
713 __isl_take isl_space *space);
714 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
716 Note that if dimensions are added or removed from a space, then
717 the name and the internal structure are lost.
721 A local space is essentially a space with
722 zero or more existentially quantified variables.
723 The local space of a basic set or relation can be obtained
724 using the following functions.
727 __isl_give isl_local_space *isl_basic_set_get_local_space(
728 __isl_keep isl_basic_set *bset);
731 __isl_give isl_local_space *isl_basic_map_get_local_space(
732 __isl_keep isl_basic_map *bmap);
734 A new local space can be created from a space using
736 #include <isl/local_space.h>
737 __isl_give isl_local_space *isl_local_space_from_space(
738 __isl_take isl_space *space);
740 They can be inspected, copied and freed using the following functions.
742 #include <isl/local_space.h>
743 isl_ctx *isl_local_space_get_ctx(
744 __isl_keep isl_local_space *ls);
745 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
746 int isl_local_space_dim(__isl_keep isl_local_space *ls,
747 enum isl_dim_type type);
748 const char *isl_local_space_get_dim_name(
749 __isl_keep isl_local_space *ls,
750 enum isl_dim_type type, unsigned pos);
751 __isl_give isl_local_space *isl_local_space_set_dim_name(
752 __isl_take isl_local_space *ls,
753 enum isl_dim_type type, unsigned pos, const char *s);
754 __isl_give isl_space *isl_local_space_get_space(
755 __isl_keep isl_local_space *ls);
756 __isl_give isl_aff *isl_local_space_get_div(
757 __isl_keep isl_local_space *ls, int pos);
758 __isl_give isl_local_space *isl_local_space_copy(
759 __isl_keep isl_local_space *ls);
760 void *isl_local_space_free(__isl_take isl_local_space *ls);
762 Two local spaces can be compared using
764 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
765 __isl_keep isl_local_space *ls2);
767 Local spaces can be created from other local spaces
768 using the following functions.
770 __isl_give isl_local_space *isl_local_space_domain(
771 __isl_take isl_local_space *ls);
772 __isl_give isl_local_space *isl_local_space_from_domain(
773 __isl_take isl_local_space *ls);
774 __isl_give isl_local_space *isl_local_space_add_dims(
775 __isl_take isl_local_space *ls,
776 enum isl_dim_type type, unsigned n);
777 __isl_give isl_local_space *isl_local_space_insert_dims(
778 __isl_take isl_local_space *ls,
779 enum isl_dim_type type, unsigned first, unsigned n);
780 __isl_give isl_local_space *isl_local_space_drop_dims(
781 __isl_take isl_local_space *ls,
782 enum isl_dim_type type, unsigned first, unsigned n);
784 =head2 Input and Output
786 C<isl> supports its own input/output format, which is similar
787 to the C<Omega> format, but also supports the C<PolyLib> format
792 The C<isl> format is similar to that of C<Omega>, but has a different
793 syntax for describing the parameters and allows for the definition
794 of an existentially quantified variable as the integer division
795 of an affine expression.
796 For example, the set of integers C<i> between C<0> and C<n>
797 such that C<i % 10 <= 6> can be described as
799 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
802 A set or relation can have several disjuncts, separated
803 by the keyword C<or>. Each disjunct is either a conjunction
804 of constraints or a projection (C<exists>) of a conjunction
805 of constraints. The constraints are separated by the keyword
808 =head3 C<PolyLib> format
810 If the represented set is a union, then the first line
811 contains a single number representing the number of disjuncts.
812 Otherwise, a line containing the number C<1> is optional.
814 Each disjunct is represented by a matrix of constraints.
815 The first line contains two numbers representing
816 the number of rows and columns,
817 where the number of rows is equal to the number of constraints
818 and the number of columns is equal to two plus the number of variables.
819 The following lines contain the actual rows of the constraint matrix.
820 In each row, the first column indicates whether the constraint
821 is an equality (C<0>) or inequality (C<1>). The final column
822 corresponds to the constant term.
824 If the set is parametric, then the coefficients of the parameters
825 appear in the last columns before the constant column.
826 The coefficients of any existentially quantified variables appear
827 between those of the set variables and those of the parameters.
829 =head3 Extended C<PolyLib> format
831 The extended C<PolyLib> format is nearly identical to the
832 C<PolyLib> format. The only difference is that the line
833 containing the number of rows and columns of a constraint matrix
834 also contains four additional numbers:
835 the number of output dimensions, the number of input dimensions,
836 the number of local dimensions (i.e., the number of existentially
837 quantified variables) and the number of parameters.
838 For sets, the number of ``output'' dimensions is equal
839 to the number of set dimensions, while the number of ``input''
845 __isl_give isl_basic_set *isl_basic_set_read_from_file(
846 isl_ctx *ctx, FILE *input);
847 __isl_give isl_basic_set *isl_basic_set_read_from_str(
848 isl_ctx *ctx, const char *str);
849 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
851 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
855 __isl_give isl_basic_map *isl_basic_map_read_from_file(
856 isl_ctx *ctx, FILE *input);
857 __isl_give isl_basic_map *isl_basic_map_read_from_str(
858 isl_ctx *ctx, const char *str);
859 __isl_give isl_map *isl_map_read_from_file(
860 isl_ctx *ctx, FILE *input);
861 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
864 #include <isl/union_set.h>
865 __isl_give isl_union_set *isl_union_set_read_from_file(
866 isl_ctx *ctx, FILE *input);
867 __isl_give isl_union_set *isl_union_set_read_from_str(
868 isl_ctx *ctx, const char *str);
870 #include <isl/union_map.h>
871 __isl_give isl_union_map *isl_union_map_read_from_file(
872 isl_ctx *ctx, FILE *input);
873 __isl_give isl_union_map *isl_union_map_read_from_str(
874 isl_ctx *ctx, const char *str);
876 The input format is autodetected and may be either the C<PolyLib> format
877 or the C<isl> format.
881 Before anything can be printed, an C<isl_printer> needs to
884 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
886 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
887 void isl_printer_free(__isl_take isl_printer *printer);
888 __isl_give char *isl_printer_get_str(
889 __isl_keep isl_printer *printer);
891 The behavior of the printer can be modified in various ways
893 __isl_give isl_printer *isl_printer_set_output_format(
894 __isl_take isl_printer *p, int output_format);
895 __isl_give isl_printer *isl_printer_set_indent(
896 __isl_take isl_printer *p, int indent);
897 __isl_give isl_printer *isl_printer_indent(
898 __isl_take isl_printer *p, int indent);
899 __isl_give isl_printer *isl_printer_set_prefix(
900 __isl_take isl_printer *p, const char *prefix);
901 __isl_give isl_printer *isl_printer_set_suffix(
902 __isl_take isl_printer *p, const char *suffix);
904 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
905 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
906 and defaults to C<ISL_FORMAT_ISL>.
907 Each line in the output is indented by C<indent> (set by
908 C<isl_printer_set_indent>) spaces
909 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
910 In the C<PolyLib> format output,
911 the coefficients of the existentially quantified variables
912 appear between those of the set variables and those
914 The function C<isl_printer_indent> increases the indentation
915 by the specified amount (which may be negative).
917 To actually print something, use
920 __isl_give isl_printer *isl_printer_print_basic_set(
921 __isl_take isl_printer *printer,
922 __isl_keep isl_basic_set *bset);
923 __isl_give isl_printer *isl_printer_print_set(
924 __isl_take isl_printer *printer,
925 __isl_keep isl_set *set);
928 __isl_give isl_printer *isl_printer_print_basic_map(
929 __isl_take isl_printer *printer,
930 __isl_keep isl_basic_map *bmap);
931 __isl_give isl_printer *isl_printer_print_map(
932 __isl_take isl_printer *printer,
933 __isl_keep isl_map *map);
935 #include <isl/union_set.h>
936 __isl_give isl_printer *isl_printer_print_union_set(
937 __isl_take isl_printer *p,
938 __isl_keep isl_union_set *uset);
940 #include <isl/union_map.h>
941 __isl_give isl_printer *isl_printer_print_union_map(
942 __isl_take isl_printer *p,
943 __isl_keep isl_union_map *umap);
945 When called on a file printer, the following function flushes
946 the file. When called on a string printer, the buffer is cleared.
948 __isl_give isl_printer *isl_printer_flush(
949 __isl_take isl_printer *p);
951 =head2 Creating New Sets and Relations
953 C<isl> has functions for creating some standard sets and relations.
957 =item * Empty sets and relations
959 __isl_give isl_basic_set *isl_basic_set_empty(
960 __isl_take isl_space *space);
961 __isl_give isl_basic_map *isl_basic_map_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_set *isl_set_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_map *isl_map_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_union_set *isl_union_set_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_union_map *isl_union_map_empty(
970 __isl_take isl_space *space);
972 For C<isl_union_set>s and C<isl_union_map>s, the space
973 is only used to specify the parameters.
975 =item * Universe sets and relations
977 __isl_give isl_basic_set *isl_basic_set_universe(
978 __isl_take isl_space *space);
979 __isl_give isl_basic_map *isl_basic_map_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_set *isl_set_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_map *isl_map_universe(
984 __isl_take isl_space *space);
985 __isl_give isl_union_set *isl_union_set_universe(
986 __isl_take isl_union_set *uset);
987 __isl_give isl_union_map *isl_union_map_universe(
988 __isl_take isl_union_map *umap);
990 The sets and relations constructed by the functions above
991 contain all integer values, while those constructed by the
992 functions below only contain non-negative values.
994 __isl_give isl_basic_set *isl_basic_set_nat_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_nat_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_nat_universe(
1001 __isl_take isl_space *space);
1003 =item * Identity relations
1005 __isl_give isl_basic_map *isl_basic_map_identity(
1006 __isl_take isl_space *space);
1007 __isl_give isl_map *isl_map_identity(
1008 __isl_take isl_space *space);
1010 The number of input and output dimensions in C<space> needs
1013 =item * Lexicographic order
1015 __isl_give isl_map *isl_map_lex_lt(
1016 __isl_take isl_space *set_space);
1017 __isl_give isl_map *isl_map_lex_le(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_gt(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_ge(
1022 __isl_take isl_space *set_space);
1023 __isl_give isl_map *isl_map_lex_lt_first(
1024 __isl_take isl_space *space, unsigned n);
1025 __isl_give isl_map *isl_map_lex_le_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_gt_first(
1028 __isl_take isl_space *space, unsigned n);
1029 __isl_give isl_map *isl_map_lex_ge_first(
1030 __isl_take isl_space *space, unsigned n);
1032 The first four functions take a space for a B<set>
1033 and return relations that express that the elements in the domain
1034 are lexicographically less
1035 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1036 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1037 than the elements in the range.
1038 The last four functions take a space for a map
1039 and return relations that express that the first C<n> dimensions
1040 in the domain are lexicographically less
1041 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1042 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1043 than the first C<n> dimensions in the range.
1047 A basic set or relation can be converted to a set or relation
1048 using the following functions.
1050 __isl_give isl_set *isl_set_from_basic_set(
1051 __isl_take isl_basic_set *bset);
1052 __isl_give isl_map *isl_map_from_basic_map(
1053 __isl_take isl_basic_map *bmap);
1055 Sets and relations can be converted to union sets and relations
1056 using the following functions.
1058 __isl_give isl_union_map *isl_union_map_from_map(
1059 __isl_take isl_map *map);
1060 __isl_give isl_union_set *isl_union_set_from_set(
1061 __isl_take isl_set *set);
1063 The inverse conversions below can only be used if the input
1064 union set or relation is known to contain elements in exactly one
1067 __isl_give isl_set *isl_set_from_union_set(
1068 __isl_take isl_union_set *uset);
1069 __isl_give isl_map *isl_map_from_union_map(
1070 __isl_take isl_union_map *umap);
1072 Sets and relations can be copied and freed again using the following
1075 __isl_give isl_basic_set *isl_basic_set_copy(
1076 __isl_keep isl_basic_set *bset);
1077 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1078 __isl_give isl_union_set *isl_union_set_copy(
1079 __isl_keep isl_union_set *uset);
1080 __isl_give isl_basic_map *isl_basic_map_copy(
1081 __isl_keep isl_basic_map *bmap);
1082 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1083 __isl_give isl_union_map *isl_union_map_copy(
1084 __isl_keep isl_union_map *umap);
1085 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1086 void isl_set_free(__isl_take isl_set *set);
1087 void *isl_union_set_free(__isl_take isl_union_set *uset);
1088 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1089 void isl_map_free(__isl_take isl_map *map);
1090 void *isl_union_map_free(__isl_take isl_union_map *umap);
1092 Other sets and relations can be constructed by starting
1093 from a universe set or relation, adding equality and/or
1094 inequality constraints and then projecting out the
1095 existentially quantified variables, if any.
1096 Constraints can be constructed, manipulated and
1097 added to (or removed from) (basic) sets and relations
1098 using the following functions.
1100 #include <isl/constraint.h>
1101 __isl_give isl_constraint *isl_equality_alloc(
1102 __isl_take isl_local_space *ls);
1103 __isl_give isl_constraint *isl_inequality_alloc(
1104 __isl_take isl_local_space *ls);
1105 __isl_give isl_constraint *isl_constraint_set_constant(
1106 __isl_take isl_constraint *constraint, isl_int v);
1107 __isl_give isl_constraint *isl_constraint_set_constant_si(
1108 __isl_take isl_constraint *constraint, int v);
1109 __isl_give isl_constraint *isl_constraint_set_coefficient(
1110 __isl_take isl_constraint *constraint,
1111 enum isl_dim_type type, int pos, isl_int v);
1112 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1113 __isl_take isl_constraint *constraint,
1114 enum isl_dim_type type, int pos, int v);
1115 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1116 __isl_take isl_basic_map *bmap,
1117 __isl_take isl_constraint *constraint);
1118 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1119 __isl_take isl_basic_set *bset,
1120 __isl_take isl_constraint *constraint);
1121 __isl_give isl_map *isl_map_add_constraint(
1122 __isl_take isl_map *map,
1123 __isl_take isl_constraint *constraint);
1124 __isl_give isl_set *isl_set_add_constraint(
1125 __isl_take isl_set *set,
1126 __isl_take isl_constraint *constraint);
1127 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1128 __isl_take isl_basic_set *bset,
1129 __isl_take isl_constraint *constraint);
1131 For example, to create a set containing the even integers
1132 between 10 and 42, you would use the following code.
1135 isl_local_space *ls;
1137 isl_basic_set *bset;
1139 space = isl_space_set_alloc(ctx, 0, 2);
1140 bset = isl_basic_set_universe(isl_space_copy(space));
1141 ls = isl_local_space_from_space(space);
1143 c = isl_equality_alloc(isl_local_space_copy(ls));
1144 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1145 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1146 bset = isl_basic_set_add_constraint(bset, c);
1148 c = isl_inequality_alloc(isl_local_space_copy(ls));
1149 c = isl_constraint_set_constant_si(c, -10);
1150 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1151 bset = isl_basic_set_add_constraint(bset, c);
1153 c = isl_inequality_alloc(ls);
1154 c = isl_constraint_set_constant_si(c, 42);
1155 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1156 bset = isl_basic_set_add_constraint(bset, c);
1158 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1162 isl_basic_set *bset;
1163 bset = isl_basic_set_read_from_str(ctx,
1164 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1166 A basic set or relation can also be constructed from two matrices
1167 describing the equalities and the inequalities.
1169 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1170 __isl_take isl_space *space,
1171 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1172 enum isl_dim_type c1,
1173 enum isl_dim_type c2, enum isl_dim_type c3,
1174 enum isl_dim_type c4);
1175 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1176 __isl_take isl_space *space,
1177 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1178 enum isl_dim_type c1,
1179 enum isl_dim_type c2, enum isl_dim_type c3,
1180 enum isl_dim_type c4, enum isl_dim_type c5);
1182 The C<isl_dim_type> arguments indicate the order in which
1183 different kinds of variables appear in the input matrices
1184 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1185 C<isl_dim_set> and C<isl_dim_div> for sets and
1186 of C<isl_dim_cst>, C<isl_dim_param>,
1187 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1189 A (basic) set or relation can also be constructed from a (piecewise)
1191 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1193 __isl_give isl_basic_map *isl_basic_map_from_aff(
1194 __isl_take isl_aff *aff);
1195 __isl_give isl_set *isl_set_from_pw_aff(
1196 __isl_take isl_pw_aff *pwaff);
1197 __isl_give isl_map *isl_map_from_pw_aff(
1198 __isl_take isl_pw_aff *pwaff);
1199 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1200 __isl_take isl_space *domain_space,
1201 __isl_take isl_aff_list *list);
1203 The C<domain_dim> argument describes the domain of the resulting
1204 basic relation. It is required because the C<list> may consist
1205 of zero affine expressions.
1207 =head2 Inspecting Sets and Relations
1209 Usually, the user should not have to care about the actual constraints
1210 of the sets and maps, but should instead apply the abstract operations
1211 explained in the following sections.
1212 Occasionally, however, it may be required to inspect the individual
1213 coefficients of the constraints. This section explains how to do so.
1214 In these cases, it may also be useful to have C<isl> compute
1215 an explicit representation of the existentially quantified variables.
1217 __isl_give isl_set *isl_set_compute_divs(
1218 __isl_take isl_set *set);
1219 __isl_give isl_map *isl_map_compute_divs(
1220 __isl_take isl_map *map);
1221 __isl_give isl_union_set *isl_union_set_compute_divs(
1222 __isl_take isl_union_set *uset);
1223 __isl_give isl_union_map *isl_union_map_compute_divs(
1224 __isl_take isl_union_map *umap);
1226 This explicit representation defines the existentially quantified
1227 variables as integer divisions of the other variables, possibly
1228 including earlier existentially quantified variables.
1229 An explicitly represented existentially quantified variable therefore
1230 has a unique value when the values of the other variables are known.
1231 If, furthermore, the same existentials, i.e., existentials
1232 with the same explicit representations, should appear in the
1233 same order in each of the disjuncts of a set or map, then the user should call
1234 either of the following functions.
1236 __isl_give isl_set *isl_set_align_divs(
1237 __isl_take isl_set *set);
1238 __isl_give isl_map *isl_map_align_divs(
1239 __isl_take isl_map *map);
1241 Alternatively, the existentially quantified variables can be removed
1242 using the following functions, which compute an overapproximation.
1244 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1245 __isl_take isl_basic_set *bset);
1246 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1247 __isl_take isl_basic_map *bmap);
1248 __isl_give isl_set *isl_set_remove_divs(
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_remove_divs(
1251 __isl_take isl_map *map);
1253 To iterate over all the sets or maps in a union set or map, use
1255 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1256 int (*fn)(__isl_take isl_set *set, void *user),
1258 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1259 int (*fn)(__isl_take isl_map *map, void *user),
1262 The number of sets or maps in a union set or map can be obtained
1265 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1266 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1268 To extract the set or map in a given space from a union, use
1270 __isl_give isl_set *isl_union_set_extract_set(
1271 __isl_keep isl_union_set *uset,
1272 __isl_take isl_space *space);
1273 __isl_give isl_map *isl_union_map_extract_map(
1274 __isl_keep isl_union_map *umap,
1275 __isl_take isl_space *space);
1277 To iterate over all the basic sets or maps in a set or map, use
1279 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1280 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1282 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1283 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1286 The callback function C<fn> should return 0 if successful and
1287 -1 if an error occurs. In the latter case, or if any other error
1288 occurs, the above functions will return -1.
1290 It should be noted that C<isl> does not guarantee that
1291 the basic sets or maps passed to C<fn> are disjoint.
1292 If this is required, then the user should call one of
1293 the following functions first.
1295 __isl_give isl_set *isl_set_make_disjoint(
1296 __isl_take isl_set *set);
1297 __isl_give isl_map *isl_map_make_disjoint(
1298 __isl_take isl_map *map);
1300 The number of basic sets in a set can be obtained
1303 int isl_set_n_basic_set(__isl_keep isl_set *set);
1305 To iterate over the constraints of a basic set or map, use
1307 #include <isl/constraint.h>
1309 int isl_basic_map_foreach_constraint(
1310 __isl_keep isl_basic_map *bmap,
1311 int (*fn)(__isl_take isl_constraint *c, void *user),
1313 void *isl_constraint_free(__isl_take isl_constraint *c);
1315 Again, the callback function C<fn> should return 0 if successful and
1316 -1 if an error occurs. In the latter case, or if any other error
1317 occurs, the above functions will return -1.
1318 The constraint C<c> represents either an equality or an inequality.
1319 Use the following function to find out whether a constraint
1320 represents an equality. If not, it represents an inequality.
1322 int isl_constraint_is_equality(
1323 __isl_keep isl_constraint *constraint);
1325 The coefficients of the constraints can be inspected using
1326 the following functions.
1328 void isl_constraint_get_constant(
1329 __isl_keep isl_constraint *constraint, isl_int *v);
1330 void isl_constraint_get_coefficient(
1331 __isl_keep isl_constraint *constraint,
1332 enum isl_dim_type type, int pos, isl_int *v);
1333 int isl_constraint_involves_dims(
1334 __isl_keep isl_constraint *constraint,
1335 enum isl_dim_type type, unsigned first, unsigned n);
1337 The explicit representations of the existentially quantified
1338 variables can be inspected using the following function.
1339 Note that the user is only allowed to use this function
1340 if the inspected set or map is the result of a call
1341 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1342 The existentially quantified variable is equal to the floor
1343 of the returned affine expression. The affine expression
1344 itself can be inspected using the functions in
1345 L<"Piecewise Quasi Affine Expressions">.
1347 __isl_give isl_aff *isl_constraint_get_div(
1348 __isl_keep isl_constraint *constraint, int pos);
1350 To obtain the constraints of a basic set or map in matrix
1351 form, use the following functions.
1353 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1354 __isl_keep isl_basic_set *bset,
1355 enum isl_dim_type c1, enum isl_dim_type c2,
1356 enum isl_dim_type c3, enum isl_dim_type c4);
1357 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1358 __isl_keep isl_basic_set *bset,
1359 enum isl_dim_type c1, enum isl_dim_type c2,
1360 enum isl_dim_type c3, enum isl_dim_type c4);
1361 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1362 __isl_keep isl_basic_map *bmap,
1363 enum isl_dim_type c1,
1364 enum isl_dim_type c2, enum isl_dim_type c3,
1365 enum isl_dim_type c4, enum isl_dim_type c5);
1366 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1367 __isl_keep isl_basic_map *bmap,
1368 enum isl_dim_type c1,
1369 enum isl_dim_type c2, enum isl_dim_type c3,
1370 enum isl_dim_type c4, enum isl_dim_type c5);
1372 The C<isl_dim_type> arguments dictate the order in which
1373 different kinds of variables appear in the resulting matrix
1374 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1375 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1377 The number of parameters, input, output or set dimensions can
1378 be obtained using the following functions.
1380 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1381 enum isl_dim_type type);
1382 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1383 enum isl_dim_type type);
1384 unsigned isl_set_dim(__isl_keep isl_set *set,
1385 enum isl_dim_type type);
1386 unsigned isl_map_dim(__isl_keep isl_map *map,
1387 enum isl_dim_type type);
1389 To check whether the description of a set or relation depends
1390 on one or more given dimensions, it is not necessary to iterate over all
1391 constraints. Instead the following functions can be used.
1393 int isl_basic_set_involves_dims(
1394 __isl_keep isl_basic_set *bset,
1395 enum isl_dim_type type, unsigned first, unsigned n);
1396 int isl_set_involves_dims(__isl_keep isl_set *set,
1397 enum isl_dim_type type, unsigned first, unsigned n);
1398 int isl_basic_map_involves_dims(
1399 __isl_keep isl_basic_map *bmap,
1400 enum isl_dim_type type, unsigned first, unsigned n);
1401 int isl_map_involves_dims(__isl_keep isl_map *map,
1402 enum isl_dim_type type, unsigned first, unsigned n);
1404 Similarly, the following functions can be used to check whether
1405 a given dimension is involved in any lower or upper bound.
1407 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1408 enum isl_dim_type type, unsigned pos);
1409 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1410 enum isl_dim_type type, unsigned pos);
1412 The identifiers or names of the domain and range spaces of a set
1413 or relation can be read off or set using the following functions.
1415 __isl_give isl_set *isl_set_set_tuple_id(
1416 __isl_take isl_set *set, __isl_take isl_id *id);
1417 __isl_give isl_set *isl_set_reset_tuple_id(
1418 __isl_take isl_set *set);
1419 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1420 __isl_give isl_id *isl_set_get_tuple_id(
1421 __isl_keep isl_set *set);
1422 __isl_give isl_map *isl_map_set_tuple_id(
1423 __isl_take isl_map *map, enum isl_dim_type type,
1424 __isl_take isl_id *id);
1425 __isl_give isl_map *isl_map_reset_tuple_id(
1426 __isl_take isl_map *map, enum isl_dim_type type);
1427 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1428 enum isl_dim_type type);
1429 __isl_give isl_id *isl_map_get_tuple_id(
1430 __isl_keep isl_map *map, enum isl_dim_type type);
1432 const char *isl_basic_set_get_tuple_name(
1433 __isl_keep isl_basic_set *bset);
1434 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1435 __isl_take isl_basic_set *set, const char *s);
1436 const char *isl_set_get_tuple_name(
1437 __isl_keep isl_set *set);
1438 const char *isl_basic_map_get_tuple_name(
1439 __isl_keep isl_basic_map *bmap,
1440 enum isl_dim_type type);
1441 const char *isl_map_get_tuple_name(
1442 __isl_keep isl_map *map,
1443 enum isl_dim_type type);
1445 As with C<isl_space_get_tuple_name>, the value returned points to
1446 an internal data structure.
1447 The identifiers, positions or names of individual dimensions can be
1448 read off using the following functions.
1450 __isl_give isl_set *isl_set_set_dim_id(
1451 __isl_take isl_set *set, enum isl_dim_type type,
1452 unsigned pos, __isl_take isl_id *id);
1453 int isl_set_has_dim_id(__isl_keep isl_set *set,
1454 enum isl_dim_type type, unsigned pos);
1455 __isl_give isl_id *isl_set_get_dim_id(
1456 __isl_keep isl_set *set, enum isl_dim_type type,
1458 __isl_give isl_map *isl_map_set_dim_id(
1459 __isl_take isl_map *map, enum isl_dim_type type,
1460 unsigned pos, __isl_take isl_id *id);
1461 int isl_map_has_dim_id(__isl_keep isl_map *map,
1462 enum isl_dim_type type, unsigned pos);
1463 __isl_give isl_id *isl_map_get_dim_id(
1464 __isl_keep isl_map *map, enum isl_dim_type type,
1467 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1468 enum isl_dim_type type, __isl_keep isl_id *id);
1469 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1470 enum isl_dim_type type, __isl_keep isl_id *id);
1472 const char *isl_constraint_get_dim_name(
1473 __isl_keep isl_constraint *constraint,
1474 enum isl_dim_type type, unsigned pos);
1475 const char *isl_basic_set_get_dim_name(
1476 __isl_keep isl_basic_set *bset,
1477 enum isl_dim_type type, unsigned pos);
1478 const char *isl_set_get_dim_name(
1479 __isl_keep isl_set *set,
1480 enum isl_dim_type type, unsigned pos);
1481 const char *isl_basic_map_get_dim_name(
1482 __isl_keep isl_basic_map *bmap,
1483 enum isl_dim_type type, unsigned pos);
1484 const char *isl_map_get_dim_name(
1485 __isl_keep isl_map *map,
1486 enum isl_dim_type type, unsigned pos);
1488 These functions are mostly useful to obtain the identifiers, positions
1489 or names of the parameters. Identifiers of individual dimensions are
1490 essentially only useful for printing. They are ignored by all other
1491 operations and may not be preserved across those operations.
1495 =head3 Unary Properties
1501 The following functions test whether the given set or relation
1502 contains any integer points. The ``plain'' variants do not perform
1503 any computations, but simply check if the given set or relation
1504 is already known to be empty.
1506 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1507 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1508 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1509 int isl_set_is_empty(__isl_keep isl_set *set);
1510 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1511 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1512 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1513 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1514 int isl_map_is_empty(__isl_keep isl_map *map);
1515 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1517 =item * Universality
1519 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1520 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1521 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1523 =item * Single-valuedness
1525 int isl_map_is_single_valued(__isl_keep isl_map *map);
1526 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1530 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1531 int isl_map_is_injective(__isl_keep isl_map *map);
1532 int isl_union_map_plain_is_injective(
1533 __isl_keep isl_union_map *umap);
1534 int isl_union_map_is_injective(
1535 __isl_keep isl_union_map *umap);
1539 int isl_map_is_bijective(__isl_keep isl_map *map);
1540 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1544 int isl_basic_map_plain_is_fixed(
1545 __isl_keep isl_basic_map *bmap,
1546 enum isl_dim_type type, unsigned pos,
1548 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1549 enum isl_dim_type type, unsigned pos,
1552 Check if the relation obviously lies on a hyperplane where the given dimension
1553 has a fixed value and if so, return that value in C<*val>.
1557 To check whether a set is a parameter domain, use this function:
1559 int isl_set_is_params(__isl_keep isl_set *set);
1563 The following functions check whether the domain of the given
1564 (basic) set is a wrapped relation.
1566 int isl_basic_set_is_wrapping(
1567 __isl_keep isl_basic_set *bset);
1568 int isl_set_is_wrapping(__isl_keep isl_set *set);
1570 =item * Internal Product
1572 int isl_basic_map_can_zip(
1573 __isl_keep isl_basic_map *bmap);
1574 int isl_map_can_zip(__isl_keep isl_map *map);
1576 Check whether the product of domain and range of the given relation
1578 i.e., whether both domain and range are nested relations.
1582 =head3 Binary Properties
1588 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1589 __isl_keep isl_set *set2);
1590 int isl_set_is_equal(__isl_keep isl_set *set1,
1591 __isl_keep isl_set *set2);
1592 int isl_union_set_is_equal(
1593 __isl_keep isl_union_set *uset1,
1594 __isl_keep isl_union_set *uset2);
1595 int isl_basic_map_is_equal(
1596 __isl_keep isl_basic_map *bmap1,
1597 __isl_keep isl_basic_map *bmap2);
1598 int isl_map_is_equal(__isl_keep isl_map *map1,
1599 __isl_keep isl_map *map2);
1600 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1601 __isl_keep isl_map *map2);
1602 int isl_union_map_is_equal(
1603 __isl_keep isl_union_map *umap1,
1604 __isl_keep isl_union_map *umap2);
1606 =item * Disjointness
1608 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1609 __isl_keep isl_set *set2);
1613 int isl_set_is_subset(__isl_keep isl_set *set1,
1614 __isl_keep isl_set *set2);
1615 int isl_set_is_strict_subset(
1616 __isl_keep isl_set *set1,
1617 __isl_keep isl_set *set2);
1618 int isl_union_set_is_subset(
1619 __isl_keep isl_union_set *uset1,
1620 __isl_keep isl_union_set *uset2);
1621 int isl_union_set_is_strict_subset(
1622 __isl_keep isl_union_set *uset1,
1623 __isl_keep isl_union_set *uset2);
1624 int isl_basic_map_is_subset(
1625 __isl_keep isl_basic_map *bmap1,
1626 __isl_keep isl_basic_map *bmap2);
1627 int isl_basic_map_is_strict_subset(
1628 __isl_keep isl_basic_map *bmap1,
1629 __isl_keep isl_basic_map *bmap2);
1630 int isl_map_is_subset(
1631 __isl_keep isl_map *map1,
1632 __isl_keep isl_map *map2);
1633 int isl_map_is_strict_subset(
1634 __isl_keep isl_map *map1,
1635 __isl_keep isl_map *map2);
1636 int isl_union_map_is_subset(
1637 __isl_keep isl_union_map *umap1,
1638 __isl_keep isl_union_map *umap2);
1639 int isl_union_map_is_strict_subset(
1640 __isl_keep isl_union_map *umap1,
1641 __isl_keep isl_union_map *umap2);
1645 =head2 Unary Operations
1651 __isl_give isl_set *isl_set_complement(
1652 __isl_take isl_set *set);
1656 __isl_give isl_basic_map *isl_basic_map_reverse(
1657 __isl_take isl_basic_map *bmap);
1658 __isl_give isl_map *isl_map_reverse(
1659 __isl_take isl_map *map);
1660 __isl_give isl_union_map *isl_union_map_reverse(
1661 __isl_take isl_union_map *umap);
1665 __isl_give isl_basic_set *isl_basic_set_project_out(
1666 __isl_take isl_basic_set *bset,
1667 enum isl_dim_type type, unsigned first, unsigned n);
1668 __isl_give isl_basic_map *isl_basic_map_project_out(
1669 __isl_take isl_basic_map *bmap,
1670 enum isl_dim_type type, unsigned first, unsigned n);
1671 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1672 enum isl_dim_type type, unsigned first, unsigned n);
1673 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1674 enum isl_dim_type type, unsigned first, unsigned n);
1675 __isl_give isl_basic_set *isl_basic_set_params(
1676 __isl_take isl_basic_set *bset);
1677 __isl_give isl_basic_set *isl_basic_map_domain(
1678 __isl_take isl_basic_map *bmap);
1679 __isl_give isl_basic_set *isl_basic_map_range(
1680 __isl_take isl_basic_map *bmap);
1681 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1682 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1683 __isl_give isl_set *isl_map_domain(
1684 __isl_take isl_map *bmap);
1685 __isl_give isl_set *isl_map_range(
1686 __isl_take isl_map *map);
1687 __isl_give isl_union_set *isl_union_map_domain(
1688 __isl_take isl_union_map *umap);
1689 __isl_give isl_union_set *isl_union_map_range(
1690 __isl_take isl_union_map *umap);
1692 __isl_give isl_basic_map *isl_basic_map_domain_map(
1693 __isl_take isl_basic_map *bmap);
1694 __isl_give isl_basic_map *isl_basic_map_range_map(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1697 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1698 __isl_give isl_union_map *isl_union_map_domain_map(
1699 __isl_take isl_union_map *umap);
1700 __isl_give isl_union_map *isl_union_map_range_map(
1701 __isl_take isl_union_map *umap);
1703 The functions above construct a (basic, regular or union) relation
1704 that maps (a wrapped version of) the input relation to its domain or range.
1708 __isl_give isl_set *isl_set_eliminate(
1709 __isl_take isl_set *set, enum isl_dim_type type,
1710 unsigned first, unsigned n);
1712 Eliminate the coefficients for the given dimensions from the constraints,
1713 without removing the dimensions.
1717 __isl_give isl_basic_set *isl_basic_set_fix(
1718 __isl_take isl_basic_set *bset,
1719 enum isl_dim_type type, unsigned pos,
1721 __isl_give isl_basic_set *isl_basic_set_fix_si(
1722 __isl_take isl_basic_set *bset,
1723 enum isl_dim_type type, unsigned pos, int value);
1724 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1725 enum isl_dim_type type, unsigned pos,
1727 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1728 enum isl_dim_type type, unsigned pos, int value);
1729 __isl_give isl_basic_map *isl_basic_map_fix_si(
1730 __isl_take isl_basic_map *bmap,
1731 enum isl_dim_type type, unsigned pos, int value);
1732 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1733 enum isl_dim_type type, unsigned pos, int value);
1735 Intersect the set or relation with the hyperplane where the given
1736 dimension has the fixed given value.
1738 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1739 enum isl_dim_type type1, int pos1,
1740 enum isl_dim_type type2, int pos2);
1741 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1742 enum isl_dim_type type1, int pos1,
1743 enum isl_dim_type type2, int pos2);
1745 Intersect the set or relation with the hyperplane where the given
1746 dimensions are equal to each other.
1748 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1749 enum isl_dim_type type1, int pos1,
1750 enum isl_dim_type type2, int pos2);
1752 Intersect the relation with the hyperplane where the given
1753 dimensions have opposite values.
1757 __isl_give isl_map *isl_set_identity(
1758 __isl_take isl_set *set);
1759 __isl_give isl_union_map *isl_union_set_identity(
1760 __isl_take isl_union_set *uset);
1762 Construct an identity relation on the given (union) set.
1766 __isl_give isl_basic_set *isl_basic_map_deltas(
1767 __isl_take isl_basic_map *bmap);
1768 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1769 __isl_give isl_union_set *isl_union_map_deltas(
1770 __isl_take isl_union_map *umap);
1772 These functions return a (basic) set containing the differences
1773 between image elements and corresponding domain elements in the input.
1775 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1776 __isl_take isl_basic_map *bmap);
1777 __isl_give isl_map *isl_map_deltas_map(
1778 __isl_take isl_map *map);
1779 __isl_give isl_union_map *isl_union_map_deltas_map(
1780 __isl_take isl_union_map *umap);
1782 The functions above construct a (basic, regular or union) relation
1783 that maps (a wrapped version of) the input relation to its delta set.
1787 Simplify the representation of a set or relation by trying
1788 to combine pairs of basic sets or relations into a single
1789 basic set or relation.
1791 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1792 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1793 __isl_give isl_union_set *isl_union_set_coalesce(
1794 __isl_take isl_union_set *uset);
1795 __isl_give isl_union_map *isl_union_map_coalesce(
1796 __isl_take isl_union_map *umap);
1798 =item * Detecting equalities
1800 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1801 __isl_take isl_basic_set *bset);
1802 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1803 __isl_take isl_basic_map *bmap);
1804 __isl_give isl_set *isl_set_detect_equalities(
1805 __isl_take isl_set *set);
1806 __isl_give isl_map *isl_map_detect_equalities(
1807 __isl_take isl_map *map);
1808 __isl_give isl_union_set *isl_union_set_detect_equalities(
1809 __isl_take isl_union_set *uset);
1810 __isl_give isl_union_map *isl_union_map_detect_equalities(
1811 __isl_take isl_union_map *umap);
1813 Simplify the representation of a set or relation by detecting implicit
1816 =item * Removing redundant constraints
1818 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1819 __isl_take isl_basic_set *bset);
1820 __isl_give isl_set *isl_set_remove_redundancies(
1821 __isl_take isl_set *set);
1822 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1823 __isl_take isl_basic_map *bmap);
1824 __isl_give isl_map *isl_map_remove_redundancies(
1825 __isl_take isl_map *map);
1829 __isl_give isl_basic_set *isl_set_convex_hull(
1830 __isl_take isl_set *set);
1831 __isl_give isl_basic_map *isl_map_convex_hull(
1832 __isl_take isl_map *map);
1834 If the input set or relation has any existentially quantified
1835 variables, then the result of these operations is currently undefined.
1839 __isl_give isl_basic_set *isl_set_simple_hull(
1840 __isl_take isl_set *set);
1841 __isl_give isl_basic_map *isl_map_simple_hull(
1842 __isl_take isl_map *map);
1843 __isl_give isl_union_map *isl_union_map_simple_hull(
1844 __isl_take isl_union_map *umap);
1846 These functions compute a single basic set or relation
1847 that contains the whole input set or relation.
1848 In particular, the output is described by translates
1849 of the constraints describing the basic sets or relations in the input.
1853 (See \autoref{s:simple hull}.)
1859 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1860 __isl_take isl_basic_set *bset);
1861 __isl_give isl_basic_set *isl_set_affine_hull(
1862 __isl_take isl_set *set);
1863 __isl_give isl_union_set *isl_union_set_affine_hull(
1864 __isl_take isl_union_set *uset);
1865 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1866 __isl_take isl_basic_map *bmap);
1867 __isl_give isl_basic_map *isl_map_affine_hull(
1868 __isl_take isl_map *map);
1869 __isl_give isl_union_map *isl_union_map_affine_hull(
1870 __isl_take isl_union_map *umap);
1872 In case of union sets and relations, the affine hull is computed
1875 =item * Polyhedral hull
1877 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1878 __isl_take isl_set *set);
1879 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1880 __isl_take isl_map *map);
1881 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1882 __isl_take isl_union_set *uset);
1883 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1884 __isl_take isl_union_map *umap);
1886 These functions compute a single basic set or relation
1887 not involving any existentially quantified variables
1888 that contains the whole input set or relation.
1889 In case of union sets and relations, the polyhedral hull is computed
1892 =item * Optimization
1894 #include <isl/ilp.h>
1895 enum isl_lp_result isl_basic_set_max(
1896 __isl_keep isl_basic_set *bset,
1897 __isl_keep isl_aff *obj, isl_int *opt)
1898 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1899 __isl_keep isl_aff *obj, isl_int *opt);
1900 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1901 __isl_keep isl_aff *obj, isl_int *opt);
1903 Compute the minimum or maximum of the integer affine expression C<obj>
1904 over the points in C<set>, returning the result in C<opt>.
1905 The return value may be one of C<isl_lp_error>,
1906 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1908 =item * Parametric optimization
1910 __isl_give isl_pw_aff *isl_set_dim_min(
1911 __isl_take isl_set *set, int pos);
1912 __isl_give isl_pw_aff *isl_set_dim_max(
1913 __isl_take isl_set *set, int pos);
1915 Compute the minimum or maximum of the given set dimension as a function of the
1916 parameters, but independently of the other set dimensions.
1917 For lexicographic optimization, see L<"Lexicographic Optimization">.
1921 The following functions compute either the set of (rational) coefficient
1922 values of valid constraints for the given set or the set of (rational)
1923 values satisfying the constraints with coefficients from the given set.
1924 Internally, these two sets of functions perform essentially the
1925 same operations, except that the set of coefficients is assumed to
1926 be a cone, while the set of values may be any polyhedron.
1927 The current implementation is based on the Farkas lemma and
1928 Fourier-Motzkin elimination, but this may change or be made optional
1929 in future. In particular, future implementations may use different
1930 dualization algorithms or skip the elimination step.
1932 __isl_give isl_basic_set *isl_basic_set_coefficients(
1933 __isl_take isl_basic_set *bset);
1934 __isl_give isl_basic_set *isl_set_coefficients(
1935 __isl_take isl_set *set);
1936 __isl_give isl_union_set *isl_union_set_coefficients(
1937 __isl_take isl_union_set *bset);
1938 __isl_give isl_basic_set *isl_basic_set_solutions(
1939 __isl_take isl_basic_set *bset);
1940 __isl_give isl_basic_set *isl_set_solutions(
1941 __isl_take isl_set *set);
1942 __isl_give isl_union_set *isl_union_set_solutions(
1943 __isl_take isl_union_set *bset);
1947 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1949 __isl_give isl_union_map *isl_union_map_power(
1950 __isl_take isl_union_map *umap, int *exact);
1952 Compute a parametric representation for all positive powers I<k> of C<map>.
1953 The result maps I<k> to a nested relation corresponding to the
1954 I<k>th power of C<map>.
1955 The result may be an overapproximation. If the result is known to be exact,
1956 then C<*exact> is set to C<1>.
1958 =item * Transitive closure
1960 __isl_give isl_map *isl_map_transitive_closure(
1961 __isl_take isl_map *map, int *exact);
1962 __isl_give isl_union_map *isl_union_map_transitive_closure(
1963 __isl_take isl_union_map *umap, int *exact);
1965 Compute the transitive closure 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 * Reaching path lengths
1971 __isl_give isl_map *isl_map_reaching_path_lengths(
1972 __isl_take isl_map *map, int *exact);
1974 Compute a relation that maps each element in the range of C<map>
1975 to the lengths of all paths composed of edges in C<map> that
1976 end up in the given element.
1977 The result may be an overapproximation. If the result is known to be exact,
1978 then C<*exact> is set to C<1>.
1979 To compute the I<maximal> path length, the resulting relation
1980 should be postprocessed by C<isl_map_lexmax>.
1981 In particular, if the input relation is a dependence relation
1982 (mapping sources to sinks), then the maximal path length corresponds
1983 to the free schedule.
1984 Note, however, that C<isl_map_lexmax> expects the maximum to be
1985 finite, so if the path lengths are unbounded (possibly due to
1986 the overapproximation), then you will get an error message.
1990 __isl_give isl_basic_set *isl_basic_map_wrap(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_give isl_set *isl_map_wrap(
1993 __isl_take isl_map *map);
1994 __isl_give isl_union_set *isl_union_map_wrap(
1995 __isl_take isl_union_map *umap);
1996 __isl_give isl_basic_map *isl_basic_set_unwrap(
1997 __isl_take isl_basic_set *bset);
1998 __isl_give isl_map *isl_set_unwrap(
1999 __isl_take isl_set *set);
2000 __isl_give isl_union_map *isl_union_set_unwrap(
2001 __isl_take isl_union_set *uset);
2005 Remove any internal structure of domain (and range) of the given
2006 set or relation. If there is any such internal structure in the input,
2007 then the name of the space is also removed.
2009 __isl_give isl_basic_set *isl_basic_set_flatten(
2010 __isl_take isl_basic_set *bset);
2011 __isl_give isl_set *isl_set_flatten(
2012 __isl_take isl_set *set);
2013 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2014 __isl_take isl_basic_map *bmap);
2015 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2016 __isl_take isl_basic_map *bmap);
2017 __isl_give isl_map *isl_map_flatten_range(
2018 __isl_take isl_map *map);
2019 __isl_give isl_map *isl_map_flatten_domain(
2020 __isl_take isl_map *map);
2021 __isl_give isl_basic_map *isl_basic_map_flatten(
2022 __isl_take isl_basic_map *bmap);
2023 __isl_give isl_map *isl_map_flatten(
2024 __isl_take isl_map *map);
2026 __isl_give isl_map *isl_set_flatten_map(
2027 __isl_take isl_set *set);
2029 The function above constructs a relation
2030 that maps the input set to a flattened version of the set.
2034 Lift the input set to a space with extra dimensions corresponding
2035 to the existentially quantified variables in the input.
2036 In particular, the result lives in a wrapped map where the domain
2037 is the original space and the range corresponds to the original
2038 existentially quantified variables.
2040 __isl_give isl_basic_set *isl_basic_set_lift(
2041 __isl_take isl_basic_set *bset);
2042 __isl_give isl_set *isl_set_lift(
2043 __isl_take isl_set *set);
2044 __isl_give isl_union_set *isl_union_set_lift(
2045 __isl_take isl_union_set *uset);
2047 =item * Internal Product
2049 __isl_give isl_basic_map *isl_basic_map_zip(
2050 __isl_take isl_basic_map *bmap);
2051 __isl_give isl_map *isl_map_zip(
2052 __isl_take isl_map *map);
2053 __isl_give isl_union_map *isl_union_map_zip(
2054 __isl_take isl_union_map *umap);
2056 Given a relation with nested relations for domain and range,
2057 interchange the range of the domain with the domain of the range.
2059 =item * Aligning parameters
2061 __isl_give isl_set *isl_set_align_params(
2062 __isl_take isl_set *set,
2063 __isl_take isl_space *model);
2064 __isl_give isl_map *isl_map_align_params(
2065 __isl_take isl_map *map,
2066 __isl_take isl_space *model);
2068 Change the order of the parameters of the given set or relation
2069 such that the first parameters match those of C<model>.
2070 This may involve the introduction of extra parameters.
2071 All parameters need to be named.
2073 =item * Dimension manipulation
2075 __isl_give isl_set *isl_set_add_dims(
2076 __isl_take isl_set *set,
2077 enum isl_dim_type type, unsigned n);
2078 __isl_give isl_map *isl_map_add_dims(
2079 __isl_take isl_map *map,
2080 enum isl_dim_type type, unsigned n);
2081 __isl_give isl_set *isl_set_insert_dims(
2082 __isl_take isl_set *set,
2083 enum isl_dim_type type, unsigned pos, unsigned n);
2084 __isl_give isl_map *isl_map_insert_dims(
2085 __isl_take isl_map *map,
2086 enum isl_dim_type type, unsigned pos, unsigned n);
2087 __isl_give isl_basic_set *isl_basic_set_move_dims(
2088 __isl_take isl_basic_set *bset,
2089 enum isl_dim_type dst_type, unsigned dst_pos,
2090 enum isl_dim_type src_type, unsigned src_pos,
2092 __isl_give isl_basic_map *isl_basic_map_move_dims(
2093 __isl_take isl_basic_map *bmap,
2094 enum isl_dim_type dst_type, unsigned dst_pos,
2095 enum isl_dim_type src_type, unsigned src_pos,
2097 __isl_give isl_set *isl_set_move_dims(
2098 __isl_take isl_set *set,
2099 enum isl_dim_type dst_type, unsigned dst_pos,
2100 enum isl_dim_type src_type, unsigned src_pos,
2102 __isl_give isl_map *isl_map_move_dims(
2103 __isl_take isl_map *map,
2104 enum isl_dim_type dst_type, unsigned dst_pos,
2105 enum isl_dim_type src_type, unsigned src_pos,
2108 It is usually not advisable to directly change the (input or output)
2109 space of a set or a relation as this removes the name and the internal
2110 structure of the space. However, the above functions can be useful
2111 to add new parameters, assuming
2112 C<isl_set_align_params> and C<isl_map_align_params>
2117 =head2 Binary Operations
2119 The two arguments of a binary operation not only need to live
2120 in the same C<isl_ctx>, they currently also need to have
2121 the same (number of) parameters.
2123 =head3 Basic Operations
2127 =item * Intersection
2129 __isl_give isl_basic_set *isl_basic_set_intersect(
2130 __isl_take isl_basic_set *bset1,
2131 __isl_take isl_basic_set *bset2);
2132 __isl_give isl_set *isl_set_intersect_params(
2133 __isl_take isl_set *set,
2134 __isl_take isl_set *params);
2135 __isl_give isl_set *isl_set_intersect(
2136 __isl_take isl_set *set1,
2137 __isl_take isl_set *set2);
2138 __isl_give isl_union_set *isl_union_set_intersect(
2139 __isl_take isl_union_set *uset1,
2140 __isl_take isl_union_set *uset2);
2141 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2142 __isl_take isl_basic_map *bmap,
2143 __isl_take isl_basic_set *bset);
2144 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2145 __isl_take isl_basic_map *bmap,
2146 __isl_take isl_basic_set *bset);
2147 __isl_give isl_basic_map *isl_basic_map_intersect(
2148 __isl_take isl_basic_map *bmap1,
2149 __isl_take isl_basic_map *bmap2);
2150 __isl_give isl_map *isl_map_intersect_params(
2151 __isl_take isl_map *map,
2152 __isl_take isl_set *params);
2153 __isl_give isl_map *isl_map_intersect_domain(
2154 __isl_take isl_map *map,
2155 __isl_take isl_set *set);
2156 __isl_give isl_map *isl_map_intersect_range(
2157 __isl_take isl_map *map,
2158 __isl_take isl_set *set);
2159 __isl_give isl_map *isl_map_intersect(
2160 __isl_take isl_map *map1,
2161 __isl_take isl_map *map2);
2162 __isl_give isl_union_map *isl_union_map_intersect_domain(
2163 __isl_take isl_union_map *umap,
2164 __isl_take isl_union_set *uset);
2165 __isl_give isl_union_map *isl_union_map_intersect_range(
2166 __isl_take isl_union_map *umap,
2167 __isl_take isl_union_set *uset);
2168 __isl_give isl_union_map *isl_union_map_intersect(
2169 __isl_take isl_union_map *umap1,
2170 __isl_take isl_union_map *umap2);
2174 __isl_give isl_set *isl_basic_set_union(
2175 __isl_take isl_basic_set *bset1,
2176 __isl_take isl_basic_set *bset2);
2177 __isl_give isl_map *isl_basic_map_union(
2178 __isl_take isl_basic_map *bmap1,
2179 __isl_take isl_basic_map *bmap2);
2180 __isl_give isl_set *isl_set_union(
2181 __isl_take isl_set *set1,
2182 __isl_take isl_set *set2);
2183 __isl_give isl_map *isl_map_union(
2184 __isl_take isl_map *map1,
2185 __isl_take isl_map *map2);
2186 __isl_give isl_union_set *isl_union_set_union(
2187 __isl_take isl_union_set *uset1,
2188 __isl_take isl_union_set *uset2);
2189 __isl_give isl_union_map *isl_union_map_union(
2190 __isl_take isl_union_map *umap1,
2191 __isl_take isl_union_map *umap2);
2193 =item * Set difference
2195 __isl_give isl_set *isl_set_subtract(
2196 __isl_take isl_set *set1,
2197 __isl_take isl_set *set2);
2198 __isl_give isl_map *isl_map_subtract(
2199 __isl_take isl_map *map1,
2200 __isl_take isl_map *map2);
2201 __isl_give isl_union_set *isl_union_set_subtract(
2202 __isl_take isl_union_set *uset1,
2203 __isl_take isl_union_set *uset2);
2204 __isl_give isl_union_map *isl_union_map_subtract(
2205 __isl_take isl_union_map *umap1,
2206 __isl_take isl_union_map *umap2);
2210 __isl_give isl_basic_set *isl_basic_set_apply(
2211 __isl_take isl_basic_set *bset,
2212 __isl_take isl_basic_map *bmap);
2213 __isl_give isl_set *isl_set_apply(
2214 __isl_take isl_set *set,
2215 __isl_take isl_map *map);
2216 __isl_give isl_union_set *isl_union_set_apply(
2217 __isl_take isl_union_set *uset,
2218 __isl_take isl_union_map *umap);
2219 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2220 __isl_take isl_basic_map *bmap1,
2221 __isl_take isl_basic_map *bmap2);
2222 __isl_give isl_basic_map *isl_basic_map_apply_range(
2223 __isl_take isl_basic_map *bmap1,
2224 __isl_take isl_basic_map *bmap2);
2225 __isl_give isl_map *isl_map_apply_domain(
2226 __isl_take isl_map *map1,
2227 __isl_take isl_map *map2);
2228 __isl_give isl_union_map *isl_union_map_apply_domain(
2229 __isl_take isl_union_map *umap1,
2230 __isl_take isl_union_map *umap2);
2231 __isl_give isl_map *isl_map_apply_range(
2232 __isl_take isl_map *map1,
2233 __isl_take isl_map *map2);
2234 __isl_give isl_union_map *isl_union_map_apply_range(
2235 __isl_take isl_union_map *umap1,
2236 __isl_take isl_union_map *umap2);
2238 =item * Cartesian Product
2240 __isl_give isl_set *isl_set_product(
2241 __isl_take isl_set *set1,
2242 __isl_take isl_set *set2);
2243 __isl_give isl_union_set *isl_union_set_product(
2244 __isl_take isl_union_set *uset1,
2245 __isl_take isl_union_set *uset2);
2246 __isl_give isl_basic_map *isl_basic_map_domain_product(
2247 __isl_take isl_basic_map *bmap1,
2248 __isl_take isl_basic_map *bmap2);
2249 __isl_give isl_basic_map *isl_basic_map_range_product(
2250 __isl_take isl_basic_map *bmap1,
2251 __isl_take isl_basic_map *bmap2);
2252 __isl_give isl_map *isl_map_domain_product(
2253 __isl_take isl_map *map1,
2254 __isl_take isl_map *map2);
2255 __isl_give isl_map *isl_map_range_product(
2256 __isl_take isl_map *map1,
2257 __isl_take isl_map *map2);
2258 __isl_give isl_union_map *isl_union_map_range_product(
2259 __isl_take isl_union_map *umap1,
2260 __isl_take isl_union_map *umap2);
2261 __isl_give isl_map *isl_map_product(
2262 __isl_take isl_map *map1,
2263 __isl_take isl_map *map2);
2264 __isl_give isl_union_map *isl_union_map_product(
2265 __isl_take isl_union_map *umap1,
2266 __isl_take isl_union_map *umap2);
2268 The above functions compute the cross product of the given
2269 sets or relations. The domains and ranges of the results
2270 are wrapped maps between domains and ranges of the inputs.
2271 To obtain a ``flat'' product, use the following functions
2274 __isl_give isl_basic_set *isl_basic_set_flat_product(
2275 __isl_take isl_basic_set *bset1,
2276 __isl_take isl_basic_set *bset2);
2277 __isl_give isl_set *isl_set_flat_product(
2278 __isl_take isl_set *set1,
2279 __isl_take isl_set *set2);
2280 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2281 __isl_take isl_basic_map *bmap1,
2282 __isl_take isl_basic_map *bmap2);
2283 __isl_give isl_map *isl_map_flat_domain_product(
2284 __isl_take isl_map *map1,
2285 __isl_take isl_map *map2);
2286 __isl_give isl_map *isl_map_flat_range_product(
2287 __isl_take isl_map *map1,
2288 __isl_take isl_map *map2);
2289 __isl_give isl_union_map *isl_union_map_flat_range_product(
2290 __isl_take isl_union_map *umap1,
2291 __isl_take isl_union_map *umap2);
2292 __isl_give isl_basic_map *isl_basic_map_flat_product(
2293 __isl_take isl_basic_map *bmap1,
2294 __isl_take isl_basic_map *bmap2);
2295 __isl_give isl_map *isl_map_flat_product(
2296 __isl_take isl_map *map1,
2297 __isl_take isl_map *map2);
2299 =item * Simplification
2301 __isl_give isl_basic_set *isl_basic_set_gist(
2302 __isl_take isl_basic_set *bset,
2303 __isl_take isl_basic_set *context);
2304 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2305 __isl_take isl_set *context);
2306 __isl_give isl_set *isl_set_gist_params(
2307 __isl_take isl_set *set,
2308 __isl_take isl_set *context);
2309 __isl_give isl_union_set *isl_union_set_gist(
2310 __isl_take isl_union_set *uset,
2311 __isl_take isl_union_set *context);
2312 __isl_give isl_basic_map *isl_basic_map_gist(
2313 __isl_take isl_basic_map *bmap,
2314 __isl_take isl_basic_map *context);
2315 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2316 __isl_take isl_map *context);
2317 __isl_give isl_map *isl_map_gist_params(
2318 __isl_take isl_map *map,
2319 __isl_take isl_set *context);
2320 __isl_give isl_union_map *isl_union_map_gist(
2321 __isl_take isl_union_map *umap,
2322 __isl_take isl_union_map *context);
2324 The gist operation returns a set or relation that has the
2325 same intersection with the context as the input set or relation.
2326 Any implicit equality in the intersection is made explicit in the result,
2327 while all inequalities that are redundant with respect to the intersection
2329 In case of union sets and relations, the gist operation is performed
2334 =head3 Lexicographic Optimization
2336 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2337 the following functions
2338 compute a set that contains the lexicographic minimum or maximum
2339 of the elements in C<set> (or C<bset>) for those values of the parameters
2340 that satisfy C<dom>.
2341 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2342 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2344 In other words, the union of the parameter values
2345 for which the result is non-empty and of C<*empty>
2348 __isl_give isl_set *isl_basic_set_partial_lexmin(
2349 __isl_take isl_basic_set *bset,
2350 __isl_take isl_basic_set *dom,
2351 __isl_give isl_set **empty);
2352 __isl_give isl_set *isl_basic_set_partial_lexmax(
2353 __isl_take isl_basic_set *bset,
2354 __isl_take isl_basic_set *dom,
2355 __isl_give isl_set **empty);
2356 __isl_give isl_set *isl_set_partial_lexmin(
2357 __isl_take isl_set *set, __isl_take isl_set *dom,
2358 __isl_give isl_set **empty);
2359 __isl_give isl_set *isl_set_partial_lexmax(
2360 __isl_take isl_set *set, __isl_take isl_set *dom,
2361 __isl_give isl_set **empty);
2363 Given a (basic) set C<set> (or C<bset>), the following functions simply
2364 return a set containing the lexicographic minimum or maximum
2365 of the elements in C<set> (or C<bset>).
2366 In case of union sets, the optimum is computed per space.
2368 __isl_give isl_set *isl_basic_set_lexmin(
2369 __isl_take isl_basic_set *bset);
2370 __isl_give isl_set *isl_basic_set_lexmax(
2371 __isl_take isl_basic_set *bset);
2372 __isl_give isl_set *isl_set_lexmin(
2373 __isl_take isl_set *set);
2374 __isl_give isl_set *isl_set_lexmax(
2375 __isl_take isl_set *set);
2376 __isl_give isl_union_set *isl_union_set_lexmin(
2377 __isl_take isl_union_set *uset);
2378 __isl_give isl_union_set *isl_union_set_lexmax(
2379 __isl_take isl_union_set *uset);
2381 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2382 the following functions
2383 compute a relation that maps each element of C<dom>
2384 to the single lexicographic minimum or maximum
2385 of the elements that are associated to that same
2386 element in C<map> (or C<bmap>).
2387 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2388 that contains the elements in C<dom> that do not map
2389 to any elements in C<map> (or C<bmap>).
2390 In other words, the union of the domain of the result and of C<*empty>
2393 __isl_give isl_map *isl_basic_map_partial_lexmax(
2394 __isl_take isl_basic_map *bmap,
2395 __isl_take isl_basic_set *dom,
2396 __isl_give isl_set **empty);
2397 __isl_give isl_map *isl_basic_map_partial_lexmin(
2398 __isl_take isl_basic_map *bmap,
2399 __isl_take isl_basic_set *dom,
2400 __isl_give isl_set **empty);
2401 __isl_give isl_map *isl_map_partial_lexmax(
2402 __isl_take isl_map *map, __isl_take isl_set *dom,
2403 __isl_give isl_set **empty);
2404 __isl_give isl_map *isl_map_partial_lexmin(
2405 __isl_take isl_map *map, __isl_take isl_set *dom,
2406 __isl_give isl_set **empty);
2408 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2409 return a map mapping each element in the domain of
2410 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2411 of all elements associated to that element.
2412 In case of union relations, the optimum is computed per space.
2414 __isl_give isl_map *isl_basic_map_lexmin(
2415 __isl_take isl_basic_map *bmap);
2416 __isl_give isl_map *isl_basic_map_lexmax(
2417 __isl_take isl_basic_map *bmap);
2418 __isl_give isl_map *isl_map_lexmin(
2419 __isl_take isl_map *map);
2420 __isl_give isl_map *isl_map_lexmax(
2421 __isl_take isl_map *map);
2422 __isl_give isl_union_map *isl_union_map_lexmin(
2423 __isl_take isl_union_map *umap);
2424 __isl_give isl_union_map *isl_union_map_lexmax(
2425 __isl_take isl_union_map *umap);
2429 Lists are defined over several element types, including
2430 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2431 Here we take lists of C<isl_set>s as an example.
2432 Lists can be created, copied and freed using the following functions.
2434 #include <isl/list.h>
2435 __isl_give isl_set_list *isl_set_list_from_set(
2436 __isl_take isl_set *el);
2437 __isl_give isl_set_list *isl_set_list_alloc(
2438 isl_ctx *ctx, int n);
2439 __isl_give isl_set_list *isl_set_list_copy(
2440 __isl_keep isl_set_list *list);
2441 __isl_give isl_set_list *isl_set_list_add(
2442 __isl_take isl_set_list *list,
2443 __isl_take isl_set *el);
2444 __isl_give isl_set_list *isl_set_list_concat(
2445 __isl_take isl_set_list *list1,
2446 __isl_take isl_set_list *list2);
2447 void *isl_set_list_free(__isl_take isl_set_list *list);
2449 C<isl_set_list_alloc> creates an empty list with a capacity for
2450 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2453 Lists can be inspected using the following functions.
2455 #include <isl/list.h>
2456 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2457 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2458 __isl_give isl_set *isl_set_list_get_set(
2459 __isl_keep isl_set_list *list, int index);
2460 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2461 int (*fn)(__isl_take isl_set *el, void *user),
2464 Lists can be printed using
2466 #include <isl/list.h>
2467 __isl_give isl_printer *isl_printer_print_set_list(
2468 __isl_take isl_printer *p,
2469 __isl_keep isl_set_list *list);
2473 Matrices can be created, copied and freed using the following functions.
2475 #include <isl/mat.h>
2476 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2477 unsigned n_row, unsigned n_col);
2478 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2479 void isl_mat_free(__isl_take isl_mat *mat);
2481 Note that the elements of a newly created matrix may have arbitrary values.
2482 The elements can be changed and inspected using the following functions.
2484 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2485 int isl_mat_rows(__isl_keep isl_mat *mat);
2486 int isl_mat_cols(__isl_keep isl_mat *mat);
2487 int isl_mat_get_element(__isl_keep isl_mat *mat,
2488 int row, int col, isl_int *v);
2489 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2490 int row, int col, isl_int v);
2491 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2492 int row, int col, int v);
2494 C<isl_mat_get_element> will return a negative value if anything went wrong.
2495 In that case, the value of C<*v> is undefined.
2497 The following function can be used to compute the (right) inverse
2498 of a matrix, i.e., a matrix such that the product of the original
2499 and the inverse (in that order) is a multiple of the identity matrix.
2500 The input matrix is assumed to be of full row-rank.
2502 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2504 The following function can be used to compute the (right) kernel
2505 (or null space) of a matrix, i.e., a matrix such that the product of
2506 the original and the kernel (in that order) is the zero matrix.
2508 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2510 =head2 Piecewise Quasi Affine Expressions
2512 The zero quasi affine expression on a given domain can be created using
2514 __isl_give isl_aff *isl_aff_zero_on_domain(
2515 __isl_take isl_local_space *ls);
2517 Note that the space in which the resulting object lives is a map space
2518 with the given space as domain and a one-dimensional range.
2520 An empty piecewise quasi affine expression (one with no cells)
2521 or a piecewise quasi affine expression with a single cell can
2522 be created using the following functions.
2524 #include <isl/aff.h>
2525 __isl_give isl_pw_aff *isl_pw_aff_empty(
2526 __isl_take isl_space *space);
2527 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2528 __isl_take isl_set *set, __isl_take isl_aff *aff);
2529 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2530 __isl_take isl_aff *aff);
2532 Quasi affine expressions can be copied and freed using
2534 #include <isl/aff.h>
2535 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2536 void *isl_aff_free(__isl_take isl_aff *aff);
2538 __isl_give isl_pw_aff *isl_pw_aff_copy(
2539 __isl_keep isl_pw_aff *pwaff);
2540 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2542 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2543 using the following function. The constraint is required to have
2544 a non-zero coefficient for the specified dimension.
2546 #include <isl/constraint.h>
2547 __isl_give isl_aff *isl_constraint_get_bound(
2548 __isl_keep isl_constraint *constraint,
2549 enum isl_dim_type type, int pos);
2551 The entire affine expression of the constraint can also be extracted
2552 using the following function.
2554 #include <isl/constraint.h>
2555 __isl_give isl_aff *isl_constraint_get_aff(
2556 __isl_keep isl_constraint *constraint);
2558 Conversely, an equality constraint equating
2559 the affine expression to zero or an inequality constraint enforcing
2560 the affine expression to be non-negative, can be constructed using
2562 __isl_give isl_constraint *isl_equality_from_aff(
2563 __isl_take isl_aff *aff);
2564 __isl_give isl_constraint *isl_inequality_from_aff(
2565 __isl_take isl_aff *aff);
2567 The expression can be inspected using
2569 #include <isl/aff.h>
2570 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2571 int isl_aff_dim(__isl_keep isl_aff *aff,
2572 enum isl_dim_type type);
2573 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2574 __isl_keep isl_aff *aff);
2575 __isl_give isl_local_space *isl_aff_get_local_space(
2576 __isl_keep isl_aff *aff);
2577 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2578 enum isl_dim_type type, unsigned pos);
2579 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2581 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2582 enum isl_dim_type type, int pos, isl_int *v);
2583 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2585 __isl_give isl_aff *isl_aff_get_div(
2586 __isl_keep isl_aff *aff, int pos);
2588 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2589 int (*fn)(__isl_take isl_set *set,
2590 __isl_take isl_aff *aff,
2591 void *user), void *user);
2593 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2594 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2596 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2597 enum isl_dim_type type, unsigned first, unsigned n);
2598 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2599 enum isl_dim_type type, unsigned first, unsigned n);
2601 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2602 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2603 enum isl_dim_type type);
2604 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2606 It can be modified using
2608 #include <isl/aff.h>
2609 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2610 __isl_take isl_pw_aff *pwaff,
2611 __isl_take isl_id *id);
2612 __isl_give isl_aff *isl_aff_set_dim_name(
2613 __isl_take isl_aff *aff, enum isl_dim_type type,
2614 unsigned pos, const char *s);
2615 __isl_give isl_aff *isl_aff_set_constant(
2616 __isl_take isl_aff *aff, isl_int v);
2617 __isl_give isl_aff *isl_aff_set_constant_si(
2618 __isl_take isl_aff *aff, int v);
2619 __isl_give isl_aff *isl_aff_set_coefficient(
2620 __isl_take isl_aff *aff,
2621 enum isl_dim_type type, int pos, isl_int v);
2622 __isl_give isl_aff *isl_aff_set_coefficient_si(
2623 __isl_take isl_aff *aff,
2624 enum isl_dim_type type, int pos, int v);
2625 __isl_give isl_aff *isl_aff_set_denominator(
2626 __isl_take isl_aff *aff, isl_int v);
2628 __isl_give isl_aff *isl_aff_add_constant(
2629 __isl_take isl_aff *aff, isl_int v);
2630 __isl_give isl_aff *isl_aff_add_constant_si(
2631 __isl_take isl_aff *aff, int v);
2632 __isl_give isl_aff *isl_aff_add_coefficient(
2633 __isl_take isl_aff *aff,
2634 enum isl_dim_type type, int pos, isl_int v);
2635 __isl_give isl_aff *isl_aff_add_coefficient_si(
2636 __isl_take isl_aff *aff,
2637 enum isl_dim_type type, int pos, int v);
2639 __isl_give isl_aff *isl_aff_insert_dims(
2640 __isl_take isl_aff *aff,
2641 enum isl_dim_type type, unsigned first, unsigned n);
2642 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2643 __isl_take isl_pw_aff *pwaff,
2644 enum isl_dim_type type, unsigned first, unsigned n);
2645 __isl_give isl_aff *isl_aff_add_dims(
2646 __isl_take isl_aff *aff,
2647 enum isl_dim_type type, unsigned n);
2648 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2649 __isl_take isl_pw_aff *pwaff,
2650 enum isl_dim_type type, unsigned n);
2651 __isl_give isl_aff *isl_aff_drop_dims(
2652 __isl_take isl_aff *aff,
2653 enum isl_dim_type type, unsigned first, unsigned n);
2654 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2655 __isl_take isl_pw_aff *pwaff,
2656 enum isl_dim_type type, unsigned first, unsigned n);
2658 Note that the C<set_constant> and C<set_coefficient> functions
2659 set the I<numerator> of the constant or coefficient, while
2660 C<add_constant> and C<add_coefficient> add an integer value to
2661 the possibly rational constant or coefficient.
2663 To check whether an affine expressions is obviously zero
2664 or obviously equal to some other affine expression, use
2666 #include <isl/aff.h>
2667 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2668 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2669 __isl_keep isl_aff *aff2);
2673 #include <isl/aff.h>
2674 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2675 __isl_take isl_aff *aff2);
2676 __isl_give isl_pw_aff *isl_pw_aff_add(
2677 __isl_take isl_pw_aff *pwaff1,
2678 __isl_take isl_pw_aff *pwaff2);
2679 __isl_give isl_pw_aff *isl_pw_aff_min(
2680 __isl_take isl_pw_aff *pwaff1,
2681 __isl_take isl_pw_aff *pwaff2);
2682 __isl_give isl_pw_aff *isl_pw_aff_max(
2683 __isl_take isl_pw_aff *pwaff1,
2684 __isl_take isl_pw_aff *pwaff2);
2685 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2686 __isl_take isl_aff *aff2);
2687 __isl_give isl_pw_aff *isl_pw_aff_sub(
2688 __isl_take isl_pw_aff *pwaff1,
2689 __isl_take isl_pw_aff *pwaff2);
2690 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2691 __isl_give isl_pw_aff *isl_pw_aff_neg(
2692 __isl_take isl_pw_aff *pwaff);
2693 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2694 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2695 __isl_take isl_pw_aff *pwaff);
2696 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2697 __isl_give isl_pw_aff *isl_pw_aff_floor(
2698 __isl_take isl_pw_aff *pwaff);
2699 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2701 __isl_give isl_pw_aff *isl_pw_aff_mod(
2702 __isl_take isl_pw_aff *pwaff, isl_int mod);
2703 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2705 __isl_give isl_pw_aff *isl_pw_aff_scale(
2706 __isl_take isl_pw_aff *pwaff, isl_int f);
2707 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2709 __isl_give isl_aff *isl_aff_scale_down_ui(
2710 __isl_take isl_aff *aff, unsigned f);
2711 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2712 __isl_take isl_pw_aff *pwaff, isl_int f);
2714 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2715 __isl_take isl_pw_aff_list *list);
2716 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2717 __isl_take isl_pw_aff_list *list);
2719 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2720 __isl_take isl_pw_aff *pwqp);
2722 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2723 __isl_take isl_pw_aff *pwaff,
2724 __isl_take isl_space *model);
2726 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2727 __isl_take isl_set *context);
2728 __isl_give isl_pw_aff *isl_pw_aff_gist(
2729 __isl_take isl_pw_aff *pwaff,
2730 __isl_take isl_set *context);
2732 __isl_give isl_set *isl_pw_aff_domain(
2733 __isl_take isl_pw_aff *pwaff);
2735 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2736 __isl_take isl_aff *aff2);
2737 __isl_give isl_pw_aff *isl_pw_aff_mul(
2738 __isl_take isl_pw_aff *pwaff1,
2739 __isl_take isl_pw_aff *pwaff2);
2741 When multiplying two affine expressions, at least one of the two needs
2744 #include <isl/aff.h>
2745 __isl_give isl_basic_set *isl_aff_le_basic_set(
2746 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2747 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2748 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2749 __isl_give isl_set *isl_pw_aff_eq_set(
2750 __isl_take isl_pw_aff *pwaff1,
2751 __isl_take isl_pw_aff *pwaff2);
2752 __isl_give isl_set *isl_pw_aff_ne_set(
2753 __isl_take isl_pw_aff *pwaff1,
2754 __isl_take isl_pw_aff *pwaff2);
2755 __isl_give isl_set *isl_pw_aff_le_set(
2756 __isl_take isl_pw_aff *pwaff1,
2757 __isl_take isl_pw_aff *pwaff2);
2758 __isl_give isl_set *isl_pw_aff_lt_set(
2759 __isl_take isl_pw_aff *pwaff1,
2760 __isl_take isl_pw_aff *pwaff2);
2761 __isl_give isl_set *isl_pw_aff_ge_set(
2762 __isl_take isl_pw_aff *pwaff1,
2763 __isl_take isl_pw_aff *pwaff2);
2764 __isl_give isl_set *isl_pw_aff_gt_set(
2765 __isl_take isl_pw_aff *pwaff1,
2766 __isl_take isl_pw_aff *pwaff2);
2768 __isl_give isl_set *isl_pw_aff_list_eq_set(
2769 __isl_take isl_pw_aff_list *list1,
2770 __isl_take isl_pw_aff_list *list2);
2771 __isl_give isl_set *isl_pw_aff_list_ne_set(
2772 __isl_take isl_pw_aff_list *list1,
2773 __isl_take isl_pw_aff_list *list2);
2774 __isl_give isl_set *isl_pw_aff_list_le_set(
2775 __isl_take isl_pw_aff_list *list1,
2776 __isl_take isl_pw_aff_list *list2);
2777 __isl_give isl_set *isl_pw_aff_list_lt_set(
2778 __isl_take isl_pw_aff_list *list1,
2779 __isl_take isl_pw_aff_list *list2);
2780 __isl_give isl_set *isl_pw_aff_list_ge_set(
2781 __isl_take isl_pw_aff_list *list1,
2782 __isl_take isl_pw_aff_list *list2);
2783 __isl_give isl_set *isl_pw_aff_list_gt_set(
2784 __isl_take isl_pw_aff_list *list1,
2785 __isl_take isl_pw_aff_list *list2);
2787 The function C<isl_aff_ge_basic_set> returns a basic set
2788 containing those elements in the shared space
2789 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2790 The function C<isl_aff_ge_set> returns a set
2791 containing those elements in the shared domain
2792 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2793 The functions operating on C<isl_pw_aff_list> apply the corresponding
2794 C<isl_pw_aff> function to each pair of elements in the two lists.
2796 #include <isl/aff.h>
2797 __isl_give isl_set *isl_pw_aff_nonneg_set(
2798 __isl_take isl_pw_aff *pwaff);
2799 __isl_give isl_set *isl_pw_aff_zero_set(
2800 __isl_take isl_pw_aff *pwaff);
2801 __isl_give isl_set *isl_pw_aff_non_zero_set(
2802 __isl_take isl_pw_aff *pwaff);
2804 The function C<isl_pw_aff_nonneg_set> returns a set
2805 containing those elements in the domain
2806 of C<pwaff> where C<pwaff> is non-negative.
2808 #include <isl/aff.h>
2809 __isl_give isl_pw_aff *isl_pw_aff_cond(
2810 __isl_take isl_set *cond,
2811 __isl_take isl_pw_aff *pwaff_true,
2812 __isl_take isl_pw_aff *pwaff_false);
2814 The function C<isl_pw_aff_cond> performs a conditional operator
2815 and returns an expression that is equal to C<pwaff_true>
2816 for elements in C<cond> and equal to C<pwaff_false> for elements
2819 #include <isl/aff.h>
2820 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2821 __isl_take isl_pw_aff *pwaff1,
2822 __isl_take isl_pw_aff *pwaff2);
2823 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2824 __isl_take isl_pw_aff *pwaff1,
2825 __isl_take isl_pw_aff *pwaff2);
2827 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2828 expression with a domain that is the union of those of C<pwaff1> and
2829 C<pwaff2> and such that on each cell, the quasi-affine expression is
2830 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2831 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2832 associated expression is the defined one.
2834 An expression can be printed using
2836 #include <isl/aff.h>
2837 __isl_give isl_printer *isl_printer_print_aff(
2838 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2840 __isl_give isl_printer *isl_printer_print_pw_aff(
2841 __isl_take isl_printer *p,
2842 __isl_keep isl_pw_aff *pwaff);
2846 Points are elements of a set. They can be used to construct
2847 simple sets (boxes) or they can be used to represent the
2848 individual elements of a set.
2849 The zero point (the origin) can be created using
2851 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2853 The coordinates of a point can be inspected, set and changed
2856 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2857 enum isl_dim_type type, int pos, isl_int *v);
2858 __isl_give isl_point *isl_point_set_coordinate(
2859 __isl_take isl_point *pnt,
2860 enum isl_dim_type type, int pos, isl_int v);
2862 __isl_give isl_point *isl_point_add_ui(
2863 __isl_take isl_point *pnt,
2864 enum isl_dim_type type, int pos, unsigned val);
2865 __isl_give isl_point *isl_point_sub_ui(
2866 __isl_take isl_point *pnt,
2867 enum isl_dim_type type, int pos, unsigned val);
2869 Other properties can be obtained using
2871 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2873 Points can be copied or freed using
2875 __isl_give isl_point *isl_point_copy(
2876 __isl_keep isl_point *pnt);
2877 void isl_point_free(__isl_take isl_point *pnt);
2879 A singleton set can be created from a point using
2881 __isl_give isl_basic_set *isl_basic_set_from_point(
2882 __isl_take isl_point *pnt);
2883 __isl_give isl_set *isl_set_from_point(
2884 __isl_take isl_point *pnt);
2886 and a box can be created from two opposite extremal points using
2888 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2889 __isl_take isl_point *pnt1,
2890 __isl_take isl_point *pnt2);
2891 __isl_give isl_set *isl_set_box_from_points(
2892 __isl_take isl_point *pnt1,
2893 __isl_take isl_point *pnt2);
2895 All elements of a B<bounded> (union) set can be enumerated using
2896 the following functions.
2898 int isl_set_foreach_point(__isl_keep isl_set *set,
2899 int (*fn)(__isl_take isl_point *pnt, void *user),
2901 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2902 int (*fn)(__isl_take isl_point *pnt, void *user),
2905 The function C<fn> is called for each integer point in
2906 C<set> with as second argument the last argument of
2907 the C<isl_set_foreach_point> call. The function C<fn>
2908 should return C<0> on success and C<-1> on failure.
2909 In the latter case, C<isl_set_foreach_point> will stop
2910 enumerating and return C<-1> as well.
2911 If the enumeration is performed successfully and to completion,
2912 then C<isl_set_foreach_point> returns C<0>.
2914 To obtain a single point of a (basic) set, use
2916 __isl_give isl_point *isl_basic_set_sample_point(
2917 __isl_take isl_basic_set *bset);
2918 __isl_give isl_point *isl_set_sample_point(
2919 __isl_take isl_set *set);
2921 If C<set> does not contain any (integer) points, then the
2922 resulting point will be ``void'', a property that can be
2925 int isl_point_is_void(__isl_keep isl_point *pnt);
2927 =head2 Piecewise Quasipolynomials
2929 A piecewise quasipolynomial is a particular kind of function that maps
2930 a parametric point to a rational value.
2931 More specifically, a quasipolynomial is a polynomial expression in greatest
2932 integer parts of affine expressions of parameters and variables.
2933 A piecewise quasipolynomial is a subdivision of a given parametric
2934 domain into disjoint cells with a quasipolynomial associated to
2935 each cell. The value of the piecewise quasipolynomial at a given
2936 point is the value of the quasipolynomial associated to the cell
2937 that contains the point. Outside of the union of cells,
2938 the value is assumed to be zero.
2939 For example, the piecewise quasipolynomial
2941 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2943 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2944 A given piecewise quasipolynomial has a fixed domain dimension.
2945 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2946 defined over different domains.
2947 Piecewise quasipolynomials are mainly used by the C<barvinok>
2948 library for representing the number of elements in a parametric set or map.
2949 For example, the piecewise quasipolynomial above represents
2950 the number of points in the map
2952 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2954 =head3 Printing (Piecewise) Quasipolynomials
2956 Quasipolynomials and piecewise quasipolynomials can be printed
2957 using the following functions.
2959 __isl_give isl_printer *isl_printer_print_qpolynomial(
2960 __isl_take isl_printer *p,
2961 __isl_keep isl_qpolynomial *qp);
2963 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2964 __isl_take isl_printer *p,
2965 __isl_keep isl_pw_qpolynomial *pwqp);
2967 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2968 __isl_take isl_printer *p,
2969 __isl_keep isl_union_pw_qpolynomial *upwqp);
2971 The output format of the printer
2972 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2973 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2975 In case of printing in C<ISL_FORMAT_C>, the user may want
2976 to set the names of all dimensions
2978 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2979 __isl_take isl_qpolynomial *qp,
2980 enum isl_dim_type type, unsigned pos,
2982 __isl_give isl_pw_qpolynomial *
2983 isl_pw_qpolynomial_set_dim_name(
2984 __isl_take isl_pw_qpolynomial *pwqp,
2985 enum isl_dim_type type, unsigned pos,
2988 =head3 Creating New (Piecewise) Quasipolynomials
2990 Some simple quasipolynomials can be created using the following functions.
2991 More complicated quasipolynomials can be created by applying
2992 operations such as addition and multiplication
2993 on the resulting quasipolynomials
2995 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2996 __isl_take isl_space *domain);
2997 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2998 __isl_take isl_space *domain);
2999 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3000 __isl_take isl_space *domain);
3001 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3002 __isl_take isl_space *domain);
3003 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3004 __isl_take isl_space *domain);
3005 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3006 __isl_take isl_space *domain,
3007 const isl_int n, const isl_int d);
3008 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3009 __isl_take isl_space *domain,
3010 enum isl_dim_type type, unsigned pos);
3011 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3012 __isl_take isl_aff *aff);
3014 Note that the space in which a quasipolynomial lives is a map space
3015 with a one-dimensional range. The C<domain> argument in some of
3016 the functions above corresponds to the domain of this map space.
3018 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3019 with a single cell can be created using the following functions.
3020 Multiple of these single cell piecewise quasipolynomials can
3021 be combined to create more complicated piecewise quasipolynomials.
3023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3024 __isl_take isl_space *space);
3025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3026 __isl_take isl_set *set,
3027 __isl_take isl_qpolynomial *qp);
3028 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3029 __isl_take isl_qpolynomial *qp);
3030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3031 __isl_take isl_pw_aff *pwaff);
3033 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3034 __isl_take isl_space *space);
3035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3036 __isl_take isl_pw_qpolynomial *pwqp);
3037 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3038 __isl_take isl_union_pw_qpolynomial *upwqp,
3039 __isl_take isl_pw_qpolynomial *pwqp);
3041 Quasipolynomials can be copied and freed again using the following
3044 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3045 __isl_keep isl_qpolynomial *qp);
3046 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3048 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3049 __isl_keep isl_pw_qpolynomial *pwqp);
3050 void *isl_pw_qpolynomial_free(
3051 __isl_take isl_pw_qpolynomial *pwqp);
3053 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3054 __isl_keep isl_union_pw_qpolynomial *upwqp);
3055 void isl_union_pw_qpolynomial_free(
3056 __isl_take isl_union_pw_qpolynomial *upwqp);
3058 =head3 Inspecting (Piecewise) Quasipolynomials
3060 To iterate over all piecewise quasipolynomials in a union
3061 piecewise quasipolynomial, use the following function
3063 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3064 __isl_keep isl_union_pw_qpolynomial *upwqp,
3065 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3068 To extract the piecewise quasipolynomial in a given space from a union, use
3070 __isl_give isl_pw_qpolynomial *
3071 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3072 __isl_keep isl_union_pw_qpolynomial *upwqp,
3073 __isl_take isl_space *space);
3075 To iterate over the cells in a piecewise quasipolynomial,
3076 use either of the following two functions
3078 int isl_pw_qpolynomial_foreach_piece(
3079 __isl_keep isl_pw_qpolynomial *pwqp,
3080 int (*fn)(__isl_take isl_set *set,
3081 __isl_take isl_qpolynomial *qp,
3082 void *user), void *user);
3083 int isl_pw_qpolynomial_foreach_lifted_piece(
3084 __isl_keep isl_pw_qpolynomial *pwqp,
3085 int (*fn)(__isl_take isl_set *set,
3086 __isl_take isl_qpolynomial *qp,
3087 void *user), void *user);
3089 As usual, the function C<fn> should return C<0> on success
3090 and C<-1> on failure. The difference between
3091 C<isl_pw_qpolynomial_foreach_piece> and
3092 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3093 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3094 compute unique representations for all existentially quantified
3095 variables and then turn these existentially quantified variables
3096 into extra set variables, adapting the associated quasipolynomial
3097 accordingly. This means that the C<set> passed to C<fn>
3098 will not have any existentially quantified variables, but that
3099 the dimensions of the sets may be different for different
3100 invocations of C<fn>.
3102 To iterate over all terms in a quasipolynomial,
3105 int isl_qpolynomial_foreach_term(
3106 __isl_keep isl_qpolynomial *qp,
3107 int (*fn)(__isl_take isl_term *term,
3108 void *user), void *user);
3110 The terms themselves can be inspected and freed using
3113 unsigned isl_term_dim(__isl_keep isl_term *term,
3114 enum isl_dim_type type);
3115 void isl_term_get_num(__isl_keep isl_term *term,
3117 void isl_term_get_den(__isl_keep isl_term *term,
3119 int isl_term_get_exp(__isl_keep isl_term *term,
3120 enum isl_dim_type type, unsigned pos);
3121 __isl_give isl_aff *isl_term_get_div(
3122 __isl_keep isl_term *term, unsigned pos);
3123 void isl_term_free(__isl_take isl_term *term);
3125 Each term is a product of parameters, set variables and
3126 integer divisions. The function C<isl_term_get_exp>
3127 returns the exponent of a given dimensions in the given term.
3128 The C<isl_int>s in the arguments of C<isl_term_get_num>
3129 and C<isl_term_get_den> need to have been initialized
3130 using C<isl_int_init> before calling these functions.
3132 =head3 Properties of (Piecewise) Quasipolynomials
3134 To check whether a quasipolynomial is actually a constant,
3135 use the following function.
3137 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3138 isl_int *n, isl_int *d);
3140 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3141 then the numerator and denominator of the constant
3142 are returned in C<*n> and C<*d>, respectively.
3144 To check whether two union piecewise quasipolynomials are
3145 obviously equal, use
3147 int isl_union_pw_qpolynomial_plain_is_equal(
3148 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3149 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3151 =head3 Operations on (Piecewise) Quasipolynomials
3153 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3154 __isl_take isl_qpolynomial *qp, isl_int v);
3155 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3156 __isl_take isl_qpolynomial *qp);
3157 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3158 __isl_take isl_qpolynomial *qp1,
3159 __isl_take isl_qpolynomial *qp2);
3160 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3161 __isl_take isl_qpolynomial *qp1,
3162 __isl_take isl_qpolynomial *qp2);
3163 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3164 __isl_take isl_qpolynomial *qp1,
3165 __isl_take isl_qpolynomial *qp2);
3166 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3167 __isl_take isl_qpolynomial *qp, unsigned exponent);
3169 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3170 __isl_take isl_pw_qpolynomial *pwqp1,
3171 __isl_take isl_pw_qpolynomial *pwqp2);
3172 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3173 __isl_take isl_pw_qpolynomial *pwqp1,
3174 __isl_take isl_pw_qpolynomial *pwqp2);
3175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3176 __isl_take isl_pw_qpolynomial *pwqp1,
3177 __isl_take isl_pw_qpolynomial *pwqp2);
3178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3179 __isl_take isl_pw_qpolynomial *pwqp);
3180 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3181 __isl_take isl_pw_qpolynomial *pwqp1,
3182 __isl_take isl_pw_qpolynomial *pwqp2);
3183 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3184 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3186 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3187 __isl_take isl_union_pw_qpolynomial *upwqp1,
3188 __isl_take isl_union_pw_qpolynomial *upwqp2);
3189 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3190 __isl_take isl_union_pw_qpolynomial *upwqp1,
3191 __isl_take isl_union_pw_qpolynomial *upwqp2);
3192 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3193 __isl_take isl_union_pw_qpolynomial *upwqp1,
3194 __isl_take isl_union_pw_qpolynomial *upwqp2);
3196 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3197 __isl_take isl_pw_qpolynomial *pwqp,
3198 __isl_take isl_point *pnt);
3200 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3201 __isl_take isl_union_pw_qpolynomial *upwqp,
3202 __isl_take isl_point *pnt);
3204 __isl_give isl_set *isl_pw_qpolynomial_domain(
3205 __isl_take isl_pw_qpolynomial *pwqp);
3206 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3207 __isl_take isl_pw_qpolynomial *pwpq,
3208 __isl_take isl_set *set);
3210 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3211 __isl_take isl_union_pw_qpolynomial *upwqp);
3212 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3213 __isl_take isl_union_pw_qpolynomial *upwpq,
3214 __isl_take isl_union_set *uset);
3216 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3217 __isl_take isl_qpolynomial *qp,
3218 __isl_take isl_space *model);
3220 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3221 __isl_take isl_qpolynomial *qp);
3222 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3223 __isl_take isl_pw_qpolynomial *pwqp);
3225 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3226 __isl_take isl_union_pw_qpolynomial *upwqp);
3228 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3229 __isl_take isl_qpolynomial *qp,
3230 __isl_take isl_set *context);
3232 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3233 __isl_take isl_pw_qpolynomial *pwqp,
3234 __isl_take isl_set *context);
3236 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3237 __isl_take isl_union_pw_qpolynomial *upwqp,
3238 __isl_take isl_union_set *context);
3240 The gist operation applies the gist operation to each of
3241 the cells in the domain of the input piecewise quasipolynomial.
3242 The context is also exploited
3243 to simplify the quasipolynomials associated to each cell.
3245 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3246 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3247 __isl_give isl_union_pw_qpolynomial *
3248 isl_union_pw_qpolynomial_to_polynomial(
3249 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3251 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3252 the polynomial will be an overapproximation. If C<sign> is negative,
3253 it will be an underapproximation. If C<sign> is zero, the approximation
3254 will lie somewhere in between.
3256 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3258 A piecewise quasipolynomial reduction is a piecewise
3259 reduction (or fold) of quasipolynomials.
3260 In particular, the reduction can be maximum or a minimum.
3261 The objects are mainly used to represent the result of
3262 an upper or lower bound on a quasipolynomial over its domain,
3263 i.e., as the result of the following function.
3265 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3266 __isl_take isl_pw_qpolynomial *pwqp,
3267 enum isl_fold type, int *tight);
3269 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3270 __isl_take isl_union_pw_qpolynomial *upwqp,
3271 enum isl_fold type, int *tight);
3273 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3274 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3275 is the returned bound is known be tight, i.e., for each value
3276 of the parameters there is at least
3277 one element in the domain that reaches the bound.
3278 If the domain of C<pwqp> is not wrapping, then the bound is computed
3279 over all elements in that domain and the result has a purely parametric
3280 domain. If the domain of C<pwqp> is wrapping, then the bound is
3281 computed over the range of the wrapped relation. The domain of the
3282 wrapped relation becomes the domain of the result.
3284 A (piecewise) quasipolynomial reduction can be copied or freed using the
3285 following functions.
3287 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3288 __isl_keep isl_qpolynomial_fold *fold);
3289 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3290 __isl_keep isl_pw_qpolynomial_fold *pwf);
3291 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3292 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3293 void isl_qpolynomial_fold_free(
3294 __isl_take isl_qpolynomial_fold *fold);
3295 void *isl_pw_qpolynomial_fold_free(
3296 __isl_take isl_pw_qpolynomial_fold *pwf);
3297 void isl_union_pw_qpolynomial_fold_free(
3298 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3300 =head3 Printing Piecewise Quasipolynomial Reductions
3302 Piecewise quasipolynomial reductions can be printed
3303 using the following function.
3305 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3306 __isl_take isl_printer *p,
3307 __isl_keep isl_pw_qpolynomial_fold *pwf);
3308 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3309 __isl_take isl_printer *p,
3310 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3312 For C<isl_printer_print_pw_qpolynomial_fold>,
3313 output format of the printer
3314 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3315 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3316 output format of the printer
3317 needs to be set to C<ISL_FORMAT_ISL>.
3318 In case of printing in C<ISL_FORMAT_C>, the user may want
3319 to set the names of all dimensions
3321 __isl_give isl_pw_qpolynomial_fold *
3322 isl_pw_qpolynomial_fold_set_dim_name(
3323 __isl_take isl_pw_qpolynomial_fold *pwf,
3324 enum isl_dim_type type, unsigned pos,
3327 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3329 To iterate over all piecewise quasipolynomial reductions in a union
3330 piecewise quasipolynomial reduction, use the following function
3332 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3333 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3334 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3335 void *user), void *user);
3337 To iterate over the cells in a piecewise quasipolynomial reduction,
3338 use either of the following two functions
3340 int isl_pw_qpolynomial_fold_foreach_piece(
3341 __isl_keep isl_pw_qpolynomial_fold *pwf,
3342 int (*fn)(__isl_take isl_set *set,
3343 __isl_take isl_qpolynomial_fold *fold,
3344 void *user), void *user);
3345 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3346 __isl_keep isl_pw_qpolynomial_fold *pwf,
3347 int (*fn)(__isl_take isl_set *set,
3348 __isl_take isl_qpolynomial_fold *fold,
3349 void *user), void *user);
3351 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3352 of the difference between these two functions.
3354 To iterate over all quasipolynomials in a reduction, use
3356 int isl_qpolynomial_fold_foreach_qpolynomial(
3357 __isl_keep isl_qpolynomial_fold *fold,
3358 int (*fn)(__isl_take isl_qpolynomial *qp,
3359 void *user), void *user);
3361 =head3 Properties of Piecewise Quasipolynomial Reductions
3363 To check whether two union piecewise quasipolynomial reductions are
3364 obviously equal, use
3366 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3367 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3368 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3370 =head3 Operations on Piecewise Quasipolynomial Reductions
3372 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3373 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3375 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3376 __isl_take isl_pw_qpolynomial_fold *pwf1,
3377 __isl_take isl_pw_qpolynomial_fold *pwf2);
3379 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3380 __isl_take isl_pw_qpolynomial_fold *pwf1,
3381 __isl_take isl_pw_qpolynomial_fold *pwf2);
3383 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3384 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3385 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3387 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3388 __isl_take isl_pw_qpolynomial_fold *pwf,
3389 __isl_take isl_point *pnt);
3391 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3392 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3393 __isl_take isl_point *pnt);
3395 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3396 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3397 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3398 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3399 __isl_take isl_union_set *uset);
3401 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3402 __isl_take isl_pw_qpolynomial_fold *pwf);
3404 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3405 __isl_take isl_pw_qpolynomial_fold *pwf);
3407 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3408 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3410 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3411 __isl_take isl_pw_qpolynomial_fold *pwf,
3412 __isl_take isl_set *context);
3414 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3415 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3416 __isl_take isl_union_set *context);
3418 The gist operation applies the gist operation to each of
3419 the cells in the domain of the input piecewise quasipolynomial reduction.
3420 In future, the operation will also exploit the context
3421 to simplify the quasipolynomial reductions associated to each cell.
3423 __isl_give isl_pw_qpolynomial_fold *
3424 isl_set_apply_pw_qpolynomial_fold(
3425 __isl_take isl_set *set,
3426 __isl_take isl_pw_qpolynomial_fold *pwf,
3428 __isl_give isl_pw_qpolynomial_fold *
3429 isl_map_apply_pw_qpolynomial_fold(
3430 __isl_take isl_map *map,
3431 __isl_take isl_pw_qpolynomial_fold *pwf,
3433 __isl_give isl_union_pw_qpolynomial_fold *
3434 isl_union_set_apply_union_pw_qpolynomial_fold(
3435 __isl_take isl_union_set *uset,
3436 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3438 __isl_give isl_union_pw_qpolynomial_fold *
3439 isl_union_map_apply_union_pw_qpolynomial_fold(
3440 __isl_take isl_union_map *umap,
3441 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3444 The functions taking a map
3445 compose the given map with the given piecewise quasipolynomial reduction.
3446 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3447 over all elements in the intersection of the range of the map
3448 and the domain of the piecewise quasipolynomial reduction
3449 as a function of an element in the domain of the map.
3450 The functions taking a set compute a bound over all elements in the
3451 intersection of the set and the domain of the
3452 piecewise quasipolynomial reduction.
3454 =head2 Dependence Analysis
3456 C<isl> contains specialized functionality for performing
3457 array dataflow analysis. That is, given a I<sink> access relation
3458 and a collection of possible I<source> access relations,
3459 C<isl> can compute relations that describe
3460 for each iteration of the sink access, which iteration
3461 of which of the source access relations was the last
3462 to access the same data element before the given iteration
3464 To compute standard flow dependences, the sink should be
3465 a read, while the sources should be writes.
3466 If any of the source accesses are marked as being I<may>
3467 accesses, then there will be a dependence to the last
3468 I<must> access B<and> to any I<may> access that follows
3469 this last I<must> access.
3470 In particular, if I<all> sources are I<may> accesses,
3471 then memory based dependence analysis is performed.
3472 If, on the other hand, all sources are I<must> accesses,
3473 then value based dependence analysis is performed.
3475 #include <isl/flow.h>
3477 typedef int (*isl_access_level_before)(void *first, void *second);
3479 __isl_give isl_access_info *isl_access_info_alloc(
3480 __isl_take isl_map *sink,
3481 void *sink_user, isl_access_level_before fn,
3483 __isl_give isl_access_info *isl_access_info_add_source(
3484 __isl_take isl_access_info *acc,
3485 __isl_take isl_map *source, int must,
3487 void isl_access_info_free(__isl_take isl_access_info *acc);
3489 __isl_give isl_flow *isl_access_info_compute_flow(
3490 __isl_take isl_access_info *acc);
3492 int isl_flow_foreach(__isl_keep isl_flow *deps,
3493 int (*fn)(__isl_take isl_map *dep, int must,
3494 void *dep_user, void *user),
3496 __isl_give isl_map *isl_flow_get_no_source(
3497 __isl_keep isl_flow *deps, int must);
3498 void isl_flow_free(__isl_take isl_flow *deps);
3500 The function C<isl_access_info_compute_flow> performs the actual
3501 dependence analysis. The other functions are used to construct
3502 the input for this function or to read off the output.
3504 The input is collected in an C<isl_access_info>, which can
3505 be created through a call to C<isl_access_info_alloc>.
3506 The arguments to this functions are the sink access relation
3507 C<sink>, a token C<sink_user> used to identify the sink
3508 access to the user, a callback function for specifying the
3509 relative order of source and sink accesses, and the number
3510 of source access relations that will be added.
3511 The callback function has type C<int (*)(void *first, void *second)>.
3512 The function is called with two user supplied tokens identifying
3513 either a source or the sink and it should return the shared nesting
3514 level and the relative order of the two accesses.
3515 In particular, let I<n> be the number of loops shared by
3516 the two accesses. If C<first> precedes C<second> textually,
3517 then the function should return I<2 * n + 1>; otherwise,
3518 it should return I<2 * n>.
3519 The sources can be added to the C<isl_access_info> by performing
3520 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3521 C<must> indicates whether the source is a I<must> access
3522 or a I<may> access. Note that a multi-valued access relation
3523 should only be marked I<must> if every iteration in the domain
3524 of the relation accesses I<all> elements in its image.
3525 The C<source_user> token is again used to identify
3526 the source access. The range of the source access relation
3527 C<source> should have the same dimension as the range
3528 of the sink access relation.
3529 The C<isl_access_info_free> function should usually not be
3530 called explicitly, because it is called implicitly by
3531 C<isl_access_info_compute_flow>.
3533 The result of the dependence analysis is collected in an
3534 C<isl_flow>. There may be elements of
3535 the sink access for which no preceding source access could be
3536 found or for which all preceding sources are I<may> accesses.
3537 The relations containing these elements can be obtained through
3538 calls to C<isl_flow_get_no_source>, the first with C<must> set
3539 and the second with C<must> unset.
3540 In the case of standard flow dependence analysis,
3541 with the sink a read and the sources I<must> writes,
3542 the first relation corresponds to the reads from uninitialized
3543 array elements and the second relation is empty.
3544 The actual flow dependences can be extracted using
3545 C<isl_flow_foreach>. This function will call the user-specified
3546 callback function C<fn> for each B<non-empty> dependence between
3547 a source and the sink. The callback function is called
3548 with four arguments, the actual flow dependence relation
3549 mapping source iterations to sink iterations, a boolean that
3550 indicates whether it is a I<must> or I<may> dependence, a token
3551 identifying the source and an additional C<void *> with value
3552 equal to the third argument of the C<isl_flow_foreach> call.
3553 A dependence is marked I<must> if it originates from a I<must>
3554 source and if it is not followed by any I<may> sources.
3556 After finishing with an C<isl_flow>, the user should call
3557 C<isl_flow_free> to free all associated memory.
3559 A higher-level interface to dependence analysis is provided
3560 by the following function.
3562 #include <isl/flow.h>
3564 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3565 __isl_take isl_union_map *must_source,
3566 __isl_take isl_union_map *may_source,
3567 __isl_take isl_union_map *schedule,
3568 __isl_give isl_union_map **must_dep,
3569 __isl_give isl_union_map **may_dep,
3570 __isl_give isl_union_map **must_no_source,
3571 __isl_give isl_union_map **may_no_source);
3573 The arrays are identified by the tuple names of the ranges
3574 of the accesses. The iteration domains by the tuple names
3575 of the domains of the accesses and of the schedule.
3576 The relative order of the iteration domains is given by the
3577 schedule. The relations returned through C<must_no_source>
3578 and C<may_no_source> are subsets of C<sink>.
3579 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3580 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3581 any of the other arguments is treated as an error.
3585 B<The functionality described in this section is fairly new
3586 and may be subject to change.>
3588 The following function can be used to compute a schedule
3589 for a union of domains. The generated schedule respects
3590 all C<validity> dependences. That is, all dependence distances
3591 over these dependences in the scheduled space are lexicographically
3592 positive. The generated schedule schedule also tries to minimize
3593 the dependence distances over C<proximity> dependences.
3594 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3595 for groups of domains where the dependence distances have only
3596 non-negative values.
3597 The algorithm used to construct the schedule is similar to that
3600 #include <isl/schedule.h>
3601 __isl_give isl_schedule *isl_union_set_compute_schedule(
3602 __isl_take isl_union_set *domain,
3603 __isl_take isl_union_map *validity,
3604 __isl_take isl_union_map *proximity);
3605 void *isl_schedule_free(__isl_take isl_schedule *sched);
3607 A mapping from the domains to the scheduled space can be obtained
3608 from an C<isl_schedule> using the following function.
3610 __isl_give isl_union_map *isl_schedule_get_map(
3611 __isl_keep isl_schedule *sched);
3613 A representation of the schedule can be printed using
3615 __isl_give isl_printer *isl_printer_print_schedule(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_schedule *schedule);
3619 A representation of the schedule as a forest of bands can be obtained
3620 using the following function.
3622 __isl_give isl_band_list *isl_schedule_get_band_forest(
3623 __isl_keep isl_schedule *schedule);
3625 The list can be manipulated as explained in L<"Lists">.
3626 The bands inside the list can be copied and freed using the following
3629 #include <isl/band.h>
3630 __isl_give isl_band *isl_band_copy(
3631 __isl_keep isl_band *band);
3632 void *isl_band_free(__isl_take isl_band *band);
3634 Each band contains zero or more scheduling dimensions.
3635 These are referred to as the members of the band.
3636 The section of the schedule that corresponds to the band is
3637 referred to as the partial schedule of the band.
3638 For those nodes that participate in a band, the outer scheduling
3639 dimensions form the prefix schedule, while the inner scheduling
3640 dimensions form the suffix schedule.
3641 That is, if we take a cut of the band forest, then the union of
3642 the concatenations of the prefix, partial and suffix schedules of
3643 each band in the cut is equal to the entire schedule (modulo
3644 some possible padding at the end with zero scheduling dimensions).
3645 The properties of a band can be inspected using the following functions.
3647 #include <isl/band.h>
3648 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3650 int isl_band_has_children(__isl_keep isl_band *band);
3651 __isl_give isl_band_list *isl_band_get_children(
3652 __isl_keep isl_band *band);
3654 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3655 __isl_keep isl_band *band);
3656 __isl_give isl_union_map *isl_band_get_partial_schedule(
3657 __isl_keep isl_band *band);
3658 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3659 __isl_keep isl_band *band);
3661 int isl_band_n_member(__isl_keep isl_band *band);
3662 int isl_band_member_is_zero_distance(
3663 __isl_keep isl_band *band, int pos);
3665 Note that a scheduling dimension is considered to be ``zero
3666 distance'' if it does not carry any proximity dependences
3668 That is, if the dependence distances of the proximity
3669 dependences are all zero in that direction (for fixed
3670 iterations of outer bands).
3672 A representation of the band can be printed using
3674 #include <isl/band.h>
3675 __isl_give isl_printer *isl_printer_print_band(
3676 __isl_take isl_printer *p,
3677 __isl_keep isl_band *band);
3679 =head2 Parametric Vertex Enumeration
3681 The parametric vertex enumeration described in this section
3682 is mainly intended to be used internally and by the C<barvinok>
3685 #include <isl/vertices.h>
3686 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3687 __isl_keep isl_basic_set *bset);
3689 The function C<isl_basic_set_compute_vertices> performs the
3690 actual computation of the parametric vertices and the chamber
3691 decomposition and store the result in an C<isl_vertices> object.
3692 This information can be queried by either iterating over all
3693 the vertices or iterating over all the chambers or cells
3694 and then iterating over all vertices that are active on the chamber.
3696 int isl_vertices_foreach_vertex(
3697 __isl_keep isl_vertices *vertices,
3698 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3701 int isl_vertices_foreach_cell(
3702 __isl_keep isl_vertices *vertices,
3703 int (*fn)(__isl_take isl_cell *cell, void *user),
3705 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3706 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3709 Other operations that can be performed on an C<isl_vertices> object are
3712 isl_ctx *isl_vertices_get_ctx(
3713 __isl_keep isl_vertices *vertices);
3714 int isl_vertices_get_n_vertices(
3715 __isl_keep isl_vertices *vertices);
3716 void isl_vertices_free(__isl_take isl_vertices *vertices);
3718 Vertices can be inspected and destroyed using the following functions.
3720 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3721 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3722 __isl_give isl_basic_set *isl_vertex_get_domain(
3723 __isl_keep isl_vertex *vertex);
3724 __isl_give isl_basic_set *isl_vertex_get_expr(
3725 __isl_keep isl_vertex *vertex);
3726 void isl_vertex_free(__isl_take isl_vertex *vertex);
3728 C<isl_vertex_get_expr> returns a singleton parametric set describing
3729 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3731 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3732 B<rational> basic sets, so they should mainly be used for inspection
3733 and should not be mixed with integer sets.
3735 Chambers can be inspected and destroyed using the following functions.
3737 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3738 __isl_give isl_basic_set *isl_cell_get_domain(
3739 __isl_keep isl_cell *cell);
3740 void isl_cell_free(__isl_take isl_cell *cell);
3744 Although C<isl> is mainly meant to be used as a library,
3745 it also contains some basic applications that use some
3746 of the functionality of C<isl>.
3747 The input may be specified in either the L<isl format>
3748 or the L<PolyLib format>.
3750 =head2 C<isl_polyhedron_sample>
3752 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3753 an integer element of the polyhedron, if there is any.
3754 The first column in the output is the denominator and is always
3755 equal to 1. If the polyhedron contains no integer points,
3756 then a vector of length zero is printed.
3760 C<isl_pip> takes the same input as the C<example> program
3761 from the C<piplib> distribution, i.e., a set of constraints
3762 on the parameters, a line containing only -1 and finally a set
3763 of constraints on a parametric polyhedron.
3764 The coefficients of the parameters appear in the last columns
3765 (but before the final constant column).
3766 The output is the lexicographic minimum of the parametric polyhedron.
3767 As C<isl> currently does not have its own output format, the output
3768 is just a dump of the internal state.
3770 =head2 C<isl_polyhedron_minimize>
3772 C<isl_polyhedron_minimize> computes the minimum of some linear
3773 or affine objective function over the integer points in a polyhedron.
3774 If an affine objective function
3775 is given, then the constant should appear in the last column.
3777 =head2 C<isl_polytope_scan>
3779 Given a polytope, C<isl_polytope_scan> prints
3780 all integer points in the polytope.