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 int isl_dim_has_dim_id(__isl_keep isl_dim *dim,
543 enum isl_dim_type type, unsigned pos);
544 __isl_give isl_id *isl_dim_get_dim_id(
545 __isl_keep isl_dim *dim,
546 enum isl_dim_type type, unsigned pos);
547 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
548 enum isl_dim_type type, unsigned pos,
549 __isl_keep const char *name);
550 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
551 enum isl_dim_type type, unsigned pos);
553 Note that C<isl_dim_get_name> returns a pointer to some internal
554 data structure, so the result can only be used while the
555 corresponding C<isl_dim> is alive.
556 Also note that every function that operates on two sets or relations
557 requires that both arguments have the same parameters. This also
558 means that if one of the arguments has named parameters, then the
559 other needs to have named parameters too and the names need to match.
560 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
561 arguments may have different parameters (as long as they are named),
562 in which case the result will have as parameters the union of the parameters of
565 Given the identifier of a dimension (typically a parameter),
566 its position can be obtained from the following function.
569 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
570 enum isl_dim_type type, __isl_keep isl_id *id);
572 The identifiers or names of entire spaces may be set or read off
573 using the following functions.
576 __isl_give isl_dim *isl_dim_set_tuple_id(
577 __isl_take isl_dim *dim,
578 enum isl_dim_type type, __isl_take isl_id *id);
579 __isl_give isl_dim *isl_dim_reset_tuple_id(
580 __isl_take isl_dim *dim, enum isl_dim_type type);
581 int isl_dim_has_tuple_id(__isl_keep isl_dim *dim,
582 enum isl_dim_type type);
583 __isl_give isl_id *isl_dim_get_tuple_id(
584 __isl_keep isl_dim *dim, enum isl_dim_type type);
585 __isl_give isl_dim *isl_dim_set_tuple_name(
586 __isl_take isl_dim *dim,
587 enum isl_dim_type type, const char *s);
588 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
589 enum isl_dim_type type);
591 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
592 or C<isl_dim_set>. As with C<isl_dim_get_name>,
593 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
595 Binary operations require the corresponding spaces of their arguments
596 to have the same name.
598 Spaces can be nested. In particular, the domain of a set or
599 the domain or range of a relation can be a nested relation.
600 The following functions can be used to construct and deconstruct
601 such nested dimension specifications.
604 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
605 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
606 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
608 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
609 be the dimension specification of a set, while that of
610 C<isl_dim_wrap> should be the dimension specification of a relation.
611 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
612 of a relation, while that of C<isl_dim_wrap> is the dimension specification
615 Dimension specifications can be created from other dimension
616 specifications using the following functions.
618 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
620 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
621 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
622 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
623 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
624 __isl_take isl_dim *right);
625 __isl_give isl_dim *isl_dim_align_params(
626 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
627 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned pos, unsigned n);
629 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
630 enum isl_dim_type type, unsigned n);
631 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
632 enum isl_dim_type type, unsigned first, unsigned n);
633 __isl_give isl_dim *isl_dim_map_from_set(
634 __isl_take isl_dim *dim);
635 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
637 Note that if dimensions are added or removed from a space, then
638 the name and the internal structure are lost.
642 A local space is essentially a dimension specification with
643 zero or more existentially quantified variables.
644 The local space of a basic set or relation can be obtained
645 using the following functions.
648 __isl_give isl_local_space *isl_basic_set_get_local_space(
649 __isl_keep isl_basic_set *bset);
652 __isl_give isl_local_space *isl_basic_map_get_local_space(
653 __isl_keep isl_basic_map *bmap);
655 A new local space can be created from a dimension specification using
657 #include <isl/local_space.h>
658 __isl_give isl_local_space *isl_local_space_from_dim(
659 __isl_take isl_dim *dim);
661 They can be inspected, copied and freed using the following functions.
663 #include <isl/local_space.h>
664 isl_ctx *isl_local_space_get_ctx(
665 __isl_keep isl_local_space *ls);
666 int isl_local_space_dim(__isl_keep isl_local_space *ls,
667 enum isl_dim_type type);
668 const char *isl_local_space_get_dim_name(
669 __isl_keep isl_local_space *ls,
670 enum isl_dim_type type, unsigned pos);
671 __isl_give isl_local_space *isl_local_space_set_dim_name(
672 __isl_take isl_local_space *ls,
673 enum isl_dim_type type, unsigned pos, const char *s);
674 __isl_give isl_dim *isl_local_space_get_dim(
675 __isl_keep isl_local_space *ls);
676 __isl_give isl_div *isl_local_space_get_div(
677 __isl_keep isl_local_space *ls, int pos);
678 __isl_give isl_local_space *isl_local_space_copy(
679 __isl_keep isl_local_space *ls);
680 void *isl_local_space_free(__isl_take isl_local_space *ls);
682 Two local spaces can be compared using
684 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
685 __isl_keep isl_local_space *ls2);
687 Local spaces can be created from other local spaces
688 using the following functions.
690 __isl_give isl_local_space *isl_local_space_from_domain(
691 __isl_take isl_local_space *ls);
692 __isl_give isl_local_space *isl_local_space_add_dims(
693 __isl_take isl_local_space *ls,
694 enum isl_dim_type type, unsigned n);
695 __isl_give isl_local_space *isl_local_space_insert_dims(
696 __isl_take isl_local_space *ls,
697 enum isl_dim_type type, unsigned first, unsigned n);
698 __isl_give isl_local_space *isl_local_space_drop_dims(
699 __isl_take isl_local_space *ls,
700 enum isl_dim_type type, unsigned first, unsigned n);
702 =head2 Input and Output
704 C<isl> supports its own input/output format, which is similar
705 to the C<Omega> format, but also supports the C<PolyLib> format
710 The C<isl> format is similar to that of C<Omega>, but has a different
711 syntax for describing the parameters and allows for the definition
712 of an existentially quantified variable as the integer division
713 of an affine expression.
714 For example, the set of integers C<i> between C<0> and C<n>
715 such that C<i % 10 <= 6> can be described as
717 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
720 A set or relation can have several disjuncts, separated
721 by the keyword C<or>. Each disjunct is either a conjunction
722 of constraints or a projection (C<exists>) of a conjunction
723 of constraints. The constraints are separated by the keyword
726 =head3 C<PolyLib> format
728 If the represented set is a union, then the first line
729 contains a single number representing the number of disjuncts.
730 Otherwise, a line containing the number C<1> is optional.
732 Each disjunct is represented by a matrix of constraints.
733 The first line contains two numbers representing
734 the number of rows and columns,
735 where the number of rows is equal to the number of constraints
736 and the number of columns is equal to two plus the number of variables.
737 The following lines contain the actual rows of the constraint matrix.
738 In each row, the first column indicates whether the constraint
739 is an equality (C<0>) or inequality (C<1>). The final column
740 corresponds to the constant term.
742 If the set is parametric, then the coefficients of the parameters
743 appear in the last columns before the constant column.
744 The coefficients of any existentially quantified variables appear
745 between those of the set variables and those of the parameters.
747 =head3 Extended C<PolyLib> format
749 The extended C<PolyLib> format is nearly identical to the
750 C<PolyLib> format. The only difference is that the line
751 containing the number of rows and columns of a constraint matrix
752 also contains four additional numbers:
753 the number of output dimensions, the number of input dimensions,
754 the number of local dimensions (i.e., the number of existentially
755 quantified variables) and the number of parameters.
756 For sets, the number of ``output'' dimensions is equal
757 to the number of set dimensions, while the number of ``input''
763 __isl_give isl_basic_set *isl_basic_set_read_from_file(
764 isl_ctx *ctx, FILE *input, int nparam);
765 __isl_give isl_basic_set *isl_basic_set_read_from_str(
766 isl_ctx *ctx, const char *str, int nparam);
767 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
768 FILE *input, int nparam);
769 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
770 const char *str, int nparam);
773 __isl_give isl_basic_map *isl_basic_map_read_from_file(
774 isl_ctx *ctx, FILE *input, int nparam);
775 __isl_give isl_basic_map *isl_basic_map_read_from_str(
776 isl_ctx *ctx, const char *str, int nparam);
777 __isl_give isl_map *isl_map_read_from_file(
778 isl_ctx *ctx, FILE *input, int nparam);
779 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
780 const char *str, int nparam);
782 #include <isl/union_set.h>
783 __isl_give isl_union_set *isl_union_set_read_from_file(
784 isl_ctx *ctx, FILE *input);
785 __isl_give isl_union_set *isl_union_set_read_from_str(
786 isl_ctx *ctx, const char *str);
788 #include <isl/union_map.h>
789 __isl_give isl_union_map *isl_union_map_read_from_file(
790 isl_ctx *ctx, FILE *input);
791 __isl_give isl_union_map *isl_union_map_read_from_str(
792 isl_ctx *ctx, const char *str);
794 The input format is autodetected and may be either the C<PolyLib> format
795 or the C<isl> format.
796 C<nparam> specifies how many of the final columns in
797 the C<PolyLib> format correspond to parameters.
798 If input is given in the C<isl> format, then the number
799 of parameters needs to be equal to C<nparam>.
800 If C<nparam> is negative, then any number of parameters
801 is accepted in the C<isl> format and zero parameters
802 are assumed in the C<PolyLib> format.
806 Before anything can be printed, an C<isl_printer> needs to
809 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
811 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
812 void isl_printer_free(__isl_take isl_printer *printer);
813 __isl_give char *isl_printer_get_str(
814 __isl_keep isl_printer *printer);
816 The behavior of the printer can be modified in various ways
818 __isl_give isl_printer *isl_printer_set_output_format(
819 __isl_take isl_printer *p, int output_format);
820 __isl_give isl_printer *isl_printer_set_indent(
821 __isl_take isl_printer *p, int indent);
822 __isl_give isl_printer *isl_printer_indent(
823 __isl_take isl_printer *p, int indent);
824 __isl_give isl_printer *isl_printer_set_prefix(
825 __isl_take isl_printer *p, const char *prefix);
826 __isl_give isl_printer *isl_printer_set_suffix(
827 __isl_take isl_printer *p, const char *suffix);
829 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
830 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
831 and defaults to C<ISL_FORMAT_ISL>.
832 Each line in the output is indented by C<indent> (set by
833 C<isl_printer_set_indent>) spaces
834 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
835 In the C<PolyLib> format output,
836 the coefficients of the existentially quantified variables
837 appear between those of the set variables and those
839 The function C<isl_printer_indent> increases the indentation
840 by the specified amount (which may be negative).
842 To actually print something, use
845 __isl_give isl_printer *isl_printer_print_basic_set(
846 __isl_take isl_printer *printer,
847 __isl_keep isl_basic_set *bset);
848 __isl_give isl_printer *isl_printer_print_set(
849 __isl_take isl_printer *printer,
850 __isl_keep isl_set *set);
853 __isl_give isl_printer *isl_printer_print_basic_map(
854 __isl_take isl_printer *printer,
855 __isl_keep isl_basic_map *bmap);
856 __isl_give isl_printer *isl_printer_print_map(
857 __isl_take isl_printer *printer,
858 __isl_keep isl_map *map);
860 #include <isl/union_set.h>
861 __isl_give isl_printer *isl_printer_print_union_set(
862 __isl_take isl_printer *p,
863 __isl_keep isl_union_set *uset);
865 #include <isl/union_map.h>
866 __isl_give isl_printer *isl_printer_print_union_map(
867 __isl_take isl_printer *p,
868 __isl_keep isl_union_map *umap);
870 When called on a file printer, the following function flushes
871 the file. When called on a string printer, the buffer is cleared.
873 __isl_give isl_printer *isl_printer_flush(
874 __isl_take isl_printer *p);
876 =head2 Creating New Sets and Relations
878 C<isl> has functions for creating some standard sets and relations.
882 =item * Empty sets and relations
884 __isl_give isl_basic_set *isl_basic_set_empty(
885 __isl_take isl_dim *dim);
886 __isl_give isl_basic_map *isl_basic_map_empty(
887 __isl_take isl_dim *dim);
888 __isl_give isl_set *isl_set_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_map *isl_map_empty(
891 __isl_take isl_dim *dim);
892 __isl_give isl_union_set *isl_union_set_empty(
893 __isl_take isl_dim *dim);
894 __isl_give isl_union_map *isl_union_map_empty(
895 __isl_take isl_dim *dim);
897 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
898 is only used to specify the parameters.
900 =item * Universe sets and relations
902 __isl_give isl_basic_set *isl_basic_set_universe(
903 __isl_take isl_dim *dim);
904 __isl_give isl_basic_map *isl_basic_map_universe(
905 __isl_take isl_dim *dim);
906 __isl_give isl_set *isl_set_universe(
907 __isl_take isl_dim *dim);
908 __isl_give isl_map *isl_map_universe(
909 __isl_take isl_dim *dim);
910 __isl_give isl_union_set *isl_union_set_universe(
911 __isl_take isl_union_set *uset);
912 __isl_give isl_union_map *isl_union_map_universe(
913 __isl_take isl_union_map *umap);
915 The sets and relations constructed by the functions above
916 contain all integer values, while those constructed by the
917 functions below only contain non-negative values.
919 __isl_give isl_basic_set *isl_basic_set_nat_universe(
920 __isl_take isl_dim *dim);
921 __isl_give isl_basic_map *isl_basic_map_nat_universe(
922 __isl_take isl_dim *dim);
923 __isl_give isl_set *isl_set_nat_universe(
924 __isl_take isl_dim *dim);
925 __isl_give isl_map *isl_map_nat_universe(
926 __isl_take isl_dim *dim);
928 =item * Identity relations
930 __isl_give isl_basic_map *isl_basic_map_identity(
931 __isl_take isl_dim *dim);
932 __isl_give isl_map *isl_map_identity(
933 __isl_take isl_dim *dim);
935 The number of input and output dimensions in C<dim> needs
938 =item * Lexicographic order
940 __isl_give isl_map *isl_map_lex_lt(
941 __isl_take isl_dim *set_dim);
942 __isl_give isl_map *isl_map_lex_le(
943 __isl_take isl_dim *set_dim);
944 __isl_give isl_map *isl_map_lex_gt(
945 __isl_take isl_dim *set_dim);
946 __isl_give isl_map *isl_map_lex_ge(
947 __isl_take isl_dim *set_dim);
948 __isl_give isl_map *isl_map_lex_lt_first(
949 __isl_take isl_dim *dim, unsigned n);
950 __isl_give isl_map *isl_map_lex_le_first(
951 __isl_take isl_dim *dim, unsigned n);
952 __isl_give isl_map *isl_map_lex_gt_first(
953 __isl_take isl_dim *dim, unsigned n);
954 __isl_give isl_map *isl_map_lex_ge_first(
955 __isl_take isl_dim *dim, unsigned n);
957 The first four functions take a dimension specification for a B<set>
958 and return relations that express that the elements in the domain
959 are lexicographically less
960 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
961 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
962 than the elements in the range.
963 The last four functions take a dimension specification for a map
964 and return relations that express that the first C<n> dimensions
965 in the domain are lexicographically less
966 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
967 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
968 than the first C<n> dimensions in the range.
972 A basic set or relation can be converted to a set or relation
973 using the following functions.
975 __isl_give isl_set *isl_set_from_basic_set(
976 __isl_take isl_basic_set *bset);
977 __isl_give isl_map *isl_map_from_basic_map(
978 __isl_take isl_basic_map *bmap);
980 Sets and relations can be converted to union sets and relations
981 using the following functions.
983 __isl_give isl_union_map *isl_union_map_from_map(
984 __isl_take isl_map *map);
985 __isl_give isl_union_set *isl_union_set_from_set(
986 __isl_take isl_set *set);
988 The inverse conversions below can only be used if the input
989 union set or relation is known to contain elements in exactly one
992 __isl_give isl_set *isl_set_from_union_set(
993 __isl_take isl_union_set *uset);
994 __isl_give isl_map *isl_map_from_union_map(
995 __isl_take isl_union_map *umap);
997 Sets and relations can be copied and freed again using the following
1000 __isl_give isl_basic_set *isl_basic_set_copy(
1001 __isl_keep isl_basic_set *bset);
1002 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1003 __isl_give isl_union_set *isl_union_set_copy(
1004 __isl_keep isl_union_set *uset);
1005 __isl_give isl_basic_map *isl_basic_map_copy(
1006 __isl_keep isl_basic_map *bmap);
1007 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1008 __isl_give isl_union_map *isl_union_map_copy(
1009 __isl_keep isl_union_map *umap);
1010 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1011 void isl_set_free(__isl_take isl_set *set);
1012 void *isl_union_set_free(__isl_take isl_union_set *uset);
1013 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1014 void isl_map_free(__isl_take isl_map *map);
1015 void *isl_union_map_free(__isl_take isl_union_map *umap);
1017 Other sets and relations can be constructed by starting
1018 from a universe set or relation, adding equality and/or
1019 inequality constraints and then projecting out the
1020 existentially quantified variables, if any.
1021 Constraints can be constructed, manipulated and
1022 added to (or removed from) (basic) sets and relations
1023 using the following functions.
1025 #include <isl/constraint.h>
1026 __isl_give isl_constraint *isl_equality_alloc(
1027 __isl_take isl_dim *dim);
1028 __isl_give isl_constraint *isl_inequality_alloc(
1029 __isl_take isl_dim *dim);
1030 __isl_give isl_constraint *isl_constraint_set_constant(
1031 __isl_take isl_constraint *constraint, isl_int v);
1032 __isl_give isl_constraint *isl_constraint_set_constant_si(
1033 __isl_take isl_constraint *constraint, int v);
1034 __isl_give isl_constraint *isl_constraint_set_coefficient(
1035 __isl_take isl_constraint *constraint,
1036 enum isl_dim_type type, int pos, isl_int v);
1037 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1038 __isl_take isl_constraint *constraint,
1039 enum isl_dim_type type, int pos, int v);
1040 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1041 __isl_take isl_basic_map *bmap,
1042 __isl_take isl_constraint *constraint);
1043 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1044 __isl_take isl_basic_set *bset,
1045 __isl_take isl_constraint *constraint);
1046 __isl_give isl_map *isl_map_add_constraint(
1047 __isl_take isl_map *map,
1048 __isl_take isl_constraint *constraint);
1049 __isl_give isl_set *isl_set_add_constraint(
1050 __isl_take isl_set *set,
1051 __isl_take isl_constraint *constraint);
1052 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1053 __isl_take isl_basic_set *bset,
1054 __isl_take isl_constraint *constraint);
1056 For example, to create a set containing the even integers
1057 between 10 and 42, you would use the following code.
1062 isl_basic_set *bset;
1065 dim = isl_dim_set_alloc(ctx, 0, 2);
1066 bset = isl_basic_set_universe(isl_dim_copy(dim));
1068 c = isl_equality_alloc(isl_dim_copy(dim));
1069 isl_int_set_si(v, -1);
1070 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1071 isl_int_set_si(v, 2);
1072 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1073 bset = isl_basic_set_add_constraint(bset, c);
1075 c = isl_inequality_alloc(isl_dim_copy(dim));
1076 isl_int_set_si(v, -10);
1077 isl_constraint_set_constant(c, v);
1078 isl_int_set_si(v, 1);
1079 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1080 bset = isl_basic_set_add_constraint(bset, c);
1082 c = isl_inequality_alloc(dim);
1083 isl_int_set_si(v, 42);
1084 isl_constraint_set_constant(c, v);
1085 isl_int_set_si(v, -1);
1086 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1087 bset = isl_basic_set_add_constraint(bset, c);
1089 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1095 isl_basic_set *bset;
1096 bset = isl_basic_set_read_from_str(ctx,
1097 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1099 A basic set or relation can also be constructed from two matrices
1100 describing the equalities and the inequalities.
1102 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1103 __isl_take isl_dim *dim,
1104 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1105 enum isl_dim_type c1,
1106 enum isl_dim_type c2, enum isl_dim_type c3,
1107 enum isl_dim_type c4);
1108 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1109 __isl_take isl_dim *dim,
1110 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1111 enum isl_dim_type c1,
1112 enum isl_dim_type c2, enum isl_dim_type c3,
1113 enum isl_dim_type c4, enum isl_dim_type c5);
1115 The C<isl_dim_type> arguments indicate the order in which
1116 different kinds of variables appear in the input matrices
1117 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1118 C<isl_dim_set> and C<isl_dim_div> for sets and
1119 of C<isl_dim_cst>, C<isl_dim_param>,
1120 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1122 A (basic) relation can also be constructed from a (piecewise) affine expression
1123 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1125 __isl_give isl_basic_map *isl_basic_map_from_aff(
1126 __isl_take isl_aff *aff);
1127 __isl_give isl_map *isl_map_from_pw_aff(
1128 __isl_take isl_pw_aff *pwaff);
1129 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1130 __isl_take isl_dim *domain_dim,
1131 __isl_take isl_aff_list *list);
1133 The C<domain_dim> argument describes the domain of the resulting
1134 basic relation. It is required because the C<list> may consist
1135 of zero affine expressions.
1137 =head2 Inspecting Sets and Relations
1139 Usually, the user should not have to care about the actual constraints
1140 of the sets and maps, but should instead apply the abstract operations
1141 explained in the following sections.
1142 Occasionally, however, it may be required to inspect the individual
1143 coefficients of the constraints. This section explains how to do so.
1144 In these cases, it may also be useful to have C<isl> compute
1145 an explicit representation of the existentially quantified variables.
1147 __isl_give isl_set *isl_set_compute_divs(
1148 __isl_take isl_set *set);
1149 __isl_give isl_map *isl_map_compute_divs(
1150 __isl_take isl_map *map);
1151 __isl_give isl_union_set *isl_union_set_compute_divs(
1152 __isl_take isl_union_set *uset);
1153 __isl_give isl_union_map *isl_union_map_compute_divs(
1154 __isl_take isl_union_map *umap);
1156 This explicit representation defines the existentially quantified
1157 variables as integer divisions of the other variables, possibly
1158 including earlier existentially quantified variables.
1159 An explicitly represented existentially quantified variable therefore
1160 has a unique value when the values of the other variables are known.
1161 If, furthermore, the same existentials, i.e., existentials
1162 with the same explicit representations, should appear in the
1163 same order in each of the disjuncts of a set or map, then the user should call
1164 either of the following functions.
1166 __isl_give isl_set *isl_set_align_divs(
1167 __isl_take isl_set *set);
1168 __isl_give isl_map *isl_map_align_divs(
1169 __isl_take isl_map *map);
1171 Alternatively, the existentially quantified variables can be removed
1172 using the following functions, which compute an overapproximation.
1174 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1175 __isl_take isl_basic_set *bset);
1176 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1177 __isl_take isl_basic_map *bmap);
1178 __isl_give isl_set *isl_set_remove_divs(
1179 __isl_take isl_set *set);
1180 __isl_give isl_map *isl_map_remove_divs(
1181 __isl_take isl_map *map);
1183 To iterate over all the sets or maps in a union set or map, use
1185 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1186 int (*fn)(__isl_take isl_set *set, void *user),
1188 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1189 int (*fn)(__isl_take isl_map *map, void *user),
1192 The number of sets or maps in a union set or map can be obtained
1195 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1196 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1198 To extract the set or map from a union with a given dimension
1201 __isl_give isl_set *isl_union_set_extract_set(
1202 __isl_keep isl_union_set *uset,
1203 __isl_take isl_dim *dim);
1204 __isl_give isl_map *isl_union_map_extract_map(
1205 __isl_keep isl_union_map *umap,
1206 __isl_take isl_dim *dim);
1208 To iterate over all the basic sets or maps in a set or map, use
1210 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1211 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1213 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1214 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1217 The callback function C<fn> should return 0 if successful and
1218 -1 if an error occurs. In the latter case, or if any other error
1219 occurs, the above functions will return -1.
1221 It should be noted that C<isl> does not guarantee that
1222 the basic sets or maps passed to C<fn> are disjoint.
1223 If this is required, then the user should call one of
1224 the following functions first.
1226 __isl_give isl_set *isl_set_make_disjoint(
1227 __isl_take isl_set *set);
1228 __isl_give isl_map *isl_map_make_disjoint(
1229 __isl_take isl_map *map);
1231 The number of basic sets in a set can be obtained
1234 int isl_set_n_basic_set(__isl_keep isl_set *set);
1236 To iterate over the constraints of a basic set or map, use
1238 #include <isl/constraint.h>
1240 int isl_basic_map_foreach_constraint(
1241 __isl_keep isl_basic_map *bmap,
1242 int (*fn)(__isl_take isl_constraint *c, void *user),
1244 void *isl_constraint_free(__isl_take isl_constraint *c);
1246 Again, the callback function C<fn> should return 0 if successful and
1247 -1 if an error occurs. In the latter case, or if any other error
1248 occurs, the above functions will return -1.
1249 The constraint C<c> represents either an equality or an inequality.
1250 Use the following function to find out whether a constraint
1251 represents an equality. If not, it represents an inequality.
1253 int isl_constraint_is_equality(
1254 __isl_keep isl_constraint *constraint);
1256 The coefficients of the constraints can be inspected using
1257 the following functions.
1259 void isl_constraint_get_constant(
1260 __isl_keep isl_constraint *constraint, isl_int *v);
1261 void isl_constraint_get_coefficient(
1262 __isl_keep isl_constraint *constraint,
1263 enum isl_dim_type type, int pos, isl_int *v);
1264 int isl_constraint_involves_dims(
1265 __isl_keep isl_constraint *constraint,
1266 enum isl_dim_type type, unsigned first, unsigned n);
1268 The explicit representations of the existentially quantified
1269 variables can be inspected using the following functions.
1270 Note that the user is only allowed to use these functions
1271 if the inspected set or map is the result of a call
1272 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1274 __isl_give isl_div *isl_constraint_div(
1275 __isl_keep isl_constraint *constraint, int pos);
1276 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1277 void isl_div_get_constant(__isl_keep isl_div *div,
1279 void isl_div_get_denominator(__isl_keep isl_div *div,
1281 void isl_div_get_coefficient(__isl_keep isl_div *div,
1282 enum isl_dim_type type, int pos, isl_int *v);
1284 To obtain the constraints of a basic set or map in matrix
1285 form, use the following functions.
1287 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1292 __isl_keep isl_basic_set *bset,
1293 enum isl_dim_type c1, enum isl_dim_type c2,
1294 enum isl_dim_type c3, enum isl_dim_type c4);
1295 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1296 __isl_keep isl_basic_map *bmap,
1297 enum isl_dim_type c1,
1298 enum isl_dim_type c2, enum isl_dim_type c3,
1299 enum isl_dim_type c4, enum isl_dim_type c5);
1300 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1301 __isl_keep isl_basic_map *bmap,
1302 enum isl_dim_type c1,
1303 enum isl_dim_type c2, enum isl_dim_type c3,
1304 enum isl_dim_type c4, enum isl_dim_type c5);
1306 The C<isl_dim_type> arguments dictate the order in which
1307 different kinds of variables appear in the resulting matrix
1308 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1309 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1311 The number of parameters, input, output or set dimensions can
1312 be obtained using the following functions.
1314 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1315 enum isl_dim_type type);
1316 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1317 enum isl_dim_type type);
1318 unsigned isl_set_dim(__isl_keep isl_set *set,
1319 enum isl_dim_type type);
1320 unsigned isl_map_dim(__isl_keep isl_map *map,
1321 enum isl_dim_type type);
1323 To check whether the description of a set or relation depends
1324 on one or more given dimensions, it is not necessary to iterate over all
1325 constraints. Instead the following functions can be used.
1327 int isl_basic_set_involves_dims(
1328 __isl_keep isl_basic_set *bset,
1329 enum isl_dim_type type, unsigned first, unsigned n);
1330 int isl_set_involves_dims(__isl_keep isl_set *set,
1331 enum isl_dim_type type, unsigned first, unsigned n);
1332 int isl_basic_map_involves_dims(
1333 __isl_keep isl_basic_map *bmap,
1334 enum isl_dim_type type, unsigned first, unsigned n);
1335 int isl_map_involves_dims(__isl_keep isl_map *map,
1336 enum isl_dim_type type, unsigned first, unsigned n);
1338 Similarly, the following functions can be used to check whether
1339 a given dimension is involved in any lower or upper bound.
1341 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1342 enum isl_dim_type type, unsigned pos);
1343 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1344 enum isl_dim_type type, unsigned pos);
1346 The identifiers or names of the domain and range spaces of a set
1347 or relation can be read off or set using the following functions.
1349 __isl_give isl_set *isl_set_set_tuple_id(
1350 __isl_take isl_set *set, __isl_take isl_id *id);
1351 __isl_give isl_set *isl_set_reset_tuple_id(
1352 __isl_take isl_set *set);
1353 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1354 __isl_give isl_id *isl_set_get_tuple_id(
1355 __isl_keep isl_set *set);
1356 __isl_give isl_map *isl_map_set_tuple_id(
1357 __isl_take isl_map *map, enum isl_dim_type type,
1358 __isl_take isl_id *id);
1359 __isl_give isl_map *isl_map_reset_tuple_id(
1360 __isl_take isl_map *map, enum isl_dim_type type);
1361 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1362 enum isl_dim_type type);
1363 __isl_give isl_id *isl_map_get_tuple_id(
1364 __isl_keep isl_map *map, enum isl_dim_type type);
1366 const char *isl_basic_set_get_tuple_name(
1367 __isl_keep isl_basic_set *bset);
1368 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1369 __isl_take isl_basic_set *set, const char *s);
1370 const char *isl_set_get_tuple_name(
1371 __isl_keep isl_set *set);
1372 const char *isl_basic_map_get_tuple_name(
1373 __isl_keep isl_basic_map *bmap,
1374 enum isl_dim_type type);
1375 const char *isl_map_get_tuple_name(
1376 __isl_keep isl_map *map,
1377 enum isl_dim_type type);
1379 As with C<isl_dim_get_tuple_name>, the value returned points to
1380 an internal data structure.
1381 The identifiers, positions or names of individual dimensions can be
1382 read off using the following functions.
1384 __isl_give isl_set *isl_set_set_dim_id(
1385 __isl_take isl_set *set, enum isl_dim_type type,
1386 unsigned pos, __isl_take isl_id *id);
1387 int isl_set_has_dim_id(__isl_keep isl_set *set,
1388 enum isl_dim_type type, unsigned pos);
1389 __isl_give isl_id *isl_set_get_dim_id(
1390 __isl_keep isl_set *set, enum isl_dim_type type,
1392 __isl_give isl_map *isl_map_set_dim_id(
1393 __isl_take isl_map *map, enum isl_dim_type type,
1394 unsigned pos, __isl_take isl_id *id);
1395 int isl_map_has_dim_id(__isl_keep isl_map *map,
1396 enum isl_dim_type type, unsigned pos);
1397 __isl_give isl_id *isl_map_get_dim_id(
1398 __isl_keep isl_map *map, enum isl_dim_type type,
1401 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1402 enum isl_dim_type type, __isl_keep isl_id *id);
1403 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1404 enum isl_dim_type type, __isl_keep isl_id *id);
1406 const char *isl_constraint_get_dim_name(
1407 __isl_keep isl_constraint *constraint,
1408 enum isl_dim_type type, unsigned pos);
1409 const char *isl_basic_set_get_dim_name(
1410 __isl_keep isl_basic_set *bset,
1411 enum isl_dim_type type, unsigned pos);
1412 const char *isl_set_get_dim_name(
1413 __isl_keep isl_set *set,
1414 enum isl_dim_type type, unsigned pos);
1415 const char *isl_basic_map_get_dim_name(
1416 __isl_keep isl_basic_map *bmap,
1417 enum isl_dim_type type, unsigned pos);
1418 const char *isl_map_get_dim_name(
1419 __isl_keep isl_map *map,
1420 enum isl_dim_type type, unsigned pos);
1422 These functions are mostly useful to obtain the identifiers, positions
1423 or names of the parameters. Identifiers of individual dimensions are
1424 essentially only useful for printing. They are ignored by all other
1425 operations and may not be preserved across those operations.
1429 =head3 Unary Properties
1435 The following functions test whether the given set or relation
1436 contains any integer points. The ``plain'' variants do not perform
1437 any computations, but simply check if the given set or relation
1438 is already known to be empty.
1440 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1441 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1442 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1443 int isl_set_is_empty(__isl_keep isl_set *set);
1444 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1445 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1446 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1447 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1448 int isl_map_is_empty(__isl_keep isl_map *map);
1449 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1451 =item * Universality
1453 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1454 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1455 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1457 =item * Single-valuedness
1459 int isl_map_is_single_valued(__isl_keep isl_map *map);
1460 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1464 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1465 int isl_map_is_injective(__isl_keep isl_map *map);
1466 int isl_union_map_plain_is_injective(
1467 __isl_keep isl_union_map *umap);
1468 int isl_union_map_is_injective(
1469 __isl_keep isl_union_map *umap);
1473 int isl_map_is_bijective(__isl_keep isl_map *map);
1474 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1478 int isl_basic_map_plain_is_fixed(
1479 __isl_keep isl_basic_map *bmap,
1480 enum isl_dim_type type, unsigned pos,
1482 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1483 enum isl_dim_type type, unsigned pos,
1486 Check if the relation obviously lies on a hyperplane where the given dimension
1487 has a fixed value and if so, return that value in C<*val>.
1491 The following functions check whether the domain of the given
1492 (basic) set is a wrapped relation.
1494 int isl_basic_set_is_wrapping(
1495 __isl_keep isl_basic_set *bset);
1496 int isl_set_is_wrapping(__isl_keep isl_set *set);
1498 =item * Internal Product
1500 int isl_basic_map_can_zip(
1501 __isl_keep isl_basic_map *bmap);
1502 int isl_map_can_zip(__isl_keep isl_map *map);
1504 Check whether the product of domain and range of the given relation
1506 i.e., whether both domain and range are nested relations.
1510 =head3 Binary Properties
1516 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1517 __isl_keep isl_set *set2);
1518 int isl_set_is_equal(__isl_keep isl_set *set1,
1519 __isl_keep isl_set *set2);
1520 int isl_union_set_is_equal(
1521 __isl_keep isl_union_set *uset1,
1522 __isl_keep isl_union_set *uset2);
1523 int isl_basic_map_is_equal(
1524 __isl_keep isl_basic_map *bmap1,
1525 __isl_keep isl_basic_map *bmap2);
1526 int isl_map_is_equal(__isl_keep isl_map *map1,
1527 __isl_keep isl_map *map2);
1528 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1529 __isl_keep isl_map *map2);
1530 int isl_union_map_is_equal(
1531 __isl_keep isl_union_map *umap1,
1532 __isl_keep isl_union_map *umap2);
1534 =item * Disjointness
1536 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1537 __isl_keep isl_set *set2);
1541 int isl_set_is_subset(__isl_keep isl_set *set1,
1542 __isl_keep isl_set *set2);
1543 int isl_set_is_strict_subset(
1544 __isl_keep isl_set *set1,
1545 __isl_keep isl_set *set2);
1546 int isl_union_set_is_subset(
1547 __isl_keep isl_union_set *uset1,
1548 __isl_keep isl_union_set *uset2);
1549 int isl_union_set_is_strict_subset(
1550 __isl_keep isl_union_set *uset1,
1551 __isl_keep isl_union_set *uset2);
1552 int isl_basic_map_is_subset(
1553 __isl_keep isl_basic_map *bmap1,
1554 __isl_keep isl_basic_map *bmap2);
1555 int isl_basic_map_is_strict_subset(
1556 __isl_keep isl_basic_map *bmap1,
1557 __isl_keep isl_basic_map *bmap2);
1558 int isl_map_is_subset(
1559 __isl_keep isl_map *map1,
1560 __isl_keep isl_map *map2);
1561 int isl_map_is_strict_subset(
1562 __isl_keep isl_map *map1,
1563 __isl_keep isl_map *map2);
1564 int isl_union_map_is_subset(
1565 __isl_keep isl_union_map *umap1,
1566 __isl_keep isl_union_map *umap2);
1567 int isl_union_map_is_strict_subset(
1568 __isl_keep isl_union_map *umap1,
1569 __isl_keep isl_union_map *umap2);
1573 =head2 Unary Operations
1579 __isl_give isl_set *isl_set_complement(
1580 __isl_take isl_set *set);
1584 __isl_give isl_basic_map *isl_basic_map_reverse(
1585 __isl_take isl_basic_map *bmap);
1586 __isl_give isl_map *isl_map_reverse(
1587 __isl_take isl_map *map);
1588 __isl_give isl_union_map *isl_union_map_reverse(
1589 __isl_take isl_union_map *umap);
1593 __isl_give isl_basic_set *isl_basic_set_project_out(
1594 __isl_take isl_basic_set *bset,
1595 enum isl_dim_type type, unsigned first, unsigned n);
1596 __isl_give isl_basic_map *isl_basic_map_project_out(
1597 __isl_take isl_basic_map *bmap,
1598 enum isl_dim_type type, unsigned first, unsigned n);
1599 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1600 enum isl_dim_type type, unsigned first, unsigned n);
1601 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1602 enum isl_dim_type type, unsigned first, unsigned n);
1603 __isl_give isl_basic_set *isl_basic_map_domain(
1604 __isl_take isl_basic_map *bmap);
1605 __isl_give isl_basic_set *isl_basic_map_range(
1606 __isl_take isl_basic_map *bmap);
1607 __isl_give isl_set *isl_map_domain(
1608 __isl_take isl_map *bmap);
1609 __isl_give isl_set *isl_map_range(
1610 __isl_take isl_map *map);
1611 __isl_give isl_union_set *isl_union_map_domain(
1612 __isl_take isl_union_map *umap);
1613 __isl_give isl_union_set *isl_union_map_range(
1614 __isl_take isl_union_map *umap);
1616 __isl_give isl_basic_map *isl_basic_map_domain_map(
1617 __isl_take isl_basic_map *bmap);
1618 __isl_give isl_basic_map *isl_basic_map_range_map(
1619 __isl_take isl_basic_map *bmap);
1620 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1621 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1622 __isl_give isl_union_map *isl_union_map_domain_map(
1623 __isl_take isl_union_map *umap);
1624 __isl_give isl_union_map *isl_union_map_range_map(
1625 __isl_take isl_union_map *umap);
1627 The functions above construct a (basic, regular or union) relation
1628 that maps (a wrapped version of) the input relation to its domain or range.
1632 __isl_give isl_set *isl_set_eliminate(
1633 __isl_take isl_set *set, enum isl_dim_type type,
1634 unsigned first, unsigned n);
1636 Eliminate the coefficients for the given dimensions from the constraints,
1637 without removing the dimensions.
1641 __isl_give isl_basic_set *isl_basic_set_fix(
1642 __isl_take isl_basic_set *bset,
1643 enum isl_dim_type type, unsigned pos,
1645 __isl_give isl_basic_set *isl_basic_set_fix_si(
1646 __isl_take isl_basic_set *bset,
1647 enum isl_dim_type type, unsigned pos, int value);
1648 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1649 enum isl_dim_type type, unsigned pos,
1651 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1652 enum isl_dim_type type, unsigned pos, int value);
1653 __isl_give isl_basic_map *isl_basic_map_fix_si(
1654 __isl_take isl_basic_map *bmap,
1655 enum isl_dim_type type, unsigned pos, int value);
1656 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1657 enum isl_dim_type type, unsigned pos, int value);
1659 Intersect the set or relation with the hyperplane where the given
1660 dimension has the fixed given value.
1662 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1663 enum isl_dim_type type1, int pos1,
1664 enum isl_dim_type type2, int pos2);
1665 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1666 enum isl_dim_type type1, int pos1,
1667 enum isl_dim_type type2, int pos2);
1669 Intersect the set or relation with the hyperplane where the given
1670 dimensions are equal to each other.
1672 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1673 enum isl_dim_type type1, int pos1,
1674 enum isl_dim_type type2, int pos2);
1676 Intersect the relation with the hyperplane where the given
1677 dimensions have opposite values.
1681 __isl_give isl_map *isl_set_identity(
1682 __isl_take isl_set *set);
1683 __isl_give isl_union_map *isl_union_set_identity(
1684 __isl_take isl_union_set *uset);
1686 Construct an identity relation on the given (union) set.
1690 __isl_give isl_basic_set *isl_basic_map_deltas(
1691 __isl_take isl_basic_map *bmap);
1692 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1693 __isl_give isl_union_set *isl_union_map_deltas(
1694 __isl_take isl_union_map *umap);
1696 These functions return a (basic) set containing the differences
1697 between image elements and corresponding domain elements in the input.
1699 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1700 __isl_take isl_basic_map *bmap);
1701 __isl_give isl_map *isl_map_deltas_map(
1702 __isl_take isl_map *map);
1703 __isl_give isl_union_map *isl_union_map_deltas_map(
1704 __isl_take isl_union_map *umap);
1706 The functions above construct a (basic, regular or union) relation
1707 that maps (a wrapped version of) the input relation to its delta set.
1711 Simplify the representation of a set or relation by trying
1712 to combine pairs of basic sets or relations into a single
1713 basic set or relation.
1715 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1716 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1717 __isl_give isl_union_set *isl_union_set_coalesce(
1718 __isl_take isl_union_set *uset);
1719 __isl_give isl_union_map *isl_union_map_coalesce(
1720 __isl_take isl_union_map *umap);
1722 =item * Detecting equalities
1724 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1725 __isl_take isl_basic_set *bset);
1726 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1727 __isl_take isl_basic_map *bmap);
1728 __isl_give isl_set *isl_set_detect_equalities(
1729 __isl_take isl_set *set);
1730 __isl_give isl_map *isl_map_detect_equalities(
1731 __isl_take isl_map *map);
1732 __isl_give isl_union_set *isl_union_set_detect_equalities(
1733 __isl_take isl_union_set *uset);
1734 __isl_give isl_union_map *isl_union_map_detect_equalities(
1735 __isl_take isl_union_map *umap);
1737 Simplify the representation of a set or relation by detecting implicit
1740 =item * Removing redundant constraints
1742 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1743 __isl_take isl_basic_set *bset);
1744 __isl_give isl_set *isl_set_remove_redundancies(
1745 __isl_take isl_set *set);
1746 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1747 __isl_take isl_basic_map *bmap);
1748 __isl_give isl_map *isl_map_remove_redundancies(
1749 __isl_take isl_map *map);
1753 __isl_give isl_basic_set *isl_set_convex_hull(
1754 __isl_take isl_set *set);
1755 __isl_give isl_basic_map *isl_map_convex_hull(
1756 __isl_take isl_map *map);
1758 If the input set or relation has any existentially quantified
1759 variables, then the result of these operations is currently undefined.
1763 __isl_give isl_basic_set *isl_set_simple_hull(
1764 __isl_take isl_set *set);
1765 __isl_give isl_basic_map *isl_map_simple_hull(
1766 __isl_take isl_map *map);
1767 __isl_give isl_union_map *isl_union_map_simple_hull(
1768 __isl_take isl_union_map *umap);
1770 These functions compute a single basic set or relation
1771 that contains the whole input set or relation.
1772 In particular, the output is described by translates
1773 of the constraints describing the basic sets or relations in the input.
1777 (See \autoref{s:simple hull}.)
1783 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1784 __isl_take isl_basic_set *bset);
1785 __isl_give isl_basic_set *isl_set_affine_hull(
1786 __isl_take isl_set *set);
1787 __isl_give isl_union_set *isl_union_set_affine_hull(
1788 __isl_take isl_union_set *uset);
1789 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1790 __isl_take isl_basic_map *bmap);
1791 __isl_give isl_basic_map *isl_map_affine_hull(
1792 __isl_take isl_map *map);
1793 __isl_give isl_union_map *isl_union_map_affine_hull(
1794 __isl_take isl_union_map *umap);
1796 In case of union sets and relations, the affine hull is computed
1799 =item * Polyhedral hull
1801 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1802 __isl_take isl_set *set);
1803 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1804 __isl_take isl_map *map);
1805 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1806 __isl_take isl_union_set *uset);
1807 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1808 __isl_take isl_union_map *umap);
1810 These functions compute a single basic set or relation
1811 not involving any existentially quantified variables
1812 that contains the whole input set or relation.
1813 In case of union sets and relations, the polyhedral hull is computed
1816 =item * Optimization
1818 #include <isl/ilp.h>
1819 enum isl_lp_result isl_basic_set_max(
1820 __isl_keep isl_basic_set *bset,
1821 __isl_keep isl_aff *obj, isl_int *opt)
1822 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1823 __isl_keep isl_aff *obj, isl_int *opt);
1824 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1825 __isl_keep isl_aff *obj, isl_int *opt);
1827 Compute the minimum or maximum of the integer affine expression C<obj>
1828 over the points in C<set>, returning the result in C<opt>.
1829 The return value may be one of C<isl_lp_error>,
1830 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1832 =item * Parametric optimization
1834 __isl_give isl_pw_aff *isl_set_dim_max(
1835 __isl_take isl_set *set, int pos);
1837 Compute the maximum of the given set dimension as a function of the
1838 parameters, but independently of the other set dimensions.
1839 For lexicographic optimization, see L<"Lexicographic Optimization">.
1843 The following functions compute either the set of (rational) coefficient
1844 values of valid constraints for the given set or the set of (rational)
1845 values satisfying the constraints with coefficients from the given set.
1846 Internally, these two sets of functions perform essentially the
1847 same operations, except that the set of coefficients is assumed to
1848 be a cone, while the set of values may be any polyhedron.
1849 The current implementation is based on the Farkas lemma and
1850 Fourier-Motzkin elimination, but this may change or be made optional
1851 in future. In particular, future implementations may use different
1852 dualization algorithms or skip the elimination step.
1854 __isl_give isl_basic_set *isl_basic_set_coefficients(
1855 __isl_take isl_basic_set *bset);
1856 __isl_give isl_basic_set *isl_set_coefficients(
1857 __isl_take isl_set *set);
1858 __isl_give isl_union_set *isl_union_set_coefficients(
1859 __isl_take isl_union_set *bset);
1860 __isl_give isl_basic_set *isl_basic_set_solutions(
1861 __isl_take isl_basic_set *bset);
1862 __isl_give isl_basic_set *isl_set_solutions(
1863 __isl_take isl_set *set);
1864 __isl_give isl_union_set *isl_union_set_solutions(
1865 __isl_take isl_union_set *bset);
1869 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1871 __isl_give isl_union_map *isl_union_map_power(
1872 __isl_take isl_union_map *umap, int *exact);
1874 Compute a parametric representation for all positive powers I<k> of C<map>.
1875 The result maps I<k> to a nested relation corresponding to the
1876 I<k>th power of C<map>.
1877 The result may be an overapproximation. If the result is known to be exact,
1878 then C<*exact> is set to C<1>.
1880 =item * Transitive closure
1882 __isl_give isl_map *isl_map_transitive_closure(
1883 __isl_take isl_map *map, int *exact);
1884 __isl_give isl_union_map *isl_union_map_transitive_closure(
1885 __isl_take isl_union_map *umap, int *exact);
1887 Compute the transitive closure of C<map>.
1888 The result may be an overapproximation. If the result is known to be exact,
1889 then C<*exact> is set to C<1>.
1891 =item * Reaching path lengths
1893 __isl_give isl_map *isl_map_reaching_path_lengths(
1894 __isl_take isl_map *map, int *exact);
1896 Compute a relation that maps each element in the range of C<map>
1897 to the lengths of all paths composed of edges in C<map> that
1898 end up in the given element.
1899 The result may be an overapproximation. If the result is known to be exact,
1900 then C<*exact> is set to C<1>.
1901 To compute the I<maximal> path length, the resulting relation
1902 should be postprocessed by C<isl_map_lexmax>.
1903 In particular, if the input relation is a dependence relation
1904 (mapping sources to sinks), then the maximal path length corresponds
1905 to the free schedule.
1906 Note, however, that C<isl_map_lexmax> expects the maximum to be
1907 finite, so if the path lengths are unbounded (possibly due to
1908 the overapproximation), then you will get an error message.
1912 __isl_give isl_basic_set *isl_basic_map_wrap(
1913 __isl_take isl_basic_map *bmap);
1914 __isl_give isl_set *isl_map_wrap(
1915 __isl_take isl_map *map);
1916 __isl_give isl_union_set *isl_union_map_wrap(
1917 __isl_take isl_union_map *umap);
1918 __isl_give isl_basic_map *isl_basic_set_unwrap(
1919 __isl_take isl_basic_set *bset);
1920 __isl_give isl_map *isl_set_unwrap(
1921 __isl_take isl_set *set);
1922 __isl_give isl_union_map *isl_union_set_unwrap(
1923 __isl_take isl_union_set *uset);
1927 Remove any internal structure of domain (and range) of the given
1928 set or relation. If there is any such internal structure in the input,
1929 then the name of the space is also removed.
1931 __isl_give isl_basic_set *isl_basic_set_flatten(
1932 __isl_take isl_basic_set *bset);
1933 __isl_give isl_set *isl_set_flatten(
1934 __isl_take isl_set *set);
1935 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1936 __isl_take isl_basic_map *bmap);
1937 __isl_give isl_map *isl_map_flatten_range(
1938 __isl_take isl_map *map);
1939 __isl_give isl_basic_map *isl_basic_map_flatten(
1940 __isl_take isl_basic_map *bmap);
1941 __isl_give isl_map *isl_map_flatten(
1942 __isl_take isl_map *map);
1944 __isl_give isl_map *isl_set_flatten_map(
1945 __isl_take isl_set *set);
1947 The function above constructs a relation
1948 that maps the input set to a flattened version of the set.
1952 Lift the input set to a space with extra dimensions corresponding
1953 to the existentially quantified variables in the input.
1954 In particular, the result lives in a wrapped map where the domain
1955 is the original space and the range corresponds to the original
1956 existentially quantified variables.
1958 __isl_give isl_basic_set *isl_basic_set_lift(
1959 __isl_take isl_basic_set *bset);
1960 __isl_give isl_set *isl_set_lift(
1961 __isl_take isl_set *set);
1962 __isl_give isl_union_set *isl_union_set_lift(
1963 __isl_take isl_union_set *uset);
1965 =item * Internal Product
1967 __isl_give isl_basic_map *isl_basic_map_zip(
1968 __isl_take isl_basic_map *bmap);
1969 __isl_give isl_map *isl_map_zip(
1970 __isl_take isl_map *map);
1971 __isl_give isl_union_map *isl_union_map_zip(
1972 __isl_take isl_union_map *umap);
1974 Given a relation with nested relations for domain and range,
1975 interchange the range of the domain with the domain of the range.
1977 =item * Aligning parameters
1979 __isl_give isl_set *isl_set_align_params(
1980 __isl_take isl_set *set,
1981 __isl_take isl_dim *model);
1982 __isl_give isl_map *isl_map_align_params(
1983 __isl_take isl_map *map,
1984 __isl_take isl_dim *model);
1986 Change the order of the parameters of the given set or relation
1987 such that the first parameters match those of C<model>.
1988 This may involve the introduction of extra parameters.
1989 All parameters need to be named.
1991 =item * Dimension manipulation
1993 __isl_give isl_set *isl_set_add_dims(
1994 __isl_take isl_set *set,
1995 enum isl_dim_type type, unsigned n);
1996 __isl_give isl_map *isl_map_add_dims(
1997 __isl_take isl_map *map,
1998 enum isl_dim_type type, unsigned n);
1999 __isl_give isl_set *isl_set_insert_dims(
2000 __isl_take isl_set *set,
2001 enum isl_dim_type type, unsigned pos, unsigned n);
2002 __isl_give isl_map *isl_map_insert_dims(
2003 __isl_take isl_map *map,
2004 enum isl_dim_type type, unsigned pos, unsigned n);
2006 It is usually not advisable to directly change the (input or output)
2007 space of a set or a relation as this removes the name and the internal
2008 structure of the space. However, the above functions can be useful
2009 to add new parameters, assuming
2010 C<isl_set_align_params> and C<isl_map_align_params>
2015 =head2 Binary Operations
2017 The two arguments of a binary operation not only need to live
2018 in the same C<isl_ctx>, they currently also need to have
2019 the same (number of) parameters.
2021 =head3 Basic Operations
2025 =item * Intersection
2027 __isl_give isl_basic_set *isl_basic_set_intersect(
2028 __isl_take isl_basic_set *bset1,
2029 __isl_take isl_basic_set *bset2);
2030 __isl_give isl_set *isl_set_intersect_params(
2031 __isl_take isl_set *set,
2032 __isl_take isl_set *params);
2033 __isl_give isl_set *isl_set_intersect(
2034 __isl_take isl_set *set1,
2035 __isl_take isl_set *set2);
2036 __isl_give isl_union_set *isl_union_set_intersect(
2037 __isl_take isl_union_set *uset1,
2038 __isl_take isl_union_set *uset2);
2039 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2040 __isl_take isl_basic_map *bmap,
2041 __isl_take isl_basic_set *bset);
2042 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2043 __isl_take isl_basic_map *bmap,
2044 __isl_take isl_basic_set *bset);
2045 __isl_give isl_basic_map *isl_basic_map_intersect(
2046 __isl_take isl_basic_map *bmap1,
2047 __isl_take isl_basic_map *bmap2);
2048 __isl_give isl_map *isl_map_intersect_params(
2049 __isl_take isl_map *map,
2050 __isl_take isl_set *params);
2051 __isl_give isl_map *isl_map_intersect_domain(
2052 __isl_take isl_map *map,
2053 __isl_take isl_set *set);
2054 __isl_give isl_map *isl_map_intersect_range(
2055 __isl_take isl_map *map,
2056 __isl_take isl_set *set);
2057 __isl_give isl_map *isl_map_intersect(
2058 __isl_take isl_map *map1,
2059 __isl_take isl_map *map2);
2060 __isl_give isl_union_map *isl_union_map_intersect_domain(
2061 __isl_take isl_union_map *umap,
2062 __isl_take isl_union_set *uset);
2063 __isl_give isl_union_map *isl_union_map_intersect_range(
2064 __isl_take isl_union_map *umap,
2065 __isl_take isl_union_set *uset);
2066 __isl_give isl_union_map *isl_union_map_intersect(
2067 __isl_take isl_union_map *umap1,
2068 __isl_take isl_union_map *umap2);
2072 __isl_give isl_set *isl_basic_set_union(
2073 __isl_take isl_basic_set *bset1,
2074 __isl_take isl_basic_set *bset2);
2075 __isl_give isl_map *isl_basic_map_union(
2076 __isl_take isl_basic_map *bmap1,
2077 __isl_take isl_basic_map *bmap2);
2078 __isl_give isl_set *isl_set_union(
2079 __isl_take isl_set *set1,
2080 __isl_take isl_set *set2);
2081 __isl_give isl_map *isl_map_union(
2082 __isl_take isl_map *map1,
2083 __isl_take isl_map *map2);
2084 __isl_give isl_union_set *isl_union_set_union(
2085 __isl_take isl_union_set *uset1,
2086 __isl_take isl_union_set *uset2);
2087 __isl_give isl_union_map *isl_union_map_union(
2088 __isl_take isl_union_map *umap1,
2089 __isl_take isl_union_map *umap2);
2091 =item * Set difference
2093 __isl_give isl_set *isl_set_subtract(
2094 __isl_take isl_set *set1,
2095 __isl_take isl_set *set2);
2096 __isl_give isl_map *isl_map_subtract(
2097 __isl_take isl_map *map1,
2098 __isl_take isl_map *map2);
2099 __isl_give isl_union_set *isl_union_set_subtract(
2100 __isl_take isl_union_set *uset1,
2101 __isl_take isl_union_set *uset2);
2102 __isl_give isl_union_map *isl_union_map_subtract(
2103 __isl_take isl_union_map *umap1,
2104 __isl_take isl_union_map *umap2);
2108 __isl_give isl_basic_set *isl_basic_set_apply(
2109 __isl_take isl_basic_set *bset,
2110 __isl_take isl_basic_map *bmap);
2111 __isl_give isl_set *isl_set_apply(
2112 __isl_take isl_set *set,
2113 __isl_take isl_map *map);
2114 __isl_give isl_union_set *isl_union_set_apply(
2115 __isl_take isl_union_set *uset,
2116 __isl_take isl_union_map *umap);
2117 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2118 __isl_take isl_basic_map *bmap1,
2119 __isl_take isl_basic_map *bmap2);
2120 __isl_give isl_basic_map *isl_basic_map_apply_range(
2121 __isl_take isl_basic_map *bmap1,
2122 __isl_take isl_basic_map *bmap2);
2123 __isl_give isl_map *isl_map_apply_domain(
2124 __isl_take isl_map *map1,
2125 __isl_take isl_map *map2);
2126 __isl_give isl_union_map *isl_union_map_apply_domain(
2127 __isl_take isl_union_map *umap1,
2128 __isl_take isl_union_map *umap2);
2129 __isl_give isl_map *isl_map_apply_range(
2130 __isl_take isl_map *map1,
2131 __isl_take isl_map *map2);
2132 __isl_give isl_union_map *isl_union_map_apply_range(
2133 __isl_take isl_union_map *umap1,
2134 __isl_take isl_union_map *umap2);
2136 =item * Cartesian Product
2138 __isl_give isl_set *isl_set_product(
2139 __isl_take isl_set *set1,
2140 __isl_take isl_set *set2);
2141 __isl_give isl_union_set *isl_union_set_product(
2142 __isl_take isl_union_set *uset1,
2143 __isl_take isl_union_set *uset2);
2144 __isl_give isl_basic_map *isl_basic_map_range_product(
2145 __isl_take isl_basic_map *bmap1,
2146 __isl_take isl_basic_map *bmap2);
2147 __isl_give isl_map *isl_map_range_product(
2148 __isl_take isl_map *map1,
2149 __isl_take isl_map *map2);
2150 __isl_give isl_union_map *isl_union_map_range_product(
2151 __isl_take isl_union_map *umap1,
2152 __isl_take isl_union_map *umap2);
2153 __isl_give isl_map *isl_map_product(
2154 __isl_take isl_map *map1,
2155 __isl_take isl_map *map2);
2156 __isl_give isl_union_map *isl_union_map_product(
2157 __isl_take isl_union_map *umap1,
2158 __isl_take isl_union_map *umap2);
2160 The above functions compute the cross product of the given
2161 sets or relations. The domains and ranges of the results
2162 are wrapped maps between domains and ranges of the inputs.
2163 To obtain a ``flat'' product, use the following functions
2166 __isl_give isl_basic_set *isl_basic_set_flat_product(
2167 __isl_take isl_basic_set *bset1,
2168 __isl_take isl_basic_set *bset2);
2169 __isl_give isl_set *isl_set_flat_product(
2170 __isl_take isl_set *set1,
2171 __isl_take isl_set *set2);
2172 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2173 __isl_take isl_basic_map *bmap1,
2174 __isl_take isl_basic_map *bmap2);
2175 __isl_give isl_map *isl_map_flat_range_product(
2176 __isl_take isl_map *map1,
2177 __isl_take isl_map *map2);
2178 __isl_give isl_union_map *isl_union_map_flat_range_product(
2179 __isl_take isl_union_map *umap1,
2180 __isl_take isl_union_map *umap2);
2181 __isl_give isl_basic_map *isl_basic_map_flat_product(
2182 __isl_take isl_basic_map *bmap1,
2183 __isl_take isl_basic_map *bmap2);
2184 __isl_give isl_map *isl_map_flat_product(
2185 __isl_take isl_map *map1,
2186 __isl_take isl_map *map2);
2188 =item * Simplification
2190 __isl_give isl_basic_set *isl_basic_set_gist(
2191 __isl_take isl_basic_set *bset,
2192 __isl_take isl_basic_set *context);
2193 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2194 __isl_take isl_set *context);
2195 __isl_give isl_union_set *isl_union_set_gist(
2196 __isl_take isl_union_set *uset,
2197 __isl_take isl_union_set *context);
2198 __isl_give isl_basic_map *isl_basic_map_gist(
2199 __isl_take isl_basic_map *bmap,
2200 __isl_take isl_basic_map *context);
2201 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2202 __isl_take isl_map *context);
2203 __isl_give isl_union_map *isl_union_map_gist(
2204 __isl_take isl_union_map *umap,
2205 __isl_take isl_union_map *context);
2207 The gist operation returns a set or relation that has the
2208 same intersection with the context as the input set or relation.
2209 Any implicit equality in the intersection is made explicit in the result,
2210 while all inequalities that are redundant with respect to the intersection
2212 In case of union sets and relations, the gist operation is performed
2217 =head3 Lexicographic Optimization
2219 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2220 the following functions
2221 compute a set that contains the lexicographic minimum or maximum
2222 of the elements in C<set> (or C<bset>) for those values of the parameters
2223 that satisfy C<dom>.
2224 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2225 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2227 In other words, the union of the parameter values
2228 for which the result is non-empty and of C<*empty>
2231 __isl_give isl_set *isl_basic_set_partial_lexmin(
2232 __isl_take isl_basic_set *bset,
2233 __isl_take isl_basic_set *dom,
2234 __isl_give isl_set **empty);
2235 __isl_give isl_set *isl_basic_set_partial_lexmax(
2236 __isl_take isl_basic_set *bset,
2237 __isl_take isl_basic_set *dom,
2238 __isl_give isl_set **empty);
2239 __isl_give isl_set *isl_set_partial_lexmin(
2240 __isl_take isl_set *set, __isl_take isl_set *dom,
2241 __isl_give isl_set **empty);
2242 __isl_give isl_set *isl_set_partial_lexmax(
2243 __isl_take isl_set *set, __isl_take isl_set *dom,
2244 __isl_give isl_set **empty);
2246 Given a (basic) set C<set> (or C<bset>), the following functions simply
2247 return a set containing the lexicographic minimum or maximum
2248 of the elements in C<set> (or C<bset>).
2249 In case of union sets, the optimum is computed per space.
2251 __isl_give isl_set *isl_basic_set_lexmin(
2252 __isl_take isl_basic_set *bset);
2253 __isl_give isl_set *isl_basic_set_lexmax(
2254 __isl_take isl_basic_set *bset);
2255 __isl_give isl_set *isl_set_lexmin(
2256 __isl_take isl_set *set);
2257 __isl_give isl_set *isl_set_lexmax(
2258 __isl_take isl_set *set);
2259 __isl_give isl_union_set *isl_union_set_lexmin(
2260 __isl_take isl_union_set *uset);
2261 __isl_give isl_union_set *isl_union_set_lexmax(
2262 __isl_take isl_union_set *uset);
2264 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2265 the following functions
2266 compute a relation that maps each element of C<dom>
2267 to the single lexicographic minimum or maximum
2268 of the elements that are associated to that same
2269 element in C<map> (or C<bmap>).
2270 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2271 that contains the elements in C<dom> that do not map
2272 to any elements in C<map> (or C<bmap>).
2273 In other words, the union of the domain of the result and of C<*empty>
2276 __isl_give isl_map *isl_basic_map_partial_lexmax(
2277 __isl_take isl_basic_map *bmap,
2278 __isl_take isl_basic_set *dom,
2279 __isl_give isl_set **empty);
2280 __isl_give isl_map *isl_basic_map_partial_lexmin(
2281 __isl_take isl_basic_map *bmap,
2282 __isl_take isl_basic_set *dom,
2283 __isl_give isl_set **empty);
2284 __isl_give isl_map *isl_map_partial_lexmax(
2285 __isl_take isl_map *map, __isl_take isl_set *dom,
2286 __isl_give isl_set **empty);
2287 __isl_give isl_map *isl_map_partial_lexmin(
2288 __isl_take isl_map *map, __isl_take isl_set *dom,
2289 __isl_give isl_set **empty);
2291 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2292 return a map mapping each element in the domain of
2293 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2294 of all elements associated to that element.
2295 In case of union relations, the optimum is computed per space.
2297 __isl_give isl_map *isl_basic_map_lexmin(
2298 __isl_take isl_basic_map *bmap);
2299 __isl_give isl_map *isl_basic_map_lexmax(
2300 __isl_take isl_basic_map *bmap);
2301 __isl_give isl_map *isl_map_lexmin(
2302 __isl_take isl_map *map);
2303 __isl_give isl_map *isl_map_lexmax(
2304 __isl_take isl_map *map);
2305 __isl_give isl_union_map *isl_union_map_lexmin(
2306 __isl_take isl_union_map *umap);
2307 __isl_give isl_union_map *isl_union_map_lexmax(
2308 __isl_take isl_union_map *umap);
2312 Lists are defined over several element types, including
2313 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2314 Here we take lists of C<isl_set>s as an example.
2315 Lists can be created, copied and freed using the following functions.
2317 #include <isl/list.h>
2318 __isl_give isl_set_list *isl_set_list_from_set(
2319 __isl_take isl_set *el);
2320 __isl_give isl_set_list *isl_set_list_alloc(
2321 isl_ctx *ctx, int n);
2322 __isl_give isl_set_list *isl_set_list_copy(
2323 __isl_keep isl_set_list *list);
2324 __isl_give isl_set_list *isl_set_list_add(
2325 __isl_take isl_set_list *list,
2326 __isl_take isl_set *el);
2327 __isl_give isl_set_list *isl_set_list_concat(
2328 __isl_take isl_set_list *list1,
2329 __isl_take isl_set_list *list2);
2330 void *isl_set_list_free(__isl_take isl_set_list *list);
2332 C<isl_set_list_alloc> creates an empty list with a capacity for
2333 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2336 Lists can be inspected using the following functions.
2338 #include <isl/list.h>
2339 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2340 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2341 __isl_give isl_set *isl_set_list_get_set(
2342 __isl_keep isl_set_list *list, int index);
2343 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2344 int (*fn)(__isl_take isl_set *el, void *user),
2347 Lists can be printed using
2349 #include <isl/list.h>
2350 __isl_give isl_printer *isl_printer_print_set_list(
2351 __isl_take isl_printer *p,
2352 __isl_keep isl_set_list *list);
2356 Matrices can be created, copied and freed using the following functions.
2358 #include <isl/mat.h>
2359 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2360 unsigned n_row, unsigned n_col);
2361 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2362 void isl_mat_free(__isl_take isl_mat *mat);
2364 Note that the elements of a newly created matrix may have arbitrary values.
2365 The elements can be changed and inspected using the following functions.
2367 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2368 int isl_mat_rows(__isl_keep isl_mat *mat);
2369 int isl_mat_cols(__isl_keep isl_mat *mat);
2370 int isl_mat_get_element(__isl_keep isl_mat *mat,
2371 int row, int col, isl_int *v);
2372 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2373 int row, int col, isl_int v);
2374 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2375 int row, int col, int v);
2377 C<isl_mat_get_element> will return a negative value if anything went wrong.
2378 In that case, the value of C<*v> is undefined.
2380 The following function can be used to compute the (right) inverse
2381 of a matrix, i.e., a matrix such that the product of the original
2382 and the inverse (in that order) is a multiple of the identity matrix.
2383 The input matrix is assumed to be of full row-rank.
2385 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2387 The following function can be used to compute the (right) kernel
2388 (or null space) of a matrix, i.e., a matrix such that the product of
2389 the original and the kernel (in that order) is the zero matrix.
2391 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2393 =head2 Piecewise Quasi Affine Expressions
2395 The zero quasi affine expression can be created using
2397 __isl_give isl_aff *isl_aff_zero(
2398 __isl_take isl_local_space *ls);
2400 A quasi affine expression can also be initialized from an C<isl_div>:
2402 #include <isl/div.h>
2403 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2405 An empty piecewise quasi affine expression (one with no cells)
2406 or a piecewise quasi affine expression with a single cell can
2407 be created using the following functions.
2409 #include <isl/aff.h>
2410 __isl_give isl_pw_aff *isl_pw_aff_empty(
2411 __isl_take isl_dim *dim);
2412 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2413 __isl_take isl_set *set, __isl_take isl_aff *aff);
2414 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2415 __isl_take isl_aff *aff);
2417 Quasi affine expressions can be copied and freed using
2419 #include <isl/aff.h>
2420 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2421 void *isl_aff_free(__isl_take isl_aff *aff);
2423 __isl_give isl_pw_aff *isl_pw_aff_copy(
2424 __isl_keep isl_pw_aff *pwaff);
2425 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2427 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2428 using the following function. The constraint is required to have
2429 a non-zero coefficient for the specified dimension.
2431 #include <isl/constraint.h>
2432 __isl_give isl_aff *isl_constraint_get_bound(
2433 __isl_keep isl_constraint *constraint,
2434 enum isl_dim_type type, int pos);
2436 The entire affine expression of the constraint can also be extracted
2437 using the following function.
2439 #include <isl/constraint.h>
2440 __isl_give isl_aff *isl_constraint_get_aff(
2441 __isl_keep isl_constraint *constraint);
2443 Conversely, an equality constraint equating
2444 the affine expression to zero or an inequality constraint enforcing
2445 the affine expression to be non-negative, can be constructed using
2447 __isl_give isl_constraint *isl_equality_from_aff(
2448 __isl_take isl_aff *aff);
2449 __isl_give isl_constraint *isl_inequality_from_aff(
2450 __isl_take isl_aff *aff);
2452 The expression can be inspected using
2454 #include <isl/aff.h>
2455 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2456 int isl_aff_dim(__isl_keep isl_aff *aff,
2457 enum isl_dim_type type);
2458 __isl_give isl_local_space *isl_aff_get_local_space(
2459 __isl_keep isl_aff *aff);
2460 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2461 enum isl_dim_type type, unsigned pos);
2462 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2464 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2465 enum isl_dim_type type, int pos, isl_int *v);
2466 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2468 __isl_give isl_div *isl_aff_get_div(
2469 __isl_keep isl_aff *aff, int pos);
2471 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2472 int (*fn)(__isl_take isl_set *set,
2473 __isl_take isl_aff *aff,
2474 void *user), void *user);
2476 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2477 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2479 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2480 enum isl_dim_type type, unsigned first, unsigned n);
2481 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2482 enum isl_dim_type type, unsigned first, unsigned n);
2484 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2485 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2486 enum isl_dim_type type);
2487 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2489 It can be modified using
2491 #include <isl/aff.h>
2492 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2493 __isl_take isl_pw_aff *pwaff,
2494 __isl_take isl_id *id);
2495 __isl_give isl_aff *isl_aff_set_dim_name(
2496 __isl_take isl_aff *aff, enum isl_dim_type type,
2497 unsigned pos, const char *s);
2498 __isl_give isl_aff *isl_aff_set_constant(
2499 __isl_take isl_aff *aff, isl_int v);
2500 __isl_give isl_aff *isl_aff_set_constant_si(
2501 __isl_take isl_aff *aff, int v);
2502 __isl_give isl_aff *isl_aff_set_coefficient(
2503 __isl_take isl_aff *aff,
2504 enum isl_dim_type type, int pos, isl_int v);
2505 __isl_give isl_aff *isl_aff_set_coefficient_si(
2506 __isl_take isl_aff *aff,
2507 enum isl_dim_type type, int pos, int v);
2508 __isl_give isl_aff *isl_aff_set_denominator(
2509 __isl_take isl_aff *aff, isl_int v);
2511 __isl_give isl_aff *isl_aff_add_constant(
2512 __isl_take isl_aff *aff, isl_int v);
2513 __isl_give isl_aff *isl_aff_add_constant_si(
2514 __isl_take isl_aff *aff, int v);
2515 __isl_give isl_aff *isl_aff_add_coefficient(
2516 __isl_take isl_aff *aff,
2517 enum isl_dim_type type, int pos, isl_int v);
2518 __isl_give isl_aff *isl_aff_add_coefficient_si(
2519 __isl_take isl_aff *aff,
2520 enum isl_dim_type type, int pos, int v);
2522 __isl_give isl_aff *isl_aff_insert_dims(
2523 __isl_take isl_aff *aff,
2524 enum isl_dim_type type, unsigned first, unsigned n);
2525 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2526 __isl_take isl_pw_aff *pwaff,
2527 enum isl_dim_type type, unsigned first, unsigned n);
2528 __isl_give isl_aff *isl_aff_add_dims(
2529 __isl_take isl_aff *aff,
2530 enum isl_dim_type type, unsigned n);
2531 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2532 __isl_take isl_pw_aff *pwaff,
2533 enum isl_dim_type type, unsigned n);
2534 __isl_give isl_aff *isl_aff_drop_dims(
2535 __isl_take isl_aff *aff,
2536 enum isl_dim_type type, unsigned first, unsigned n);
2537 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2538 __isl_take isl_pw_aff *pwaff,
2539 enum isl_dim_type type, unsigned first, unsigned n);
2541 Note that the C<set_constant> and C<set_coefficient> functions
2542 set the I<numerator> of the constant or coefficient, while
2543 C<add_constant> and C<add_coefficient> add an integer value to
2544 the possibly rational constant or coefficient.
2546 To check whether an affine expressions is obviously zero
2547 or obviously equal to some other affine expression, use
2549 #include <isl/aff.h>
2550 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2551 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2552 __isl_keep isl_aff *aff2);
2556 #include <isl/aff.h>
2557 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2558 __isl_take isl_aff *aff2);
2559 __isl_give isl_pw_aff *isl_pw_aff_add(
2560 __isl_take isl_pw_aff *pwaff1,
2561 __isl_take isl_pw_aff *pwaff2);
2562 __isl_give isl_pw_aff *isl_pw_aff_min(
2563 __isl_take isl_pw_aff *pwaff1,
2564 __isl_take isl_pw_aff *pwaff2);
2565 __isl_give isl_pw_aff *isl_pw_aff_max(
2566 __isl_take isl_pw_aff *pwaff1,
2567 __isl_take isl_pw_aff *pwaff2);
2568 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2569 __isl_take isl_aff *aff2);
2570 __isl_give isl_pw_aff *isl_pw_aff_sub(
2571 __isl_take isl_pw_aff *pwaff1,
2572 __isl_take isl_pw_aff *pwaff2);
2573 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2574 __isl_give isl_pw_aff *isl_pw_aff_neg(
2575 __isl_take isl_pw_aff *pwaff);
2576 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2577 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2578 __isl_take isl_pw_aff *pwaff);
2579 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2580 __isl_give isl_pw_aff *isl_pw_aff_floor(
2581 __isl_take isl_pw_aff *pwaff);
2582 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2584 __isl_give isl_pw_aff *isl_pw_aff_mod(
2585 __isl_take isl_pw_aff *pwaff, isl_int mod);
2586 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2588 __isl_give isl_pw_aff *isl_pw_aff_scale(
2589 __isl_take isl_pw_aff *pwaff, isl_int f);
2590 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2592 __isl_give isl_aff *isl_aff_scale_down_ui(
2593 __isl_take isl_aff *aff, unsigned f);
2594 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2595 __isl_take isl_pw_aff *pwaff, isl_int f);
2597 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2598 __isl_take isl_pw_aff_list *list);
2599 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2600 __isl_take isl_pw_aff_list *list);
2602 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2603 __isl_take isl_pw_aff *pwqp);
2605 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2606 __isl_take isl_pw_aff *pwaff,
2607 __isl_take isl_dim *model);
2609 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2610 __isl_take isl_set *context);
2611 __isl_give isl_pw_aff *isl_pw_aff_gist(
2612 __isl_take isl_pw_aff *pwaff,
2613 __isl_take isl_set *context);
2615 __isl_give isl_set *isl_pw_aff_domain(
2616 __isl_take isl_pw_aff *pwaff);
2618 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2619 __isl_take isl_aff *aff2);
2620 __isl_give isl_pw_aff *isl_pw_aff_mul(
2621 __isl_take isl_pw_aff *pwaff1,
2622 __isl_take isl_pw_aff *pwaff2);
2624 When multiplying two affine expressions, at least one of the two needs
2627 #include <isl/aff.h>
2628 __isl_give isl_basic_set *isl_aff_le_basic_set(
2629 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2630 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2631 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2632 __isl_give isl_set *isl_pw_aff_eq_set(
2633 __isl_take isl_pw_aff *pwaff1,
2634 __isl_take isl_pw_aff *pwaff2);
2635 __isl_give isl_set *isl_pw_aff_ne_set(
2636 __isl_take isl_pw_aff *pwaff1,
2637 __isl_take isl_pw_aff *pwaff2);
2638 __isl_give isl_set *isl_pw_aff_le_set(
2639 __isl_take isl_pw_aff *pwaff1,
2640 __isl_take isl_pw_aff *pwaff2);
2641 __isl_give isl_set *isl_pw_aff_lt_set(
2642 __isl_take isl_pw_aff *pwaff1,
2643 __isl_take isl_pw_aff *pwaff2);
2644 __isl_give isl_set *isl_pw_aff_ge_set(
2645 __isl_take isl_pw_aff *pwaff1,
2646 __isl_take isl_pw_aff *pwaff2);
2647 __isl_give isl_set *isl_pw_aff_gt_set(
2648 __isl_take isl_pw_aff *pwaff1,
2649 __isl_take isl_pw_aff *pwaff2);
2651 __isl_give isl_set *isl_pw_aff_list_eq_set(
2652 __isl_take isl_pw_aff_list *list1,
2653 __isl_take isl_pw_aff_list *list2);
2654 __isl_give isl_set *isl_pw_aff_list_ne_set(
2655 __isl_take isl_pw_aff_list *list1,
2656 __isl_take isl_pw_aff_list *list2);
2657 __isl_give isl_set *isl_pw_aff_list_le_set(
2658 __isl_take isl_pw_aff_list *list1,
2659 __isl_take isl_pw_aff_list *list2);
2660 __isl_give isl_set *isl_pw_aff_list_lt_set(
2661 __isl_take isl_pw_aff_list *list1,
2662 __isl_take isl_pw_aff_list *list2);
2663 __isl_give isl_set *isl_pw_aff_list_ge_set(
2664 __isl_take isl_pw_aff_list *list1,
2665 __isl_take isl_pw_aff_list *list2);
2666 __isl_give isl_set *isl_pw_aff_list_gt_set(
2667 __isl_take isl_pw_aff_list *list1,
2668 __isl_take isl_pw_aff_list *list2);
2670 The function C<isl_aff_ge_basic_set> returns a basic set
2671 containing those elements in the shared space
2672 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2673 The function C<isl_aff_ge_set> returns a set
2674 containing those elements in the shared domain
2675 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2676 The functions operating on C<isl_pw_aff_list> apply the corresponding
2677 C<isl_pw_aff> function to each pair of elements in the two lists.
2679 #include <isl/aff.h>
2680 __isl_give isl_set *isl_pw_aff_nonneg_set(
2681 __isl_take isl_pw_aff *pwaff);
2682 __isl_give isl_set *isl_pw_aff_zero_set(
2683 __isl_take isl_pw_aff *pwaff);
2684 __isl_give isl_set *isl_pw_aff_non_zero_set(
2685 __isl_take isl_pw_aff *pwaff);
2687 The function C<isl_pw_aff_nonneg_set> returns a set
2688 containing those elements in the domain
2689 of C<pwaff> where C<pwaff> is non-negative.
2691 #include <isl/aff.h>
2692 __isl_give isl_pw_aff *isl_pw_aff_cond(
2693 __isl_take isl_set *cond,
2694 __isl_take isl_pw_aff *pwaff_true,
2695 __isl_take isl_pw_aff *pwaff_false);
2697 The function C<isl_pw_aff_cond> performs a conditional operator
2698 and returns an expression that is equal to C<pwaff_true>
2699 for elements in C<cond> and equal to C<pwaff_false> for elements
2702 #include <isl/aff.h>
2703 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2704 __isl_take isl_pw_aff *pwaff1,
2705 __isl_take isl_pw_aff *pwaff2);
2706 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2707 __isl_take isl_pw_aff *pwaff1,
2708 __isl_take isl_pw_aff *pwaff2);
2710 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2711 expression with a domain that is the union of those of C<pwaff1> and
2712 C<pwaff2> and such that on each cell, the quasi-affine expression is
2713 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2714 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2715 associated expression is the defined one.
2717 An expression can be printed using
2719 #include <isl/aff.h>
2720 __isl_give isl_printer *isl_printer_print_aff(
2721 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2723 __isl_give isl_printer *isl_printer_print_pw_aff(
2724 __isl_take isl_printer *p,
2725 __isl_keep isl_pw_aff *pwaff);
2729 Points are elements of a set. They can be used to construct
2730 simple sets (boxes) or they can be used to represent the
2731 individual elements of a set.
2732 The zero point (the origin) can be created using
2734 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2736 The coordinates of a point can be inspected, set and changed
2739 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2740 enum isl_dim_type type, int pos, isl_int *v);
2741 __isl_give isl_point *isl_point_set_coordinate(
2742 __isl_take isl_point *pnt,
2743 enum isl_dim_type type, int pos, isl_int v);
2745 __isl_give isl_point *isl_point_add_ui(
2746 __isl_take isl_point *pnt,
2747 enum isl_dim_type type, int pos, unsigned val);
2748 __isl_give isl_point *isl_point_sub_ui(
2749 __isl_take isl_point *pnt,
2750 enum isl_dim_type type, int pos, unsigned val);
2752 Other properties can be obtained using
2754 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2756 Points can be copied or freed using
2758 __isl_give isl_point *isl_point_copy(
2759 __isl_keep isl_point *pnt);
2760 void isl_point_free(__isl_take isl_point *pnt);
2762 A singleton set can be created from a point using
2764 __isl_give isl_basic_set *isl_basic_set_from_point(
2765 __isl_take isl_point *pnt);
2766 __isl_give isl_set *isl_set_from_point(
2767 __isl_take isl_point *pnt);
2769 and a box can be created from two opposite extremal points using
2771 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2772 __isl_take isl_point *pnt1,
2773 __isl_take isl_point *pnt2);
2774 __isl_give isl_set *isl_set_box_from_points(
2775 __isl_take isl_point *pnt1,
2776 __isl_take isl_point *pnt2);
2778 All elements of a B<bounded> (union) set can be enumerated using
2779 the following functions.
2781 int isl_set_foreach_point(__isl_keep isl_set *set,
2782 int (*fn)(__isl_take isl_point *pnt, void *user),
2784 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2785 int (*fn)(__isl_take isl_point *pnt, void *user),
2788 The function C<fn> is called for each integer point in
2789 C<set> with as second argument the last argument of
2790 the C<isl_set_foreach_point> call. The function C<fn>
2791 should return C<0> on success and C<-1> on failure.
2792 In the latter case, C<isl_set_foreach_point> will stop
2793 enumerating and return C<-1> as well.
2794 If the enumeration is performed successfully and to completion,
2795 then C<isl_set_foreach_point> returns C<0>.
2797 To obtain a single point of a (basic) set, use
2799 __isl_give isl_point *isl_basic_set_sample_point(
2800 __isl_take isl_basic_set *bset);
2801 __isl_give isl_point *isl_set_sample_point(
2802 __isl_take isl_set *set);
2804 If C<set> does not contain any (integer) points, then the
2805 resulting point will be ``void'', a property that can be
2808 int isl_point_is_void(__isl_keep isl_point *pnt);
2810 =head2 Piecewise Quasipolynomials
2812 A piecewise quasipolynomial is a particular kind of function that maps
2813 a parametric point to a rational value.
2814 More specifically, a quasipolynomial is a polynomial expression in greatest
2815 integer parts of affine expressions of parameters and variables.
2816 A piecewise quasipolynomial is a subdivision of a given parametric
2817 domain into disjoint cells with a quasipolynomial associated to
2818 each cell. The value of the piecewise quasipolynomial at a given
2819 point is the value of the quasipolynomial associated to the cell
2820 that contains the point. Outside of the union of cells,
2821 the value is assumed to be zero.
2822 For example, the piecewise quasipolynomial
2824 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2826 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2827 A given piecewise quasipolynomial has a fixed domain dimension.
2828 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2829 defined over different domains.
2830 Piecewise quasipolynomials are mainly used by the C<barvinok>
2831 library for representing the number of elements in a parametric set or map.
2832 For example, the piecewise quasipolynomial above represents
2833 the number of points in the map
2835 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2837 =head3 Printing (Piecewise) Quasipolynomials
2839 Quasipolynomials and piecewise quasipolynomials can be printed
2840 using the following functions.
2842 __isl_give isl_printer *isl_printer_print_qpolynomial(
2843 __isl_take isl_printer *p,
2844 __isl_keep isl_qpolynomial *qp);
2846 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2847 __isl_take isl_printer *p,
2848 __isl_keep isl_pw_qpolynomial *pwqp);
2850 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2851 __isl_take isl_printer *p,
2852 __isl_keep isl_union_pw_qpolynomial *upwqp);
2854 The output format of the printer
2855 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2856 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2858 In case of printing in C<ISL_FORMAT_C>, the user may want
2859 to set the names of all dimensions
2861 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2862 __isl_take isl_qpolynomial *qp,
2863 enum isl_dim_type type, unsigned pos,
2865 __isl_give isl_pw_qpolynomial *
2866 isl_pw_qpolynomial_set_dim_name(
2867 __isl_take isl_pw_qpolynomial *pwqp,
2868 enum isl_dim_type type, unsigned pos,
2871 =head3 Creating New (Piecewise) Quasipolynomials
2873 Some simple quasipolynomials can be created using the following functions.
2874 More complicated quasipolynomials can be created by applying
2875 operations such as addition and multiplication
2876 on the resulting quasipolynomials
2878 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2879 __isl_take isl_dim *dim);
2880 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2881 __isl_take isl_dim *dim);
2882 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2883 __isl_take isl_dim *dim);
2884 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2885 __isl_take isl_dim *dim);
2886 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2887 __isl_take isl_dim *dim);
2888 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2889 __isl_take isl_dim *dim,
2890 const isl_int n, const isl_int d);
2891 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2892 __isl_take isl_div *div);
2893 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2894 __isl_take isl_dim *dim,
2895 enum isl_dim_type type, unsigned pos);
2896 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2897 __isl_take isl_aff *aff);
2899 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2900 with a single cell can be created using the following functions.
2901 Multiple of these single cell piecewise quasipolynomials can
2902 be combined to create more complicated piecewise quasipolynomials.
2904 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2905 __isl_take isl_dim *dim);
2906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2907 __isl_take isl_set *set,
2908 __isl_take isl_qpolynomial *qp);
2909 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2910 __isl_take isl_qpolynomial *qp);
2911 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2912 __isl_take isl_pw_aff *pwaff);
2914 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2915 __isl_take isl_dim *dim);
2916 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2917 __isl_take isl_pw_qpolynomial *pwqp);
2918 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2919 __isl_take isl_union_pw_qpolynomial *upwqp,
2920 __isl_take isl_pw_qpolynomial *pwqp);
2922 Quasipolynomials can be copied and freed again using the following
2925 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2926 __isl_keep isl_qpolynomial *qp);
2927 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2930 __isl_keep isl_pw_qpolynomial *pwqp);
2931 void *isl_pw_qpolynomial_free(
2932 __isl_take isl_pw_qpolynomial *pwqp);
2934 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2935 __isl_keep isl_union_pw_qpolynomial *upwqp);
2936 void isl_union_pw_qpolynomial_free(
2937 __isl_take isl_union_pw_qpolynomial *upwqp);
2939 =head3 Inspecting (Piecewise) Quasipolynomials
2941 To iterate over all piecewise quasipolynomials in a union
2942 piecewise quasipolynomial, use the following function
2944 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2945 __isl_keep isl_union_pw_qpolynomial *upwqp,
2946 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2949 To extract the piecewise quasipolynomial from a union with a given dimension
2952 __isl_give isl_pw_qpolynomial *
2953 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2954 __isl_keep isl_union_pw_qpolynomial *upwqp,
2955 __isl_take isl_dim *dim);
2957 To iterate over the cells in a piecewise quasipolynomial,
2958 use either of the following two functions
2960 int isl_pw_qpolynomial_foreach_piece(
2961 __isl_keep isl_pw_qpolynomial *pwqp,
2962 int (*fn)(__isl_take isl_set *set,
2963 __isl_take isl_qpolynomial *qp,
2964 void *user), void *user);
2965 int isl_pw_qpolynomial_foreach_lifted_piece(
2966 __isl_keep isl_pw_qpolynomial *pwqp,
2967 int (*fn)(__isl_take isl_set *set,
2968 __isl_take isl_qpolynomial *qp,
2969 void *user), void *user);
2971 As usual, the function C<fn> should return C<0> on success
2972 and C<-1> on failure. The difference between
2973 C<isl_pw_qpolynomial_foreach_piece> and
2974 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2975 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2976 compute unique representations for all existentially quantified
2977 variables and then turn these existentially quantified variables
2978 into extra set variables, adapting the associated quasipolynomial
2979 accordingly. This means that the C<set> passed to C<fn>
2980 will not have any existentially quantified variables, but that
2981 the dimensions of the sets may be different for different
2982 invocations of C<fn>.
2984 To iterate over all terms in a quasipolynomial,
2987 int isl_qpolynomial_foreach_term(
2988 __isl_keep isl_qpolynomial *qp,
2989 int (*fn)(__isl_take isl_term *term,
2990 void *user), void *user);
2992 The terms themselves can be inspected and freed using
2995 unsigned isl_term_dim(__isl_keep isl_term *term,
2996 enum isl_dim_type type);
2997 void isl_term_get_num(__isl_keep isl_term *term,
2999 void isl_term_get_den(__isl_keep isl_term *term,
3001 int isl_term_get_exp(__isl_keep isl_term *term,
3002 enum isl_dim_type type, unsigned pos);
3003 __isl_give isl_div *isl_term_get_div(
3004 __isl_keep isl_term *term, unsigned pos);
3005 void isl_term_free(__isl_take isl_term *term);
3007 Each term is a product of parameters, set variables and
3008 integer divisions. The function C<isl_term_get_exp>
3009 returns the exponent of a given dimensions in the given term.
3010 The C<isl_int>s in the arguments of C<isl_term_get_num>
3011 and C<isl_term_get_den> need to have been initialized
3012 using C<isl_int_init> before calling these functions.
3014 =head3 Properties of (Piecewise) Quasipolynomials
3016 To check whether a quasipolynomial is actually a constant,
3017 use the following function.
3019 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3020 isl_int *n, isl_int *d);
3022 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3023 then the numerator and denominator of the constant
3024 are returned in C<*n> and C<*d>, respectively.
3026 =head3 Operations on (Piecewise) Quasipolynomials
3028 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3029 __isl_take isl_qpolynomial *qp, isl_int v);
3030 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3031 __isl_take isl_qpolynomial *qp);
3032 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3033 __isl_take isl_qpolynomial *qp1,
3034 __isl_take isl_qpolynomial *qp2);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3036 __isl_take isl_qpolynomial *qp1,
3037 __isl_take isl_qpolynomial *qp2);
3038 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3039 __isl_take isl_qpolynomial *qp1,
3040 __isl_take isl_qpolynomial *qp2);
3041 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3042 __isl_take isl_qpolynomial *qp, unsigned exponent);
3044 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3045 __isl_take isl_pw_qpolynomial *pwqp1,
3046 __isl_take isl_pw_qpolynomial *pwqp2);
3047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3048 __isl_take isl_pw_qpolynomial *pwqp1,
3049 __isl_take isl_pw_qpolynomial *pwqp2);
3050 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3051 __isl_take isl_pw_qpolynomial *pwqp1,
3052 __isl_take isl_pw_qpolynomial *pwqp2);
3053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3054 __isl_take isl_pw_qpolynomial *pwqp);
3055 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3056 __isl_take isl_pw_qpolynomial *pwqp1,
3057 __isl_take isl_pw_qpolynomial *pwqp2);
3058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3059 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3061 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3062 __isl_take isl_union_pw_qpolynomial *upwqp1,
3063 __isl_take isl_union_pw_qpolynomial *upwqp2);
3064 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3065 __isl_take isl_union_pw_qpolynomial *upwqp1,
3066 __isl_take isl_union_pw_qpolynomial *upwqp2);
3067 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3068 __isl_take isl_union_pw_qpolynomial *upwqp1,
3069 __isl_take isl_union_pw_qpolynomial *upwqp2);
3071 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3072 __isl_take isl_pw_qpolynomial *pwqp,
3073 __isl_take isl_point *pnt);
3075 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3076 __isl_take isl_union_pw_qpolynomial *upwqp,
3077 __isl_take isl_point *pnt);
3079 __isl_give isl_set *isl_pw_qpolynomial_domain(
3080 __isl_take isl_pw_qpolynomial *pwqp);
3081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3082 __isl_take isl_pw_qpolynomial *pwpq,
3083 __isl_take isl_set *set);
3085 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3086 __isl_take isl_union_pw_qpolynomial *upwqp);
3087 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3088 __isl_take isl_union_pw_qpolynomial *upwpq,
3089 __isl_take isl_union_set *uset);
3091 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3092 __isl_take isl_qpolynomial *qp,
3093 __isl_take isl_dim *model);
3095 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3096 __isl_take isl_union_pw_qpolynomial *upwqp);
3098 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3099 __isl_take isl_qpolynomial *qp,
3100 __isl_take isl_set *context);
3102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3103 __isl_take isl_pw_qpolynomial *pwqp,
3104 __isl_take isl_set *context);
3106 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3107 __isl_take isl_union_pw_qpolynomial *upwqp,
3108 __isl_take isl_union_set *context);
3110 The gist operation applies the gist operation to each of
3111 the cells in the domain of the input piecewise quasipolynomial.
3112 The context is also exploited
3113 to simplify the quasipolynomials associated to each cell.
3115 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3116 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3117 __isl_give isl_union_pw_qpolynomial *
3118 isl_union_pw_qpolynomial_to_polynomial(
3119 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3121 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3122 the polynomial will be an overapproximation. If C<sign> is negative,
3123 it will be an underapproximation. If C<sign> is zero, the approximation
3124 will lie somewhere in between.
3126 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3128 A piecewise quasipolynomial reduction is a piecewise
3129 reduction (or fold) of quasipolynomials.
3130 In particular, the reduction can be maximum or a minimum.
3131 The objects are mainly used to represent the result of
3132 an upper or lower bound on a quasipolynomial over its domain,
3133 i.e., as the result of the following function.
3135 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3136 __isl_take isl_pw_qpolynomial *pwqp,
3137 enum isl_fold type, int *tight);
3139 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3140 __isl_take isl_union_pw_qpolynomial *upwqp,
3141 enum isl_fold type, int *tight);
3143 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3144 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3145 is the returned bound is known be tight, i.e., for each value
3146 of the parameters there is at least
3147 one element in the domain that reaches the bound.
3148 If the domain of C<pwqp> is not wrapping, then the bound is computed
3149 over all elements in that domain and the result has a purely parametric
3150 domain. If the domain of C<pwqp> is wrapping, then the bound is
3151 computed over the range of the wrapped relation. The domain of the
3152 wrapped relation becomes the domain of the result.
3154 A (piecewise) quasipolynomial reduction can be copied or freed using the
3155 following functions.
3157 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3158 __isl_keep isl_qpolynomial_fold *fold);
3159 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3160 __isl_keep isl_pw_qpolynomial_fold *pwf);
3161 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3162 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3163 void isl_qpolynomial_fold_free(
3164 __isl_take isl_qpolynomial_fold *fold);
3165 void *isl_pw_qpolynomial_fold_free(
3166 __isl_take isl_pw_qpolynomial_fold *pwf);
3167 void isl_union_pw_qpolynomial_fold_free(
3168 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3170 =head3 Printing Piecewise Quasipolynomial Reductions
3172 Piecewise quasipolynomial reductions can be printed
3173 using the following function.
3175 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3176 __isl_take isl_printer *p,
3177 __isl_keep isl_pw_qpolynomial_fold *pwf);
3178 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3179 __isl_take isl_printer *p,
3180 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3182 For C<isl_printer_print_pw_qpolynomial_fold>,
3183 output format of the printer
3184 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3185 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3186 output format of the printer
3187 needs to be set to C<ISL_FORMAT_ISL>.
3188 In case of printing in C<ISL_FORMAT_C>, the user may want
3189 to set the names of all dimensions
3191 __isl_give isl_pw_qpolynomial_fold *
3192 isl_pw_qpolynomial_fold_set_dim_name(
3193 __isl_take isl_pw_qpolynomial_fold *pwf,
3194 enum isl_dim_type type, unsigned pos,
3197 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3199 To iterate over all piecewise quasipolynomial reductions in a union
3200 piecewise quasipolynomial reduction, use the following function
3202 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3203 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3204 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3205 void *user), void *user);
3207 To iterate over the cells in a piecewise quasipolynomial reduction,
3208 use either of the following two functions
3210 int isl_pw_qpolynomial_fold_foreach_piece(
3211 __isl_keep isl_pw_qpolynomial_fold *pwf,
3212 int (*fn)(__isl_take isl_set *set,
3213 __isl_take isl_qpolynomial_fold *fold,
3214 void *user), void *user);
3215 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3216 __isl_keep isl_pw_qpolynomial_fold *pwf,
3217 int (*fn)(__isl_take isl_set *set,
3218 __isl_take isl_qpolynomial_fold *fold,
3219 void *user), void *user);
3221 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3222 of the difference between these two functions.
3224 To iterate over all quasipolynomials in a reduction, use
3226 int isl_qpolynomial_fold_foreach_qpolynomial(
3227 __isl_keep isl_qpolynomial_fold *fold,
3228 int (*fn)(__isl_take isl_qpolynomial *qp,
3229 void *user), void *user);
3231 =head3 Operations on Piecewise Quasipolynomial Reductions
3233 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3234 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3236 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3237 __isl_take isl_pw_qpolynomial_fold *pwf1,
3238 __isl_take isl_pw_qpolynomial_fold *pwf2);
3240 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3241 __isl_take isl_pw_qpolynomial_fold *pwf1,
3242 __isl_take isl_pw_qpolynomial_fold *pwf2);
3244 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3245 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3246 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3248 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3249 __isl_take isl_pw_qpolynomial_fold *pwf,
3250 __isl_take isl_point *pnt);
3252 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3253 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3254 __isl_take isl_point *pnt);
3256 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3257 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3258 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3259 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3260 __isl_take isl_union_set *uset);
3262 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3263 __isl_take isl_pw_qpolynomial_fold *pwf);
3265 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3266 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3268 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3269 __isl_take isl_pw_qpolynomial_fold *pwf,
3270 __isl_take isl_set *context);
3272 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3273 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3274 __isl_take isl_union_set *context);
3276 The gist operation applies the gist operation to each of
3277 the cells in the domain of the input piecewise quasipolynomial reduction.
3278 In future, the operation will also exploit the context
3279 to simplify the quasipolynomial reductions associated to each cell.
3281 __isl_give isl_pw_qpolynomial_fold *
3282 isl_set_apply_pw_qpolynomial_fold(
3283 __isl_take isl_set *set,
3284 __isl_take isl_pw_qpolynomial_fold *pwf,
3286 __isl_give isl_pw_qpolynomial_fold *
3287 isl_map_apply_pw_qpolynomial_fold(
3288 __isl_take isl_map *map,
3289 __isl_take isl_pw_qpolynomial_fold *pwf,
3291 __isl_give isl_union_pw_qpolynomial_fold *
3292 isl_union_set_apply_union_pw_qpolynomial_fold(
3293 __isl_take isl_union_set *uset,
3294 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3296 __isl_give isl_union_pw_qpolynomial_fold *
3297 isl_union_map_apply_union_pw_qpolynomial_fold(
3298 __isl_take isl_union_map *umap,
3299 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3302 The functions taking a map
3303 compose the given map with the given piecewise quasipolynomial reduction.
3304 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3305 over all elements in the intersection of the range of the map
3306 and the domain of the piecewise quasipolynomial reduction
3307 as a function of an element in the domain of the map.
3308 The functions taking a set compute a bound over all elements in the
3309 intersection of the set and the domain of the
3310 piecewise quasipolynomial reduction.
3312 =head2 Dependence Analysis
3314 C<isl> contains specialized functionality for performing
3315 array dataflow analysis. That is, given a I<sink> access relation
3316 and a collection of possible I<source> access relations,
3317 C<isl> can compute relations that describe
3318 for each iteration of the sink access, which iteration
3319 of which of the source access relations was the last
3320 to access the same data element before the given iteration
3322 To compute standard flow dependences, the sink should be
3323 a read, while the sources should be writes.
3324 If any of the source accesses are marked as being I<may>
3325 accesses, then there will be a dependence to the last
3326 I<must> access B<and> to any I<may> access that follows
3327 this last I<must> access.
3328 In particular, if I<all> sources are I<may> accesses,
3329 then memory based dependence analysis is performed.
3330 If, on the other hand, all sources are I<must> accesses,
3331 then value based dependence analysis is performed.
3333 #include <isl/flow.h>
3335 typedef int (*isl_access_level_before)(void *first, void *second);
3337 __isl_give isl_access_info *isl_access_info_alloc(
3338 __isl_take isl_map *sink,
3339 void *sink_user, isl_access_level_before fn,
3341 __isl_give isl_access_info *isl_access_info_add_source(
3342 __isl_take isl_access_info *acc,
3343 __isl_take isl_map *source, int must,
3345 void isl_access_info_free(__isl_take isl_access_info *acc);
3347 __isl_give isl_flow *isl_access_info_compute_flow(
3348 __isl_take isl_access_info *acc);
3350 int isl_flow_foreach(__isl_keep isl_flow *deps,
3351 int (*fn)(__isl_take isl_map *dep, int must,
3352 void *dep_user, void *user),
3354 __isl_give isl_map *isl_flow_get_no_source(
3355 __isl_keep isl_flow *deps, int must);
3356 void isl_flow_free(__isl_take isl_flow *deps);
3358 The function C<isl_access_info_compute_flow> performs the actual
3359 dependence analysis. The other functions are used to construct
3360 the input for this function or to read off the output.
3362 The input is collected in an C<isl_access_info>, which can
3363 be created through a call to C<isl_access_info_alloc>.
3364 The arguments to this functions are the sink access relation
3365 C<sink>, a token C<sink_user> used to identify the sink
3366 access to the user, a callback function for specifying the
3367 relative order of source and sink accesses, and the number
3368 of source access relations that will be added.
3369 The callback function has type C<int (*)(void *first, void *second)>.
3370 The function is called with two user supplied tokens identifying
3371 either a source or the sink and it should return the shared nesting
3372 level and the relative order of the two accesses.
3373 In particular, let I<n> be the number of loops shared by
3374 the two accesses. If C<first> precedes C<second> textually,
3375 then the function should return I<2 * n + 1>; otherwise,
3376 it should return I<2 * n>.
3377 The sources can be added to the C<isl_access_info> by performing
3378 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3379 C<must> indicates whether the source is a I<must> access
3380 or a I<may> access. Note that a multi-valued access relation
3381 should only be marked I<must> if every iteration in the domain
3382 of the relation accesses I<all> elements in its image.
3383 The C<source_user> token is again used to identify
3384 the source access. The range of the source access relation
3385 C<source> should have the same dimension as the range
3386 of the sink access relation.
3387 The C<isl_access_info_free> function should usually not be
3388 called explicitly, because it is called implicitly by
3389 C<isl_access_info_compute_flow>.
3391 The result of the dependence analysis is collected in an
3392 C<isl_flow>. There may be elements of
3393 the sink access for which no preceding source access could be
3394 found or for which all preceding sources are I<may> accesses.
3395 The relations containing these elements can be obtained through
3396 calls to C<isl_flow_get_no_source>, the first with C<must> set
3397 and the second with C<must> unset.
3398 In the case of standard flow dependence analysis,
3399 with the sink a read and the sources I<must> writes,
3400 the first relation corresponds to the reads from uninitialized
3401 array elements and the second relation is empty.
3402 The actual flow dependences can be extracted using
3403 C<isl_flow_foreach>. This function will call the user-specified
3404 callback function C<fn> for each B<non-empty> dependence between
3405 a source and the sink. The callback function is called
3406 with four arguments, the actual flow dependence relation
3407 mapping source iterations to sink iterations, a boolean that
3408 indicates whether it is a I<must> or I<may> dependence, a token
3409 identifying the source and an additional C<void *> with value
3410 equal to the third argument of the C<isl_flow_foreach> call.
3411 A dependence is marked I<must> if it originates from a I<must>
3412 source and if it is not followed by any I<may> sources.
3414 After finishing with an C<isl_flow>, the user should call
3415 C<isl_flow_free> to free all associated memory.
3417 A higher-level interface to dependence analysis is provided
3418 by the following function.
3420 #include <isl/flow.h>
3422 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3423 __isl_take isl_union_map *must_source,
3424 __isl_take isl_union_map *may_source,
3425 __isl_take isl_union_map *schedule,
3426 __isl_give isl_union_map **must_dep,
3427 __isl_give isl_union_map **may_dep,
3428 __isl_give isl_union_map **must_no_source,
3429 __isl_give isl_union_map **may_no_source);
3431 The arrays are identified by the tuple names of the ranges
3432 of the accesses. The iteration domains by the tuple names
3433 of the domains of the accesses and of the schedule.
3434 The relative order of the iteration domains is given by the
3435 schedule. The relations returned through C<must_no_source>
3436 and C<may_no_source> are subsets of C<sink>.
3437 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3438 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3439 any of the other arguments is treated as an error.
3443 B<The functionality described in this section is fairly new
3444 and may be subject to change.>
3446 The following function can be used to compute a schedule
3447 for a union of domains. The generated schedule respects
3448 all C<validity> dependences. That is, all dependence distances
3449 over these dependences in the scheduled space are lexicographically
3450 positive. The generated schedule schedule also tries to minimize
3451 the dependence distances over C<proximity> dependences.
3452 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3453 for groups of domains where the dependence distances have only
3454 non-negative values.
3455 The algorithm used to construct the schedule is similar to that
3458 #include <isl/schedule.h>
3459 __isl_give isl_schedule *isl_union_set_compute_schedule(
3460 __isl_take isl_union_set *domain,
3461 __isl_take isl_union_map *validity,
3462 __isl_take isl_union_map *proximity);
3463 void *isl_schedule_free(__isl_take isl_schedule *sched);
3465 A mapping from the domains to the scheduled space can be obtained
3466 from an C<isl_schedule> using the following function.
3468 __isl_give isl_union_map *isl_schedule_get_map(
3469 __isl_keep isl_schedule *sched);
3471 A representation of the schedule can be printed using
3473 __isl_give isl_printer *isl_printer_print_schedule(
3474 __isl_take isl_printer *p,
3475 __isl_keep isl_schedule *schedule);
3477 A representation of the schedule as a forest of bands can be obtained
3478 using the following function.
3480 __isl_give isl_band_list *isl_schedule_get_band_forest(
3481 __isl_keep isl_schedule *schedule);
3483 The list can be manipulated as explained in L<"Lists">.
3484 The bands inside the list can be copied and freed using the following
3487 #include <isl/band.h>
3488 __isl_give isl_band *isl_band_copy(
3489 __isl_keep isl_band *band);
3490 void *isl_band_free(__isl_take isl_band *band);
3492 Each band contains zero or more scheduling dimensions.
3493 These are referred to as the members of the band.
3494 The section of the schedule that corresponds to the band is
3495 referred to as the partial schedule of the band.
3496 For those nodes that participate in a band, the outer scheduling
3497 dimensions form the prefix schedule, while the inner scheduling
3498 dimensions form the suffix schedule.
3499 That is, if we take a cut of the band forest, then the union of
3500 the concatenations of the prefix, partial and suffix schedules of
3501 each band in the cut is equal to the entire schedule (modulo
3502 some possible padding at the end with zero scheduling dimensions).
3503 The properties of a band can be inspected using the following functions.
3505 #include <isl/band.h>
3506 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3508 int isl_band_has_children(__isl_keep isl_band *band);
3509 __isl_give isl_band_list *isl_band_get_children(
3510 __isl_keep isl_band *band);
3512 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3513 __isl_keep isl_band *band);
3514 __isl_give isl_union_map *isl_band_get_partial_schedule(
3515 __isl_keep isl_band *band);
3516 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3517 __isl_keep isl_band *band);
3519 int isl_band_n_member(__isl_keep isl_band *band);
3520 int isl_band_member_is_zero_distance(
3521 __isl_keep isl_band *band, int pos);
3523 Note that a scheduling dimension is considered to be ``zero
3524 distance'' if it does not carry any proximity dependences
3526 That is, if the dependence distances of the proximity
3527 dependences are all zero in that direction (for fixed
3528 iterations of outer bands).
3530 A representation of the band can be printed using
3532 #include <isl/band.h>
3533 __isl_give isl_printer *isl_printer_print_band(
3534 __isl_take isl_printer *p,
3535 __isl_keep isl_band *band);
3537 =head2 Parametric Vertex Enumeration
3539 The parametric vertex enumeration described in this section
3540 is mainly intended to be used internally and by the C<barvinok>
3543 #include <isl/vertices.h>
3544 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3545 __isl_keep isl_basic_set *bset);
3547 The function C<isl_basic_set_compute_vertices> performs the
3548 actual computation of the parametric vertices and the chamber
3549 decomposition and store the result in an C<isl_vertices> object.
3550 This information can be queried by either iterating over all
3551 the vertices or iterating over all the chambers or cells
3552 and then iterating over all vertices that are active on the chamber.
3554 int isl_vertices_foreach_vertex(
3555 __isl_keep isl_vertices *vertices,
3556 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3559 int isl_vertices_foreach_cell(
3560 __isl_keep isl_vertices *vertices,
3561 int (*fn)(__isl_take isl_cell *cell, void *user),
3563 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3564 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3567 Other operations that can be performed on an C<isl_vertices> object are
3570 isl_ctx *isl_vertices_get_ctx(
3571 __isl_keep isl_vertices *vertices);
3572 int isl_vertices_get_n_vertices(
3573 __isl_keep isl_vertices *vertices);
3574 void isl_vertices_free(__isl_take isl_vertices *vertices);
3576 Vertices can be inspected and destroyed using the following functions.
3578 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3579 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3580 __isl_give isl_basic_set *isl_vertex_get_domain(
3581 __isl_keep isl_vertex *vertex);
3582 __isl_give isl_basic_set *isl_vertex_get_expr(
3583 __isl_keep isl_vertex *vertex);
3584 void isl_vertex_free(__isl_take isl_vertex *vertex);
3586 C<isl_vertex_get_expr> returns a singleton parametric set describing
3587 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3589 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3590 B<rational> basic sets, so they should mainly be used for inspection
3591 and should not be mixed with integer sets.
3593 Chambers can be inspected and destroyed using the following functions.
3595 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3596 __isl_give isl_basic_set *isl_cell_get_domain(
3597 __isl_keep isl_cell *cell);
3598 void isl_cell_free(__isl_take isl_cell *cell);
3602 Although C<isl> is mainly meant to be used as a library,
3603 it also contains some basic applications that use some
3604 of the functionality of C<isl>.
3605 The input may be specified in either the L<isl format>
3606 or the L<PolyLib format>.
3608 =head2 C<isl_polyhedron_sample>
3610 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3611 an integer element of the polyhedron, if there is any.
3612 The first column in the output is the denominator and is always
3613 equal to 1. If the polyhedron contains no integer points,
3614 then a vector of length zero is printed.
3618 C<isl_pip> takes the same input as the C<example> program
3619 from the C<piplib> distribution, i.e., a set of constraints
3620 on the parameters, a line containing only -1 and finally a set
3621 of constraints on a parametric polyhedron.
3622 The coefficients of the parameters appear in the last columns
3623 (but before the final constant column).
3624 The output is the lexicographic minimum of the parametric polyhedron.
3625 As C<isl> currently does not have its own output format, the output
3626 is just a dump of the internal state.
3628 =head2 C<isl_polyhedron_minimize>
3630 C<isl_polyhedron_minimize> computes the minimum of some linear
3631 or affine objective function over the integer points in a polyhedron.
3632 If an affine objective function
3633 is given, then the constant should appear in the last column.
3635 =head2 C<isl_polytope_scan>
3637 Given a polytope, C<isl_polytope_scan> prints
3638 all integer points in the polytope.