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 documents 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 the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
433 Identifiers are used to identify both individual dimensions
434 and tuples of dimensions. They consist of a name and an optional
435 pointer. Identifiers with the same name but different pointer values
436 are considered to be distinct.
437 Identifiers can be constructed, copied, freed, inspected and printed
438 using the following functions.
441 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
442 __isl_keep const char *name, void *user);
443 __isl_give isl_id *isl_id_copy(isl_id *id);
444 void *isl_id_free(__isl_take isl_id *id);
446 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
447 void *isl_id_get_user(__isl_keep isl_id *id);
448 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
450 __isl_give isl_printer *isl_printer_print_id(
451 __isl_take isl_printer *p, __isl_keep isl_id *id);
453 Note that C<isl_id_get_name> returns a pointer to some internal
454 data structure, so the result can only be used while the
455 corresponding C<isl_id> is alive.
457 =head2 Dimension Specifications
459 Whenever a new set or relation is created from scratch,
460 its dimension needs to be specified using an C<isl_dim>.
463 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
464 unsigned nparam, unsigned n_in, unsigned n_out);
465 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
466 unsigned nparam, unsigned dim);
467 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
468 void isl_dim_free(__isl_take isl_dim *dim);
469 unsigned isl_dim_size(__isl_keep isl_dim *dim,
470 enum isl_dim_type type);
472 The dimension specification used for creating a set
473 needs to be created using C<isl_dim_set_alloc>, while
474 that for creating a relation
475 needs to be created using C<isl_dim_alloc>.
476 C<isl_dim_size> can be used
477 to find out the number of dimensions of each type in
478 a dimension specification, where type may be
479 C<isl_dim_param>, C<isl_dim_in> (only for relations),
480 C<isl_dim_out> (only for relations), C<isl_dim_set>
481 (only for sets) or C<isl_dim_all>.
483 It is often useful to create objects that live in the
484 same space as some other object. This can be accomplished
485 by creating the new objects
486 (see L<Creating New Sets and Relations> or
487 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
488 specification of the original object.
491 __isl_give isl_dim *isl_basic_set_get_dim(
492 __isl_keep isl_basic_set *bset);
493 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
495 #include <isl/union_set.h>
496 __isl_give isl_dim *isl_union_set_get_dim(
497 __isl_keep isl_union_set *uset);
500 __isl_give isl_dim *isl_basic_map_get_dim(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
504 #include <isl/union_map.h>
505 __isl_give isl_dim *isl_union_map_get_dim(
506 __isl_keep isl_union_map *umap);
508 #include <isl/constraint.h>
509 __isl_give isl_dim *isl_constraint_get_dim(
510 __isl_keep isl_constraint *constraint);
512 #include <isl/polynomial.h>
513 __isl_give isl_dim *isl_qpolynomial_get_dim(
514 __isl_keep isl_qpolynomial *qp);
515 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
516 __isl_keep isl_qpolynomial_fold *fold);
517 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
518 __isl_keep isl_pw_qpolynomial *pwqp);
519 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
520 __isl_keep isl_union_pw_qpolynomial *upwqp);
521 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
522 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
525 __isl_give isl_dim *isl_aff_get_dim(
526 __isl_keep isl_aff *aff);
527 __isl_give isl_dim *isl_pw_aff_get_dim(
528 __isl_keep isl_pw_aff *pwaff);
530 #include <isl/point.h>
531 __isl_give isl_dim *isl_point_get_dim(
532 __isl_keep isl_point *pnt);
534 The identifiers or names of the individual dimensions may be set or read off
535 using the following functions.
538 __isl_give isl_dim *isl_dim_set_dim_id(
539 __isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos,
541 __isl_take isl_id *id);
542 __isl_give isl_id *isl_dim_get_dim_id(
543 __isl_keep isl_dim *dim,
544 enum isl_dim_type type, unsigned pos);
545 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
546 enum isl_dim_type type, unsigned pos,
547 __isl_keep const char *name);
548 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
549 enum isl_dim_type type, unsigned pos);
551 Note that C<isl_dim_get_name> returns a pointer to some internal
552 data structure, so the result can only be used while the
553 corresponding C<isl_dim> is alive.
554 Also note that every function that operates on two sets or relations
555 requires that both arguments have the same parameters. This also
556 means that if one of the arguments has named parameters, then the
557 other needs to have named parameters too and the names need to match.
558 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
559 arguments may have different parameters (as long as they are named),
560 in which case the result will have as parameters the union of the parameters of
563 Given the identifier of a dimension (typically a parameter),
564 its position can be obtained from the following function.
567 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
568 enum isl_dim_type type, __isl_keep isl_id *id);
570 The identifiers or names of entire spaces may be set or read off
571 using the following functions.
574 __isl_give isl_dim *isl_dim_set_tuple_id(
575 __isl_take isl_dim *dim,
576 enum isl_dim_type type, __isl_take isl_id *id);
577 __isl_give isl_dim *isl_dim_reset_tuple_id(
578 __isl_take isl_dim *dim, enum isl_dim_type type);
579 __isl_give isl_id *isl_dim_get_tuple_id(
580 __isl_keep isl_dim *dim, enum isl_dim_type type);
581 __isl_give isl_dim *isl_dim_set_tuple_name(
582 __isl_take isl_dim *dim,
583 enum isl_dim_type type, const char *s);
584 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
585 enum isl_dim_type type);
587 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
588 or C<isl_dim_set>. As with C<isl_dim_get_name>,
589 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
591 Binary operations require the corresponding spaces of their arguments
592 to have the same name.
594 Spaces can be nested. In particular, the domain of a set or
595 the domain or range of a relation can be a nested relation.
596 The following functions can be used to construct and deconstruct
597 such nested dimension specifications.
600 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
601 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
602 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
604 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
605 be the dimension specification of a set, while that of
606 C<isl_dim_wrap> should be the dimension specification of a relation.
607 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
608 of a relation, while that of C<isl_dim_wrap> is the dimension specification
611 Dimension specifications can be created from other dimension
612 specifications using the following functions.
614 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
615 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
616 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
617 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
618 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
620 __isl_take isl_dim *right);
621 __isl_give isl_dim *isl_dim_align_params(
622 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
623 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
624 enum isl_dim_type type, unsigned pos, unsigned n);
625 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
626 enum isl_dim_type type, unsigned n);
627 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned first, unsigned n);
629 __isl_give isl_dim *isl_dim_map_from_set(
630 __isl_take isl_dim *dim);
631 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
633 Note that if dimensions are added or removed from a space, then
634 the name and the internal structure are lost.
638 A local space is essentially a dimension specification with
639 zero or more existentially quantified variables.
640 The local space of a basic set or relation can be obtained
641 using the following functions.
644 __isl_give isl_local_space *isl_basic_set_get_local_space(
645 __isl_keep isl_basic_set *bset);
648 __isl_give isl_local_space *isl_basic_map_get_local_space(
649 __isl_keep isl_basic_map *bmap);
651 A new local space can be created from a dimension specification using
653 #include <isl/local_space.h>
654 __isl_give isl_local_space *isl_local_space_from_dim(
655 __isl_take isl_dim *dim);
657 They can be inspected, copied and freed using the following functions.
659 #include <isl/local_space.h>
660 isl_ctx *isl_local_space_get_ctx(
661 __isl_keep isl_local_space *ls);
662 int isl_local_space_dim(__isl_keep isl_local_space *ls,
663 enum isl_dim_type type);
664 const char *isl_local_space_get_dim_name(
665 __isl_keep isl_local_space *ls,
666 enum isl_dim_type type, unsigned pos);
667 __isl_give isl_local_space *isl_local_space_set_dim_name(
668 __isl_take isl_local_space *ls,
669 enum isl_dim_type type, unsigned pos, const char *s);
670 __isl_give isl_dim *isl_local_space_get_dim(
671 __isl_keep isl_local_space *ls);
672 __isl_give isl_div *isl_local_space_get_div(
673 __isl_keep isl_local_space *ls, int pos);
674 __isl_give isl_local_space *isl_local_space_copy(
675 __isl_keep isl_local_space *ls);
676 void *isl_local_space_free(__isl_take isl_local_space *ls);
678 Two local spaces can be compared using
680 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
681 __isl_keep isl_local_space *ls2);
683 Local spaces can be created from other local spaces
684 using the following functions.
686 __isl_give isl_local_space *isl_local_space_from_domain(
687 __isl_take isl_local_space *ls);
688 __isl_give isl_local_space *isl_local_space_add_dims(
689 __isl_take isl_local_space *ls,
690 enum isl_dim_type type, unsigned n);
691 __isl_give isl_local_space *isl_local_space_insert_dims(
692 __isl_take isl_local_space *ls,
693 enum isl_dim_type type, unsigned first, unsigned n);
694 __isl_give isl_local_space *isl_local_space_drop_dims(
695 __isl_take isl_local_space *ls,
696 enum isl_dim_type type, unsigned first, unsigned n);
698 =head2 Input and Output
700 C<isl> supports its own input/output format, which is similar
701 to the C<Omega> format, but also supports the C<PolyLib> format
706 The C<isl> format is similar to that of C<Omega>, but has a different
707 syntax for describing the parameters and allows for the definition
708 of an existentially quantified variable as the integer division
709 of an affine expression.
710 For example, the set of integers C<i> between C<0> and C<n>
711 such that C<i % 10 <= 6> can be described as
713 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
716 A set or relation can have several disjuncts, separated
717 by the keyword C<or>. Each disjunct is either a conjunction
718 of constraints or a projection (C<exists>) of a conjunction
719 of constraints. The constraints are separated by the keyword
722 =head3 C<PolyLib> format
724 If the represented set is a union, then the first line
725 contains a single number representing the number of disjuncts.
726 Otherwise, a line containing the number C<1> is optional.
728 Each disjunct is represented by a matrix of constraints.
729 The first line contains two numbers representing
730 the number of rows and columns,
731 where the number of rows is equal to the number of constraints
732 and the number of columns is equal to two plus the number of variables.
733 The following lines contain the actual rows of the constraint matrix.
734 In each row, the first column indicates whether the constraint
735 is an equality (C<0>) or inequality (C<1>). The final column
736 corresponds to the constant term.
738 If the set is parametric, then the coefficients of the parameters
739 appear in the last columns before the constant column.
740 The coefficients of any existentially quantified variables appear
741 between those of the set variables and those of the parameters.
743 =head3 Extended C<PolyLib> format
745 The extended C<PolyLib> format is nearly identical to the
746 C<PolyLib> format. The only difference is that the line
747 containing the number of rows and columns of a constraint matrix
748 also contains four additional numbers:
749 the number of output dimensions, the number of input dimensions,
750 the number of local dimensions (i.e., the number of existentially
751 quantified variables) and the number of parameters.
752 For sets, the number of ``output'' dimensions is equal
753 to the number of set dimensions, while the number of ``input''
759 __isl_give isl_basic_set *isl_basic_set_read_from_file(
760 isl_ctx *ctx, FILE *input, int nparam);
761 __isl_give isl_basic_set *isl_basic_set_read_from_str(
762 isl_ctx *ctx, const char *str, int nparam);
763 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
764 FILE *input, int nparam);
765 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
766 const char *str, int nparam);
769 __isl_give isl_basic_map *isl_basic_map_read_from_file(
770 isl_ctx *ctx, FILE *input, int nparam);
771 __isl_give isl_basic_map *isl_basic_map_read_from_str(
772 isl_ctx *ctx, const char *str, int nparam);
773 __isl_give isl_map *isl_map_read_from_file(
774 struct isl_ctx *ctx, FILE *input, int nparam);
775 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
776 const char *str, int nparam);
778 #include <isl/union_set.h>
779 __isl_give isl_union_set *isl_union_set_read_from_file(
780 isl_ctx *ctx, FILE *input);
781 __isl_give isl_union_set *isl_union_set_read_from_str(
782 struct isl_ctx *ctx, const char *str);
784 #include <isl/union_map.h>
785 __isl_give isl_union_map *isl_union_map_read_from_file(
786 isl_ctx *ctx, FILE *input);
787 __isl_give isl_union_map *isl_union_map_read_from_str(
788 struct isl_ctx *ctx, const char *str);
790 The input format is autodetected and may be either the C<PolyLib> format
791 or the C<isl> format.
792 C<nparam> specifies how many of the final columns in
793 the C<PolyLib> format correspond to parameters.
794 If input is given in the C<isl> format, then the number
795 of parameters needs to be equal to C<nparam>.
796 If C<nparam> is negative, then any number of parameters
797 is accepted in the C<isl> format and zero parameters
798 are assumed in the C<PolyLib> format.
802 Before anything can be printed, an C<isl_printer> needs to
805 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
807 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
808 void isl_printer_free(__isl_take isl_printer *printer);
809 __isl_give char *isl_printer_get_str(
810 __isl_keep isl_printer *printer);
812 The behavior of the printer can be modified in various ways
814 __isl_give isl_printer *isl_printer_set_output_format(
815 __isl_take isl_printer *p, int output_format);
816 __isl_give isl_printer *isl_printer_set_indent(
817 __isl_take isl_printer *p, int indent);
818 __isl_give isl_printer *isl_printer_indent(
819 __isl_take isl_printer *p, int indent);
820 __isl_give isl_printer *isl_printer_set_prefix(
821 __isl_take isl_printer *p, const char *prefix);
822 __isl_give isl_printer *isl_printer_set_suffix(
823 __isl_take isl_printer *p, const char *suffix);
825 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
826 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
827 and defaults to C<ISL_FORMAT_ISL>.
828 Each line in the output is indented by C<indent> (set by
829 C<isl_printer_set_indent>) spaces
830 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
831 In the C<PolyLib> format output,
832 the coefficients of the existentially quantified variables
833 appear between those of the set variables and those
835 The function C<isl_printer_indent> increases the indentation
836 by the specified amount (which may be negative).
838 To actually print something, use
841 __isl_give isl_printer *isl_printer_print_basic_set(
842 __isl_take isl_printer *printer,
843 __isl_keep isl_basic_set *bset);
844 __isl_give isl_printer *isl_printer_print_set(
845 __isl_take isl_printer *printer,
846 __isl_keep isl_set *set);
849 __isl_give isl_printer *isl_printer_print_basic_map(
850 __isl_take isl_printer *printer,
851 __isl_keep isl_basic_map *bmap);
852 __isl_give isl_printer *isl_printer_print_map(
853 __isl_take isl_printer *printer,
854 __isl_keep isl_map *map);
856 #include <isl/union_set.h>
857 __isl_give isl_printer *isl_printer_print_union_set(
858 __isl_take isl_printer *p,
859 __isl_keep isl_union_set *uset);
861 #include <isl/union_map.h>
862 __isl_give isl_printer *isl_printer_print_union_map(
863 __isl_take isl_printer *p,
864 __isl_keep isl_union_map *umap);
866 When called on a file printer, the following function flushes
867 the file. When called on a string printer, the buffer is cleared.
869 __isl_give isl_printer *isl_printer_flush(
870 __isl_take isl_printer *p);
872 =head2 Creating New Sets and Relations
874 C<isl> has functions for creating some standard sets and relations.
878 =item * Empty sets and relations
880 __isl_give isl_basic_set *isl_basic_set_empty(
881 __isl_take isl_dim *dim);
882 __isl_give isl_basic_map *isl_basic_map_empty(
883 __isl_take isl_dim *dim);
884 __isl_give isl_set *isl_set_empty(
885 __isl_take isl_dim *dim);
886 __isl_give isl_map *isl_map_empty(
887 __isl_take isl_dim *dim);
888 __isl_give isl_union_set *isl_union_set_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_union_map *isl_union_map_empty(
891 __isl_take isl_dim *dim);
893 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
894 is only used to specify the parameters.
896 =item * Universe sets and relations
898 __isl_give isl_basic_set *isl_basic_set_universe(
899 __isl_take isl_dim *dim);
900 __isl_give isl_basic_map *isl_basic_map_universe(
901 __isl_take isl_dim *dim);
902 __isl_give isl_set *isl_set_universe(
903 __isl_take isl_dim *dim);
904 __isl_give isl_map *isl_map_universe(
905 __isl_take isl_dim *dim);
906 __isl_give isl_union_set *isl_union_set_universe(
907 __isl_take isl_union_set *uset);
908 __isl_give isl_union_map *isl_union_map_universe(
909 __isl_take isl_union_map *umap);
911 The sets and relations constructed by the functions above
912 contain all integer values, while those constructed by the
913 functions below only contain non-negative values.
915 __isl_give isl_basic_set *isl_basic_set_nat_universe(
916 __isl_take isl_dim *dim);
917 __isl_give isl_basic_map *isl_basic_map_nat_universe(
918 __isl_take isl_dim *dim);
919 __isl_give isl_set *isl_set_nat_universe(
920 __isl_take isl_dim *dim);
921 __isl_give isl_map *isl_map_nat_universe(
922 __isl_take isl_dim *dim);
924 =item * Identity relations
926 __isl_give isl_basic_map *isl_basic_map_identity(
927 __isl_take isl_dim *dim);
928 __isl_give isl_map *isl_map_identity(
929 __isl_take isl_dim *dim);
931 The number of input and output dimensions in C<dim> needs
934 =item * Lexicographic order
936 __isl_give isl_map *isl_map_lex_lt(
937 __isl_take isl_dim *set_dim);
938 __isl_give isl_map *isl_map_lex_le(
939 __isl_take isl_dim *set_dim);
940 __isl_give isl_map *isl_map_lex_gt(
941 __isl_take isl_dim *set_dim);
942 __isl_give isl_map *isl_map_lex_ge(
943 __isl_take isl_dim *set_dim);
944 __isl_give isl_map *isl_map_lex_lt_first(
945 __isl_take isl_dim *dim, unsigned n);
946 __isl_give isl_map *isl_map_lex_le_first(
947 __isl_take isl_dim *dim, unsigned n);
948 __isl_give isl_map *isl_map_lex_gt_first(
949 __isl_take isl_dim *dim, unsigned n);
950 __isl_give isl_map *isl_map_lex_ge_first(
951 __isl_take isl_dim *dim, unsigned n);
953 The first four functions take a dimension specification for a B<set>
954 and return relations that express that the elements in the domain
955 are lexicographically less
956 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
957 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
958 than the elements in the range.
959 The last four functions take a dimension specification for a map
960 and return relations that express that the first C<n> dimensions
961 in the domain are lexicographically less
962 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
963 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
964 than the first C<n> dimensions in the range.
968 A basic set or relation can be converted to a set or relation
969 using the following functions.
971 __isl_give isl_set *isl_set_from_basic_set(
972 __isl_take isl_basic_set *bset);
973 __isl_give isl_map *isl_map_from_basic_map(
974 __isl_take isl_basic_map *bmap);
976 Sets and relations can be converted to union sets and relations
977 using the following functions.
979 __isl_give isl_union_map *isl_union_map_from_map(
980 __isl_take isl_map *map);
981 __isl_give isl_union_set *isl_union_set_from_set(
982 __isl_take isl_set *set);
984 The inverse conversions below can only be used if the input
985 union set or relation is known to contain elements in exactly one
988 __isl_give isl_set *isl_set_from_union_set(
989 __isl_take isl_union_set *uset);
990 __isl_give isl_map *isl_map_from_union_map(
991 __isl_take isl_union_map *umap);
993 Sets and relations can be copied and freed again using the following
996 __isl_give isl_basic_set *isl_basic_set_copy(
997 __isl_keep isl_basic_set *bset);
998 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
999 __isl_give isl_union_set *isl_union_set_copy(
1000 __isl_keep isl_union_set *uset);
1001 __isl_give isl_basic_map *isl_basic_map_copy(
1002 __isl_keep isl_basic_map *bmap);
1003 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1004 __isl_give isl_union_map *isl_union_map_copy(
1005 __isl_keep isl_union_map *umap);
1006 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1007 void isl_set_free(__isl_take isl_set *set);
1008 void *isl_union_set_free(__isl_take isl_union_set *uset);
1009 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1010 void isl_map_free(__isl_take isl_map *map);
1011 void *isl_union_map_free(__isl_take isl_union_map *umap);
1013 Other sets and relations can be constructed by starting
1014 from a universe set or relation, adding equality and/or
1015 inequality constraints and then projecting out the
1016 existentially quantified variables, if any.
1017 Constraints can be constructed, manipulated and
1018 added to (or removed from) (basic) sets and relations
1019 using the following functions.
1021 #include <isl/constraint.h>
1022 __isl_give isl_constraint *isl_equality_alloc(
1023 __isl_take isl_dim *dim);
1024 __isl_give isl_constraint *isl_inequality_alloc(
1025 __isl_take isl_dim *dim);
1026 void isl_constraint_set_constant(
1027 __isl_keep isl_constraint *constraint, isl_int v);
1028 void isl_constraint_set_coefficient(
1029 __isl_keep isl_constraint *constraint,
1030 enum isl_dim_type type, int pos, isl_int v);
1031 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1032 __isl_take isl_basic_map *bmap,
1033 __isl_take isl_constraint *constraint);
1034 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1035 __isl_take isl_basic_set *bset,
1036 __isl_take isl_constraint *constraint);
1037 __isl_give isl_map *isl_map_add_constraint(
1038 __isl_take isl_map *map,
1039 __isl_take isl_constraint *constraint);
1040 __isl_give isl_set *isl_set_add_constraint(
1041 __isl_take isl_set *set,
1042 __isl_take isl_constraint *constraint);
1043 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1044 __isl_take isl_basic_set *bset,
1045 __isl_take isl_constraint *constraint);
1047 For example, to create a set containing the even integers
1048 between 10 and 42, you would use the following code.
1051 struct isl_dim *dim;
1052 struct isl_constraint *c;
1053 struct isl_basic_set *bset;
1056 dim = isl_dim_set_alloc(ctx, 0, 2);
1057 bset = isl_basic_set_universe(isl_dim_copy(dim));
1059 c = isl_equality_alloc(isl_dim_copy(dim));
1060 isl_int_set_si(v, -1);
1061 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1062 isl_int_set_si(v, 2);
1063 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1064 bset = isl_basic_set_add_constraint(bset, c);
1066 c = isl_inequality_alloc(isl_dim_copy(dim));
1067 isl_int_set_si(v, -10);
1068 isl_constraint_set_constant(c, v);
1069 isl_int_set_si(v, 1);
1070 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1071 bset = isl_basic_set_add_constraint(bset, c);
1073 c = isl_inequality_alloc(dim);
1074 isl_int_set_si(v, 42);
1075 isl_constraint_set_constant(c, v);
1076 isl_int_set_si(v, -1);
1077 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1078 bset = isl_basic_set_add_constraint(bset, c);
1080 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1086 struct isl_basic_set *bset;
1087 bset = isl_basic_set_read_from_str(ctx,
1088 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1090 A basic set or relation can also be constructed from two matrices
1091 describing the equalities and the inequalities.
1093 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1094 __isl_take isl_dim *dim,
1095 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1096 enum isl_dim_type c1,
1097 enum isl_dim_type c2, enum isl_dim_type c3,
1098 enum isl_dim_type c4);
1099 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1100 __isl_take isl_dim *dim,
1101 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1102 enum isl_dim_type c1,
1103 enum isl_dim_type c2, enum isl_dim_type c3,
1104 enum isl_dim_type c4, enum isl_dim_type c5);
1106 The C<isl_dim_type> arguments indicate the order in which
1107 different kinds of variables appear in the input matrices
1108 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1109 C<isl_dim_set> and C<isl_dim_div> for sets and
1110 of C<isl_dim_cst>, C<isl_dim_param>,
1111 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1113 A (basic) relation can also be constructed from a (piecewise) affine expression
1114 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1116 __isl_give isl_basic_map *isl_basic_map_from_aff(
1117 __isl_take isl_aff *aff);
1118 __isl_give isl_map *isl_map_from_pw_aff(
1119 __isl_take isl_pw_aff *pwaff);
1120 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1121 __isl_take isl_dim *domain_dim,
1122 __isl_take isl_aff_list *list);
1124 The C<domain_dim> argument describes the domain of the resulting
1125 basic relation. It is required because the C<list> may consist
1126 of zero affine expressions.
1128 =head2 Inspecting Sets and Relations
1130 Usually, the user should not have to care about the actual constraints
1131 of the sets and maps, but should instead apply the abstract operations
1132 explained in the following sections.
1133 Occasionally, however, it may be required to inspect the individual
1134 coefficients of the constraints. This section explains how to do so.
1135 In these cases, it may also be useful to have C<isl> compute
1136 an explicit representation of the existentially quantified variables.
1138 __isl_give isl_set *isl_set_compute_divs(
1139 __isl_take isl_set *set);
1140 __isl_give isl_map *isl_map_compute_divs(
1141 __isl_take isl_map *map);
1142 __isl_give isl_union_set *isl_union_set_compute_divs(
1143 __isl_take isl_union_set *uset);
1144 __isl_give isl_union_map *isl_union_map_compute_divs(
1145 __isl_take isl_union_map *umap);
1147 This explicit representation defines the existentially quantified
1148 variables as integer divisions of the other variables, possibly
1149 including earlier existentially quantified variables.
1150 An explicitly represented existentially quantified variable therefore
1151 has a unique value when the values of the other variables are known.
1152 If, furthermore, the same existentials, i.e., existentials
1153 with the same explicit representations, should appear in the
1154 same order in each of the disjuncts of a set or map, then the user should call
1155 either of the following functions.
1157 __isl_give isl_set *isl_set_align_divs(
1158 __isl_take isl_set *set);
1159 __isl_give isl_map *isl_map_align_divs(
1160 __isl_take isl_map *map);
1162 Alternatively, the existentially quantified variables can be removed
1163 using the following functions, which compute an overapproximation.
1165 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1166 __isl_take isl_basic_set *bset);
1167 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1168 __isl_take isl_basic_map *bmap);
1169 __isl_give isl_set *isl_set_remove_divs(
1170 __isl_take isl_set *set);
1171 __isl_give isl_map *isl_map_remove_divs(
1172 __isl_take isl_map *map);
1174 To iterate over all the sets or maps in a union set or map, use
1176 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1177 int (*fn)(__isl_take isl_set *set, void *user),
1179 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1180 int (*fn)(__isl_take isl_map *map, void *user),
1183 The number of sets or maps in a union set or map can be obtained
1186 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1187 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1189 To extract the set or map from a union with a given dimension
1192 __isl_give isl_set *isl_union_set_extract_set(
1193 __isl_keep isl_union_set *uset,
1194 __isl_take isl_dim *dim);
1195 __isl_give isl_map *isl_union_map_extract_map(
1196 __isl_keep isl_union_map *umap,
1197 __isl_take isl_dim *dim);
1199 To iterate over all the basic sets or maps in a set or map, use
1201 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1202 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1204 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1205 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1208 The callback function C<fn> should return 0 if successful and
1209 -1 if an error occurs. In the latter case, or if any other error
1210 occurs, the above functions will return -1.
1212 It should be noted that C<isl> does not guarantee that
1213 the basic sets or maps passed to C<fn> are disjoint.
1214 If this is required, then the user should call one of
1215 the following functions first.
1217 __isl_give isl_set *isl_set_make_disjoint(
1218 __isl_take isl_set *set);
1219 __isl_give isl_map *isl_map_make_disjoint(
1220 __isl_take isl_map *map);
1222 The number of basic sets in a set can be obtained
1225 int isl_set_n_basic_set(__isl_keep isl_set *set);
1227 To iterate over the constraints of a basic set or map, use
1229 #include <isl/constraint.h>
1231 int isl_basic_map_foreach_constraint(
1232 __isl_keep isl_basic_map *bmap,
1233 int (*fn)(__isl_take isl_constraint *c, void *user),
1235 void isl_constraint_free(struct isl_constraint *c);
1237 Again, the callback function C<fn> should return 0 if successful and
1238 -1 if an error occurs. In the latter case, or if any other error
1239 occurs, the above functions will return -1.
1240 The constraint C<c> represents either an equality or an inequality.
1241 Use the following function to find out whether a constraint
1242 represents an equality. If not, it represents an inequality.
1244 int isl_constraint_is_equality(
1245 __isl_keep isl_constraint *constraint);
1247 The coefficients of the constraints can be inspected using
1248 the following functions.
1250 void isl_constraint_get_constant(
1251 __isl_keep isl_constraint *constraint, isl_int *v);
1252 void isl_constraint_get_coefficient(
1253 __isl_keep isl_constraint *constraint,
1254 enum isl_dim_type type, int pos, isl_int *v);
1255 int isl_constraint_involves_dims(
1256 __isl_keep isl_constraint *constraint,
1257 enum isl_dim_type type, unsigned first, unsigned n);
1259 The explicit representations of the existentially quantified
1260 variables can be inspected using the following functions.
1261 Note that the user is only allowed to use these functions
1262 if the inspected set or map is the result of a call
1263 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1265 __isl_give isl_div *isl_constraint_div(
1266 __isl_keep isl_constraint *constraint, int pos);
1267 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1268 void isl_div_get_constant(__isl_keep isl_div *div,
1270 void isl_div_get_denominator(__isl_keep isl_div *div,
1272 void isl_div_get_coefficient(__isl_keep isl_div *div,
1273 enum isl_dim_type type, int pos, isl_int *v);
1275 To obtain the constraints of a basic set or map in matrix
1276 form, use the following functions.
1278 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1279 __isl_keep isl_basic_set *bset,
1280 enum isl_dim_type c1, enum isl_dim_type c2,
1281 enum isl_dim_type c3, enum isl_dim_type c4);
1282 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1283 __isl_keep isl_basic_set *bset,
1284 enum isl_dim_type c1, enum isl_dim_type c2,
1285 enum isl_dim_type c3, enum isl_dim_type c4);
1286 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1287 __isl_keep isl_basic_map *bmap,
1288 enum isl_dim_type c1,
1289 enum isl_dim_type c2, enum isl_dim_type c3,
1290 enum isl_dim_type c4, enum isl_dim_type c5);
1291 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type c1,
1294 enum isl_dim_type c2, enum isl_dim_type c3,
1295 enum isl_dim_type c4, enum isl_dim_type c5);
1297 The C<isl_dim_type> arguments dictate the order in which
1298 different kinds of variables appear in the resulting matrix
1299 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1300 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1302 To check whether the description of a set or relation depends
1303 on one or more given dimensions, it is not necessary to iterate over all
1304 constraints. Instead the following functions can be used.
1306 int isl_basic_set_involves_dims(
1307 __isl_keep isl_basic_set *bset,
1308 enum isl_dim_type type, unsigned first, unsigned n);
1309 int isl_set_involves_dims(__isl_keep isl_set *set,
1310 enum isl_dim_type type, unsigned first, unsigned n);
1311 int isl_basic_map_involves_dims(
1312 __isl_keep isl_basic_map *bmap,
1313 enum isl_dim_type type, unsigned first, unsigned n);
1314 int isl_map_involves_dims(__isl_keep isl_map *map,
1315 enum isl_dim_type type, unsigned first, unsigned n);
1317 The identifiers or names of the domain and range spaces of a set
1318 or relation can be read off or set using the following functions.
1320 __isl_give isl_set *isl_set_set_tuple_id(
1321 __isl_take isl_set *set, __isl_take isl_id *id);
1322 __isl_give isl_id *isl_set_get_tuple_id(
1323 __isl_keep isl_set *set);
1324 __isl_give isl_map *isl_map_set_tuple_id(
1325 __isl_take isl_map *map, enum isl_dim_type type,
1326 __isl_take isl_id *id);
1327 __isl_give isl_map *isl_map_reset_tuple_id(
1328 __isl_take isl_map *map, enum isl_dim_type type);
1329 __isl_give isl_id *isl_map_get_tuple_id(
1330 __isl_keep isl_map *map, enum isl_dim_type type);
1332 const char *isl_basic_set_get_tuple_name(
1333 __isl_keep isl_basic_set *bset);
1334 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1335 __isl_take isl_basic_set *set, const char *s);
1336 const char *isl_set_get_tuple_name(
1337 __isl_keep isl_set *set);
1338 const char *isl_basic_map_get_tuple_name(
1339 __isl_keep isl_basic_map *bmap,
1340 enum isl_dim_type type);
1341 const char *isl_map_get_tuple_name(
1342 __isl_keep isl_map *map,
1343 enum isl_dim_type type);
1345 As with C<isl_dim_get_tuple_name>, the value returned points to
1346 an internal data structure.
1347 The identifiers, positions or names of individual dimensions can be
1348 read off using the following functions.
1350 __isl_give isl_set *isl_set_set_dim_id(
1351 __isl_take isl_set *set, enum isl_dim_type type,
1352 unsigned pos, __isl_take isl_id *id);
1353 __isl_give isl_id *isl_set_get_dim_id(
1354 __isl_keep isl_set *set, enum isl_dim_type type,
1356 __isl_give isl_map *isl_map_set_dim_id(
1357 __isl_take isl_map *map, enum isl_dim_type type,
1358 unsigned pos, __isl_take isl_id *id);
1359 __isl_give isl_id *isl_map_get_dim_id(
1360 __isl_keep isl_map *map, enum isl_dim_type type,
1363 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1364 enum isl_dim_type type, __isl_keep isl_id *id);
1365 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1366 enum isl_dim_type type, __isl_keep isl_id *id);
1368 const char *isl_constraint_get_dim_name(
1369 __isl_keep isl_constraint *constraint,
1370 enum isl_dim_type type, unsigned pos);
1371 const char *isl_basic_set_get_dim_name(
1372 __isl_keep isl_basic_set *bset,
1373 enum isl_dim_type type, unsigned pos);
1374 const char *isl_set_get_dim_name(
1375 __isl_keep isl_set *set,
1376 enum isl_dim_type type, unsigned pos);
1377 const char *isl_basic_map_get_dim_name(
1378 __isl_keep isl_basic_map *bmap,
1379 enum isl_dim_type type, unsigned pos);
1380 const char *isl_map_get_dim_name(
1381 __isl_keep isl_map *map,
1382 enum isl_dim_type type, unsigned pos);
1384 These functions are mostly useful to obtain the identifiers, positions
1385 or names of the parameters.
1389 =head3 Unary Properties
1395 The following functions test whether the given set or relation
1396 contains any integer points. The ``plain'' variants do not perform
1397 any computations, but simply check if the given set or relation
1398 is already known to be empty.
1400 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1401 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1402 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1403 int isl_set_is_empty(__isl_keep isl_set *set);
1404 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1405 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1406 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1407 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1408 int isl_map_is_empty(__isl_keep isl_map *map);
1409 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1411 =item * Universality
1413 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1414 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1415 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1417 =item * Single-valuedness
1419 int isl_map_is_single_valued(__isl_keep isl_map *map);
1420 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1424 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1425 int isl_map_is_injective(__isl_keep isl_map *map);
1426 int isl_union_map_plain_is_injective(
1427 __isl_keep isl_union_map *umap);
1428 int isl_union_map_is_injective(
1429 __isl_keep isl_union_map *umap);
1433 int isl_map_is_bijective(__isl_keep isl_map *map);
1434 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1438 The following functions check whether the domain of the given
1439 (basic) set is a wrapped relation.
1441 int isl_basic_set_is_wrapping(
1442 __isl_keep isl_basic_set *bset);
1443 int isl_set_is_wrapping(__isl_keep isl_set *set);
1445 =item * Internal Product
1447 int isl_basic_map_can_zip(
1448 __isl_keep isl_basic_map *bmap);
1449 int isl_map_can_zip(__isl_keep isl_map *map);
1451 Check whether the product of domain and range of the given relation
1453 i.e., whether both domain and range are nested relations.
1457 =head3 Binary Properties
1463 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1464 __isl_keep isl_set *set2);
1465 int isl_set_is_equal(__isl_keep isl_set *set1,
1466 __isl_keep isl_set *set2);
1467 int isl_union_set_is_equal(
1468 __isl_keep isl_union_set *uset1,
1469 __isl_keep isl_union_set *uset2);
1470 int isl_basic_map_is_equal(
1471 __isl_keep isl_basic_map *bmap1,
1472 __isl_keep isl_basic_map *bmap2);
1473 int isl_map_is_equal(__isl_keep isl_map *map1,
1474 __isl_keep isl_map *map2);
1475 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1476 __isl_keep isl_map *map2);
1477 int isl_union_map_is_equal(
1478 __isl_keep isl_union_map *umap1,
1479 __isl_keep isl_union_map *umap2);
1481 =item * Disjointness
1483 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1484 __isl_keep isl_set *set2);
1488 int isl_set_is_subset(__isl_keep isl_set *set1,
1489 __isl_keep isl_set *set2);
1490 int isl_set_is_strict_subset(
1491 __isl_keep isl_set *set1,
1492 __isl_keep isl_set *set2);
1493 int isl_union_set_is_subset(
1494 __isl_keep isl_union_set *uset1,
1495 __isl_keep isl_union_set *uset2);
1496 int isl_union_set_is_strict_subset(
1497 __isl_keep isl_union_set *uset1,
1498 __isl_keep isl_union_set *uset2);
1499 int isl_basic_map_is_subset(
1500 __isl_keep isl_basic_map *bmap1,
1501 __isl_keep isl_basic_map *bmap2);
1502 int isl_basic_map_is_strict_subset(
1503 __isl_keep isl_basic_map *bmap1,
1504 __isl_keep isl_basic_map *bmap2);
1505 int isl_map_is_subset(
1506 __isl_keep isl_map *map1,
1507 __isl_keep isl_map *map2);
1508 int isl_map_is_strict_subset(
1509 __isl_keep isl_map *map1,
1510 __isl_keep isl_map *map2);
1511 int isl_union_map_is_subset(
1512 __isl_keep isl_union_map *umap1,
1513 __isl_keep isl_union_map *umap2);
1514 int isl_union_map_is_strict_subset(
1515 __isl_keep isl_union_map *umap1,
1516 __isl_keep isl_union_map *umap2);
1520 =head2 Unary Operations
1526 __isl_give isl_set *isl_set_complement(
1527 __isl_take isl_set *set);
1531 __isl_give isl_basic_map *isl_basic_map_reverse(
1532 __isl_take isl_basic_map *bmap);
1533 __isl_give isl_map *isl_map_reverse(
1534 __isl_take isl_map *map);
1535 __isl_give isl_union_map *isl_union_map_reverse(
1536 __isl_take isl_union_map *umap);
1540 __isl_give isl_basic_set *isl_basic_set_project_out(
1541 __isl_take isl_basic_set *bset,
1542 enum isl_dim_type type, unsigned first, unsigned n);
1543 __isl_give isl_basic_map *isl_basic_map_project_out(
1544 __isl_take isl_basic_map *bmap,
1545 enum isl_dim_type type, unsigned first, unsigned n);
1546 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1547 enum isl_dim_type type, unsigned first, unsigned n);
1548 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1549 enum isl_dim_type type, unsigned first, unsigned n);
1550 __isl_give isl_basic_set *isl_basic_map_domain(
1551 __isl_take isl_basic_map *bmap);
1552 __isl_give isl_basic_set *isl_basic_map_range(
1553 __isl_take isl_basic_map *bmap);
1554 __isl_give isl_set *isl_map_domain(
1555 __isl_take isl_map *bmap);
1556 __isl_give isl_set *isl_map_range(
1557 __isl_take isl_map *map);
1558 __isl_give isl_union_set *isl_union_map_domain(
1559 __isl_take isl_union_map *umap);
1560 __isl_give isl_union_set *isl_union_map_range(
1561 __isl_take isl_union_map *umap);
1563 __isl_give isl_basic_map *isl_basic_map_domain_map(
1564 __isl_take isl_basic_map *bmap);
1565 __isl_give isl_basic_map *isl_basic_map_range_map(
1566 __isl_take isl_basic_map *bmap);
1567 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1568 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1569 __isl_give isl_union_map *isl_union_map_domain_map(
1570 __isl_take isl_union_map *umap);
1571 __isl_give isl_union_map *isl_union_map_range_map(
1572 __isl_take isl_union_map *umap);
1574 The functions above construct a (basic, regular or union) relation
1575 that maps (a wrapped version of) the input relation to its domain or range.
1579 __isl_give isl_set *isl_set_eliminate(
1580 __isl_take isl_set *set, enum isl_dim_type type,
1581 unsigned first, unsigned n);
1583 Eliminate the coefficients for the given dimensions from the constraints,
1584 without removing the dimensions.
1588 __isl_give isl_basic_set *isl_basic_set_fix(
1589 __isl_take isl_basic_set *bset,
1590 enum isl_dim_type type, unsigned pos,
1592 __isl_give isl_basic_set *isl_basic_set_fix_si(
1593 __isl_take isl_basic_set *bset,
1594 enum isl_dim_type type, unsigned pos, int value);
1595 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1596 enum isl_dim_type type, unsigned pos,
1598 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1599 enum isl_dim_type type, unsigned pos, int value);
1600 __isl_give isl_basic_map *isl_basic_map_fix_si(
1601 __isl_take isl_basic_map *bmap,
1602 enum isl_dim_type type, unsigned pos, int value);
1603 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1604 enum isl_dim_type type, unsigned pos, int value);
1606 Intersect the set or relation with the hyperplane where the given
1607 dimension has the fixed given value.
1609 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1610 enum isl_dim_type type1, int pos1,
1611 enum isl_dim_type type2, int pos2);
1612 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1613 enum isl_dim_type type1, int pos1,
1614 enum isl_dim_type type2, int pos2);
1616 Intersect the set or relation with the hyperplane where the given
1617 dimensions are equal to each other.
1619 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1620 enum isl_dim_type type1, int pos1,
1621 enum isl_dim_type type2, int pos2);
1623 Intersect the relation with the hyperplane where the given
1624 dimensions have opposite values.
1628 __isl_give isl_map *isl_set_identity(
1629 __isl_take isl_set *set);
1630 __isl_give isl_union_map *isl_union_set_identity(
1631 __isl_take isl_union_set *uset);
1633 Construct an identity relation on the given (union) set.
1637 __isl_give isl_basic_set *isl_basic_map_deltas(
1638 __isl_take isl_basic_map *bmap);
1639 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1640 __isl_give isl_union_set *isl_union_map_deltas(
1641 __isl_take isl_union_map *umap);
1643 These functions return a (basic) set containing the differences
1644 between image elements and corresponding domain elements in the input.
1646 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1647 __isl_take isl_basic_map *bmap);
1648 __isl_give isl_map *isl_map_deltas_map(
1649 __isl_take isl_map *map);
1650 __isl_give isl_union_map *isl_union_map_deltas_map(
1651 __isl_take isl_union_map *umap);
1653 The functions above construct a (basic, regular or union) relation
1654 that maps (a wrapped version of) the input relation to its delta set.
1658 Simplify the representation of a set or relation by trying
1659 to combine pairs of basic sets or relations into a single
1660 basic set or relation.
1662 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1664 __isl_give isl_union_set *isl_union_set_coalesce(
1665 __isl_take isl_union_set *uset);
1666 __isl_give isl_union_map *isl_union_map_coalesce(
1667 __isl_take isl_union_map *umap);
1669 =item * Detecting equalities
1671 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1672 __isl_take isl_basic_set *bset);
1673 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1674 __isl_take isl_basic_map *bmap);
1675 __isl_give isl_set *isl_set_detect_equalities(
1676 __isl_take isl_set *set);
1677 __isl_give isl_map *isl_map_detect_equalities(
1678 __isl_take isl_map *map);
1679 __isl_give isl_union_set *isl_union_set_detect_equalities(
1680 __isl_take isl_union_set *uset);
1681 __isl_give isl_union_map *isl_union_map_detect_equalities(
1682 __isl_take isl_union_map *umap);
1684 Simplify the representation of a set or relation by detecting implicit
1687 =item * Removing redundant constraints
1689 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1690 __isl_take isl_basic_set *bset);
1691 __isl_give isl_set *isl_set_remove_redundancies(
1692 __isl_take isl_set *set);
1693 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1694 __isl_take isl_basic_map *bmap);
1695 __isl_give isl_map *isl_map_remove_redundancies(
1696 __isl_take isl_map *map);
1700 __isl_give isl_basic_set *isl_set_convex_hull(
1701 __isl_take isl_set *set);
1702 __isl_give isl_basic_map *isl_map_convex_hull(
1703 __isl_take isl_map *map);
1705 If the input set or relation has any existentially quantified
1706 variables, then the result of these operations is currently undefined.
1710 __isl_give isl_basic_set *isl_set_simple_hull(
1711 __isl_take isl_set *set);
1712 __isl_give isl_basic_map *isl_map_simple_hull(
1713 __isl_take isl_map *map);
1714 __isl_give isl_union_map *isl_union_map_simple_hull(
1715 __isl_take isl_union_map *umap);
1717 These functions compute a single basic set or relation
1718 that contains the whole input set or relation.
1719 In particular, the output is described by translates
1720 of the constraints describing the basic sets or relations in the input.
1724 (See \autoref{s:simple hull}.)
1730 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1731 __isl_take isl_basic_set *bset);
1732 __isl_give isl_basic_set *isl_set_affine_hull(
1733 __isl_take isl_set *set);
1734 __isl_give isl_union_set *isl_union_set_affine_hull(
1735 __isl_take isl_union_set *uset);
1736 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1737 __isl_take isl_basic_map *bmap);
1738 __isl_give isl_basic_map *isl_map_affine_hull(
1739 __isl_take isl_map *map);
1740 __isl_give isl_union_map *isl_union_map_affine_hull(
1741 __isl_take isl_union_map *umap);
1743 In case of union sets and relations, the affine hull is computed
1746 =item * Polyhedral hull
1748 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1749 __isl_take isl_set *set);
1750 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1751 __isl_take isl_map *map);
1752 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1753 __isl_take isl_union_set *uset);
1754 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1755 __isl_take isl_union_map *umap);
1757 These functions compute a single basic set or relation
1758 not involving any existentially quantified variables
1759 that contains the whole input set or relation.
1760 In case of union sets and relations, the polyhedral hull is computed
1763 =item * Optimization
1765 #include <isl/ilp.h>
1766 enum isl_lp_result isl_basic_set_max(
1767 __isl_keep isl_basic_set *bset,
1768 __isl_keep isl_aff *obj, isl_int *opt)
1769 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1770 __isl_keep isl_aff *obj, isl_int *opt);
1771 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1772 __isl_keep isl_aff *obj, isl_int *opt);
1774 Compute the minimum or maximum of the integer affine expression C<obj>
1775 over the points in C<set>, returning the result in C<opt>.
1776 The return value may be one of C<isl_lp_error>,
1777 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1779 =item * Parametric optimization
1781 __isl_give isl_pw_aff *isl_set_dim_max(
1782 __isl_take isl_set *set, int pos);
1784 Compute the maximum of the given set dimension as a function of the
1785 parameters, but independently of the other set dimensions.
1786 For lexicographic optimization, see L<"Lexicographic Optimization">.
1790 The following functions compute either the set of (rational) coefficient
1791 values of valid constraints for the given set or the set of (rational)
1792 values satisfying the constraints with coefficients from the given set.
1793 Internally, these two sets of functions perform essentially the
1794 same operations, except that the set of coefficients is assumed to
1795 be a cone, while the set of values may be any polyhedron.
1796 The current implementation is based on the Farkas lemma and
1797 Fourier-Motzkin elimination, but this may change or be made optional
1798 in future. In particular, future implementations may use different
1799 dualization algorithms or skip the elimination step.
1801 __isl_give isl_basic_set *isl_basic_set_coefficients(
1802 __isl_take isl_basic_set *bset);
1803 __isl_give isl_basic_set *isl_set_coefficients(
1804 __isl_take isl_set *set);
1805 __isl_give isl_union_set *isl_union_set_coefficients(
1806 __isl_take isl_union_set *bset);
1807 __isl_give isl_basic_set *isl_basic_set_solutions(
1808 __isl_take isl_basic_set *bset);
1809 __isl_give isl_basic_set *isl_set_solutions(
1810 __isl_take isl_set *set);
1811 __isl_give isl_union_set *isl_union_set_solutions(
1812 __isl_take isl_union_set *bset);
1816 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1818 __isl_give isl_union_map *isl_union_map_power(
1819 __isl_take isl_union_map *umap, int *exact);
1821 Compute a parametric representation for all positive powers I<k> of C<map>.
1822 The result maps I<k> to a nested relation corresponding to the
1823 I<k>th power of C<map>.
1824 The result may be an overapproximation. If the result is known to be exact,
1825 then C<*exact> is set to C<1>.
1827 =item * Transitive closure
1829 __isl_give isl_map *isl_map_transitive_closure(
1830 __isl_take isl_map *map, int *exact);
1831 __isl_give isl_union_map *isl_union_map_transitive_closure(
1832 __isl_take isl_union_map *umap, int *exact);
1834 Compute the transitive closure of C<map>.
1835 The result may be an overapproximation. If the result is known to be exact,
1836 then C<*exact> is set to C<1>.
1838 =item * Reaching path lengths
1840 __isl_give isl_map *isl_map_reaching_path_lengths(
1841 __isl_take isl_map *map, int *exact);
1843 Compute a relation that maps each element in the range of C<map>
1844 to the lengths of all paths composed of edges in C<map> that
1845 end up in the given element.
1846 The result may be an overapproximation. If the result is known to be exact,
1847 then C<*exact> is set to C<1>.
1848 To compute the I<maximal> path length, the resulting relation
1849 should be postprocessed by C<isl_map_lexmax>.
1850 In particular, if the input relation is a dependence relation
1851 (mapping sources to sinks), then the maximal path length corresponds
1852 to the free schedule.
1853 Note, however, that C<isl_map_lexmax> expects the maximum to be
1854 finite, so if the path lengths are unbounded (possibly due to
1855 the overapproximation), then you will get an error message.
1859 __isl_give isl_basic_set *isl_basic_map_wrap(
1860 __isl_take isl_basic_map *bmap);
1861 __isl_give isl_set *isl_map_wrap(
1862 __isl_take isl_map *map);
1863 __isl_give isl_union_set *isl_union_map_wrap(
1864 __isl_take isl_union_map *umap);
1865 __isl_give isl_basic_map *isl_basic_set_unwrap(
1866 __isl_take isl_basic_set *bset);
1867 __isl_give isl_map *isl_set_unwrap(
1868 __isl_take isl_set *set);
1869 __isl_give isl_union_map *isl_union_set_unwrap(
1870 __isl_take isl_union_set *uset);
1874 Remove any internal structure of domain (and range) of the given
1875 set or relation. If there is any such internal structure in the input,
1876 then the name of the space is also removed.
1878 __isl_give isl_basic_set *isl_basic_set_flatten(
1879 __isl_take isl_basic_set *bset);
1880 __isl_give isl_set *isl_set_flatten(
1881 __isl_take isl_set *set);
1882 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1883 __isl_take isl_basic_map *bmap);
1884 __isl_give isl_map *isl_map_flatten_range(
1885 __isl_take isl_map *map);
1886 __isl_give isl_basic_map *isl_basic_map_flatten(
1887 __isl_take isl_basic_map *bmap);
1888 __isl_give isl_map *isl_map_flatten(
1889 __isl_take isl_map *map);
1891 __isl_give isl_map *isl_set_flatten_map(
1892 __isl_take isl_set *set);
1894 The function above constructs a relation
1895 that maps the input set to a flattened version of the set.
1899 Lift the input set to a space with extra dimensions corresponding
1900 to the existentially quantified variables in the input.
1901 In particular, the result lives in a wrapped map where the domain
1902 is the original space and the range corresponds to the original
1903 existentially quantified variables.
1905 __isl_give isl_basic_set *isl_basic_set_lift(
1906 __isl_take isl_basic_set *bset);
1907 __isl_give isl_set *isl_set_lift(
1908 __isl_take isl_set *set);
1909 __isl_give isl_union_set *isl_union_set_lift(
1910 __isl_take isl_union_set *uset);
1912 =item * Internal Product
1914 __isl_give isl_basic_map *isl_basic_map_zip(
1915 __isl_take isl_basic_map *bmap);
1916 __isl_give isl_map *isl_map_zip(
1917 __isl_take isl_map *map);
1918 __isl_give isl_union_map *isl_union_map_zip(
1919 __isl_take isl_union_map *umap);
1921 Given a relation with nested relations for domain and range,
1922 interchange the range of the domain with the domain of the range.
1924 =item * Aligning parameters
1926 __isl_give isl_set *isl_set_align_params(
1927 __isl_take isl_set *set,
1928 __isl_take isl_dim *model);
1929 __isl_give isl_map *isl_map_align_params(
1930 __isl_take isl_map *map,
1931 __isl_take isl_dim *model);
1933 Change the order of the parameters of the given set or relation
1934 such that the first parameters match those of C<model>.
1935 This may involve the introduction of extra parameters.
1936 All parameters need to be named.
1938 =item * Dimension manipulation
1940 __isl_give isl_set *isl_set_add_dims(
1941 __isl_take isl_set *set,
1942 enum isl_dim_type type, unsigned n);
1943 __isl_give isl_map *isl_map_add_dims(
1944 __isl_take isl_map *map,
1945 enum isl_dim_type type, unsigned n);
1947 It is usually not advisable to directly change the (input or output)
1948 space of a set or a relation as this removes the name and the internal
1949 structure of the space. However, the above functions can be useful
1950 to add new parameters, assuming
1951 C<isl_set_align_params> and C<isl_map_align_params>
1956 =head2 Binary Operations
1958 The two arguments of a binary operation not only need to live
1959 in the same C<isl_ctx>, they currently also need to have
1960 the same (number of) parameters.
1962 =head3 Basic Operations
1966 =item * Intersection
1968 __isl_give isl_basic_set *isl_basic_set_intersect(
1969 __isl_take isl_basic_set *bset1,
1970 __isl_take isl_basic_set *bset2);
1971 __isl_give isl_set *isl_set_intersect_params(
1972 __isl_take isl_set *set,
1973 __isl_take isl_set *params);
1974 __isl_give isl_set *isl_set_intersect(
1975 __isl_take isl_set *set1,
1976 __isl_take isl_set *set2);
1977 __isl_give isl_union_set *isl_union_set_intersect(
1978 __isl_take isl_union_set *uset1,
1979 __isl_take isl_union_set *uset2);
1980 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1981 __isl_take isl_basic_map *bmap,
1982 __isl_take isl_basic_set *bset);
1983 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1984 __isl_take isl_basic_map *bmap,
1985 __isl_take isl_basic_set *bset);
1986 __isl_give isl_basic_map *isl_basic_map_intersect(
1987 __isl_take isl_basic_map *bmap1,
1988 __isl_take isl_basic_map *bmap2);
1989 __isl_give isl_map *isl_map_intersect_params(
1990 __isl_take isl_map *map,
1991 __isl_take isl_set *params);
1992 __isl_give isl_map *isl_map_intersect_domain(
1993 __isl_take isl_map *map,
1994 __isl_take isl_set *set);
1995 __isl_give isl_map *isl_map_intersect_range(
1996 __isl_take isl_map *map,
1997 __isl_take isl_set *set);
1998 __isl_give isl_map *isl_map_intersect(
1999 __isl_take isl_map *map1,
2000 __isl_take isl_map *map2);
2001 __isl_give isl_union_map *isl_union_map_intersect_domain(
2002 __isl_take isl_union_map *umap,
2003 __isl_take isl_union_set *uset);
2004 __isl_give isl_union_map *isl_union_map_intersect_range(
2005 __isl_take isl_union_map *umap,
2006 __isl_take isl_union_set *uset);
2007 __isl_give isl_union_map *isl_union_map_intersect(
2008 __isl_take isl_union_map *umap1,
2009 __isl_take isl_union_map *umap2);
2013 __isl_give isl_set *isl_basic_set_union(
2014 __isl_take isl_basic_set *bset1,
2015 __isl_take isl_basic_set *bset2);
2016 __isl_give isl_map *isl_basic_map_union(
2017 __isl_take isl_basic_map *bmap1,
2018 __isl_take isl_basic_map *bmap2);
2019 __isl_give isl_set *isl_set_union(
2020 __isl_take isl_set *set1,
2021 __isl_take isl_set *set2);
2022 __isl_give isl_map *isl_map_union(
2023 __isl_take isl_map *map1,
2024 __isl_take isl_map *map2);
2025 __isl_give isl_union_set *isl_union_set_union(
2026 __isl_take isl_union_set *uset1,
2027 __isl_take isl_union_set *uset2);
2028 __isl_give isl_union_map *isl_union_map_union(
2029 __isl_take isl_union_map *umap1,
2030 __isl_take isl_union_map *umap2);
2032 =item * Set difference
2034 __isl_give isl_set *isl_set_subtract(
2035 __isl_take isl_set *set1,
2036 __isl_take isl_set *set2);
2037 __isl_give isl_map *isl_map_subtract(
2038 __isl_take isl_map *map1,
2039 __isl_take isl_map *map2);
2040 __isl_give isl_union_set *isl_union_set_subtract(
2041 __isl_take isl_union_set *uset1,
2042 __isl_take isl_union_set *uset2);
2043 __isl_give isl_union_map *isl_union_map_subtract(
2044 __isl_take isl_union_map *umap1,
2045 __isl_take isl_union_map *umap2);
2049 __isl_give isl_basic_set *isl_basic_set_apply(
2050 __isl_take isl_basic_set *bset,
2051 __isl_take isl_basic_map *bmap);
2052 __isl_give isl_set *isl_set_apply(
2053 __isl_take isl_set *set,
2054 __isl_take isl_map *map);
2055 __isl_give isl_union_set *isl_union_set_apply(
2056 __isl_take isl_union_set *uset,
2057 __isl_take isl_union_map *umap);
2058 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2059 __isl_take isl_basic_map *bmap1,
2060 __isl_take isl_basic_map *bmap2);
2061 __isl_give isl_basic_map *isl_basic_map_apply_range(
2062 __isl_take isl_basic_map *bmap1,
2063 __isl_take isl_basic_map *bmap2);
2064 __isl_give isl_map *isl_map_apply_domain(
2065 __isl_take isl_map *map1,
2066 __isl_take isl_map *map2);
2067 __isl_give isl_union_map *isl_union_map_apply_domain(
2068 __isl_take isl_union_map *umap1,
2069 __isl_take isl_union_map *umap2);
2070 __isl_give isl_map *isl_map_apply_range(
2071 __isl_take isl_map *map1,
2072 __isl_take isl_map *map2);
2073 __isl_give isl_union_map *isl_union_map_apply_range(
2074 __isl_take isl_union_map *umap1,
2075 __isl_take isl_union_map *umap2);
2077 =item * Cartesian Product
2079 __isl_give isl_set *isl_set_product(
2080 __isl_take isl_set *set1,
2081 __isl_take isl_set *set2);
2082 __isl_give isl_union_set *isl_union_set_product(
2083 __isl_take isl_union_set *uset1,
2084 __isl_take isl_union_set *uset2);
2085 __isl_give isl_basic_map *isl_basic_map_range_product(
2086 __isl_take isl_basic_map *bmap1,
2087 __isl_take isl_basic_map *bmap2);
2088 __isl_give isl_map *isl_map_range_product(
2089 __isl_take isl_map *map1,
2090 __isl_take isl_map *map2);
2091 __isl_give isl_union_map *isl_union_map_range_product(
2092 __isl_take isl_union_map *umap1,
2093 __isl_take isl_union_map *umap2);
2094 __isl_give isl_map *isl_map_product(
2095 __isl_take isl_map *map1,
2096 __isl_take isl_map *map2);
2097 __isl_give isl_union_map *isl_union_map_product(
2098 __isl_take isl_union_map *umap1,
2099 __isl_take isl_union_map *umap2);
2101 The above functions compute the cross product of the given
2102 sets or relations. The domains and ranges of the results
2103 are wrapped maps between domains and ranges of the inputs.
2104 To obtain a ``flat'' product, use the following functions
2107 __isl_give isl_basic_set *isl_basic_set_flat_product(
2108 __isl_take isl_basic_set *bset1,
2109 __isl_take isl_basic_set *bset2);
2110 __isl_give isl_set *isl_set_flat_product(
2111 __isl_take isl_set *set1,
2112 __isl_take isl_set *set2);
2113 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2114 __isl_take isl_basic_map *bmap1,
2115 __isl_take isl_basic_map *bmap2);
2116 __isl_give isl_map *isl_map_flat_range_product(
2117 __isl_take isl_map *map1,
2118 __isl_take isl_map *map2);
2119 __isl_give isl_union_map *isl_union_map_flat_range_product(
2120 __isl_take isl_union_map *umap1,
2121 __isl_take isl_union_map *umap2);
2122 __isl_give isl_basic_map *isl_basic_map_flat_product(
2123 __isl_take isl_basic_map *bmap1,
2124 __isl_take isl_basic_map *bmap2);
2125 __isl_give isl_map *isl_map_flat_product(
2126 __isl_take isl_map *map1,
2127 __isl_take isl_map *map2);
2129 =item * Simplification
2131 __isl_give isl_basic_set *isl_basic_set_gist(
2132 __isl_take isl_basic_set *bset,
2133 __isl_take isl_basic_set *context);
2134 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2135 __isl_take isl_set *context);
2136 __isl_give isl_union_set *isl_union_set_gist(
2137 __isl_take isl_union_set *uset,
2138 __isl_take isl_union_set *context);
2139 __isl_give isl_basic_map *isl_basic_map_gist(
2140 __isl_take isl_basic_map *bmap,
2141 __isl_take isl_basic_map *context);
2142 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2143 __isl_take isl_map *context);
2144 __isl_give isl_union_map *isl_union_map_gist(
2145 __isl_take isl_union_map *umap,
2146 __isl_take isl_union_map *context);
2148 The gist operation returns a set or relation that has the
2149 same intersection with the context as the input set or relation.
2150 Any implicit equality in the intersection is made explicit in the result,
2151 while all inequalities that are redundant with respect to the intersection
2153 In case of union sets and relations, the gist operation is performed
2158 =head3 Lexicographic Optimization
2160 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2161 the following functions
2162 compute a set that contains the lexicographic minimum or maximum
2163 of the elements in C<set> (or C<bset>) for those values of the parameters
2164 that satisfy C<dom>.
2165 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2166 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2168 In other words, the union of the parameter values
2169 for which the result is non-empty and of C<*empty>
2172 __isl_give isl_set *isl_basic_set_partial_lexmin(
2173 __isl_take isl_basic_set *bset,
2174 __isl_take isl_basic_set *dom,
2175 __isl_give isl_set **empty);
2176 __isl_give isl_set *isl_basic_set_partial_lexmax(
2177 __isl_take isl_basic_set *bset,
2178 __isl_take isl_basic_set *dom,
2179 __isl_give isl_set **empty);
2180 __isl_give isl_set *isl_set_partial_lexmin(
2181 __isl_take isl_set *set, __isl_take isl_set *dom,
2182 __isl_give isl_set **empty);
2183 __isl_give isl_set *isl_set_partial_lexmax(
2184 __isl_take isl_set *set, __isl_take isl_set *dom,
2185 __isl_give isl_set **empty);
2187 Given a (basic) set C<set> (or C<bset>), the following functions simply
2188 return a set containing the lexicographic minimum or maximum
2189 of the elements in C<set> (or C<bset>).
2190 In case of union sets, the optimum is computed per space.
2192 __isl_give isl_set *isl_basic_set_lexmin(
2193 __isl_take isl_basic_set *bset);
2194 __isl_give isl_set *isl_basic_set_lexmax(
2195 __isl_take isl_basic_set *bset);
2196 __isl_give isl_set *isl_set_lexmin(
2197 __isl_take isl_set *set);
2198 __isl_give isl_set *isl_set_lexmax(
2199 __isl_take isl_set *set);
2200 __isl_give isl_union_set *isl_union_set_lexmin(
2201 __isl_take isl_union_set *uset);
2202 __isl_give isl_union_set *isl_union_set_lexmax(
2203 __isl_take isl_union_set *uset);
2205 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2206 the following functions
2207 compute a relation that maps each element of C<dom>
2208 to the single lexicographic minimum or maximum
2209 of the elements that are associated to that same
2210 element in C<map> (or C<bmap>).
2211 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2212 that contains the elements in C<dom> that do not map
2213 to any elements in C<map> (or C<bmap>).
2214 In other words, the union of the domain of the result and of C<*empty>
2217 __isl_give isl_map *isl_basic_map_partial_lexmax(
2218 __isl_take isl_basic_map *bmap,
2219 __isl_take isl_basic_set *dom,
2220 __isl_give isl_set **empty);
2221 __isl_give isl_map *isl_basic_map_partial_lexmin(
2222 __isl_take isl_basic_map *bmap,
2223 __isl_take isl_basic_set *dom,
2224 __isl_give isl_set **empty);
2225 __isl_give isl_map *isl_map_partial_lexmax(
2226 __isl_take isl_map *map, __isl_take isl_set *dom,
2227 __isl_give isl_set **empty);
2228 __isl_give isl_map *isl_map_partial_lexmin(
2229 __isl_take isl_map *map, __isl_take isl_set *dom,
2230 __isl_give isl_set **empty);
2232 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2233 return a map mapping each element in the domain of
2234 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2235 of all elements associated to that element.
2236 In case of union relations, the optimum is computed per space.
2238 __isl_give isl_map *isl_basic_map_lexmin(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_give isl_map *isl_basic_map_lexmax(
2241 __isl_take isl_basic_map *bmap);
2242 __isl_give isl_map *isl_map_lexmin(
2243 __isl_take isl_map *map);
2244 __isl_give isl_map *isl_map_lexmax(
2245 __isl_take isl_map *map);
2246 __isl_give isl_union_map *isl_union_map_lexmin(
2247 __isl_take isl_union_map *umap);
2248 __isl_give isl_union_map *isl_union_map_lexmax(
2249 __isl_take isl_union_map *umap);
2253 Lists are defined over several element types, including
2254 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2255 Here we take lists of C<isl_set>s as an example.
2256 Lists can be created, copied and freed using the following functions.
2258 #include <isl/list.h>
2259 __isl_give isl_set_list *isl_set_list_alloc(
2260 isl_ctx *ctx, int n);
2261 __isl_give isl_set_list *isl_set_list_copy(
2262 __isl_keep isl_set_list *list);
2263 __isl_give isl_set_list *isl_set_list_add(
2264 __isl_take isl_set_list *list,
2265 __isl_take isl_set *el);
2266 void isl_set_list_free(__isl_take isl_set_list *list);
2268 C<isl_set_list_alloc> creates an empty list with a capacity for
2271 Lists can be inspected using the following functions.
2273 #include <isl/list.h>
2274 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2275 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2276 __isl_give struct isl_set *isl_set_list_get_set(
2277 __isl_keep isl_set_list *list, int index);
2278 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2279 int (*fn)(__isl_take struct isl_set *el, void *user),
2282 Lists can be printed using
2284 #include <isl/list.h>
2285 __isl_give isl_printer *isl_printer_print_set_list(
2286 __isl_take isl_printer *p,
2287 __isl_keep isl_set_list *list);
2291 Matrices can be created, copied and freed using the following functions.
2293 #include <isl/mat.h>
2294 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2295 unsigned n_row, unsigned n_col);
2296 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2297 void isl_mat_free(__isl_take isl_mat *mat);
2299 Note that the elements of a newly created matrix may have arbitrary values.
2300 The elements can be changed and inspected using the following functions.
2302 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2303 int isl_mat_rows(__isl_keep isl_mat *mat);
2304 int isl_mat_cols(__isl_keep isl_mat *mat);
2305 int isl_mat_get_element(__isl_keep isl_mat *mat,
2306 int row, int col, isl_int *v);
2307 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2308 int row, int col, isl_int v);
2309 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2310 int row, int col, int v);
2312 C<isl_mat_get_element> will return a negative value if anything went wrong.
2313 In that case, the value of C<*v> is undefined.
2315 The following function can be used to compute the (right) inverse
2316 of a matrix, i.e., a matrix such that the product of the original
2317 and the inverse (in that order) is a multiple of the identity matrix.
2318 The input matrix is assumed to be of full row-rank.
2320 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2322 The following function can be used to compute the (right) kernel
2323 (or null space) of a matrix, i.e., a matrix such that the product of
2324 the original and the kernel (in that order) is the zero matrix.
2326 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2328 =head2 Piecewise Quasi Affine Expressions
2330 The zero quasi affine expression can be created using
2332 __isl_give isl_aff *isl_aff_zero(
2333 __isl_take isl_local_space *ls);
2335 A quasi affine expression can also be initialized from an C<isl_div>:
2337 #include <isl/div.h>
2338 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2340 An empty piecewise quasi affine expression (one with no cells)
2341 or a piecewise quasi affine expression with a single cell can
2342 be created using the following functions.
2344 #include <isl/aff.h>
2345 __isl_give isl_pw_aff *isl_pw_aff_empty(
2346 __isl_take isl_dim *dim);
2347 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2348 __isl_take isl_set *set, __isl_take isl_aff *aff);
2350 Quasi affine expressions can be copied and freed using
2352 #include <isl/aff.h>
2353 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2354 void *isl_aff_free(__isl_take isl_aff *aff);
2356 __isl_give isl_pw_aff *isl_pw_aff_copy(
2357 __isl_keep isl_pw_aff *pwaff);
2358 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2360 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2361 using the following function. The constraint is required to have
2362 a non-zero coefficient for the specified dimension.
2364 #include <isl/constraint.h>
2365 __isl_give isl_aff *isl_constraint_get_bound(
2366 __isl_keep isl_constraint *constraint,
2367 enum isl_dim_type type, int pos);
2369 The entire affine expression of the constraint can also be extracted
2370 using the following function.
2372 #include <isl/constraint.h>
2373 __isl_give isl_aff *isl_constraint_get_aff(
2374 __isl_keep isl_constraint *constraint);
2376 Conversely, an equality constraint equating
2377 the affine expression to zero or an inequality constraint enforcing
2378 the affine expression to be non-negative, can be constructed using
2380 __isl_give isl_constraint *isl_equality_from_aff(
2381 __isl_take isl_aff *aff);
2382 __isl_give isl_constraint *isl_inequality_from_aff(
2383 __isl_take isl_aff *aff);
2385 The expression can be inspected using
2387 #include <isl/aff.h>
2388 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2389 int isl_aff_dim(__isl_keep isl_aff *aff,
2390 enum isl_dim_type type);
2391 __isl_give isl_local_space *isl_aff_get_local_space(
2392 __isl_keep isl_aff *aff);
2393 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2394 enum isl_dim_type type, unsigned pos);
2395 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2397 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2398 enum isl_dim_type type, int pos, isl_int *v);
2399 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2401 __isl_give isl_div *isl_aff_get_div(
2402 __isl_keep isl_aff *aff, int pos);
2404 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2405 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2407 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2408 enum isl_dim_type type, unsigned first, unsigned n);
2409 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2410 enum isl_dim_type type, unsigned first, unsigned n);
2412 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2413 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2414 enum isl_dim_type type);
2415 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2417 It can be modified using
2419 #include <isl/aff.h>
2420 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2421 __isl_take isl_pw_aff *pwaff,
2422 __isl_take isl_id *id);
2423 __isl_give isl_aff *isl_aff_set_dim_name(
2424 __isl_take isl_aff *aff, enum isl_dim_type type,
2425 unsigned pos, const char *s);
2426 __isl_give isl_aff *isl_aff_set_constant(
2427 __isl_take isl_aff *aff, isl_int v);
2428 __isl_give isl_aff *isl_aff_set_constant_si(
2429 __isl_take isl_aff *aff, int v);
2430 __isl_give isl_aff *isl_aff_set_coefficient(
2431 __isl_take isl_aff *aff,
2432 enum isl_dim_type type, int pos, isl_int v);
2433 __isl_give isl_aff *isl_aff_set_coefficient_si(
2434 __isl_take isl_aff *aff,
2435 enum isl_dim_type type, int pos, int v);
2436 __isl_give isl_aff *isl_aff_set_denominator(
2437 __isl_take isl_aff *aff, isl_int v);
2439 __isl_give isl_aff *isl_aff_add_constant(
2440 __isl_take isl_aff *aff, isl_int v);
2441 __isl_give isl_aff *isl_aff_add_constant_si(
2442 __isl_take isl_aff *aff, int v);
2443 __isl_give isl_aff *isl_aff_add_coefficient(
2444 __isl_take isl_aff *aff,
2445 enum isl_dim_type type, int pos, isl_int v);
2446 __isl_give isl_aff *isl_aff_add_coefficient_si(
2447 __isl_take isl_aff *aff,
2448 enum isl_dim_type type, int pos, int v);
2450 __isl_give isl_aff *isl_aff_insert_dims(
2451 __isl_take isl_aff *aff,
2452 enum isl_dim_type type, unsigned first, unsigned n);
2453 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2454 __isl_take isl_pw_aff *pwaff,
2455 enum isl_dim_type type, unsigned first, unsigned n);
2456 __isl_give isl_aff *isl_aff_add_dims(
2457 __isl_take isl_aff *aff,
2458 enum isl_dim_type type, unsigned n);
2459 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2460 __isl_take isl_pw_aff *pwaff,
2461 enum isl_dim_type type, unsigned n);
2462 __isl_give isl_aff *isl_aff_drop_dims(
2463 __isl_take isl_aff *aff,
2464 enum isl_dim_type type, unsigned first, unsigned n);
2465 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2466 __isl_take isl_pw_aff *pwaff,
2467 enum isl_dim_type type, unsigned first, unsigned n);
2469 Note that the C<set_constant> and C<set_coefficient> functions
2470 set the I<numerator> of the constant or coefficient, while
2471 C<add_constant> and C<add_coefficient> add an integer value to
2472 the possibly rational constant or coefficient.
2474 To check whether an affine expressions is obviously zero
2475 or obviously equal to some other affine expression, use
2477 #include <isl/aff.h>
2478 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2479 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2480 __isl_keep isl_aff *aff2);
2484 #include <isl/aff.h>
2485 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2486 __isl_take isl_aff *aff2);
2487 __isl_give isl_pw_aff *isl_pw_aff_add(
2488 __isl_take isl_pw_aff *pwaff1,
2489 __isl_take isl_pw_aff *pwaff2);
2490 __isl_give isl_pw_aff *isl_pw_aff_min(
2491 __isl_take isl_pw_aff *pwaff1,
2492 __isl_take isl_pw_aff *pwaff2);
2493 __isl_give isl_pw_aff *isl_pw_aff_max(
2494 __isl_take isl_pw_aff *pwaff1,
2495 __isl_take isl_pw_aff *pwaff2);
2496 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2497 __isl_take isl_aff *aff2);
2498 __isl_give isl_pw_aff *isl_pw_aff_sub(
2499 __isl_take isl_pw_aff *pwaff1,
2500 __isl_take isl_pw_aff *pwaff2);
2501 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2502 __isl_give isl_pw_aff *isl_pw_aff_neg(
2503 __isl_take isl_pw_aff *pwaff);
2504 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2505 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2506 __isl_take isl_pw_aff *pwaff);
2507 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2508 __isl_give isl_pw_aff *isl_pw_aff_floor(
2509 __isl_take isl_pw_aff *pwaff);
2510 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2512 __isl_give isl_pw_aff *isl_pw_aff_scale(
2513 __isl_take isl_pw_aff *pwaff, isl_int f);
2514 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2516 __isl_give isl_aff *isl_aff_scale_down_ui(
2517 __isl_take isl_aff *aff, unsigned f);
2518 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2519 __isl_take isl_pw_aff *pwaff, isl_int f);
2521 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2522 __isl_take isl_pw_aff *pwqp);
2524 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2525 __isl_take isl_pw_aff *pwaff,
2526 __isl_take isl_dim *model);
2528 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2529 __isl_take isl_set *context);
2530 __isl_give isl_pw_aff *isl_pw_aff_gist(
2531 __isl_take isl_pw_aff *pwaff,
2532 __isl_take isl_set *context);
2534 __isl_give isl_set *isl_pw_aff_domain(
2535 __isl_take isl_pw_aff *pwaff);
2537 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2538 __isl_take isl_aff *aff2);
2539 __isl_give isl_pw_aff *isl_pw_aff_mul(
2540 __isl_take isl_pw_aff *pwaff1,
2541 __isl_take isl_pw_aff *pwaff2);
2543 When multiplying two affine expressions, at least one of the two needs
2546 #include <isl/aff.h>
2547 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2548 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2549 __isl_give isl_set *isl_pw_aff_eq_set(
2550 __isl_take isl_pw_aff *pwaff1,
2551 __isl_take isl_pw_aff *pwaff2);
2552 __isl_give isl_set *isl_pw_aff_ne_set(
2553 __isl_take isl_pw_aff *pwaff1,
2554 __isl_take isl_pw_aff *pwaff2);
2555 __isl_give isl_set *isl_pw_aff_le_set(
2556 __isl_take isl_pw_aff *pwaff1,
2557 __isl_take isl_pw_aff *pwaff2);
2558 __isl_give isl_set *isl_pw_aff_lt_set(
2559 __isl_take isl_pw_aff *pwaff1,
2560 __isl_take isl_pw_aff *pwaff2);
2561 __isl_give isl_set *isl_pw_aff_ge_set(
2562 __isl_take isl_pw_aff *pwaff1,
2563 __isl_take isl_pw_aff *pwaff2);
2564 __isl_give isl_set *isl_pw_aff_gt_set(
2565 __isl_take isl_pw_aff *pwaff1,
2566 __isl_take isl_pw_aff *pwaff2);
2568 The function C<isl_aff_ge_basic_set> returns a basic set
2569 containing those elements in the shared space
2570 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2571 The function C<isl_aff_ge_set> returns a set
2572 containing those elements in the shared domain
2573 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2575 #include <isl/aff.h>
2576 __isl_give isl_set *isl_pw_aff_nonneg_set(
2577 __isl_take isl_pw_aff *pwaff);
2579 The function C<isl_pw_aff_nonneg_set> returns a set
2580 containing those elements in the domain
2581 of C<pwaff> where C<pwaff> is non-negative.
2583 #include <isl/aff.h>
2584 __isl_give isl_pw_aff *isl_pw_aff_cond(
2585 __isl_take isl_set *cond,
2586 __isl_take isl_pw_aff *pwaff_true,
2587 __isl_take isl_pw_aff *pwaff_false);
2589 The function C<isl_pw_aff_cond> performs a conditional operator
2590 and returns an expression that is equal to C<pwaff_true>
2591 for elements in C<cond> and equal to C<pwaff_false> for elements
2594 #include <isl/aff.h>
2595 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2596 __isl_take isl_pw_aff *pwaff1,
2597 __isl_take isl_pw_aff *pwaff2);
2599 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2600 expression with a domain that is the union of those of C<pwaff1> and
2601 C<pwaff2> and such that on each cell, the quasi-affine expression is
2602 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2603 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2604 associated expression is the defined one.
2606 An expression can be printed using
2608 #include <isl/aff.h>
2609 __isl_give isl_printer *isl_printer_print_aff(
2610 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2612 __isl_give isl_printer *isl_printer_print_pw_aff(
2613 __isl_take isl_printer *p,
2614 __isl_keep isl_pw_aff *pwaff);
2618 Points are elements of a set. They can be used to construct
2619 simple sets (boxes) or they can be used to represent the
2620 individual elements of a set.
2621 The zero point (the origin) can be created using
2623 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2625 The coordinates of a point can be inspected, set and changed
2628 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2629 enum isl_dim_type type, int pos, isl_int *v);
2630 __isl_give isl_point *isl_point_set_coordinate(
2631 __isl_take isl_point *pnt,
2632 enum isl_dim_type type, int pos, isl_int v);
2634 __isl_give isl_point *isl_point_add_ui(
2635 __isl_take isl_point *pnt,
2636 enum isl_dim_type type, int pos, unsigned val);
2637 __isl_give isl_point *isl_point_sub_ui(
2638 __isl_take isl_point *pnt,
2639 enum isl_dim_type type, int pos, unsigned val);
2641 Other properties can be obtained using
2643 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2645 Points can be copied or freed using
2647 __isl_give isl_point *isl_point_copy(
2648 __isl_keep isl_point *pnt);
2649 void isl_point_free(__isl_take isl_point *pnt);
2651 A singleton set can be created from a point using
2653 __isl_give isl_basic_set *isl_basic_set_from_point(
2654 __isl_take isl_point *pnt);
2655 __isl_give isl_set *isl_set_from_point(
2656 __isl_take isl_point *pnt);
2658 and a box can be created from two opposite extremal points using
2660 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2661 __isl_take isl_point *pnt1,
2662 __isl_take isl_point *pnt2);
2663 __isl_give isl_set *isl_set_box_from_points(
2664 __isl_take isl_point *pnt1,
2665 __isl_take isl_point *pnt2);
2667 All elements of a B<bounded> (union) set can be enumerated using
2668 the following functions.
2670 int isl_set_foreach_point(__isl_keep isl_set *set,
2671 int (*fn)(__isl_take isl_point *pnt, void *user),
2673 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2674 int (*fn)(__isl_take isl_point *pnt, void *user),
2677 The function C<fn> is called for each integer point in
2678 C<set> with as second argument the last argument of
2679 the C<isl_set_foreach_point> call. The function C<fn>
2680 should return C<0> on success and C<-1> on failure.
2681 In the latter case, C<isl_set_foreach_point> will stop
2682 enumerating and return C<-1> as well.
2683 If the enumeration is performed successfully and to completion,
2684 then C<isl_set_foreach_point> returns C<0>.
2686 To obtain a single point of a (basic) set, use
2688 __isl_give isl_point *isl_basic_set_sample_point(
2689 __isl_take isl_basic_set *bset);
2690 __isl_give isl_point *isl_set_sample_point(
2691 __isl_take isl_set *set);
2693 If C<set> does not contain any (integer) points, then the
2694 resulting point will be ``void'', a property that can be
2697 int isl_point_is_void(__isl_keep isl_point *pnt);
2699 =head2 Piecewise Quasipolynomials
2701 A piecewise quasipolynomial is a particular kind of function that maps
2702 a parametric point to a rational value.
2703 More specifically, a quasipolynomial is a polynomial expression in greatest
2704 integer parts of affine expressions of parameters and variables.
2705 A piecewise quasipolynomial is a subdivision of a given parametric
2706 domain into disjoint cells with a quasipolynomial associated to
2707 each cell. The value of the piecewise quasipolynomial at a given
2708 point is the value of the quasipolynomial associated to the cell
2709 that contains the point. Outside of the union of cells,
2710 the value is assumed to be zero.
2711 For example, the piecewise quasipolynomial
2713 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2715 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2716 A given piecewise quasipolynomial has a fixed domain dimension.
2717 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2718 defined over different domains.
2719 Piecewise quasipolynomials are mainly used by the C<barvinok>
2720 library for representing the number of elements in a parametric set or map.
2721 For example, the piecewise quasipolynomial above represents
2722 the number of points in the map
2724 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2726 =head3 Printing (Piecewise) Quasipolynomials
2728 Quasipolynomials and piecewise quasipolynomials can be printed
2729 using the following functions.
2731 __isl_give isl_printer *isl_printer_print_qpolynomial(
2732 __isl_take isl_printer *p,
2733 __isl_keep isl_qpolynomial *qp);
2735 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2736 __isl_take isl_printer *p,
2737 __isl_keep isl_pw_qpolynomial *pwqp);
2739 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2740 __isl_take isl_printer *p,
2741 __isl_keep isl_union_pw_qpolynomial *upwqp);
2743 The output format of the printer
2744 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2745 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2747 In case of printing in C<ISL_FORMAT_C>, the user may want
2748 to set the names of all dimensions
2750 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2751 __isl_take isl_qpolynomial *qp,
2752 enum isl_dim_type type, unsigned pos,
2754 __isl_give isl_pw_qpolynomial *
2755 isl_pw_qpolynomial_set_dim_name(
2756 __isl_take isl_pw_qpolynomial *pwqp,
2757 enum isl_dim_type type, unsigned pos,
2760 =head3 Creating New (Piecewise) Quasipolynomials
2762 Some simple quasipolynomials can be created using the following functions.
2763 More complicated quasipolynomials can be created by applying
2764 operations such as addition and multiplication
2765 on the resulting quasipolynomials
2767 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2768 __isl_take isl_dim *dim);
2769 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2770 __isl_take isl_dim *dim);
2771 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2772 __isl_take isl_dim *dim);
2773 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2774 __isl_take isl_dim *dim);
2775 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2776 __isl_take isl_dim *dim);
2777 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2778 __isl_take isl_dim *dim,
2779 const isl_int n, const isl_int d);
2780 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2781 __isl_take isl_div *div);
2782 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2783 __isl_take isl_dim *dim,
2784 enum isl_dim_type type, unsigned pos);
2785 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2786 __isl_take isl_aff *aff);
2788 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2789 with a single cell can be created using the following functions.
2790 Multiple of these single cell piecewise quasipolynomials can
2791 be combined to create more complicated piecewise quasipolynomials.
2793 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2794 __isl_take isl_dim *dim);
2795 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2796 __isl_take isl_set *set,
2797 __isl_take isl_qpolynomial *qp);
2799 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2800 __isl_take isl_dim *dim);
2801 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2802 __isl_take isl_pw_qpolynomial *pwqp);
2803 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2804 __isl_take isl_union_pw_qpolynomial *upwqp,
2805 __isl_take isl_pw_qpolynomial *pwqp);
2807 Quasipolynomials can be copied and freed again using the following
2810 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2811 __isl_keep isl_qpolynomial *qp);
2812 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2815 __isl_keep isl_pw_qpolynomial *pwqp);
2816 void *isl_pw_qpolynomial_free(
2817 __isl_take isl_pw_qpolynomial *pwqp);
2819 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2820 __isl_keep isl_union_pw_qpolynomial *upwqp);
2821 void isl_union_pw_qpolynomial_free(
2822 __isl_take isl_union_pw_qpolynomial *upwqp);
2824 =head3 Inspecting (Piecewise) Quasipolynomials
2826 To iterate over all piecewise quasipolynomials in a union
2827 piecewise quasipolynomial, use the following function
2829 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2830 __isl_keep isl_union_pw_qpolynomial *upwqp,
2831 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2834 To extract the piecewise quasipolynomial from a union with a given dimension
2837 __isl_give isl_pw_qpolynomial *
2838 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2839 __isl_keep isl_union_pw_qpolynomial *upwqp,
2840 __isl_take isl_dim *dim);
2842 To iterate over the cells in a piecewise quasipolynomial,
2843 use either of the following two functions
2845 int isl_pw_qpolynomial_foreach_piece(
2846 __isl_keep isl_pw_qpolynomial *pwqp,
2847 int (*fn)(__isl_take isl_set *set,
2848 __isl_take isl_qpolynomial *qp,
2849 void *user), void *user);
2850 int isl_pw_qpolynomial_foreach_lifted_piece(
2851 __isl_keep isl_pw_qpolynomial *pwqp,
2852 int (*fn)(__isl_take isl_set *set,
2853 __isl_take isl_qpolynomial *qp,
2854 void *user), void *user);
2856 As usual, the function C<fn> should return C<0> on success
2857 and C<-1> on failure. The difference between
2858 C<isl_pw_qpolynomial_foreach_piece> and
2859 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2860 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2861 compute unique representations for all existentially quantified
2862 variables and then turn these existentially quantified variables
2863 into extra set variables, adapting the associated quasipolynomial
2864 accordingly. This means that the C<set> passed to C<fn>
2865 will not have any existentially quantified variables, but that
2866 the dimensions of the sets may be different for different
2867 invocations of C<fn>.
2869 To iterate over all terms in a quasipolynomial,
2872 int isl_qpolynomial_foreach_term(
2873 __isl_keep isl_qpolynomial *qp,
2874 int (*fn)(__isl_take isl_term *term,
2875 void *user), void *user);
2877 The terms themselves can be inspected and freed using
2880 unsigned isl_term_dim(__isl_keep isl_term *term,
2881 enum isl_dim_type type);
2882 void isl_term_get_num(__isl_keep isl_term *term,
2884 void isl_term_get_den(__isl_keep isl_term *term,
2886 int isl_term_get_exp(__isl_keep isl_term *term,
2887 enum isl_dim_type type, unsigned pos);
2888 __isl_give isl_div *isl_term_get_div(
2889 __isl_keep isl_term *term, unsigned pos);
2890 void isl_term_free(__isl_take isl_term *term);
2892 Each term is a product of parameters, set variables and
2893 integer divisions. The function C<isl_term_get_exp>
2894 returns the exponent of a given dimensions in the given term.
2895 The C<isl_int>s in the arguments of C<isl_term_get_num>
2896 and C<isl_term_get_den> need to have been initialized
2897 using C<isl_int_init> before calling these functions.
2899 =head3 Properties of (Piecewise) Quasipolynomials
2901 To check whether a quasipolynomial is actually a constant,
2902 use the following function.
2904 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2905 isl_int *n, isl_int *d);
2907 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2908 then the numerator and denominator of the constant
2909 are returned in C<*n> and C<*d>, respectively.
2911 =head3 Operations on (Piecewise) Quasipolynomials
2913 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2914 __isl_take isl_qpolynomial *qp, isl_int v);
2915 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2916 __isl_take isl_qpolynomial *qp);
2917 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2918 __isl_take isl_qpolynomial *qp1,
2919 __isl_take isl_qpolynomial *qp2);
2920 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2921 __isl_take isl_qpolynomial *qp1,
2922 __isl_take isl_qpolynomial *qp2);
2923 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2924 __isl_take isl_qpolynomial *qp1,
2925 __isl_take isl_qpolynomial *qp2);
2926 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2927 __isl_take isl_qpolynomial *qp, unsigned exponent);
2929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2930 __isl_take isl_pw_qpolynomial *pwqp1,
2931 __isl_take isl_pw_qpolynomial *pwqp2);
2932 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2933 __isl_take isl_pw_qpolynomial *pwqp1,
2934 __isl_take isl_pw_qpolynomial *pwqp2);
2935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2936 __isl_take isl_pw_qpolynomial *pwqp1,
2937 __isl_take isl_pw_qpolynomial *pwqp2);
2938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2939 __isl_take isl_pw_qpolynomial *pwqp);
2940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2941 __isl_take isl_pw_qpolynomial *pwqp1,
2942 __isl_take isl_pw_qpolynomial *pwqp2);
2944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2945 __isl_take isl_union_pw_qpolynomial *upwqp1,
2946 __isl_take isl_union_pw_qpolynomial *upwqp2);
2947 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2948 __isl_take isl_union_pw_qpolynomial *upwqp1,
2949 __isl_take isl_union_pw_qpolynomial *upwqp2);
2950 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2951 __isl_take isl_union_pw_qpolynomial *upwqp1,
2952 __isl_take isl_union_pw_qpolynomial *upwqp2);
2954 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2955 __isl_take isl_pw_qpolynomial *pwqp,
2956 __isl_take isl_point *pnt);
2958 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2959 __isl_take isl_union_pw_qpolynomial *upwqp,
2960 __isl_take isl_point *pnt);
2962 __isl_give isl_set *isl_pw_qpolynomial_domain(
2963 __isl_take isl_pw_qpolynomial *pwqp);
2964 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2965 __isl_take isl_pw_qpolynomial *pwpq,
2966 __isl_take isl_set *set);
2968 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2969 __isl_take isl_union_pw_qpolynomial *upwqp);
2970 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2971 __isl_take isl_union_pw_qpolynomial *upwpq,
2972 __isl_take isl_union_set *uset);
2974 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2975 __isl_take isl_qpolynomial *qp,
2976 __isl_take isl_dim *model);
2978 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2979 __isl_take isl_union_pw_qpolynomial *upwqp);
2981 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2982 __isl_take isl_qpolynomial *qp,
2983 __isl_take isl_set *context);
2985 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2986 __isl_take isl_pw_qpolynomial *pwqp,
2987 __isl_take isl_set *context);
2989 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2990 __isl_take isl_union_pw_qpolynomial *upwqp,
2991 __isl_take isl_union_set *context);
2993 The gist operation applies the gist operation to each of
2994 the cells in the domain of the input piecewise quasipolynomial.
2995 The context is also exploited
2996 to simplify the quasipolynomials associated to each cell.
2998 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2999 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3000 __isl_give isl_union_pw_qpolynomial *
3001 isl_union_pw_qpolynomial_to_polynomial(
3002 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3004 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3005 the polynomial will be an overapproximation. If C<sign> is negative,
3006 it will be an underapproximation. If C<sign> is zero, the approximation
3007 will lie somewhere in between.
3009 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3011 A piecewise quasipolynomial reduction is a piecewise
3012 reduction (or fold) of quasipolynomials.
3013 In particular, the reduction can be maximum or a minimum.
3014 The objects are mainly used to represent the result of
3015 an upper or lower bound on a quasipolynomial over its domain,
3016 i.e., as the result of the following function.
3018 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3019 __isl_take isl_pw_qpolynomial *pwqp,
3020 enum isl_fold type, int *tight);
3022 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3023 __isl_take isl_union_pw_qpolynomial *upwqp,
3024 enum isl_fold type, int *tight);
3026 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3027 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3028 is the returned bound is known be tight, i.e., for each value
3029 of the parameters there is at least
3030 one element in the domain that reaches the bound.
3031 If the domain of C<pwqp> is not wrapping, then the bound is computed
3032 over all elements in that domain and the result has a purely parametric
3033 domain. If the domain of C<pwqp> is wrapping, then the bound is
3034 computed over the range of the wrapped relation. The domain of the
3035 wrapped relation becomes the domain of the result.
3037 A (piecewise) quasipolynomial reduction can be copied or freed using the
3038 following functions.
3040 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3041 __isl_keep isl_qpolynomial_fold *fold);
3042 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3043 __isl_keep isl_pw_qpolynomial_fold *pwf);
3044 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3045 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3046 void isl_qpolynomial_fold_free(
3047 __isl_take isl_qpolynomial_fold *fold);
3048 void *isl_pw_qpolynomial_fold_free(
3049 __isl_take isl_pw_qpolynomial_fold *pwf);
3050 void isl_union_pw_qpolynomial_fold_free(
3051 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3053 =head3 Printing Piecewise Quasipolynomial Reductions
3055 Piecewise quasipolynomial reductions can be printed
3056 using the following function.
3058 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3059 __isl_take isl_printer *p,
3060 __isl_keep isl_pw_qpolynomial_fold *pwf);
3061 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3062 __isl_take isl_printer *p,
3063 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3065 For C<isl_printer_print_pw_qpolynomial_fold>,
3066 output format of the printer
3067 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3068 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3069 output format of the printer
3070 needs to be set to C<ISL_FORMAT_ISL>.
3071 In case of printing in C<ISL_FORMAT_C>, the user may want
3072 to set the names of all dimensions
3074 __isl_give isl_pw_qpolynomial_fold *
3075 isl_pw_qpolynomial_fold_set_dim_name(
3076 __isl_take isl_pw_qpolynomial_fold *pwf,
3077 enum isl_dim_type type, unsigned pos,
3080 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3082 To iterate over all piecewise quasipolynomial reductions in a union
3083 piecewise quasipolynomial reduction, use the following function
3085 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3086 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3087 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3088 void *user), void *user);
3090 To iterate over the cells in a piecewise quasipolynomial reduction,
3091 use either of the following two functions
3093 int isl_pw_qpolynomial_fold_foreach_piece(
3094 __isl_keep isl_pw_qpolynomial_fold *pwf,
3095 int (*fn)(__isl_take isl_set *set,
3096 __isl_take isl_qpolynomial_fold *fold,
3097 void *user), void *user);
3098 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3099 __isl_keep isl_pw_qpolynomial_fold *pwf,
3100 int (*fn)(__isl_take isl_set *set,
3101 __isl_take isl_qpolynomial_fold *fold,
3102 void *user), void *user);
3104 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3105 of the difference between these two functions.
3107 To iterate over all quasipolynomials in a reduction, use
3109 int isl_qpolynomial_fold_foreach_qpolynomial(
3110 __isl_keep isl_qpolynomial_fold *fold,
3111 int (*fn)(__isl_take isl_qpolynomial *qp,
3112 void *user), void *user);
3114 =head3 Operations on Piecewise Quasipolynomial Reductions
3116 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3117 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3119 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3120 __isl_take isl_pw_qpolynomial_fold *pwf1,
3121 __isl_take isl_pw_qpolynomial_fold *pwf2);
3123 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3124 __isl_take isl_pw_qpolynomial_fold *pwf1,
3125 __isl_take isl_pw_qpolynomial_fold *pwf2);
3127 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3128 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3129 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3131 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3132 __isl_take isl_pw_qpolynomial_fold *pwf,
3133 __isl_take isl_point *pnt);
3135 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3136 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3137 __isl_take isl_point *pnt);
3139 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3140 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3141 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3142 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3143 __isl_take isl_union_set *uset);
3145 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3146 __isl_take isl_pw_qpolynomial_fold *pwf);
3148 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3149 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3151 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3152 __isl_take isl_pw_qpolynomial_fold *pwf,
3153 __isl_take isl_set *context);
3155 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3156 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3157 __isl_take isl_union_set *context);
3159 The gist operation applies the gist operation to each of
3160 the cells in the domain of the input piecewise quasipolynomial reduction.
3161 In future, the operation will also exploit the context
3162 to simplify the quasipolynomial reductions associated to each cell.
3164 __isl_give isl_pw_qpolynomial_fold *
3165 isl_set_apply_pw_qpolynomial_fold(
3166 __isl_take isl_set *set,
3167 __isl_take isl_pw_qpolynomial_fold *pwf,
3169 __isl_give isl_pw_qpolynomial_fold *
3170 isl_map_apply_pw_qpolynomial_fold(
3171 __isl_take isl_map *map,
3172 __isl_take isl_pw_qpolynomial_fold *pwf,
3174 __isl_give isl_union_pw_qpolynomial_fold *
3175 isl_union_set_apply_union_pw_qpolynomial_fold(
3176 __isl_take isl_union_set *uset,
3177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3179 __isl_give isl_union_pw_qpolynomial_fold *
3180 isl_union_map_apply_union_pw_qpolynomial_fold(
3181 __isl_take isl_union_map *umap,
3182 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3185 The functions taking a map
3186 compose the given map with the given piecewise quasipolynomial reduction.
3187 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3188 over all elements in the intersection of the range of the map
3189 and the domain of the piecewise quasipolynomial reduction
3190 as a function of an element in the domain of the map.
3191 The functions taking a set compute a bound over all elements in the
3192 intersection of the set and the domain of the
3193 piecewise quasipolynomial reduction.
3195 =head2 Dependence Analysis
3197 C<isl> contains specialized functionality for performing
3198 array dataflow analysis. That is, given a I<sink> access relation
3199 and a collection of possible I<source> access relations,
3200 C<isl> can compute relations that describe
3201 for each iteration of the sink access, which iteration
3202 of which of the source access relations was the last
3203 to access the same data element before the given iteration
3205 To compute standard flow dependences, the sink should be
3206 a read, while the sources should be writes.
3207 If any of the source accesses are marked as being I<may>
3208 accesses, then there will be a dependence to the last
3209 I<must> access B<and> to any I<may> access that follows
3210 this last I<must> access.
3211 In particular, if I<all> sources are I<may> accesses,
3212 then memory based dependence analysis is performed.
3213 If, on the other hand, all sources are I<must> accesses,
3214 then value based dependence analysis is performed.
3216 #include <isl/flow.h>
3218 typedef int (*isl_access_level_before)(void *first, void *second);
3220 __isl_give isl_access_info *isl_access_info_alloc(
3221 __isl_take isl_map *sink,
3222 void *sink_user, isl_access_level_before fn,
3224 __isl_give isl_access_info *isl_access_info_add_source(
3225 __isl_take isl_access_info *acc,
3226 __isl_take isl_map *source, int must,
3228 void isl_access_info_free(__isl_take isl_access_info *acc);
3230 __isl_give isl_flow *isl_access_info_compute_flow(
3231 __isl_take isl_access_info *acc);
3233 int isl_flow_foreach(__isl_keep isl_flow *deps,
3234 int (*fn)(__isl_take isl_map *dep, int must,
3235 void *dep_user, void *user),
3237 __isl_give isl_map *isl_flow_get_no_source(
3238 __isl_keep isl_flow *deps, int must);
3239 void isl_flow_free(__isl_take isl_flow *deps);
3241 The function C<isl_access_info_compute_flow> performs the actual
3242 dependence analysis. The other functions are used to construct
3243 the input for this function or to read off the output.
3245 The input is collected in an C<isl_access_info>, which can
3246 be created through a call to C<isl_access_info_alloc>.
3247 The arguments to this functions are the sink access relation
3248 C<sink>, a token C<sink_user> used to identify the sink
3249 access to the user, a callback function for specifying the
3250 relative order of source and sink accesses, and the number
3251 of source access relations that will be added.
3252 The callback function has type C<int (*)(void *first, void *second)>.
3253 The function is called with two user supplied tokens identifying
3254 either a source or the sink and it should return the shared nesting
3255 level and the relative order of the two accesses.
3256 In particular, let I<n> be the number of loops shared by
3257 the two accesses. If C<first> precedes C<second> textually,
3258 then the function should return I<2 * n + 1>; otherwise,
3259 it should return I<2 * n>.
3260 The sources can be added to the C<isl_access_info> by performing
3261 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3262 C<must> indicates whether the source is a I<must> access
3263 or a I<may> access. Note that a multi-valued access relation
3264 should only be marked I<must> if every iteration in the domain
3265 of the relation accesses I<all> elements in its image.
3266 The C<source_user> token is again used to identify
3267 the source access. The range of the source access relation
3268 C<source> should have the same dimension as the range
3269 of the sink access relation.
3270 The C<isl_access_info_free> function should usually not be
3271 called explicitly, because it is called implicitly by
3272 C<isl_access_info_compute_flow>.
3274 The result of the dependence analysis is collected in an
3275 C<isl_flow>. There may be elements of
3276 the sink access for which no preceding source access could be
3277 found or for which all preceding sources are I<may> accesses.
3278 The relations containing these elements can be obtained through
3279 calls to C<isl_flow_get_no_source>, the first with C<must> set
3280 and the second with C<must> unset.
3281 In the case of standard flow dependence analysis,
3282 with the sink a read and the sources I<must> writes,
3283 the first relation corresponds to the reads from uninitialized
3284 array elements and the second relation is empty.
3285 The actual flow dependences can be extracted using
3286 C<isl_flow_foreach>. This function will call the user-specified
3287 callback function C<fn> for each B<non-empty> dependence between
3288 a source and the sink. The callback function is called
3289 with four arguments, the actual flow dependence relation
3290 mapping source iterations to sink iterations, a boolean that
3291 indicates whether it is a I<must> or I<may> dependence, a token
3292 identifying the source and an additional C<void *> with value
3293 equal to the third argument of the C<isl_flow_foreach> call.
3294 A dependence is marked I<must> if it originates from a I<must>
3295 source and if it is not followed by any I<may> sources.
3297 After finishing with an C<isl_flow>, the user should call
3298 C<isl_flow_free> to free all associated memory.
3300 A higher-level interface to dependence analysis is provided
3301 by the following function.
3303 #include <isl/flow.h>
3305 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3306 __isl_take isl_union_map *must_source,
3307 __isl_take isl_union_map *may_source,
3308 __isl_take isl_union_map *schedule,
3309 __isl_give isl_union_map **must_dep,
3310 __isl_give isl_union_map **may_dep,
3311 __isl_give isl_union_map **must_no_source,
3312 __isl_give isl_union_map **may_no_source);
3314 The arrays are identified by the tuple names of the ranges
3315 of the accesses. The iteration domains by the tuple names
3316 of the domains of the accesses and of the schedule.
3317 The relative order of the iteration domains is given by the
3318 schedule. The relations returned through C<must_no_source>
3319 and C<may_no_source> are subsets of C<sink>.
3320 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3321 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3322 any of the other arguments is treated as an error.
3326 B<The functionality described in this section is fairly new
3327 and may be subject to change.>
3329 The following function can be used to compute a schedule
3330 for a union of domains. The generated schedule respects
3331 all C<validity> dependences. That is, all dependence distances
3332 over these dependences in the scheduled space are lexicographically
3333 positive. The generated schedule schedule also tries to minimize
3334 the dependence distances over C<proximity> dependences.
3335 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3336 for groups of domains where the dependence distances have only
3337 non-negative values.
3338 The algorithm used to construct the schedule is similar to that
3341 #include <isl/schedule.h>
3342 __isl_give isl_schedule *isl_union_set_compute_schedule(
3343 __isl_take isl_union_set *domain,
3344 __isl_take isl_union_map *validity,
3345 __isl_take isl_union_map *proximity);
3346 void *isl_schedule_free(__isl_take isl_schedule *sched);
3348 A mapping from the domains to the scheduled space can be obtained
3349 from an C<isl_schedule> using the following function.
3351 __isl_give isl_union_map *isl_schedule_get_map(
3352 __isl_keep isl_schedule *sched);
3354 A representation of the schedule can be printed using
3356 __isl_give isl_printer *isl_printer_print_schedule(
3357 __isl_take isl_printer *p,
3358 __isl_keep isl_schedule *schedule);
3360 A representation of the schedule as a forest of bands can be obtained
3361 using the following function.
3363 __isl_give isl_band_list *isl_schedule_get_band_forest(
3364 __isl_keep isl_schedule *schedule);
3366 The list can be manipulated as explained in L<"Lists">.
3367 The bands inside the list can be copied and freed using the following
3370 #include <isl/band.h>
3371 __isl_give isl_band *isl_band_copy(
3372 __isl_keep isl_band *band);
3373 void *isl_band_free(__isl_take isl_band *band);
3375 Each band contains zero or more scheduling dimensions.
3376 These are referred to as the members of the band.
3377 The section of the schedule that corresponds to the band is
3378 referred to as the partial schedule of the band.
3379 For those nodes that participate in a band, the outer scheduling
3380 dimensions form the prefix schedule, while the inner scheduling
3381 dimensions form the suffix schedule.
3382 That is, if we take a cut of the band forest, then the union of
3383 the concatenations of the prefix, partial and suffix schedules of
3384 each band in the cut is equal to the entire schedule (modulo
3385 some possible padding at the end with zero scheduling dimensions).
3386 The properties of a band can be inspected using the following functions.
3388 #include <isl/band.h>
3389 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3391 int isl_band_has_children(__isl_keep isl_band *band);
3392 __isl_give isl_band_list *isl_band_get_children(
3393 __isl_keep isl_band *band);
3395 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3396 __isl_keep isl_band *band);
3397 __isl_give isl_union_map *isl_band_get_partial_schedule(
3398 __isl_keep isl_band *band);
3399 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3400 __isl_keep isl_band *band);
3402 int isl_band_n_member(__isl_keep isl_band *band);
3403 int isl_band_member_is_zero_distance(
3404 __isl_keep isl_band *band, int pos);
3406 Note that a scheduling dimension is considered to be ``zero
3407 distance'' if it does not carry any proximity dependences
3409 That is, if the dependence distances of the proximity
3410 dependences are all zero in that direction (for fixed
3411 iterations of outer bands).
3413 A representation of the band can be printed using
3415 #include <isl/band.h>
3416 __isl_give isl_printer *isl_printer_print_band(
3417 __isl_take isl_printer *p,
3418 __isl_keep isl_band *band);
3420 =head2 Parametric Vertex Enumeration
3422 The parametric vertex enumeration described in this section
3423 is mainly intended to be used internally and by the C<barvinok>
3426 #include <isl/vertices.h>
3427 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3428 __isl_keep isl_basic_set *bset);
3430 The function C<isl_basic_set_compute_vertices> performs the
3431 actual computation of the parametric vertices and the chamber
3432 decomposition and store the result in an C<isl_vertices> object.
3433 This information can be queried by either iterating over all
3434 the vertices or iterating over all the chambers or cells
3435 and then iterating over all vertices that are active on the chamber.
3437 int isl_vertices_foreach_vertex(
3438 __isl_keep isl_vertices *vertices,
3439 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3442 int isl_vertices_foreach_cell(
3443 __isl_keep isl_vertices *vertices,
3444 int (*fn)(__isl_take isl_cell *cell, void *user),
3446 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3447 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3450 Other operations that can be performed on an C<isl_vertices> object are
3453 isl_ctx *isl_vertices_get_ctx(
3454 __isl_keep isl_vertices *vertices);
3455 int isl_vertices_get_n_vertices(
3456 __isl_keep isl_vertices *vertices);
3457 void isl_vertices_free(__isl_take isl_vertices *vertices);
3459 Vertices can be inspected and destroyed using the following functions.
3461 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3462 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3463 __isl_give isl_basic_set *isl_vertex_get_domain(
3464 __isl_keep isl_vertex *vertex);
3465 __isl_give isl_basic_set *isl_vertex_get_expr(
3466 __isl_keep isl_vertex *vertex);
3467 void isl_vertex_free(__isl_take isl_vertex *vertex);
3469 C<isl_vertex_get_expr> returns a singleton parametric set describing
3470 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3472 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3473 B<rational> basic sets, so they should mainly be used for inspection
3474 and should not be mixed with integer sets.
3476 Chambers can be inspected and destroyed using the following functions.
3478 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3479 __isl_give isl_basic_set *isl_cell_get_domain(
3480 __isl_keep isl_cell *cell);
3481 void isl_cell_free(__isl_take isl_cell *cell);
3485 Although C<isl> is mainly meant to be used as a library,
3486 it also contains some basic applications that use some
3487 of the functionality of C<isl>.
3488 The input may be specified in either the L<isl format>
3489 or the L<PolyLib format>.
3491 =head2 C<isl_polyhedron_sample>
3493 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3494 an integer element of the polyhedron, if there is any.
3495 The first column in the output is the denominator and is always
3496 equal to 1. If the polyhedron contains no integer points,
3497 then a vector of length zero is printed.
3501 C<isl_pip> takes the same input as the C<example> program
3502 from the C<piplib> distribution, i.e., a set of constraints
3503 on the parameters, a line containing only -1 and finally a set
3504 of constraints on a parametric polyhedron.
3505 The coefficients of the parameters appear in the last columns
3506 (but before the final constant column).
3507 The output is the lexicographic minimum of the parametric polyhedron.
3508 As C<isl> currently does not have its own output format, the output
3509 is just a dump of the internal state.
3511 =head2 C<isl_polyhedron_minimize>
3513 C<isl_polyhedron_minimize> computes the minimum of some linear
3514 or affine objective function over the integer points in a polyhedron.
3515 If an affine objective function
3516 is given, then the constant should appear in the last column.
3518 =head2 C<isl_polytope_scan>
3520 Given a polytope, C<isl_polytope_scan> prints
3521 all integer points in the polytope.