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 the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
96 =head3 Changes since isl-0.07
100 =item * The function C<isl_pw_aff_max> has been renamed to
101 C<isl_pw_aff_union_max>.
107 The source of C<isl> can be obtained either as a tarball
108 or from the git repository. Both are available from
109 L<http://freshmeat.net/projects/isl/>.
110 The installation process depends on how you obtained
113 =head2 Installation from the git repository
117 =item 1 Clone or update the repository
119 The first time the source is obtained, you need to clone
122 git clone git://repo.or.cz/isl.git
124 To obtain updates, you need to pull in the latest changes
128 =item 2 Generate C<configure>
134 After performing the above steps, continue
135 with the L<Common installation instructions>.
137 =head2 Common installation instructions
141 =item 1 Obtain C<GMP>
143 Building C<isl> requires C<GMP>, including its headers files.
144 Your distribution may not provide these header files by default
145 and you may need to install a package called C<gmp-devel> or something
146 similar. Alternatively, C<GMP> can be built from
147 source, available from L<http://gmplib.org/>.
151 C<isl> uses the standard C<autoconf> C<configure> script.
156 optionally followed by some configure options.
157 A complete list of options can be obtained by running
161 Below we discuss some of the more common options.
163 C<isl> can optionally use C<piplib>, but no
164 C<piplib> functionality is currently used by default.
165 The C<--with-piplib> option can
166 be used to specify which C<piplib>
167 library to use, either an installed version (C<system>),
168 an externally built version (C<build>)
169 or no version (C<no>). The option C<build> is mostly useful
170 in C<configure> scripts of larger projects that bundle both C<isl>
177 Installation prefix for C<isl>
179 =item C<--with-gmp-prefix>
181 Installation prefix for C<GMP> (architecture-independent files).
183 =item C<--with-gmp-exec-prefix>
185 Installation prefix for C<GMP> (architecture-dependent files).
187 =item C<--with-piplib>
189 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
191 =item C<--with-piplib-prefix>
193 Installation prefix for C<system> C<piplib> (architecture-independent files).
195 =item C<--with-piplib-exec-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-dependent files).
199 =item C<--with-piplib-builddir>
201 Location where C<build> C<piplib> was built.
209 =item 4 Install (optional)
217 =head2 Initialization
219 All manipulations of integer sets and relations occur within
220 the context of an C<isl_ctx>.
221 A given C<isl_ctx> can only be used within a single thread.
222 All arguments of a function are required to have been allocated
223 within the same context.
224 There are currently no functions available for moving an object
225 from one C<isl_ctx> to another C<isl_ctx>. This means that
226 there is currently no way of safely moving an object from one
227 thread to another, unless the whole C<isl_ctx> is moved.
229 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
230 freed using C<isl_ctx_free>.
231 All objects allocated within an C<isl_ctx> should be freed
232 before the C<isl_ctx> itself is freed.
234 isl_ctx *isl_ctx_alloc();
235 void isl_ctx_free(isl_ctx *ctx);
239 All operations on integers, mainly the coefficients
240 of the constraints describing the sets and relations,
241 are performed in exact integer arithmetic using C<GMP>.
242 However, to allow future versions of C<isl> to optionally
243 support fixed integer arithmetic, all calls to C<GMP>
244 are wrapped inside C<isl> specific macros.
245 The basic type is C<isl_int> and the operations below
246 are available on this type.
247 The meanings of these operations are essentially the same
248 as their C<GMP> C<mpz_> counterparts.
249 As always with C<GMP> types, C<isl_int>s need to be
250 initialized with C<isl_int_init> before they can be used
251 and they need to be released with C<isl_int_clear>
253 The user should not assume that an C<isl_int> is represented
254 as a C<mpz_t>, but should instead explicitly convert between
255 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
256 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
260 =item isl_int_init(i)
262 =item isl_int_clear(i)
264 =item isl_int_set(r,i)
266 =item isl_int_set_si(r,i)
268 =item isl_int_set_gmp(r,g)
270 =item isl_int_get_gmp(i,g)
272 =item isl_int_abs(r,i)
274 =item isl_int_neg(r,i)
276 =item isl_int_swap(i,j)
278 =item isl_int_swap_or_set(i,j)
280 =item isl_int_add_ui(r,i,j)
282 =item isl_int_sub_ui(r,i,j)
284 =item isl_int_add(r,i,j)
286 =item isl_int_sub(r,i,j)
288 =item isl_int_mul(r,i,j)
290 =item isl_int_mul_ui(r,i,j)
292 =item isl_int_addmul(r,i,j)
294 =item isl_int_submul(r,i,j)
296 =item isl_int_gcd(r,i,j)
298 =item isl_int_lcm(r,i,j)
300 =item isl_int_divexact(r,i,j)
302 =item isl_int_cdiv_q(r,i,j)
304 =item isl_int_fdiv_q(r,i,j)
306 =item isl_int_fdiv_r(r,i,j)
308 =item isl_int_fdiv_q_ui(r,i,j)
310 =item isl_int_read(r,s)
312 =item isl_int_print(out,i,width)
316 =item isl_int_cmp(i,j)
318 =item isl_int_cmp_si(i,si)
320 =item isl_int_eq(i,j)
322 =item isl_int_ne(i,j)
324 =item isl_int_lt(i,j)
326 =item isl_int_le(i,j)
328 =item isl_int_gt(i,j)
330 =item isl_int_ge(i,j)
332 =item isl_int_abs_eq(i,j)
334 =item isl_int_abs_ne(i,j)
336 =item isl_int_abs_lt(i,j)
338 =item isl_int_abs_gt(i,j)
340 =item isl_int_abs_ge(i,j)
342 =item isl_int_is_zero(i)
344 =item isl_int_is_one(i)
346 =item isl_int_is_negone(i)
348 =item isl_int_is_pos(i)
350 =item isl_int_is_neg(i)
352 =item isl_int_is_nonpos(i)
354 =item isl_int_is_nonneg(i)
356 =item isl_int_is_divisible_by(i,j)
360 =head2 Sets and Relations
362 C<isl> uses six types of objects for representing sets and relations,
363 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
364 C<isl_union_set> and C<isl_union_map>.
365 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
366 can be described as a conjunction of affine constraints, while
367 C<isl_set> and C<isl_map> represent unions of
368 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
369 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
370 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
371 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
372 where dimensions with different space names
373 (see L<Dimension Specifications>) are considered different as well.
374 The difference between sets and relations (maps) is that sets have
375 one set of variables, while relations have two sets of variables,
376 input variables and output variables.
378 =head2 Memory Management
380 Since a high-level operation on sets and/or relations usually involves
381 several substeps and since the user is usually not interested in
382 the intermediate results, most functions that return a new object
383 will also release all the objects passed as arguments.
384 If the user still wants to use one or more of these arguments
385 after the function call, she should pass along a copy of the
386 object rather than the object itself.
387 The user is then responsible for making sure that the original
388 object gets used somewhere else or is explicitly freed.
390 The arguments and return values of all documented functions are
391 annotated to make clear which arguments are released and which
392 arguments are preserved. In particular, the following annotations
399 C<__isl_give> means that a new object is returned.
400 The user should make sure that the returned pointer is
401 used exactly once as a value for an C<__isl_take> argument.
402 In between, it can be used as a value for as many
403 C<__isl_keep> arguments as the user likes.
404 There is one exception, and that is the case where the
405 pointer returned is C<NULL>. Is this case, the user
406 is free to use it as an C<__isl_take> argument or not.
410 C<__isl_take> means that the object the argument points to
411 is taken over by the function and may no longer be used
412 by the user as an argument to any other function.
413 The pointer value must be one returned by a function
414 returning an C<__isl_give> pointer.
415 If the user passes in a C<NULL> value, then this will
416 be treated as an error in the sense that the function will
417 not perform its usual operation. However, it will still
418 make sure that all the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
433 Identifiers are used to identify both individual dimensions
434 and tuples of dimensions. They consist of a name and an optional
435 pointer. Identifiers with the same name but different pointer values
436 are considered to be distinct.
437 Identifiers can be constructed, copied, freed, inspected and printed
438 using the following functions.
441 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
442 __isl_keep const char *name, void *user);
443 __isl_give isl_id *isl_id_copy(isl_id *id);
444 void *isl_id_free(__isl_take isl_id *id);
446 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
447 void *isl_id_get_user(__isl_keep isl_id *id);
448 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
450 __isl_give isl_printer *isl_printer_print_id(
451 __isl_take isl_printer *p, __isl_keep isl_id *id);
453 Note that C<isl_id_get_name> returns a pointer to some internal
454 data structure, so the result can only be used while the
455 corresponding C<isl_id> is alive.
457 =head2 Dimension Specifications
459 Whenever a new set or relation is created from scratch,
460 its dimension needs to be specified using an C<isl_dim>.
463 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
464 unsigned nparam, unsigned n_in, unsigned n_out);
465 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
466 unsigned nparam, unsigned dim);
467 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
468 void isl_dim_free(__isl_take isl_dim *dim);
469 unsigned isl_dim_size(__isl_keep isl_dim *dim,
470 enum isl_dim_type type);
472 The dimension specification used for creating a set
473 needs to be created using C<isl_dim_set_alloc>, while
474 that for creating a relation
475 needs to be created using C<isl_dim_alloc>.
476 C<isl_dim_size> can be used
477 to find out the number of dimensions of each type in
478 a dimension specification, where type may be
479 C<isl_dim_param>, C<isl_dim_in> (only for relations),
480 C<isl_dim_out> (only for relations), C<isl_dim_set>
481 (only for sets) or C<isl_dim_all>.
483 It is often useful to create objects that live in the
484 same space as some other object. This can be accomplished
485 by creating the new objects
486 (see L<Creating New Sets and Relations> or
487 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
488 specification of the original object.
491 __isl_give isl_dim *isl_basic_set_get_dim(
492 __isl_keep isl_basic_set *bset);
493 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
495 #include <isl/union_set.h>
496 __isl_give isl_dim *isl_union_set_get_dim(
497 __isl_keep isl_union_set *uset);
500 __isl_give isl_dim *isl_basic_map_get_dim(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
504 #include <isl/union_map.h>
505 __isl_give isl_dim *isl_union_map_get_dim(
506 __isl_keep isl_union_map *umap);
508 #include <isl/constraint.h>
509 __isl_give isl_dim *isl_constraint_get_dim(
510 __isl_keep isl_constraint *constraint);
512 #include <isl/polynomial.h>
513 __isl_give isl_dim *isl_qpolynomial_get_dim(
514 __isl_keep isl_qpolynomial *qp);
515 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
516 __isl_keep isl_qpolynomial_fold *fold);
517 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
518 __isl_keep isl_pw_qpolynomial *pwqp);
519 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
520 __isl_keep isl_union_pw_qpolynomial *upwqp);
521 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
522 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
525 __isl_give isl_dim *isl_aff_get_dim(
526 __isl_keep isl_aff *aff);
527 __isl_give isl_dim *isl_pw_aff_get_dim(
528 __isl_keep isl_pw_aff *pwaff);
530 #include <isl/point.h>
531 __isl_give isl_dim *isl_point_get_dim(
532 __isl_keep isl_point *pnt);
534 The identifiers or names of the individual dimensions may be set or read off
535 using the following functions.
538 __isl_give isl_dim *isl_dim_set_dim_id(
539 __isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos,
541 __isl_take isl_id *id);
542 __isl_give isl_id *isl_dim_get_dim_id(
543 __isl_keep isl_dim *dim,
544 enum isl_dim_type type, unsigned pos);
545 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
546 enum isl_dim_type type, unsigned pos,
547 __isl_keep const char *name);
548 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
549 enum isl_dim_type type, unsigned pos);
551 Note that C<isl_dim_get_name> returns a pointer to some internal
552 data structure, so the result can only be used while the
553 corresponding C<isl_dim> is alive.
554 Also note that every function that operates on two sets or relations
555 requires that both arguments have the same parameters. This also
556 means that if one of the arguments has named parameters, then the
557 other needs to have named parameters too and the names need to match.
558 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
559 arguments may have different parameters (as long as they are named),
560 in which case the result will have as parameters the union of the parameters of
563 Given the identifier of a dimension (typically a parameter),
564 its position can be obtained from the following function.
567 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
568 enum isl_dim_type type, __isl_keep isl_id *id);
570 The identifiers or names of entire spaces may be set or read off
571 using the following functions.
574 __isl_give isl_dim *isl_dim_set_tuple_id(
575 __isl_take isl_dim *dim,
576 enum isl_dim_type type, __isl_take isl_id *id);
577 __isl_give isl_dim *isl_dim_reset_tuple_id(
578 __isl_take isl_dim *dim, enum isl_dim_type type);
579 __isl_give isl_id *isl_dim_get_tuple_id(
580 __isl_keep isl_dim *dim, enum isl_dim_type type);
581 __isl_give isl_dim *isl_dim_set_tuple_name(
582 __isl_take isl_dim *dim,
583 enum isl_dim_type type, const char *s);
584 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
585 enum isl_dim_type type);
587 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
588 or C<isl_dim_set>. As with C<isl_dim_get_name>,
589 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
591 Binary operations require the corresponding spaces of their arguments
592 to have the same name.
594 Spaces can be nested. In particular, the domain of a set or
595 the domain or range of a relation can be a nested relation.
596 The following functions can be used to construct and deconstruct
597 such nested dimension specifications.
600 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
601 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
602 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
604 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
605 be the dimension specification of a set, while that of
606 C<isl_dim_wrap> should be the dimension specification of a relation.
607 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
608 of a relation, while that of C<isl_dim_wrap> is the dimension specification
611 Dimension specifications can be created from other dimension
612 specifications using the following functions.
614 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
615 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
616 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
617 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
618 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
620 __isl_take isl_dim *right);
621 __isl_give isl_dim *isl_dim_align_params(
622 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
623 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
624 enum isl_dim_type type, unsigned pos, unsigned n);
625 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
626 enum isl_dim_type type, unsigned n);
627 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned first, unsigned n);
629 __isl_give isl_dim *isl_dim_map_from_set(
630 __isl_take isl_dim *dim);
631 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
633 Note that if dimensions are added or removed from a space, then
634 the name and the internal structure are lost.
638 A local space is essentially a dimension specification with
639 zero or more existentially quantified variables.
640 The local space of a basic set or relation can be obtained
641 using the following functions.
644 __isl_give isl_local_space *isl_basic_set_get_local_space(
645 __isl_keep isl_basic_set *bset);
648 __isl_give isl_local_space *isl_basic_map_get_local_space(
649 __isl_keep isl_basic_map *bmap);
651 A new local space can be created from a dimension specification using
653 #include <isl/local_space.h>
654 __isl_give isl_local_space *isl_local_space_from_dim(
655 __isl_take isl_dim *dim);
657 They can be inspected, copied and freed using the following functions.
659 #include <isl/local_space.h>
660 isl_ctx *isl_local_space_get_ctx(
661 __isl_keep isl_local_space *ls);
662 int isl_local_space_dim(__isl_keep isl_local_space *ls,
663 enum isl_dim_type type);
664 const char *isl_local_space_get_dim_name(
665 __isl_keep isl_local_space *ls,
666 enum isl_dim_type type, unsigned pos);
667 __isl_give isl_local_space *isl_local_space_set_dim_name(
668 __isl_take isl_local_space *ls,
669 enum isl_dim_type type, unsigned pos, const char *s);
670 __isl_give isl_dim *isl_local_space_get_dim(
671 __isl_keep isl_local_space *ls);
672 __isl_give isl_div *isl_local_space_get_div(
673 __isl_keep isl_local_space *ls, int pos);
674 __isl_give isl_local_space *isl_local_space_copy(
675 __isl_keep isl_local_space *ls);
676 void *isl_local_space_free(__isl_take isl_local_space *ls);
678 Two local spaces can be compared using
680 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
681 __isl_keep isl_local_space *ls2);
683 Local spaces can be created from other local spaces
684 using the following functions.
686 __isl_give isl_local_space *isl_local_space_from_domain(
687 __isl_take isl_local_space *ls);
688 __isl_give isl_local_space *isl_local_space_add_dims(
689 __isl_take isl_local_space *ls,
690 enum isl_dim_type type, unsigned n);
691 __isl_give isl_local_space *isl_local_space_insert_dims(
692 __isl_take isl_local_space *ls,
693 enum isl_dim_type type, unsigned first, unsigned n);
694 __isl_give isl_local_space *isl_local_space_drop_dims(
695 __isl_take isl_local_space *ls,
696 enum isl_dim_type type, unsigned first, unsigned n);
698 =head2 Input and Output
700 C<isl> supports its own input/output format, which is similar
701 to the C<Omega> format, but also supports the C<PolyLib> format
706 The C<isl> format is similar to that of C<Omega>, but has a different
707 syntax for describing the parameters and allows for the definition
708 of an existentially quantified variable as the integer division
709 of an affine expression.
710 For example, the set of integers C<i> between C<0> and C<n>
711 such that C<i % 10 <= 6> can be described as
713 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
716 A set or relation can have several disjuncts, separated
717 by the keyword C<or>. Each disjunct is either a conjunction
718 of constraints or a projection (C<exists>) of a conjunction
719 of constraints. The constraints are separated by the keyword
722 =head3 C<PolyLib> format
724 If the represented set is a union, then the first line
725 contains a single number representing the number of disjuncts.
726 Otherwise, a line containing the number C<1> is optional.
728 Each disjunct is represented by a matrix of constraints.
729 The first line contains two numbers representing
730 the number of rows and columns,
731 where the number of rows is equal to the number of constraints
732 and the number of columns is equal to two plus the number of variables.
733 The following lines contain the actual rows of the constraint matrix.
734 In each row, the first column indicates whether the constraint
735 is an equality (C<0>) or inequality (C<1>). The final column
736 corresponds to the constant term.
738 If the set is parametric, then the coefficients of the parameters
739 appear in the last columns before the constant column.
740 The coefficients of any existentially quantified variables appear
741 between those of the set variables and those of the parameters.
743 =head3 Extended C<PolyLib> format
745 The extended C<PolyLib> format is nearly identical to the
746 C<PolyLib> format. The only difference is that the line
747 containing the number of rows and columns of a constraint matrix
748 also contains four additional numbers:
749 the number of output dimensions, the number of input dimensions,
750 the number of local dimensions (i.e., the number of existentially
751 quantified variables) and the number of parameters.
752 For sets, the number of ``output'' dimensions is equal
753 to the number of set dimensions, while the number of ``input''
759 __isl_give isl_basic_set *isl_basic_set_read_from_file(
760 isl_ctx *ctx, FILE *input, int nparam);
761 __isl_give isl_basic_set *isl_basic_set_read_from_str(
762 isl_ctx *ctx, const char *str, int nparam);
763 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
764 FILE *input, int nparam);
765 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
766 const char *str, int nparam);
769 __isl_give isl_basic_map *isl_basic_map_read_from_file(
770 isl_ctx *ctx, FILE *input, int nparam);
771 __isl_give isl_basic_map *isl_basic_map_read_from_str(
772 isl_ctx *ctx, const char *str, int nparam);
773 __isl_give isl_map *isl_map_read_from_file(
774 struct isl_ctx *ctx, FILE *input, int nparam);
775 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
776 const char *str, int nparam);
778 #include <isl/union_set.h>
779 __isl_give isl_union_set *isl_union_set_read_from_file(
780 isl_ctx *ctx, FILE *input);
781 __isl_give isl_union_set *isl_union_set_read_from_str(
782 struct isl_ctx *ctx, const char *str);
784 #include <isl/union_map.h>
785 __isl_give isl_union_map *isl_union_map_read_from_file(
786 isl_ctx *ctx, FILE *input);
787 __isl_give isl_union_map *isl_union_map_read_from_str(
788 struct isl_ctx *ctx, const char *str);
790 The input format is autodetected and may be either the C<PolyLib> format
791 or the C<isl> format.
792 C<nparam> specifies how many of the final columns in
793 the C<PolyLib> format correspond to parameters.
794 If input is given in the C<isl> format, then the number
795 of parameters needs to be equal to C<nparam>.
796 If C<nparam> is negative, then any number of parameters
797 is accepted in the C<isl> format and zero parameters
798 are assumed in the C<PolyLib> format.
802 Before anything can be printed, an C<isl_printer> needs to
805 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
807 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
808 void isl_printer_free(__isl_take isl_printer *printer);
809 __isl_give char *isl_printer_get_str(
810 __isl_keep isl_printer *printer);
812 The behavior of the printer can be modified in various ways
814 __isl_give isl_printer *isl_printer_set_output_format(
815 __isl_take isl_printer *p, int output_format);
816 __isl_give isl_printer *isl_printer_set_indent(
817 __isl_take isl_printer *p, int indent);
818 __isl_give isl_printer *isl_printer_indent(
819 __isl_take isl_printer *p, int indent);
820 __isl_give isl_printer *isl_printer_set_prefix(
821 __isl_take isl_printer *p, const char *prefix);
822 __isl_give isl_printer *isl_printer_set_suffix(
823 __isl_take isl_printer *p, const char *suffix);
825 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
826 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
827 and defaults to C<ISL_FORMAT_ISL>.
828 Each line in the output is indented by C<indent> (set by
829 C<isl_printer_set_indent>) spaces
830 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
831 In the C<PolyLib> format output,
832 the coefficients of the existentially quantified variables
833 appear between those of the set variables and those
835 The function C<isl_printer_indent> increases the indentation
836 by the specified amount (which may be negative).
838 To actually print something, use
841 __isl_give isl_printer *isl_printer_print_basic_set(
842 __isl_take isl_printer *printer,
843 __isl_keep isl_basic_set *bset);
844 __isl_give isl_printer *isl_printer_print_set(
845 __isl_take isl_printer *printer,
846 __isl_keep isl_set *set);
849 __isl_give isl_printer *isl_printer_print_basic_map(
850 __isl_take isl_printer *printer,
851 __isl_keep isl_basic_map *bmap);
852 __isl_give isl_printer *isl_printer_print_map(
853 __isl_take isl_printer *printer,
854 __isl_keep isl_map *map);
856 #include <isl/union_set.h>
857 __isl_give isl_printer *isl_printer_print_union_set(
858 __isl_take isl_printer *p,
859 __isl_keep isl_union_set *uset);
861 #include <isl/union_map.h>
862 __isl_give isl_printer *isl_printer_print_union_map(
863 __isl_take isl_printer *p,
864 __isl_keep isl_union_map *umap);
866 When called on a file printer, the following function flushes
867 the file. When called on a string printer, the buffer is cleared.
869 __isl_give isl_printer *isl_printer_flush(
870 __isl_take isl_printer *p);
872 =head2 Creating New Sets and Relations
874 C<isl> has functions for creating some standard sets and relations.
878 =item * Empty sets and relations
880 __isl_give isl_basic_set *isl_basic_set_empty(
881 __isl_take isl_dim *dim);
882 __isl_give isl_basic_map *isl_basic_map_empty(
883 __isl_take isl_dim *dim);
884 __isl_give isl_set *isl_set_empty(
885 __isl_take isl_dim *dim);
886 __isl_give isl_map *isl_map_empty(
887 __isl_take isl_dim *dim);
888 __isl_give isl_union_set *isl_union_set_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_union_map *isl_union_map_empty(
891 __isl_take isl_dim *dim);
893 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
894 is only used to specify the parameters.
896 =item * Universe sets and relations
898 __isl_give isl_basic_set *isl_basic_set_universe(
899 __isl_take isl_dim *dim);
900 __isl_give isl_basic_map *isl_basic_map_universe(
901 __isl_take isl_dim *dim);
902 __isl_give isl_set *isl_set_universe(
903 __isl_take isl_dim *dim);
904 __isl_give isl_map *isl_map_universe(
905 __isl_take isl_dim *dim);
906 __isl_give isl_union_set *isl_union_set_universe(
907 __isl_take isl_union_set *uset);
908 __isl_give isl_union_map *isl_union_map_universe(
909 __isl_take isl_union_map *umap);
911 The sets and relations constructed by the functions above
912 contain all integer values, while those constructed by the
913 functions below only contain non-negative values.
915 __isl_give isl_basic_set *isl_basic_set_nat_universe(
916 __isl_take isl_dim *dim);
917 __isl_give isl_basic_map *isl_basic_map_nat_universe(
918 __isl_take isl_dim *dim);
919 __isl_give isl_set *isl_set_nat_universe(
920 __isl_take isl_dim *dim);
921 __isl_give isl_map *isl_map_nat_universe(
922 __isl_take isl_dim *dim);
924 =item * Identity relations
926 __isl_give isl_basic_map *isl_basic_map_identity(
927 __isl_take isl_dim *dim);
928 __isl_give isl_map *isl_map_identity(
929 __isl_take isl_dim *dim);
931 The number of input and output dimensions in C<dim> needs
934 =item * Lexicographic order
936 __isl_give isl_map *isl_map_lex_lt(
937 __isl_take isl_dim *set_dim);
938 __isl_give isl_map *isl_map_lex_le(
939 __isl_take isl_dim *set_dim);
940 __isl_give isl_map *isl_map_lex_gt(
941 __isl_take isl_dim *set_dim);
942 __isl_give isl_map *isl_map_lex_ge(
943 __isl_take isl_dim *set_dim);
944 __isl_give isl_map *isl_map_lex_lt_first(
945 __isl_take isl_dim *dim, unsigned n);
946 __isl_give isl_map *isl_map_lex_le_first(
947 __isl_take isl_dim *dim, unsigned n);
948 __isl_give isl_map *isl_map_lex_gt_first(
949 __isl_take isl_dim *dim, unsigned n);
950 __isl_give isl_map *isl_map_lex_ge_first(
951 __isl_take isl_dim *dim, unsigned n);
953 The first four functions take a dimension specification for a B<set>
954 and return relations that express that the elements in the domain
955 are lexicographically less
956 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
957 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
958 than the elements in the range.
959 The last four functions take a dimension specification for a map
960 and return relations that express that the first C<n> dimensions
961 in the domain are lexicographically less
962 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
963 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
964 than the first C<n> dimensions in the range.
968 A basic set or relation can be converted to a set or relation
969 using the following functions.
971 __isl_give isl_set *isl_set_from_basic_set(
972 __isl_take isl_basic_set *bset);
973 __isl_give isl_map *isl_map_from_basic_map(
974 __isl_take isl_basic_map *bmap);
976 Sets and relations can be converted to union sets and relations
977 using the following functions.
979 __isl_give isl_union_map *isl_union_map_from_map(
980 __isl_take isl_map *map);
981 __isl_give isl_union_set *isl_union_set_from_set(
982 __isl_take isl_set *set);
984 The inverse conversions below can only be used if the input
985 union set or relation is known to contain elements in exactly one
988 __isl_give isl_set *isl_set_from_union_set(
989 __isl_take isl_union_set *uset);
990 __isl_give isl_map *isl_map_from_union_map(
991 __isl_take isl_union_map *umap);
993 Sets and relations can be copied and freed again using the following
996 __isl_give isl_basic_set *isl_basic_set_copy(
997 __isl_keep isl_basic_set *bset);
998 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
999 __isl_give isl_union_set *isl_union_set_copy(
1000 __isl_keep isl_union_set *uset);
1001 __isl_give isl_basic_map *isl_basic_map_copy(
1002 __isl_keep isl_basic_map *bmap);
1003 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1004 __isl_give isl_union_map *isl_union_map_copy(
1005 __isl_keep isl_union_map *umap);
1006 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1007 void isl_set_free(__isl_take isl_set *set);
1008 void *isl_union_set_free(__isl_take isl_union_set *uset);
1009 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1010 void isl_map_free(__isl_take isl_map *map);
1011 void *isl_union_map_free(__isl_take isl_union_map *umap);
1013 Other sets and relations can be constructed by starting
1014 from a universe set or relation, adding equality and/or
1015 inequality constraints and then projecting out the
1016 existentially quantified variables, if any.
1017 Constraints can be constructed, manipulated and
1018 added to (or removed from) (basic) sets and relations
1019 using the following functions.
1021 #include <isl/constraint.h>
1022 __isl_give isl_constraint *isl_equality_alloc(
1023 __isl_take isl_dim *dim);
1024 __isl_give isl_constraint *isl_inequality_alloc(
1025 __isl_take isl_dim *dim);
1026 __isl_give isl_constraint *isl_constraint_set_constant(
1027 __isl_take isl_constraint *constraint, isl_int v);
1028 __isl_give isl_constraint *isl_constraint_set_constant_si(
1029 __isl_take isl_constraint *constraint, int v);
1030 __isl_give isl_constraint *isl_constraint_set_coefficient(
1031 __isl_take isl_constraint *constraint,
1032 enum isl_dim_type type, int pos, isl_int v);
1033 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1034 __isl_take isl_constraint *constraint,
1035 enum isl_dim_type type, int pos, int v);
1036 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1037 __isl_take isl_basic_map *bmap,
1038 __isl_take isl_constraint *constraint);
1039 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1040 __isl_take isl_basic_set *bset,
1041 __isl_take isl_constraint *constraint);
1042 __isl_give isl_map *isl_map_add_constraint(
1043 __isl_take isl_map *map,
1044 __isl_take isl_constraint *constraint);
1045 __isl_give isl_set *isl_set_add_constraint(
1046 __isl_take isl_set *set,
1047 __isl_take isl_constraint *constraint);
1048 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1049 __isl_take isl_basic_set *bset,
1050 __isl_take isl_constraint *constraint);
1052 For example, to create a set containing the even integers
1053 between 10 and 42, you would use the following code.
1056 struct isl_dim *dim;
1057 struct isl_constraint *c;
1058 struct isl_basic_set *bset;
1061 dim = isl_dim_set_alloc(ctx, 0, 2);
1062 bset = isl_basic_set_universe(isl_dim_copy(dim));
1064 c = isl_equality_alloc(isl_dim_copy(dim));
1065 isl_int_set_si(v, -1);
1066 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1067 isl_int_set_si(v, 2);
1068 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1069 bset = isl_basic_set_add_constraint(bset, c);
1071 c = isl_inequality_alloc(isl_dim_copy(dim));
1072 isl_int_set_si(v, -10);
1073 isl_constraint_set_constant(c, v);
1074 isl_int_set_si(v, 1);
1075 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1076 bset = isl_basic_set_add_constraint(bset, c);
1078 c = isl_inequality_alloc(dim);
1079 isl_int_set_si(v, 42);
1080 isl_constraint_set_constant(c, v);
1081 isl_int_set_si(v, -1);
1082 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1083 bset = isl_basic_set_add_constraint(bset, c);
1085 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1091 struct isl_basic_set *bset;
1092 bset = isl_basic_set_read_from_str(ctx,
1093 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1095 A basic set or relation can also be constructed from two matrices
1096 describing the equalities and the inequalities.
1098 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1099 __isl_take isl_dim *dim,
1100 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1101 enum isl_dim_type c1,
1102 enum isl_dim_type c2, enum isl_dim_type c3,
1103 enum isl_dim_type c4);
1104 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1105 __isl_take isl_dim *dim,
1106 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1107 enum isl_dim_type c1,
1108 enum isl_dim_type c2, enum isl_dim_type c3,
1109 enum isl_dim_type c4, enum isl_dim_type c5);
1111 The C<isl_dim_type> arguments indicate the order in which
1112 different kinds of variables appear in the input matrices
1113 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1114 C<isl_dim_set> and C<isl_dim_div> for sets and
1115 of C<isl_dim_cst>, C<isl_dim_param>,
1116 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1118 A (basic) relation can also be constructed from a (piecewise) affine expression
1119 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1121 __isl_give isl_basic_map *isl_basic_map_from_aff(
1122 __isl_take isl_aff *aff);
1123 __isl_give isl_map *isl_map_from_pw_aff(
1124 __isl_take isl_pw_aff *pwaff);
1125 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1126 __isl_take isl_dim *domain_dim,
1127 __isl_take isl_aff_list *list);
1129 The C<domain_dim> argument describes the domain of the resulting
1130 basic relation. It is required because the C<list> may consist
1131 of zero affine expressions.
1133 =head2 Inspecting Sets and Relations
1135 Usually, the user should not have to care about the actual constraints
1136 of the sets and maps, but should instead apply the abstract operations
1137 explained in the following sections.
1138 Occasionally, however, it may be required to inspect the individual
1139 coefficients of the constraints. This section explains how to do so.
1140 In these cases, it may also be useful to have C<isl> compute
1141 an explicit representation of the existentially quantified variables.
1143 __isl_give isl_set *isl_set_compute_divs(
1144 __isl_take isl_set *set);
1145 __isl_give isl_map *isl_map_compute_divs(
1146 __isl_take isl_map *map);
1147 __isl_give isl_union_set *isl_union_set_compute_divs(
1148 __isl_take isl_union_set *uset);
1149 __isl_give isl_union_map *isl_union_map_compute_divs(
1150 __isl_take isl_union_map *umap);
1152 This explicit representation defines the existentially quantified
1153 variables as integer divisions of the other variables, possibly
1154 including earlier existentially quantified variables.
1155 An explicitly represented existentially quantified variable therefore
1156 has a unique value when the values of the other variables are known.
1157 If, furthermore, the same existentials, i.e., existentials
1158 with the same explicit representations, should appear in the
1159 same order in each of the disjuncts of a set or map, then the user should call
1160 either of the following functions.
1162 __isl_give isl_set *isl_set_align_divs(
1163 __isl_take isl_set *set);
1164 __isl_give isl_map *isl_map_align_divs(
1165 __isl_take isl_map *map);
1167 Alternatively, the existentially quantified variables can be removed
1168 using the following functions, which compute an overapproximation.
1170 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1171 __isl_take isl_basic_set *bset);
1172 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1173 __isl_take isl_basic_map *bmap);
1174 __isl_give isl_set *isl_set_remove_divs(
1175 __isl_take isl_set *set);
1176 __isl_give isl_map *isl_map_remove_divs(
1177 __isl_take isl_map *map);
1179 To iterate over all the sets or maps in a union set or map, use
1181 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1182 int (*fn)(__isl_take isl_set *set, void *user),
1184 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1185 int (*fn)(__isl_take isl_map *map, void *user),
1188 The number of sets or maps in a union set or map can be obtained
1191 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1192 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1194 To extract the set or map from a union with a given dimension
1197 __isl_give isl_set *isl_union_set_extract_set(
1198 __isl_keep isl_union_set *uset,
1199 __isl_take isl_dim *dim);
1200 __isl_give isl_map *isl_union_map_extract_map(
1201 __isl_keep isl_union_map *umap,
1202 __isl_take isl_dim *dim);
1204 To iterate over all the basic sets or maps in a set or map, use
1206 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1207 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1209 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1210 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1213 The callback function C<fn> should return 0 if successful and
1214 -1 if an error occurs. In the latter case, or if any other error
1215 occurs, the above functions will return -1.
1217 It should be noted that C<isl> does not guarantee that
1218 the basic sets or maps passed to C<fn> are disjoint.
1219 If this is required, then the user should call one of
1220 the following functions first.
1222 __isl_give isl_set *isl_set_make_disjoint(
1223 __isl_take isl_set *set);
1224 __isl_give isl_map *isl_map_make_disjoint(
1225 __isl_take isl_map *map);
1227 The number of basic sets in a set can be obtained
1230 int isl_set_n_basic_set(__isl_keep isl_set *set);
1232 To iterate over the constraints of a basic set or map, use
1234 #include <isl/constraint.h>
1236 int isl_basic_map_foreach_constraint(
1237 __isl_keep isl_basic_map *bmap,
1238 int (*fn)(__isl_take isl_constraint *c, void *user),
1240 void isl_constraint_free(struct isl_constraint *c);
1242 Again, the callback function C<fn> should return 0 if successful and
1243 -1 if an error occurs. In the latter case, or if any other error
1244 occurs, the above functions will return -1.
1245 The constraint C<c> represents either an equality or an inequality.
1246 Use the following function to find out whether a constraint
1247 represents an equality. If not, it represents an inequality.
1249 int isl_constraint_is_equality(
1250 __isl_keep isl_constraint *constraint);
1252 The coefficients of the constraints can be inspected using
1253 the following functions.
1255 void isl_constraint_get_constant(
1256 __isl_keep isl_constraint *constraint, isl_int *v);
1257 void isl_constraint_get_coefficient(
1258 __isl_keep isl_constraint *constraint,
1259 enum isl_dim_type type, int pos, isl_int *v);
1260 int isl_constraint_involves_dims(
1261 __isl_keep isl_constraint *constraint,
1262 enum isl_dim_type type, unsigned first, unsigned n);
1264 The explicit representations of the existentially quantified
1265 variables can be inspected using the following functions.
1266 Note that the user is only allowed to use these functions
1267 if the inspected set or map is the result of a call
1268 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1270 __isl_give isl_div *isl_constraint_div(
1271 __isl_keep isl_constraint *constraint, int pos);
1272 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1273 void isl_div_get_constant(__isl_keep isl_div *div,
1275 void isl_div_get_denominator(__isl_keep isl_div *div,
1277 void isl_div_get_coefficient(__isl_keep isl_div *div,
1278 enum isl_dim_type type, int pos, isl_int *v);
1280 To obtain the constraints of a basic set or map in matrix
1281 form, use the following functions.
1283 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1284 __isl_keep isl_basic_set *bset,
1285 enum isl_dim_type c1, enum isl_dim_type c2,
1286 enum isl_dim_type c3, enum isl_dim_type c4);
1287 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1288 __isl_keep isl_basic_set *bset,
1289 enum isl_dim_type c1, enum isl_dim_type c2,
1290 enum isl_dim_type c3, enum isl_dim_type c4);
1291 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type c1,
1294 enum isl_dim_type c2, enum isl_dim_type c3,
1295 enum isl_dim_type c4, enum isl_dim_type c5);
1296 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1297 __isl_keep isl_basic_map *bmap,
1298 enum isl_dim_type c1,
1299 enum isl_dim_type c2, enum isl_dim_type c3,
1300 enum isl_dim_type c4, enum isl_dim_type c5);
1302 The C<isl_dim_type> arguments dictate the order in which
1303 different kinds of variables appear in the resulting matrix
1304 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1305 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1307 To check whether the description of a set or relation depends
1308 on one or more given dimensions, it is not necessary to iterate over all
1309 constraints. Instead the following functions can be used.
1311 int isl_basic_set_involves_dims(
1312 __isl_keep isl_basic_set *bset,
1313 enum isl_dim_type type, unsigned first, unsigned n);
1314 int isl_set_involves_dims(__isl_keep isl_set *set,
1315 enum isl_dim_type type, unsigned first, unsigned n);
1316 int isl_basic_map_involves_dims(
1317 __isl_keep isl_basic_map *bmap,
1318 enum isl_dim_type type, unsigned first, unsigned n);
1319 int isl_map_involves_dims(__isl_keep isl_map *map,
1320 enum isl_dim_type type, unsigned first, unsigned n);
1322 Similarly, the following functions can be used to check whether
1323 a given dimension is involved in any lower or upper bound.
1325 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1326 enum isl_dim_type type, unsigned pos);
1327 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1328 enum isl_dim_type type, unsigned pos);
1330 The identifiers or names of the domain and range spaces of a set
1331 or relation can be read off or set using the following functions.
1333 __isl_give isl_set *isl_set_set_tuple_id(
1334 __isl_take isl_set *set, __isl_take isl_id *id);
1335 __isl_give isl_set *isl_set_reset_tuple_id(
1336 __isl_take isl_set *set);
1337 __isl_give isl_id *isl_set_get_tuple_id(
1338 __isl_keep isl_set *set);
1339 __isl_give isl_map *isl_map_set_tuple_id(
1340 __isl_take isl_map *map, enum isl_dim_type type,
1341 __isl_take isl_id *id);
1342 __isl_give isl_map *isl_map_reset_tuple_id(
1343 __isl_take isl_map *map, enum isl_dim_type type);
1344 __isl_give isl_id *isl_map_get_tuple_id(
1345 __isl_keep isl_map *map, enum isl_dim_type type);
1347 const char *isl_basic_set_get_tuple_name(
1348 __isl_keep isl_basic_set *bset);
1349 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1350 __isl_take isl_basic_set *set, const char *s);
1351 const char *isl_set_get_tuple_name(
1352 __isl_keep isl_set *set);
1353 const char *isl_basic_map_get_tuple_name(
1354 __isl_keep isl_basic_map *bmap,
1355 enum isl_dim_type type);
1356 const char *isl_map_get_tuple_name(
1357 __isl_keep isl_map *map,
1358 enum isl_dim_type type);
1360 As with C<isl_dim_get_tuple_name>, the value returned points to
1361 an internal data structure.
1362 The identifiers, positions or names of individual dimensions can be
1363 read off using the following functions.
1365 __isl_give isl_set *isl_set_set_dim_id(
1366 __isl_take isl_set *set, enum isl_dim_type type,
1367 unsigned pos, __isl_take isl_id *id);
1368 __isl_give isl_id *isl_set_get_dim_id(
1369 __isl_keep isl_set *set, enum isl_dim_type type,
1371 __isl_give isl_map *isl_map_set_dim_id(
1372 __isl_take isl_map *map, enum isl_dim_type type,
1373 unsigned pos, __isl_take isl_id *id);
1374 __isl_give isl_id *isl_map_get_dim_id(
1375 __isl_keep isl_map *map, enum isl_dim_type type,
1378 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1379 enum isl_dim_type type, __isl_keep isl_id *id);
1380 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1381 enum isl_dim_type type, __isl_keep isl_id *id);
1383 const char *isl_constraint_get_dim_name(
1384 __isl_keep isl_constraint *constraint,
1385 enum isl_dim_type type, unsigned pos);
1386 const char *isl_basic_set_get_dim_name(
1387 __isl_keep isl_basic_set *bset,
1388 enum isl_dim_type type, unsigned pos);
1389 const char *isl_set_get_dim_name(
1390 __isl_keep isl_set *set,
1391 enum isl_dim_type type, unsigned pos);
1392 const char *isl_basic_map_get_dim_name(
1393 __isl_keep isl_basic_map *bmap,
1394 enum isl_dim_type type, unsigned pos);
1395 const char *isl_map_get_dim_name(
1396 __isl_keep isl_map *map,
1397 enum isl_dim_type type, unsigned pos);
1399 These functions are mostly useful to obtain the identifiers, positions
1400 or names of the parameters.
1404 =head3 Unary Properties
1410 The following functions test whether the given set or relation
1411 contains any integer points. The ``plain'' variants do not perform
1412 any computations, but simply check if the given set or relation
1413 is already known to be empty.
1415 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1416 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1417 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1418 int isl_set_is_empty(__isl_keep isl_set *set);
1419 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1420 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1421 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1422 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1423 int isl_map_is_empty(__isl_keep isl_map *map);
1424 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1426 =item * Universality
1428 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1429 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1430 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1432 =item * Single-valuedness
1434 int isl_map_is_single_valued(__isl_keep isl_map *map);
1435 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1439 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1440 int isl_map_is_injective(__isl_keep isl_map *map);
1441 int isl_union_map_plain_is_injective(
1442 __isl_keep isl_union_map *umap);
1443 int isl_union_map_is_injective(
1444 __isl_keep isl_union_map *umap);
1448 int isl_map_is_bijective(__isl_keep isl_map *map);
1449 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1453 The following functions check whether the domain of the given
1454 (basic) set is a wrapped relation.
1456 int isl_basic_set_is_wrapping(
1457 __isl_keep isl_basic_set *bset);
1458 int isl_set_is_wrapping(__isl_keep isl_set *set);
1460 =item * Internal Product
1462 int isl_basic_map_can_zip(
1463 __isl_keep isl_basic_map *bmap);
1464 int isl_map_can_zip(__isl_keep isl_map *map);
1466 Check whether the product of domain and range of the given relation
1468 i.e., whether both domain and range are nested relations.
1472 =head3 Binary Properties
1478 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1479 __isl_keep isl_set *set2);
1480 int isl_set_is_equal(__isl_keep isl_set *set1,
1481 __isl_keep isl_set *set2);
1482 int isl_union_set_is_equal(
1483 __isl_keep isl_union_set *uset1,
1484 __isl_keep isl_union_set *uset2);
1485 int isl_basic_map_is_equal(
1486 __isl_keep isl_basic_map *bmap1,
1487 __isl_keep isl_basic_map *bmap2);
1488 int isl_map_is_equal(__isl_keep isl_map *map1,
1489 __isl_keep isl_map *map2);
1490 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1491 __isl_keep isl_map *map2);
1492 int isl_union_map_is_equal(
1493 __isl_keep isl_union_map *umap1,
1494 __isl_keep isl_union_map *umap2);
1496 =item * Disjointness
1498 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1499 __isl_keep isl_set *set2);
1503 int isl_set_is_subset(__isl_keep isl_set *set1,
1504 __isl_keep isl_set *set2);
1505 int isl_set_is_strict_subset(
1506 __isl_keep isl_set *set1,
1507 __isl_keep isl_set *set2);
1508 int isl_union_set_is_subset(
1509 __isl_keep isl_union_set *uset1,
1510 __isl_keep isl_union_set *uset2);
1511 int isl_union_set_is_strict_subset(
1512 __isl_keep isl_union_set *uset1,
1513 __isl_keep isl_union_set *uset2);
1514 int isl_basic_map_is_subset(
1515 __isl_keep isl_basic_map *bmap1,
1516 __isl_keep isl_basic_map *bmap2);
1517 int isl_basic_map_is_strict_subset(
1518 __isl_keep isl_basic_map *bmap1,
1519 __isl_keep isl_basic_map *bmap2);
1520 int isl_map_is_subset(
1521 __isl_keep isl_map *map1,
1522 __isl_keep isl_map *map2);
1523 int isl_map_is_strict_subset(
1524 __isl_keep isl_map *map1,
1525 __isl_keep isl_map *map2);
1526 int isl_union_map_is_subset(
1527 __isl_keep isl_union_map *umap1,
1528 __isl_keep isl_union_map *umap2);
1529 int isl_union_map_is_strict_subset(
1530 __isl_keep isl_union_map *umap1,
1531 __isl_keep isl_union_map *umap2);
1535 =head2 Unary Operations
1541 __isl_give isl_set *isl_set_complement(
1542 __isl_take isl_set *set);
1546 __isl_give isl_basic_map *isl_basic_map_reverse(
1547 __isl_take isl_basic_map *bmap);
1548 __isl_give isl_map *isl_map_reverse(
1549 __isl_take isl_map *map);
1550 __isl_give isl_union_map *isl_union_map_reverse(
1551 __isl_take isl_union_map *umap);
1555 __isl_give isl_basic_set *isl_basic_set_project_out(
1556 __isl_take isl_basic_set *bset,
1557 enum isl_dim_type type, unsigned first, unsigned n);
1558 __isl_give isl_basic_map *isl_basic_map_project_out(
1559 __isl_take isl_basic_map *bmap,
1560 enum isl_dim_type type, unsigned first, unsigned n);
1561 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1562 enum isl_dim_type type, unsigned first, unsigned n);
1563 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1564 enum isl_dim_type type, unsigned first, unsigned n);
1565 __isl_give isl_basic_set *isl_basic_map_domain(
1566 __isl_take isl_basic_map *bmap);
1567 __isl_give isl_basic_set *isl_basic_map_range(
1568 __isl_take isl_basic_map *bmap);
1569 __isl_give isl_set *isl_map_domain(
1570 __isl_take isl_map *bmap);
1571 __isl_give isl_set *isl_map_range(
1572 __isl_take isl_map *map);
1573 __isl_give isl_union_set *isl_union_map_domain(
1574 __isl_take isl_union_map *umap);
1575 __isl_give isl_union_set *isl_union_map_range(
1576 __isl_take isl_union_map *umap);
1578 __isl_give isl_basic_map *isl_basic_map_domain_map(
1579 __isl_take isl_basic_map *bmap);
1580 __isl_give isl_basic_map *isl_basic_map_range_map(
1581 __isl_take isl_basic_map *bmap);
1582 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1583 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1584 __isl_give isl_union_map *isl_union_map_domain_map(
1585 __isl_take isl_union_map *umap);
1586 __isl_give isl_union_map *isl_union_map_range_map(
1587 __isl_take isl_union_map *umap);
1589 The functions above construct a (basic, regular or union) relation
1590 that maps (a wrapped version of) the input relation to its domain or range.
1594 __isl_give isl_set *isl_set_eliminate(
1595 __isl_take isl_set *set, enum isl_dim_type type,
1596 unsigned first, unsigned n);
1598 Eliminate the coefficients for the given dimensions from the constraints,
1599 without removing the dimensions.
1603 __isl_give isl_basic_set *isl_basic_set_fix(
1604 __isl_take isl_basic_set *bset,
1605 enum isl_dim_type type, unsigned pos,
1607 __isl_give isl_basic_set *isl_basic_set_fix_si(
1608 __isl_take isl_basic_set *bset,
1609 enum isl_dim_type type, unsigned pos, int value);
1610 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1611 enum isl_dim_type type, unsigned pos,
1613 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1614 enum isl_dim_type type, unsigned pos, int value);
1615 __isl_give isl_basic_map *isl_basic_map_fix_si(
1616 __isl_take isl_basic_map *bmap,
1617 enum isl_dim_type type, unsigned pos, int value);
1618 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1619 enum isl_dim_type type, unsigned pos, int value);
1621 Intersect the set or relation with the hyperplane where the given
1622 dimension has the fixed given value.
1624 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1625 enum isl_dim_type type1, int pos1,
1626 enum isl_dim_type type2, int pos2);
1627 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1628 enum isl_dim_type type1, int pos1,
1629 enum isl_dim_type type2, int pos2);
1631 Intersect the set or relation with the hyperplane where the given
1632 dimensions are equal to each other.
1634 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1635 enum isl_dim_type type1, int pos1,
1636 enum isl_dim_type type2, int pos2);
1638 Intersect the relation with the hyperplane where the given
1639 dimensions have opposite values.
1643 __isl_give isl_map *isl_set_identity(
1644 __isl_take isl_set *set);
1645 __isl_give isl_union_map *isl_union_set_identity(
1646 __isl_take isl_union_set *uset);
1648 Construct an identity relation on the given (union) set.
1652 __isl_give isl_basic_set *isl_basic_map_deltas(
1653 __isl_take isl_basic_map *bmap);
1654 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1655 __isl_give isl_union_set *isl_union_map_deltas(
1656 __isl_take isl_union_map *umap);
1658 These functions return a (basic) set containing the differences
1659 between image elements and corresponding domain elements in the input.
1661 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1662 __isl_take isl_basic_map *bmap);
1663 __isl_give isl_map *isl_map_deltas_map(
1664 __isl_take isl_map *map);
1665 __isl_give isl_union_map *isl_union_map_deltas_map(
1666 __isl_take isl_union_map *umap);
1668 The functions above construct a (basic, regular or union) relation
1669 that maps (a wrapped version of) the input relation to its delta set.
1673 Simplify the representation of a set or relation by trying
1674 to combine pairs of basic sets or relations into a single
1675 basic set or relation.
1677 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1678 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1679 __isl_give isl_union_set *isl_union_set_coalesce(
1680 __isl_take isl_union_set *uset);
1681 __isl_give isl_union_map *isl_union_map_coalesce(
1682 __isl_take isl_union_map *umap);
1684 =item * Detecting equalities
1686 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1687 __isl_take isl_basic_set *bset);
1688 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1689 __isl_take isl_basic_map *bmap);
1690 __isl_give isl_set *isl_set_detect_equalities(
1691 __isl_take isl_set *set);
1692 __isl_give isl_map *isl_map_detect_equalities(
1693 __isl_take isl_map *map);
1694 __isl_give isl_union_set *isl_union_set_detect_equalities(
1695 __isl_take isl_union_set *uset);
1696 __isl_give isl_union_map *isl_union_map_detect_equalities(
1697 __isl_take isl_union_map *umap);
1699 Simplify the representation of a set or relation by detecting implicit
1702 =item * Removing redundant constraints
1704 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1705 __isl_take isl_basic_set *bset);
1706 __isl_give isl_set *isl_set_remove_redundancies(
1707 __isl_take isl_set *set);
1708 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1709 __isl_take isl_basic_map *bmap);
1710 __isl_give isl_map *isl_map_remove_redundancies(
1711 __isl_take isl_map *map);
1715 __isl_give isl_basic_set *isl_set_convex_hull(
1716 __isl_take isl_set *set);
1717 __isl_give isl_basic_map *isl_map_convex_hull(
1718 __isl_take isl_map *map);
1720 If the input set or relation has any existentially quantified
1721 variables, then the result of these operations is currently undefined.
1725 __isl_give isl_basic_set *isl_set_simple_hull(
1726 __isl_take isl_set *set);
1727 __isl_give isl_basic_map *isl_map_simple_hull(
1728 __isl_take isl_map *map);
1729 __isl_give isl_union_map *isl_union_map_simple_hull(
1730 __isl_take isl_union_map *umap);
1732 These functions compute a single basic set or relation
1733 that contains the whole input set or relation.
1734 In particular, the output is described by translates
1735 of the constraints describing the basic sets or relations in the input.
1739 (See \autoref{s:simple hull}.)
1745 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1746 __isl_take isl_basic_set *bset);
1747 __isl_give isl_basic_set *isl_set_affine_hull(
1748 __isl_take isl_set *set);
1749 __isl_give isl_union_set *isl_union_set_affine_hull(
1750 __isl_take isl_union_set *uset);
1751 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1752 __isl_take isl_basic_map *bmap);
1753 __isl_give isl_basic_map *isl_map_affine_hull(
1754 __isl_take isl_map *map);
1755 __isl_give isl_union_map *isl_union_map_affine_hull(
1756 __isl_take isl_union_map *umap);
1758 In case of union sets and relations, the affine hull is computed
1761 =item * Polyhedral hull
1763 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1764 __isl_take isl_set *set);
1765 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1766 __isl_take isl_map *map);
1767 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1768 __isl_take isl_union_set *uset);
1769 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1770 __isl_take isl_union_map *umap);
1772 These functions compute a single basic set or relation
1773 not involving any existentially quantified variables
1774 that contains the whole input set or relation.
1775 In case of union sets and relations, the polyhedral hull is computed
1778 =item * Optimization
1780 #include <isl/ilp.h>
1781 enum isl_lp_result isl_basic_set_max(
1782 __isl_keep isl_basic_set *bset,
1783 __isl_keep isl_aff *obj, isl_int *opt)
1784 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1785 __isl_keep isl_aff *obj, isl_int *opt);
1786 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1787 __isl_keep isl_aff *obj, isl_int *opt);
1789 Compute the minimum or maximum of the integer affine expression C<obj>
1790 over the points in C<set>, returning the result in C<opt>.
1791 The return value may be one of C<isl_lp_error>,
1792 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1794 =item * Parametric optimization
1796 __isl_give isl_pw_aff *isl_set_dim_max(
1797 __isl_take isl_set *set, int pos);
1799 Compute the maximum of the given set dimension as a function of the
1800 parameters, but independently of the other set dimensions.
1801 For lexicographic optimization, see L<"Lexicographic Optimization">.
1805 The following functions compute either the set of (rational) coefficient
1806 values of valid constraints for the given set or the set of (rational)
1807 values satisfying the constraints with coefficients from the given set.
1808 Internally, these two sets of functions perform essentially the
1809 same operations, except that the set of coefficients is assumed to
1810 be a cone, while the set of values may be any polyhedron.
1811 The current implementation is based on the Farkas lemma and
1812 Fourier-Motzkin elimination, but this may change or be made optional
1813 in future. In particular, future implementations may use different
1814 dualization algorithms or skip the elimination step.
1816 __isl_give isl_basic_set *isl_basic_set_coefficients(
1817 __isl_take isl_basic_set *bset);
1818 __isl_give isl_basic_set *isl_set_coefficients(
1819 __isl_take isl_set *set);
1820 __isl_give isl_union_set *isl_union_set_coefficients(
1821 __isl_take isl_union_set *bset);
1822 __isl_give isl_basic_set *isl_basic_set_solutions(
1823 __isl_take isl_basic_set *bset);
1824 __isl_give isl_basic_set *isl_set_solutions(
1825 __isl_take isl_set *set);
1826 __isl_give isl_union_set *isl_union_set_solutions(
1827 __isl_take isl_union_set *bset);
1831 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1833 __isl_give isl_union_map *isl_union_map_power(
1834 __isl_take isl_union_map *umap, int *exact);
1836 Compute a parametric representation for all positive powers I<k> of C<map>.
1837 The result maps I<k> to a nested relation corresponding to the
1838 I<k>th power of C<map>.
1839 The result may be an overapproximation. If the result is known to be exact,
1840 then C<*exact> is set to C<1>.
1842 =item * Transitive closure
1844 __isl_give isl_map *isl_map_transitive_closure(
1845 __isl_take isl_map *map, int *exact);
1846 __isl_give isl_union_map *isl_union_map_transitive_closure(
1847 __isl_take isl_union_map *umap, int *exact);
1849 Compute the transitive closure of C<map>.
1850 The result may be an overapproximation. If the result is known to be exact,
1851 then C<*exact> is set to C<1>.
1853 =item * Reaching path lengths
1855 __isl_give isl_map *isl_map_reaching_path_lengths(
1856 __isl_take isl_map *map, int *exact);
1858 Compute a relation that maps each element in the range of C<map>
1859 to the lengths of all paths composed of edges in C<map> that
1860 end up in the given element.
1861 The result may be an overapproximation. If the result is known to be exact,
1862 then C<*exact> is set to C<1>.
1863 To compute the I<maximal> path length, the resulting relation
1864 should be postprocessed by C<isl_map_lexmax>.
1865 In particular, if the input relation is a dependence relation
1866 (mapping sources to sinks), then the maximal path length corresponds
1867 to the free schedule.
1868 Note, however, that C<isl_map_lexmax> expects the maximum to be
1869 finite, so if the path lengths are unbounded (possibly due to
1870 the overapproximation), then you will get an error message.
1874 __isl_give isl_basic_set *isl_basic_map_wrap(
1875 __isl_take isl_basic_map *bmap);
1876 __isl_give isl_set *isl_map_wrap(
1877 __isl_take isl_map *map);
1878 __isl_give isl_union_set *isl_union_map_wrap(
1879 __isl_take isl_union_map *umap);
1880 __isl_give isl_basic_map *isl_basic_set_unwrap(
1881 __isl_take isl_basic_set *bset);
1882 __isl_give isl_map *isl_set_unwrap(
1883 __isl_take isl_set *set);
1884 __isl_give isl_union_map *isl_union_set_unwrap(
1885 __isl_take isl_union_set *uset);
1889 Remove any internal structure of domain (and range) of the given
1890 set or relation. If there is any such internal structure in the input,
1891 then the name of the space is also removed.
1893 __isl_give isl_basic_set *isl_basic_set_flatten(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_set *isl_set_flatten(
1896 __isl_take isl_set *set);
1897 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1898 __isl_take isl_basic_map *bmap);
1899 __isl_give isl_map *isl_map_flatten_range(
1900 __isl_take isl_map *map);
1901 __isl_give isl_basic_map *isl_basic_map_flatten(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_give isl_map *isl_map_flatten(
1904 __isl_take isl_map *map);
1906 __isl_give isl_map *isl_set_flatten_map(
1907 __isl_take isl_set *set);
1909 The function above constructs a relation
1910 that maps the input set to a flattened version of the set.
1914 Lift the input set to a space with extra dimensions corresponding
1915 to the existentially quantified variables in the input.
1916 In particular, the result lives in a wrapped map where the domain
1917 is the original space and the range corresponds to the original
1918 existentially quantified variables.
1920 __isl_give isl_basic_set *isl_basic_set_lift(
1921 __isl_take isl_basic_set *bset);
1922 __isl_give isl_set *isl_set_lift(
1923 __isl_take isl_set *set);
1924 __isl_give isl_union_set *isl_union_set_lift(
1925 __isl_take isl_union_set *uset);
1927 =item * Internal Product
1929 __isl_give isl_basic_map *isl_basic_map_zip(
1930 __isl_take isl_basic_map *bmap);
1931 __isl_give isl_map *isl_map_zip(
1932 __isl_take isl_map *map);
1933 __isl_give isl_union_map *isl_union_map_zip(
1934 __isl_take isl_union_map *umap);
1936 Given a relation with nested relations for domain and range,
1937 interchange the range of the domain with the domain of the range.
1939 =item * Aligning parameters
1941 __isl_give isl_set *isl_set_align_params(
1942 __isl_take isl_set *set,
1943 __isl_take isl_dim *model);
1944 __isl_give isl_map *isl_map_align_params(
1945 __isl_take isl_map *map,
1946 __isl_take isl_dim *model);
1948 Change the order of the parameters of the given set or relation
1949 such that the first parameters match those of C<model>.
1950 This may involve the introduction of extra parameters.
1951 All parameters need to be named.
1953 =item * Dimension manipulation
1955 __isl_give isl_set *isl_set_add_dims(
1956 __isl_take isl_set *set,
1957 enum isl_dim_type type, unsigned n);
1958 __isl_give isl_map *isl_map_add_dims(
1959 __isl_take isl_map *map,
1960 enum isl_dim_type type, unsigned n);
1962 It is usually not advisable to directly change the (input or output)
1963 space of a set or a relation as this removes the name and the internal
1964 structure of the space. However, the above functions can be useful
1965 to add new parameters, assuming
1966 C<isl_set_align_params> and C<isl_map_align_params>
1971 =head2 Binary Operations
1973 The two arguments of a binary operation not only need to live
1974 in the same C<isl_ctx>, they currently also need to have
1975 the same (number of) parameters.
1977 =head3 Basic Operations
1981 =item * Intersection
1983 __isl_give isl_basic_set *isl_basic_set_intersect(
1984 __isl_take isl_basic_set *bset1,
1985 __isl_take isl_basic_set *bset2);
1986 __isl_give isl_set *isl_set_intersect_params(
1987 __isl_take isl_set *set,
1988 __isl_take isl_set *params);
1989 __isl_give isl_set *isl_set_intersect(
1990 __isl_take isl_set *set1,
1991 __isl_take isl_set *set2);
1992 __isl_give isl_union_set *isl_union_set_intersect(
1993 __isl_take isl_union_set *uset1,
1994 __isl_take isl_union_set *uset2);
1995 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1996 __isl_take isl_basic_map *bmap,
1997 __isl_take isl_basic_set *bset);
1998 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1999 __isl_take isl_basic_map *bmap,
2000 __isl_take isl_basic_set *bset);
2001 __isl_give isl_basic_map *isl_basic_map_intersect(
2002 __isl_take isl_basic_map *bmap1,
2003 __isl_take isl_basic_map *bmap2);
2004 __isl_give isl_map *isl_map_intersect_params(
2005 __isl_take isl_map *map,
2006 __isl_take isl_set *params);
2007 __isl_give isl_map *isl_map_intersect_domain(
2008 __isl_take isl_map *map,
2009 __isl_take isl_set *set);
2010 __isl_give isl_map *isl_map_intersect_range(
2011 __isl_take isl_map *map,
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_intersect(
2014 __isl_take isl_map *map1,
2015 __isl_take isl_map *map2);
2016 __isl_give isl_union_map *isl_union_map_intersect_domain(
2017 __isl_take isl_union_map *umap,
2018 __isl_take isl_union_set *uset);
2019 __isl_give isl_union_map *isl_union_map_intersect_range(
2020 __isl_take isl_union_map *umap,
2021 __isl_take isl_union_set *uset);
2022 __isl_give isl_union_map *isl_union_map_intersect(
2023 __isl_take isl_union_map *umap1,
2024 __isl_take isl_union_map *umap2);
2028 __isl_give isl_set *isl_basic_set_union(
2029 __isl_take isl_basic_set *bset1,
2030 __isl_take isl_basic_set *bset2);
2031 __isl_give isl_map *isl_basic_map_union(
2032 __isl_take isl_basic_map *bmap1,
2033 __isl_take isl_basic_map *bmap2);
2034 __isl_give isl_set *isl_set_union(
2035 __isl_take isl_set *set1,
2036 __isl_take isl_set *set2);
2037 __isl_give isl_map *isl_map_union(
2038 __isl_take isl_map *map1,
2039 __isl_take isl_map *map2);
2040 __isl_give isl_union_set *isl_union_set_union(
2041 __isl_take isl_union_set *uset1,
2042 __isl_take isl_union_set *uset2);
2043 __isl_give isl_union_map *isl_union_map_union(
2044 __isl_take isl_union_map *umap1,
2045 __isl_take isl_union_map *umap2);
2047 =item * Set difference
2049 __isl_give isl_set *isl_set_subtract(
2050 __isl_take isl_set *set1,
2051 __isl_take isl_set *set2);
2052 __isl_give isl_map *isl_map_subtract(
2053 __isl_take isl_map *map1,
2054 __isl_take isl_map *map2);
2055 __isl_give isl_union_set *isl_union_set_subtract(
2056 __isl_take isl_union_set *uset1,
2057 __isl_take isl_union_set *uset2);
2058 __isl_give isl_union_map *isl_union_map_subtract(
2059 __isl_take isl_union_map *umap1,
2060 __isl_take isl_union_map *umap2);
2064 __isl_give isl_basic_set *isl_basic_set_apply(
2065 __isl_take isl_basic_set *bset,
2066 __isl_take isl_basic_map *bmap);
2067 __isl_give isl_set *isl_set_apply(
2068 __isl_take isl_set *set,
2069 __isl_take isl_map *map);
2070 __isl_give isl_union_set *isl_union_set_apply(
2071 __isl_take isl_union_set *uset,
2072 __isl_take isl_union_map *umap);
2073 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2074 __isl_take isl_basic_map *bmap1,
2075 __isl_take isl_basic_map *bmap2);
2076 __isl_give isl_basic_map *isl_basic_map_apply_range(
2077 __isl_take isl_basic_map *bmap1,
2078 __isl_take isl_basic_map *bmap2);
2079 __isl_give isl_map *isl_map_apply_domain(
2080 __isl_take isl_map *map1,
2081 __isl_take isl_map *map2);
2082 __isl_give isl_union_map *isl_union_map_apply_domain(
2083 __isl_take isl_union_map *umap1,
2084 __isl_take isl_union_map *umap2);
2085 __isl_give isl_map *isl_map_apply_range(
2086 __isl_take isl_map *map1,
2087 __isl_take isl_map *map2);
2088 __isl_give isl_union_map *isl_union_map_apply_range(
2089 __isl_take isl_union_map *umap1,
2090 __isl_take isl_union_map *umap2);
2092 =item * Cartesian Product
2094 __isl_give isl_set *isl_set_product(
2095 __isl_take isl_set *set1,
2096 __isl_take isl_set *set2);
2097 __isl_give isl_union_set *isl_union_set_product(
2098 __isl_take isl_union_set *uset1,
2099 __isl_take isl_union_set *uset2);
2100 __isl_give isl_basic_map *isl_basic_map_range_product(
2101 __isl_take isl_basic_map *bmap1,
2102 __isl_take isl_basic_map *bmap2);
2103 __isl_give isl_map *isl_map_range_product(
2104 __isl_take isl_map *map1,
2105 __isl_take isl_map *map2);
2106 __isl_give isl_union_map *isl_union_map_range_product(
2107 __isl_take isl_union_map *umap1,
2108 __isl_take isl_union_map *umap2);
2109 __isl_give isl_map *isl_map_product(
2110 __isl_take isl_map *map1,
2111 __isl_take isl_map *map2);
2112 __isl_give isl_union_map *isl_union_map_product(
2113 __isl_take isl_union_map *umap1,
2114 __isl_take isl_union_map *umap2);
2116 The above functions compute the cross product of the given
2117 sets or relations. The domains and ranges of the results
2118 are wrapped maps between domains and ranges of the inputs.
2119 To obtain a ``flat'' product, use the following functions
2122 __isl_give isl_basic_set *isl_basic_set_flat_product(
2123 __isl_take isl_basic_set *bset1,
2124 __isl_take isl_basic_set *bset2);
2125 __isl_give isl_set *isl_set_flat_product(
2126 __isl_take isl_set *set1,
2127 __isl_take isl_set *set2);
2128 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2129 __isl_take isl_basic_map *bmap1,
2130 __isl_take isl_basic_map *bmap2);
2131 __isl_give isl_map *isl_map_flat_range_product(
2132 __isl_take isl_map *map1,
2133 __isl_take isl_map *map2);
2134 __isl_give isl_union_map *isl_union_map_flat_range_product(
2135 __isl_take isl_union_map *umap1,
2136 __isl_take isl_union_map *umap2);
2137 __isl_give isl_basic_map *isl_basic_map_flat_product(
2138 __isl_take isl_basic_map *bmap1,
2139 __isl_take isl_basic_map *bmap2);
2140 __isl_give isl_map *isl_map_flat_product(
2141 __isl_take isl_map *map1,
2142 __isl_take isl_map *map2);
2144 =item * Simplification
2146 __isl_give isl_basic_set *isl_basic_set_gist(
2147 __isl_take isl_basic_set *bset,
2148 __isl_take isl_basic_set *context);
2149 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2150 __isl_take isl_set *context);
2151 __isl_give isl_union_set *isl_union_set_gist(
2152 __isl_take isl_union_set *uset,
2153 __isl_take isl_union_set *context);
2154 __isl_give isl_basic_map *isl_basic_map_gist(
2155 __isl_take isl_basic_map *bmap,
2156 __isl_take isl_basic_map *context);
2157 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2158 __isl_take isl_map *context);
2159 __isl_give isl_union_map *isl_union_map_gist(
2160 __isl_take isl_union_map *umap,
2161 __isl_take isl_union_map *context);
2163 The gist operation returns a set or relation that has the
2164 same intersection with the context as the input set or relation.
2165 Any implicit equality in the intersection is made explicit in the result,
2166 while all inequalities that are redundant with respect to the intersection
2168 In case of union sets and relations, the gist operation is performed
2173 =head3 Lexicographic Optimization
2175 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2176 the following functions
2177 compute a set that contains the lexicographic minimum or maximum
2178 of the elements in C<set> (or C<bset>) for those values of the parameters
2179 that satisfy C<dom>.
2180 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2181 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2183 In other words, the union of the parameter values
2184 for which the result is non-empty and of C<*empty>
2187 __isl_give isl_set *isl_basic_set_partial_lexmin(
2188 __isl_take isl_basic_set *bset,
2189 __isl_take isl_basic_set *dom,
2190 __isl_give isl_set **empty);
2191 __isl_give isl_set *isl_basic_set_partial_lexmax(
2192 __isl_take isl_basic_set *bset,
2193 __isl_take isl_basic_set *dom,
2194 __isl_give isl_set **empty);
2195 __isl_give isl_set *isl_set_partial_lexmin(
2196 __isl_take isl_set *set, __isl_take isl_set *dom,
2197 __isl_give isl_set **empty);
2198 __isl_give isl_set *isl_set_partial_lexmax(
2199 __isl_take isl_set *set, __isl_take isl_set *dom,
2200 __isl_give isl_set **empty);
2202 Given a (basic) set C<set> (or C<bset>), the following functions simply
2203 return a set containing the lexicographic minimum or maximum
2204 of the elements in C<set> (or C<bset>).
2205 In case of union sets, the optimum is computed per space.
2207 __isl_give isl_set *isl_basic_set_lexmin(
2208 __isl_take isl_basic_set *bset);
2209 __isl_give isl_set *isl_basic_set_lexmax(
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_set *isl_set_lexmin(
2212 __isl_take isl_set *set);
2213 __isl_give isl_set *isl_set_lexmax(
2214 __isl_take isl_set *set);
2215 __isl_give isl_union_set *isl_union_set_lexmin(
2216 __isl_take isl_union_set *uset);
2217 __isl_give isl_union_set *isl_union_set_lexmax(
2218 __isl_take isl_union_set *uset);
2220 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2221 the following functions
2222 compute a relation that maps each element of C<dom>
2223 to the single lexicographic minimum or maximum
2224 of the elements that are associated to that same
2225 element in C<map> (or C<bmap>).
2226 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2227 that contains the elements in C<dom> that do not map
2228 to any elements in C<map> (or C<bmap>).
2229 In other words, the union of the domain of the result and of C<*empty>
2232 __isl_give isl_map *isl_basic_map_partial_lexmax(
2233 __isl_take isl_basic_map *bmap,
2234 __isl_take isl_basic_set *dom,
2235 __isl_give isl_set **empty);
2236 __isl_give isl_map *isl_basic_map_partial_lexmin(
2237 __isl_take isl_basic_map *bmap,
2238 __isl_take isl_basic_set *dom,
2239 __isl_give isl_set **empty);
2240 __isl_give isl_map *isl_map_partial_lexmax(
2241 __isl_take isl_map *map, __isl_take isl_set *dom,
2242 __isl_give isl_set **empty);
2243 __isl_give isl_map *isl_map_partial_lexmin(
2244 __isl_take isl_map *map, __isl_take isl_set *dom,
2245 __isl_give isl_set **empty);
2247 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2248 return a map mapping each element in the domain of
2249 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2250 of all elements associated to that element.
2251 In case of union relations, the optimum is computed per space.
2253 __isl_give isl_map *isl_basic_map_lexmin(
2254 __isl_take isl_basic_map *bmap);
2255 __isl_give isl_map *isl_basic_map_lexmax(
2256 __isl_take isl_basic_map *bmap);
2257 __isl_give isl_map *isl_map_lexmin(
2258 __isl_take isl_map *map);
2259 __isl_give isl_map *isl_map_lexmax(
2260 __isl_take isl_map *map);
2261 __isl_give isl_union_map *isl_union_map_lexmin(
2262 __isl_take isl_union_map *umap);
2263 __isl_give isl_union_map *isl_union_map_lexmax(
2264 __isl_take isl_union_map *umap);
2268 Lists are defined over several element types, including
2269 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2270 Here we take lists of C<isl_set>s as an example.
2271 Lists can be created, copied and freed using the following functions.
2273 #include <isl/list.h>
2274 __isl_give isl_set_list *isl_set_list_from_set(
2275 __isl_take struct isl_set *el);
2276 __isl_give isl_set_list *isl_set_list_alloc(
2277 isl_ctx *ctx, int n);
2278 __isl_give isl_set_list *isl_set_list_copy(
2279 __isl_keep isl_set_list *list);
2280 __isl_give isl_set_list *isl_set_list_add(
2281 __isl_take isl_set_list *list,
2282 __isl_take isl_set *el);
2283 __isl_give isl_set_list *isl_set_list_concat(
2284 __isl_take isl_set_list *list1,
2285 __isl_take isl_set_list *list2);
2286 void *isl_set_list_free(__isl_take isl_set_list *list);
2288 C<isl_set_list_alloc> creates an empty list with a capacity for
2289 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2292 Lists can be inspected using the following functions.
2294 #include <isl/list.h>
2295 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2296 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2297 __isl_give struct isl_set *isl_set_list_get_set(
2298 __isl_keep isl_set_list *list, int index);
2299 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2300 int (*fn)(__isl_take struct isl_set *el, void *user),
2303 Lists can be printed using
2305 #include <isl/list.h>
2306 __isl_give isl_printer *isl_printer_print_set_list(
2307 __isl_take isl_printer *p,
2308 __isl_keep isl_set_list *list);
2312 Matrices can be created, copied and freed using the following functions.
2314 #include <isl/mat.h>
2315 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2316 unsigned n_row, unsigned n_col);
2317 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2318 void isl_mat_free(__isl_take isl_mat *mat);
2320 Note that the elements of a newly created matrix may have arbitrary values.
2321 The elements can be changed and inspected using the following functions.
2323 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2324 int isl_mat_rows(__isl_keep isl_mat *mat);
2325 int isl_mat_cols(__isl_keep isl_mat *mat);
2326 int isl_mat_get_element(__isl_keep isl_mat *mat,
2327 int row, int col, isl_int *v);
2328 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2329 int row, int col, isl_int v);
2330 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2331 int row, int col, int v);
2333 C<isl_mat_get_element> will return a negative value if anything went wrong.
2334 In that case, the value of C<*v> is undefined.
2336 The following function can be used to compute the (right) inverse
2337 of a matrix, i.e., a matrix such that the product of the original
2338 and the inverse (in that order) is a multiple of the identity matrix.
2339 The input matrix is assumed to be of full row-rank.
2341 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2343 The following function can be used to compute the (right) kernel
2344 (or null space) of a matrix, i.e., a matrix such that the product of
2345 the original and the kernel (in that order) is the zero matrix.
2347 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2349 =head2 Piecewise Quasi Affine Expressions
2351 The zero quasi affine expression can be created using
2353 __isl_give isl_aff *isl_aff_zero(
2354 __isl_take isl_local_space *ls);
2356 A quasi affine expression can also be initialized from an C<isl_div>:
2358 #include <isl/div.h>
2359 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2361 An empty piecewise quasi affine expression (one with no cells)
2362 or a piecewise quasi affine expression with a single cell can
2363 be created using the following functions.
2365 #include <isl/aff.h>
2366 __isl_give isl_pw_aff *isl_pw_aff_empty(
2367 __isl_take isl_dim *dim);
2368 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2369 __isl_take isl_set *set, __isl_take isl_aff *aff);
2370 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2371 __isl_take isl_aff *aff);
2373 Quasi affine expressions can be copied and freed using
2375 #include <isl/aff.h>
2376 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2377 void *isl_aff_free(__isl_take isl_aff *aff);
2379 __isl_give isl_pw_aff *isl_pw_aff_copy(
2380 __isl_keep isl_pw_aff *pwaff);
2381 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2383 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2384 using the following function. The constraint is required to have
2385 a non-zero coefficient for the specified dimension.
2387 #include <isl/constraint.h>
2388 __isl_give isl_aff *isl_constraint_get_bound(
2389 __isl_keep isl_constraint *constraint,
2390 enum isl_dim_type type, int pos);
2392 The entire affine expression of the constraint can also be extracted
2393 using the following function.
2395 #include <isl/constraint.h>
2396 __isl_give isl_aff *isl_constraint_get_aff(
2397 __isl_keep isl_constraint *constraint);
2399 Conversely, an equality constraint equating
2400 the affine expression to zero or an inequality constraint enforcing
2401 the affine expression to be non-negative, can be constructed using
2403 __isl_give isl_constraint *isl_equality_from_aff(
2404 __isl_take isl_aff *aff);
2405 __isl_give isl_constraint *isl_inequality_from_aff(
2406 __isl_take isl_aff *aff);
2408 The expression can be inspected using
2410 #include <isl/aff.h>
2411 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2412 int isl_aff_dim(__isl_keep isl_aff *aff,
2413 enum isl_dim_type type);
2414 __isl_give isl_local_space *isl_aff_get_local_space(
2415 __isl_keep isl_aff *aff);
2416 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2417 enum isl_dim_type type, unsigned pos);
2418 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2420 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2421 enum isl_dim_type type, int pos, isl_int *v);
2422 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2424 __isl_give isl_div *isl_aff_get_div(
2425 __isl_keep isl_aff *aff, int pos);
2427 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2428 int (*fn)(__isl_take isl_set *set,
2429 __isl_take isl_aff *aff,
2430 void *user), void *user);
2432 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2433 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2435 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2436 enum isl_dim_type type, unsigned first, unsigned n);
2437 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2438 enum isl_dim_type type, unsigned first, unsigned n);
2440 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2441 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2442 enum isl_dim_type type);
2443 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2445 It can be modified using
2447 #include <isl/aff.h>
2448 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2449 __isl_take isl_pw_aff *pwaff,
2450 __isl_take isl_id *id);
2451 __isl_give isl_aff *isl_aff_set_dim_name(
2452 __isl_take isl_aff *aff, enum isl_dim_type type,
2453 unsigned pos, const char *s);
2454 __isl_give isl_aff *isl_aff_set_constant(
2455 __isl_take isl_aff *aff, isl_int v);
2456 __isl_give isl_aff *isl_aff_set_constant_si(
2457 __isl_take isl_aff *aff, int v);
2458 __isl_give isl_aff *isl_aff_set_coefficient(
2459 __isl_take isl_aff *aff,
2460 enum isl_dim_type type, int pos, isl_int v);
2461 __isl_give isl_aff *isl_aff_set_coefficient_si(
2462 __isl_take isl_aff *aff,
2463 enum isl_dim_type type, int pos, int v);
2464 __isl_give isl_aff *isl_aff_set_denominator(
2465 __isl_take isl_aff *aff, isl_int v);
2467 __isl_give isl_aff *isl_aff_add_constant(
2468 __isl_take isl_aff *aff, isl_int v);
2469 __isl_give isl_aff *isl_aff_add_constant_si(
2470 __isl_take isl_aff *aff, int v);
2471 __isl_give isl_aff *isl_aff_add_coefficient(
2472 __isl_take isl_aff *aff,
2473 enum isl_dim_type type, int pos, isl_int v);
2474 __isl_give isl_aff *isl_aff_add_coefficient_si(
2475 __isl_take isl_aff *aff,
2476 enum isl_dim_type type, int pos, int v);
2478 __isl_give isl_aff *isl_aff_insert_dims(
2479 __isl_take isl_aff *aff,
2480 enum isl_dim_type type, unsigned first, unsigned n);
2481 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2482 __isl_take isl_pw_aff *pwaff,
2483 enum isl_dim_type type, unsigned first, unsigned n);
2484 __isl_give isl_aff *isl_aff_add_dims(
2485 __isl_take isl_aff *aff,
2486 enum isl_dim_type type, unsigned n);
2487 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2488 __isl_take isl_pw_aff *pwaff,
2489 enum isl_dim_type type, unsigned n);
2490 __isl_give isl_aff *isl_aff_drop_dims(
2491 __isl_take isl_aff *aff,
2492 enum isl_dim_type type, unsigned first, unsigned n);
2493 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2494 __isl_take isl_pw_aff *pwaff,
2495 enum isl_dim_type type, unsigned first, unsigned n);
2497 Note that the C<set_constant> and C<set_coefficient> functions
2498 set the I<numerator> of the constant or coefficient, while
2499 C<add_constant> and C<add_coefficient> add an integer value to
2500 the possibly rational constant or coefficient.
2502 To check whether an affine expressions is obviously zero
2503 or obviously equal to some other affine expression, use
2505 #include <isl/aff.h>
2506 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2507 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2508 __isl_keep isl_aff *aff2);
2512 #include <isl/aff.h>
2513 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2514 __isl_take isl_aff *aff2);
2515 __isl_give isl_pw_aff *isl_pw_aff_add(
2516 __isl_take isl_pw_aff *pwaff1,
2517 __isl_take isl_pw_aff *pwaff2);
2518 __isl_give isl_pw_aff *isl_pw_aff_min(
2519 __isl_take isl_pw_aff *pwaff1,
2520 __isl_take isl_pw_aff *pwaff2);
2521 __isl_give isl_pw_aff *isl_pw_aff_max(
2522 __isl_take isl_pw_aff *pwaff1,
2523 __isl_take isl_pw_aff *pwaff2);
2524 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2525 __isl_take isl_aff *aff2);
2526 __isl_give isl_pw_aff *isl_pw_aff_sub(
2527 __isl_take isl_pw_aff *pwaff1,
2528 __isl_take isl_pw_aff *pwaff2);
2529 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2530 __isl_give isl_pw_aff *isl_pw_aff_neg(
2531 __isl_take isl_pw_aff *pwaff);
2532 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2533 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2534 __isl_take isl_pw_aff *pwaff);
2535 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2536 __isl_give isl_pw_aff *isl_pw_aff_floor(
2537 __isl_take isl_pw_aff *pwaff);
2538 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2540 __isl_give isl_pw_aff *isl_pw_aff_mod(
2541 __isl_take isl_pw_aff *pwaff, isl_int mod);
2542 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2544 __isl_give isl_pw_aff *isl_pw_aff_scale(
2545 __isl_take isl_pw_aff *pwaff, isl_int f);
2546 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2548 __isl_give isl_aff *isl_aff_scale_down_ui(
2549 __isl_take isl_aff *aff, unsigned f);
2550 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2551 __isl_take isl_pw_aff *pwaff, isl_int f);
2553 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2554 __isl_take isl_pw_aff_list *list);
2555 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2556 __isl_take isl_pw_aff_list *list);
2558 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2559 __isl_take isl_pw_aff *pwqp);
2561 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2562 __isl_take isl_pw_aff *pwaff,
2563 __isl_take isl_dim *model);
2565 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2566 __isl_take isl_set *context);
2567 __isl_give isl_pw_aff *isl_pw_aff_gist(
2568 __isl_take isl_pw_aff *pwaff,
2569 __isl_take isl_set *context);
2571 __isl_give isl_set *isl_pw_aff_domain(
2572 __isl_take isl_pw_aff *pwaff);
2574 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2575 __isl_take isl_aff *aff2);
2576 __isl_give isl_pw_aff *isl_pw_aff_mul(
2577 __isl_take isl_pw_aff *pwaff1,
2578 __isl_take isl_pw_aff *pwaff2);
2580 When multiplying two affine expressions, at least one of the two needs
2583 #include <isl/aff.h>
2584 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2585 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2586 __isl_give isl_set *isl_pw_aff_eq_set(
2587 __isl_take isl_pw_aff *pwaff1,
2588 __isl_take isl_pw_aff *pwaff2);
2589 __isl_give isl_set *isl_pw_aff_ne_set(
2590 __isl_take isl_pw_aff *pwaff1,
2591 __isl_take isl_pw_aff *pwaff2);
2592 __isl_give isl_set *isl_pw_aff_le_set(
2593 __isl_take isl_pw_aff *pwaff1,
2594 __isl_take isl_pw_aff *pwaff2);
2595 __isl_give isl_set *isl_pw_aff_lt_set(
2596 __isl_take isl_pw_aff *pwaff1,
2597 __isl_take isl_pw_aff *pwaff2);
2598 __isl_give isl_set *isl_pw_aff_ge_set(
2599 __isl_take isl_pw_aff *pwaff1,
2600 __isl_take isl_pw_aff *pwaff2);
2601 __isl_give isl_set *isl_pw_aff_gt_set(
2602 __isl_take isl_pw_aff *pwaff1,
2603 __isl_take isl_pw_aff *pwaff2);
2605 __isl_give isl_set *isl_pw_aff_list_eq_set(
2606 __isl_take isl_pw_aff_list *list1,
2607 __isl_take isl_pw_aff_list *list2);
2608 __isl_give isl_set *isl_pw_aff_list_ne_set(
2609 __isl_take isl_pw_aff_list *list1,
2610 __isl_take isl_pw_aff_list *list2);
2611 __isl_give isl_set *isl_pw_aff_list_le_set(
2612 __isl_take isl_pw_aff_list *list1,
2613 __isl_take isl_pw_aff_list *list2);
2614 __isl_give isl_set *isl_pw_aff_list_lt_set(
2615 __isl_take isl_pw_aff_list *list1,
2616 __isl_take isl_pw_aff_list *list2);
2617 __isl_give isl_set *isl_pw_aff_list_ge_set(
2618 __isl_take isl_pw_aff_list *list1,
2619 __isl_take isl_pw_aff_list *list2);
2620 __isl_give isl_set *isl_pw_aff_list_gt_set(
2621 __isl_take isl_pw_aff_list *list1,
2622 __isl_take isl_pw_aff_list *list2);
2624 The function C<isl_aff_ge_basic_set> returns a basic set
2625 containing those elements in the shared space
2626 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2627 The function C<isl_aff_ge_set> returns a set
2628 containing those elements in the shared domain
2629 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2630 The functions operating on C<isl_pw_aff_list> apply the corresponding
2631 C<isl_pw_aff> function to each pair of elements in the two lists.
2633 #include <isl/aff.h>
2634 __isl_give isl_set *isl_pw_aff_nonneg_set(
2635 __isl_take isl_pw_aff *pwaff);
2636 __isl_give isl_set *isl_pw_aff_zero_set(
2637 __isl_take isl_pw_aff *pwaff);
2638 __isl_give isl_set *isl_pw_aff_non_zero_set(
2639 __isl_take isl_pw_aff *pwaff);
2641 The function C<isl_pw_aff_nonneg_set> returns a set
2642 containing those elements in the domain
2643 of C<pwaff> where C<pwaff> is non-negative.
2645 #include <isl/aff.h>
2646 __isl_give isl_pw_aff *isl_pw_aff_cond(
2647 __isl_take isl_set *cond,
2648 __isl_take isl_pw_aff *pwaff_true,
2649 __isl_take isl_pw_aff *pwaff_false);
2651 The function C<isl_pw_aff_cond> performs a conditional operator
2652 and returns an expression that is equal to C<pwaff_true>
2653 for elements in C<cond> and equal to C<pwaff_false> for elements
2656 #include <isl/aff.h>
2657 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2658 __isl_take isl_pw_aff *pwaff1,
2659 __isl_take isl_pw_aff *pwaff2);
2661 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2662 expression with a domain that is the union of those of C<pwaff1> and
2663 C<pwaff2> and such that on each cell, the quasi-affine expression is
2664 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2665 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2666 associated expression is the defined one.
2668 An expression can be printed using
2670 #include <isl/aff.h>
2671 __isl_give isl_printer *isl_printer_print_aff(
2672 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2674 __isl_give isl_printer *isl_printer_print_pw_aff(
2675 __isl_take isl_printer *p,
2676 __isl_keep isl_pw_aff *pwaff);
2680 Points are elements of a set. They can be used to construct
2681 simple sets (boxes) or they can be used to represent the
2682 individual elements of a set.
2683 The zero point (the origin) can be created using
2685 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2687 The coordinates of a point can be inspected, set and changed
2690 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2691 enum isl_dim_type type, int pos, isl_int *v);
2692 __isl_give isl_point *isl_point_set_coordinate(
2693 __isl_take isl_point *pnt,
2694 enum isl_dim_type type, int pos, isl_int v);
2696 __isl_give isl_point *isl_point_add_ui(
2697 __isl_take isl_point *pnt,
2698 enum isl_dim_type type, int pos, unsigned val);
2699 __isl_give isl_point *isl_point_sub_ui(
2700 __isl_take isl_point *pnt,
2701 enum isl_dim_type type, int pos, unsigned val);
2703 Other properties can be obtained using
2705 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2707 Points can be copied or freed using
2709 __isl_give isl_point *isl_point_copy(
2710 __isl_keep isl_point *pnt);
2711 void isl_point_free(__isl_take isl_point *pnt);
2713 A singleton set can be created from a point using
2715 __isl_give isl_basic_set *isl_basic_set_from_point(
2716 __isl_take isl_point *pnt);
2717 __isl_give isl_set *isl_set_from_point(
2718 __isl_take isl_point *pnt);
2720 and a box can be created from two opposite extremal points using
2722 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2723 __isl_take isl_point *pnt1,
2724 __isl_take isl_point *pnt2);
2725 __isl_give isl_set *isl_set_box_from_points(
2726 __isl_take isl_point *pnt1,
2727 __isl_take isl_point *pnt2);
2729 All elements of a B<bounded> (union) set can be enumerated using
2730 the following functions.
2732 int isl_set_foreach_point(__isl_keep isl_set *set,
2733 int (*fn)(__isl_take isl_point *pnt, void *user),
2735 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2736 int (*fn)(__isl_take isl_point *pnt, void *user),
2739 The function C<fn> is called for each integer point in
2740 C<set> with as second argument the last argument of
2741 the C<isl_set_foreach_point> call. The function C<fn>
2742 should return C<0> on success and C<-1> on failure.
2743 In the latter case, C<isl_set_foreach_point> will stop
2744 enumerating and return C<-1> as well.
2745 If the enumeration is performed successfully and to completion,
2746 then C<isl_set_foreach_point> returns C<0>.
2748 To obtain a single point of a (basic) set, use
2750 __isl_give isl_point *isl_basic_set_sample_point(
2751 __isl_take isl_basic_set *bset);
2752 __isl_give isl_point *isl_set_sample_point(
2753 __isl_take isl_set *set);
2755 If C<set> does not contain any (integer) points, then the
2756 resulting point will be ``void'', a property that can be
2759 int isl_point_is_void(__isl_keep isl_point *pnt);
2761 =head2 Piecewise Quasipolynomials
2763 A piecewise quasipolynomial is a particular kind of function that maps
2764 a parametric point to a rational value.
2765 More specifically, a quasipolynomial is a polynomial expression in greatest
2766 integer parts of affine expressions of parameters and variables.
2767 A piecewise quasipolynomial is a subdivision of a given parametric
2768 domain into disjoint cells with a quasipolynomial associated to
2769 each cell. The value of the piecewise quasipolynomial at a given
2770 point is the value of the quasipolynomial associated to the cell
2771 that contains the point. Outside of the union of cells,
2772 the value is assumed to be zero.
2773 For example, the piecewise quasipolynomial
2775 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2777 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2778 A given piecewise quasipolynomial has a fixed domain dimension.
2779 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2780 defined over different domains.
2781 Piecewise quasipolynomials are mainly used by the C<barvinok>
2782 library for representing the number of elements in a parametric set or map.
2783 For example, the piecewise quasipolynomial above represents
2784 the number of points in the map
2786 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2788 =head3 Printing (Piecewise) Quasipolynomials
2790 Quasipolynomials and piecewise quasipolynomials can be printed
2791 using the following functions.
2793 __isl_give isl_printer *isl_printer_print_qpolynomial(
2794 __isl_take isl_printer *p,
2795 __isl_keep isl_qpolynomial *qp);
2797 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2798 __isl_take isl_printer *p,
2799 __isl_keep isl_pw_qpolynomial *pwqp);
2801 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2802 __isl_take isl_printer *p,
2803 __isl_keep isl_union_pw_qpolynomial *upwqp);
2805 The output format of the printer
2806 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2807 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2809 In case of printing in C<ISL_FORMAT_C>, the user may want
2810 to set the names of all dimensions
2812 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2813 __isl_take isl_qpolynomial *qp,
2814 enum isl_dim_type type, unsigned pos,
2816 __isl_give isl_pw_qpolynomial *
2817 isl_pw_qpolynomial_set_dim_name(
2818 __isl_take isl_pw_qpolynomial *pwqp,
2819 enum isl_dim_type type, unsigned pos,
2822 =head3 Creating New (Piecewise) Quasipolynomials
2824 Some simple quasipolynomials can be created using the following functions.
2825 More complicated quasipolynomials can be created by applying
2826 operations such as addition and multiplication
2827 on the resulting quasipolynomials
2829 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2830 __isl_take isl_dim *dim);
2831 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2832 __isl_take isl_dim *dim);
2833 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2834 __isl_take isl_dim *dim);
2835 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2836 __isl_take isl_dim *dim);
2837 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2838 __isl_take isl_dim *dim);
2839 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2840 __isl_take isl_dim *dim,
2841 const isl_int n, const isl_int d);
2842 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2843 __isl_take isl_div *div);
2844 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2845 __isl_take isl_dim *dim,
2846 enum isl_dim_type type, unsigned pos);
2847 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2848 __isl_take isl_aff *aff);
2850 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2851 with a single cell can be created using the following functions.
2852 Multiple of these single cell piecewise quasipolynomials can
2853 be combined to create more complicated piecewise quasipolynomials.
2855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2856 __isl_take isl_dim *dim);
2857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2858 __isl_take isl_set *set,
2859 __isl_take isl_qpolynomial *qp);
2860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2861 __isl_take isl_qpolynomial *qp);
2862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2863 __isl_take isl_pw_aff *pwaff);
2865 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2866 __isl_take isl_dim *dim);
2867 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2868 __isl_take isl_pw_qpolynomial *pwqp);
2869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2870 __isl_take isl_union_pw_qpolynomial *upwqp,
2871 __isl_take isl_pw_qpolynomial *pwqp);
2873 Quasipolynomials can be copied and freed again using the following
2876 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2877 __isl_keep isl_qpolynomial *qp);
2878 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2881 __isl_keep isl_pw_qpolynomial *pwqp);
2882 void *isl_pw_qpolynomial_free(
2883 __isl_take isl_pw_qpolynomial *pwqp);
2885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2886 __isl_keep isl_union_pw_qpolynomial *upwqp);
2887 void isl_union_pw_qpolynomial_free(
2888 __isl_take isl_union_pw_qpolynomial *upwqp);
2890 =head3 Inspecting (Piecewise) Quasipolynomials
2892 To iterate over all piecewise quasipolynomials in a union
2893 piecewise quasipolynomial, use the following function
2895 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2896 __isl_keep isl_union_pw_qpolynomial *upwqp,
2897 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2900 To extract the piecewise quasipolynomial from a union with a given dimension
2903 __isl_give isl_pw_qpolynomial *
2904 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2905 __isl_keep isl_union_pw_qpolynomial *upwqp,
2906 __isl_take isl_dim *dim);
2908 To iterate over the cells in a piecewise quasipolynomial,
2909 use either of the following two functions
2911 int isl_pw_qpolynomial_foreach_piece(
2912 __isl_keep isl_pw_qpolynomial *pwqp,
2913 int (*fn)(__isl_take isl_set *set,
2914 __isl_take isl_qpolynomial *qp,
2915 void *user), void *user);
2916 int isl_pw_qpolynomial_foreach_lifted_piece(
2917 __isl_keep isl_pw_qpolynomial *pwqp,
2918 int (*fn)(__isl_take isl_set *set,
2919 __isl_take isl_qpolynomial *qp,
2920 void *user), void *user);
2922 As usual, the function C<fn> should return C<0> on success
2923 and C<-1> on failure. The difference between
2924 C<isl_pw_qpolynomial_foreach_piece> and
2925 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2926 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2927 compute unique representations for all existentially quantified
2928 variables and then turn these existentially quantified variables
2929 into extra set variables, adapting the associated quasipolynomial
2930 accordingly. This means that the C<set> passed to C<fn>
2931 will not have any existentially quantified variables, but that
2932 the dimensions of the sets may be different for different
2933 invocations of C<fn>.
2935 To iterate over all terms in a quasipolynomial,
2938 int isl_qpolynomial_foreach_term(
2939 __isl_keep isl_qpolynomial *qp,
2940 int (*fn)(__isl_take isl_term *term,
2941 void *user), void *user);
2943 The terms themselves can be inspected and freed using
2946 unsigned isl_term_dim(__isl_keep isl_term *term,
2947 enum isl_dim_type type);
2948 void isl_term_get_num(__isl_keep isl_term *term,
2950 void isl_term_get_den(__isl_keep isl_term *term,
2952 int isl_term_get_exp(__isl_keep isl_term *term,
2953 enum isl_dim_type type, unsigned pos);
2954 __isl_give isl_div *isl_term_get_div(
2955 __isl_keep isl_term *term, unsigned pos);
2956 void isl_term_free(__isl_take isl_term *term);
2958 Each term is a product of parameters, set variables and
2959 integer divisions. The function C<isl_term_get_exp>
2960 returns the exponent of a given dimensions in the given term.
2961 The C<isl_int>s in the arguments of C<isl_term_get_num>
2962 and C<isl_term_get_den> need to have been initialized
2963 using C<isl_int_init> before calling these functions.
2965 =head3 Properties of (Piecewise) Quasipolynomials
2967 To check whether a quasipolynomial is actually a constant,
2968 use the following function.
2970 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2971 isl_int *n, isl_int *d);
2973 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2974 then the numerator and denominator of the constant
2975 are returned in C<*n> and C<*d>, respectively.
2977 =head3 Operations on (Piecewise) Quasipolynomials
2979 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2980 __isl_take isl_qpolynomial *qp, isl_int v);
2981 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2982 __isl_take isl_qpolynomial *qp);
2983 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2984 __isl_take isl_qpolynomial *qp1,
2985 __isl_take isl_qpolynomial *qp2);
2986 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2987 __isl_take isl_qpolynomial *qp1,
2988 __isl_take isl_qpolynomial *qp2);
2989 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2990 __isl_take isl_qpolynomial *qp1,
2991 __isl_take isl_qpolynomial *qp2);
2992 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2993 __isl_take isl_qpolynomial *qp, unsigned exponent);
2995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2996 __isl_take isl_pw_qpolynomial *pwqp1,
2997 __isl_take isl_pw_qpolynomial *pwqp2);
2998 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2999 __isl_take isl_pw_qpolynomial *pwqp1,
3000 __isl_take isl_pw_qpolynomial *pwqp2);
3001 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3002 __isl_take isl_pw_qpolynomial *pwqp1,
3003 __isl_take isl_pw_qpolynomial *pwqp2);
3004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3005 __isl_take isl_pw_qpolynomial *pwqp);
3006 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3007 __isl_take isl_pw_qpolynomial *pwqp1,
3008 __isl_take isl_pw_qpolynomial *pwqp2);
3009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3010 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3012 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3013 __isl_take isl_union_pw_qpolynomial *upwqp1,
3014 __isl_take isl_union_pw_qpolynomial *upwqp2);
3015 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3016 __isl_take isl_union_pw_qpolynomial *upwqp1,
3017 __isl_take isl_union_pw_qpolynomial *upwqp2);
3018 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3019 __isl_take isl_union_pw_qpolynomial *upwqp1,
3020 __isl_take isl_union_pw_qpolynomial *upwqp2);
3022 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3023 __isl_take isl_pw_qpolynomial *pwqp,
3024 __isl_take isl_point *pnt);
3026 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3027 __isl_take isl_union_pw_qpolynomial *upwqp,
3028 __isl_take isl_point *pnt);
3030 __isl_give isl_set *isl_pw_qpolynomial_domain(
3031 __isl_take isl_pw_qpolynomial *pwqp);
3032 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3033 __isl_take isl_pw_qpolynomial *pwpq,
3034 __isl_take isl_set *set);
3036 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3037 __isl_take isl_union_pw_qpolynomial *upwqp);
3038 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3039 __isl_take isl_union_pw_qpolynomial *upwpq,
3040 __isl_take isl_union_set *uset);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3043 __isl_take isl_qpolynomial *qp,
3044 __isl_take isl_dim *model);
3046 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3047 __isl_take isl_union_pw_qpolynomial *upwqp);
3049 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3050 __isl_take isl_qpolynomial *qp,
3051 __isl_take isl_set *context);
3053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3054 __isl_take isl_pw_qpolynomial *pwqp,
3055 __isl_take isl_set *context);
3057 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3058 __isl_take isl_union_pw_qpolynomial *upwqp,
3059 __isl_take isl_union_set *context);
3061 The gist operation applies the gist operation to each of
3062 the cells in the domain of the input piecewise quasipolynomial.
3063 The context is also exploited
3064 to simplify the quasipolynomials associated to each cell.
3066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3067 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3068 __isl_give isl_union_pw_qpolynomial *
3069 isl_union_pw_qpolynomial_to_polynomial(
3070 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3072 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3073 the polynomial will be an overapproximation. If C<sign> is negative,
3074 it will be an underapproximation. If C<sign> is zero, the approximation
3075 will lie somewhere in between.
3077 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3079 A piecewise quasipolynomial reduction is a piecewise
3080 reduction (or fold) of quasipolynomials.
3081 In particular, the reduction can be maximum or a minimum.
3082 The objects are mainly used to represent the result of
3083 an upper or lower bound on a quasipolynomial over its domain,
3084 i.e., as the result of the following function.
3086 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3087 __isl_take isl_pw_qpolynomial *pwqp,
3088 enum isl_fold type, int *tight);
3090 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3091 __isl_take isl_union_pw_qpolynomial *upwqp,
3092 enum isl_fold type, int *tight);
3094 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3095 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3096 is the returned bound is known be tight, i.e., for each value
3097 of the parameters there is at least
3098 one element in the domain that reaches the bound.
3099 If the domain of C<pwqp> is not wrapping, then the bound is computed
3100 over all elements in that domain and the result has a purely parametric
3101 domain. If the domain of C<pwqp> is wrapping, then the bound is
3102 computed over the range of the wrapped relation. The domain of the
3103 wrapped relation becomes the domain of the result.
3105 A (piecewise) quasipolynomial reduction can be copied or freed using the
3106 following functions.
3108 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3109 __isl_keep isl_qpolynomial_fold *fold);
3110 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3111 __isl_keep isl_pw_qpolynomial_fold *pwf);
3112 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3113 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3114 void isl_qpolynomial_fold_free(
3115 __isl_take isl_qpolynomial_fold *fold);
3116 void *isl_pw_qpolynomial_fold_free(
3117 __isl_take isl_pw_qpolynomial_fold *pwf);
3118 void isl_union_pw_qpolynomial_fold_free(
3119 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3121 =head3 Printing Piecewise Quasipolynomial Reductions
3123 Piecewise quasipolynomial reductions can be printed
3124 using the following function.
3126 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3127 __isl_take isl_printer *p,
3128 __isl_keep isl_pw_qpolynomial_fold *pwf);
3129 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3130 __isl_take isl_printer *p,
3131 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3133 For C<isl_printer_print_pw_qpolynomial_fold>,
3134 output format of the printer
3135 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3136 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3137 output format of the printer
3138 needs to be set to C<ISL_FORMAT_ISL>.
3139 In case of printing in C<ISL_FORMAT_C>, the user may want
3140 to set the names of all dimensions
3142 __isl_give isl_pw_qpolynomial_fold *
3143 isl_pw_qpolynomial_fold_set_dim_name(
3144 __isl_take isl_pw_qpolynomial_fold *pwf,
3145 enum isl_dim_type type, unsigned pos,
3148 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3150 To iterate over all piecewise quasipolynomial reductions in a union
3151 piecewise quasipolynomial reduction, use the following function
3153 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3154 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3155 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3156 void *user), void *user);
3158 To iterate over the cells in a piecewise quasipolynomial reduction,
3159 use either of the following two functions
3161 int isl_pw_qpolynomial_fold_foreach_piece(
3162 __isl_keep isl_pw_qpolynomial_fold *pwf,
3163 int (*fn)(__isl_take isl_set *set,
3164 __isl_take isl_qpolynomial_fold *fold,
3165 void *user), void *user);
3166 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3167 __isl_keep isl_pw_qpolynomial_fold *pwf,
3168 int (*fn)(__isl_take isl_set *set,
3169 __isl_take isl_qpolynomial_fold *fold,
3170 void *user), void *user);
3172 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3173 of the difference between these two functions.
3175 To iterate over all quasipolynomials in a reduction, use
3177 int isl_qpolynomial_fold_foreach_qpolynomial(
3178 __isl_keep isl_qpolynomial_fold *fold,
3179 int (*fn)(__isl_take isl_qpolynomial *qp,
3180 void *user), void *user);
3182 =head3 Operations on Piecewise Quasipolynomial Reductions
3184 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3185 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3187 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3188 __isl_take isl_pw_qpolynomial_fold *pwf1,
3189 __isl_take isl_pw_qpolynomial_fold *pwf2);
3191 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3192 __isl_take isl_pw_qpolynomial_fold *pwf1,
3193 __isl_take isl_pw_qpolynomial_fold *pwf2);
3195 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3196 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3197 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3199 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3200 __isl_take isl_pw_qpolynomial_fold *pwf,
3201 __isl_take isl_point *pnt);
3203 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3204 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3205 __isl_take isl_point *pnt);
3207 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3208 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3209 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3210 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3211 __isl_take isl_union_set *uset);
3213 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3214 __isl_take isl_pw_qpolynomial_fold *pwf);
3216 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3217 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3219 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3220 __isl_take isl_pw_qpolynomial_fold *pwf,
3221 __isl_take isl_set *context);
3223 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3224 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3225 __isl_take isl_union_set *context);
3227 The gist operation applies the gist operation to each of
3228 the cells in the domain of the input piecewise quasipolynomial reduction.
3229 In future, the operation will also exploit the context
3230 to simplify the quasipolynomial reductions associated to each cell.
3232 __isl_give isl_pw_qpolynomial_fold *
3233 isl_set_apply_pw_qpolynomial_fold(
3234 __isl_take isl_set *set,
3235 __isl_take isl_pw_qpolynomial_fold *pwf,
3237 __isl_give isl_pw_qpolynomial_fold *
3238 isl_map_apply_pw_qpolynomial_fold(
3239 __isl_take isl_map *map,
3240 __isl_take isl_pw_qpolynomial_fold *pwf,
3242 __isl_give isl_union_pw_qpolynomial_fold *
3243 isl_union_set_apply_union_pw_qpolynomial_fold(
3244 __isl_take isl_union_set *uset,
3245 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3247 __isl_give isl_union_pw_qpolynomial_fold *
3248 isl_union_map_apply_union_pw_qpolynomial_fold(
3249 __isl_take isl_union_map *umap,
3250 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3253 The functions taking a map
3254 compose the given map with the given piecewise quasipolynomial reduction.
3255 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3256 over all elements in the intersection of the range of the map
3257 and the domain of the piecewise quasipolynomial reduction
3258 as a function of an element in the domain of the map.
3259 The functions taking a set compute a bound over all elements in the
3260 intersection of the set and the domain of the
3261 piecewise quasipolynomial reduction.
3263 =head2 Dependence Analysis
3265 C<isl> contains specialized functionality for performing
3266 array dataflow analysis. That is, given a I<sink> access relation
3267 and a collection of possible I<source> access relations,
3268 C<isl> can compute relations that describe
3269 for each iteration of the sink access, which iteration
3270 of which of the source access relations was the last
3271 to access the same data element before the given iteration
3273 To compute standard flow dependences, the sink should be
3274 a read, while the sources should be writes.
3275 If any of the source accesses are marked as being I<may>
3276 accesses, then there will be a dependence to the last
3277 I<must> access B<and> to any I<may> access that follows
3278 this last I<must> access.
3279 In particular, if I<all> sources are I<may> accesses,
3280 then memory based dependence analysis is performed.
3281 If, on the other hand, all sources are I<must> accesses,
3282 then value based dependence analysis is performed.
3284 #include <isl/flow.h>
3286 typedef int (*isl_access_level_before)(void *first, void *second);
3288 __isl_give isl_access_info *isl_access_info_alloc(
3289 __isl_take isl_map *sink,
3290 void *sink_user, isl_access_level_before fn,
3292 __isl_give isl_access_info *isl_access_info_add_source(
3293 __isl_take isl_access_info *acc,
3294 __isl_take isl_map *source, int must,
3296 void isl_access_info_free(__isl_take isl_access_info *acc);
3298 __isl_give isl_flow *isl_access_info_compute_flow(
3299 __isl_take isl_access_info *acc);
3301 int isl_flow_foreach(__isl_keep isl_flow *deps,
3302 int (*fn)(__isl_take isl_map *dep, int must,
3303 void *dep_user, void *user),
3305 __isl_give isl_map *isl_flow_get_no_source(
3306 __isl_keep isl_flow *deps, int must);
3307 void isl_flow_free(__isl_take isl_flow *deps);
3309 The function C<isl_access_info_compute_flow> performs the actual
3310 dependence analysis. The other functions are used to construct
3311 the input for this function or to read off the output.
3313 The input is collected in an C<isl_access_info>, which can
3314 be created through a call to C<isl_access_info_alloc>.
3315 The arguments to this functions are the sink access relation
3316 C<sink>, a token C<sink_user> used to identify the sink
3317 access to the user, a callback function for specifying the
3318 relative order of source and sink accesses, and the number
3319 of source access relations that will be added.
3320 The callback function has type C<int (*)(void *first, void *second)>.
3321 The function is called with two user supplied tokens identifying
3322 either a source or the sink and it should return the shared nesting
3323 level and the relative order of the two accesses.
3324 In particular, let I<n> be the number of loops shared by
3325 the two accesses. If C<first> precedes C<second> textually,
3326 then the function should return I<2 * n + 1>; otherwise,
3327 it should return I<2 * n>.
3328 The sources can be added to the C<isl_access_info> by performing
3329 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3330 C<must> indicates whether the source is a I<must> access
3331 or a I<may> access. Note that a multi-valued access relation
3332 should only be marked I<must> if every iteration in the domain
3333 of the relation accesses I<all> elements in its image.
3334 The C<source_user> token is again used to identify
3335 the source access. The range of the source access relation
3336 C<source> should have the same dimension as the range
3337 of the sink access relation.
3338 The C<isl_access_info_free> function should usually not be
3339 called explicitly, because it is called implicitly by
3340 C<isl_access_info_compute_flow>.
3342 The result of the dependence analysis is collected in an
3343 C<isl_flow>. There may be elements of
3344 the sink access for which no preceding source access could be
3345 found or for which all preceding sources are I<may> accesses.
3346 The relations containing these elements can be obtained through
3347 calls to C<isl_flow_get_no_source>, the first with C<must> set
3348 and the second with C<must> unset.
3349 In the case of standard flow dependence analysis,
3350 with the sink a read and the sources I<must> writes,
3351 the first relation corresponds to the reads from uninitialized
3352 array elements and the second relation is empty.
3353 The actual flow dependences can be extracted using
3354 C<isl_flow_foreach>. This function will call the user-specified
3355 callback function C<fn> for each B<non-empty> dependence between
3356 a source and the sink. The callback function is called
3357 with four arguments, the actual flow dependence relation
3358 mapping source iterations to sink iterations, a boolean that
3359 indicates whether it is a I<must> or I<may> dependence, a token
3360 identifying the source and an additional C<void *> with value
3361 equal to the third argument of the C<isl_flow_foreach> call.
3362 A dependence is marked I<must> if it originates from a I<must>
3363 source and if it is not followed by any I<may> sources.
3365 After finishing with an C<isl_flow>, the user should call
3366 C<isl_flow_free> to free all associated memory.
3368 A higher-level interface to dependence analysis is provided
3369 by the following function.
3371 #include <isl/flow.h>
3373 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3374 __isl_take isl_union_map *must_source,
3375 __isl_take isl_union_map *may_source,
3376 __isl_take isl_union_map *schedule,
3377 __isl_give isl_union_map **must_dep,
3378 __isl_give isl_union_map **may_dep,
3379 __isl_give isl_union_map **must_no_source,
3380 __isl_give isl_union_map **may_no_source);
3382 The arrays are identified by the tuple names of the ranges
3383 of the accesses. The iteration domains by the tuple names
3384 of the domains of the accesses and of the schedule.
3385 The relative order of the iteration domains is given by the
3386 schedule. The relations returned through C<must_no_source>
3387 and C<may_no_source> are subsets of C<sink>.
3388 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3389 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3390 any of the other arguments is treated as an error.
3394 B<The functionality described in this section is fairly new
3395 and may be subject to change.>
3397 The following function can be used to compute a schedule
3398 for a union of domains. The generated schedule respects
3399 all C<validity> dependences. That is, all dependence distances
3400 over these dependences in the scheduled space are lexicographically
3401 positive. The generated schedule schedule also tries to minimize
3402 the dependence distances over C<proximity> dependences.
3403 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3404 for groups of domains where the dependence distances have only
3405 non-negative values.
3406 The algorithm used to construct the schedule is similar to that
3409 #include <isl/schedule.h>
3410 __isl_give isl_schedule *isl_union_set_compute_schedule(
3411 __isl_take isl_union_set *domain,
3412 __isl_take isl_union_map *validity,
3413 __isl_take isl_union_map *proximity);
3414 void *isl_schedule_free(__isl_take isl_schedule *sched);
3416 A mapping from the domains to the scheduled space can be obtained
3417 from an C<isl_schedule> using the following function.
3419 __isl_give isl_union_map *isl_schedule_get_map(
3420 __isl_keep isl_schedule *sched);
3422 A representation of the schedule can be printed using
3424 __isl_give isl_printer *isl_printer_print_schedule(
3425 __isl_take isl_printer *p,
3426 __isl_keep isl_schedule *schedule);
3428 A representation of the schedule as a forest of bands can be obtained
3429 using the following function.
3431 __isl_give isl_band_list *isl_schedule_get_band_forest(
3432 __isl_keep isl_schedule *schedule);
3434 The list can be manipulated as explained in L<"Lists">.
3435 The bands inside the list can be copied and freed using the following
3438 #include <isl/band.h>
3439 __isl_give isl_band *isl_band_copy(
3440 __isl_keep isl_band *band);
3441 void *isl_band_free(__isl_take isl_band *band);
3443 Each band contains zero or more scheduling dimensions.
3444 These are referred to as the members of the band.
3445 The section of the schedule that corresponds to the band is
3446 referred to as the partial schedule of the band.
3447 For those nodes that participate in a band, the outer scheduling
3448 dimensions form the prefix schedule, while the inner scheduling
3449 dimensions form the suffix schedule.
3450 That is, if we take a cut of the band forest, then the union of
3451 the concatenations of the prefix, partial and suffix schedules of
3452 each band in the cut is equal to the entire schedule (modulo
3453 some possible padding at the end with zero scheduling dimensions).
3454 The properties of a band can be inspected using the following functions.
3456 #include <isl/band.h>
3457 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3459 int isl_band_has_children(__isl_keep isl_band *band);
3460 __isl_give isl_band_list *isl_band_get_children(
3461 __isl_keep isl_band *band);
3463 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3464 __isl_keep isl_band *band);
3465 __isl_give isl_union_map *isl_band_get_partial_schedule(
3466 __isl_keep isl_band *band);
3467 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3468 __isl_keep isl_band *band);
3470 int isl_band_n_member(__isl_keep isl_band *band);
3471 int isl_band_member_is_zero_distance(
3472 __isl_keep isl_band *band, int pos);
3474 Note that a scheduling dimension is considered to be ``zero
3475 distance'' if it does not carry any proximity dependences
3477 That is, if the dependence distances of the proximity
3478 dependences are all zero in that direction (for fixed
3479 iterations of outer bands).
3481 A representation of the band can be printed using
3483 #include <isl/band.h>
3484 __isl_give isl_printer *isl_printer_print_band(
3485 __isl_take isl_printer *p,
3486 __isl_keep isl_band *band);
3488 =head2 Parametric Vertex Enumeration
3490 The parametric vertex enumeration described in this section
3491 is mainly intended to be used internally and by the C<barvinok>
3494 #include <isl/vertices.h>
3495 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3496 __isl_keep isl_basic_set *bset);
3498 The function C<isl_basic_set_compute_vertices> performs the
3499 actual computation of the parametric vertices and the chamber
3500 decomposition and store the result in an C<isl_vertices> object.
3501 This information can be queried by either iterating over all
3502 the vertices or iterating over all the chambers or cells
3503 and then iterating over all vertices that are active on the chamber.
3505 int isl_vertices_foreach_vertex(
3506 __isl_keep isl_vertices *vertices,
3507 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3510 int isl_vertices_foreach_cell(
3511 __isl_keep isl_vertices *vertices,
3512 int (*fn)(__isl_take isl_cell *cell, void *user),
3514 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3515 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3518 Other operations that can be performed on an C<isl_vertices> object are
3521 isl_ctx *isl_vertices_get_ctx(
3522 __isl_keep isl_vertices *vertices);
3523 int isl_vertices_get_n_vertices(
3524 __isl_keep isl_vertices *vertices);
3525 void isl_vertices_free(__isl_take isl_vertices *vertices);
3527 Vertices can be inspected and destroyed using the following functions.
3529 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3530 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3531 __isl_give isl_basic_set *isl_vertex_get_domain(
3532 __isl_keep isl_vertex *vertex);
3533 __isl_give isl_basic_set *isl_vertex_get_expr(
3534 __isl_keep isl_vertex *vertex);
3535 void isl_vertex_free(__isl_take isl_vertex *vertex);
3537 C<isl_vertex_get_expr> returns a singleton parametric set describing
3538 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3540 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3541 B<rational> basic sets, so they should mainly be used for inspection
3542 and should not be mixed with integer sets.
3544 Chambers can be inspected and destroyed using the following functions.
3546 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3547 __isl_give isl_basic_set *isl_cell_get_domain(
3548 __isl_keep isl_cell *cell);
3549 void isl_cell_free(__isl_take isl_cell *cell);
3553 Although C<isl> is mainly meant to be used as a library,
3554 it also contains some basic applications that use some
3555 of the functionality of C<isl>.
3556 The input may be specified in either the L<isl format>
3557 or the L<PolyLib format>.
3559 =head2 C<isl_polyhedron_sample>
3561 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3562 an integer element of the polyhedron, if there is any.
3563 The first column in the output is the denominator and is always
3564 equal to 1. If the polyhedron contains no integer points,
3565 then a vector of length zero is printed.
3569 C<isl_pip> takes the same input as the C<example> program
3570 from the C<piplib> distribution, i.e., a set of constraints
3571 on the parameters, a line containing only -1 and finally a set
3572 of constraints on a parametric polyhedron.
3573 The coefficients of the parameters appear in the last columns
3574 (but before the final constant column).
3575 The output is the lexicographic minimum of the parametric polyhedron.
3576 As C<isl> currently does not have its own output format, the output
3577 is just a dump of the internal state.
3579 =head2 C<isl_polyhedron_minimize>
3581 C<isl_polyhedron_minimize> computes the minimum of some linear
3582 or affine objective function over the integer points in a polyhedron.
3583 If an affine objective function
3584 is given, then the constant should appear in the last column.
3586 =head2 C<isl_polytope_scan>
3588 Given a polytope, C<isl_polytope_scan> prints
3589 all integer points in the polytope.