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>.
133 The source of C<isl> can be obtained either as a tarball
134 or from the git repository. Both are available from
135 L<http://freshmeat.net/projects/isl/>.
136 The installation process depends on how you obtained
139 =head2 Installation from the git repository
143 =item 1 Clone or update the repository
145 The first time the source is obtained, you need to clone
148 git clone git://repo.or.cz/isl.git
150 To obtain updates, you need to pull in the latest changes
154 =item 2 Generate C<configure>
160 After performing the above steps, continue
161 with the L<Common installation instructions>.
163 =head2 Common installation instructions
167 =item 1 Obtain C<GMP>
169 Building C<isl> requires C<GMP>, including its headers files.
170 Your distribution may not provide these header files by default
171 and you may need to install a package called C<gmp-devel> or something
172 similar. Alternatively, C<GMP> can be built from
173 source, available from L<http://gmplib.org/>.
177 C<isl> uses the standard C<autoconf> C<configure> script.
182 optionally followed by some configure options.
183 A complete list of options can be obtained by running
187 Below we discuss some of the more common options.
189 C<isl> can optionally use C<piplib>, but no
190 C<piplib> functionality is currently used by default.
191 The C<--with-piplib> option can
192 be used to specify which C<piplib>
193 library to use, either an installed version (C<system>),
194 an externally built version (C<build>)
195 or no version (C<no>). The option C<build> is mostly useful
196 in C<configure> scripts of larger projects that bundle both C<isl>
203 Installation prefix for C<isl>
205 =item C<--with-gmp-prefix>
207 Installation prefix for C<GMP> (architecture-independent files).
209 =item C<--with-gmp-exec-prefix>
211 Installation prefix for C<GMP> (architecture-dependent files).
213 =item C<--with-piplib>
215 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
217 =item C<--with-piplib-prefix>
219 Installation prefix for C<system> C<piplib> (architecture-independent files).
221 =item C<--with-piplib-exec-prefix>
223 Installation prefix for C<system> C<piplib> (architecture-dependent files).
225 =item C<--with-piplib-builddir>
227 Location where C<build> C<piplib> was built.
235 =item 4 Install (optional)
243 =head2 Initialization
245 All manipulations of integer sets and relations occur within
246 the context of an C<isl_ctx>.
247 A given C<isl_ctx> can only be used within a single thread.
248 All arguments of a function are required to have been allocated
249 within the same context.
250 There are currently no functions available for moving an object
251 from one C<isl_ctx> to another C<isl_ctx>. This means that
252 there is currently no way of safely moving an object from one
253 thread to another, unless the whole C<isl_ctx> is moved.
255 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
256 freed using C<isl_ctx_free>.
257 All objects allocated within an C<isl_ctx> should be freed
258 before the C<isl_ctx> itself is freed.
260 isl_ctx *isl_ctx_alloc();
261 void isl_ctx_free(isl_ctx *ctx);
265 All operations on integers, mainly the coefficients
266 of the constraints describing the sets and relations,
267 are performed in exact integer arithmetic using C<GMP>.
268 However, to allow future versions of C<isl> to optionally
269 support fixed integer arithmetic, all calls to C<GMP>
270 are wrapped inside C<isl> specific macros.
271 The basic type is C<isl_int> and the operations below
272 are available on this type.
273 The meanings of these operations are essentially the same
274 as their C<GMP> C<mpz_> counterparts.
275 As always with C<GMP> types, C<isl_int>s need to be
276 initialized with C<isl_int_init> before they can be used
277 and they need to be released with C<isl_int_clear>
279 The user should not assume that an C<isl_int> is represented
280 as a C<mpz_t>, but should instead explicitly convert between
281 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
282 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
286 =item isl_int_init(i)
288 =item isl_int_clear(i)
290 =item isl_int_set(r,i)
292 =item isl_int_set_si(r,i)
294 =item isl_int_set_gmp(r,g)
296 =item isl_int_get_gmp(i,g)
298 =item isl_int_abs(r,i)
300 =item isl_int_neg(r,i)
302 =item isl_int_swap(i,j)
304 =item isl_int_swap_or_set(i,j)
306 =item isl_int_add_ui(r,i,j)
308 =item isl_int_sub_ui(r,i,j)
310 =item isl_int_add(r,i,j)
312 =item isl_int_sub(r,i,j)
314 =item isl_int_mul(r,i,j)
316 =item isl_int_mul_ui(r,i,j)
318 =item isl_int_addmul(r,i,j)
320 =item isl_int_submul(r,i,j)
322 =item isl_int_gcd(r,i,j)
324 =item isl_int_lcm(r,i,j)
326 =item isl_int_divexact(r,i,j)
328 =item isl_int_cdiv_q(r,i,j)
330 =item isl_int_fdiv_q(r,i,j)
332 =item isl_int_fdiv_r(r,i,j)
334 =item isl_int_fdiv_q_ui(r,i,j)
336 =item isl_int_read(r,s)
338 =item isl_int_print(out,i,width)
342 =item isl_int_cmp(i,j)
344 =item isl_int_cmp_si(i,si)
346 =item isl_int_eq(i,j)
348 =item isl_int_ne(i,j)
350 =item isl_int_lt(i,j)
352 =item isl_int_le(i,j)
354 =item isl_int_gt(i,j)
356 =item isl_int_ge(i,j)
358 =item isl_int_abs_eq(i,j)
360 =item isl_int_abs_ne(i,j)
362 =item isl_int_abs_lt(i,j)
364 =item isl_int_abs_gt(i,j)
366 =item isl_int_abs_ge(i,j)
368 =item isl_int_is_zero(i)
370 =item isl_int_is_one(i)
372 =item isl_int_is_negone(i)
374 =item isl_int_is_pos(i)
376 =item isl_int_is_neg(i)
378 =item isl_int_is_nonpos(i)
380 =item isl_int_is_nonneg(i)
382 =item isl_int_is_divisible_by(i,j)
386 =head2 Sets and Relations
388 C<isl> uses six types of objects for representing sets and relations,
389 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
390 C<isl_union_set> and C<isl_union_map>.
391 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
392 can be described as a conjunction of affine constraints, while
393 C<isl_set> and C<isl_map> represent unions of
394 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
395 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
396 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
397 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
398 where spaces are considered different if they have a different number
399 of dimensions and/or different names (see L<"Spaces">).
400 The difference between sets and relations (maps) is that sets have
401 one set of variables, while relations have two sets of variables,
402 input variables and output variables.
404 =head2 Memory Management
406 Since a high-level operation on sets and/or relations usually involves
407 several substeps and since the user is usually not interested in
408 the intermediate results, most functions that return a new object
409 will also release all the objects passed as arguments.
410 If the user still wants to use one or more of these arguments
411 after the function call, she should pass along a copy of the
412 object rather than the object itself.
413 The user is then responsible for making sure that the original
414 object gets used somewhere else or is explicitly freed.
416 The arguments and return values of all documented functions are
417 annotated to make clear which arguments are released and which
418 arguments are preserved. In particular, the following annotations
425 C<__isl_give> means that a new object is returned.
426 The user should make sure that the returned pointer is
427 used exactly once as a value for an C<__isl_take> argument.
428 In between, it can be used as a value for as many
429 C<__isl_keep> arguments as the user likes.
430 There is one exception, and that is the case where the
431 pointer returned is C<NULL>. Is this case, the user
432 is free to use it as an C<__isl_take> argument or not.
436 C<__isl_take> means that the object the argument points to
437 is taken over by the function and may no longer be used
438 by the user as an argument to any other function.
439 The pointer value must be one returned by a function
440 returning an C<__isl_give> pointer.
441 If the user passes in a C<NULL> value, then this will
442 be treated as an error in the sense that the function will
443 not perform its usual operation. However, it will still
444 make sure that all the other C<__isl_take> arguments
449 C<__isl_keep> means that the function will only use the object
450 temporarily. After the function has finished, the user
451 can still use it as an argument to other functions.
452 A C<NULL> value will be treated in the same way as
453 a C<NULL> value for an C<__isl_take> argument.
459 Identifiers are used to identify both individual dimensions
460 and tuples of dimensions. They consist of a name and an optional
461 pointer. Identifiers with the same name but different pointer values
462 are considered to be distinct.
463 Identifiers can be constructed, copied, freed, inspected and printed
464 using the following functions.
467 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
468 __isl_keep const char *name, void *user);
469 __isl_give isl_id *isl_id_copy(isl_id *id);
470 void *isl_id_free(__isl_take isl_id *id);
472 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
473 void *isl_id_get_user(__isl_keep isl_id *id);
474 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
476 __isl_give isl_printer *isl_printer_print_id(
477 __isl_take isl_printer *p, __isl_keep isl_id *id);
479 Note that C<isl_id_get_name> returns a pointer to some internal
480 data structure, so the result can only be used while the
481 corresponding C<isl_id> is alive.
485 Whenever a new set or relation is created from scratch,
486 the space in which it lives needs to be specified using an C<isl_space>.
488 #include <isl/space.h>
489 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
490 unsigned nparam, unsigned n_in, unsigned n_out);
491 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
493 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
494 unsigned nparam, unsigned dim);
495 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
496 void isl_space_free(__isl_take isl_space *space);
497 unsigned isl_space_dim(__isl_keep isl_space *space,
498 enum isl_dim_type type);
500 The space used for creating a parameter domain
501 needs to be created using C<isl_space_params_alloc>.
502 For other sets, the space
503 needs to be created using C<isl_space_set_alloc>, while
504 for a relation, the space
505 needs to be created using C<isl_space_alloc>.
506 C<isl_space_dim> can be used
507 to find out the number of dimensions of each type in
508 a space, where type may be
509 C<isl_dim_param>, C<isl_dim_in> (only for relations),
510 C<isl_dim_out> (only for relations), C<isl_dim_set>
511 (only for sets) or C<isl_dim_all>.
513 To check whether a given space is that of a set or a map
514 or whether it is a parameter space, use these functions:
516 #include <isl/space.h>
517 int isl_space_is_params(__isl_keep isl_space *space);
518 int isl_space_is_set(__isl_keep isl_space *space);
520 It is often useful to create objects that live in the
521 same space as some other object. This can be accomplished
522 by creating the new objects
523 (see L<Creating New Sets and Relations> or
524 L<Creating New (Piecewise) Quasipolynomials>) based on the space
525 of the original object.
528 __isl_give isl_space *isl_basic_set_get_space(
529 __isl_keep isl_basic_set *bset);
530 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
532 #include <isl/union_set.h>
533 __isl_give isl_space *isl_union_set_get_space(
534 __isl_keep isl_union_set *uset);
537 __isl_give isl_space *isl_basic_map_get_space(
538 __isl_keep isl_basic_map *bmap);
539 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
541 #include <isl/union_map.h>
542 __isl_give isl_space *isl_union_map_get_space(
543 __isl_keep isl_union_map *umap);
545 #include <isl/constraint.h>
546 __isl_give isl_space *isl_constraint_get_space(
547 __isl_keep isl_constraint *constraint);
549 #include <isl/polynomial.h>
550 __isl_give isl_space *isl_qpolynomial_get_domain_space(
551 __isl_keep isl_qpolynomial *qp);
552 __isl_give isl_space *isl_qpolynomial_get_space(
553 __isl_keep isl_qpolynomial *qp);
554 __isl_give isl_space *isl_qpolynomial_fold_get_space(
555 __isl_keep isl_qpolynomial_fold *fold);
556 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
557 __isl_keep isl_pw_qpolynomial *pwqp);
558 __isl_give isl_space *isl_pw_qpolynomial_get_space(
559 __isl_keep isl_pw_qpolynomial *pwqp);
560 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
561 __isl_keep isl_pw_qpolynomial_fold *pwf);
562 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
563 __isl_keep isl_pw_qpolynomial_fold *pwf);
564 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
565 __isl_keep isl_union_pw_qpolynomial *upwqp);
566 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
567 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
570 __isl_give isl_space *isl_aff_get_domain_space(
571 __isl_keep isl_aff *aff);
572 __isl_give isl_space *isl_aff_get_space(
573 __isl_keep isl_aff *aff);
574 __isl_give isl_space *isl_pw_aff_get_domain_space(
575 __isl_keep isl_pw_aff *pwaff);
576 __isl_give isl_space *isl_pw_aff_get_space(
577 __isl_keep isl_pw_aff *pwaff);
579 #include <isl/point.h>
580 __isl_give isl_space *isl_point_get_space(
581 __isl_keep isl_point *pnt);
583 The identifiers or names of the individual dimensions may be set or read off
584 using the following functions.
586 #include <isl/space.h>
587 __isl_give isl_space *isl_space_set_dim_id(
588 __isl_take isl_space *space,
589 enum isl_dim_type type, unsigned pos,
590 __isl_take isl_id *id);
591 int isl_space_has_dim_id(__isl_keep isl_space *space,
592 enum isl_dim_type type, unsigned pos);
593 __isl_give isl_id *isl_space_get_dim_id(
594 __isl_keep isl_space *space,
595 enum isl_dim_type type, unsigned pos);
596 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
597 enum isl_dim_type type, unsigned pos,
598 __isl_keep const char *name);
599 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
600 enum isl_dim_type type, unsigned pos);
602 Note that C<isl_space_get_name> returns a pointer to some internal
603 data structure, so the result can only be used while the
604 corresponding C<isl_space> is alive.
605 Also note that every function that operates on two sets or relations
606 requires that both arguments have the same parameters. This also
607 means that if one of the arguments has named parameters, then the
608 other needs to have named parameters too and the names need to match.
609 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
610 arguments may have different parameters (as long as they are named),
611 in which case the result will have as parameters the union of the parameters of
614 Given the identifier of a dimension (typically a parameter),
615 its position can be obtained from the following function.
617 #include <isl/space.h>
618 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
619 enum isl_dim_type type, __isl_keep isl_id *id);
621 The identifiers or names of entire spaces may be set or read off
622 using the following functions.
624 #include <isl/space.h>
625 __isl_give isl_space *isl_space_set_tuple_id(
626 __isl_take isl_space *space,
627 enum isl_dim_type type, __isl_take isl_id *id);
628 __isl_give isl_space *isl_space_reset_tuple_id(
629 __isl_take isl_space *space, enum isl_dim_type type);
630 int isl_space_has_tuple_id(__isl_keep isl_space *space,
631 enum isl_dim_type type);
632 __isl_give isl_id *isl_space_get_tuple_id(
633 __isl_keep isl_space *space, enum isl_dim_type type);
634 __isl_give isl_space *isl_space_set_tuple_name(
635 __isl_take isl_space *space,
636 enum isl_dim_type type, const char *s);
637 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
638 enum isl_dim_type type);
640 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
641 or C<isl_dim_set>. As with C<isl_space_get_name>,
642 the C<isl_space_get_tuple_name> function returns a pointer to some internal
644 Binary operations require the corresponding spaces of their arguments
645 to have the same name.
647 Spaces can be nested. In particular, the domain of a set or
648 the domain or range of a relation can be a nested relation.
649 The following functions can be used to construct and deconstruct
652 #include <isl/space.h>
653 int isl_space_is_wrapping(__isl_keep isl_space *space);
654 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
655 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
657 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
658 be the space of a set, while that of
659 C<isl_space_wrap> should be the space of a relation.
660 Conversely, the output of C<isl_space_unwrap> is the space
661 of a relation, while that of C<isl_space_wrap> is the space of a set.
663 Spaces can be created from other spaces
664 using the following functions.
666 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
667 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
668 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
669 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
670 __isl_give isl_space *isl_space_params(
671 __isl_take isl_space *space);
672 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
673 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
674 __isl_take isl_space *right);
675 __isl_give isl_space *isl_space_align_params(
676 __isl_take isl_space *space1, __isl_take isl_space *space2)
677 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
678 enum isl_dim_type type, unsigned pos, unsigned n);
679 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
680 enum isl_dim_type type, unsigned n);
681 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
682 enum isl_dim_type type, unsigned first, unsigned n);
683 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
684 enum isl_dim_type dst_type, unsigned dst_pos,
685 enum isl_dim_type src_type, unsigned src_pos,
687 __isl_give isl_space *isl_space_map_from_set(
688 __isl_take isl_space *space);
689 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
691 Note that if dimensions are added or removed from a space, then
692 the name and the internal structure are lost.
696 A local space is essentially a space with
697 zero or more existentially quantified variables.
698 The local space of a basic set or relation can be obtained
699 using the following functions.
702 __isl_give isl_local_space *isl_basic_set_get_local_space(
703 __isl_keep isl_basic_set *bset);
706 __isl_give isl_local_space *isl_basic_map_get_local_space(
707 __isl_keep isl_basic_map *bmap);
709 A new local space can be created from a space using
711 #include <isl/local_space.h>
712 __isl_give isl_local_space *isl_local_space_from_space(
713 __isl_take isl_space *space);
715 They can be inspected, copied and freed using the following functions.
717 #include <isl/local_space.h>
718 isl_ctx *isl_local_space_get_ctx(
719 __isl_keep isl_local_space *ls);
720 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
721 int isl_local_space_dim(__isl_keep isl_local_space *ls,
722 enum isl_dim_type type);
723 const char *isl_local_space_get_dim_name(
724 __isl_keep isl_local_space *ls,
725 enum isl_dim_type type, unsigned pos);
726 __isl_give isl_local_space *isl_local_space_set_dim_name(
727 __isl_take isl_local_space *ls,
728 enum isl_dim_type type, unsigned pos, const char *s);
729 __isl_give isl_space *isl_local_space_get_space(
730 __isl_keep isl_local_space *ls);
731 __isl_give isl_div *isl_local_space_get_div(
732 __isl_keep isl_local_space *ls, int pos);
733 __isl_give isl_local_space *isl_local_space_copy(
734 __isl_keep isl_local_space *ls);
735 void *isl_local_space_free(__isl_take isl_local_space *ls);
737 Two local spaces can be compared using
739 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
740 __isl_keep isl_local_space *ls2);
742 Local spaces can be created from other local spaces
743 using the following functions.
745 __isl_give isl_local_space *isl_local_space_domain(
746 __isl_take isl_local_space *ls);
747 __isl_give isl_local_space *isl_local_space_from_domain(
748 __isl_take isl_local_space *ls);
749 __isl_give isl_local_space *isl_local_space_add_dims(
750 __isl_take isl_local_space *ls,
751 enum isl_dim_type type, unsigned n);
752 __isl_give isl_local_space *isl_local_space_insert_dims(
753 __isl_take isl_local_space *ls,
754 enum isl_dim_type type, unsigned first, unsigned n);
755 __isl_give isl_local_space *isl_local_space_drop_dims(
756 __isl_take isl_local_space *ls,
757 enum isl_dim_type type, unsigned first, unsigned n);
759 =head2 Input and Output
761 C<isl> supports its own input/output format, which is similar
762 to the C<Omega> format, but also supports the C<PolyLib> format
767 The C<isl> format is similar to that of C<Omega>, but has a different
768 syntax for describing the parameters and allows for the definition
769 of an existentially quantified variable as the integer division
770 of an affine expression.
771 For example, the set of integers C<i> between C<0> and C<n>
772 such that C<i % 10 <= 6> can be described as
774 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
777 A set or relation can have several disjuncts, separated
778 by the keyword C<or>. Each disjunct is either a conjunction
779 of constraints or a projection (C<exists>) of a conjunction
780 of constraints. The constraints are separated by the keyword
783 =head3 C<PolyLib> format
785 If the represented set is a union, then the first line
786 contains a single number representing the number of disjuncts.
787 Otherwise, a line containing the number C<1> is optional.
789 Each disjunct is represented by a matrix of constraints.
790 The first line contains two numbers representing
791 the number of rows and columns,
792 where the number of rows is equal to the number of constraints
793 and the number of columns is equal to two plus the number of variables.
794 The following lines contain the actual rows of the constraint matrix.
795 In each row, the first column indicates whether the constraint
796 is an equality (C<0>) or inequality (C<1>). The final column
797 corresponds to the constant term.
799 If the set is parametric, then the coefficients of the parameters
800 appear in the last columns before the constant column.
801 The coefficients of any existentially quantified variables appear
802 between those of the set variables and those of the parameters.
804 =head3 Extended C<PolyLib> format
806 The extended C<PolyLib> format is nearly identical to the
807 C<PolyLib> format. The only difference is that the line
808 containing the number of rows and columns of a constraint matrix
809 also contains four additional numbers:
810 the number of output dimensions, the number of input dimensions,
811 the number of local dimensions (i.e., the number of existentially
812 quantified variables) and the number of parameters.
813 For sets, the number of ``output'' dimensions is equal
814 to the number of set dimensions, while the number of ``input''
820 __isl_give isl_basic_set *isl_basic_set_read_from_file(
821 isl_ctx *ctx, FILE *input, int nparam);
822 __isl_give isl_basic_set *isl_basic_set_read_from_str(
823 isl_ctx *ctx, const char *str, int nparam);
824 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
825 FILE *input, int nparam);
826 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
827 const char *str, int nparam);
830 __isl_give isl_basic_map *isl_basic_map_read_from_file(
831 isl_ctx *ctx, FILE *input, int nparam);
832 __isl_give isl_basic_map *isl_basic_map_read_from_str(
833 isl_ctx *ctx, const char *str, int nparam);
834 __isl_give isl_map *isl_map_read_from_file(
835 isl_ctx *ctx, FILE *input, int nparam);
836 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
837 const char *str, int nparam);
839 #include <isl/union_set.h>
840 __isl_give isl_union_set *isl_union_set_read_from_file(
841 isl_ctx *ctx, FILE *input);
842 __isl_give isl_union_set *isl_union_set_read_from_str(
843 isl_ctx *ctx, const char *str);
845 #include <isl/union_map.h>
846 __isl_give isl_union_map *isl_union_map_read_from_file(
847 isl_ctx *ctx, FILE *input);
848 __isl_give isl_union_map *isl_union_map_read_from_str(
849 isl_ctx *ctx, const char *str);
851 The input format is autodetected and may be either the C<PolyLib> format
852 or the C<isl> format.
853 C<nparam> specifies how many of the final columns in
854 the C<PolyLib> format correspond to parameters.
855 If input is given in the C<isl> format, then the number
856 of parameters needs to be equal to C<nparam>.
857 If C<nparam> is negative, then any number of parameters
858 is accepted in the C<isl> format and zero parameters
859 are assumed in the C<PolyLib> format.
863 Before anything can be printed, an C<isl_printer> needs to
866 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
868 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
869 void isl_printer_free(__isl_take isl_printer *printer);
870 __isl_give char *isl_printer_get_str(
871 __isl_keep isl_printer *printer);
873 The behavior of the printer can be modified in various ways
875 __isl_give isl_printer *isl_printer_set_output_format(
876 __isl_take isl_printer *p, int output_format);
877 __isl_give isl_printer *isl_printer_set_indent(
878 __isl_take isl_printer *p, int indent);
879 __isl_give isl_printer *isl_printer_indent(
880 __isl_take isl_printer *p, int indent);
881 __isl_give isl_printer *isl_printer_set_prefix(
882 __isl_take isl_printer *p, const char *prefix);
883 __isl_give isl_printer *isl_printer_set_suffix(
884 __isl_take isl_printer *p, const char *suffix);
886 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
887 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
888 and defaults to C<ISL_FORMAT_ISL>.
889 Each line in the output is indented by C<indent> (set by
890 C<isl_printer_set_indent>) spaces
891 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
892 In the C<PolyLib> format output,
893 the coefficients of the existentially quantified variables
894 appear between those of the set variables and those
896 The function C<isl_printer_indent> increases the indentation
897 by the specified amount (which may be negative).
899 To actually print something, use
902 __isl_give isl_printer *isl_printer_print_basic_set(
903 __isl_take isl_printer *printer,
904 __isl_keep isl_basic_set *bset);
905 __isl_give isl_printer *isl_printer_print_set(
906 __isl_take isl_printer *printer,
907 __isl_keep isl_set *set);
910 __isl_give isl_printer *isl_printer_print_basic_map(
911 __isl_take isl_printer *printer,
912 __isl_keep isl_basic_map *bmap);
913 __isl_give isl_printer *isl_printer_print_map(
914 __isl_take isl_printer *printer,
915 __isl_keep isl_map *map);
917 #include <isl/union_set.h>
918 __isl_give isl_printer *isl_printer_print_union_set(
919 __isl_take isl_printer *p,
920 __isl_keep isl_union_set *uset);
922 #include <isl/union_map.h>
923 __isl_give isl_printer *isl_printer_print_union_map(
924 __isl_take isl_printer *p,
925 __isl_keep isl_union_map *umap);
927 When called on a file printer, the following function flushes
928 the file. When called on a string printer, the buffer is cleared.
930 __isl_give isl_printer *isl_printer_flush(
931 __isl_take isl_printer *p);
933 =head2 Creating New Sets and Relations
935 C<isl> has functions for creating some standard sets and relations.
939 =item * Empty sets and relations
941 __isl_give isl_basic_set *isl_basic_set_empty(
942 __isl_take isl_space *space);
943 __isl_give isl_basic_map *isl_basic_map_empty(
944 __isl_take isl_space *space);
945 __isl_give isl_set *isl_set_empty(
946 __isl_take isl_space *space);
947 __isl_give isl_map *isl_map_empty(
948 __isl_take isl_space *space);
949 __isl_give isl_union_set *isl_union_set_empty(
950 __isl_take isl_space *space);
951 __isl_give isl_union_map *isl_union_map_empty(
952 __isl_take isl_space *space);
954 For C<isl_union_set>s and C<isl_union_map>s, the space
955 is only used to specify the parameters.
957 =item * Universe sets and relations
959 __isl_give isl_basic_set *isl_basic_set_universe(
960 __isl_take isl_space *space);
961 __isl_give isl_basic_map *isl_basic_map_universe(
962 __isl_take isl_space *space);
963 __isl_give isl_set *isl_set_universe(
964 __isl_take isl_space *space);
965 __isl_give isl_map *isl_map_universe(
966 __isl_take isl_space *space);
967 __isl_give isl_union_set *isl_union_set_universe(
968 __isl_take isl_union_set *uset);
969 __isl_give isl_union_map *isl_union_map_universe(
970 __isl_take isl_union_map *umap);
972 The sets and relations constructed by the functions above
973 contain all integer values, while those constructed by the
974 functions below only contain non-negative values.
976 __isl_give isl_basic_set *isl_basic_set_nat_universe(
977 __isl_take isl_space *space);
978 __isl_give isl_basic_map *isl_basic_map_nat_universe(
979 __isl_take isl_space *space);
980 __isl_give isl_set *isl_set_nat_universe(
981 __isl_take isl_space *space);
982 __isl_give isl_map *isl_map_nat_universe(
983 __isl_take isl_space *space);
985 =item * Identity relations
987 __isl_give isl_basic_map *isl_basic_map_identity(
988 __isl_take isl_space *space);
989 __isl_give isl_map *isl_map_identity(
990 __isl_take isl_space *space);
992 The number of input and output dimensions in C<space> needs
995 =item * Lexicographic order
997 __isl_give isl_map *isl_map_lex_lt(
998 __isl_take isl_space *set_space);
999 __isl_give isl_map *isl_map_lex_le(
1000 __isl_take isl_space *set_space);
1001 __isl_give isl_map *isl_map_lex_gt(
1002 __isl_take isl_space *set_space);
1003 __isl_give isl_map *isl_map_lex_ge(
1004 __isl_take isl_space *set_space);
1005 __isl_give isl_map *isl_map_lex_lt_first(
1006 __isl_take isl_space *space, unsigned n);
1007 __isl_give isl_map *isl_map_lex_le_first(
1008 __isl_take isl_space *space, unsigned n);
1009 __isl_give isl_map *isl_map_lex_gt_first(
1010 __isl_take isl_space *space, unsigned n);
1011 __isl_give isl_map *isl_map_lex_ge_first(
1012 __isl_take isl_space *space, unsigned n);
1014 The first four functions take a space for a B<set>
1015 and return relations that express that the elements in the domain
1016 are lexicographically less
1017 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1018 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1019 than the elements in the range.
1020 The last four functions take a space for a map
1021 and return relations that express that the first C<n> dimensions
1022 in the domain are lexicographically less
1023 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1024 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1025 than the first C<n> dimensions in the range.
1029 A basic set or relation can be converted to a set or relation
1030 using the following functions.
1032 __isl_give isl_set *isl_set_from_basic_set(
1033 __isl_take isl_basic_set *bset);
1034 __isl_give isl_map *isl_map_from_basic_map(
1035 __isl_take isl_basic_map *bmap);
1037 Sets and relations can be converted to union sets and relations
1038 using the following functions.
1040 __isl_give isl_union_map *isl_union_map_from_map(
1041 __isl_take isl_map *map);
1042 __isl_give isl_union_set *isl_union_set_from_set(
1043 __isl_take isl_set *set);
1045 The inverse conversions below can only be used if the input
1046 union set or relation is known to contain elements in exactly one
1049 __isl_give isl_set *isl_set_from_union_set(
1050 __isl_take isl_union_set *uset);
1051 __isl_give isl_map *isl_map_from_union_map(
1052 __isl_take isl_union_map *umap);
1054 Sets and relations can be copied and freed again using the following
1057 __isl_give isl_basic_set *isl_basic_set_copy(
1058 __isl_keep isl_basic_set *bset);
1059 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1060 __isl_give isl_union_set *isl_union_set_copy(
1061 __isl_keep isl_union_set *uset);
1062 __isl_give isl_basic_map *isl_basic_map_copy(
1063 __isl_keep isl_basic_map *bmap);
1064 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1065 __isl_give isl_union_map *isl_union_map_copy(
1066 __isl_keep isl_union_map *umap);
1067 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1068 void isl_set_free(__isl_take isl_set *set);
1069 void *isl_union_set_free(__isl_take isl_union_set *uset);
1070 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1071 void isl_map_free(__isl_take isl_map *map);
1072 void *isl_union_map_free(__isl_take isl_union_map *umap);
1074 Other sets and relations can be constructed by starting
1075 from a universe set or relation, adding equality and/or
1076 inequality constraints and then projecting out the
1077 existentially quantified variables, if any.
1078 Constraints can be constructed, manipulated and
1079 added to (or removed from) (basic) sets and relations
1080 using the following functions.
1082 #include <isl/constraint.h>
1083 __isl_give isl_constraint *isl_equality_alloc(
1084 __isl_take isl_local_space *ls);
1085 __isl_give isl_constraint *isl_inequality_alloc(
1086 __isl_take isl_local_space *ls);
1087 __isl_give isl_constraint *isl_constraint_set_constant(
1088 __isl_take isl_constraint *constraint, isl_int v);
1089 __isl_give isl_constraint *isl_constraint_set_constant_si(
1090 __isl_take isl_constraint *constraint, int v);
1091 __isl_give isl_constraint *isl_constraint_set_coefficient(
1092 __isl_take isl_constraint *constraint,
1093 enum isl_dim_type type, int pos, isl_int v);
1094 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1095 __isl_take isl_constraint *constraint,
1096 enum isl_dim_type type, int pos, int v);
1097 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1098 __isl_take isl_basic_map *bmap,
1099 __isl_take isl_constraint *constraint);
1100 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1101 __isl_take isl_basic_set *bset,
1102 __isl_take isl_constraint *constraint);
1103 __isl_give isl_map *isl_map_add_constraint(
1104 __isl_take isl_map *map,
1105 __isl_take isl_constraint *constraint);
1106 __isl_give isl_set *isl_set_add_constraint(
1107 __isl_take isl_set *set,
1108 __isl_take isl_constraint *constraint);
1109 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1110 __isl_take isl_basic_set *bset,
1111 __isl_take isl_constraint *constraint);
1113 For example, to create a set containing the even integers
1114 between 10 and 42, you would use the following code.
1117 isl_local_space *ls;
1119 isl_basic_set *bset;
1121 space = isl_space_set_alloc(ctx, 0, 2);
1122 bset = isl_basic_set_universe(isl_space_copy(space));
1123 ls = isl_local_space_from_space(space);
1125 c = isl_equality_alloc(isl_local_space_copy(ls));
1126 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1127 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1128 bset = isl_basic_set_add_constraint(bset, c);
1130 c = isl_inequality_alloc(isl_local_space_copy(ls));
1131 c = isl_constraint_set_constant_si(c, -10);
1132 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1133 bset = isl_basic_set_add_constraint(bset, c);
1135 c = isl_inequality_alloc(ls);
1136 c = isl_constraint_set_constant_si(c, 42);
1137 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1138 bset = isl_basic_set_add_constraint(bset, c);
1140 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1144 isl_basic_set *bset;
1145 bset = isl_basic_set_read_from_str(ctx,
1146 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1148 A basic set or relation can also be constructed from two matrices
1149 describing the equalities and the inequalities.
1151 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1152 __isl_take isl_space *space,
1153 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1154 enum isl_dim_type c1,
1155 enum isl_dim_type c2, enum isl_dim_type c3,
1156 enum isl_dim_type c4);
1157 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1158 __isl_take isl_space *space,
1159 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1160 enum isl_dim_type c1,
1161 enum isl_dim_type c2, enum isl_dim_type c3,
1162 enum isl_dim_type c4, enum isl_dim_type c5);
1164 The C<isl_dim_type> arguments indicate the order in which
1165 different kinds of variables appear in the input matrices
1166 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1167 C<isl_dim_set> and C<isl_dim_div> for sets and
1168 of C<isl_dim_cst>, C<isl_dim_param>,
1169 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1171 A (basic) set or relation can also be constructed from a (piecewise)
1173 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1175 __isl_give isl_basic_map *isl_basic_map_from_aff(
1176 __isl_take isl_aff *aff);
1177 __isl_give isl_set *isl_set_from_pw_aff(
1178 __isl_take isl_pw_aff *pwaff);
1179 __isl_give isl_map *isl_map_from_pw_aff(
1180 __isl_take isl_pw_aff *pwaff);
1181 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1182 __isl_take isl_space *domain_space,
1183 __isl_take isl_aff_list *list);
1185 The C<domain_dim> argument describes the domain of the resulting
1186 basic relation. It is required because the C<list> may consist
1187 of zero affine expressions.
1189 =head2 Inspecting Sets and Relations
1191 Usually, the user should not have to care about the actual constraints
1192 of the sets and maps, but should instead apply the abstract operations
1193 explained in the following sections.
1194 Occasionally, however, it may be required to inspect the individual
1195 coefficients of the constraints. This section explains how to do so.
1196 In these cases, it may also be useful to have C<isl> compute
1197 an explicit representation of the existentially quantified variables.
1199 __isl_give isl_set *isl_set_compute_divs(
1200 __isl_take isl_set *set);
1201 __isl_give isl_map *isl_map_compute_divs(
1202 __isl_take isl_map *map);
1203 __isl_give isl_union_set *isl_union_set_compute_divs(
1204 __isl_take isl_union_set *uset);
1205 __isl_give isl_union_map *isl_union_map_compute_divs(
1206 __isl_take isl_union_map *umap);
1208 This explicit representation defines the existentially quantified
1209 variables as integer divisions of the other variables, possibly
1210 including earlier existentially quantified variables.
1211 An explicitly represented existentially quantified variable therefore
1212 has a unique value when the values of the other variables are known.
1213 If, furthermore, the same existentials, i.e., existentials
1214 with the same explicit representations, should appear in the
1215 same order in each of the disjuncts of a set or map, then the user should call
1216 either of the following functions.
1218 __isl_give isl_set *isl_set_align_divs(
1219 __isl_take isl_set *set);
1220 __isl_give isl_map *isl_map_align_divs(
1221 __isl_take isl_map *map);
1223 Alternatively, the existentially quantified variables can be removed
1224 using the following functions, which compute an overapproximation.
1226 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1227 __isl_take isl_basic_set *bset);
1228 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1229 __isl_take isl_basic_map *bmap);
1230 __isl_give isl_set *isl_set_remove_divs(
1231 __isl_take isl_set *set);
1232 __isl_give isl_map *isl_map_remove_divs(
1233 __isl_take isl_map *map);
1235 To iterate over all the sets or maps in a union set or map, use
1237 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1238 int (*fn)(__isl_take isl_set *set, void *user),
1240 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1241 int (*fn)(__isl_take isl_map *map, void *user),
1244 The number of sets or maps in a union set or map can be obtained
1247 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1248 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1250 To extract the set or map in a given space from a union, use
1252 __isl_give isl_set *isl_union_set_extract_set(
1253 __isl_keep isl_union_set *uset,
1254 __isl_take isl_space *space);
1255 __isl_give isl_map *isl_union_map_extract_map(
1256 __isl_keep isl_union_map *umap,
1257 __isl_take isl_space *space);
1259 To iterate over all the basic sets or maps in a set or map, use
1261 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1262 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1264 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1265 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1268 The callback function C<fn> should return 0 if successful and
1269 -1 if an error occurs. In the latter case, or if any other error
1270 occurs, the above functions will return -1.
1272 It should be noted that C<isl> does not guarantee that
1273 the basic sets or maps passed to C<fn> are disjoint.
1274 If this is required, then the user should call one of
1275 the following functions first.
1277 __isl_give isl_set *isl_set_make_disjoint(
1278 __isl_take isl_set *set);
1279 __isl_give isl_map *isl_map_make_disjoint(
1280 __isl_take isl_map *map);
1282 The number of basic sets in a set can be obtained
1285 int isl_set_n_basic_set(__isl_keep isl_set *set);
1287 To iterate over the constraints of a basic set or map, use
1289 #include <isl/constraint.h>
1291 int isl_basic_map_foreach_constraint(
1292 __isl_keep isl_basic_map *bmap,
1293 int (*fn)(__isl_take isl_constraint *c, void *user),
1295 void *isl_constraint_free(__isl_take isl_constraint *c);
1297 Again, the callback function C<fn> should return 0 if successful and
1298 -1 if an error occurs. In the latter case, or if any other error
1299 occurs, the above functions will return -1.
1300 The constraint C<c> represents either an equality or an inequality.
1301 Use the following function to find out whether a constraint
1302 represents an equality. If not, it represents an inequality.
1304 int isl_constraint_is_equality(
1305 __isl_keep isl_constraint *constraint);
1307 The coefficients of the constraints can be inspected using
1308 the following functions.
1310 void isl_constraint_get_constant(
1311 __isl_keep isl_constraint *constraint, isl_int *v);
1312 void isl_constraint_get_coefficient(
1313 __isl_keep isl_constraint *constraint,
1314 enum isl_dim_type type, int pos, isl_int *v);
1315 int isl_constraint_involves_dims(
1316 __isl_keep isl_constraint *constraint,
1317 enum isl_dim_type type, unsigned first, unsigned n);
1319 The explicit representations of the existentially quantified
1320 variables can be inspected using the following functions.
1321 Note that the user is only allowed to use these functions
1322 if the inspected set or map is the result of a call
1323 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1325 __isl_give isl_div *isl_constraint_div(
1326 __isl_keep isl_constraint *constraint, int pos);
1327 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1328 void isl_div_get_constant(__isl_keep isl_div *div,
1330 void isl_div_get_denominator(__isl_keep isl_div *div,
1332 void isl_div_get_coefficient(__isl_keep isl_div *div,
1333 enum isl_dim_type type, int pos, isl_int *v);
1335 To obtain the constraints of a basic set or map in matrix
1336 form, use the following functions.
1338 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1339 __isl_keep isl_basic_set *bset,
1340 enum isl_dim_type c1, enum isl_dim_type c2,
1341 enum isl_dim_type c3, enum isl_dim_type c4);
1342 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1343 __isl_keep isl_basic_set *bset,
1344 enum isl_dim_type c1, enum isl_dim_type c2,
1345 enum isl_dim_type c3, enum isl_dim_type c4);
1346 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1347 __isl_keep isl_basic_map *bmap,
1348 enum isl_dim_type c1,
1349 enum isl_dim_type c2, enum isl_dim_type c3,
1350 enum isl_dim_type c4, enum isl_dim_type c5);
1351 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1352 __isl_keep isl_basic_map *bmap,
1353 enum isl_dim_type c1,
1354 enum isl_dim_type c2, enum isl_dim_type c3,
1355 enum isl_dim_type c4, enum isl_dim_type c5);
1357 The C<isl_dim_type> arguments dictate the order in which
1358 different kinds of variables appear in the resulting matrix
1359 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1360 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1362 The number of parameters, input, output or set dimensions can
1363 be obtained using the following functions.
1365 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1366 enum isl_dim_type type);
1367 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1368 enum isl_dim_type type);
1369 unsigned isl_set_dim(__isl_keep isl_set *set,
1370 enum isl_dim_type type);
1371 unsigned isl_map_dim(__isl_keep isl_map *map,
1372 enum isl_dim_type type);
1374 To check whether the description of a set or relation depends
1375 on one or more given dimensions, it is not necessary to iterate over all
1376 constraints. Instead the following functions can be used.
1378 int isl_basic_set_involves_dims(
1379 __isl_keep isl_basic_set *bset,
1380 enum isl_dim_type type, unsigned first, unsigned n);
1381 int isl_set_involves_dims(__isl_keep isl_set *set,
1382 enum isl_dim_type type, unsigned first, unsigned n);
1383 int isl_basic_map_involves_dims(
1384 __isl_keep isl_basic_map *bmap,
1385 enum isl_dim_type type, unsigned first, unsigned n);
1386 int isl_map_involves_dims(__isl_keep isl_map *map,
1387 enum isl_dim_type type, unsigned first, unsigned n);
1389 Similarly, the following functions can be used to check whether
1390 a given dimension is involved in any lower or upper bound.
1392 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1393 enum isl_dim_type type, unsigned pos);
1394 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1395 enum isl_dim_type type, unsigned pos);
1397 The identifiers or names of the domain and range spaces of a set
1398 or relation can be read off or set using the following functions.
1400 __isl_give isl_set *isl_set_set_tuple_id(
1401 __isl_take isl_set *set, __isl_take isl_id *id);
1402 __isl_give isl_set *isl_set_reset_tuple_id(
1403 __isl_take isl_set *set);
1404 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1405 __isl_give isl_id *isl_set_get_tuple_id(
1406 __isl_keep isl_set *set);
1407 __isl_give isl_map *isl_map_set_tuple_id(
1408 __isl_take isl_map *map, enum isl_dim_type type,
1409 __isl_take isl_id *id);
1410 __isl_give isl_map *isl_map_reset_tuple_id(
1411 __isl_take isl_map *map, enum isl_dim_type type);
1412 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1413 enum isl_dim_type type);
1414 __isl_give isl_id *isl_map_get_tuple_id(
1415 __isl_keep isl_map *map, enum isl_dim_type type);
1417 const char *isl_basic_set_get_tuple_name(
1418 __isl_keep isl_basic_set *bset);
1419 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1420 __isl_take isl_basic_set *set, const char *s);
1421 const char *isl_set_get_tuple_name(
1422 __isl_keep isl_set *set);
1423 const char *isl_basic_map_get_tuple_name(
1424 __isl_keep isl_basic_map *bmap,
1425 enum isl_dim_type type);
1426 const char *isl_map_get_tuple_name(
1427 __isl_keep isl_map *map,
1428 enum isl_dim_type type);
1430 As with C<isl_space_get_tuple_name>, the value returned points to
1431 an internal data structure.
1432 The identifiers, positions or names of individual dimensions can be
1433 read off using the following functions.
1435 __isl_give isl_set *isl_set_set_dim_id(
1436 __isl_take isl_set *set, enum isl_dim_type type,
1437 unsigned pos, __isl_take isl_id *id);
1438 int isl_set_has_dim_id(__isl_keep isl_set *set,
1439 enum isl_dim_type type, unsigned pos);
1440 __isl_give isl_id *isl_set_get_dim_id(
1441 __isl_keep isl_set *set, enum isl_dim_type type,
1443 __isl_give isl_map *isl_map_set_dim_id(
1444 __isl_take isl_map *map, enum isl_dim_type type,
1445 unsigned pos, __isl_take isl_id *id);
1446 int isl_map_has_dim_id(__isl_keep isl_map *map,
1447 enum isl_dim_type type, unsigned pos);
1448 __isl_give isl_id *isl_map_get_dim_id(
1449 __isl_keep isl_map *map, enum isl_dim_type type,
1452 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1453 enum isl_dim_type type, __isl_keep isl_id *id);
1454 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1455 enum isl_dim_type type, __isl_keep isl_id *id);
1457 const char *isl_constraint_get_dim_name(
1458 __isl_keep isl_constraint *constraint,
1459 enum isl_dim_type type, unsigned pos);
1460 const char *isl_basic_set_get_dim_name(
1461 __isl_keep isl_basic_set *bset,
1462 enum isl_dim_type type, unsigned pos);
1463 const char *isl_set_get_dim_name(
1464 __isl_keep isl_set *set,
1465 enum isl_dim_type type, unsigned pos);
1466 const char *isl_basic_map_get_dim_name(
1467 __isl_keep isl_basic_map *bmap,
1468 enum isl_dim_type type, unsigned pos);
1469 const char *isl_map_get_dim_name(
1470 __isl_keep isl_map *map,
1471 enum isl_dim_type type, unsigned pos);
1473 These functions are mostly useful to obtain the identifiers, positions
1474 or names of the parameters. Identifiers of individual dimensions are
1475 essentially only useful for printing. They are ignored by all other
1476 operations and may not be preserved across those operations.
1480 =head3 Unary Properties
1486 The following functions test whether the given set or relation
1487 contains any integer points. The ``plain'' variants do not perform
1488 any computations, but simply check if the given set or relation
1489 is already known to be empty.
1491 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1492 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1493 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1494 int isl_set_is_empty(__isl_keep isl_set *set);
1495 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1496 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1497 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1498 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1499 int isl_map_is_empty(__isl_keep isl_map *map);
1500 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1502 =item * Universality
1504 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1505 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1506 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1508 =item * Single-valuedness
1510 int isl_map_is_single_valued(__isl_keep isl_map *map);
1511 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1515 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1516 int isl_map_is_injective(__isl_keep isl_map *map);
1517 int isl_union_map_plain_is_injective(
1518 __isl_keep isl_union_map *umap);
1519 int isl_union_map_is_injective(
1520 __isl_keep isl_union_map *umap);
1524 int isl_map_is_bijective(__isl_keep isl_map *map);
1525 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1529 int isl_basic_map_plain_is_fixed(
1530 __isl_keep isl_basic_map *bmap,
1531 enum isl_dim_type type, unsigned pos,
1533 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1534 enum isl_dim_type type, unsigned pos,
1537 Check if the relation obviously lies on a hyperplane where the given dimension
1538 has a fixed value and if so, return that value in C<*val>.
1542 To check whether a set is a parameter domain, use this function:
1544 int isl_set_is_params(__isl_keep isl_set *set);
1548 The following functions check whether the domain of the given
1549 (basic) set is a wrapped relation.
1551 int isl_basic_set_is_wrapping(
1552 __isl_keep isl_basic_set *bset);
1553 int isl_set_is_wrapping(__isl_keep isl_set *set);
1555 =item * Internal Product
1557 int isl_basic_map_can_zip(
1558 __isl_keep isl_basic_map *bmap);
1559 int isl_map_can_zip(__isl_keep isl_map *map);
1561 Check whether the product of domain and range of the given relation
1563 i.e., whether both domain and range are nested relations.
1567 =head3 Binary Properties
1573 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1574 __isl_keep isl_set *set2);
1575 int isl_set_is_equal(__isl_keep isl_set *set1,
1576 __isl_keep isl_set *set2);
1577 int isl_union_set_is_equal(
1578 __isl_keep isl_union_set *uset1,
1579 __isl_keep isl_union_set *uset2);
1580 int isl_basic_map_is_equal(
1581 __isl_keep isl_basic_map *bmap1,
1582 __isl_keep isl_basic_map *bmap2);
1583 int isl_map_is_equal(__isl_keep isl_map *map1,
1584 __isl_keep isl_map *map2);
1585 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1586 __isl_keep isl_map *map2);
1587 int isl_union_map_is_equal(
1588 __isl_keep isl_union_map *umap1,
1589 __isl_keep isl_union_map *umap2);
1591 =item * Disjointness
1593 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1594 __isl_keep isl_set *set2);
1598 int isl_set_is_subset(__isl_keep isl_set *set1,
1599 __isl_keep isl_set *set2);
1600 int isl_set_is_strict_subset(
1601 __isl_keep isl_set *set1,
1602 __isl_keep isl_set *set2);
1603 int isl_union_set_is_subset(
1604 __isl_keep isl_union_set *uset1,
1605 __isl_keep isl_union_set *uset2);
1606 int isl_union_set_is_strict_subset(
1607 __isl_keep isl_union_set *uset1,
1608 __isl_keep isl_union_set *uset2);
1609 int isl_basic_map_is_subset(
1610 __isl_keep isl_basic_map *bmap1,
1611 __isl_keep isl_basic_map *bmap2);
1612 int isl_basic_map_is_strict_subset(
1613 __isl_keep isl_basic_map *bmap1,
1614 __isl_keep isl_basic_map *bmap2);
1615 int isl_map_is_subset(
1616 __isl_keep isl_map *map1,
1617 __isl_keep isl_map *map2);
1618 int isl_map_is_strict_subset(
1619 __isl_keep isl_map *map1,
1620 __isl_keep isl_map *map2);
1621 int isl_union_map_is_subset(
1622 __isl_keep isl_union_map *umap1,
1623 __isl_keep isl_union_map *umap2);
1624 int isl_union_map_is_strict_subset(
1625 __isl_keep isl_union_map *umap1,
1626 __isl_keep isl_union_map *umap2);
1630 =head2 Unary Operations
1636 __isl_give isl_set *isl_set_complement(
1637 __isl_take isl_set *set);
1641 __isl_give isl_basic_map *isl_basic_map_reverse(
1642 __isl_take isl_basic_map *bmap);
1643 __isl_give isl_map *isl_map_reverse(
1644 __isl_take isl_map *map);
1645 __isl_give isl_union_map *isl_union_map_reverse(
1646 __isl_take isl_union_map *umap);
1650 __isl_give isl_basic_set *isl_basic_set_project_out(
1651 __isl_take isl_basic_set *bset,
1652 enum isl_dim_type type, unsigned first, unsigned n);
1653 __isl_give isl_basic_map *isl_basic_map_project_out(
1654 __isl_take isl_basic_map *bmap,
1655 enum isl_dim_type type, unsigned first, unsigned n);
1656 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1657 enum isl_dim_type type, unsigned first, unsigned n);
1658 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1659 enum isl_dim_type type, unsigned first, unsigned n);
1660 __isl_give isl_basic_set *isl_basic_set_params(
1661 __isl_take isl_basic_set *bset);
1662 __isl_give isl_basic_set *isl_basic_map_domain(
1663 __isl_take isl_basic_map *bmap);
1664 __isl_give isl_basic_set *isl_basic_map_range(
1665 __isl_take isl_basic_map *bmap);
1666 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1667 __isl_give isl_set *isl_map_domain(
1668 __isl_take isl_map *bmap);
1669 __isl_give isl_set *isl_map_range(
1670 __isl_take isl_map *map);
1671 __isl_give isl_union_set *isl_union_map_domain(
1672 __isl_take isl_union_map *umap);
1673 __isl_give isl_union_set *isl_union_map_range(
1674 __isl_take isl_union_map *umap);
1676 __isl_give isl_basic_map *isl_basic_map_domain_map(
1677 __isl_take isl_basic_map *bmap);
1678 __isl_give isl_basic_map *isl_basic_map_range_map(
1679 __isl_take isl_basic_map *bmap);
1680 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1681 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1682 __isl_give isl_union_map *isl_union_map_domain_map(
1683 __isl_take isl_union_map *umap);
1684 __isl_give isl_union_map *isl_union_map_range_map(
1685 __isl_take isl_union_map *umap);
1687 The functions above construct a (basic, regular or union) relation
1688 that maps (a wrapped version of) the input relation to its domain or range.
1692 __isl_give isl_set *isl_set_eliminate(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1696 Eliminate the coefficients for the given dimensions from the constraints,
1697 without removing the dimensions.
1701 __isl_give isl_basic_set *isl_basic_set_fix(
1702 __isl_take isl_basic_set *bset,
1703 enum isl_dim_type type, unsigned pos,
1705 __isl_give isl_basic_set *isl_basic_set_fix_si(
1706 __isl_take isl_basic_set *bset,
1707 enum isl_dim_type type, unsigned pos, int value);
1708 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1709 enum isl_dim_type type, unsigned pos,
1711 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1712 enum isl_dim_type type, unsigned pos, int value);
1713 __isl_give isl_basic_map *isl_basic_map_fix_si(
1714 __isl_take isl_basic_map *bmap,
1715 enum isl_dim_type type, unsigned pos, int value);
1716 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1717 enum isl_dim_type type, unsigned pos, int value);
1719 Intersect the set or relation with the hyperplane where the given
1720 dimension has the fixed given value.
1722 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1723 enum isl_dim_type type1, int pos1,
1724 enum isl_dim_type type2, int pos2);
1725 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1726 enum isl_dim_type type1, int pos1,
1727 enum isl_dim_type type2, int pos2);
1729 Intersect the set or relation with the hyperplane where the given
1730 dimensions are equal to each other.
1732 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1733 enum isl_dim_type type1, int pos1,
1734 enum isl_dim_type type2, int pos2);
1736 Intersect the relation with the hyperplane where the given
1737 dimensions have opposite values.
1741 __isl_give isl_map *isl_set_identity(
1742 __isl_take isl_set *set);
1743 __isl_give isl_union_map *isl_union_set_identity(
1744 __isl_take isl_union_set *uset);
1746 Construct an identity relation on the given (union) set.
1750 __isl_give isl_basic_set *isl_basic_map_deltas(
1751 __isl_take isl_basic_map *bmap);
1752 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1753 __isl_give isl_union_set *isl_union_map_deltas(
1754 __isl_take isl_union_map *umap);
1756 These functions return a (basic) set containing the differences
1757 between image elements and corresponding domain elements in the input.
1759 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1760 __isl_take isl_basic_map *bmap);
1761 __isl_give isl_map *isl_map_deltas_map(
1762 __isl_take isl_map *map);
1763 __isl_give isl_union_map *isl_union_map_deltas_map(
1764 __isl_take isl_union_map *umap);
1766 The functions above construct a (basic, regular or union) relation
1767 that maps (a wrapped version of) the input relation to its delta set.
1771 Simplify the representation of a set or relation by trying
1772 to combine pairs of basic sets or relations into a single
1773 basic set or relation.
1775 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1776 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1777 __isl_give isl_union_set *isl_union_set_coalesce(
1778 __isl_take isl_union_set *uset);
1779 __isl_give isl_union_map *isl_union_map_coalesce(
1780 __isl_take isl_union_map *umap);
1782 =item * Detecting equalities
1784 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1785 __isl_take isl_basic_set *bset);
1786 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1787 __isl_take isl_basic_map *bmap);
1788 __isl_give isl_set *isl_set_detect_equalities(
1789 __isl_take isl_set *set);
1790 __isl_give isl_map *isl_map_detect_equalities(
1791 __isl_take isl_map *map);
1792 __isl_give isl_union_set *isl_union_set_detect_equalities(
1793 __isl_take isl_union_set *uset);
1794 __isl_give isl_union_map *isl_union_map_detect_equalities(
1795 __isl_take isl_union_map *umap);
1797 Simplify the representation of a set or relation by detecting implicit
1800 =item * Removing redundant constraints
1802 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1803 __isl_take isl_basic_set *bset);
1804 __isl_give isl_set *isl_set_remove_redundancies(
1805 __isl_take isl_set *set);
1806 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1807 __isl_take isl_basic_map *bmap);
1808 __isl_give isl_map *isl_map_remove_redundancies(
1809 __isl_take isl_map *map);
1813 __isl_give isl_basic_set *isl_set_convex_hull(
1814 __isl_take isl_set *set);
1815 __isl_give isl_basic_map *isl_map_convex_hull(
1816 __isl_take isl_map *map);
1818 If the input set or relation has any existentially quantified
1819 variables, then the result of these operations is currently undefined.
1823 __isl_give isl_basic_set *isl_set_simple_hull(
1824 __isl_take isl_set *set);
1825 __isl_give isl_basic_map *isl_map_simple_hull(
1826 __isl_take isl_map *map);
1827 __isl_give isl_union_map *isl_union_map_simple_hull(
1828 __isl_take isl_union_map *umap);
1830 These functions compute a single basic set or relation
1831 that contains the whole input set or relation.
1832 In particular, the output is described by translates
1833 of the constraints describing the basic sets or relations in the input.
1837 (See \autoref{s:simple hull}.)
1843 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1844 __isl_take isl_basic_set *bset);
1845 __isl_give isl_basic_set *isl_set_affine_hull(
1846 __isl_take isl_set *set);
1847 __isl_give isl_union_set *isl_union_set_affine_hull(
1848 __isl_take isl_union_set *uset);
1849 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1850 __isl_take isl_basic_map *bmap);
1851 __isl_give isl_basic_map *isl_map_affine_hull(
1852 __isl_take isl_map *map);
1853 __isl_give isl_union_map *isl_union_map_affine_hull(
1854 __isl_take isl_union_map *umap);
1856 In case of union sets and relations, the affine hull is computed
1859 =item * Polyhedral hull
1861 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1862 __isl_take isl_set *set);
1863 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1864 __isl_take isl_map *map);
1865 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1866 __isl_take isl_union_set *uset);
1867 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1868 __isl_take isl_union_map *umap);
1870 These functions compute a single basic set or relation
1871 not involving any existentially quantified variables
1872 that contains the whole input set or relation.
1873 In case of union sets and relations, the polyhedral hull is computed
1876 =item * Optimization
1878 #include <isl/ilp.h>
1879 enum isl_lp_result isl_basic_set_max(
1880 __isl_keep isl_basic_set *bset,
1881 __isl_keep isl_aff *obj, isl_int *opt)
1882 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1883 __isl_keep isl_aff *obj, isl_int *opt);
1884 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1885 __isl_keep isl_aff *obj, isl_int *opt);
1887 Compute the minimum or maximum of the integer affine expression C<obj>
1888 over the points in C<set>, returning the result in C<opt>.
1889 The return value may be one of C<isl_lp_error>,
1890 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1892 =item * Parametric optimization
1894 __isl_give isl_pw_aff *isl_set_dim_min(
1895 __isl_take isl_set *set, int pos);
1896 __isl_give isl_pw_aff *isl_set_dim_max(
1897 __isl_take isl_set *set, int pos);
1899 Compute the minimum or maximum of the given set dimension as a function of the
1900 parameters, but independently of the other set dimensions.
1901 For lexicographic optimization, see L<"Lexicographic Optimization">.
1905 The following functions compute either the set of (rational) coefficient
1906 values of valid constraints for the given set or the set of (rational)
1907 values satisfying the constraints with coefficients from the given set.
1908 Internally, these two sets of functions perform essentially the
1909 same operations, except that the set of coefficients is assumed to
1910 be a cone, while the set of values may be any polyhedron.
1911 The current implementation is based on the Farkas lemma and
1912 Fourier-Motzkin elimination, but this may change or be made optional
1913 in future. In particular, future implementations may use different
1914 dualization algorithms or skip the elimination step.
1916 __isl_give isl_basic_set *isl_basic_set_coefficients(
1917 __isl_take isl_basic_set *bset);
1918 __isl_give isl_basic_set *isl_set_coefficients(
1919 __isl_take isl_set *set);
1920 __isl_give isl_union_set *isl_union_set_coefficients(
1921 __isl_take isl_union_set *bset);
1922 __isl_give isl_basic_set *isl_basic_set_solutions(
1923 __isl_take isl_basic_set *bset);
1924 __isl_give isl_basic_set *isl_set_solutions(
1925 __isl_take isl_set *set);
1926 __isl_give isl_union_set *isl_union_set_solutions(
1927 __isl_take isl_union_set *bset);
1931 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1933 __isl_give isl_union_map *isl_union_map_power(
1934 __isl_take isl_union_map *umap, int *exact);
1936 Compute a parametric representation for all positive powers I<k> of C<map>.
1937 The result maps I<k> to a nested relation corresponding to the
1938 I<k>th power of C<map>.
1939 The result may be an overapproximation. If the result is known to be exact,
1940 then C<*exact> is set to C<1>.
1942 =item * Transitive closure
1944 __isl_give isl_map *isl_map_transitive_closure(
1945 __isl_take isl_map *map, int *exact);
1946 __isl_give isl_union_map *isl_union_map_transitive_closure(
1947 __isl_take isl_union_map *umap, int *exact);
1949 Compute the transitive closure of C<map>.
1950 The result may be an overapproximation. If the result is known to be exact,
1951 then C<*exact> is set to C<1>.
1953 =item * Reaching path lengths
1955 __isl_give isl_map *isl_map_reaching_path_lengths(
1956 __isl_take isl_map *map, int *exact);
1958 Compute a relation that maps each element in the range of C<map>
1959 to the lengths of all paths composed of edges in C<map> that
1960 end up in the given element.
1961 The result may be an overapproximation. If the result is known to be exact,
1962 then C<*exact> is set to C<1>.
1963 To compute the I<maximal> path length, the resulting relation
1964 should be postprocessed by C<isl_map_lexmax>.
1965 In particular, if the input relation is a dependence relation
1966 (mapping sources to sinks), then the maximal path length corresponds
1967 to the free schedule.
1968 Note, however, that C<isl_map_lexmax> expects the maximum to be
1969 finite, so if the path lengths are unbounded (possibly due to
1970 the overapproximation), then you will get an error message.
1974 __isl_give isl_basic_set *isl_basic_map_wrap(
1975 __isl_take isl_basic_map *bmap);
1976 __isl_give isl_set *isl_map_wrap(
1977 __isl_take isl_map *map);
1978 __isl_give isl_union_set *isl_union_map_wrap(
1979 __isl_take isl_union_map *umap);
1980 __isl_give isl_basic_map *isl_basic_set_unwrap(
1981 __isl_take isl_basic_set *bset);
1982 __isl_give isl_map *isl_set_unwrap(
1983 __isl_take isl_set *set);
1984 __isl_give isl_union_map *isl_union_set_unwrap(
1985 __isl_take isl_union_set *uset);
1989 Remove any internal structure of domain (and range) of the given
1990 set or relation. If there is any such internal structure in the input,
1991 then the name of the space is also removed.
1993 __isl_give isl_basic_set *isl_basic_set_flatten(
1994 __isl_take isl_basic_set *bset);
1995 __isl_give isl_set *isl_set_flatten(
1996 __isl_take isl_set *set);
1997 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1998 __isl_take isl_basic_map *bmap);
1999 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2000 __isl_take isl_basic_map *bmap);
2001 __isl_give isl_map *isl_map_flatten_range(
2002 __isl_take isl_map *map);
2003 __isl_give isl_map *isl_map_flatten_domain(
2004 __isl_take isl_map *map);
2005 __isl_give isl_basic_map *isl_basic_map_flatten(
2006 __isl_take isl_basic_map *bmap);
2007 __isl_give isl_map *isl_map_flatten(
2008 __isl_take isl_map *map);
2010 __isl_give isl_map *isl_set_flatten_map(
2011 __isl_take isl_set *set);
2013 The function above constructs a relation
2014 that maps the input set to a flattened version of the set.
2018 Lift the input set to a space with extra dimensions corresponding
2019 to the existentially quantified variables in the input.
2020 In particular, the result lives in a wrapped map where the domain
2021 is the original space and the range corresponds to the original
2022 existentially quantified variables.
2024 __isl_give isl_basic_set *isl_basic_set_lift(
2025 __isl_take isl_basic_set *bset);
2026 __isl_give isl_set *isl_set_lift(
2027 __isl_take isl_set *set);
2028 __isl_give isl_union_set *isl_union_set_lift(
2029 __isl_take isl_union_set *uset);
2031 =item * Internal Product
2033 __isl_give isl_basic_map *isl_basic_map_zip(
2034 __isl_take isl_basic_map *bmap);
2035 __isl_give isl_map *isl_map_zip(
2036 __isl_take isl_map *map);
2037 __isl_give isl_union_map *isl_union_map_zip(
2038 __isl_take isl_union_map *umap);
2040 Given a relation with nested relations for domain and range,
2041 interchange the range of the domain with the domain of the range.
2043 =item * Aligning parameters
2045 __isl_give isl_set *isl_set_align_params(
2046 __isl_take isl_set *set,
2047 __isl_take isl_space *model);
2048 __isl_give isl_map *isl_map_align_params(
2049 __isl_take isl_map *map,
2050 __isl_take isl_space *model);
2052 Change the order of the parameters of the given set or relation
2053 such that the first parameters match those of C<model>.
2054 This may involve the introduction of extra parameters.
2055 All parameters need to be named.
2057 =item * Dimension manipulation
2059 __isl_give isl_set *isl_set_add_dims(
2060 __isl_take isl_set *set,
2061 enum isl_dim_type type, unsigned n);
2062 __isl_give isl_map *isl_map_add_dims(
2063 __isl_take isl_map *map,
2064 enum isl_dim_type type, unsigned n);
2065 __isl_give isl_set *isl_set_insert_dims(
2066 __isl_take isl_set *set,
2067 enum isl_dim_type type, unsigned pos, unsigned n);
2068 __isl_give isl_map *isl_map_insert_dims(
2069 __isl_take isl_map *map,
2070 enum isl_dim_type type, unsigned pos, unsigned n);
2072 It is usually not advisable to directly change the (input or output)
2073 space of a set or a relation as this removes the name and the internal
2074 structure of the space. However, the above functions can be useful
2075 to add new parameters, assuming
2076 C<isl_set_align_params> and C<isl_map_align_params>
2081 =head2 Binary Operations
2083 The two arguments of a binary operation not only need to live
2084 in the same C<isl_ctx>, they currently also need to have
2085 the same (number of) parameters.
2087 =head3 Basic Operations
2091 =item * Intersection
2093 __isl_give isl_basic_set *isl_basic_set_intersect(
2094 __isl_take isl_basic_set *bset1,
2095 __isl_take isl_basic_set *bset2);
2096 __isl_give isl_set *isl_set_intersect_params(
2097 __isl_take isl_set *set,
2098 __isl_take isl_set *params);
2099 __isl_give isl_set *isl_set_intersect(
2100 __isl_take isl_set *set1,
2101 __isl_take isl_set *set2);
2102 __isl_give isl_union_set *isl_union_set_intersect(
2103 __isl_take isl_union_set *uset1,
2104 __isl_take isl_union_set *uset2);
2105 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2106 __isl_take isl_basic_map *bmap,
2107 __isl_take isl_basic_set *bset);
2108 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2109 __isl_take isl_basic_map *bmap,
2110 __isl_take isl_basic_set *bset);
2111 __isl_give isl_basic_map *isl_basic_map_intersect(
2112 __isl_take isl_basic_map *bmap1,
2113 __isl_take isl_basic_map *bmap2);
2114 __isl_give isl_map *isl_map_intersect_params(
2115 __isl_take isl_map *map,
2116 __isl_take isl_set *params);
2117 __isl_give isl_map *isl_map_intersect_domain(
2118 __isl_take isl_map *map,
2119 __isl_take isl_set *set);
2120 __isl_give isl_map *isl_map_intersect_range(
2121 __isl_take isl_map *map,
2122 __isl_take isl_set *set);
2123 __isl_give isl_map *isl_map_intersect(
2124 __isl_take isl_map *map1,
2125 __isl_take isl_map *map2);
2126 __isl_give isl_union_map *isl_union_map_intersect_domain(
2127 __isl_take isl_union_map *umap,
2128 __isl_take isl_union_set *uset);
2129 __isl_give isl_union_map *isl_union_map_intersect_range(
2130 __isl_take isl_union_map *umap,
2131 __isl_take isl_union_set *uset);
2132 __isl_give isl_union_map *isl_union_map_intersect(
2133 __isl_take isl_union_map *umap1,
2134 __isl_take isl_union_map *umap2);
2138 __isl_give isl_set *isl_basic_set_union(
2139 __isl_take isl_basic_set *bset1,
2140 __isl_take isl_basic_set *bset2);
2141 __isl_give isl_map *isl_basic_map_union(
2142 __isl_take isl_basic_map *bmap1,
2143 __isl_take isl_basic_map *bmap2);
2144 __isl_give isl_set *isl_set_union(
2145 __isl_take isl_set *set1,
2146 __isl_take isl_set *set2);
2147 __isl_give isl_map *isl_map_union(
2148 __isl_take isl_map *map1,
2149 __isl_take isl_map *map2);
2150 __isl_give isl_union_set *isl_union_set_union(
2151 __isl_take isl_union_set *uset1,
2152 __isl_take isl_union_set *uset2);
2153 __isl_give isl_union_map *isl_union_map_union(
2154 __isl_take isl_union_map *umap1,
2155 __isl_take isl_union_map *umap2);
2157 =item * Set difference
2159 __isl_give isl_set *isl_set_subtract(
2160 __isl_take isl_set *set1,
2161 __isl_take isl_set *set2);
2162 __isl_give isl_map *isl_map_subtract(
2163 __isl_take isl_map *map1,
2164 __isl_take isl_map *map2);
2165 __isl_give isl_union_set *isl_union_set_subtract(
2166 __isl_take isl_union_set *uset1,
2167 __isl_take isl_union_set *uset2);
2168 __isl_give isl_union_map *isl_union_map_subtract(
2169 __isl_take isl_union_map *umap1,
2170 __isl_take isl_union_map *umap2);
2174 __isl_give isl_basic_set *isl_basic_set_apply(
2175 __isl_take isl_basic_set *bset,
2176 __isl_take isl_basic_map *bmap);
2177 __isl_give isl_set *isl_set_apply(
2178 __isl_take isl_set *set,
2179 __isl_take isl_map *map);
2180 __isl_give isl_union_set *isl_union_set_apply(
2181 __isl_take isl_union_set *uset,
2182 __isl_take isl_union_map *umap);
2183 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2184 __isl_take isl_basic_map *bmap1,
2185 __isl_take isl_basic_map *bmap2);
2186 __isl_give isl_basic_map *isl_basic_map_apply_range(
2187 __isl_take isl_basic_map *bmap1,
2188 __isl_take isl_basic_map *bmap2);
2189 __isl_give isl_map *isl_map_apply_domain(
2190 __isl_take isl_map *map1,
2191 __isl_take isl_map *map2);
2192 __isl_give isl_union_map *isl_union_map_apply_domain(
2193 __isl_take isl_union_map *umap1,
2194 __isl_take isl_union_map *umap2);
2195 __isl_give isl_map *isl_map_apply_range(
2196 __isl_take isl_map *map1,
2197 __isl_take isl_map *map2);
2198 __isl_give isl_union_map *isl_union_map_apply_range(
2199 __isl_take isl_union_map *umap1,
2200 __isl_take isl_union_map *umap2);
2202 =item * Cartesian Product
2204 __isl_give isl_set *isl_set_product(
2205 __isl_take isl_set *set1,
2206 __isl_take isl_set *set2);
2207 __isl_give isl_union_set *isl_union_set_product(
2208 __isl_take isl_union_set *uset1,
2209 __isl_take isl_union_set *uset2);
2210 __isl_give isl_basic_map *isl_basic_map_domain_product(
2211 __isl_take isl_basic_map *bmap1,
2212 __isl_take isl_basic_map *bmap2);
2213 __isl_give isl_basic_map *isl_basic_map_range_product(
2214 __isl_take isl_basic_map *bmap1,
2215 __isl_take isl_basic_map *bmap2);
2216 __isl_give isl_map *isl_map_domain_product(
2217 __isl_take isl_map *map1,
2218 __isl_take isl_map *map2);
2219 __isl_give isl_map *isl_map_range_product(
2220 __isl_take isl_map *map1,
2221 __isl_take isl_map *map2);
2222 __isl_give isl_union_map *isl_union_map_range_product(
2223 __isl_take isl_union_map *umap1,
2224 __isl_take isl_union_map *umap2);
2225 __isl_give isl_map *isl_map_product(
2226 __isl_take isl_map *map1,
2227 __isl_take isl_map *map2);
2228 __isl_give isl_union_map *isl_union_map_product(
2229 __isl_take isl_union_map *umap1,
2230 __isl_take isl_union_map *umap2);
2232 The above functions compute the cross product of the given
2233 sets or relations. The domains and ranges of the results
2234 are wrapped maps between domains and ranges of the inputs.
2235 To obtain a ``flat'' product, use the following functions
2238 __isl_give isl_basic_set *isl_basic_set_flat_product(
2239 __isl_take isl_basic_set *bset1,
2240 __isl_take isl_basic_set *bset2);
2241 __isl_give isl_set *isl_set_flat_product(
2242 __isl_take isl_set *set1,
2243 __isl_take isl_set *set2);
2244 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2245 __isl_take isl_basic_map *bmap1,
2246 __isl_take isl_basic_map *bmap2);
2247 __isl_give isl_map *isl_map_flat_domain_product(
2248 __isl_take isl_map *map1,
2249 __isl_take isl_map *map2);
2250 __isl_give isl_map *isl_map_flat_range_product(
2251 __isl_take isl_map *map1,
2252 __isl_take isl_map *map2);
2253 __isl_give isl_union_map *isl_union_map_flat_range_product(
2254 __isl_take isl_union_map *umap1,
2255 __isl_take isl_union_map *umap2);
2256 __isl_give isl_basic_map *isl_basic_map_flat_product(
2257 __isl_take isl_basic_map *bmap1,
2258 __isl_take isl_basic_map *bmap2);
2259 __isl_give isl_map *isl_map_flat_product(
2260 __isl_take isl_map *map1,
2261 __isl_take isl_map *map2);
2263 =item * Simplification
2265 __isl_give isl_basic_set *isl_basic_set_gist(
2266 __isl_take isl_basic_set *bset,
2267 __isl_take isl_basic_set *context);
2268 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2269 __isl_take isl_set *context);
2270 __isl_give isl_set *isl_set_gist_params(
2271 __isl_take isl_set *set,
2272 __isl_take isl_set *context);
2273 __isl_give isl_union_set *isl_union_set_gist(
2274 __isl_take isl_union_set *uset,
2275 __isl_take isl_union_set *context);
2276 __isl_give isl_basic_map *isl_basic_map_gist(
2277 __isl_take isl_basic_map *bmap,
2278 __isl_take isl_basic_map *context);
2279 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2280 __isl_take isl_map *context);
2281 __isl_give isl_map *isl_map_gist_params(
2282 __isl_take isl_map *map,
2283 __isl_take isl_set *context);
2284 __isl_give isl_union_map *isl_union_map_gist(
2285 __isl_take isl_union_map *umap,
2286 __isl_take isl_union_map *context);
2288 The gist operation returns a set or relation that has the
2289 same intersection with the context as the input set or relation.
2290 Any implicit equality in the intersection is made explicit in the result,
2291 while all inequalities that are redundant with respect to the intersection
2293 In case of union sets and relations, the gist operation is performed
2298 =head3 Lexicographic Optimization
2300 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2301 the following functions
2302 compute a set that contains the lexicographic minimum or maximum
2303 of the elements in C<set> (or C<bset>) for those values of the parameters
2304 that satisfy C<dom>.
2305 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2306 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2308 In other words, the union of the parameter values
2309 for which the result is non-empty and of C<*empty>
2312 __isl_give isl_set *isl_basic_set_partial_lexmin(
2313 __isl_take isl_basic_set *bset,
2314 __isl_take isl_basic_set *dom,
2315 __isl_give isl_set **empty);
2316 __isl_give isl_set *isl_basic_set_partial_lexmax(
2317 __isl_take isl_basic_set *bset,
2318 __isl_take isl_basic_set *dom,
2319 __isl_give isl_set **empty);
2320 __isl_give isl_set *isl_set_partial_lexmin(
2321 __isl_take isl_set *set, __isl_take isl_set *dom,
2322 __isl_give isl_set **empty);
2323 __isl_give isl_set *isl_set_partial_lexmax(
2324 __isl_take isl_set *set, __isl_take isl_set *dom,
2325 __isl_give isl_set **empty);
2327 Given a (basic) set C<set> (or C<bset>), the following functions simply
2328 return a set containing the lexicographic minimum or maximum
2329 of the elements in C<set> (or C<bset>).
2330 In case of union sets, the optimum is computed per space.
2332 __isl_give isl_set *isl_basic_set_lexmin(
2333 __isl_take isl_basic_set *bset);
2334 __isl_give isl_set *isl_basic_set_lexmax(
2335 __isl_take isl_basic_set *bset);
2336 __isl_give isl_set *isl_set_lexmin(
2337 __isl_take isl_set *set);
2338 __isl_give isl_set *isl_set_lexmax(
2339 __isl_take isl_set *set);
2340 __isl_give isl_union_set *isl_union_set_lexmin(
2341 __isl_take isl_union_set *uset);
2342 __isl_give isl_union_set *isl_union_set_lexmax(
2343 __isl_take isl_union_set *uset);
2345 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2346 the following functions
2347 compute a relation that maps each element of C<dom>
2348 to the single lexicographic minimum or maximum
2349 of the elements that are associated to that same
2350 element in C<map> (or C<bmap>).
2351 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2352 that contains the elements in C<dom> that do not map
2353 to any elements in C<map> (or C<bmap>).
2354 In other words, the union of the domain of the result and of C<*empty>
2357 __isl_give isl_map *isl_basic_map_partial_lexmax(
2358 __isl_take isl_basic_map *bmap,
2359 __isl_take isl_basic_set *dom,
2360 __isl_give isl_set **empty);
2361 __isl_give isl_map *isl_basic_map_partial_lexmin(
2362 __isl_take isl_basic_map *bmap,
2363 __isl_take isl_basic_set *dom,
2364 __isl_give isl_set **empty);
2365 __isl_give isl_map *isl_map_partial_lexmax(
2366 __isl_take isl_map *map, __isl_take isl_set *dom,
2367 __isl_give isl_set **empty);
2368 __isl_give isl_map *isl_map_partial_lexmin(
2369 __isl_take isl_map *map, __isl_take isl_set *dom,
2370 __isl_give isl_set **empty);
2372 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2373 return a map mapping each element in the domain of
2374 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2375 of all elements associated to that element.
2376 In case of union relations, the optimum is computed per space.
2378 __isl_give isl_map *isl_basic_map_lexmin(
2379 __isl_take isl_basic_map *bmap);
2380 __isl_give isl_map *isl_basic_map_lexmax(
2381 __isl_take isl_basic_map *bmap);
2382 __isl_give isl_map *isl_map_lexmin(
2383 __isl_take isl_map *map);
2384 __isl_give isl_map *isl_map_lexmax(
2385 __isl_take isl_map *map);
2386 __isl_give isl_union_map *isl_union_map_lexmin(
2387 __isl_take isl_union_map *umap);
2388 __isl_give isl_union_map *isl_union_map_lexmax(
2389 __isl_take isl_union_map *umap);
2393 Lists are defined over several element types, including
2394 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2395 Here we take lists of C<isl_set>s as an example.
2396 Lists can be created, copied and freed using the following functions.
2398 #include <isl/list.h>
2399 __isl_give isl_set_list *isl_set_list_from_set(
2400 __isl_take isl_set *el);
2401 __isl_give isl_set_list *isl_set_list_alloc(
2402 isl_ctx *ctx, int n);
2403 __isl_give isl_set_list *isl_set_list_copy(
2404 __isl_keep isl_set_list *list);
2405 __isl_give isl_set_list *isl_set_list_add(
2406 __isl_take isl_set_list *list,
2407 __isl_take isl_set *el);
2408 __isl_give isl_set_list *isl_set_list_concat(
2409 __isl_take isl_set_list *list1,
2410 __isl_take isl_set_list *list2);
2411 void *isl_set_list_free(__isl_take isl_set_list *list);
2413 C<isl_set_list_alloc> creates an empty list with a capacity for
2414 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2417 Lists can be inspected using the following functions.
2419 #include <isl/list.h>
2420 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2421 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2422 __isl_give isl_set *isl_set_list_get_set(
2423 __isl_keep isl_set_list *list, int index);
2424 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2425 int (*fn)(__isl_take isl_set *el, void *user),
2428 Lists can be printed using
2430 #include <isl/list.h>
2431 __isl_give isl_printer *isl_printer_print_set_list(
2432 __isl_take isl_printer *p,
2433 __isl_keep isl_set_list *list);
2437 Matrices can be created, copied and freed using the following functions.
2439 #include <isl/mat.h>
2440 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2441 unsigned n_row, unsigned n_col);
2442 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2443 void isl_mat_free(__isl_take isl_mat *mat);
2445 Note that the elements of a newly created matrix may have arbitrary values.
2446 The elements can be changed and inspected using the following functions.
2448 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2449 int isl_mat_rows(__isl_keep isl_mat *mat);
2450 int isl_mat_cols(__isl_keep isl_mat *mat);
2451 int isl_mat_get_element(__isl_keep isl_mat *mat,
2452 int row, int col, isl_int *v);
2453 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2454 int row, int col, isl_int v);
2455 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2456 int row, int col, int v);
2458 C<isl_mat_get_element> will return a negative value if anything went wrong.
2459 In that case, the value of C<*v> is undefined.
2461 The following function can be used to compute the (right) inverse
2462 of a matrix, i.e., a matrix such that the product of the original
2463 and the inverse (in that order) is a multiple of the identity matrix.
2464 The input matrix is assumed to be of full row-rank.
2466 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2468 The following function can be used to compute the (right) kernel
2469 (or null space) of a matrix, i.e., a matrix such that the product of
2470 the original and the kernel (in that order) is the zero matrix.
2472 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2474 =head2 Piecewise Quasi Affine Expressions
2476 The zero quasi affine expression on a given domain can be created using
2478 __isl_give isl_aff *isl_aff_zero_on_domain(
2479 __isl_take isl_local_space *ls);
2481 Note that the space in which the resulting object lives is a map space
2482 with the given space as domain and a one-dimensional range.
2484 A quasi affine expression can also be initialized from an C<isl_div>:
2486 #include <isl/div.h>
2487 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2489 An empty piecewise quasi affine expression (one with no cells)
2490 or a piecewise quasi affine expression with a single cell can
2491 be created using the following functions.
2493 #include <isl/aff.h>
2494 __isl_give isl_pw_aff *isl_pw_aff_empty(
2495 __isl_take isl_space *space);
2496 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2497 __isl_take isl_set *set, __isl_take isl_aff *aff);
2498 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2499 __isl_take isl_aff *aff);
2501 Quasi affine expressions can be copied and freed using
2503 #include <isl/aff.h>
2504 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2505 void *isl_aff_free(__isl_take isl_aff *aff);
2507 __isl_give isl_pw_aff *isl_pw_aff_copy(
2508 __isl_keep isl_pw_aff *pwaff);
2509 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2511 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2512 using the following function. The constraint is required to have
2513 a non-zero coefficient for the specified dimension.
2515 #include <isl/constraint.h>
2516 __isl_give isl_aff *isl_constraint_get_bound(
2517 __isl_keep isl_constraint *constraint,
2518 enum isl_dim_type type, int pos);
2520 The entire affine expression of the constraint can also be extracted
2521 using the following function.
2523 #include <isl/constraint.h>
2524 __isl_give isl_aff *isl_constraint_get_aff(
2525 __isl_keep isl_constraint *constraint);
2527 Conversely, an equality constraint equating
2528 the affine expression to zero or an inequality constraint enforcing
2529 the affine expression to be non-negative, can be constructed using
2531 __isl_give isl_constraint *isl_equality_from_aff(
2532 __isl_take isl_aff *aff);
2533 __isl_give isl_constraint *isl_inequality_from_aff(
2534 __isl_take isl_aff *aff);
2536 The expression can be inspected using
2538 #include <isl/aff.h>
2539 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2540 int isl_aff_dim(__isl_keep isl_aff *aff,
2541 enum isl_dim_type type);
2542 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2543 __isl_keep isl_aff *aff);
2544 __isl_give isl_local_space *isl_aff_get_local_space(
2545 __isl_keep isl_aff *aff);
2546 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2547 enum isl_dim_type type, unsigned pos);
2548 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2550 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2551 enum isl_dim_type type, int pos, isl_int *v);
2552 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2554 __isl_give isl_div *isl_aff_get_div(
2555 __isl_keep isl_aff *aff, int pos);
2557 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2558 int (*fn)(__isl_take isl_set *set,
2559 __isl_take isl_aff *aff,
2560 void *user), void *user);
2562 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2563 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2565 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2566 enum isl_dim_type type, unsigned first, unsigned n);
2567 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2568 enum isl_dim_type type, unsigned first, unsigned n);
2570 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2571 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2572 enum isl_dim_type type);
2573 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2575 It can be modified using
2577 #include <isl/aff.h>
2578 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2579 __isl_take isl_pw_aff *pwaff,
2580 __isl_take isl_id *id);
2581 __isl_give isl_aff *isl_aff_set_dim_name(
2582 __isl_take isl_aff *aff, enum isl_dim_type type,
2583 unsigned pos, const char *s);
2584 __isl_give isl_aff *isl_aff_set_constant(
2585 __isl_take isl_aff *aff, isl_int v);
2586 __isl_give isl_aff *isl_aff_set_constant_si(
2587 __isl_take isl_aff *aff, int v);
2588 __isl_give isl_aff *isl_aff_set_coefficient(
2589 __isl_take isl_aff *aff,
2590 enum isl_dim_type type, int pos, isl_int v);
2591 __isl_give isl_aff *isl_aff_set_coefficient_si(
2592 __isl_take isl_aff *aff,
2593 enum isl_dim_type type, int pos, int v);
2594 __isl_give isl_aff *isl_aff_set_denominator(
2595 __isl_take isl_aff *aff, isl_int v);
2597 __isl_give isl_aff *isl_aff_add_constant(
2598 __isl_take isl_aff *aff, isl_int v);
2599 __isl_give isl_aff *isl_aff_add_constant_si(
2600 __isl_take isl_aff *aff, int v);
2601 __isl_give isl_aff *isl_aff_add_coefficient(
2602 __isl_take isl_aff *aff,
2603 enum isl_dim_type type, int pos, isl_int v);
2604 __isl_give isl_aff *isl_aff_add_coefficient_si(
2605 __isl_take isl_aff *aff,
2606 enum isl_dim_type type, int pos, int v);
2608 __isl_give isl_aff *isl_aff_insert_dims(
2609 __isl_take isl_aff *aff,
2610 enum isl_dim_type type, unsigned first, unsigned n);
2611 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2612 __isl_take isl_pw_aff *pwaff,
2613 enum isl_dim_type type, unsigned first, unsigned n);
2614 __isl_give isl_aff *isl_aff_add_dims(
2615 __isl_take isl_aff *aff,
2616 enum isl_dim_type type, unsigned n);
2617 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2618 __isl_take isl_pw_aff *pwaff,
2619 enum isl_dim_type type, unsigned n);
2620 __isl_give isl_aff *isl_aff_drop_dims(
2621 __isl_take isl_aff *aff,
2622 enum isl_dim_type type, unsigned first, unsigned n);
2623 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2624 __isl_take isl_pw_aff *pwaff,
2625 enum isl_dim_type type, unsigned first, unsigned n);
2627 Note that the C<set_constant> and C<set_coefficient> functions
2628 set the I<numerator> of the constant or coefficient, while
2629 C<add_constant> and C<add_coefficient> add an integer value to
2630 the possibly rational constant or coefficient.
2632 To check whether an affine expressions is obviously zero
2633 or obviously equal to some other affine expression, use
2635 #include <isl/aff.h>
2636 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2637 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2638 __isl_keep isl_aff *aff2);
2642 #include <isl/aff.h>
2643 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2644 __isl_take isl_aff *aff2);
2645 __isl_give isl_pw_aff *isl_pw_aff_add(
2646 __isl_take isl_pw_aff *pwaff1,
2647 __isl_take isl_pw_aff *pwaff2);
2648 __isl_give isl_pw_aff *isl_pw_aff_min(
2649 __isl_take isl_pw_aff *pwaff1,
2650 __isl_take isl_pw_aff *pwaff2);
2651 __isl_give isl_pw_aff *isl_pw_aff_max(
2652 __isl_take isl_pw_aff *pwaff1,
2653 __isl_take isl_pw_aff *pwaff2);
2654 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2655 __isl_take isl_aff *aff2);
2656 __isl_give isl_pw_aff *isl_pw_aff_sub(
2657 __isl_take isl_pw_aff *pwaff1,
2658 __isl_take isl_pw_aff *pwaff2);
2659 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2660 __isl_give isl_pw_aff *isl_pw_aff_neg(
2661 __isl_take isl_pw_aff *pwaff);
2662 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2663 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2664 __isl_take isl_pw_aff *pwaff);
2665 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2666 __isl_give isl_pw_aff *isl_pw_aff_floor(
2667 __isl_take isl_pw_aff *pwaff);
2668 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2670 __isl_give isl_pw_aff *isl_pw_aff_mod(
2671 __isl_take isl_pw_aff *pwaff, isl_int mod);
2672 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2674 __isl_give isl_pw_aff *isl_pw_aff_scale(
2675 __isl_take isl_pw_aff *pwaff, isl_int f);
2676 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2678 __isl_give isl_aff *isl_aff_scale_down_ui(
2679 __isl_take isl_aff *aff, unsigned f);
2680 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2681 __isl_take isl_pw_aff *pwaff, isl_int f);
2683 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2684 __isl_take isl_pw_aff_list *list);
2685 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2686 __isl_take isl_pw_aff_list *list);
2688 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2689 __isl_take isl_pw_aff *pwqp);
2691 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2692 __isl_take isl_pw_aff *pwaff,
2693 __isl_take isl_space *model);
2695 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2696 __isl_take isl_set *context);
2697 __isl_give isl_pw_aff *isl_pw_aff_gist(
2698 __isl_take isl_pw_aff *pwaff,
2699 __isl_take isl_set *context);
2701 __isl_give isl_set *isl_pw_aff_domain(
2702 __isl_take isl_pw_aff *pwaff);
2704 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2705 __isl_take isl_aff *aff2);
2706 __isl_give isl_pw_aff *isl_pw_aff_mul(
2707 __isl_take isl_pw_aff *pwaff1,
2708 __isl_take isl_pw_aff *pwaff2);
2710 When multiplying two affine expressions, at least one of the two needs
2713 #include <isl/aff.h>
2714 __isl_give isl_basic_set *isl_aff_le_basic_set(
2715 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2716 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2717 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2718 __isl_give isl_set *isl_pw_aff_eq_set(
2719 __isl_take isl_pw_aff *pwaff1,
2720 __isl_take isl_pw_aff *pwaff2);
2721 __isl_give isl_set *isl_pw_aff_ne_set(
2722 __isl_take isl_pw_aff *pwaff1,
2723 __isl_take isl_pw_aff *pwaff2);
2724 __isl_give isl_set *isl_pw_aff_le_set(
2725 __isl_take isl_pw_aff *pwaff1,
2726 __isl_take isl_pw_aff *pwaff2);
2727 __isl_give isl_set *isl_pw_aff_lt_set(
2728 __isl_take isl_pw_aff *pwaff1,
2729 __isl_take isl_pw_aff *pwaff2);
2730 __isl_give isl_set *isl_pw_aff_ge_set(
2731 __isl_take isl_pw_aff *pwaff1,
2732 __isl_take isl_pw_aff *pwaff2);
2733 __isl_give isl_set *isl_pw_aff_gt_set(
2734 __isl_take isl_pw_aff *pwaff1,
2735 __isl_take isl_pw_aff *pwaff2);
2737 __isl_give isl_set *isl_pw_aff_list_eq_set(
2738 __isl_take isl_pw_aff_list *list1,
2739 __isl_take isl_pw_aff_list *list2);
2740 __isl_give isl_set *isl_pw_aff_list_ne_set(
2741 __isl_take isl_pw_aff_list *list1,
2742 __isl_take isl_pw_aff_list *list2);
2743 __isl_give isl_set *isl_pw_aff_list_le_set(
2744 __isl_take isl_pw_aff_list *list1,
2745 __isl_take isl_pw_aff_list *list2);
2746 __isl_give isl_set *isl_pw_aff_list_lt_set(
2747 __isl_take isl_pw_aff_list *list1,
2748 __isl_take isl_pw_aff_list *list2);
2749 __isl_give isl_set *isl_pw_aff_list_ge_set(
2750 __isl_take isl_pw_aff_list *list1,
2751 __isl_take isl_pw_aff_list *list2);
2752 __isl_give isl_set *isl_pw_aff_list_gt_set(
2753 __isl_take isl_pw_aff_list *list1,
2754 __isl_take isl_pw_aff_list *list2);
2756 The function C<isl_aff_ge_basic_set> returns a basic set
2757 containing those elements in the shared space
2758 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2759 The function C<isl_aff_ge_set> returns a set
2760 containing those elements in the shared domain
2761 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2762 The functions operating on C<isl_pw_aff_list> apply the corresponding
2763 C<isl_pw_aff> function to each pair of elements in the two lists.
2765 #include <isl/aff.h>
2766 __isl_give isl_set *isl_pw_aff_nonneg_set(
2767 __isl_take isl_pw_aff *pwaff);
2768 __isl_give isl_set *isl_pw_aff_zero_set(
2769 __isl_take isl_pw_aff *pwaff);
2770 __isl_give isl_set *isl_pw_aff_non_zero_set(
2771 __isl_take isl_pw_aff *pwaff);
2773 The function C<isl_pw_aff_nonneg_set> returns a set
2774 containing those elements in the domain
2775 of C<pwaff> where C<pwaff> is non-negative.
2777 #include <isl/aff.h>
2778 __isl_give isl_pw_aff *isl_pw_aff_cond(
2779 __isl_take isl_set *cond,
2780 __isl_take isl_pw_aff *pwaff_true,
2781 __isl_take isl_pw_aff *pwaff_false);
2783 The function C<isl_pw_aff_cond> performs a conditional operator
2784 and returns an expression that is equal to C<pwaff_true>
2785 for elements in C<cond> and equal to C<pwaff_false> for elements
2788 #include <isl/aff.h>
2789 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2790 __isl_take isl_pw_aff *pwaff1,
2791 __isl_take isl_pw_aff *pwaff2);
2792 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2793 __isl_take isl_pw_aff *pwaff1,
2794 __isl_take isl_pw_aff *pwaff2);
2796 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2797 expression with a domain that is the union of those of C<pwaff1> and
2798 C<pwaff2> and such that on each cell, the quasi-affine expression is
2799 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2800 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2801 associated expression is the defined one.
2803 An expression can be printed using
2805 #include <isl/aff.h>
2806 __isl_give isl_printer *isl_printer_print_aff(
2807 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2809 __isl_give isl_printer *isl_printer_print_pw_aff(
2810 __isl_take isl_printer *p,
2811 __isl_keep isl_pw_aff *pwaff);
2815 Points are elements of a set. They can be used to construct
2816 simple sets (boxes) or they can be used to represent the
2817 individual elements of a set.
2818 The zero point (the origin) can be created using
2820 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2822 The coordinates of a point can be inspected, set and changed
2825 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2826 enum isl_dim_type type, int pos, isl_int *v);
2827 __isl_give isl_point *isl_point_set_coordinate(
2828 __isl_take isl_point *pnt,
2829 enum isl_dim_type type, int pos, isl_int v);
2831 __isl_give isl_point *isl_point_add_ui(
2832 __isl_take isl_point *pnt,
2833 enum isl_dim_type type, int pos, unsigned val);
2834 __isl_give isl_point *isl_point_sub_ui(
2835 __isl_take isl_point *pnt,
2836 enum isl_dim_type type, int pos, unsigned val);
2838 Other properties can be obtained using
2840 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2842 Points can be copied or freed using
2844 __isl_give isl_point *isl_point_copy(
2845 __isl_keep isl_point *pnt);
2846 void isl_point_free(__isl_take isl_point *pnt);
2848 A singleton set can be created from a point using
2850 __isl_give isl_basic_set *isl_basic_set_from_point(
2851 __isl_take isl_point *pnt);
2852 __isl_give isl_set *isl_set_from_point(
2853 __isl_take isl_point *pnt);
2855 and a box can be created from two opposite extremal points using
2857 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2858 __isl_take isl_point *pnt1,
2859 __isl_take isl_point *pnt2);
2860 __isl_give isl_set *isl_set_box_from_points(
2861 __isl_take isl_point *pnt1,
2862 __isl_take isl_point *pnt2);
2864 All elements of a B<bounded> (union) set can be enumerated using
2865 the following functions.
2867 int isl_set_foreach_point(__isl_keep isl_set *set,
2868 int (*fn)(__isl_take isl_point *pnt, void *user),
2870 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2871 int (*fn)(__isl_take isl_point *pnt, void *user),
2874 The function C<fn> is called for each integer point in
2875 C<set> with as second argument the last argument of
2876 the C<isl_set_foreach_point> call. The function C<fn>
2877 should return C<0> on success and C<-1> on failure.
2878 In the latter case, C<isl_set_foreach_point> will stop
2879 enumerating and return C<-1> as well.
2880 If the enumeration is performed successfully and to completion,
2881 then C<isl_set_foreach_point> returns C<0>.
2883 To obtain a single point of a (basic) set, use
2885 __isl_give isl_point *isl_basic_set_sample_point(
2886 __isl_take isl_basic_set *bset);
2887 __isl_give isl_point *isl_set_sample_point(
2888 __isl_take isl_set *set);
2890 If C<set> does not contain any (integer) points, then the
2891 resulting point will be ``void'', a property that can be
2894 int isl_point_is_void(__isl_keep isl_point *pnt);
2896 =head2 Piecewise Quasipolynomials
2898 A piecewise quasipolynomial is a particular kind of function that maps
2899 a parametric point to a rational value.
2900 More specifically, a quasipolynomial is a polynomial expression in greatest
2901 integer parts of affine expressions of parameters and variables.
2902 A piecewise quasipolynomial is a subdivision of a given parametric
2903 domain into disjoint cells with a quasipolynomial associated to
2904 each cell. The value of the piecewise quasipolynomial at a given
2905 point is the value of the quasipolynomial associated to the cell
2906 that contains the point. Outside of the union of cells,
2907 the value is assumed to be zero.
2908 For example, the piecewise quasipolynomial
2910 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2912 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2913 A given piecewise quasipolynomial has a fixed domain dimension.
2914 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2915 defined over different domains.
2916 Piecewise quasipolynomials are mainly used by the C<barvinok>
2917 library for representing the number of elements in a parametric set or map.
2918 For example, the piecewise quasipolynomial above represents
2919 the number of points in the map
2921 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2923 =head3 Printing (Piecewise) Quasipolynomials
2925 Quasipolynomials and piecewise quasipolynomials can be printed
2926 using the following functions.
2928 __isl_give isl_printer *isl_printer_print_qpolynomial(
2929 __isl_take isl_printer *p,
2930 __isl_keep isl_qpolynomial *qp);
2932 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2933 __isl_take isl_printer *p,
2934 __isl_keep isl_pw_qpolynomial *pwqp);
2936 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2937 __isl_take isl_printer *p,
2938 __isl_keep isl_union_pw_qpolynomial *upwqp);
2940 The output format of the printer
2941 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2942 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2944 In case of printing in C<ISL_FORMAT_C>, the user may want
2945 to set the names of all dimensions
2947 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2948 __isl_take isl_qpolynomial *qp,
2949 enum isl_dim_type type, unsigned pos,
2951 __isl_give isl_pw_qpolynomial *
2952 isl_pw_qpolynomial_set_dim_name(
2953 __isl_take isl_pw_qpolynomial *pwqp,
2954 enum isl_dim_type type, unsigned pos,
2957 =head3 Creating New (Piecewise) Quasipolynomials
2959 Some simple quasipolynomials can be created using the following functions.
2960 More complicated quasipolynomials can be created by applying
2961 operations such as addition and multiplication
2962 on the resulting quasipolynomials
2964 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2965 __isl_take isl_space *domain);
2966 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2967 __isl_take isl_space *domain);
2968 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2969 __isl_take isl_space *domain);
2970 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2971 __isl_take isl_space *domain);
2972 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2973 __isl_take isl_space *domain);
2974 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2975 __isl_take isl_space *domain,
2976 const isl_int n, const isl_int d);
2977 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2978 __isl_take isl_div *div);
2979 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2980 __isl_take isl_space *domain,
2981 enum isl_dim_type type, unsigned pos);
2982 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2983 __isl_take isl_aff *aff);
2985 Note that the space in which a quasipolynomial lives is a map space
2986 with a one-dimensional range. The C<domain> argument in some of
2987 the functions above corresponds to the domain of this map space.
2989 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2990 with a single cell can be created using the following functions.
2991 Multiple of these single cell piecewise quasipolynomials can
2992 be combined to create more complicated piecewise quasipolynomials.
2994 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2995 __isl_take isl_space *space);
2996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2997 __isl_take isl_set *set,
2998 __isl_take isl_qpolynomial *qp);
2999 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3000 __isl_take isl_qpolynomial *qp);
3001 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3002 __isl_take isl_pw_aff *pwaff);
3004 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3005 __isl_take isl_space *space);
3006 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3007 __isl_take isl_pw_qpolynomial *pwqp);
3008 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3009 __isl_take isl_union_pw_qpolynomial *upwqp,
3010 __isl_take isl_pw_qpolynomial *pwqp);
3012 Quasipolynomials can be copied and freed again using the following
3015 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3016 __isl_keep isl_qpolynomial *qp);
3017 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3019 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3020 __isl_keep isl_pw_qpolynomial *pwqp);
3021 void *isl_pw_qpolynomial_free(
3022 __isl_take isl_pw_qpolynomial *pwqp);
3024 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3025 __isl_keep isl_union_pw_qpolynomial *upwqp);
3026 void isl_union_pw_qpolynomial_free(
3027 __isl_take isl_union_pw_qpolynomial *upwqp);
3029 =head3 Inspecting (Piecewise) Quasipolynomials
3031 To iterate over all piecewise quasipolynomials in a union
3032 piecewise quasipolynomial, use the following function
3034 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3035 __isl_keep isl_union_pw_qpolynomial *upwqp,
3036 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3039 To extract the piecewise quasipolynomial in a given space from a union, use
3041 __isl_give isl_pw_qpolynomial *
3042 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3043 __isl_keep isl_union_pw_qpolynomial *upwqp,
3044 __isl_take isl_space *space);
3046 To iterate over the cells in a piecewise quasipolynomial,
3047 use either of the following two functions
3049 int isl_pw_qpolynomial_foreach_piece(
3050 __isl_keep isl_pw_qpolynomial *pwqp,
3051 int (*fn)(__isl_take isl_set *set,
3052 __isl_take isl_qpolynomial *qp,
3053 void *user), void *user);
3054 int isl_pw_qpolynomial_foreach_lifted_piece(
3055 __isl_keep isl_pw_qpolynomial *pwqp,
3056 int (*fn)(__isl_take isl_set *set,
3057 __isl_take isl_qpolynomial *qp,
3058 void *user), void *user);
3060 As usual, the function C<fn> should return C<0> on success
3061 and C<-1> on failure. The difference between
3062 C<isl_pw_qpolynomial_foreach_piece> and
3063 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3064 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3065 compute unique representations for all existentially quantified
3066 variables and then turn these existentially quantified variables
3067 into extra set variables, adapting the associated quasipolynomial
3068 accordingly. This means that the C<set> passed to C<fn>
3069 will not have any existentially quantified variables, but that
3070 the dimensions of the sets may be different for different
3071 invocations of C<fn>.
3073 To iterate over all terms in a quasipolynomial,
3076 int isl_qpolynomial_foreach_term(
3077 __isl_keep isl_qpolynomial *qp,
3078 int (*fn)(__isl_take isl_term *term,
3079 void *user), void *user);
3081 The terms themselves can be inspected and freed using
3084 unsigned isl_term_dim(__isl_keep isl_term *term,
3085 enum isl_dim_type type);
3086 void isl_term_get_num(__isl_keep isl_term *term,
3088 void isl_term_get_den(__isl_keep isl_term *term,
3090 int isl_term_get_exp(__isl_keep isl_term *term,
3091 enum isl_dim_type type, unsigned pos);
3092 __isl_give isl_div *isl_term_get_div(
3093 __isl_keep isl_term *term, unsigned pos);
3094 void isl_term_free(__isl_take isl_term *term);
3096 Each term is a product of parameters, set variables and
3097 integer divisions. The function C<isl_term_get_exp>
3098 returns the exponent of a given dimensions in the given term.
3099 The C<isl_int>s in the arguments of C<isl_term_get_num>
3100 and C<isl_term_get_den> need to have been initialized
3101 using C<isl_int_init> before calling these functions.
3103 =head3 Properties of (Piecewise) Quasipolynomials
3105 To check whether a quasipolynomial is actually a constant,
3106 use the following function.
3108 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3109 isl_int *n, isl_int *d);
3111 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3112 then the numerator and denominator of the constant
3113 are returned in C<*n> and C<*d>, respectively.
3115 =head3 Operations on (Piecewise) Quasipolynomials
3117 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3118 __isl_take isl_qpolynomial *qp, isl_int v);
3119 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3120 __isl_take isl_qpolynomial *qp);
3121 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3122 __isl_take isl_qpolynomial *qp1,
3123 __isl_take isl_qpolynomial *qp2);
3124 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3125 __isl_take isl_qpolynomial *qp1,
3126 __isl_take isl_qpolynomial *qp2);
3127 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3128 __isl_take isl_qpolynomial *qp1,
3129 __isl_take isl_qpolynomial *qp2);
3130 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3131 __isl_take isl_qpolynomial *qp, unsigned exponent);
3133 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3134 __isl_take isl_pw_qpolynomial *pwqp1,
3135 __isl_take isl_pw_qpolynomial *pwqp2);
3136 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3137 __isl_take isl_pw_qpolynomial *pwqp1,
3138 __isl_take isl_pw_qpolynomial *pwqp2);
3139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3140 __isl_take isl_pw_qpolynomial *pwqp1,
3141 __isl_take isl_pw_qpolynomial *pwqp2);
3142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3143 __isl_take isl_pw_qpolynomial *pwqp);
3144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3145 __isl_take isl_pw_qpolynomial *pwqp1,
3146 __isl_take isl_pw_qpolynomial *pwqp2);
3147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3148 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3150 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3151 __isl_take isl_union_pw_qpolynomial *upwqp1,
3152 __isl_take isl_union_pw_qpolynomial *upwqp2);
3153 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3154 __isl_take isl_union_pw_qpolynomial *upwqp1,
3155 __isl_take isl_union_pw_qpolynomial *upwqp2);
3156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3157 __isl_take isl_union_pw_qpolynomial *upwqp1,
3158 __isl_take isl_union_pw_qpolynomial *upwqp2);
3160 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3161 __isl_take isl_pw_qpolynomial *pwqp,
3162 __isl_take isl_point *pnt);
3164 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3165 __isl_take isl_union_pw_qpolynomial *upwqp,
3166 __isl_take isl_point *pnt);
3168 __isl_give isl_set *isl_pw_qpolynomial_domain(
3169 __isl_take isl_pw_qpolynomial *pwqp);
3170 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3171 __isl_take isl_pw_qpolynomial *pwpq,
3172 __isl_take isl_set *set);
3174 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3175 __isl_take isl_union_pw_qpolynomial *upwqp);
3176 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3177 __isl_take isl_union_pw_qpolynomial *upwpq,
3178 __isl_take isl_union_set *uset);
3180 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3181 __isl_take isl_qpolynomial *qp,
3182 __isl_take isl_space *model);
3184 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3185 __isl_take isl_qpolynomial *qp);
3186 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3187 __isl_take isl_pw_qpolynomial *pwqp);
3189 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3190 __isl_take isl_union_pw_qpolynomial *upwqp);
3192 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3193 __isl_take isl_qpolynomial *qp,
3194 __isl_take isl_set *context);
3196 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3197 __isl_take isl_pw_qpolynomial *pwqp,
3198 __isl_take isl_set *context);
3200 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3201 __isl_take isl_union_pw_qpolynomial *upwqp,
3202 __isl_take isl_union_set *context);
3204 The gist operation applies the gist operation to each of
3205 the cells in the domain of the input piecewise quasipolynomial.
3206 The context is also exploited
3207 to simplify the quasipolynomials associated to each cell.
3209 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3210 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3211 __isl_give isl_union_pw_qpolynomial *
3212 isl_union_pw_qpolynomial_to_polynomial(
3213 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3215 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3216 the polynomial will be an overapproximation. If C<sign> is negative,
3217 it will be an underapproximation. If C<sign> is zero, the approximation
3218 will lie somewhere in between.
3220 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3222 A piecewise quasipolynomial reduction is a piecewise
3223 reduction (or fold) of quasipolynomials.
3224 In particular, the reduction can be maximum or a minimum.
3225 The objects are mainly used to represent the result of
3226 an upper or lower bound on a quasipolynomial over its domain,
3227 i.e., as the result of the following function.
3229 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3230 __isl_take isl_pw_qpolynomial *pwqp,
3231 enum isl_fold type, int *tight);
3233 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3234 __isl_take isl_union_pw_qpolynomial *upwqp,
3235 enum isl_fold type, int *tight);
3237 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3238 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3239 is the returned bound is known be tight, i.e., for each value
3240 of the parameters there is at least
3241 one element in the domain that reaches the bound.
3242 If the domain of C<pwqp> is not wrapping, then the bound is computed
3243 over all elements in that domain and the result has a purely parametric
3244 domain. If the domain of C<pwqp> is wrapping, then the bound is
3245 computed over the range of the wrapped relation. The domain of the
3246 wrapped relation becomes the domain of the result.
3248 A (piecewise) quasipolynomial reduction can be copied or freed using the
3249 following functions.
3251 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3252 __isl_keep isl_qpolynomial_fold *fold);
3253 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3254 __isl_keep isl_pw_qpolynomial_fold *pwf);
3255 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3256 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3257 void isl_qpolynomial_fold_free(
3258 __isl_take isl_qpolynomial_fold *fold);
3259 void *isl_pw_qpolynomial_fold_free(
3260 __isl_take isl_pw_qpolynomial_fold *pwf);
3261 void isl_union_pw_qpolynomial_fold_free(
3262 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3264 =head3 Printing Piecewise Quasipolynomial Reductions
3266 Piecewise quasipolynomial reductions can be printed
3267 using the following function.
3269 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3270 __isl_take isl_printer *p,
3271 __isl_keep isl_pw_qpolynomial_fold *pwf);
3272 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3273 __isl_take isl_printer *p,
3274 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3276 For C<isl_printer_print_pw_qpolynomial_fold>,
3277 output format of the printer
3278 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3279 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3280 output format of the printer
3281 needs to be set to C<ISL_FORMAT_ISL>.
3282 In case of printing in C<ISL_FORMAT_C>, the user may want
3283 to set the names of all dimensions
3285 __isl_give isl_pw_qpolynomial_fold *
3286 isl_pw_qpolynomial_fold_set_dim_name(
3287 __isl_take isl_pw_qpolynomial_fold *pwf,
3288 enum isl_dim_type type, unsigned pos,
3291 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3293 To iterate over all piecewise quasipolynomial reductions in a union
3294 piecewise quasipolynomial reduction, use the following function
3296 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3297 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3298 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3299 void *user), void *user);
3301 To iterate over the cells in a piecewise quasipolynomial reduction,
3302 use either of the following two functions
3304 int isl_pw_qpolynomial_fold_foreach_piece(
3305 __isl_keep isl_pw_qpolynomial_fold *pwf,
3306 int (*fn)(__isl_take isl_set *set,
3307 __isl_take isl_qpolynomial_fold *fold,
3308 void *user), void *user);
3309 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3310 __isl_keep isl_pw_qpolynomial_fold *pwf,
3311 int (*fn)(__isl_take isl_set *set,
3312 __isl_take isl_qpolynomial_fold *fold,
3313 void *user), void *user);
3315 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3316 of the difference between these two functions.
3318 To iterate over all quasipolynomials in a reduction, use
3320 int isl_qpolynomial_fold_foreach_qpolynomial(
3321 __isl_keep isl_qpolynomial_fold *fold,
3322 int (*fn)(__isl_take isl_qpolynomial *qp,
3323 void *user), void *user);
3325 =head3 Operations on Piecewise Quasipolynomial Reductions
3327 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3328 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3330 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3331 __isl_take isl_pw_qpolynomial_fold *pwf1,
3332 __isl_take isl_pw_qpolynomial_fold *pwf2);
3334 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3335 __isl_take isl_pw_qpolynomial_fold *pwf1,
3336 __isl_take isl_pw_qpolynomial_fold *pwf2);
3338 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3339 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3340 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3342 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3343 __isl_take isl_pw_qpolynomial_fold *pwf,
3344 __isl_take isl_point *pnt);
3346 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3347 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3348 __isl_take isl_point *pnt);
3350 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3351 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3352 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3353 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3354 __isl_take isl_union_set *uset);
3356 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3357 __isl_take isl_pw_qpolynomial_fold *pwf);
3359 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3360 __isl_take isl_pw_qpolynomial_fold *pwf);
3362 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3363 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3365 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3366 __isl_take isl_pw_qpolynomial_fold *pwf,
3367 __isl_take isl_set *context);
3369 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3370 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3371 __isl_take isl_union_set *context);
3373 The gist operation applies the gist operation to each of
3374 the cells in the domain of the input piecewise quasipolynomial reduction.
3375 In future, the operation will also exploit the context
3376 to simplify the quasipolynomial reductions associated to each cell.
3378 __isl_give isl_pw_qpolynomial_fold *
3379 isl_set_apply_pw_qpolynomial_fold(
3380 __isl_take isl_set *set,
3381 __isl_take isl_pw_qpolynomial_fold *pwf,
3383 __isl_give isl_pw_qpolynomial_fold *
3384 isl_map_apply_pw_qpolynomial_fold(
3385 __isl_take isl_map *map,
3386 __isl_take isl_pw_qpolynomial_fold *pwf,
3388 __isl_give isl_union_pw_qpolynomial_fold *
3389 isl_union_set_apply_union_pw_qpolynomial_fold(
3390 __isl_take isl_union_set *uset,
3391 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3393 __isl_give isl_union_pw_qpolynomial_fold *
3394 isl_union_map_apply_union_pw_qpolynomial_fold(
3395 __isl_take isl_union_map *umap,
3396 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3399 The functions taking a map
3400 compose the given map with the given piecewise quasipolynomial reduction.
3401 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3402 over all elements in the intersection of the range of the map
3403 and the domain of the piecewise quasipolynomial reduction
3404 as a function of an element in the domain of the map.
3405 The functions taking a set compute a bound over all elements in the
3406 intersection of the set and the domain of the
3407 piecewise quasipolynomial reduction.
3409 =head2 Dependence Analysis
3411 C<isl> contains specialized functionality for performing
3412 array dataflow analysis. That is, given a I<sink> access relation
3413 and a collection of possible I<source> access relations,
3414 C<isl> can compute relations that describe
3415 for each iteration of the sink access, which iteration
3416 of which of the source access relations was the last
3417 to access the same data element before the given iteration
3419 To compute standard flow dependences, the sink should be
3420 a read, while the sources should be writes.
3421 If any of the source accesses are marked as being I<may>
3422 accesses, then there will be a dependence to the last
3423 I<must> access B<and> to any I<may> access that follows
3424 this last I<must> access.
3425 In particular, if I<all> sources are I<may> accesses,
3426 then memory based dependence analysis is performed.
3427 If, on the other hand, all sources are I<must> accesses,
3428 then value based dependence analysis is performed.
3430 #include <isl/flow.h>
3432 typedef int (*isl_access_level_before)(void *first, void *second);
3434 __isl_give isl_access_info *isl_access_info_alloc(
3435 __isl_take isl_map *sink,
3436 void *sink_user, isl_access_level_before fn,
3438 __isl_give isl_access_info *isl_access_info_add_source(
3439 __isl_take isl_access_info *acc,
3440 __isl_take isl_map *source, int must,
3442 void isl_access_info_free(__isl_take isl_access_info *acc);
3444 __isl_give isl_flow *isl_access_info_compute_flow(
3445 __isl_take isl_access_info *acc);
3447 int isl_flow_foreach(__isl_keep isl_flow *deps,
3448 int (*fn)(__isl_take isl_map *dep, int must,
3449 void *dep_user, void *user),
3451 __isl_give isl_map *isl_flow_get_no_source(
3452 __isl_keep isl_flow *deps, int must);
3453 void isl_flow_free(__isl_take isl_flow *deps);
3455 The function C<isl_access_info_compute_flow> performs the actual
3456 dependence analysis. The other functions are used to construct
3457 the input for this function or to read off the output.
3459 The input is collected in an C<isl_access_info>, which can
3460 be created through a call to C<isl_access_info_alloc>.
3461 The arguments to this functions are the sink access relation
3462 C<sink>, a token C<sink_user> used to identify the sink
3463 access to the user, a callback function for specifying the
3464 relative order of source and sink accesses, and the number
3465 of source access relations that will be added.
3466 The callback function has type C<int (*)(void *first, void *second)>.
3467 The function is called with two user supplied tokens identifying
3468 either a source or the sink and it should return the shared nesting
3469 level and the relative order of the two accesses.
3470 In particular, let I<n> be the number of loops shared by
3471 the two accesses. If C<first> precedes C<second> textually,
3472 then the function should return I<2 * n + 1>; otherwise,
3473 it should return I<2 * n>.
3474 The sources can be added to the C<isl_access_info> by performing
3475 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3476 C<must> indicates whether the source is a I<must> access
3477 or a I<may> access. Note that a multi-valued access relation
3478 should only be marked I<must> if every iteration in the domain
3479 of the relation accesses I<all> elements in its image.
3480 The C<source_user> token is again used to identify
3481 the source access. The range of the source access relation
3482 C<source> should have the same dimension as the range
3483 of the sink access relation.
3484 The C<isl_access_info_free> function should usually not be
3485 called explicitly, because it is called implicitly by
3486 C<isl_access_info_compute_flow>.
3488 The result of the dependence analysis is collected in an
3489 C<isl_flow>. There may be elements of
3490 the sink access for which no preceding source access could be
3491 found or for which all preceding sources are I<may> accesses.
3492 The relations containing these elements can be obtained through
3493 calls to C<isl_flow_get_no_source>, the first with C<must> set
3494 and the second with C<must> unset.
3495 In the case of standard flow dependence analysis,
3496 with the sink a read and the sources I<must> writes,
3497 the first relation corresponds to the reads from uninitialized
3498 array elements and the second relation is empty.
3499 The actual flow dependences can be extracted using
3500 C<isl_flow_foreach>. This function will call the user-specified
3501 callback function C<fn> for each B<non-empty> dependence between
3502 a source and the sink. The callback function is called
3503 with four arguments, the actual flow dependence relation
3504 mapping source iterations to sink iterations, a boolean that
3505 indicates whether it is a I<must> or I<may> dependence, a token
3506 identifying the source and an additional C<void *> with value
3507 equal to the third argument of the C<isl_flow_foreach> call.
3508 A dependence is marked I<must> if it originates from a I<must>
3509 source and if it is not followed by any I<may> sources.
3511 After finishing with an C<isl_flow>, the user should call
3512 C<isl_flow_free> to free all associated memory.
3514 A higher-level interface to dependence analysis is provided
3515 by the following function.
3517 #include <isl/flow.h>
3519 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3520 __isl_take isl_union_map *must_source,
3521 __isl_take isl_union_map *may_source,
3522 __isl_take isl_union_map *schedule,
3523 __isl_give isl_union_map **must_dep,
3524 __isl_give isl_union_map **may_dep,
3525 __isl_give isl_union_map **must_no_source,
3526 __isl_give isl_union_map **may_no_source);
3528 The arrays are identified by the tuple names of the ranges
3529 of the accesses. The iteration domains by the tuple names
3530 of the domains of the accesses and of the schedule.
3531 The relative order of the iteration domains is given by the
3532 schedule. The relations returned through C<must_no_source>
3533 and C<may_no_source> are subsets of C<sink>.
3534 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3535 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3536 any of the other arguments is treated as an error.
3540 B<The functionality described in this section is fairly new
3541 and may be subject to change.>
3543 The following function can be used to compute a schedule
3544 for a union of domains. The generated schedule respects
3545 all C<validity> dependences. That is, all dependence distances
3546 over these dependences in the scheduled space are lexicographically
3547 positive. The generated schedule schedule also tries to minimize
3548 the dependence distances over C<proximity> dependences.
3549 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3550 for groups of domains where the dependence distances have only
3551 non-negative values.
3552 The algorithm used to construct the schedule is similar to that
3555 #include <isl/schedule.h>
3556 __isl_give isl_schedule *isl_union_set_compute_schedule(
3557 __isl_take isl_union_set *domain,
3558 __isl_take isl_union_map *validity,
3559 __isl_take isl_union_map *proximity);
3560 void *isl_schedule_free(__isl_take isl_schedule *sched);
3562 A mapping from the domains to the scheduled space can be obtained
3563 from an C<isl_schedule> using the following function.
3565 __isl_give isl_union_map *isl_schedule_get_map(
3566 __isl_keep isl_schedule *sched);
3568 A representation of the schedule can be printed using
3570 __isl_give isl_printer *isl_printer_print_schedule(
3571 __isl_take isl_printer *p,
3572 __isl_keep isl_schedule *schedule);
3574 A representation of the schedule as a forest of bands can be obtained
3575 using the following function.
3577 __isl_give isl_band_list *isl_schedule_get_band_forest(
3578 __isl_keep isl_schedule *schedule);
3580 The list can be manipulated as explained in L<"Lists">.
3581 The bands inside the list can be copied and freed using the following
3584 #include <isl/band.h>
3585 __isl_give isl_band *isl_band_copy(
3586 __isl_keep isl_band *band);
3587 void *isl_band_free(__isl_take isl_band *band);
3589 Each band contains zero or more scheduling dimensions.
3590 These are referred to as the members of the band.
3591 The section of the schedule that corresponds to the band is
3592 referred to as the partial schedule of the band.
3593 For those nodes that participate in a band, the outer scheduling
3594 dimensions form the prefix schedule, while the inner scheduling
3595 dimensions form the suffix schedule.
3596 That is, if we take a cut of the band forest, then the union of
3597 the concatenations of the prefix, partial and suffix schedules of
3598 each band in the cut is equal to the entire schedule (modulo
3599 some possible padding at the end with zero scheduling dimensions).
3600 The properties of a band can be inspected using the following functions.
3602 #include <isl/band.h>
3603 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3605 int isl_band_has_children(__isl_keep isl_band *band);
3606 __isl_give isl_band_list *isl_band_get_children(
3607 __isl_keep isl_band *band);
3609 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3610 __isl_keep isl_band *band);
3611 __isl_give isl_union_map *isl_band_get_partial_schedule(
3612 __isl_keep isl_band *band);
3613 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3614 __isl_keep isl_band *band);
3616 int isl_band_n_member(__isl_keep isl_band *band);
3617 int isl_band_member_is_zero_distance(
3618 __isl_keep isl_band *band, int pos);
3620 Note that a scheduling dimension is considered to be ``zero
3621 distance'' if it does not carry any proximity dependences
3623 That is, if the dependence distances of the proximity
3624 dependences are all zero in that direction (for fixed
3625 iterations of outer bands).
3627 A representation of the band can be printed using
3629 #include <isl/band.h>
3630 __isl_give isl_printer *isl_printer_print_band(
3631 __isl_take isl_printer *p,
3632 __isl_keep isl_band *band);
3634 =head2 Parametric Vertex Enumeration
3636 The parametric vertex enumeration described in this section
3637 is mainly intended to be used internally and by the C<barvinok>
3640 #include <isl/vertices.h>
3641 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3642 __isl_keep isl_basic_set *bset);
3644 The function C<isl_basic_set_compute_vertices> performs the
3645 actual computation of the parametric vertices and the chamber
3646 decomposition and store the result in an C<isl_vertices> object.
3647 This information can be queried by either iterating over all
3648 the vertices or iterating over all the chambers or cells
3649 and then iterating over all vertices that are active on the chamber.
3651 int isl_vertices_foreach_vertex(
3652 __isl_keep isl_vertices *vertices,
3653 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3656 int isl_vertices_foreach_cell(
3657 __isl_keep isl_vertices *vertices,
3658 int (*fn)(__isl_take isl_cell *cell, void *user),
3660 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3661 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3664 Other operations that can be performed on an C<isl_vertices> object are
3667 isl_ctx *isl_vertices_get_ctx(
3668 __isl_keep isl_vertices *vertices);
3669 int isl_vertices_get_n_vertices(
3670 __isl_keep isl_vertices *vertices);
3671 void isl_vertices_free(__isl_take isl_vertices *vertices);
3673 Vertices can be inspected and destroyed using the following functions.
3675 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3676 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3677 __isl_give isl_basic_set *isl_vertex_get_domain(
3678 __isl_keep isl_vertex *vertex);
3679 __isl_give isl_basic_set *isl_vertex_get_expr(
3680 __isl_keep isl_vertex *vertex);
3681 void isl_vertex_free(__isl_take isl_vertex *vertex);
3683 C<isl_vertex_get_expr> returns a singleton parametric set describing
3684 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3686 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3687 B<rational> basic sets, so they should mainly be used for inspection
3688 and should not be mixed with integer sets.
3690 Chambers can be inspected and destroyed using the following functions.
3692 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3693 __isl_give isl_basic_set *isl_cell_get_domain(
3694 __isl_keep isl_cell *cell);
3695 void isl_cell_free(__isl_take isl_cell *cell);
3699 Although C<isl> is mainly meant to be used as a library,
3700 it also contains some basic applications that use some
3701 of the functionality of C<isl>.
3702 The input may be specified in either the L<isl format>
3703 or the L<PolyLib format>.
3705 =head2 C<isl_polyhedron_sample>
3707 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3708 an integer element of the polyhedron, if there is any.
3709 The first column in the output is the denominator and is always
3710 equal to 1. If the polyhedron contains no integer points,
3711 then a vector of length zero is printed.
3715 C<isl_pip> takes the same input as the C<example> program
3716 from the C<piplib> distribution, i.e., a set of constraints
3717 on the parameters, a line containing only -1 and finally a set
3718 of constraints on a parametric polyhedron.
3719 The coefficients of the parameters appear in the last columns
3720 (but before the final constant column).
3721 The output is the lexicographic minimum of the parametric polyhedron.
3722 As C<isl> currently does not have its own output format, the output
3723 is just a dump of the internal state.
3725 =head2 C<isl_polyhedron_minimize>
3727 C<isl_polyhedron_minimize> computes the minimum of some linear
3728 or affine objective function over the integer points in a polyhedron.
3729 If an affine objective function
3730 is given, then the constant should appear in the last column.
3732 =head2 C<isl_polytope_scan>
3734 Given a polytope, C<isl_polytope_scan> prints
3735 all integer points in the polytope.