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_reverse(__isl_take isl_space *space);
696 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
697 __isl_take isl_space *right);
698 __isl_give isl_space *isl_space_align_params(
699 __isl_take isl_space *space1, __isl_take isl_space *space2)
700 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
701 enum isl_dim_type type, unsigned pos, unsigned n);
702 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
703 enum isl_dim_type type, unsigned n);
704 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned first, unsigned n);
706 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
707 enum isl_dim_type dst_type, unsigned dst_pos,
708 enum isl_dim_type src_type, unsigned src_pos,
710 __isl_give isl_space *isl_space_map_from_set(
711 __isl_take isl_space *space);
712 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
714 Note that if dimensions are added or removed from a space, then
715 the name and the internal structure are lost.
719 A local space is essentially a space with
720 zero or more existentially quantified variables.
721 The local space of a basic set or relation can be obtained
722 using the following functions.
725 __isl_give isl_local_space *isl_basic_set_get_local_space(
726 __isl_keep isl_basic_set *bset);
729 __isl_give isl_local_space *isl_basic_map_get_local_space(
730 __isl_keep isl_basic_map *bmap);
732 A new local space can be created from a space using
734 #include <isl/local_space.h>
735 __isl_give isl_local_space *isl_local_space_from_space(
736 __isl_take isl_space *space);
738 They can be inspected, copied and freed using the following functions.
740 #include <isl/local_space.h>
741 isl_ctx *isl_local_space_get_ctx(
742 __isl_keep isl_local_space *ls);
743 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
744 int isl_local_space_dim(__isl_keep isl_local_space *ls,
745 enum isl_dim_type type);
746 const char *isl_local_space_get_dim_name(
747 __isl_keep isl_local_space *ls,
748 enum isl_dim_type type, unsigned pos);
749 __isl_give isl_local_space *isl_local_space_set_dim_name(
750 __isl_take isl_local_space *ls,
751 enum isl_dim_type type, unsigned pos, const char *s);
752 __isl_give isl_space *isl_local_space_get_space(
753 __isl_keep isl_local_space *ls);
754 __isl_give isl_aff *isl_local_space_get_div(
755 __isl_keep isl_local_space *ls, int pos);
756 __isl_give isl_local_space *isl_local_space_copy(
757 __isl_keep isl_local_space *ls);
758 void *isl_local_space_free(__isl_take isl_local_space *ls);
760 Two local spaces can be compared using
762 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
763 __isl_keep isl_local_space *ls2);
765 Local spaces can be created from other local spaces
766 using the following functions.
768 __isl_give isl_local_space *isl_local_space_domain(
769 __isl_take isl_local_space *ls);
770 __isl_give isl_local_space *isl_local_space_from_domain(
771 __isl_take isl_local_space *ls);
772 __isl_give isl_local_space *isl_local_space_add_dims(
773 __isl_take isl_local_space *ls,
774 enum isl_dim_type type, unsigned n);
775 __isl_give isl_local_space *isl_local_space_insert_dims(
776 __isl_take isl_local_space *ls,
777 enum isl_dim_type type, unsigned first, unsigned n);
778 __isl_give isl_local_space *isl_local_space_drop_dims(
779 __isl_take isl_local_space *ls,
780 enum isl_dim_type type, unsigned first, unsigned n);
782 =head2 Input and Output
784 C<isl> supports its own input/output format, which is similar
785 to the C<Omega> format, but also supports the C<PolyLib> format
790 The C<isl> format is similar to that of C<Omega>, but has a different
791 syntax for describing the parameters and allows for the definition
792 of an existentially quantified variable as the integer division
793 of an affine expression.
794 For example, the set of integers C<i> between C<0> and C<n>
795 such that C<i % 10 <= 6> can be described as
797 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
800 A set or relation can have several disjuncts, separated
801 by the keyword C<or>. Each disjunct is either a conjunction
802 of constraints or a projection (C<exists>) of a conjunction
803 of constraints. The constraints are separated by the keyword
806 =head3 C<PolyLib> format
808 If the represented set is a union, then the first line
809 contains a single number representing the number of disjuncts.
810 Otherwise, a line containing the number C<1> is optional.
812 Each disjunct is represented by a matrix of constraints.
813 The first line contains two numbers representing
814 the number of rows and columns,
815 where the number of rows is equal to the number of constraints
816 and the number of columns is equal to two plus the number of variables.
817 The following lines contain the actual rows of the constraint matrix.
818 In each row, the first column indicates whether the constraint
819 is an equality (C<0>) or inequality (C<1>). The final column
820 corresponds to the constant term.
822 If the set is parametric, then the coefficients of the parameters
823 appear in the last columns before the constant column.
824 The coefficients of any existentially quantified variables appear
825 between those of the set variables and those of the parameters.
827 =head3 Extended C<PolyLib> format
829 The extended C<PolyLib> format is nearly identical to the
830 C<PolyLib> format. The only difference is that the line
831 containing the number of rows and columns of a constraint matrix
832 also contains four additional numbers:
833 the number of output dimensions, the number of input dimensions,
834 the number of local dimensions (i.e., the number of existentially
835 quantified variables) and the number of parameters.
836 For sets, the number of ``output'' dimensions is equal
837 to the number of set dimensions, while the number of ``input''
843 __isl_give isl_basic_set *isl_basic_set_read_from_file(
844 isl_ctx *ctx, FILE *input);
845 __isl_give isl_basic_set *isl_basic_set_read_from_str(
846 isl_ctx *ctx, const char *str);
847 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
849 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
853 __isl_give isl_basic_map *isl_basic_map_read_from_file(
854 isl_ctx *ctx, FILE *input);
855 __isl_give isl_basic_map *isl_basic_map_read_from_str(
856 isl_ctx *ctx, const char *str);
857 __isl_give isl_map *isl_map_read_from_file(
858 isl_ctx *ctx, FILE *input);
859 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
862 #include <isl/union_set.h>
863 __isl_give isl_union_set *isl_union_set_read_from_file(
864 isl_ctx *ctx, FILE *input);
865 __isl_give isl_union_set *isl_union_set_read_from_str(
866 isl_ctx *ctx, const char *str);
868 #include <isl/union_map.h>
869 __isl_give isl_union_map *isl_union_map_read_from_file(
870 isl_ctx *ctx, FILE *input);
871 __isl_give isl_union_map *isl_union_map_read_from_str(
872 isl_ctx *ctx, const char *str);
874 The input format is autodetected and may be either the C<PolyLib> format
875 or the C<isl> format.
879 Before anything can be printed, an C<isl_printer> needs to
882 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
884 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
885 void isl_printer_free(__isl_take isl_printer *printer);
886 __isl_give char *isl_printer_get_str(
887 __isl_keep isl_printer *printer);
889 The behavior of the printer can be modified in various ways
891 __isl_give isl_printer *isl_printer_set_output_format(
892 __isl_take isl_printer *p, int output_format);
893 __isl_give isl_printer *isl_printer_set_indent(
894 __isl_take isl_printer *p, int indent);
895 __isl_give isl_printer *isl_printer_indent(
896 __isl_take isl_printer *p, int indent);
897 __isl_give isl_printer *isl_printer_set_prefix(
898 __isl_take isl_printer *p, const char *prefix);
899 __isl_give isl_printer *isl_printer_set_suffix(
900 __isl_take isl_printer *p, const char *suffix);
902 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
903 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
904 and defaults to C<ISL_FORMAT_ISL>.
905 Each line in the output is indented by C<indent> (set by
906 C<isl_printer_set_indent>) spaces
907 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
908 In the C<PolyLib> format output,
909 the coefficients of the existentially quantified variables
910 appear between those of the set variables and those
912 The function C<isl_printer_indent> increases the indentation
913 by the specified amount (which may be negative).
915 To actually print something, use
918 __isl_give isl_printer *isl_printer_print_basic_set(
919 __isl_take isl_printer *printer,
920 __isl_keep isl_basic_set *bset);
921 __isl_give isl_printer *isl_printer_print_set(
922 __isl_take isl_printer *printer,
923 __isl_keep isl_set *set);
926 __isl_give isl_printer *isl_printer_print_basic_map(
927 __isl_take isl_printer *printer,
928 __isl_keep isl_basic_map *bmap);
929 __isl_give isl_printer *isl_printer_print_map(
930 __isl_take isl_printer *printer,
931 __isl_keep isl_map *map);
933 #include <isl/union_set.h>
934 __isl_give isl_printer *isl_printer_print_union_set(
935 __isl_take isl_printer *p,
936 __isl_keep isl_union_set *uset);
938 #include <isl/union_map.h>
939 __isl_give isl_printer *isl_printer_print_union_map(
940 __isl_take isl_printer *p,
941 __isl_keep isl_union_map *umap);
943 When called on a file printer, the following function flushes
944 the file. When called on a string printer, the buffer is cleared.
946 __isl_give isl_printer *isl_printer_flush(
947 __isl_take isl_printer *p);
949 =head2 Creating New Sets and Relations
951 C<isl> has functions for creating some standard sets and relations.
955 =item * Empty sets and relations
957 __isl_give isl_basic_set *isl_basic_set_empty(
958 __isl_take isl_space *space);
959 __isl_give isl_basic_map *isl_basic_map_empty(
960 __isl_take isl_space *space);
961 __isl_give isl_set *isl_set_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_map *isl_map_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_union_set *isl_union_set_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_union_map *isl_union_map_empty(
968 __isl_take isl_space *space);
970 For C<isl_union_set>s and C<isl_union_map>s, the space
971 is only used to specify the parameters.
973 =item * Universe sets and relations
975 __isl_give isl_basic_set *isl_basic_set_universe(
976 __isl_take isl_space *space);
977 __isl_give isl_basic_map *isl_basic_map_universe(
978 __isl_take isl_space *space);
979 __isl_give isl_set *isl_set_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_map *isl_map_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_union_set *isl_union_set_universe(
984 __isl_take isl_union_set *uset);
985 __isl_give isl_union_map *isl_union_map_universe(
986 __isl_take isl_union_map *umap);
988 The sets and relations constructed by the functions above
989 contain all integer values, while those constructed by the
990 functions below only contain non-negative values.
992 __isl_give isl_basic_set *isl_basic_set_nat_universe(
993 __isl_take isl_space *space);
994 __isl_give isl_basic_map *isl_basic_map_nat_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_set *isl_set_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_map *isl_map_nat_universe(
999 __isl_take isl_space *space);
1001 =item * Identity relations
1003 __isl_give isl_basic_map *isl_basic_map_identity(
1004 __isl_take isl_space *space);
1005 __isl_give isl_map *isl_map_identity(
1006 __isl_take isl_space *space);
1008 The number of input and output dimensions in C<space> needs
1011 =item * Lexicographic order
1013 __isl_give isl_map *isl_map_lex_lt(
1014 __isl_take isl_space *set_space);
1015 __isl_give isl_map *isl_map_lex_le(
1016 __isl_take isl_space *set_space);
1017 __isl_give isl_map *isl_map_lex_gt(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_ge(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_lt_first(
1022 __isl_take isl_space *space, unsigned n);
1023 __isl_give isl_map *isl_map_lex_le_first(
1024 __isl_take isl_space *space, unsigned n);
1025 __isl_give isl_map *isl_map_lex_gt_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_ge_first(
1028 __isl_take isl_space *space, unsigned n);
1030 The first four functions take a space for a B<set>
1031 and return relations that express that the elements in the domain
1032 are lexicographically less
1033 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1034 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1035 than the elements in the range.
1036 The last four functions take a space for a map
1037 and return relations that express that the first C<n> dimensions
1038 in the domain are lexicographically less
1039 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1040 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1041 than the first C<n> dimensions in the range.
1045 A basic set or relation can be converted to a set or relation
1046 using the following functions.
1048 __isl_give isl_set *isl_set_from_basic_set(
1049 __isl_take isl_basic_set *bset);
1050 __isl_give isl_map *isl_map_from_basic_map(
1051 __isl_take isl_basic_map *bmap);
1053 Sets and relations can be converted to union sets and relations
1054 using the following functions.
1056 __isl_give isl_union_map *isl_union_map_from_map(
1057 __isl_take isl_map *map);
1058 __isl_give isl_union_set *isl_union_set_from_set(
1059 __isl_take isl_set *set);
1061 The inverse conversions below can only be used if the input
1062 union set or relation is known to contain elements in exactly one
1065 __isl_give isl_set *isl_set_from_union_set(
1066 __isl_take isl_union_set *uset);
1067 __isl_give isl_map *isl_map_from_union_map(
1068 __isl_take isl_union_map *umap);
1070 Sets and relations can be copied and freed again using the following
1073 __isl_give isl_basic_set *isl_basic_set_copy(
1074 __isl_keep isl_basic_set *bset);
1075 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1076 __isl_give isl_union_set *isl_union_set_copy(
1077 __isl_keep isl_union_set *uset);
1078 __isl_give isl_basic_map *isl_basic_map_copy(
1079 __isl_keep isl_basic_map *bmap);
1080 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1081 __isl_give isl_union_map *isl_union_map_copy(
1082 __isl_keep isl_union_map *umap);
1083 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1084 void isl_set_free(__isl_take isl_set *set);
1085 void *isl_union_set_free(__isl_take isl_union_set *uset);
1086 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1087 void isl_map_free(__isl_take isl_map *map);
1088 void *isl_union_map_free(__isl_take isl_union_map *umap);
1090 Other sets and relations can be constructed by starting
1091 from a universe set or relation, adding equality and/or
1092 inequality constraints and then projecting out the
1093 existentially quantified variables, if any.
1094 Constraints can be constructed, manipulated and
1095 added to (or removed from) (basic) sets and relations
1096 using the following functions.
1098 #include <isl/constraint.h>
1099 __isl_give isl_constraint *isl_equality_alloc(
1100 __isl_take isl_local_space *ls);
1101 __isl_give isl_constraint *isl_inequality_alloc(
1102 __isl_take isl_local_space *ls);
1103 __isl_give isl_constraint *isl_constraint_set_constant(
1104 __isl_take isl_constraint *constraint, isl_int v);
1105 __isl_give isl_constraint *isl_constraint_set_constant_si(
1106 __isl_take isl_constraint *constraint, int v);
1107 __isl_give isl_constraint *isl_constraint_set_coefficient(
1108 __isl_take isl_constraint *constraint,
1109 enum isl_dim_type type, int pos, isl_int v);
1110 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1111 __isl_take isl_constraint *constraint,
1112 enum isl_dim_type type, int pos, int v);
1113 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1114 __isl_take isl_basic_map *bmap,
1115 __isl_take isl_constraint *constraint);
1116 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1117 __isl_take isl_basic_set *bset,
1118 __isl_take isl_constraint *constraint);
1119 __isl_give isl_map *isl_map_add_constraint(
1120 __isl_take isl_map *map,
1121 __isl_take isl_constraint *constraint);
1122 __isl_give isl_set *isl_set_add_constraint(
1123 __isl_take isl_set *set,
1124 __isl_take isl_constraint *constraint);
1125 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1126 __isl_take isl_basic_set *bset,
1127 __isl_take isl_constraint *constraint);
1129 For example, to create a set containing the even integers
1130 between 10 and 42, you would use the following code.
1133 isl_local_space *ls;
1135 isl_basic_set *bset;
1137 space = isl_space_set_alloc(ctx, 0, 2);
1138 bset = isl_basic_set_universe(isl_space_copy(space));
1139 ls = isl_local_space_from_space(space);
1141 c = isl_equality_alloc(isl_local_space_copy(ls));
1142 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1143 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1144 bset = isl_basic_set_add_constraint(bset, c);
1146 c = isl_inequality_alloc(isl_local_space_copy(ls));
1147 c = isl_constraint_set_constant_si(c, -10);
1148 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1149 bset = isl_basic_set_add_constraint(bset, c);
1151 c = isl_inequality_alloc(ls);
1152 c = isl_constraint_set_constant_si(c, 42);
1153 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1154 bset = isl_basic_set_add_constraint(bset, c);
1156 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1160 isl_basic_set *bset;
1161 bset = isl_basic_set_read_from_str(ctx,
1162 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1164 A basic set or relation can also be constructed from two matrices
1165 describing the equalities and the inequalities.
1167 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1168 __isl_take isl_space *space,
1169 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1170 enum isl_dim_type c1,
1171 enum isl_dim_type c2, enum isl_dim_type c3,
1172 enum isl_dim_type c4);
1173 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1174 __isl_take isl_space *space,
1175 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1176 enum isl_dim_type c1,
1177 enum isl_dim_type c2, enum isl_dim_type c3,
1178 enum isl_dim_type c4, enum isl_dim_type c5);
1180 The C<isl_dim_type> arguments indicate the order in which
1181 different kinds of variables appear in the input matrices
1182 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1183 C<isl_dim_set> and C<isl_dim_div> for sets and
1184 of C<isl_dim_cst>, C<isl_dim_param>,
1185 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1187 A (basic) set or relation can also be constructed from a (piecewise)
1189 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1191 __isl_give isl_basic_map *isl_basic_map_from_aff(
1192 __isl_take isl_aff *aff);
1193 __isl_give isl_set *isl_set_from_pw_aff(
1194 __isl_take isl_pw_aff *pwaff);
1195 __isl_give isl_map *isl_map_from_pw_aff(
1196 __isl_take isl_pw_aff *pwaff);
1197 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1198 __isl_take isl_space *domain_space,
1199 __isl_take isl_aff_list *list);
1201 The C<domain_dim> argument describes the domain of the resulting
1202 basic relation. It is required because the C<list> may consist
1203 of zero affine expressions.
1205 =head2 Inspecting Sets and Relations
1207 Usually, the user should not have to care about the actual constraints
1208 of the sets and maps, but should instead apply the abstract operations
1209 explained in the following sections.
1210 Occasionally, however, it may be required to inspect the individual
1211 coefficients of the constraints. This section explains how to do so.
1212 In these cases, it may also be useful to have C<isl> compute
1213 an explicit representation of the existentially quantified variables.
1215 __isl_give isl_set *isl_set_compute_divs(
1216 __isl_take isl_set *set);
1217 __isl_give isl_map *isl_map_compute_divs(
1218 __isl_take isl_map *map);
1219 __isl_give isl_union_set *isl_union_set_compute_divs(
1220 __isl_take isl_union_set *uset);
1221 __isl_give isl_union_map *isl_union_map_compute_divs(
1222 __isl_take isl_union_map *umap);
1224 This explicit representation defines the existentially quantified
1225 variables as integer divisions of the other variables, possibly
1226 including earlier existentially quantified variables.
1227 An explicitly represented existentially quantified variable therefore
1228 has a unique value when the values of the other variables are known.
1229 If, furthermore, the same existentials, i.e., existentials
1230 with the same explicit representations, should appear in the
1231 same order in each of the disjuncts of a set or map, then the user should call
1232 either of the following functions.
1234 __isl_give isl_set *isl_set_align_divs(
1235 __isl_take isl_set *set);
1236 __isl_give isl_map *isl_map_align_divs(
1237 __isl_take isl_map *map);
1239 Alternatively, the existentially quantified variables can be removed
1240 using the following functions, which compute an overapproximation.
1242 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1243 __isl_take isl_basic_set *bset);
1244 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1245 __isl_take isl_basic_map *bmap);
1246 __isl_give isl_set *isl_set_remove_divs(
1247 __isl_take isl_set *set);
1248 __isl_give isl_map *isl_map_remove_divs(
1249 __isl_take isl_map *map);
1251 To iterate over all the sets or maps in a union set or map, use
1253 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1254 int (*fn)(__isl_take isl_set *set, void *user),
1256 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1257 int (*fn)(__isl_take isl_map *map, void *user),
1260 The number of sets or maps in a union set or map can be obtained
1263 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1264 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1266 To extract the set or map in a given space from a union, use
1268 __isl_give isl_set *isl_union_set_extract_set(
1269 __isl_keep isl_union_set *uset,
1270 __isl_take isl_space *space);
1271 __isl_give isl_map *isl_union_map_extract_map(
1272 __isl_keep isl_union_map *umap,
1273 __isl_take isl_space *space);
1275 To iterate over all the basic sets or maps in a set or map, use
1277 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1278 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1280 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1281 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1284 The callback function C<fn> should return 0 if successful and
1285 -1 if an error occurs. In the latter case, or if any other error
1286 occurs, the above functions will return -1.
1288 It should be noted that C<isl> does not guarantee that
1289 the basic sets or maps passed to C<fn> are disjoint.
1290 If this is required, then the user should call one of
1291 the following functions first.
1293 __isl_give isl_set *isl_set_make_disjoint(
1294 __isl_take isl_set *set);
1295 __isl_give isl_map *isl_map_make_disjoint(
1296 __isl_take isl_map *map);
1298 The number of basic sets in a set can be obtained
1301 int isl_set_n_basic_set(__isl_keep isl_set *set);
1303 To iterate over the constraints of a basic set or map, use
1305 #include <isl/constraint.h>
1307 int isl_basic_map_foreach_constraint(
1308 __isl_keep isl_basic_map *bmap,
1309 int (*fn)(__isl_take isl_constraint *c, void *user),
1311 void *isl_constraint_free(__isl_take isl_constraint *c);
1313 Again, the callback function C<fn> should return 0 if successful and
1314 -1 if an error occurs. In the latter case, or if any other error
1315 occurs, the above functions will return -1.
1316 The constraint C<c> represents either an equality or an inequality.
1317 Use the following function to find out whether a constraint
1318 represents an equality. If not, it represents an inequality.
1320 int isl_constraint_is_equality(
1321 __isl_keep isl_constraint *constraint);
1323 The coefficients of the constraints can be inspected using
1324 the following functions.
1326 void isl_constraint_get_constant(
1327 __isl_keep isl_constraint *constraint, isl_int *v);
1328 void isl_constraint_get_coefficient(
1329 __isl_keep isl_constraint *constraint,
1330 enum isl_dim_type type, int pos, isl_int *v);
1331 int isl_constraint_involves_dims(
1332 __isl_keep isl_constraint *constraint,
1333 enum isl_dim_type type, unsigned first, unsigned n);
1335 The explicit representations of the existentially quantified
1336 variables can be inspected using the following function.
1337 Note that the user is only allowed to use this function
1338 if the inspected set or map is the result of a call
1339 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1340 The existentially quantified variable is equal to the floor
1341 of the returned affine expression. The affine expression
1342 itself can be inspected using the functions in
1343 L<"Piecewise Quasi Affine Expressions">.
1345 __isl_give isl_aff *isl_constraint_get_div(
1346 __isl_keep isl_constraint *constraint, int pos);
1348 To obtain the constraints of a basic set or map in matrix
1349 form, use the following functions.
1351 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1352 __isl_keep isl_basic_set *bset,
1353 enum isl_dim_type c1, enum isl_dim_type c2,
1354 enum isl_dim_type c3, enum isl_dim_type c4);
1355 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1356 __isl_keep isl_basic_set *bset,
1357 enum isl_dim_type c1, enum isl_dim_type c2,
1358 enum isl_dim_type c3, enum isl_dim_type c4);
1359 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1360 __isl_keep isl_basic_map *bmap,
1361 enum isl_dim_type c1,
1362 enum isl_dim_type c2, enum isl_dim_type c3,
1363 enum isl_dim_type c4, enum isl_dim_type c5);
1364 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1365 __isl_keep isl_basic_map *bmap,
1366 enum isl_dim_type c1,
1367 enum isl_dim_type c2, enum isl_dim_type c3,
1368 enum isl_dim_type c4, enum isl_dim_type c5);
1370 The C<isl_dim_type> arguments dictate the order in which
1371 different kinds of variables appear in the resulting matrix
1372 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1373 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1375 The number of parameters, input, output or set dimensions can
1376 be obtained using the following functions.
1378 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1379 enum isl_dim_type type);
1380 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1381 enum isl_dim_type type);
1382 unsigned isl_set_dim(__isl_keep isl_set *set,
1383 enum isl_dim_type type);
1384 unsigned isl_map_dim(__isl_keep isl_map *map,
1385 enum isl_dim_type type);
1387 To check whether the description of a set or relation depends
1388 on one or more given dimensions, it is not necessary to iterate over all
1389 constraints. Instead the following functions can be used.
1391 int isl_basic_set_involves_dims(
1392 __isl_keep isl_basic_set *bset,
1393 enum isl_dim_type type, unsigned first, unsigned n);
1394 int isl_set_involves_dims(__isl_keep isl_set *set,
1395 enum isl_dim_type type, unsigned first, unsigned n);
1396 int isl_basic_map_involves_dims(
1397 __isl_keep isl_basic_map *bmap,
1398 enum isl_dim_type type, unsigned first, unsigned n);
1399 int isl_map_involves_dims(__isl_keep isl_map *map,
1400 enum isl_dim_type type, unsigned first, unsigned n);
1402 Similarly, the following functions can be used to check whether
1403 a given dimension is involved in any lower or upper bound.
1405 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1406 enum isl_dim_type type, unsigned pos);
1407 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1408 enum isl_dim_type type, unsigned pos);
1410 The identifiers or names of the domain and range spaces of a set
1411 or relation can be read off or set using the following functions.
1413 __isl_give isl_set *isl_set_set_tuple_id(
1414 __isl_take isl_set *set, __isl_take isl_id *id);
1415 __isl_give isl_set *isl_set_reset_tuple_id(
1416 __isl_take isl_set *set);
1417 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1418 __isl_give isl_id *isl_set_get_tuple_id(
1419 __isl_keep isl_set *set);
1420 __isl_give isl_map *isl_map_set_tuple_id(
1421 __isl_take isl_map *map, enum isl_dim_type type,
1422 __isl_take isl_id *id);
1423 __isl_give isl_map *isl_map_reset_tuple_id(
1424 __isl_take isl_map *map, enum isl_dim_type type);
1425 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1426 enum isl_dim_type type);
1427 __isl_give isl_id *isl_map_get_tuple_id(
1428 __isl_keep isl_map *map, enum isl_dim_type type);
1430 const char *isl_basic_set_get_tuple_name(
1431 __isl_keep isl_basic_set *bset);
1432 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1433 __isl_take isl_basic_set *set, const char *s);
1434 const char *isl_set_get_tuple_name(
1435 __isl_keep isl_set *set);
1436 const char *isl_basic_map_get_tuple_name(
1437 __isl_keep isl_basic_map *bmap,
1438 enum isl_dim_type type);
1439 const char *isl_map_get_tuple_name(
1440 __isl_keep isl_map *map,
1441 enum isl_dim_type type);
1443 As with C<isl_space_get_tuple_name>, the value returned points to
1444 an internal data structure.
1445 The identifiers, positions or names of individual dimensions can be
1446 read off using the following functions.
1448 __isl_give isl_set *isl_set_set_dim_id(
1449 __isl_take isl_set *set, enum isl_dim_type type,
1450 unsigned pos, __isl_take isl_id *id);
1451 int isl_set_has_dim_id(__isl_keep isl_set *set,
1452 enum isl_dim_type type, unsigned pos);
1453 __isl_give isl_id *isl_set_get_dim_id(
1454 __isl_keep isl_set *set, enum isl_dim_type type,
1456 __isl_give isl_map *isl_map_set_dim_id(
1457 __isl_take isl_map *map, enum isl_dim_type type,
1458 unsigned pos, __isl_take isl_id *id);
1459 int isl_map_has_dim_id(__isl_keep isl_map *map,
1460 enum isl_dim_type type, unsigned pos);
1461 __isl_give isl_id *isl_map_get_dim_id(
1462 __isl_keep isl_map *map, enum isl_dim_type type,
1465 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1468 enum isl_dim_type type, __isl_keep isl_id *id);
1470 const char *isl_constraint_get_dim_name(
1471 __isl_keep isl_constraint *constraint,
1472 enum isl_dim_type type, unsigned pos);
1473 const char *isl_basic_set_get_dim_name(
1474 __isl_keep isl_basic_set *bset,
1475 enum isl_dim_type type, unsigned pos);
1476 const char *isl_set_get_dim_name(
1477 __isl_keep isl_set *set,
1478 enum isl_dim_type type, unsigned pos);
1479 const char *isl_basic_map_get_dim_name(
1480 __isl_keep isl_basic_map *bmap,
1481 enum isl_dim_type type, unsigned pos);
1482 const char *isl_map_get_dim_name(
1483 __isl_keep isl_map *map,
1484 enum isl_dim_type type, unsigned pos);
1486 These functions are mostly useful to obtain the identifiers, positions
1487 or names of the parameters. Identifiers of individual dimensions are
1488 essentially only useful for printing. They are ignored by all other
1489 operations and may not be preserved across those operations.
1493 =head3 Unary Properties
1499 The following functions test whether the given set or relation
1500 contains any integer points. The ``plain'' variants do not perform
1501 any computations, but simply check if the given set or relation
1502 is already known to be empty.
1504 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1505 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1506 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1507 int isl_set_is_empty(__isl_keep isl_set *set);
1508 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1509 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1510 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1511 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1512 int isl_map_is_empty(__isl_keep isl_map *map);
1513 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1515 =item * Universality
1517 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1518 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1519 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1521 =item * Single-valuedness
1523 int isl_map_is_single_valued(__isl_keep isl_map *map);
1524 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1528 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1529 int isl_map_is_injective(__isl_keep isl_map *map);
1530 int isl_union_map_plain_is_injective(
1531 __isl_keep isl_union_map *umap);
1532 int isl_union_map_is_injective(
1533 __isl_keep isl_union_map *umap);
1537 int isl_map_is_bijective(__isl_keep isl_map *map);
1538 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1542 int isl_basic_map_plain_is_fixed(
1543 __isl_keep isl_basic_map *bmap,
1544 enum isl_dim_type type, unsigned pos,
1546 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1547 enum isl_dim_type type, unsigned pos,
1550 Check if the relation obviously lies on a hyperplane where the given dimension
1551 has a fixed value and if so, return that value in C<*val>.
1555 To check whether a set is a parameter domain, use this function:
1557 int isl_set_is_params(__isl_keep isl_set *set);
1561 The following functions check whether the domain of the given
1562 (basic) set is a wrapped relation.
1564 int isl_basic_set_is_wrapping(
1565 __isl_keep isl_basic_set *bset);
1566 int isl_set_is_wrapping(__isl_keep isl_set *set);
1568 =item * Internal Product
1570 int isl_basic_map_can_zip(
1571 __isl_keep isl_basic_map *bmap);
1572 int isl_map_can_zip(__isl_keep isl_map *map);
1574 Check whether the product of domain and range of the given relation
1576 i.e., whether both domain and range are nested relations.
1580 =head3 Binary Properties
1586 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1587 __isl_keep isl_set *set2);
1588 int isl_set_is_equal(__isl_keep isl_set *set1,
1589 __isl_keep isl_set *set2);
1590 int isl_union_set_is_equal(
1591 __isl_keep isl_union_set *uset1,
1592 __isl_keep isl_union_set *uset2);
1593 int isl_basic_map_is_equal(
1594 __isl_keep isl_basic_map *bmap1,
1595 __isl_keep isl_basic_map *bmap2);
1596 int isl_map_is_equal(__isl_keep isl_map *map1,
1597 __isl_keep isl_map *map2);
1598 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1599 __isl_keep isl_map *map2);
1600 int isl_union_map_is_equal(
1601 __isl_keep isl_union_map *umap1,
1602 __isl_keep isl_union_map *umap2);
1604 =item * Disjointness
1606 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1607 __isl_keep isl_set *set2);
1611 int isl_set_is_subset(__isl_keep isl_set *set1,
1612 __isl_keep isl_set *set2);
1613 int isl_set_is_strict_subset(
1614 __isl_keep isl_set *set1,
1615 __isl_keep isl_set *set2);
1616 int isl_union_set_is_subset(
1617 __isl_keep isl_union_set *uset1,
1618 __isl_keep isl_union_set *uset2);
1619 int isl_union_set_is_strict_subset(
1620 __isl_keep isl_union_set *uset1,
1621 __isl_keep isl_union_set *uset2);
1622 int isl_basic_map_is_subset(
1623 __isl_keep isl_basic_map *bmap1,
1624 __isl_keep isl_basic_map *bmap2);
1625 int isl_basic_map_is_strict_subset(
1626 __isl_keep isl_basic_map *bmap1,
1627 __isl_keep isl_basic_map *bmap2);
1628 int isl_map_is_subset(
1629 __isl_keep isl_map *map1,
1630 __isl_keep isl_map *map2);
1631 int isl_map_is_strict_subset(
1632 __isl_keep isl_map *map1,
1633 __isl_keep isl_map *map2);
1634 int isl_union_map_is_subset(
1635 __isl_keep isl_union_map *umap1,
1636 __isl_keep isl_union_map *umap2);
1637 int isl_union_map_is_strict_subset(
1638 __isl_keep isl_union_map *umap1,
1639 __isl_keep isl_union_map *umap2);
1643 =head2 Unary Operations
1649 __isl_give isl_set *isl_set_complement(
1650 __isl_take isl_set *set);
1654 __isl_give isl_basic_map *isl_basic_map_reverse(
1655 __isl_take isl_basic_map *bmap);
1656 __isl_give isl_map *isl_map_reverse(
1657 __isl_take isl_map *map);
1658 __isl_give isl_union_map *isl_union_map_reverse(
1659 __isl_take isl_union_map *umap);
1663 __isl_give isl_basic_set *isl_basic_set_project_out(
1664 __isl_take isl_basic_set *bset,
1665 enum isl_dim_type type, unsigned first, unsigned n);
1666 __isl_give isl_basic_map *isl_basic_map_project_out(
1667 __isl_take isl_basic_map *bmap,
1668 enum isl_dim_type type, unsigned first, unsigned n);
1669 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1670 enum isl_dim_type type, unsigned first, unsigned n);
1671 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1672 enum isl_dim_type type, unsigned first, unsigned n);
1673 __isl_give isl_basic_set *isl_basic_set_params(
1674 __isl_take isl_basic_set *bset);
1675 __isl_give isl_basic_set *isl_basic_map_domain(
1676 __isl_take isl_basic_map *bmap);
1677 __isl_give isl_basic_set *isl_basic_map_range(
1678 __isl_take isl_basic_map *bmap);
1679 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1680 __isl_give isl_set *isl_map_domain(
1681 __isl_take isl_map *bmap);
1682 __isl_give isl_set *isl_map_range(
1683 __isl_take isl_map *map);
1684 __isl_give isl_union_set *isl_union_map_domain(
1685 __isl_take isl_union_map *umap);
1686 __isl_give isl_union_set *isl_union_map_range(
1687 __isl_take isl_union_map *umap);
1689 __isl_give isl_basic_map *isl_basic_map_domain_map(
1690 __isl_take isl_basic_map *bmap);
1691 __isl_give isl_basic_map *isl_basic_map_range_map(
1692 __isl_take isl_basic_map *bmap);
1693 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1694 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1695 __isl_give isl_union_map *isl_union_map_domain_map(
1696 __isl_take isl_union_map *umap);
1697 __isl_give isl_union_map *isl_union_map_range_map(
1698 __isl_take isl_union_map *umap);
1700 The functions above construct a (basic, regular or union) relation
1701 that maps (a wrapped version of) the input relation to its domain or range.
1705 __isl_give isl_set *isl_set_eliminate(
1706 __isl_take isl_set *set, enum isl_dim_type type,
1707 unsigned first, unsigned n);
1709 Eliminate the coefficients for the given dimensions from the constraints,
1710 without removing the dimensions.
1714 __isl_give isl_basic_set *isl_basic_set_fix(
1715 __isl_take isl_basic_set *bset,
1716 enum isl_dim_type type, unsigned pos,
1718 __isl_give isl_basic_set *isl_basic_set_fix_si(
1719 __isl_take isl_basic_set *bset,
1720 enum isl_dim_type type, unsigned pos, int value);
1721 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1722 enum isl_dim_type type, unsigned pos,
1724 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1725 enum isl_dim_type type, unsigned pos, int value);
1726 __isl_give isl_basic_map *isl_basic_map_fix_si(
1727 __isl_take isl_basic_map *bmap,
1728 enum isl_dim_type type, unsigned pos, int value);
1729 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1730 enum isl_dim_type type, unsigned pos, int value);
1732 Intersect the set or relation with the hyperplane where the given
1733 dimension has the fixed given value.
1735 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1736 enum isl_dim_type type1, int pos1,
1737 enum isl_dim_type type2, int pos2);
1738 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1739 enum isl_dim_type type1, int pos1,
1740 enum isl_dim_type type2, int pos2);
1742 Intersect the set or relation with the hyperplane where the given
1743 dimensions are equal to each other.
1745 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1746 enum isl_dim_type type1, int pos1,
1747 enum isl_dim_type type2, int pos2);
1749 Intersect the relation with the hyperplane where the given
1750 dimensions have opposite values.
1754 __isl_give isl_map *isl_set_identity(
1755 __isl_take isl_set *set);
1756 __isl_give isl_union_map *isl_union_set_identity(
1757 __isl_take isl_union_set *uset);
1759 Construct an identity relation on the given (union) set.
1763 __isl_give isl_basic_set *isl_basic_map_deltas(
1764 __isl_take isl_basic_map *bmap);
1765 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1766 __isl_give isl_union_set *isl_union_map_deltas(
1767 __isl_take isl_union_map *umap);
1769 These functions return a (basic) set containing the differences
1770 between image elements and corresponding domain elements in the input.
1772 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_map *isl_map_deltas_map(
1775 __isl_take isl_map *map);
1776 __isl_give isl_union_map *isl_union_map_deltas_map(
1777 __isl_take isl_union_map *umap);
1779 The functions above construct a (basic, regular or union) relation
1780 that maps (a wrapped version of) the input relation to its delta set.
1784 Simplify the representation of a set or relation by trying
1785 to combine pairs of basic sets or relations into a single
1786 basic set or relation.
1788 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1789 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1790 __isl_give isl_union_set *isl_union_set_coalesce(
1791 __isl_take isl_union_set *uset);
1792 __isl_give isl_union_map *isl_union_map_coalesce(
1793 __isl_take isl_union_map *umap);
1795 =item * Detecting equalities
1797 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1798 __isl_take isl_basic_set *bset);
1799 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_set *isl_set_detect_equalities(
1802 __isl_take isl_set *set);
1803 __isl_give isl_map *isl_map_detect_equalities(
1804 __isl_take isl_map *map);
1805 __isl_give isl_union_set *isl_union_set_detect_equalities(
1806 __isl_take isl_union_set *uset);
1807 __isl_give isl_union_map *isl_union_map_detect_equalities(
1808 __isl_take isl_union_map *umap);
1810 Simplify the representation of a set or relation by detecting implicit
1813 =item * Removing redundant constraints
1815 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1816 __isl_take isl_basic_set *bset);
1817 __isl_give isl_set *isl_set_remove_redundancies(
1818 __isl_take isl_set *set);
1819 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1820 __isl_take isl_basic_map *bmap);
1821 __isl_give isl_map *isl_map_remove_redundancies(
1822 __isl_take isl_map *map);
1826 __isl_give isl_basic_set *isl_set_convex_hull(
1827 __isl_take isl_set *set);
1828 __isl_give isl_basic_map *isl_map_convex_hull(
1829 __isl_take isl_map *map);
1831 If the input set or relation has any existentially quantified
1832 variables, then the result of these operations is currently undefined.
1836 __isl_give isl_basic_set *isl_set_simple_hull(
1837 __isl_take isl_set *set);
1838 __isl_give isl_basic_map *isl_map_simple_hull(
1839 __isl_take isl_map *map);
1840 __isl_give isl_union_map *isl_union_map_simple_hull(
1841 __isl_take isl_union_map *umap);
1843 These functions compute a single basic set or relation
1844 that contains the whole input set or relation.
1845 In particular, the output is described by translates
1846 of the constraints describing the basic sets or relations in the input.
1850 (See \autoref{s:simple hull}.)
1856 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1857 __isl_take isl_basic_set *bset);
1858 __isl_give isl_basic_set *isl_set_affine_hull(
1859 __isl_take isl_set *set);
1860 __isl_give isl_union_set *isl_union_set_affine_hull(
1861 __isl_take isl_union_set *uset);
1862 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1863 __isl_take isl_basic_map *bmap);
1864 __isl_give isl_basic_map *isl_map_affine_hull(
1865 __isl_take isl_map *map);
1866 __isl_give isl_union_map *isl_union_map_affine_hull(
1867 __isl_take isl_union_map *umap);
1869 In case of union sets and relations, the affine hull is computed
1872 =item * Polyhedral hull
1874 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1875 __isl_take isl_set *set);
1876 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1877 __isl_take isl_map *map);
1878 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1879 __isl_take isl_union_set *uset);
1880 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1881 __isl_take isl_union_map *umap);
1883 These functions compute a single basic set or relation
1884 not involving any existentially quantified variables
1885 that contains the whole input set or relation.
1886 In case of union sets and relations, the polyhedral hull is computed
1889 =item * Optimization
1891 #include <isl/ilp.h>
1892 enum isl_lp_result isl_basic_set_max(
1893 __isl_keep isl_basic_set *bset,
1894 __isl_keep isl_aff *obj, isl_int *opt)
1895 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1896 __isl_keep isl_aff *obj, isl_int *opt);
1897 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1898 __isl_keep isl_aff *obj, isl_int *opt);
1900 Compute the minimum or maximum of the integer affine expression C<obj>
1901 over the points in C<set>, returning the result in C<opt>.
1902 The return value may be one of C<isl_lp_error>,
1903 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1905 =item * Parametric optimization
1907 __isl_give isl_pw_aff *isl_set_dim_min(
1908 __isl_take isl_set *set, int pos);
1909 __isl_give isl_pw_aff *isl_set_dim_max(
1910 __isl_take isl_set *set, int pos);
1912 Compute the minimum or maximum of the given set dimension as a function of the
1913 parameters, but independently of the other set dimensions.
1914 For lexicographic optimization, see L<"Lexicographic Optimization">.
1918 The following functions compute either the set of (rational) coefficient
1919 values of valid constraints for the given set or the set of (rational)
1920 values satisfying the constraints with coefficients from the given set.
1921 Internally, these two sets of functions perform essentially the
1922 same operations, except that the set of coefficients is assumed to
1923 be a cone, while the set of values may be any polyhedron.
1924 The current implementation is based on the Farkas lemma and
1925 Fourier-Motzkin elimination, but this may change or be made optional
1926 in future. In particular, future implementations may use different
1927 dualization algorithms or skip the elimination step.
1929 __isl_give isl_basic_set *isl_basic_set_coefficients(
1930 __isl_take isl_basic_set *bset);
1931 __isl_give isl_basic_set *isl_set_coefficients(
1932 __isl_take isl_set *set);
1933 __isl_give isl_union_set *isl_union_set_coefficients(
1934 __isl_take isl_union_set *bset);
1935 __isl_give isl_basic_set *isl_basic_set_solutions(
1936 __isl_take isl_basic_set *bset);
1937 __isl_give isl_basic_set *isl_set_solutions(
1938 __isl_take isl_set *set);
1939 __isl_give isl_union_set *isl_union_set_solutions(
1940 __isl_take isl_union_set *bset);
1944 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1946 __isl_give isl_union_map *isl_union_map_power(
1947 __isl_take isl_union_map *umap, int *exact);
1949 Compute a parametric representation for all positive powers I<k> of C<map>.
1950 The result maps I<k> to a nested relation corresponding to the
1951 I<k>th power of C<map>.
1952 The result may be an overapproximation. If the result is known to be exact,
1953 then C<*exact> is set to C<1>.
1955 =item * Transitive closure
1957 __isl_give isl_map *isl_map_transitive_closure(
1958 __isl_take isl_map *map, int *exact);
1959 __isl_give isl_union_map *isl_union_map_transitive_closure(
1960 __isl_take isl_union_map *umap, int *exact);
1962 Compute the transitive closure of C<map>.
1963 The result may be an overapproximation. If the result is known to be exact,
1964 then C<*exact> is set to C<1>.
1966 =item * Reaching path lengths
1968 __isl_give isl_map *isl_map_reaching_path_lengths(
1969 __isl_take isl_map *map, int *exact);
1971 Compute a relation that maps each element in the range of C<map>
1972 to the lengths of all paths composed of edges in C<map> that
1973 end up in the given element.
1974 The result may be an overapproximation. If the result is known to be exact,
1975 then C<*exact> is set to C<1>.
1976 To compute the I<maximal> path length, the resulting relation
1977 should be postprocessed by C<isl_map_lexmax>.
1978 In particular, if the input relation is a dependence relation
1979 (mapping sources to sinks), then the maximal path length corresponds
1980 to the free schedule.
1981 Note, however, that C<isl_map_lexmax> expects the maximum to be
1982 finite, so if the path lengths are unbounded (possibly due to
1983 the overapproximation), then you will get an error message.
1987 __isl_give isl_basic_set *isl_basic_map_wrap(
1988 __isl_take isl_basic_map *bmap);
1989 __isl_give isl_set *isl_map_wrap(
1990 __isl_take isl_map *map);
1991 __isl_give isl_union_set *isl_union_map_wrap(
1992 __isl_take isl_union_map *umap);
1993 __isl_give isl_basic_map *isl_basic_set_unwrap(
1994 __isl_take isl_basic_set *bset);
1995 __isl_give isl_map *isl_set_unwrap(
1996 __isl_take isl_set *set);
1997 __isl_give isl_union_map *isl_union_set_unwrap(
1998 __isl_take isl_union_set *uset);
2002 Remove any internal structure of domain (and range) of the given
2003 set or relation. If there is any such internal structure in the input,
2004 then the name of the space is also removed.
2006 __isl_give isl_basic_set *isl_basic_set_flatten(
2007 __isl_take isl_basic_set *bset);
2008 __isl_give isl_set *isl_set_flatten(
2009 __isl_take isl_set *set);
2010 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2011 __isl_take isl_basic_map *bmap);
2012 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2013 __isl_take isl_basic_map *bmap);
2014 __isl_give isl_map *isl_map_flatten_range(
2015 __isl_take isl_map *map);
2016 __isl_give isl_map *isl_map_flatten_domain(
2017 __isl_take isl_map *map);
2018 __isl_give isl_basic_map *isl_basic_map_flatten(
2019 __isl_take isl_basic_map *bmap);
2020 __isl_give isl_map *isl_map_flatten(
2021 __isl_take isl_map *map);
2023 __isl_give isl_map *isl_set_flatten_map(
2024 __isl_take isl_set *set);
2026 The function above constructs a relation
2027 that maps the input set to a flattened version of the set.
2031 Lift the input set to a space with extra dimensions corresponding
2032 to the existentially quantified variables in the input.
2033 In particular, the result lives in a wrapped map where the domain
2034 is the original space and the range corresponds to the original
2035 existentially quantified variables.
2037 __isl_give isl_basic_set *isl_basic_set_lift(
2038 __isl_take isl_basic_set *bset);
2039 __isl_give isl_set *isl_set_lift(
2040 __isl_take isl_set *set);
2041 __isl_give isl_union_set *isl_union_set_lift(
2042 __isl_take isl_union_set *uset);
2044 =item * Internal Product
2046 __isl_give isl_basic_map *isl_basic_map_zip(
2047 __isl_take isl_basic_map *bmap);
2048 __isl_give isl_map *isl_map_zip(
2049 __isl_take isl_map *map);
2050 __isl_give isl_union_map *isl_union_map_zip(
2051 __isl_take isl_union_map *umap);
2053 Given a relation with nested relations for domain and range,
2054 interchange the range of the domain with the domain of the range.
2056 =item * Aligning parameters
2058 __isl_give isl_set *isl_set_align_params(
2059 __isl_take isl_set *set,
2060 __isl_take isl_space *model);
2061 __isl_give isl_map *isl_map_align_params(
2062 __isl_take isl_map *map,
2063 __isl_take isl_space *model);
2065 Change the order of the parameters of the given set or relation
2066 such that the first parameters match those of C<model>.
2067 This may involve the introduction of extra parameters.
2068 All parameters need to be named.
2070 =item * Dimension manipulation
2072 __isl_give isl_set *isl_set_add_dims(
2073 __isl_take isl_set *set,
2074 enum isl_dim_type type, unsigned n);
2075 __isl_give isl_map *isl_map_add_dims(
2076 __isl_take isl_map *map,
2077 enum isl_dim_type type, unsigned n);
2078 __isl_give isl_set *isl_set_insert_dims(
2079 __isl_take isl_set *set,
2080 enum isl_dim_type type, unsigned pos, unsigned n);
2081 __isl_give isl_map *isl_map_insert_dims(
2082 __isl_take isl_map *map,
2083 enum isl_dim_type type, unsigned pos, unsigned n);
2084 __isl_give isl_basic_set *isl_basic_set_move_dims(
2085 __isl_take isl_basic_set *bset,
2086 enum isl_dim_type dst_type, unsigned dst_pos,
2087 enum isl_dim_type src_type, unsigned src_pos,
2089 __isl_give isl_basic_map *isl_basic_map_move_dims(
2090 __isl_take isl_basic_map *bmap,
2091 enum isl_dim_type dst_type, unsigned dst_pos,
2092 enum isl_dim_type src_type, unsigned src_pos,
2094 __isl_give isl_set *isl_set_move_dims(
2095 __isl_take isl_set *set,
2096 enum isl_dim_type dst_type, unsigned dst_pos,
2097 enum isl_dim_type src_type, unsigned src_pos,
2099 __isl_give isl_map *isl_map_move_dims(
2100 __isl_take isl_map *map,
2101 enum isl_dim_type dst_type, unsigned dst_pos,
2102 enum isl_dim_type src_type, unsigned src_pos,
2105 It is usually not advisable to directly change the (input or output)
2106 space of a set or a relation as this removes the name and the internal
2107 structure of the space. However, the above functions can be useful
2108 to add new parameters, assuming
2109 C<isl_set_align_params> and C<isl_map_align_params>
2114 =head2 Binary Operations
2116 The two arguments of a binary operation not only need to live
2117 in the same C<isl_ctx>, they currently also need to have
2118 the same (number of) parameters.
2120 =head3 Basic Operations
2124 =item * Intersection
2126 __isl_give isl_basic_set *isl_basic_set_intersect(
2127 __isl_take isl_basic_set *bset1,
2128 __isl_take isl_basic_set *bset2);
2129 __isl_give isl_set *isl_set_intersect_params(
2130 __isl_take isl_set *set,
2131 __isl_take isl_set *params);
2132 __isl_give isl_set *isl_set_intersect(
2133 __isl_take isl_set *set1,
2134 __isl_take isl_set *set2);
2135 __isl_give isl_union_set *isl_union_set_intersect(
2136 __isl_take isl_union_set *uset1,
2137 __isl_take isl_union_set *uset2);
2138 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2139 __isl_take isl_basic_map *bmap,
2140 __isl_take isl_basic_set *bset);
2141 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2142 __isl_take isl_basic_map *bmap,
2143 __isl_take isl_basic_set *bset);
2144 __isl_give isl_basic_map *isl_basic_map_intersect(
2145 __isl_take isl_basic_map *bmap1,
2146 __isl_take isl_basic_map *bmap2);
2147 __isl_give isl_map *isl_map_intersect_params(
2148 __isl_take isl_map *map,
2149 __isl_take isl_set *params);
2150 __isl_give isl_map *isl_map_intersect_domain(
2151 __isl_take isl_map *map,
2152 __isl_take isl_set *set);
2153 __isl_give isl_map *isl_map_intersect_range(
2154 __isl_take isl_map *map,
2155 __isl_take isl_set *set);
2156 __isl_give isl_map *isl_map_intersect(
2157 __isl_take isl_map *map1,
2158 __isl_take isl_map *map2);
2159 __isl_give isl_union_map *isl_union_map_intersect_domain(
2160 __isl_take isl_union_map *umap,
2161 __isl_take isl_union_set *uset);
2162 __isl_give isl_union_map *isl_union_map_intersect_range(
2163 __isl_take isl_union_map *umap,
2164 __isl_take isl_union_set *uset);
2165 __isl_give isl_union_map *isl_union_map_intersect(
2166 __isl_take isl_union_map *umap1,
2167 __isl_take isl_union_map *umap2);
2171 __isl_give isl_set *isl_basic_set_union(
2172 __isl_take isl_basic_set *bset1,
2173 __isl_take isl_basic_set *bset2);
2174 __isl_give isl_map *isl_basic_map_union(
2175 __isl_take isl_basic_map *bmap1,
2176 __isl_take isl_basic_map *bmap2);
2177 __isl_give isl_set *isl_set_union(
2178 __isl_take isl_set *set1,
2179 __isl_take isl_set *set2);
2180 __isl_give isl_map *isl_map_union(
2181 __isl_take isl_map *map1,
2182 __isl_take isl_map *map2);
2183 __isl_give isl_union_set *isl_union_set_union(
2184 __isl_take isl_union_set *uset1,
2185 __isl_take isl_union_set *uset2);
2186 __isl_give isl_union_map *isl_union_map_union(
2187 __isl_take isl_union_map *umap1,
2188 __isl_take isl_union_map *umap2);
2190 =item * Set difference
2192 __isl_give isl_set *isl_set_subtract(
2193 __isl_take isl_set *set1,
2194 __isl_take isl_set *set2);
2195 __isl_give isl_map *isl_map_subtract(
2196 __isl_take isl_map *map1,
2197 __isl_take isl_map *map2);
2198 __isl_give isl_union_set *isl_union_set_subtract(
2199 __isl_take isl_union_set *uset1,
2200 __isl_take isl_union_set *uset2);
2201 __isl_give isl_union_map *isl_union_map_subtract(
2202 __isl_take isl_union_map *umap1,
2203 __isl_take isl_union_map *umap2);
2207 __isl_give isl_basic_set *isl_basic_set_apply(
2208 __isl_take isl_basic_set *bset,
2209 __isl_take isl_basic_map *bmap);
2210 __isl_give isl_set *isl_set_apply(
2211 __isl_take isl_set *set,
2212 __isl_take isl_map *map);
2213 __isl_give isl_union_set *isl_union_set_apply(
2214 __isl_take isl_union_set *uset,
2215 __isl_take isl_union_map *umap);
2216 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2217 __isl_take isl_basic_map *bmap1,
2218 __isl_take isl_basic_map *bmap2);
2219 __isl_give isl_basic_map *isl_basic_map_apply_range(
2220 __isl_take isl_basic_map *bmap1,
2221 __isl_take isl_basic_map *bmap2);
2222 __isl_give isl_map *isl_map_apply_domain(
2223 __isl_take isl_map *map1,
2224 __isl_take isl_map *map2);
2225 __isl_give isl_union_map *isl_union_map_apply_domain(
2226 __isl_take isl_union_map *umap1,
2227 __isl_take isl_union_map *umap2);
2228 __isl_give isl_map *isl_map_apply_range(
2229 __isl_take isl_map *map1,
2230 __isl_take isl_map *map2);
2231 __isl_give isl_union_map *isl_union_map_apply_range(
2232 __isl_take isl_union_map *umap1,
2233 __isl_take isl_union_map *umap2);
2235 =item * Cartesian Product
2237 __isl_give isl_set *isl_set_product(
2238 __isl_take isl_set *set1,
2239 __isl_take isl_set *set2);
2240 __isl_give isl_union_set *isl_union_set_product(
2241 __isl_take isl_union_set *uset1,
2242 __isl_take isl_union_set *uset2);
2243 __isl_give isl_basic_map *isl_basic_map_domain_product(
2244 __isl_take isl_basic_map *bmap1,
2245 __isl_take isl_basic_map *bmap2);
2246 __isl_give isl_basic_map *isl_basic_map_range_product(
2247 __isl_take isl_basic_map *bmap1,
2248 __isl_take isl_basic_map *bmap2);
2249 __isl_give isl_map *isl_map_domain_product(
2250 __isl_take isl_map *map1,
2251 __isl_take isl_map *map2);
2252 __isl_give isl_map *isl_map_range_product(
2253 __isl_take isl_map *map1,
2254 __isl_take isl_map *map2);
2255 __isl_give isl_union_map *isl_union_map_range_product(
2256 __isl_take isl_union_map *umap1,
2257 __isl_take isl_union_map *umap2);
2258 __isl_give isl_map *isl_map_product(
2259 __isl_take isl_map *map1,
2260 __isl_take isl_map *map2);
2261 __isl_give isl_union_map *isl_union_map_product(
2262 __isl_take isl_union_map *umap1,
2263 __isl_take isl_union_map *umap2);
2265 The above functions compute the cross product of the given
2266 sets or relations. The domains and ranges of the results
2267 are wrapped maps between domains and ranges of the inputs.
2268 To obtain a ``flat'' product, use the following functions
2271 __isl_give isl_basic_set *isl_basic_set_flat_product(
2272 __isl_take isl_basic_set *bset1,
2273 __isl_take isl_basic_set *bset2);
2274 __isl_give isl_set *isl_set_flat_product(
2275 __isl_take isl_set *set1,
2276 __isl_take isl_set *set2);
2277 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2278 __isl_take isl_basic_map *bmap1,
2279 __isl_take isl_basic_map *bmap2);
2280 __isl_give isl_map *isl_map_flat_domain_product(
2281 __isl_take isl_map *map1,
2282 __isl_take isl_map *map2);
2283 __isl_give isl_map *isl_map_flat_range_product(
2284 __isl_take isl_map *map1,
2285 __isl_take isl_map *map2);
2286 __isl_give isl_union_map *isl_union_map_flat_range_product(
2287 __isl_take isl_union_map *umap1,
2288 __isl_take isl_union_map *umap2);
2289 __isl_give isl_basic_map *isl_basic_map_flat_product(
2290 __isl_take isl_basic_map *bmap1,
2291 __isl_take isl_basic_map *bmap2);
2292 __isl_give isl_map *isl_map_flat_product(
2293 __isl_take isl_map *map1,
2294 __isl_take isl_map *map2);
2296 =item * Simplification
2298 __isl_give isl_basic_set *isl_basic_set_gist(
2299 __isl_take isl_basic_set *bset,
2300 __isl_take isl_basic_set *context);
2301 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2302 __isl_take isl_set *context);
2303 __isl_give isl_set *isl_set_gist_params(
2304 __isl_take isl_set *set,
2305 __isl_take isl_set *context);
2306 __isl_give isl_union_set *isl_union_set_gist(
2307 __isl_take isl_union_set *uset,
2308 __isl_take isl_union_set *context);
2309 __isl_give isl_basic_map *isl_basic_map_gist(
2310 __isl_take isl_basic_map *bmap,
2311 __isl_take isl_basic_map *context);
2312 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2313 __isl_take isl_map *context);
2314 __isl_give isl_map *isl_map_gist_params(
2315 __isl_take isl_map *map,
2316 __isl_take isl_set *context);
2317 __isl_give isl_union_map *isl_union_map_gist(
2318 __isl_take isl_union_map *umap,
2319 __isl_take isl_union_map *context);
2321 The gist operation returns a set or relation that has the
2322 same intersection with the context as the input set or relation.
2323 Any implicit equality in the intersection is made explicit in the result,
2324 while all inequalities that are redundant with respect to the intersection
2326 In case of union sets and relations, the gist operation is performed
2331 =head3 Lexicographic Optimization
2333 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2334 the following functions
2335 compute a set that contains the lexicographic minimum or maximum
2336 of the elements in C<set> (or C<bset>) for those values of the parameters
2337 that satisfy C<dom>.
2338 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2339 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2341 In other words, the union of the parameter values
2342 for which the result is non-empty and of C<*empty>
2345 __isl_give isl_set *isl_basic_set_partial_lexmin(
2346 __isl_take isl_basic_set *bset,
2347 __isl_take isl_basic_set *dom,
2348 __isl_give isl_set **empty);
2349 __isl_give isl_set *isl_basic_set_partial_lexmax(
2350 __isl_take isl_basic_set *bset,
2351 __isl_take isl_basic_set *dom,
2352 __isl_give isl_set **empty);
2353 __isl_give isl_set *isl_set_partial_lexmin(
2354 __isl_take isl_set *set, __isl_take isl_set *dom,
2355 __isl_give isl_set **empty);
2356 __isl_give isl_set *isl_set_partial_lexmax(
2357 __isl_take isl_set *set, __isl_take isl_set *dom,
2358 __isl_give isl_set **empty);
2360 Given a (basic) set C<set> (or C<bset>), the following functions simply
2361 return a set containing the lexicographic minimum or maximum
2362 of the elements in C<set> (or C<bset>).
2363 In case of union sets, the optimum is computed per space.
2365 __isl_give isl_set *isl_basic_set_lexmin(
2366 __isl_take isl_basic_set *bset);
2367 __isl_give isl_set *isl_basic_set_lexmax(
2368 __isl_take isl_basic_set *bset);
2369 __isl_give isl_set *isl_set_lexmin(
2370 __isl_take isl_set *set);
2371 __isl_give isl_set *isl_set_lexmax(
2372 __isl_take isl_set *set);
2373 __isl_give isl_union_set *isl_union_set_lexmin(
2374 __isl_take isl_union_set *uset);
2375 __isl_give isl_union_set *isl_union_set_lexmax(
2376 __isl_take isl_union_set *uset);
2378 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2379 the following functions
2380 compute a relation that maps each element of C<dom>
2381 to the single lexicographic minimum or maximum
2382 of the elements that are associated to that same
2383 element in C<map> (or C<bmap>).
2384 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2385 that contains the elements in C<dom> that do not map
2386 to any elements in C<map> (or C<bmap>).
2387 In other words, the union of the domain of the result and of C<*empty>
2390 __isl_give isl_map *isl_basic_map_partial_lexmax(
2391 __isl_take isl_basic_map *bmap,
2392 __isl_take isl_basic_set *dom,
2393 __isl_give isl_set **empty);
2394 __isl_give isl_map *isl_basic_map_partial_lexmin(
2395 __isl_take isl_basic_map *bmap,
2396 __isl_take isl_basic_set *dom,
2397 __isl_give isl_set **empty);
2398 __isl_give isl_map *isl_map_partial_lexmax(
2399 __isl_take isl_map *map, __isl_take isl_set *dom,
2400 __isl_give isl_set **empty);
2401 __isl_give isl_map *isl_map_partial_lexmin(
2402 __isl_take isl_map *map, __isl_take isl_set *dom,
2403 __isl_give isl_set **empty);
2405 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2406 return a map mapping each element in the domain of
2407 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2408 of all elements associated to that element.
2409 In case of union relations, the optimum is computed per space.
2411 __isl_give isl_map *isl_basic_map_lexmin(
2412 __isl_take isl_basic_map *bmap);
2413 __isl_give isl_map *isl_basic_map_lexmax(
2414 __isl_take isl_basic_map *bmap);
2415 __isl_give isl_map *isl_map_lexmin(
2416 __isl_take isl_map *map);
2417 __isl_give isl_map *isl_map_lexmax(
2418 __isl_take isl_map *map);
2419 __isl_give isl_union_map *isl_union_map_lexmin(
2420 __isl_take isl_union_map *umap);
2421 __isl_give isl_union_map *isl_union_map_lexmax(
2422 __isl_take isl_union_map *umap);
2426 Lists are defined over several element types, including
2427 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2428 Here we take lists of C<isl_set>s as an example.
2429 Lists can be created, copied and freed using the following functions.
2431 #include <isl/list.h>
2432 __isl_give isl_set_list *isl_set_list_from_set(
2433 __isl_take isl_set *el);
2434 __isl_give isl_set_list *isl_set_list_alloc(
2435 isl_ctx *ctx, int n);
2436 __isl_give isl_set_list *isl_set_list_copy(
2437 __isl_keep isl_set_list *list);
2438 __isl_give isl_set_list *isl_set_list_add(
2439 __isl_take isl_set_list *list,
2440 __isl_take isl_set *el);
2441 __isl_give isl_set_list *isl_set_list_concat(
2442 __isl_take isl_set_list *list1,
2443 __isl_take isl_set_list *list2);
2444 void *isl_set_list_free(__isl_take isl_set_list *list);
2446 C<isl_set_list_alloc> creates an empty list with a capacity for
2447 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2450 Lists can be inspected using the following functions.
2452 #include <isl/list.h>
2453 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2454 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2455 __isl_give isl_set *isl_set_list_get_set(
2456 __isl_keep isl_set_list *list, int index);
2457 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2458 int (*fn)(__isl_take isl_set *el, void *user),
2461 Lists can be printed using
2463 #include <isl/list.h>
2464 __isl_give isl_printer *isl_printer_print_set_list(
2465 __isl_take isl_printer *p,
2466 __isl_keep isl_set_list *list);
2470 Matrices can be created, copied and freed using the following functions.
2472 #include <isl/mat.h>
2473 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2474 unsigned n_row, unsigned n_col);
2475 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2476 void isl_mat_free(__isl_take isl_mat *mat);
2478 Note that the elements of a newly created matrix may have arbitrary values.
2479 The elements can be changed and inspected using the following functions.
2481 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2482 int isl_mat_rows(__isl_keep isl_mat *mat);
2483 int isl_mat_cols(__isl_keep isl_mat *mat);
2484 int isl_mat_get_element(__isl_keep isl_mat *mat,
2485 int row, int col, isl_int *v);
2486 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2487 int row, int col, isl_int v);
2488 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2489 int row, int col, int v);
2491 C<isl_mat_get_element> will return a negative value if anything went wrong.
2492 In that case, the value of C<*v> is undefined.
2494 The following function can be used to compute the (right) inverse
2495 of a matrix, i.e., a matrix such that the product of the original
2496 and the inverse (in that order) is a multiple of the identity matrix.
2497 The input matrix is assumed to be of full row-rank.
2499 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2501 The following function can be used to compute the (right) kernel
2502 (or null space) of a matrix, i.e., a matrix such that the product of
2503 the original and the kernel (in that order) is the zero matrix.
2505 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2507 =head2 Piecewise Quasi Affine Expressions
2509 The zero quasi affine expression on a given domain can be created using
2511 __isl_give isl_aff *isl_aff_zero_on_domain(
2512 __isl_take isl_local_space *ls);
2514 Note that the space in which the resulting object lives is a map space
2515 with the given space as domain and a one-dimensional range.
2517 An empty piecewise quasi affine expression (one with no cells)
2518 or a piecewise quasi affine expression with a single cell can
2519 be created using the following functions.
2521 #include <isl/aff.h>
2522 __isl_give isl_pw_aff *isl_pw_aff_empty(
2523 __isl_take isl_space *space);
2524 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2525 __isl_take isl_set *set, __isl_take isl_aff *aff);
2526 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2527 __isl_take isl_aff *aff);
2529 Quasi affine expressions can be copied and freed using
2531 #include <isl/aff.h>
2532 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2533 void *isl_aff_free(__isl_take isl_aff *aff);
2535 __isl_give isl_pw_aff *isl_pw_aff_copy(
2536 __isl_keep isl_pw_aff *pwaff);
2537 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2539 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2540 using the following function. The constraint is required to have
2541 a non-zero coefficient for the specified dimension.
2543 #include <isl/constraint.h>
2544 __isl_give isl_aff *isl_constraint_get_bound(
2545 __isl_keep isl_constraint *constraint,
2546 enum isl_dim_type type, int pos);
2548 The entire affine expression of the constraint can also be extracted
2549 using the following function.
2551 #include <isl/constraint.h>
2552 __isl_give isl_aff *isl_constraint_get_aff(
2553 __isl_keep isl_constraint *constraint);
2555 Conversely, an equality constraint equating
2556 the affine expression to zero or an inequality constraint enforcing
2557 the affine expression to be non-negative, can be constructed using
2559 __isl_give isl_constraint *isl_equality_from_aff(
2560 __isl_take isl_aff *aff);
2561 __isl_give isl_constraint *isl_inequality_from_aff(
2562 __isl_take isl_aff *aff);
2564 The expression can be inspected using
2566 #include <isl/aff.h>
2567 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2568 int isl_aff_dim(__isl_keep isl_aff *aff,
2569 enum isl_dim_type type);
2570 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2571 __isl_keep isl_aff *aff);
2572 __isl_give isl_local_space *isl_aff_get_local_space(
2573 __isl_keep isl_aff *aff);
2574 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2575 enum isl_dim_type type, unsigned pos);
2576 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2578 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2579 enum isl_dim_type type, int pos, isl_int *v);
2580 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2582 __isl_give isl_aff *isl_aff_get_div(
2583 __isl_keep isl_aff *aff, int pos);
2585 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2586 int (*fn)(__isl_take isl_set *set,
2587 __isl_take isl_aff *aff,
2588 void *user), void *user);
2590 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2591 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2593 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2594 enum isl_dim_type type, unsigned first, unsigned n);
2595 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2596 enum isl_dim_type type, unsigned first, unsigned n);
2598 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2599 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2600 enum isl_dim_type type);
2601 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2603 It can be modified using
2605 #include <isl/aff.h>
2606 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2607 __isl_take isl_pw_aff *pwaff,
2608 __isl_take isl_id *id);
2609 __isl_give isl_aff *isl_aff_set_dim_name(
2610 __isl_take isl_aff *aff, enum isl_dim_type type,
2611 unsigned pos, const char *s);
2612 __isl_give isl_aff *isl_aff_set_constant(
2613 __isl_take isl_aff *aff, isl_int v);
2614 __isl_give isl_aff *isl_aff_set_constant_si(
2615 __isl_take isl_aff *aff, int v);
2616 __isl_give isl_aff *isl_aff_set_coefficient(
2617 __isl_take isl_aff *aff,
2618 enum isl_dim_type type, int pos, isl_int v);
2619 __isl_give isl_aff *isl_aff_set_coefficient_si(
2620 __isl_take isl_aff *aff,
2621 enum isl_dim_type type, int pos, int v);
2622 __isl_give isl_aff *isl_aff_set_denominator(
2623 __isl_take isl_aff *aff, isl_int v);
2625 __isl_give isl_aff *isl_aff_add_constant(
2626 __isl_take isl_aff *aff, isl_int v);
2627 __isl_give isl_aff *isl_aff_add_constant_si(
2628 __isl_take isl_aff *aff, int v);
2629 __isl_give isl_aff *isl_aff_add_coefficient(
2630 __isl_take isl_aff *aff,
2631 enum isl_dim_type type, int pos, isl_int v);
2632 __isl_give isl_aff *isl_aff_add_coefficient_si(
2633 __isl_take isl_aff *aff,
2634 enum isl_dim_type type, int pos, int v);
2636 __isl_give isl_aff *isl_aff_insert_dims(
2637 __isl_take isl_aff *aff,
2638 enum isl_dim_type type, unsigned first, unsigned n);
2639 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2640 __isl_take isl_pw_aff *pwaff,
2641 enum isl_dim_type type, unsigned first, unsigned n);
2642 __isl_give isl_aff *isl_aff_add_dims(
2643 __isl_take isl_aff *aff,
2644 enum isl_dim_type type, unsigned n);
2645 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2646 __isl_take isl_pw_aff *pwaff,
2647 enum isl_dim_type type, unsigned n);
2648 __isl_give isl_aff *isl_aff_drop_dims(
2649 __isl_take isl_aff *aff,
2650 enum isl_dim_type type, unsigned first, unsigned n);
2651 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2652 __isl_take isl_pw_aff *pwaff,
2653 enum isl_dim_type type, unsigned first, unsigned n);
2655 Note that the C<set_constant> and C<set_coefficient> functions
2656 set the I<numerator> of the constant or coefficient, while
2657 C<add_constant> and C<add_coefficient> add an integer value to
2658 the possibly rational constant or coefficient.
2660 To check whether an affine expressions is obviously zero
2661 or obviously equal to some other affine expression, use
2663 #include <isl/aff.h>
2664 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2665 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2666 __isl_keep isl_aff *aff2);
2670 #include <isl/aff.h>
2671 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2672 __isl_take isl_aff *aff2);
2673 __isl_give isl_pw_aff *isl_pw_aff_add(
2674 __isl_take isl_pw_aff *pwaff1,
2675 __isl_take isl_pw_aff *pwaff2);
2676 __isl_give isl_pw_aff *isl_pw_aff_min(
2677 __isl_take isl_pw_aff *pwaff1,
2678 __isl_take isl_pw_aff *pwaff2);
2679 __isl_give isl_pw_aff *isl_pw_aff_max(
2680 __isl_take isl_pw_aff *pwaff1,
2681 __isl_take isl_pw_aff *pwaff2);
2682 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2683 __isl_take isl_aff *aff2);
2684 __isl_give isl_pw_aff *isl_pw_aff_sub(
2685 __isl_take isl_pw_aff *pwaff1,
2686 __isl_take isl_pw_aff *pwaff2);
2687 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2688 __isl_give isl_pw_aff *isl_pw_aff_neg(
2689 __isl_take isl_pw_aff *pwaff);
2690 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2691 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2692 __isl_take isl_pw_aff *pwaff);
2693 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2694 __isl_give isl_pw_aff *isl_pw_aff_floor(
2695 __isl_take isl_pw_aff *pwaff);
2696 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2698 __isl_give isl_pw_aff *isl_pw_aff_mod(
2699 __isl_take isl_pw_aff *pwaff, isl_int mod);
2700 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2702 __isl_give isl_pw_aff *isl_pw_aff_scale(
2703 __isl_take isl_pw_aff *pwaff, isl_int f);
2704 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2706 __isl_give isl_aff *isl_aff_scale_down_ui(
2707 __isl_take isl_aff *aff, unsigned f);
2708 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2709 __isl_take isl_pw_aff *pwaff, isl_int f);
2711 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2712 __isl_take isl_pw_aff_list *list);
2713 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2714 __isl_take isl_pw_aff_list *list);
2716 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2717 __isl_take isl_pw_aff *pwqp);
2719 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2720 __isl_take isl_pw_aff *pwaff,
2721 __isl_take isl_space *model);
2723 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2724 __isl_take isl_set *context);
2725 __isl_give isl_pw_aff *isl_pw_aff_gist(
2726 __isl_take isl_pw_aff *pwaff,
2727 __isl_take isl_set *context);
2729 __isl_give isl_set *isl_pw_aff_domain(
2730 __isl_take isl_pw_aff *pwaff);
2732 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2733 __isl_take isl_aff *aff2);
2734 __isl_give isl_pw_aff *isl_pw_aff_mul(
2735 __isl_take isl_pw_aff *pwaff1,
2736 __isl_take isl_pw_aff *pwaff2);
2738 When multiplying two affine expressions, at least one of the two needs
2741 #include <isl/aff.h>
2742 __isl_give isl_basic_set *isl_aff_le_basic_set(
2743 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2744 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2745 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2746 __isl_give isl_set *isl_pw_aff_eq_set(
2747 __isl_take isl_pw_aff *pwaff1,
2748 __isl_take isl_pw_aff *pwaff2);
2749 __isl_give isl_set *isl_pw_aff_ne_set(
2750 __isl_take isl_pw_aff *pwaff1,
2751 __isl_take isl_pw_aff *pwaff2);
2752 __isl_give isl_set *isl_pw_aff_le_set(
2753 __isl_take isl_pw_aff *pwaff1,
2754 __isl_take isl_pw_aff *pwaff2);
2755 __isl_give isl_set *isl_pw_aff_lt_set(
2756 __isl_take isl_pw_aff *pwaff1,
2757 __isl_take isl_pw_aff *pwaff2);
2758 __isl_give isl_set *isl_pw_aff_ge_set(
2759 __isl_take isl_pw_aff *pwaff1,
2760 __isl_take isl_pw_aff *pwaff2);
2761 __isl_give isl_set *isl_pw_aff_gt_set(
2762 __isl_take isl_pw_aff *pwaff1,
2763 __isl_take isl_pw_aff *pwaff2);
2765 __isl_give isl_set *isl_pw_aff_list_eq_set(
2766 __isl_take isl_pw_aff_list *list1,
2767 __isl_take isl_pw_aff_list *list2);
2768 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
2781 __isl_take isl_pw_aff_list *list1,
2782 __isl_take isl_pw_aff_list *list2);
2784 The function C<isl_aff_ge_basic_set> returns a basic set
2785 containing those elements in the shared space
2786 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2787 The function C<isl_aff_ge_set> returns a set
2788 containing those elements in the shared domain
2789 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2790 The functions operating on C<isl_pw_aff_list> apply the corresponding
2791 C<isl_pw_aff> function to each pair of elements in the two lists.
2793 #include <isl/aff.h>
2794 __isl_give isl_set *isl_pw_aff_nonneg_set(
2795 __isl_take isl_pw_aff *pwaff);
2796 __isl_give isl_set *isl_pw_aff_zero_set(
2797 __isl_take isl_pw_aff *pwaff);
2798 __isl_give isl_set *isl_pw_aff_non_zero_set(
2799 __isl_take isl_pw_aff *pwaff);
2801 The function C<isl_pw_aff_nonneg_set> returns a set
2802 containing those elements in the domain
2803 of C<pwaff> where C<pwaff> is non-negative.
2805 #include <isl/aff.h>
2806 __isl_give isl_pw_aff *isl_pw_aff_cond(
2807 __isl_take isl_set *cond,
2808 __isl_take isl_pw_aff *pwaff_true,
2809 __isl_take isl_pw_aff *pwaff_false);
2811 The function C<isl_pw_aff_cond> performs a conditional operator
2812 and returns an expression that is equal to C<pwaff_true>
2813 for elements in C<cond> and equal to C<pwaff_false> for elements
2816 #include <isl/aff.h>
2817 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2818 __isl_take isl_pw_aff *pwaff1,
2819 __isl_take isl_pw_aff *pwaff2);
2820 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2821 __isl_take isl_pw_aff *pwaff1,
2822 __isl_take isl_pw_aff *pwaff2);
2824 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2825 expression with a domain that is the union of those of C<pwaff1> and
2826 C<pwaff2> and such that on each cell, the quasi-affine expression is
2827 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2828 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2829 associated expression is the defined one.
2831 An expression can be printed using
2833 #include <isl/aff.h>
2834 __isl_give isl_printer *isl_printer_print_aff(
2835 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2837 __isl_give isl_printer *isl_printer_print_pw_aff(
2838 __isl_take isl_printer *p,
2839 __isl_keep isl_pw_aff *pwaff);
2843 Points are elements of a set. They can be used to construct
2844 simple sets (boxes) or they can be used to represent the
2845 individual elements of a set.
2846 The zero point (the origin) can be created using
2848 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2850 The coordinates of a point can be inspected, set and changed
2853 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2854 enum isl_dim_type type, int pos, isl_int *v);
2855 __isl_give isl_point *isl_point_set_coordinate(
2856 __isl_take isl_point *pnt,
2857 enum isl_dim_type type, int pos, isl_int v);
2859 __isl_give isl_point *isl_point_add_ui(
2860 __isl_take isl_point *pnt,
2861 enum isl_dim_type type, int pos, unsigned val);
2862 __isl_give isl_point *isl_point_sub_ui(
2863 __isl_take isl_point *pnt,
2864 enum isl_dim_type type, int pos, unsigned val);
2866 Other properties can be obtained using
2868 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2870 Points can be copied or freed using
2872 __isl_give isl_point *isl_point_copy(
2873 __isl_keep isl_point *pnt);
2874 void isl_point_free(__isl_take isl_point *pnt);
2876 A singleton set can be created from a point using
2878 __isl_give isl_basic_set *isl_basic_set_from_point(
2879 __isl_take isl_point *pnt);
2880 __isl_give isl_set *isl_set_from_point(
2881 __isl_take isl_point *pnt);
2883 and a box can be created from two opposite extremal points using
2885 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2886 __isl_take isl_point *pnt1,
2887 __isl_take isl_point *pnt2);
2888 __isl_give isl_set *isl_set_box_from_points(
2889 __isl_take isl_point *pnt1,
2890 __isl_take isl_point *pnt2);
2892 All elements of a B<bounded> (union) set can be enumerated using
2893 the following functions.
2895 int isl_set_foreach_point(__isl_keep isl_set *set,
2896 int (*fn)(__isl_take isl_point *pnt, void *user),
2898 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2899 int (*fn)(__isl_take isl_point *pnt, void *user),
2902 The function C<fn> is called for each integer point in
2903 C<set> with as second argument the last argument of
2904 the C<isl_set_foreach_point> call. The function C<fn>
2905 should return C<0> on success and C<-1> on failure.
2906 In the latter case, C<isl_set_foreach_point> will stop
2907 enumerating and return C<-1> as well.
2908 If the enumeration is performed successfully and to completion,
2909 then C<isl_set_foreach_point> returns C<0>.
2911 To obtain a single point of a (basic) set, use
2913 __isl_give isl_point *isl_basic_set_sample_point(
2914 __isl_take isl_basic_set *bset);
2915 __isl_give isl_point *isl_set_sample_point(
2916 __isl_take isl_set *set);
2918 If C<set> does not contain any (integer) points, then the
2919 resulting point will be ``void'', a property that can be
2922 int isl_point_is_void(__isl_keep isl_point *pnt);
2924 =head2 Piecewise Quasipolynomials
2926 A piecewise quasipolynomial is a particular kind of function that maps
2927 a parametric point to a rational value.
2928 More specifically, a quasipolynomial is a polynomial expression in greatest
2929 integer parts of affine expressions of parameters and variables.
2930 A piecewise quasipolynomial is a subdivision of a given parametric
2931 domain into disjoint cells with a quasipolynomial associated to
2932 each cell. The value of the piecewise quasipolynomial at a given
2933 point is the value of the quasipolynomial associated to the cell
2934 that contains the point. Outside of the union of cells,
2935 the value is assumed to be zero.
2936 For example, the piecewise quasipolynomial
2938 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2940 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2941 A given piecewise quasipolynomial has a fixed domain dimension.
2942 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2943 defined over different domains.
2944 Piecewise quasipolynomials are mainly used by the C<barvinok>
2945 library for representing the number of elements in a parametric set or map.
2946 For example, the piecewise quasipolynomial above represents
2947 the number of points in the map
2949 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2951 =head3 Printing (Piecewise) Quasipolynomials
2953 Quasipolynomials and piecewise quasipolynomials can be printed
2954 using the following functions.
2956 __isl_give isl_printer *isl_printer_print_qpolynomial(
2957 __isl_take isl_printer *p,
2958 __isl_keep isl_qpolynomial *qp);
2960 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2961 __isl_take isl_printer *p,
2962 __isl_keep isl_pw_qpolynomial *pwqp);
2964 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2965 __isl_take isl_printer *p,
2966 __isl_keep isl_union_pw_qpolynomial *upwqp);
2968 The output format of the printer
2969 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2970 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2972 In case of printing in C<ISL_FORMAT_C>, the user may want
2973 to set the names of all dimensions
2975 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2976 __isl_take isl_qpolynomial *qp,
2977 enum isl_dim_type type, unsigned pos,
2979 __isl_give isl_pw_qpolynomial *
2980 isl_pw_qpolynomial_set_dim_name(
2981 __isl_take isl_pw_qpolynomial *pwqp,
2982 enum isl_dim_type type, unsigned pos,
2985 =head3 Creating New (Piecewise) Quasipolynomials
2987 Some simple quasipolynomials can be created using the following functions.
2988 More complicated quasipolynomials can be created by applying
2989 operations such as addition and multiplication
2990 on the resulting quasipolynomials
2992 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2993 __isl_take isl_space *domain);
2994 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2995 __isl_take isl_space *domain);
2996 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2997 __isl_take isl_space *domain);
2998 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2999 __isl_take isl_space *domain);
3000 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3001 __isl_take isl_space *domain);
3002 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3003 __isl_take isl_space *domain,
3004 const isl_int n, const isl_int d);
3005 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3006 __isl_take isl_space *domain,
3007 enum isl_dim_type type, unsigned pos);
3008 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3009 __isl_take isl_aff *aff);
3011 Note that the space in which a quasipolynomial lives is a map space
3012 with a one-dimensional range. The C<domain> argument in some of
3013 the functions above corresponds to the domain of this map space.
3015 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3016 with a single cell can be created using the following functions.
3017 Multiple of these single cell piecewise quasipolynomials can
3018 be combined to create more complicated piecewise quasipolynomials.
3020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3021 __isl_take isl_space *space);
3022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3023 __isl_take isl_set *set,
3024 __isl_take isl_qpolynomial *qp);
3025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3026 __isl_take isl_qpolynomial *qp);
3027 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3028 __isl_take isl_pw_aff *pwaff);
3030 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3031 __isl_take isl_space *space);
3032 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3033 __isl_take isl_pw_qpolynomial *pwqp);
3034 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3035 __isl_take isl_union_pw_qpolynomial *upwqp,
3036 __isl_take isl_pw_qpolynomial *pwqp);
3038 Quasipolynomials can be copied and freed again using the following
3041 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3042 __isl_keep isl_qpolynomial *qp);
3043 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3046 __isl_keep isl_pw_qpolynomial *pwqp);
3047 void *isl_pw_qpolynomial_free(
3048 __isl_take isl_pw_qpolynomial *pwqp);
3050 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3051 __isl_keep isl_union_pw_qpolynomial *upwqp);
3052 void isl_union_pw_qpolynomial_free(
3053 __isl_take isl_union_pw_qpolynomial *upwqp);
3055 =head3 Inspecting (Piecewise) Quasipolynomials
3057 To iterate over all piecewise quasipolynomials in a union
3058 piecewise quasipolynomial, use the following function
3060 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3061 __isl_keep isl_union_pw_qpolynomial *upwqp,
3062 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3065 To extract the piecewise quasipolynomial in a given space from a union, use
3067 __isl_give isl_pw_qpolynomial *
3068 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3069 __isl_keep isl_union_pw_qpolynomial *upwqp,
3070 __isl_take isl_space *space);
3072 To iterate over the cells in a piecewise quasipolynomial,
3073 use either of the following two functions
3075 int isl_pw_qpolynomial_foreach_piece(
3076 __isl_keep isl_pw_qpolynomial *pwqp,
3077 int (*fn)(__isl_take isl_set *set,
3078 __isl_take isl_qpolynomial *qp,
3079 void *user), void *user);
3080 int isl_pw_qpolynomial_foreach_lifted_piece(
3081 __isl_keep isl_pw_qpolynomial *pwqp,
3082 int (*fn)(__isl_take isl_set *set,
3083 __isl_take isl_qpolynomial *qp,
3084 void *user), void *user);
3086 As usual, the function C<fn> should return C<0> on success
3087 and C<-1> on failure. The difference between
3088 C<isl_pw_qpolynomial_foreach_piece> and
3089 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3090 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3091 compute unique representations for all existentially quantified
3092 variables and then turn these existentially quantified variables
3093 into extra set variables, adapting the associated quasipolynomial
3094 accordingly. This means that the C<set> passed to C<fn>
3095 will not have any existentially quantified variables, but that
3096 the dimensions of the sets may be different for different
3097 invocations of C<fn>.
3099 To iterate over all terms in a quasipolynomial,
3102 int isl_qpolynomial_foreach_term(
3103 __isl_keep isl_qpolynomial *qp,
3104 int (*fn)(__isl_take isl_term *term,
3105 void *user), void *user);
3107 The terms themselves can be inspected and freed using
3110 unsigned isl_term_dim(__isl_keep isl_term *term,
3111 enum isl_dim_type type);
3112 void isl_term_get_num(__isl_keep isl_term *term,
3114 void isl_term_get_den(__isl_keep isl_term *term,
3116 int isl_term_get_exp(__isl_keep isl_term *term,
3117 enum isl_dim_type type, unsigned pos);
3118 __isl_give isl_aff *isl_term_get_div(
3119 __isl_keep isl_term *term, unsigned pos);
3120 void isl_term_free(__isl_take isl_term *term);
3122 Each term is a product of parameters, set variables and
3123 integer divisions. The function C<isl_term_get_exp>
3124 returns the exponent of a given dimensions in the given term.
3125 The C<isl_int>s in the arguments of C<isl_term_get_num>
3126 and C<isl_term_get_den> need to have been initialized
3127 using C<isl_int_init> before calling these functions.
3129 =head3 Properties of (Piecewise) Quasipolynomials
3131 To check whether a quasipolynomial is actually a constant,
3132 use the following function.
3134 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3135 isl_int *n, isl_int *d);
3137 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3138 then the numerator and denominator of the constant
3139 are returned in C<*n> and C<*d>, respectively.
3141 =head3 Operations on (Piecewise) Quasipolynomials
3143 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3144 __isl_take isl_qpolynomial *qp, isl_int v);
3145 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3146 __isl_take isl_qpolynomial *qp);
3147 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3148 __isl_take isl_qpolynomial *qp1,
3149 __isl_take isl_qpolynomial *qp2);
3150 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3151 __isl_take isl_qpolynomial *qp1,
3152 __isl_take isl_qpolynomial *qp2);
3153 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3154 __isl_take isl_qpolynomial *qp1,
3155 __isl_take isl_qpolynomial *qp2);
3156 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3157 __isl_take isl_qpolynomial *qp, unsigned exponent);
3159 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3160 __isl_take isl_pw_qpolynomial *pwqp1,
3161 __isl_take isl_pw_qpolynomial *pwqp2);
3162 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3163 __isl_take isl_pw_qpolynomial *pwqp1,
3164 __isl_take isl_pw_qpolynomial *pwqp2);
3165 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3166 __isl_take isl_pw_qpolynomial *pwqp1,
3167 __isl_take isl_pw_qpolynomial *pwqp2);
3168 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3169 __isl_take isl_pw_qpolynomial *pwqp);
3170 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3171 __isl_take isl_pw_qpolynomial *pwqp1,
3172 __isl_take isl_pw_qpolynomial *pwqp2);
3173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3174 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3176 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3177 __isl_take isl_union_pw_qpolynomial *upwqp1,
3178 __isl_take isl_union_pw_qpolynomial *upwqp2);
3179 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3180 __isl_take isl_union_pw_qpolynomial *upwqp1,
3181 __isl_take isl_union_pw_qpolynomial *upwqp2);
3182 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3183 __isl_take isl_union_pw_qpolynomial *upwqp1,
3184 __isl_take isl_union_pw_qpolynomial *upwqp2);
3186 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3187 __isl_take isl_pw_qpolynomial *pwqp,
3188 __isl_take isl_point *pnt);
3190 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3191 __isl_take isl_union_pw_qpolynomial *upwqp,
3192 __isl_take isl_point *pnt);
3194 __isl_give isl_set *isl_pw_qpolynomial_domain(
3195 __isl_take isl_pw_qpolynomial *pwqp);
3196 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3197 __isl_take isl_pw_qpolynomial *pwpq,
3198 __isl_take isl_set *set);
3200 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3201 __isl_take isl_union_pw_qpolynomial *upwqp);
3202 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3203 __isl_take isl_union_pw_qpolynomial *upwpq,
3204 __isl_take isl_union_set *uset);
3206 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3207 __isl_take isl_qpolynomial *qp,
3208 __isl_take isl_space *model);
3210 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3211 __isl_take isl_qpolynomial *qp);
3212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3213 __isl_take isl_pw_qpolynomial *pwqp);
3215 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3216 __isl_take isl_union_pw_qpolynomial *upwqp);
3218 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3219 __isl_take isl_qpolynomial *qp,
3220 __isl_take isl_set *context);
3222 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3223 __isl_take isl_pw_qpolynomial *pwqp,
3224 __isl_take isl_set *context);
3226 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3227 __isl_take isl_union_pw_qpolynomial *upwqp,
3228 __isl_take isl_union_set *context);
3230 The gist operation applies the gist operation to each of
3231 the cells in the domain of the input piecewise quasipolynomial.
3232 The context is also exploited
3233 to simplify the quasipolynomials associated to each cell.
3235 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3236 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3237 __isl_give isl_union_pw_qpolynomial *
3238 isl_union_pw_qpolynomial_to_polynomial(
3239 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3241 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3242 the polynomial will be an overapproximation. If C<sign> is negative,
3243 it will be an underapproximation. If C<sign> is zero, the approximation
3244 will lie somewhere in between.
3246 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3248 A piecewise quasipolynomial reduction is a piecewise
3249 reduction (or fold) of quasipolynomials.
3250 In particular, the reduction can be maximum or a minimum.
3251 The objects are mainly used to represent the result of
3252 an upper or lower bound on a quasipolynomial over its domain,
3253 i.e., as the result of the following function.
3255 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3256 __isl_take isl_pw_qpolynomial *pwqp,
3257 enum isl_fold type, int *tight);
3259 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3260 __isl_take isl_union_pw_qpolynomial *upwqp,
3261 enum isl_fold type, int *tight);
3263 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3264 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3265 is the returned bound is known be tight, i.e., for each value
3266 of the parameters there is at least
3267 one element in the domain that reaches the bound.
3268 If the domain of C<pwqp> is not wrapping, then the bound is computed
3269 over all elements in that domain and the result has a purely parametric
3270 domain. If the domain of C<pwqp> is wrapping, then the bound is
3271 computed over the range of the wrapped relation. The domain of the
3272 wrapped relation becomes the domain of the result.
3274 A (piecewise) quasipolynomial reduction can be copied or freed using the
3275 following functions.
3277 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3278 __isl_keep isl_qpolynomial_fold *fold);
3279 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3280 __isl_keep isl_pw_qpolynomial_fold *pwf);
3281 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3282 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3283 void isl_qpolynomial_fold_free(
3284 __isl_take isl_qpolynomial_fold *fold);
3285 void *isl_pw_qpolynomial_fold_free(
3286 __isl_take isl_pw_qpolynomial_fold *pwf);
3287 void isl_union_pw_qpolynomial_fold_free(
3288 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3290 =head3 Printing Piecewise Quasipolynomial Reductions
3292 Piecewise quasipolynomial reductions can be printed
3293 using the following function.
3295 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3296 __isl_take isl_printer *p,
3297 __isl_keep isl_pw_qpolynomial_fold *pwf);
3298 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3299 __isl_take isl_printer *p,
3300 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3302 For C<isl_printer_print_pw_qpolynomial_fold>,
3303 output format of the printer
3304 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3305 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3306 output format of the printer
3307 needs to be set to C<ISL_FORMAT_ISL>.
3308 In case of printing in C<ISL_FORMAT_C>, the user may want
3309 to set the names of all dimensions
3311 __isl_give isl_pw_qpolynomial_fold *
3312 isl_pw_qpolynomial_fold_set_dim_name(
3313 __isl_take isl_pw_qpolynomial_fold *pwf,
3314 enum isl_dim_type type, unsigned pos,
3317 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3319 To iterate over all piecewise quasipolynomial reductions in a union
3320 piecewise quasipolynomial reduction, use the following function
3322 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3323 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3324 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3325 void *user), void *user);
3327 To iterate over the cells in a piecewise quasipolynomial reduction,
3328 use either of the following two functions
3330 int isl_pw_qpolynomial_fold_foreach_piece(
3331 __isl_keep isl_pw_qpolynomial_fold *pwf,
3332 int (*fn)(__isl_take isl_set *set,
3333 __isl_take isl_qpolynomial_fold *fold,
3334 void *user), void *user);
3335 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3336 __isl_keep isl_pw_qpolynomial_fold *pwf,
3337 int (*fn)(__isl_take isl_set *set,
3338 __isl_take isl_qpolynomial_fold *fold,
3339 void *user), void *user);
3341 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3342 of the difference between these two functions.
3344 To iterate over all quasipolynomials in a reduction, use
3346 int isl_qpolynomial_fold_foreach_qpolynomial(
3347 __isl_keep isl_qpolynomial_fold *fold,
3348 int (*fn)(__isl_take isl_qpolynomial *qp,
3349 void *user), void *user);
3351 =head3 Operations on Piecewise Quasipolynomial Reductions
3353 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3354 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3356 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3357 __isl_take isl_pw_qpolynomial_fold *pwf1,
3358 __isl_take isl_pw_qpolynomial_fold *pwf2);
3360 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3361 __isl_take isl_pw_qpolynomial_fold *pwf1,
3362 __isl_take isl_pw_qpolynomial_fold *pwf2);
3364 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3365 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3366 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3368 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3369 __isl_take isl_pw_qpolynomial_fold *pwf,
3370 __isl_take isl_point *pnt);
3372 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3373 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3374 __isl_take isl_point *pnt);
3376 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3377 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3378 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3379 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3380 __isl_take isl_union_set *uset);
3382 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3383 __isl_take isl_pw_qpolynomial_fold *pwf);
3385 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3386 __isl_take isl_pw_qpolynomial_fold *pwf);
3388 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3389 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3391 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3392 __isl_take isl_pw_qpolynomial_fold *pwf,
3393 __isl_take isl_set *context);
3395 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3396 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3397 __isl_take isl_union_set *context);
3399 The gist operation applies the gist operation to each of
3400 the cells in the domain of the input piecewise quasipolynomial reduction.
3401 In future, the operation will also exploit the context
3402 to simplify the quasipolynomial reductions associated to each cell.
3404 __isl_give isl_pw_qpolynomial_fold *
3405 isl_set_apply_pw_qpolynomial_fold(
3406 __isl_take isl_set *set,
3407 __isl_take isl_pw_qpolynomial_fold *pwf,
3409 __isl_give isl_pw_qpolynomial_fold *
3410 isl_map_apply_pw_qpolynomial_fold(
3411 __isl_take isl_map *map,
3412 __isl_take isl_pw_qpolynomial_fold *pwf,
3414 __isl_give isl_union_pw_qpolynomial_fold *
3415 isl_union_set_apply_union_pw_qpolynomial_fold(
3416 __isl_take isl_union_set *uset,
3417 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3419 __isl_give isl_union_pw_qpolynomial_fold *
3420 isl_union_map_apply_union_pw_qpolynomial_fold(
3421 __isl_take isl_union_map *umap,
3422 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3425 The functions taking a map
3426 compose the given map with the given piecewise quasipolynomial reduction.
3427 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3428 over all elements in the intersection of the range of the map
3429 and the domain of the piecewise quasipolynomial reduction
3430 as a function of an element in the domain of the map.
3431 The functions taking a set compute a bound over all elements in the
3432 intersection of the set and the domain of the
3433 piecewise quasipolynomial reduction.
3435 =head2 Dependence Analysis
3437 C<isl> contains specialized functionality for performing
3438 array dataflow analysis. That is, given a I<sink> access relation
3439 and a collection of possible I<source> access relations,
3440 C<isl> can compute relations that describe
3441 for each iteration of the sink access, which iteration
3442 of which of the source access relations was the last
3443 to access the same data element before the given iteration
3445 To compute standard flow dependences, the sink should be
3446 a read, while the sources should be writes.
3447 If any of the source accesses are marked as being I<may>
3448 accesses, then there will be a dependence to the last
3449 I<must> access B<and> to any I<may> access that follows
3450 this last I<must> access.
3451 In particular, if I<all> sources are I<may> accesses,
3452 then memory based dependence analysis is performed.
3453 If, on the other hand, all sources are I<must> accesses,
3454 then value based dependence analysis is performed.
3456 #include <isl/flow.h>
3458 typedef int (*isl_access_level_before)(void *first, void *second);
3460 __isl_give isl_access_info *isl_access_info_alloc(
3461 __isl_take isl_map *sink,
3462 void *sink_user, isl_access_level_before fn,
3464 __isl_give isl_access_info *isl_access_info_add_source(
3465 __isl_take isl_access_info *acc,
3466 __isl_take isl_map *source, int must,
3468 void isl_access_info_free(__isl_take isl_access_info *acc);
3470 __isl_give isl_flow *isl_access_info_compute_flow(
3471 __isl_take isl_access_info *acc);
3473 int isl_flow_foreach(__isl_keep isl_flow *deps,
3474 int (*fn)(__isl_take isl_map *dep, int must,
3475 void *dep_user, void *user),
3477 __isl_give isl_map *isl_flow_get_no_source(
3478 __isl_keep isl_flow *deps, int must);
3479 void isl_flow_free(__isl_take isl_flow *deps);
3481 The function C<isl_access_info_compute_flow> performs the actual
3482 dependence analysis. The other functions are used to construct
3483 the input for this function or to read off the output.
3485 The input is collected in an C<isl_access_info>, which can
3486 be created through a call to C<isl_access_info_alloc>.
3487 The arguments to this functions are the sink access relation
3488 C<sink>, a token C<sink_user> used to identify the sink
3489 access to the user, a callback function for specifying the
3490 relative order of source and sink accesses, and the number
3491 of source access relations that will be added.
3492 The callback function has type C<int (*)(void *first, void *second)>.
3493 The function is called with two user supplied tokens identifying
3494 either a source or the sink and it should return the shared nesting
3495 level and the relative order of the two accesses.
3496 In particular, let I<n> be the number of loops shared by
3497 the two accesses. If C<first> precedes C<second> textually,
3498 then the function should return I<2 * n + 1>; otherwise,
3499 it should return I<2 * n>.
3500 The sources can be added to the C<isl_access_info> by performing
3501 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3502 C<must> indicates whether the source is a I<must> access
3503 or a I<may> access. Note that a multi-valued access relation
3504 should only be marked I<must> if every iteration in the domain
3505 of the relation accesses I<all> elements in its image.
3506 The C<source_user> token is again used to identify
3507 the source access. The range of the source access relation
3508 C<source> should have the same dimension as the range
3509 of the sink access relation.
3510 The C<isl_access_info_free> function should usually not be
3511 called explicitly, because it is called implicitly by
3512 C<isl_access_info_compute_flow>.
3514 The result of the dependence analysis is collected in an
3515 C<isl_flow>. There may be elements of
3516 the sink access for which no preceding source access could be
3517 found or for which all preceding sources are I<may> accesses.
3518 The relations containing these elements can be obtained through
3519 calls to C<isl_flow_get_no_source>, the first with C<must> set
3520 and the second with C<must> unset.
3521 In the case of standard flow dependence analysis,
3522 with the sink a read and the sources I<must> writes,
3523 the first relation corresponds to the reads from uninitialized
3524 array elements and the second relation is empty.
3525 The actual flow dependences can be extracted using
3526 C<isl_flow_foreach>. This function will call the user-specified
3527 callback function C<fn> for each B<non-empty> dependence between
3528 a source and the sink. The callback function is called
3529 with four arguments, the actual flow dependence relation
3530 mapping source iterations to sink iterations, a boolean that
3531 indicates whether it is a I<must> or I<may> dependence, a token
3532 identifying the source and an additional C<void *> with value
3533 equal to the third argument of the C<isl_flow_foreach> call.
3534 A dependence is marked I<must> if it originates from a I<must>
3535 source and if it is not followed by any I<may> sources.
3537 After finishing with an C<isl_flow>, the user should call
3538 C<isl_flow_free> to free all associated memory.
3540 A higher-level interface to dependence analysis is provided
3541 by the following function.
3543 #include <isl/flow.h>
3545 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3546 __isl_take isl_union_map *must_source,
3547 __isl_take isl_union_map *may_source,
3548 __isl_take isl_union_map *schedule,
3549 __isl_give isl_union_map **must_dep,
3550 __isl_give isl_union_map **may_dep,
3551 __isl_give isl_union_map **must_no_source,
3552 __isl_give isl_union_map **may_no_source);
3554 The arrays are identified by the tuple names of the ranges
3555 of the accesses. The iteration domains by the tuple names
3556 of the domains of the accesses and of the schedule.
3557 The relative order of the iteration domains is given by the
3558 schedule. The relations returned through C<must_no_source>
3559 and C<may_no_source> are subsets of C<sink>.
3560 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3561 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3562 any of the other arguments is treated as an error.
3566 B<The functionality described in this section is fairly new
3567 and may be subject to change.>
3569 The following function can be used to compute a schedule
3570 for a union of domains. The generated schedule respects
3571 all C<validity> dependences. That is, all dependence distances
3572 over these dependences in the scheduled space are lexicographically
3573 positive. The generated schedule schedule also tries to minimize
3574 the dependence distances over C<proximity> dependences.
3575 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3576 for groups of domains where the dependence distances have only
3577 non-negative values.
3578 The algorithm used to construct the schedule is similar to that
3581 #include <isl/schedule.h>
3582 __isl_give isl_schedule *isl_union_set_compute_schedule(
3583 __isl_take isl_union_set *domain,
3584 __isl_take isl_union_map *validity,
3585 __isl_take isl_union_map *proximity);
3586 void *isl_schedule_free(__isl_take isl_schedule *sched);
3588 A mapping from the domains to the scheduled space can be obtained
3589 from an C<isl_schedule> using the following function.
3591 __isl_give isl_union_map *isl_schedule_get_map(
3592 __isl_keep isl_schedule *sched);
3594 A representation of the schedule can be printed using
3596 __isl_give isl_printer *isl_printer_print_schedule(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_schedule *schedule);
3600 A representation of the schedule as a forest of bands can be obtained
3601 using the following function.
3603 __isl_give isl_band_list *isl_schedule_get_band_forest(
3604 __isl_keep isl_schedule *schedule);
3606 The list can be manipulated as explained in L<"Lists">.
3607 The bands inside the list can be copied and freed using the following
3610 #include <isl/band.h>
3611 __isl_give isl_band *isl_band_copy(
3612 __isl_keep isl_band *band);
3613 void *isl_band_free(__isl_take isl_band *band);
3615 Each band contains zero or more scheduling dimensions.
3616 These are referred to as the members of the band.
3617 The section of the schedule that corresponds to the band is
3618 referred to as the partial schedule of the band.
3619 For those nodes that participate in a band, the outer scheduling
3620 dimensions form the prefix schedule, while the inner scheduling
3621 dimensions form the suffix schedule.
3622 That is, if we take a cut of the band forest, then the union of
3623 the concatenations of the prefix, partial and suffix schedules of
3624 each band in the cut is equal to the entire schedule (modulo
3625 some possible padding at the end with zero scheduling dimensions).
3626 The properties of a band can be inspected using the following functions.
3628 #include <isl/band.h>
3629 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3631 int isl_band_has_children(__isl_keep isl_band *band);
3632 __isl_give isl_band_list *isl_band_get_children(
3633 __isl_keep isl_band *band);
3635 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3636 __isl_keep isl_band *band);
3637 __isl_give isl_union_map *isl_band_get_partial_schedule(
3638 __isl_keep isl_band *band);
3639 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3640 __isl_keep isl_band *band);
3642 int isl_band_n_member(__isl_keep isl_band *band);
3643 int isl_band_member_is_zero_distance(
3644 __isl_keep isl_band *band, int pos);
3646 Note that a scheduling dimension is considered to be ``zero
3647 distance'' if it does not carry any proximity dependences
3649 That is, if the dependence distances of the proximity
3650 dependences are all zero in that direction (for fixed
3651 iterations of outer bands).
3653 A representation of the band can be printed using
3655 #include <isl/band.h>
3656 __isl_give isl_printer *isl_printer_print_band(
3657 __isl_take isl_printer *p,
3658 __isl_keep isl_band *band);
3660 =head2 Parametric Vertex Enumeration
3662 The parametric vertex enumeration described in this section
3663 is mainly intended to be used internally and by the C<barvinok>
3666 #include <isl/vertices.h>
3667 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3668 __isl_keep isl_basic_set *bset);
3670 The function C<isl_basic_set_compute_vertices> performs the
3671 actual computation of the parametric vertices and the chamber
3672 decomposition and store the result in an C<isl_vertices> object.
3673 This information can be queried by either iterating over all
3674 the vertices or iterating over all the chambers or cells
3675 and then iterating over all vertices that are active on the chamber.
3677 int isl_vertices_foreach_vertex(
3678 __isl_keep isl_vertices *vertices,
3679 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3682 int isl_vertices_foreach_cell(
3683 __isl_keep isl_vertices *vertices,
3684 int (*fn)(__isl_take isl_cell *cell, void *user),
3686 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3687 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3690 Other operations that can be performed on an C<isl_vertices> object are
3693 isl_ctx *isl_vertices_get_ctx(
3694 __isl_keep isl_vertices *vertices);
3695 int isl_vertices_get_n_vertices(
3696 __isl_keep isl_vertices *vertices);
3697 void isl_vertices_free(__isl_take isl_vertices *vertices);
3699 Vertices can be inspected and destroyed using the following functions.
3701 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3702 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3703 __isl_give isl_basic_set *isl_vertex_get_domain(
3704 __isl_keep isl_vertex *vertex);
3705 __isl_give isl_basic_set *isl_vertex_get_expr(
3706 __isl_keep isl_vertex *vertex);
3707 void isl_vertex_free(__isl_take isl_vertex *vertex);
3709 C<isl_vertex_get_expr> returns a singleton parametric set describing
3710 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3712 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3713 B<rational> basic sets, so they should mainly be used for inspection
3714 and should not be mixed with integer sets.
3716 Chambers can be inspected and destroyed using the following functions.
3718 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3719 __isl_give isl_basic_set *isl_cell_get_domain(
3720 __isl_keep isl_cell *cell);
3721 void isl_cell_free(__isl_take isl_cell *cell);
3725 Although C<isl> is mainly meant to be used as a library,
3726 it also contains some basic applications that use some
3727 of the functionality of C<isl>.
3728 The input may be specified in either the L<isl format>
3729 or the L<PolyLib format>.
3731 =head2 C<isl_polyhedron_sample>
3733 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3734 an integer element of the polyhedron, if there is any.
3735 The first column in the output is the denominator and is always
3736 equal to 1. If the polyhedron contains no integer points,
3737 then a vector of length zero is printed.
3741 C<isl_pip> takes the same input as the C<example> program
3742 from the C<piplib> distribution, i.e., a set of constraints
3743 on the parameters, a line containing only -1 and finally a set
3744 of constraints on a parametric polyhedron.
3745 The coefficients of the parameters appear in the last columns
3746 (but before the final constant column).
3747 The output is the lexicographic minimum of the parametric polyhedron.
3748 As C<isl> currently does not have its own output format, the output
3749 is just a dump of the internal state.
3751 =head2 C<isl_polyhedron_minimize>
3753 C<isl_polyhedron_minimize> computes the minimum of some linear
3754 or affine objective function over the integer points in a polyhedron.
3755 If an affine objective function
3756 is given, then the constant should appear in the last column.
3758 =head2 C<isl_polytope_scan>
3760 Given a polytope, C<isl_polytope_scan> prints
3761 all integer points in the polytope.