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 __isl_give isl_constraint *isl_constraint_set_constant(
1027 __isl_take isl_constraint *constraint, isl_int v);
1028 __isl_give isl_constraint *isl_constraint_set_constant_si(
1029 __isl_take isl_constraint *constraint, int v);
1030 __isl_give isl_constraint *isl_constraint_set_coefficient(
1031 __isl_take isl_constraint *constraint,
1032 enum isl_dim_type type, int pos, isl_int v);
1033 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1034 __isl_take isl_constraint *constraint,
1035 enum isl_dim_type type, int pos, int v);
1036 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1037 __isl_take isl_basic_map *bmap,
1038 __isl_take isl_constraint *constraint);
1039 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1040 __isl_take isl_basic_set *bset,
1041 __isl_take isl_constraint *constraint);
1042 __isl_give isl_map *isl_map_add_constraint(
1043 __isl_take isl_map *map,
1044 __isl_take isl_constraint *constraint);
1045 __isl_give isl_set *isl_set_add_constraint(
1046 __isl_take isl_set *set,
1047 __isl_take isl_constraint *constraint);
1048 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1049 __isl_take isl_basic_set *bset,
1050 __isl_take isl_constraint *constraint);
1052 For example, to create a set containing the even integers
1053 between 10 and 42, you would use the following code.
1056 struct isl_dim *dim;
1057 struct isl_constraint *c;
1058 struct isl_basic_set *bset;
1061 dim = isl_dim_set_alloc(ctx, 0, 2);
1062 bset = isl_basic_set_universe(isl_dim_copy(dim));
1064 c = isl_equality_alloc(isl_dim_copy(dim));
1065 isl_int_set_si(v, -1);
1066 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1067 isl_int_set_si(v, 2);
1068 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1069 bset = isl_basic_set_add_constraint(bset, c);
1071 c = isl_inequality_alloc(isl_dim_copy(dim));
1072 isl_int_set_si(v, -10);
1073 isl_constraint_set_constant(c, v);
1074 isl_int_set_si(v, 1);
1075 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1076 bset = isl_basic_set_add_constraint(bset, c);
1078 c = isl_inequality_alloc(dim);
1079 isl_int_set_si(v, 42);
1080 isl_constraint_set_constant(c, v);
1081 isl_int_set_si(v, -1);
1082 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1083 bset = isl_basic_set_add_constraint(bset, c);
1085 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1091 struct isl_basic_set *bset;
1092 bset = isl_basic_set_read_from_str(ctx,
1093 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1095 A basic set or relation can also be constructed from two matrices
1096 describing the equalities and the inequalities.
1098 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1099 __isl_take isl_dim *dim,
1100 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1101 enum isl_dim_type c1,
1102 enum isl_dim_type c2, enum isl_dim_type c3,
1103 enum isl_dim_type c4);
1104 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1105 __isl_take isl_dim *dim,
1106 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1107 enum isl_dim_type c1,
1108 enum isl_dim_type c2, enum isl_dim_type c3,
1109 enum isl_dim_type c4, enum isl_dim_type c5);
1111 The C<isl_dim_type> arguments indicate the order in which
1112 different kinds of variables appear in the input matrices
1113 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1114 C<isl_dim_set> and C<isl_dim_div> for sets and
1115 of C<isl_dim_cst>, C<isl_dim_param>,
1116 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1118 A (basic) relation can also be constructed from a (piecewise) affine expression
1119 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1121 __isl_give isl_basic_map *isl_basic_map_from_aff(
1122 __isl_take isl_aff *aff);
1123 __isl_give isl_map *isl_map_from_pw_aff(
1124 __isl_take isl_pw_aff *pwaff);
1125 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1126 __isl_take isl_dim *domain_dim,
1127 __isl_take isl_aff_list *list);
1129 The C<domain_dim> argument describes the domain of the resulting
1130 basic relation. It is required because the C<list> may consist
1131 of zero affine expressions.
1133 =head2 Inspecting Sets and Relations
1135 Usually, the user should not have to care about the actual constraints
1136 of the sets and maps, but should instead apply the abstract operations
1137 explained in the following sections.
1138 Occasionally, however, it may be required to inspect the individual
1139 coefficients of the constraints. This section explains how to do so.
1140 In these cases, it may also be useful to have C<isl> compute
1141 an explicit representation of the existentially quantified variables.
1143 __isl_give isl_set *isl_set_compute_divs(
1144 __isl_take isl_set *set);
1145 __isl_give isl_map *isl_map_compute_divs(
1146 __isl_take isl_map *map);
1147 __isl_give isl_union_set *isl_union_set_compute_divs(
1148 __isl_take isl_union_set *uset);
1149 __isl_give isl_union_map *isl_union_map_compute_divs(
1150 __isl_take isl_union_map *umap);
1152 This explicit representation defines the existentially quantified
1153 variables as integer divisions of the other variables, possibly
1154 including earlier existentially quantified variables.
1155 An explicitly represented existentially quantified variable therefore
1156 has a unique value when the values of the other variables are known.
1157 If, furthermore, the same existentials, i.e., existentials
1158 with the same explicit representations, should appear in the
1159 same order in each of the disjuncts of a set or map, then the user should call
1160 either of the following functions.
1162 __isl_give isl_set *isl_set_align_divs(
1163 __isl_take isl_set *set);
1164 __isl_give isl_map *isl_map_align_divs(
1165 __isl_take isl_map *map);
1167 Alternatively, the existentially quantified variables can be removed
1168 using the following functions, which compute an overapproximation.
1170 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1171 __isl_take isl_basic_set *bset);
1172 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1173 __isl_take isl_basic_map *bmap);
1174 __isl_give isl_set *isl_set_remove_divs(
1175 __isl_take isl_set *set);
1176 __isl_give isl_map *isl_map_remove_divs(
1177 __isl_take isl_map *map);
1179 To iterate over all the sets or maps in a union set or map, use
1181 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1182 int (*fn)(__isl_take isl_set *set, void *user),
1184 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1185 int (*fn)(__isl_take isl_map *map, void *user),
1188 The number of sets or maps in a union set or map can be obtained
1191 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1192 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1194 To extract the set or map from a union with a given dimension
1197 __isl_give isl_set *isl_union_set_extract_set(
1198 __isl_keep isl_union_set *uset,
1199 __isl_take isl_dim *dim);
1200 __isl_give isl_map *isl_union_map_extract_map(
1201 __isl_keep isl_union_map *umap,
1202 __isl_take isl_dim *dim);
1204 To iterate over all the basic sets or maps in a set or map, use
1206 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1207 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1209 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1210 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1213 The callback function C<fn> should return 0 if successful and
1214 -1 if an error occurs. In the latter case, or if any other error
1215 occurs, the above functions will return -1.
1217 It should be noted that C<isl> does not guarantee that
1218 the basic sets or maps passed to C<fn> are disjoint.
1219 If this is required, then the user should call one of
1220 the following functions first.
1222 __isl_give isl_set *isl_set_make_disjoint(
1223 __isl_take isl_set *set);
1224 __isl_give isl_map *isl_map_make_disjoint(
1225 __isl_take isl_map *map);
1227 The number of basic sets in a set can be obtained
1230 int isl_set_n_basic_set(__isl_keep isl_set *set);
1232 To iterate over the constraints of a basic set or map, use
1234 #include <isl/constraint.h>
1236 int isl_basic_map_foreach_constraint(
1237 __isl_keep isl_basic_map *bmap,
1238 int (*fn)(__isl_take isl_constraint *c, void *user),
1240 void isl_constraint_free(struct isl_constraint *c);
1242 Again, the callback function C<fn> should return 0 if successful and
1243 -1 if an error occurs. In the latter case, or if any other error
1244 occurs, the above functions will return -1.
1245 The constraint C<c> represents either an equality or an inequality.
1246 Use the following function to find out whether a constraint
1247 represents an equality. If not, it represents an inequality.
1249 int isl_constraint_is_equality(
1250 __isl_keep isl_constraint *constraint);
1252 The coefficients of the constraints can be inspected using
1253 the following functions.
1255 void isl_constraint_get_constant(
1256 __isl_keep isl_constraint *constraint, isl_int *v);
1257 void isl_constraint_get_coefficient(
1258 __isl_keep isl_constraint *constraint,
1259 enum isl_dim_type type, int pos, isl_int *v);
1260 int isl_constraint_involves_dims(
1261 __isl_keep isl_constraint *constraint,
1262 enum isl_dim_type type, unsigned first, unsigned n);
1264 The explicit representations of the existentially quantified
1265 variables can be inspected using the following functions.
1266 Note that the user is only allowed to use these functions
1267 if the inspected set or map is the result of a call
1268 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1270 __isl_give isl_div *isl_constraint_div(
1271 __isl_keep isl_constraint *constraint, int pos);
1272 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1273 void isl_div_get_constant(__isl_keep isl_div *div,
1275 void isl_div_get_denominator(__isl_keep isl_div *div,
1277 void isl_div_get_coefficient(__isl_keep isl_div *div,
1278 enum isl_dim_type type, int pos, isl_int *v);
1280 To obtain the constraints of a basic set or map in matrix
1281 form, use the following functions.
1283 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1284 __isl_keep isl_basic_set *bset,
1285 enum isl_dim_type c1, enum isl_dim_type c2,
1286 enum isl_dim_type c3, enum isl_dim_type c4);
1287 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1288 __isl_keep isl_basic_set *bset,
1289 enum isl_dim_type c1, enum isl_dim_type c2,
1290 enum isl_dim_type c3, enum isl_dim_type c4);
1291 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type c1,
1294 enum isl_dim_type c2, enum isl_dim_type c3,
1295 enum isl_dim_type c4, enum isl_dim_type c5);
1296 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1297 __isl_keep isl_basic_map *bmap,
1298 enum isl_dim_type c1,
1299 enum isl_dim_type c2, enum isl_dim_type c3,
1300 enum isl_dim_type c4, enum isl_dim_type c5);
1302 The C<isl_dim_type> arguments dictate the order in which
1303 different kinds of variables appear in the resulting matrix
1304 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1305 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1307 To check whether the description of a set or relation depends
1308 on one or more given dimensions, it is not necessary to iterate over all
1309 constraints. Instead the following functions can be used.
1311 int isl_basic_set_involves_dims(
1312 __isl_keep isl_basic_set *bset,
1313 enum isl_dim_type type, unsigned first, unsigned n);
1314 int isl_set_involves_dims(__isl_keep isl_set *set,
1315 enum isl_dim_type type, unsigned first, unsigned n);
1316 int isl_basic_map_involves_dims(
1317 __isl_keep isl_basic_map *bmap,
1318 enum isl_dim_type type, unsigned first, unsigned n);
1319 int isl_map_involves_dims(__isl_keep isl_map *map,
1320 enum isl_dim_type type, unsigned first, unsigned n);
1322 The identifiers or names of the domain and range spaces of a set
1323 or relation can be read off or set using the following functions.
1325 __isl_give isl_set *isl_set_set_tuple_id(
1326 __isl_take isl_set *set, __isl_take isl_id *id);
1327 __isl_give isl_id *isl_set_get_tuple_id(
1328 __isl_keep isl_set *set);
1329 __isl_give isl_map *isl_map_set_tuple_id(
1330 __isl_take isl_map *map, enum isl_dim_type type,
1331 __isl_take isl_id *id);
1332 __isl_give isl_map *isl_map_reset_tuple_id(
1333 __isl_take isl_map *map, enum isl_dim_type type);
1334 __isl_give isl_id *isl_map_get_tuple_id(
1335 __isl_keep isl_map *map, enum isl_dim_type type);
1337 const char *isl_basic_set_get_tuple_name(
1338 __isl_keep isl_basic_set *bset);
1339 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1340 __isl_take isl_basic_set *set, const char *s);
1341 const char *isl_set_get_tuple_name(
1342 __isl_keep isl_set *set);
1343 const char *isl_basic_map_get_tuple_name(
1344 __isl_keep isl_basic_map *bmap,
1345 enum isl_dim_type type);
1346 const char *isl_map_get_tuple_name(
1347 __isl_keep isl_map *map,
1348 enum isl_dim_type type);
1350 As with C<isl_dim_get_tuple_name>, the value returned points to
1351 an internal data structure.
1352 The identifiers, positions or names of individual dimensions can be
1353 read off using the following functions.
1355 __isl_give isl_set *isl_set_set_dim_id(
1356 __isl_take isl_set *set, enum isl_dim_type type,
1357 unsigned pos, __isl_take isl_id *id);
1358 __isl_give isl_id *isl_set_get_dim_id(
1359 __isl_keep isl_set *set, enum isl_dim_type type,
1361 __isl_give isl_map *isl_map_set_dim_id(
1362 __isl_take isl_map *map, enum isl_dim_type type,
1363 unsigned pos, __isl_take isl_id *id);
1364 __isl_give isl_id *isl_map_get_dim_id(
1365 __isl_keep isl_map *map, enum isl_dim_type type,
1368 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1369 enum isl_dim_type type, __isl_keep isl_id *id);
1370 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1371 enum isl_dim_type type, __isl_keep isl_id *id);
1373 const char *isl_constraint_get_dim_name(
1374 __isl_keep isl_constraint *constraint,
1375 enum isl_dim_type type, unsigned pos);
1376 const char *isl_basic_set_get_dim_name(
1377 __isl_keep isl_basic_set *bset,
1378 enum isl_dim_type type, unsigned pos);
1379 const char *isl_set_get_dim_name(
1380 __isl_keep isl_set *set,
1381 enum isl_dim_type type, unsigned pos);
1382 const char *isl_basic_map_get_dim_name(
1383 __isl_keep isl_basic_map *bmap,
1384 enum isl_dim_type type, unsigned pos);
1385 const char *isl_map_get_dim_name(
1386 __isl_keep isl_map *map,
1387 enum isl_dim_type type, unsigned pos);
1389 These functions are mostly useful to obtain the identifiers, positions
1390 or names of the parameters.
1394 =head3 Unary Properties
1400 The following functions test whether the given set or relation
1401 contains any integer points. The ``plain'' variants do not perform
1402 any computations, but simply check if the given set or relation
1403 is already known to be empty.
1405 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1406 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1407 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1408 int isl_set_is_empty(__isl_keep isl_set *set);
1409 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1410 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1411 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1412 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1413 int isl_map_is_empty(__isl_keep isl_map *map);
1414 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1416 =item * Universality
1418 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1419 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1420 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1422 =item * Single-valuedness
1424 int isl_map_is_single_valued(__isl_keep isl_map *map);
1425 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1429 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1430 int isl_map_is_injective(__isl_keep isl_map *map);
1431 int isl_union_map_plain_is_injective(
1432 __isl_keep isl_union_map *umap);
1433 int isl_union_map_is_injective(
1434 __isl_keep isl_union_map *umap);
1438 int isl_map_is_bijective(__isl_keep isl_map *map);
1439 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1443 The following functions check whether the domain of the given
1444 (basic) set is a wrapped relation.
1446 int isl_basic_set_is_wrapping(
1447 __isl_keep isl_basic_set *bset);
1448 int isl_set_is_wrapping(__isl_keep isl_set *set);
1450 =item * Internal Product
1452 int isl_basic_map_can_zip(
1453 __isl_keep isl_basic_map *bmap);
1454 int isl_map_can_zip(__isl_keep isl_map *map);
1456 Check whether the product of domain and range of the given relation
1458 i.e., whether both domain and range are nested relations.
1462 =head3 Binary Properties
1468 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1469 __isl_keep isl_set *set2);
1470 int isl_set_is_equal(__isl_keep isl_set *set1,
1471 __isl_keep isl_set *set2);
1472 int isl_union_set_is_equal(
1473 __isl_keep isl_union_set *uset1,
1474 __isl_keep isl_union_set *uset2);
1475 int isl_basic_map_is_equal(
1476 __isl_keep isl_basic_map *bmap1,
1477 __isl_keep isl_basic_map *bmap2);
1478 int isl_map_is_equal(__isl_keep isl_map *map1,
1479 __isl_keep isl_map *map2);
1480 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1481 __isl_keep isl_map *map2);
1482 int isl_union_map_is_equal(
1483 __isl_keep isl_union_map *umap1,
1484 __isl_keep isl_union_map *umap2);
1486 =item * Disjointness
1488 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1489 __isl_keep isl_set *set2);
1493 int isl_set_is_subset(__isl_keep isl_set *set1,
1494 __isl_keep isl_set *set2);
1495 int isl_set_is_strict_subset(
1496 __isl_keep isl_set *set1,
1497 __isl_keep isl_set *set2);
1498 int isl_union_set_is_subset(
1499 __isl_keep isl_union_set *uset1,
1500 __isl_keep isl_union_set *uset2);
1501 int isl_union_set_is_strict_subset(
1502 __isl_keep isl_union_set *uset1,
1503 __isl_keep isl_union_set *uset2);
1504 int isl_basic_map_is_subset(
1505 __isl_keep isl_basic_map *bmap1,
1506 __isl_keep isl_basic_map *bmap2);
1507 int isl_basic_map_is_strict_subset(
1508 __isl_keep isl_basic_map *bmap1,
1509 __isl_keep isl_basic_map *bmap2);
1510 int isl_map_is_subset(
1511 __isl_keep isl_map *map1,
1512 __isl_keep isl_map *map2);
1513 int isl_map_is_strict_subset(
1514 __isl_keep isl_map *map1,
1515 __isl_keep isl_map *map2);
1516 int isl_union_map_is_subset(
1517 __isl_keep isl_union_map *umap1,
1518 __isl_keep isl_union_map *umap2);
1519 int isl_union_map_is_strict_subset(
1520 __isl_keep isl_union_map *umap1,
1521 __isl_keep isl_union_map *umap2);
1525 =head2 Unary Operations
1531 __isl_give isl_set *isl_set_complement(
1532 __isl_take isl_set *set);
1536 __isl_give isl_basic_map *isl_basic_map_reverse(
1537 __isl_take isl_basic_map *bmap);
1538 __isl_give isl_map *isl_map_reverse(
1539 __isl_take isl_map *map);
1540 __isl_give isl_union_map *isl_union_map_reverse(
1541 __isl_take isl_union_map *umap);
1545 __isl_give isl_basic_set *isl_basic_set_project_out(
1546 __isl_take isl_basic_set *bset,
1547 enum isl_dim_type type, unsigned first, unsigned n);
1548 __isl_give isl_basic_map *isl_basic_map_project_out(
1549 __isl_take isl_basic_map *bmap,
1550 enum isl_dim_type type, unsigned first, unsigned n);
1551 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1552 enum isl_dim_type type, unsigned first, unsigned n);
1553 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1554 enum isl_dim_type type, unsigned first, unsigned n);
1555 __isl_give isl_basic_set *isl_basic_map_domain(
1556 __isl_take isl_basic_map *bmap);
1557 __isl_give isl_basic_set *isl_basic_map_range(
1558 __isl_take isl_basic_map *bmap);
1559 __isl_give isl_set *isl_map_domain(
1560 __isl_take isl_map *bmap);
1561 __isl_give isl_set *isl_map_range(
1562 __isl_take isl_map *map);
1563 __isl_give isl_union_set *isl_union_map_domain(
1564 __isl_take isl_union_map *umap);
1565 __isl_give isl_union_set *isl_union_map_range(
1566 __isl_take isl_union_map *umap);
1568 __isl_give isl_basic_map *isl_basic_map_domain_map(
1569 __isl_take isl_basic_map *bmap);
1570 __isl_give isl_basic_map *isl_basic_map_range_map(
1571 __isl_take isl_basic_map *bmap);
1572 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1573 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1574 __isl_give isl_union_map *isl_union_map_domain_map(
1575 __isl_take isl_union_map *umap);
1576 __isl_give isl_union_map *isl_union_map_range_map(
1577 __isl_take isl_union_map *umap);
1579 The functions above construct a (basic, regular or union) relation
1580 that maps (a wrapped version of) the input relation to its domain or range.
1584 __isl_give isl_set *isl_set_eliminate(
1585 __isl_take isl_set *set, enum isl_dim_type type,
1586 unsigned first, unsigned n);
1588 Eliminate the coefficients for the given dimensions from the constraints,
1589 without removing the dimensions.
1593 __isl_give isl_basic_set *isl_basic_set_fix(
1594 __isl_take isl_basic_set *bset,
1595 enum isl_dim_type type, unsigned pos,
1597 __isl_give isl_basic_set *isl_basic_set_fix_si(
1598 __isl_take isl_basic_set *bset,
1599 enum isl_dim_type type, unsigned pos, int value);
1600 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1601 enum isl_dim_type type, unsigned pos,
1603 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1604 enum isl_dim_type type, unsigned pos, int value);
1605 __isl_give isl_basic_map *isl_basic_map_fix_si(
1606 __isl_take isl_basic_map *bmap,
1607 enum isl_dim_type type, unsigned pos, int value);
1608 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1609 enum isl_dim_type type, unsigned pos, int value);
1611 Intersect the set or relation with the hyperplane where the given
1612 dimension has the fixed given value.
1614 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1615 enum isl_dim_type type1, int pos1,
1616 enum isl_dim_type type2, int pos2);
1617 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1618 enum isl_dim_type type1, int pos1,
1619 enum isl_dim_type type2, int pos2);
1621 Intersect the set or relation with the hyperplane where the given
1622 dimensions are equal to each other.
1624 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1625 enum isl_dim_type type1, int pos1,
1626 enum isl_dim_type type2, int pos2);
1628 Intersect the relation with the hyperplane where the given
1629 dimensions have opposite values.
1633 __isl_give isl_map *isl_set_identity(
1634 __isl_take isl_set *set);
1635 __isl_give isl_union_map *isl_union_set_identity(
1636 __isl_take isl_union_set *uset);
1638 Construct an identity relation on the given (union) set.
1642 __isl_give isl_basic_set *isl_basic_map_deltas(
1643 __isl_take isl_basic_map *bmap);
1644 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1645 __isl_give isl_union_set *isl_union_map_deltas(
1646 __isl_take isl_union_map *umap);
1648 These functions return a (basic) set containing the differences
1649 between image elements and corresponding domain elements in the input.
1651 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1652 __isl_take isl_basic_map *bmap);
1653 __isl_give isl_map *isl_map_deltas_map(
1654 __isl_take isl_map *map);
1655 __isl_give isl_union_map *isl_union_map_deltas_map(
1656 __isl_take isl_union_map *umap);
1658 The functions above construct a (basic, regular or union) relation
1659 that maps (a wrapped version of) the input relation to its delta set.
1663 Simplify the representation of a set or relation by trying
1664 to combine pairs of basic sets or relations into a single
1665 basic set or relation.
1667 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1668 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1669 __isl_give isl_union_set *isl_union_set_coalesce(
1670 __isl_take isl_union_set *uset);
1671 __isl_give isl_union_map *isl_union_map_coalesce(
1672 __isl_take isl_union_map *umap);
1674 =item * Detecting equalities
1676 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1677 __isl_take isl_basic_set *bset);
1678 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1679 __isl_take isl_basic_map *bmap);
1680 __isl_give isl_set *isl_set_detect_equalities(
1681 __isl_take isl_set *set);
1682 __isl_give isl_map *isl_map_detect_equalities(
1683 __isl_take isl_map *map);
1684 __isl_give isl_union_set *isl_union_set_detect_equalities(
1685 __isl_take isl_union_set *uset);
1686 __isl_give isl_union_map *isl_union_map_detect_equalities(
1687 __isl_take isl_union_map *umap);
1689 Simplify the representation of a set or relation by detecting implicit
1692 =item * Removing redundant constraints
1694 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1695 __isl_take isl_basic_set *bset);
1696 __isl_give isl_set *isl_set_remove_redundancies(
1697 __isl_take isl_set *set);
1698 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1699 __isl_take isl_basic_map *bmap);
1700 __isl_give isl_map *isl_map_remove_redundancies(
1701 __isl_take isl_map *map);
1705 __isl_give isl_basic_set *isl_set_convex_hull(
1706 __isl_take isl_set *set);
1707 __isl_give isl_basic_map *isl_map_convex_hull(
1708 __isl_take isl_map *map);
1710 If the input set or relation has any existentially quantified
1711 variables, then the result of these operations is currently undefined.
1715 __isl_give isl_basic_set *isl_set_simple_hull(
1716 __isl_take isl_set *set);
1717 __isl_give isl_basic_map *isl_map_simple_hull(
1718 __isl_take isl_map *map);
1719 __isl_give isl_union_map *isl_union_map_simple_hull(
1720 __isl_take isl_union_map *umap);
1722 These functions compute a single basic set or relation
1723 that contains the whole input set or relation.
1724 In particular, the output is described by translates
1725 of the constraints describing the basic sets or relations in the input.
1729 (See \autoref{s:simple hull}.)
1735 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1736 __isl_take isl_basic_set *bset);
1737 __isl_give isl_basic_set *isl_set_affine_hull(
1738 __isl_take isl_set *set);
1739 __isl_give isl_union_set *isl_union_set_affine_hull(
1740 __isl_take isl_union_set *uset);
1741 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1742 __isl_take isl_basic_map *bmap);
1743 __isl_give isl_basic_map *isl_map_affine_hull(
1744 __isl_take isl_map *map);
1745 __isl_give isl_union_map *isl_union_map_affine_hull(
1746 __isl_take isl_union_map *umap);
1748 In case of union sets and relations, the affine hull is computed
1751 =item * Polyhedral hull
1753 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1754 __isl_take isl_set *set);
1755 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1756 __isl_take isl_map *map);
1757 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1758 __isl_take isl_union_set *uset);
1759 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1760 __isl_take isl_union_map *umap);
1762 These functions compute a single basic set or relation
1763 not involving any existentially quantified variables
1764 that contains the whole input set or relation.
1765 In case of union sets and relations, the polyhedral hull is computed
1768 =item * Optimization
1770 #include <isl/ilp.h>
1771 enum isl_lp_result isl_basic_set_max(
1772 __isl_keep isl_basic_set *bset,
1773 __isl_keep isl_aff *obj, isl_int *opt)
1774 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1775 __isl_keep isl_aff *obj, isl_int *opt);
1776 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1777 __isl_keep isl_aff *obj, isl_int *opt);
1779 Compute the minimum or maximum of the integer affine expression C<obj>
1780 over the points in C<set>, returning the result in C<opt>.
1781 The return value may be one of C<isl_lp_error>,
1782 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1784 =item * Parametric optimization
1786 __isl_give isl_pw_aff *isl_set_dim_max(
1787 __isl_take isl_set *set, int pos);
1789 Compute the maximum of the given set dimension as a function of the
1790 parameters, but independently of the other set dimensions.
1791 For lexicographic optimization, see L<"Lexicographic Optimization">.
1795 The following functions compute either the set of (rational) coefficient
1796 values of valid constraints for the given set or the set of (rational)
1797 values satisfying the constraints with coefficients from the given set.
1798 Internally, these two sets of functions perform essentially the
1799 same operations, except that the set of coefficients is assumed to
1800 be a cone, while the set of values may be any polyhedron.
1801 The current implementation is based on the Farkas lemma and
1802 Fourier-Motzkin elimination, but this may change or be made optional
1803 in future. In particular, future implementations may use different
1804 dualization algorithms or skip the elimination step.
1806 __isl_give isl_basic_set *isl_basic_set_coefficients(
1807 __isl_take isl_basic_set *bset);
1808 __isl_give isl_basic_set *isl_set_coefficients(
1809 __isl_take isl_set *set);
1810 __isl_give isl_union_set *isl_union_set_coefficients(
1811 __isl_take isl_union_set *bset);
1812 __isl_give isl_basic_set *isl_basic_set_solutions(
1813 __isl_take isl_basic_set *bset);
1814 __isl_give isl_basic_set *isl_set_solutions(
1815 __isl_take isl_set *set);
1816 __isl_give isl_union_set *isl_union_set_solutions(
1817 __isl_take isl_union_set *bset);
1821 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1823 __isl_give isl_union_map *isl_union_map_power(
1824 __isl_take isl_union_map *umap, int *exact);
1826 Compute a parametric representation for all positive powers I<k> of C<map>.
1827 The result maps I<k> to a nested relation corresponding to the
1828 I<k>th power of C<map>.
1829 The result may be an overapproximation. If the result is known to be exact,
1830 then C<*exact> is set to C<1>.
1832 =item * Transitive closure
1834 __isl_give isl_map *isl_map_transitive_closure(
1835 __isl_take isl_map *map, int *exact);
1836 __isl_give isl_union_map *isl_union_map_transitive_closure(
1837 __isl_take isl_union_map *umap, int *exact);
1839 Compute the transitive closure of C<map>.
1840 The result may be an overapproximation. If the result is known to be exact,
1841 then C<*exact> is set to C<1>.
1843 =item * Reaching path lengths
1845 __isl_give isl_map *isl_map_reaching_path_lengths(
1846 __isl_take isl_map *map, int *exact);
1848 Compute a relation that maps each element in the range of C<map>
1849 to the lengths of all paths composed of edges in C<map> that
1850 end up in the given element.
1851 The result may be an overapproximation. If the result is known to be exact,
1852 then C<*exact> is set to C<1>.
1853 To compute the I<maximal> path length, the resulting relation
1854 should be postprocessed by C<isl_map_lexmax>.
1855 In particular, if the input relation is a dependence relation
1856 (mapping sources to sinks), then the maximal path length corresponds
1857 to the free schedule.
1858 Note, however, that C<isl_map_lexmax> expects the maximum to be
1859 finite, so if the path lengths are unbounded (possibly due to
1860 the overapproximation), then you will get an error message.
1864 __isl_give isl_basic_set *isl_basic_map_wrap(
1865 __isl_take isl_basic_map *bmap);
1866 __isl_give isl_set *isl_map_wrap(
1867 __isl_take isl_map *map);
1868 __isl_give isl_union_set *isl_union_map_wrap(
1869 __isl_take isl_union_map *umap);
1870 __isl_give isl_basic_map *isl_basic_set_unwrap(
1871 __isl_take isl_basic_set *bset);
1872 __isl_give isl_map *isl_set_unwrap(
1873 __isl_take isl_set *set);
1874 __isl_give isl_union_map *isl_union_set_unwrap(
1875 __isl_take isl_union_set *uset);
1879 Remove any internal structure of domain (and range) of the given
1880 set or relation. If there is any such internal structure in the input,
1881 then the name of the space is also removed.
1883 __isl_give isl_basic_set *isl_basic_set_flatten(
1884 __isl_take isl_basic_set *bset);
1885 __isl_give isl_set *isl_set_flatten(
1886 __isl_take isl_set *set);
1887 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1888 __isl_take isl_basic_map *bmap);
1889 __isl_give isl_map *isl_map_flatten_range(
1890 __isl_take isl_map *map);
1891 __isl_give isl_basic_map *isl_basic_map_flatten(
1892 __isl_take isl_basic_map *bmap);
1893 __isl_give isl_map *isl_map_flatten(
1894 __isl_take isl_map *map);
1896 __isl_give isl_map *isl_set_flatten_map(
1897 __isl_take isl_set *set);
1899 The function above constructs a relation
1900 that maps the input set to a flattened version of the set.
1904 Lift the input set to a space with extra dimensions corresponding
1905 to the existentially quantified variables in the input.
1906 In particular, the result lives in a wrapped map where the domain
1907 is the original space and the range corresponds to the original
1908 existentially quantified variables.
1910 __isl_give isl_basic_set *isl_basic_set_lift(
1911 __isl_take isl_basic_set *bset);
1912 __isl_give isl_set *isl_set_lift(
1913 __isl_take isl_set *set);
1914 __isl_give isl_union_set *isl_union_set_lift(
1915 __isl_take isl_union_set *uset);
1917 =item * Internal Product
1919 __isl_give isl_basic_map *isl_basic_map_zip(
1920 __isl_take isl_basic_map *bmap);
1921 __isl_give isl_map *isl_map_zip(
1922 __isl_take isl_map *map);
1923 __isl_give isl_union_map *isl_union_map_zip(
1924 __isl_take isl_union_map *umap);
1926 Given a relation with nested relations for domain and range,
1927 interchange the range of the domain with the domain of the range.
1929 =item * Aligning parameters
1931 __isl_give isl_set *isl_set_align_params(
1932 __isl_take isl_set *set,
1933 __isl_take isl_dim *model);
1934 __isl_give isl_map *isl_map_align_params(
1935 __isl_take isl_map *map,
1936 __isl_take isl_dim *model);
1938 Change the order of the parameters of the given set or relation
1939 such that the first parameters match those of C<model>.
1940 This may involve the introduction of extra parameters.
1941 All parameters need to be named.
1943 =item * Dimension manipulation
1945 __isl_give isl_set *isl_set_add_dims(
1946 __isl_take isl_set *set,
1947 enum isl_dim_type type, unsigned n);
1948 __isl_give isl_map *isl_map_add_dims(
1949 __isl_take isl_map *map,
1950 enum isl_dim_type type, unsigned n);
1952 It is usually not advisable to directly change the (input or output)
1953 space of a set or a relation as this removes the name and the internal
1954 structure of the space. However, the above functions can be useful
1955 to add new parameters, assuming
1956 C<isl_set_align_params> and C<isl_map_align_params>
1961 =head2 Binary Operations
1963 The two arguments of a binary operation not only need to live
1964 in the same C<isl_ctx>, they currently also need to have
1965 the same (number of) parameters.
1967 =head3 Basic Operations
1971 =item * Intersection
1973 __isl_give isl_basic_set *isl_basic_set_intersect(
1974 __isl_take isl_basic_set *bset1,
1975 __isl_take isl_basic_set *bset2);
1976 __isl_give isl_set *isl_set_intersect_params(
1977 __isl_take isl_set *set,
1978 __isl_take isl_set *params);
1979 __isl_give isl_set *isl_set_intersect(
1980 __isl_take isl_set *set1,
1981 __isl_take isl_set *set2);
1982 __isl_give isl_union_set *isl_union_set_intersect(
1983 __isl_take isl_union_set *uset1,
1984 __isl_take isl_union_set *uset2);
1985 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1986 __isl_take isl_basic_map *bmap,
1987 __isl_take isl_basic_set *bset);
1988 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1989 __isl_take isl_basic_map *bmap,
1990 __isl_take isl_basic_set *bset);
1991 __isl_give isl_basic_map *isl_basic_map_intersect(
1992 __isl_take isl_basic_map *bmap1,
1993 __isl_take isl_basic_map *bmap2);
1994 __isl_give isl_map *isl_map_intersect_params(
1995 __isl_take isl_map *map,
1996 __isl_take isl_set *params);
1997 __isl_give isl_map *isl_map_intersect_domain(
1998 __isl_take isl_map *map,
1999 __isl_take isl_set *set);
2000 __isl_give isl_map *isl_map_intersect_range(
2001 __isl_take isl_map *map,
2002 __isl_take isl_set *set);
2003 __isl_give isl_map *isl_map_intersect(
2004 __isl_take isl_map *map1,
2005 __isl_take isl_map *map2);
2006 __isl_give isl_union_map *isl_union_map_intersect_domain(
2007 __isl_take isl_union_map *umap,
2008 __isl_take isl_union_set *uset);
2009 __isl_give isl_union_map *isl_union_map_intersect_range(
2010 __isl_take isl_union_map *umap,
2011 __isl_take isl_union_set *uset);
2012 __isl_give isl_union_map *isl_union_map_intersect(
2013 __isl_take isl_union_map *umap1,
2014 __isl_take isl_union_map *umap2);
2018 __isl_give isl_set *isl_basic_set_union(
2019 __isl_take isl_basic_set *bset1,
2020 __isl_take isl_basic_set *bset2);
2021 __isl_give isl_map *isl_basic_map_union(
2022 __isl_take isl_basic_map *bmap1,
2023 __isl_take isl_basic_map *bmap2);
2024 __isl_give isl_set *isl_set_union(
2025 __isl_take isl_set *set1,
2026 __isl_take isl_set *set2);
2027 __isl_give isl_map *isl_map_union(
2028 __isl_take isl_map *map1,
2029 __isl_take isl_map *map2);
2030 __isl_give isl_union_set *isl_union_set_union(
2031 __isl_take isl_union_set *uset1,
2032 __isl_take isl_union_set *uset2);
2033 __isl_give isl_union_map *isl_union_map_union(
2034 __isl_take isl_union_map *umap1,
2035 __isl_take isl_union_map *umap2);
2037 =item * Set difference
2039 __isl_give isl_set *isl_set_subtract(
2040 __isl_take isl_set *set1,
2041 __isl_take isl_set *set2);
2042 __isl_give isl_map *isl_map_subtract(
2043 __isl_take isl_map *map1,
2044 __isl_take isl_map *map2);
2045 __isl_give isl_union_set *isl_union_set_subtract(
2046 __isl_take isl_union_set *uset1,
2047 __isl_take isl_union_set *uset2);
2048 __isl_give isl_union_map *isl_union_map_subtract(
2049 __isl_take isl_union_map *umap1,
2050 __isl_take isl_union_map *umap2);
2054 __isl_give isl_basic_set *isl_basic_set_apply(
2055 __isl_take isl_basic_set *bset,
2056 __isl_take isl_basic_map *bmap);
2057 __isl_give isl_set *isl_set_apply(
2058 __isl_take isl_set *set,
2059 __isl_take isl_map *map);
2060 __isl_give isl_union_set *isl_union_set_apply(
2061 __isl_take isl_union_set *uset,
2062 __isl_take isl_union_map *umap);
2063 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2064 __isl_take isl_basic_map *bmap1,
2065 __isl_take isl_basic_map *bmap2);
2066 __isl_give isl_basic_map *isl_basic_map_apply_range(
2067 __isl_take isl_basic_map *bmap1,
2068 __isl_take isl_basic_map *bmap2);
2069 __isl_give isl_map *isl_map_apply_domain(
2070 __isl_take isl_map *map1,
2071 __isl_take isl_map *map2);
2072 __isl_give isl_union_map *isl_union_map_apply_domain(
2073 __isl_take isl_union_map *umap1,
2074 __isl_take isl_union_map *umap2);
2075 __isl_give isl_map *isl_map_apply_range(
2076 __isl_take isl_map *map1,
2077 __isl_take isl_map *map2);
2078 __isl_give isl_union_map *isl_union_map_apply_range(
2079 __isl_take isl_union_map *umap1,
2080 __isl_take isl_union_map *umap2);
2082 =item * Cartesian Product
2084 __isl_give isl_set *isl_set_product(
2085 __isl_take isl_set *set1,
2086 __isl_take isl_set *set2);
2087 __isl_give isl_union_set *isl_union_set_product(
2088 __isl_take isl_union_set *uset1,
2089 __isl_take isl_union_set *uset2);
2090 __isl_give isl_basic_map *isl_basic_map_range_product(
2091 __isl_take isl_basic_map *bmap1,
2092 __isl_take isl_basic_map *bmap2);
2093 __isl_give isl_map *isl_map_range_product(
2094 __isl_take isl_map *map1,
2095 __isl_take isl_map *map2);
2096 __isl_give isl_union_map *isl_union_map_range_product(
2097 __isl_take isl_union_map *umap1,
2098 __isl_take isl_union_map *umap2);
2099 __isl_give isl_map *isl_map_product(
2100 __isl_take isl_map *map1,
2101 __isl_take isl_map *map2);
2102 __isl_give isl_union_map *isl_union_map_product(
2103 __isl_take isl_union_map *umap1,
2104 __isl_take isl_union_map *umap2);
2106 The above functions compute the cross product of the given
2107 sets or relations. The domains and ranges of the results
2108 are wrapped maps between domains and ranges of the inputs.
2109 To obtain a ``flat'' product, use the following functions
2112 __isl_give isl_basic_set *isl_basic_set_flat_product(
2113 __isl_take isl_basic_set *bset1,
2114 __isl_take isl_basic_set *bset2);
2115 __isl_give isl_set *isl_set_flat_product(
2116 __isl_take isl_set *set1,
2117 __isl_take isl_set *set2);
2118 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2119 __isl_take isl_basic_map *bmap1,
2120 __isl_take isl_basic_map *bmap2);
2121 __isl_give isl_map *isl_map_flat_range_product(
2122 __isl_take isl_map *map1,
2123 __isl_take isl_map *map2);
2124 __isl_give isl_union_map *isl_union_map_flat_range_product(
2125 __isl_take isl_union_map *umap1,
2126 __isl_take isl_union_map *umap2);
2127 __isl_give isl_basic_map *isl_basic_map_flat_product(
2128 __isl_take isl_basic_map *bmap1,
2129 __isl_take isl_basic_map *bmap2);
2130 __isl_give isl_map *isl_map_flat_product(
2131 __isl_take isl_map *map1,
2132 __isl_take isl_map *map2);
2134 =item * Simplification
2136 __isl_give isl_basic_set *isl_basic_set_gist(
2137 __isl_take isl_basic_set *bset,
2138 __isl_take isl_basic_set *context);
2139 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2140 __isl_take isl_set *context);
2141 __isl_give isl_union_set *isl_union_set_gist(
2142 __isl_take isl_union_set *uset,
2143 __isl_take isl_union_set *context);
2144 __isl_give isl_basic_map *isl_basic_map_gist(
2145 __isl_take isl_basic_map *bmap,
2146 __isl_take isl_basic_map *context);
2147 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2148 __isl_take isl_map *context);
2149 __isl_give isl_union_map *isl_union_map_gist(
2150 __isl_take isl_union_map *umap,
2151 __isl_take isl_union_map *context);
2153 The gist operation returns a set or relation that has the
2154 same intersection with the context as the input set or relation.
2155 Any implicit equality in the intersection is made explicit in the result,
2156 while all inequalities that are redundant with respect to the intersection
2158 In case of union sets and relations, the gist operation is performed
2163 =head3 Lexicographic Optimization
2165 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2166 the following functions
2167 compute a set that contains the lexicographic minimum or maximum
2168 of the elements in C<set> (or C<bset>) for those values of the parameters
2169 that satisfy C<dom>.
2170 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2171 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2173 In other words, the union of the parameter values
2174 for which the result is non-empty and of C<*empty>
2177 __isl_give isl_set *isl_basic_set_partial_lexmin(
2178 __isl_take isl_basic_set *bset,
2179 __isl_take isl_basic_set *dom,
2180 __isl_give isl_set **empty);
2181 __isl_give isl_set *isl_basic_set_partial_lexmax(
2182 __isl_take isl_basic_set *bset,
2183 __isl_take isl_basic_set *dom,
2184 __isl_give isl_set **empty);
2185 __isl_give isl_set *isl_set_partial_lexmin(
2186 __isl_take isl_set *set, __isl_take isl_set *dom,
2187 __isl_give isl_set **empty);
2188 __isl_give isl_set *isl_set_partial_lexmax(
2189 __isl_take isl_set *set, __isl_take isl_set *dom,
2190 __isl_give isl_set **empty);
2192 Given a (basic) set C<set> (or C<bset>), the following functions simply
2193 return a set containing the lexicographic minimum or maximum
2194 of the elements in C<set> (or C<bset>).
2195 In case of union sets, the optimum is computed per space.
2197 __isl_give isl_set *isl_basic_set_lexmin(
2198 __isl_take isl_basic_set *bset);
2199 __isl_give isl_set *isl_basic_set_lexmax(
2200 __isl_take isl_basic_set *bset);
2201 __isl_give isl_set *isl_set_lexmin(
2202 __isl_take isl_set *set);
2203 __isl_give isl_set *isl_set_lexmax(
2204 __isl_take isl_set *set);
2205 __isl_give isl_union_set *isl_union_set_lexmin(
2206 __isl_take isl_union_set *uset);
2207 __isl_give isl_union_set *isl_union_set_lexmax(
2208 __isl_take isl_union_set *uset);
2210 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2211 the following functions
2212 compute a relation that maps each element of C<dom>
2213 to the single lexicographic minimum or maximum
2214 of the elements that are associated to that same
2215 element in C<map> (or C<bmap>).
2216 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2217 that contains the elements in C<dom> that do not map
2218 to any elements in C<map> (or C<bmap>).
2219 In other words, the union of the domain of the result and of C<*empty>
2222 __isl_give isl_map *isl_basic_map_partial_lexmax(
2223 __isl_take isl_basic_map *bmap,
2224 __isl_take isl_basic_set *dom,
2225 __isl_give isl_set **empty);
2226 __isl_give isl_map *isl_basic_map_partial_lexmin(
2227 __isl_take isl_basic_map *bmap,
2228 __isl_take isl_basic_set *dom,
2229 __isl_give isl_set **empty);
2230 __isl_give isl_map *isl_map_partial_lexmax(
2231 __isl_take isl_map *map, __isl_take isl_set *dom,
2232 __isl_give isl_set **empty);
2233 __isl_give isl_map *isl_map_partial_lexmin(
2234 __isl_take isl_map *map, __isl_take isl_set *dom,
2235 __isl_give isl_set **empty);
2237 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2238 return a map mapping each element in the domain of
2239 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2240 of all elements associated to that element.
2241 In case of union relations, the optimum is computed per space.
2243 __isl_give isl_map *isl_basic_map_lexmin(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_map *isl_basic_map_lexmax(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_lexmin(
2248 __isl_take isl_map *map);
2249 __isl_give isl_map *isl_map_lexmax(
2250 __isl_take isl_map *map);
2251 __isl_give isl_union_map *isl_union_map_lexmin(
2252 __isl_take isl_union_map *umap);
2253 __isl_give isl_union_map *isl_union_map_lexmax(
2254 __isl_take isl_union_map *umap);
2258 Lists are defined over several element types, including
2259 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2260 Here we take lists of C<isl_set>s as an example.
2261 Lists can be created, copied and freed using the following functions.
2263 #include <isl/list.h>
2264 __isl_give isl_set_list *isl_set_list_alloc(
2265 isl_ctx *ctx, int n);
2266 __isl_give isl_set_list *isl_set_list_copy(
2267 __isl_keep isl_set_list *list);
2268 __isl_give isl_set_list *isl_set_list_add(
2269 __isl_take isl_set_list *list,
2270 __isl_take isl_set *el);
2271 void isl_set_list_free(__isl_take isl_set_list *list);
2273 C<isl_set_list_alloc> creates an empty list with a capacity for
2276 Lists can be inspected using the following functions.
2278 #include <isl/list.h>
2279 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2280 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2281 __isl_give struct isl_set *isl_set_list_get_set(
2282 __isl_keep isl_set_list *list, int index);
2283 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2284 int (*fn)(__isl_take struct isl_set *el, void *user),
2287 Lists can be printed using
2289 #include <isl/list.h>
2290 __isl_give isl_printer *isl_printer_print_set_list(
2291 __isl_take isl_printer *p,
2292 __isl_keep isl_set_list *list);
2296 Matrices can be created, copied and freed using the following functions.
2298 #include <isl/mat.h>
2299 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2300 unsigned n_row, unsigned n_col);
2301 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2302 void isl_mat_free(__isl_take isl_mat *mat);
2304 Note that the elements of a newly created matrix may have arbitrary values.
2305 The elements can be changed and inspected using the following functions.
2307 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2308 int isl_mat_rows(__isl_keep isl_mat *mat);
2309 int isl_mat_cols(__isl_keep isl_mat *mat);
2310 int isl_mat_get_element(__isl_keep isl_mat *mat,
2311 int row, int col, isl_int *v);
2312 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2313 int row, int col, isl_int v);
2314 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2315 int row, int col, int v);
2317 C<isl_mat_get_element> will return a negative value if anything went wrong.
2318 In that case, the value of C<*v> is undefined.
2320 The following function can be used to compute the (right) inverse
2321 of a matrix, i.e., a matrix such that the product of the original
2322 and the inverse (in that order) is a multiple of the identity matrix.
2323 The input matrix is assumed to be of full row-rank.
2325 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2327 The following function can be used to compute the (right) kernel
2328 (or null space) of a matrix, i.e., a matrix such that the product of
2329 the original and the kernel (in that order) is the zero matrix.
2331 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2333 =head2 Piecewise Quasi Affine Expressions
2335 The zero quasi affine expression can be created using
2337 __isl_give isl_aff *isl_aff_zero(
2338 __isl_take isl_local_space *ls);
2340 A quasi affine expression can also be initialized from an C<isl_div>:
2342 #include <isl/div.h>
2343 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2345 An empty piecewise quasi affine expression (one with no cells)
2346 or a piecewise quasi affine expression with a single cell can
2347 be created using the following functions.
2349 #include <isl/aff.h>
2350 __isl_give isl_pw_aff *isl_pw_aff_empty(
2351 __isl_take isl_dim *dim);
2352 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2353 __isl_take isl_set *set, __isl_take isl_aff *aff);
2355 Quasi affine expressions can be copied and freed using
2357 #include <isl/aff.h>
2358 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2359 void *isl_aff_free(__isl_take isl_aff *aff);
2361 __isl_give isl_pw_aff *isl_pw_aff_copy(
2362 __isl_keep isl_pw_aff *pwaff);
2363 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2365 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2366 using the following function. The constraint is required to have
2367 a non-zero coefficient for the specified dimension.
2369 #include <isl/constraint.h>
2370 __isl_give isl_aff *isl_constraint_get_bound(
2371 __isl_keep isl_constraint *constraint,
2372 enum isl_dim_type type, int pos);
2374 The entire affine expression of the constraint can also be extracted
2375 using the following function.
2377 #include <isl/constraint.h>
2378 __isl_give isl_aff *isl_constraint_get_aff(
2379 __isl_keep isl_constraint *constraint);
2381 Conversely, an equality constraint equating
2382 the affine expression to zero or an inequality constraint enforcing
2383 the affine expression to be non-negative, can be constructed using
2385 __isl_give isl_constraint *isl_equality_from_aff(
2386 __isl_take isl_aff *aff);
2387 __isl_give isl_constraint *isl_inequality_from_aff(
2388 __isl_take isl_aff *aff);
2390 The expression can be inspected using
2392 #include <isl/aff.h>
2393 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2394 int isl_aff_dim(__isl_keep isl_aff *aff,
2395 enum isl_dim_type type);
2396 __isl_give isl_local_space *isl_aff_get_local_space(
2397 __isl_keep isl_aff *aff);
2398 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2399 enum isl_dim_type type, unsigned pos);
2400 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2402 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2403 enum isl_dim_type type, int pos, isl_int *v);
2404 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2406 __isl_give isl_div *isl_aff_get_div(
2407 __isl_keep isl_aff *aff, int pos);
2409 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2410 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2412 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2413 enum isl_dim_type type, unsigned first, unsigned n);
2414 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2415 enum isl_dim_type type, unsigned first, unsigned n);
2417 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2418 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2419 enum isl_dim_type type);
2420 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2422 It can be modified using
2424 #include <isl/aff.h>
2425 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2426 __isl_take isl_pw_aff *pwaff,
2427 __isl_take isl_id *id);
2428 __isl_give isl_aff *isl_aff_set_dim_name(
2429 __isl_take isl_aff *aff, enum isl_dim_type type,
2430 unsigned pos, const char *s);
2431 __isl_give isl_aff *isl_aff_set_constant(
2432 __isl_take isl_aff *aff, isl_int v);
2433 __isl_give isl_aff *isl_aff_set_constant_si(
2434 __isl_take isl_aff *aff, int v);
2435 __isl_give isl_aff *isl_aff_set_coefficient(
2436 __isl_take isl_aff *aff,
2437 enum isl_dim_type type, int pos, isl_int v);
2438 __isl_give isl_aff *isl_aff_set_coefficient_si(
2439 __isl_take isl_aff *aff,
2440 enum isl_dim_type type, int pos, int v);
2441 __isl_give isl_aff *isl_aff_set_denominator(
2442 __isl_take isl_aff *aff, isl_int v);
2444 __isl_give isl_aff *isl_aff_add_constant(
2445 __isl_take isl_aff *aff, isl_int v);
2446 __isl_give isl_aff *isl_aff_add_constant_si(
2447 __isl_take isl_aff *aff, int v);
2448 __isl_give isl_aff *isl_aff_add_coefficient(
2449 __isl_take isl_aff *aff,
2450 enum isl_dim_type type, int pos, isl_int v);
2451 __isl_give isl_aff *isl_aff_add_coefficient_si(
2452 __isl_take isl_aff *aff,
2453 enum isl_dim_type type, int pos, int v);
2455 __isl_give isl_aff *isl_aff_insert_dims(
2456 __isl_take isl_aff *aff,
2457 enum isl_dim_type type, unsigned first, unsigned n);
2458 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2459 __isl_take isl_pw_aff *pwaff,
2460 enum isl_dim_type type, unsigned first, unsigned n);
2461 __isl_give isl_aff *isl_aff_add_dims(
2462 __isl_take isl_aff *aff,
2463 enum isl_dim_type type, unsigned n);
2464 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2465 __isl_take isl_pw_aff *pwaff,
2466 enum isl_dim_type type, unsigned n);
2467 __isl_give isl_aff *isl_aff_drop_dims(
2468 __isl_take isl_aff *aff,
2469 enum isl_dim_type type, unsigned first, unsigned n);
2470 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2471 __isl_take isl_pw_aff *pwaff,
2472 enum isl_dim_type type, unsigned first, unsigned n);
2474 Note that the C<set_constant> and C<set_coefficient> functions
2475 set the I<numerator> of the constant or coefficient, while
2476 C<add_constant> and C<add_coefficient> add an integer value to
2477 the possibly rational constant or coefficient.
2479 To check whether an affine expressions is obviously zero
2480 or obviously equal to some other affine expression, use
2482 #include <isl/aff.h>
2483 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2484 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2485 __isl_keep isl_aff *aff2);
2489 #include <isl/aff.h>
2490 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2491 __isl_take isl_aff *aff2);
2492 __isl_give isl_pw_aff *isl_pw_aff_add(
2493 __isl_take isl_pw_aff *pwaff1,
2494 __isl_take isl_pw_aff *pwaff2);
2495 __isl_give isl_pw_aff *isl_pw_aff_min(
2496 __isl_take isl_pw_aff *pwaff1,
2497 __isl_take isl_pw_aff *pwaff2);
2498 __isl_give isl_pw_aff *isl_pw_aff_max(
2499 __isl_take isl_pw_aff *pwaff1,
2500 __isl_take isl_pw_aff *pwaff2);
2501 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2502 __isl_take isl_aff *aff2);
2503 __isl_give isl_pw_aff *isl_pw_aff_sub(
2504 __isl_take isl_pw_aff *pwaff1,
2505 __isl_take isl_pw_aff *pwaff2);
2506 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2507 __isl_give isl_pw_aff *isl_pw_aff_neg(
2508 __isl_take isl_pw_aff *pwaff);
2509 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2510 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2511 __isl_take isl_pw_aff *pwaff);
2512 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2513 __isl_give isl_pw_aff *isl_pw_aff_floor(
2514 __isl_take isl_pw_aff *pwaff);
2515 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2517 __isl_give isl_pw_aff *isl_pw_aff_scale(
2518 __isl_take isl_pw_aff *pwaff, isl_int f);
2519 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2521 __isl_give isl_aff *isl_aff_scale_down_ui(
2522 __isl_take isl_aff *aff, unsigned f);
2523 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2524 __isl_take isl_pw_aff *pwaff, isl_int f);
2526 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2527 __isl_take isl_pw_aff *pwqp);
2529 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2530 __isl_take isl_pw_aff *pwaff,
2531 __isl_take isl_dim *model);
2533 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2534 __isl_take isl_set *context);
2535 __isl_give isl_pw_aff *isl_pw_aff_gist(
2536 __isl_take isl_pw_aff *pwaff,
2537 __isl_take isl_set *context);
2539 __isl_give isl_set *isl_pw_aff_domain(
2540 __isl_take isl_pw_aff *pwaff);
2542 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2543 __isl_take isl_aff *aff2);
2544 __isl_give isl_pw_aff *isl_pw_aff_mul(
2545 __isl_take isl_pw_aff *pwaff1,
2546 __isl_take isl_pw_aff *pwaff2);
2548 When multiplying two affine expressions, at least one of the two needs
2551 #include <isl/aff.h>
2552 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2553 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2554 __isl_give isl_set *isl_pw_aff_eq_set(
2555 __isl_take isl_pw_aff *pwaff1,
2556 __isl_take isl_pw_aff *pwaff2);
2557 __isl_give isl_set *isl_pw_aff_ne_set(
2558 __isl_take isl_pw_aff *pwaff1,
2559 __isl_take isl_pw_aff *pwaff2);
2560 __isl_give isl_set *isl_pw_aff_le_set(
2561 __isl_take isl_pw_aff *pwaff1,
2562 __isl_take isl_pw_aff *pwaff2);
2563 __isl_give isl_set *isl_pw_aff_lt_set(
2564 __isl_take isl_pw_aff *pwaff1,
2565 __isl_take isl_pw_aff *pwaff2);
2566 __isl_give isl_set *isl_pw_aff_ge_set(
2567 __isl_take isl_pw_aff *pwaff1,
2568 __isl_take isl_pw_aff *pwaff2);
2569 __isl_give isl_set *isl_pw_aff_gt_set(
2570 __isl_take isl_pw_aff *pwaff1,
2571 __isl_take isl_pw_aff *pwaff2);
2573 The function C<isl_aff_ge_basic_set> returns a basic set
2574 containing those elements in the shared space
2575 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2576 The function C<isl_aff_ge_set> returns a set
2577 containing those elements in the shared domain
2578 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2580 #include <isl/aff.h>
2581 __isl_give isl_set *isl_pw_aff_nonneg_set(
2582 __isl_take isl_pw_aff *pwaff);
2584 The function C<isl_pw_aff_nonneg_set> returns a set
2585 containing those elements in the domain
2586 of C<pwaff> where C<pwaff> is non-negative.
2588 #include <isl/aff.h>
2589 __isl_give isl_pw_aff *isl_pw_aff_cond(
2590 __isl_take isl_set *cond,
2591 __isl_take isl_pw_aff *pwaff_true,
2592 __isl_take isl_pw_aff *pwaff_false);
2594 The function C<isl_pw_aff_cond> performs a conditional operator
2595 and returns an expression that is equal to C<pwaff_true>
2596 for elements in C<cond> and equal to C<pwaff_false> for elements
2599 #include <isl/aff.h>
2600 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2601 __isl_take isl_pw_aff *pwaff1,
2602 __isl_take isl_pw_aff *pwaff2);
2604 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2605 expression with a domain that is the union of those of C<pwaff1> and
2606 C<pwaff2> and such that on each cell, the quasi-affine expression is
2607 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2608 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2609 associated expression is the defined one.
2611 An expression can be printed using
2613 #include <isl/aff.h>
2614 __isl_give isl_printer *isl_printer_print_aff(
2615 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2617 __isl_give isl_printer *isl_printer_print_pw_aff(
2618 __isl_take isl_printer *p,
2619 __isl_keep isl_pw_aff *pwaff);
2623 Points are elements of a set. They can be used to construct
2624 simple sets (boxes) or they can be used to represent the
2625 individual elements of a set.
2626 The zero point (the origin) can be created using
2628 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2630 The coordinates of a point can be inspected, set and changed
2633 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2634 enum isl_dim_type type, int pos, isl_int *v);
2635 __isl_give isl_point *isl_point_set_coordinate(
2636 __isl_take isl_point *pnt,
2637 enum isl_dim_type type, int pos, isl_int v);
2639 __isl_give isl_point *isl_point_add_ui(
2640 __isl_take isl_point *pnt,
2641 enum isl_dim_type type, int pos, unsigned val);
2642 __isl_give isl_point *isl_point_sub_ui(
2643 __isl_take isl_point *pnt,
2644 enum isl_dim_type type, int pos, unsigned val);
2646 Other properties can be obtained using
2648 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2650 Points can be copied or freed using
2652 __isl_give isl_point *isl_point_copy(
2653 __isl_keep isl_point *pnt);
2654 void isl_point_free(__isl_take isl_point *pnt);
2656 A singleton set can be created from a point using
2658 __isl_give isl_basic_set *isl_basic_set_from_point(
2659 __isl_take isl_point *pnt);
2660 __isl_give isl_set *isl_set_from_point(
2661 __isl_take isl_point *pnt);
2663 and a box can be created from two opposite extremal points using
2665 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2666 __isl_take isl_point *pnt1,
2667 __isl_take isl_point *pnt2);
2668 __isl_give isl_set *isl_set_box_from_points(
2669 __isl_take isl_point *pnt1,
2670 __isl_take isl_point *pnt2);
2672 All elements of a B<bounded> (union) set can be enumerated using
2673 the following functions.
2675 int isl_set_foreach_point(__isl_keep isl_set *set,
2676 int (*fn)(__isl_take isl_point *pnt, void *user),
2678 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2679 int (*fn)(__isl_take isl_point *pnt, void *user),
2682 The function C<fn> is called for each integer point in
2683 C<set> with as second argument the last argument of
2684 the C<isl_set_foreach_point> call. The function C<fn>
2685 should return C<0> on success and C<-1> on failure.
2686 In the latter case, C<isl_set_foreach_point> will stop
2687 enumerating and return C<-1> as well.
2688 If the enumeration is performed successfully and to completion,
2689 then C<isl_set_foreach_point> returns C<0>.
2691 To obtain a single point of a (basic) set, use
2693 __isl_give isl_point *isl_basic_set_sample_point(
2694 __isl_take isl_basic_set *bset);
2695 __isl_give isl_point *isl_set_sample_point(
2696 __isl_take isl_set *set);
2698 If C<set> does not contain any (integer) points, then the
2699 resulting point will be ``void'', a property that can be
2702 int isl_point_is_void(__isl_keep isl_point *pnt);
2704 =head2 Piecewise Quasipolynomials
2706 A piecewise quasipolynomial is a particular kind of function that maps
2707 a parametric point to a rational value.
2708 More specifically, a quasipolynomial is a polynomial expression in greatest
2709 integer parts of affine expressions of parameters and variables.
2710 A piecewise quasipolynomial is a subdivision of a given parametric
2711 domain into disjoint cells with a quasipolynomial associated to
2712 each cell. The value of the piecewise quasipolynomial at a given
2713 point is the value of the quasipolynomial associated to the cell
2714 that contains the point. Outside of the union of cells,
2715 the value is assumed to be zero.
2716 For example, the piecewise quasipolynomial
2718 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2720 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2721 A given piecewise quasipolynomial has a fixed domain dimension.
2722 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2723 defined over different domains.
2724 Piecewise quasipolynomials are mainly used by the C<barvinok>
2725 library for representing the number of elements in a parametric set or map.
2726 For example, the piecewise quasipolynomial above represents
2727 the number of points in the map
2729 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2731 =head3 Printing (Piecewise) Quasipolynomials
2733 Quasipolynomials and piecewise quasipolynomials can be printed
2734 using the following functions.
2736 __isl_give isl_printer *isl_printer_print_qpolynomial(
2737 __isl_take isl_printer *p,
2738 __isl_keep isl_qpolynomial *qp);
2740 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2741 __isl_take isl_printer *p,
2742 __isl_keep isl_pw_qpolynomial *pwqp);
2744 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2745 __isl_take isl_printer *p,
2746 __isl_keep isl_union_pw_qpolynomial *upwqp);
2748 The output format of the printer
2749 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2750 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2752 In case of printing in C<ISL_FORMAT_C>, the user may want
2753 to set the names of all dimensions
2755 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2756 __isl_take isl_qpolynomial *qp,
2757 enum isl_dim_type type, unsigned pos,
2759 __isl_give isl_pw_qpolynomial *
2760 isl_pw_qpolynomial_set_dim_name(
2761 __isl_take isl_pw_qpolynomial *pwqp,
2762 enum isl_dim_type type, unsigned pos,
2765 =head3 Creating New (Piecewise) Quasipolynomials
2767 Some simple quasipolynomials can be created using the following functions.
2768 More complicated quasipolynomials can be created by applying
2769 operations such as addition and multiplication
2770 on the resulting quasipolynomials
2772 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2773 __isl_take isl_dim *dim);
2774 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2775 __isl_take isl_dim *dim);
2776 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2777 __isl_take isl_dim *dim);
2778 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2779 __isl_take isl_dim *dim);
2780 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2781 __isl_take isl_dim *dim);
2782 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2783 __isl_take isl_dim *dim,
2784 const isl_int n, const isl_int d);
2785 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2786 __isl_take isl_div *div);
2787 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2788 __isl_take isl_dim *dim,
2789 enum isl_dim_type type, unsigned pos);
2790 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2791 __isl_take isl_aff *aff);
2793 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2794 with a single cell can be created using the following functions.
2795 Multiple of these single cell piecewise quasipolynomials can
2796 be combined to create more complicated piecewise quasipolynomials.
2798 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2799 __isl_take isl_dim *dim);
2800 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2801 __isl_take isl_set *set,
2802 __isl_take isl_qpolynomial *qp);
2804 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2805 __isl_take isl_dim *dim);
2806 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2807 __isl_take isl_pw_qpolynomial *pwqp);
2808 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2809 __isl_take isl_union_pw_qpolynomial *upwqp,
2810 __isl_take isl_pw_qpolynomial *pwqp);
2812 Quasipolynomials can be copied and freed again using the following
2815 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2816 __isl_keep isl_qpolynomial *qp);
2817 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2820 __isl_keep isl_pw_qpolynomial *pwqp);
2821 void *isl_pw_qpolynomial_free(
2822 __isl_take isl_pw_qpolynomial *pwqp);
2824 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2825 __isl_keep isl_union_pw_qpolynomial *upwqp);
2826 void isl_union_pw_qpolynomial_free(
2827 __isl_take isl_union_pw_qpolynomial *upwqp);
2829 =head3 Inspecting (Piecewise) Quasipolynomials
2831 To iterate over all piecewise quasipolynomials in a union
2832 piecewise quasipolynomial, use the following function
2834 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2835 __isl_keep isl_union_pw_qpolynomial *upwqp,
2836 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2839 To extract the piecewise quasipolynomial from a union with a given dimension
2842 __isl_give isl_pw_qpolynomial *
2843 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2844 __isl_keep isl_union_pw_qpolynomial *upwqp,
2845 __isl_take isl_dim *dim);
2847 To iterate over the cells in a piecewise quasipolynomial,
2848 use either of the following two functions
2850 int isl_pw_qpolynomial_foreach_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);
2855 int isl_pw_qpolynomial_foreach_lifted_piece(
2856 __isl_keep isl_pw_qpolynomial *pwqp,
2857 int (*fn)(__isl_take isl_set *set,
2858 __isl_take isl_qpolynomial *qp,
2859 void *user), void *user);
2861 As usual, the function C<fn> should return C<0> on success
2862 and C<-1> on failure. The difference between
2863 C<isl_pw_qpolynomial_foreach_piece> and
2864 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2865 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2866 compute unique representations for all existentially quantified
2867 variables and then turn these existentially quantified variables
2868 into extra set variables, adapting the associated quasipolynomial
2869 accordingly. This means that the C<set> passed to C<fn>
2870 will not have any existentially quantified variables, but that
2871 the dimensions of the sets may be different for different
2872 invocations of C<fn>.
2874 To iterate over all terms in a quasipolynomial,
2877 int isl_qpolynomial_foreach_term(
2878 __isl_keep isl_qpolynomial *qp,
2879 int (*fn)(__isl_take isl_term *term,
2880 void *user), void *user);
2882 The terms themselves can be inspected and freed using
2885 unsigned isl_term_dim(__isl_keep isl_term *term,
2886 enum isl_dim_type type);
2887 void isl_term_get_num(__isl_keep isl_term *term,
2889 void isl_term_get_den(__isl_keep isl_term *term,
2891 int isl_term_get_exp(__isl_keep isl_term *term,
2892 enum isl_dim_type type, unsigned pos);
2893 __isl_give isl_div *isl_term_get_div(
2894 __isl_keep isl_term *term, unsigned pos);
2895 void isl_term_free(__isl_take isl_term *term);
2897 Each term is a product of parameters, set variables and
2898 integer divisions. The function C<isl_term_get_exp>
2899 returns the exponent of a given dimensions in the given term.
2900 The C<isl_int>s in the arguments of C<isl_term_get_num>
2901 and C<isl_term_get_den> need to have been initialized
2902 using C<isl_int_init> before calling these functions.
2904 =head3 Properties of (Piecewise) Quasipolynomials
2906 To check whether a quasipolynomial is actually a constant,
2907 use the following function.
2909 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2910 isl_int *n, isl_int *d);
2912 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2913 then the numerator and denominator of the constant
2914 are returned in C<*n> and C<*d>, respectively.
2916 =head3 Operations on (Piecewise) Quasipolynomials
2918 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2919 __isl_take isl_qpolynomial *qp, isl_int v);
2920 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2921 __isl_take isl_qpolynomial *qp);
2922 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2923 __isl_take isl_qpolynomial *qp1,
2924 __isl_take isl_qpolynomial *qp2);
2925 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2926 __isl_take isl_qpolynomial *qp1,
2927 __isl_take isl_qpolynomial *qp2);
2928 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2929 __isl_take isl_qpolynomial *qp1,
2930 __isl_take isl_qpolynomial *qp2);
2931 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2932 __isl_take isl_qpolynomial *qp, unsigned exponent);
2934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2935 __isl_take isl_pw_qpolynomial *pwqp1,
2936 __isl_take isl_pw_qpolynomial *pwqp2);
2937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2938 __isl_take isl_pw_qpolynomial *pwqp1,
2939 __isl_take isl_pw_qpolynomial *pwqp2);
2940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2941 __isl_take isl_pw_qpolynomial *pwqp1,
2942 __isl_take isl_pw_qpolynomial *pwqp2);
2943 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2944 __isl_take isl_pw_qpolynomial *pwqp);
2945 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2946 __isl_take isl_pw_qpolynomial *pwqp1,
2947 __isl_take isl_pw_qpolynomial *pwqp2);
2949 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2950 __isl_take isl_union_pw_qpolynomial *upwqp1,
2951 __isl_take isl_union_pw_qpolynomial *upwqp2);
2952 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2953 __isl_take isl_union_pw_qpolynomial *upwqp1,
2954 __isl_take isl_union_pw_qpolynomial *upwqp2);
2955 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2956 __isl_take isl_union_pw_qpolynomial *upwqp1,
2957 __isl_take isl_union_pw_qpolynomial *upwqp2);
2959 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2960 __isl_take isl_pw_qpolynomial *pwqp,
2961 __isl_take isl_point *pnt);
2963 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2964 __isl_take isl_union_pw_qpolynomial *upwqp,
2965 __isl_take isl_point *pnt);
2967 __isl_give isl_set *isl_pw_qpolynomial_domain(
2968 __isl_take isl_pw_qpolynomial *pwqp);
2969 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2970 __isl_take isl_pw_qpolynomial *pwpq,
2971 __isl_take isl_set *set);
2973 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2974 __isl_take isl_union_pw_qpolynomial *upwqp);
2975 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2976 __isl_take isl_union_pw_qpolynomial *upwpq,
2977 __isl_take isl_union_set *uset);
2979 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2980 __isl_take isl_qpolynomial *qp,
2981 __isl_take isl_dim *model);
2983 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2984 __isl_take isl_union_pw_qpolynomial *upwqp);
2986 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2987 __isl_take isl_qpolynomial *qp,
2988 __isl_take isl_set *context);
2990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2991 __isl_take isl_pw_qpolynomial *pwqp,
2992 __isl_take isl_set *context);
2994 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2995 __isl_take isl_union_pw_qpolynomial *upwqp,
2996 __isl_take isl_union_set *context);
2998 The gist operation applies the gist operation to each of
2999 the cells in the domain of the input piecewise quasipolynomial.
3000 The context is also exploited
3001 to simplify the quasipolynomials associated to each cell.
3003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3004 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3005 __isl_give isl_union_pw_qpolynomial *
3006 isl_union_pw_qpolynomial_to_polynomial(
3007 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3009 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3010 the polynomial will be an overapproximation. If C<sign> is negative,
3011 it will be an underapproximation. If C<sign> is zero, the approximation
3012 will lie somewhere in between.
3014 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3016 A piecewise quasipolynomial reduction is a piecewise
3017 reduction (or fold) of quasipolynomials.
3018 In particular, the reduction can be maximum or a minimum.
3019 The objects are mainly used to represent the result of
3020 an upper or lower bound on a quasipolynomial over its domain,
3021 i.e., as the result of the following function.
3023 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3024 __isl_take isl_pw_qpolynomial *pwqp,
3025 enum isl_fold type, int *tight);
3027 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3028 __isl_take isl_union_pw_qpolynomial *upwqp,
3029 enum isl_fold type, int *tight);
3031 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3032 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3033 is the returned bound is known be tight, i.e., for each value
3034 of the parameters there is at least
3035 one element in the domain that reaches the bound.
3036 If the domain of C<pwqp> is not wrapping, then the bound is computed
3037 over all elements in that domain and the result has a purely parametric
3038 domain. If the domain of C<pwqp> is wrapping, then the bound is
3039 computed over the range of the wrapped relation. The domain of the
3040 wrapped relation becomes the domain of the result.
3042 A (piecewise) quasipolynomial reduction can be copied or freed using the
3043 following functions.
3045 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3046 __isl_keep isl_qpolynomial_fold *fold);
3047 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3048 __isl_keep isl_pw_qpolynomial_fold *pwf);
3049 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3050 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3051 void isl_qpolynomial_fold_free(
3052 __isl_take isl_qpolynomial_fold *fold);
3053 void *isl_pw_qpolynomial_fold_free(
3054 __isl_take isl_pw_qpolynomial_fold *pwf);
3055 void isl_union_pw_qpolynomial_fold_free(
3056 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3058 =head3 Printing Piecewise Quasipolynomial Reductions
3060 Piecewise quasipolynomial reductions can be printed
3061 using the following function.
3063 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3064 __isl_take isl_printer *p,
3065 __isl_keep isl_pw_qpolynomial_fold *pwf);
3066 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3067 __isl_take isl_printer *p,
3068 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3070 For C<isl_printer_print_pw_qpolynomial_fold>,
3071 output format of the printer
3072 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3073 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3074 output format of the printer
3075 needs to be set to C<ISL_FORMAT_ISL>.
3076 In case of printing in C<ISL_FORMAT_C>, the user may want
3077 to set the names of all dimensions
3079 __isl_give isl_pw_qpolynomial_fold *
3080 isl_pw_qpolynomial_fold_set_dim_name(
3081 __isl_take isl_pw_qpolynomial_fold *pwf,
3082 enum isl_dim_type type, unsigned pos,
3085 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3087 To iterate over all piecewise quasipolynomial reductions in a union
3088 piecewise quasipolynomial reduction, use the following function
3090 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3091 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3092 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3093 void *user), void *user);
3095 To iterate over the cells in a piecewise quasipolynomial reduction,
3096 use either of the following two functions
3098 int isl_pw_qpolynomial_fold_foreach_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);
3103 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3104 __isl_keep isl_pw_qpolynomial_fold *pwf,
3105 int (*fn)(__isl_take isl_set *set,
3106 __isl_take isl_qpolynomial_fold *fold,
3107 void *user), void *user);
3109 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3110 of the difference between these two functions.
3112 To iterate over all quasipolynomials in a reduction, use
3114 int isl_qpolynomial_fold_foreach_qpolynomial(
3115 __isl_keep isl_qpolynomial_fold *fold,
3116 int (*fn)(__isl_take isl_qpolynomial *qp,
3117 void *user), void *user);
3119 =head3 Operations on Piecewise Quasipolynomial Reductions
3121 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3122 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3124 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3125 __isl_take isl_pw_qpolynomial_fold *pwf1,
3126 __isl_take isl_pw_qpolynomial_fold *pwf2);
3128 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3129 __isl_take isl_pw_qpolynomial_fold *pwf1,
3130 __isl_take isl_pw_qpolynomial_fold *pwf2);
3132 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3133 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3134 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3136 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3137 __isl_take isl_pw_qpolynomial_fold *pwf,
3138 __isl_take isl_point *pnt);
3140 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3141 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3142 __isl_take isl_point *pnt);
3144 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3145 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3146 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3148 __isl_take isl_union_set *uset);
3150 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3151 __isl_take isl_pw_qpolynomial_fold *pwf);
3153 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3154 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3156 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3157 __isl_take isl_pw_qpolynomial_fold *pwf,
3158 __isl_take isl_set *context);
3160 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3161 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3162 __isl_take isl_union_set *context);
3164 The gist operation applies the gist operation to each of
3165 the cells in the domain of the input piecewise quasipolynomial reduction.
3166 In future, the operation will also exploit the context
3167 to simplify the quasipolynomial reductions associated to each cell.
3169 __isl_give isl_pw_qpolynomial_fold *
3170 isl_set_apply_pw_qpolynomial_fold(
3171 __isl_take isl_set *set,
3172 __isl_take isl_pw_qpolynomial_fold *pwf,
3174 __isl_give isl_pw_qpolynomial_fold *
3175 isl_map_apply_pw_qpolynomial_fold(
3176 __isl_take isl_map *map,
3177 __isl_take isl_pw_qpolynomial_fold *pwf,
3179 __isl_give isl_union_pw_qpolynomial_fold *
3180 isl_union_set_apply_union_pw_qpolynomial_fold(
3181 __isl_take isl_union_set *uset,
3182 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3184 __isl_give isl_union_pw_qpolynomial_fold *
3185 isl_union_map_apply_union_pw_qpolynomial_fold(
3186 __isl_take isl_union_map *umap,
3187 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3190 The functions taking a map
3191 compose the given map with the given piecewise quasipolynomial reduction.
3192 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3193 over all elements in the intersection of the range of the map
3194 and the domain of the piecewise quasipolynomial reduction
3195 as a function of an element in the domain of the map.
3196 The functions taking a set compute a bound over all elements in the
3197 intersection of the set and the domain of the
3198 piecewise quasipolynomial reduction.
3200 =head2 Dependence Analysis
3202 C<isl> contains specialized functionality for performing
3203 array dataflow analysis. That is, given a I<sink> access relation
3204 and a collection of possible I<source> access relations,
3205 C<isl> can compute relations that describe
3206 for each iteration of the sink access, which iteration
3207 of which of the source access relations was the last
3208 to access the same data element before the given iteration
3210 To compute standard flow dependences, the sink should be
3211 a read, while the sources should be writes.
3212 If any of the source accesses are marked as being I<may>
3213 accesses, then there will be a dependence to the last
3214 I<must> access B<and> to any I<may> access that follows
3215 this last I<must> access.
3216 In particular, if I<all> sources are I<may> accesses,
3217 then memory based dependence analysis is performed.
3218 If, on the other hand, all sources are I<must> accesses,
3219 then value based dependence analysis is performed.
3221 #include <isl/flow.h>
3223 typedef int (*isl_access_level_before)(void *first, void *second);
3225 __isl_give isl_access_info *isl_access_info_alloc(
3226 __isl_take isl_map *sink,
3227 void *sink_user, isl_access_level_before fn,
3229 __isl_give isl_access_info *isl_access_info_add_source(
3230 __isl_take isl_access_info *acc,
3231 __isl_take isl_map *source, int must,
3233 void isl_access_info_free(__isl_take isl_access_info *acc);
3235 __isl_give isl_flow *isl_access_info_compute_flow(
3236 __isl_take isl_access_info *acc);
3238 int isl_flow_foreach(__isl_keep isl_flow *deps,
3239 int (*fn)(__isl_take isl_map *dep, int must,
3240 void *dep_user, void *user),
3242 __isl_give isl_map *isl_flow_get_no_source(
3243 __isl_keep isl_flow *deps, int must);
3244 void isl_flow_free(__isl_take isl_flow *deps);
3246 The function C<isl_access_info_compute_flow> performs the actual
3247 dependence analysis. The other functions are used to construct
3248 the input for this function or to read off the output.
3250 The input is collected in an C<isl_access_info>, which can
3251 be created through a call to C<isl_access_info_alloc>.
3252 The arguments to this functions are the sink access relation
3253 C<sink>, a token C<sink_user> used to identify the sink
3254 access to the user, a callback function for specifying the
3255 relative order of source and sink accesses, and the number
3256 of source access relations that will be added.
3257 The callback function has type C<int (*)(void *first, void *second)>.
3258 The function is called with two user supplied tokens identifying
3259 either a source or the sink and it should return the shared nesting
3260 level and the relative order of the two accesses.
3261 In particular, let I<n> be the number of loops shared by
3262 the two accesses. If C<first> precedes C<second> textually,
3263 then the function should return I<2 * n + 1>; otherwise,
3264 it should return I<2 * n>.
3265 The sources can be added to the C<isl_access_info> by performing
3266 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3267 C<must> indicates whether the source is a I<must> access
3268 or a I<may> access. Note that a multi-valued access relation
3269 should only be marked I<must> if every iteration in the domain
3270 of the relation accesses I<all> elements in its image.
3271 The C<source_user> token is again used to identify
3272 the source access. The range of the source access relation
3273 C<source> should have the same dimension as the range
3274 of the sink access relation.
3275 The C<isl_access_info_free> function should usually not be
3276 called explicitly, because it is called implicitly by
3277 C<isl_access_info_compute_flow>.
3279 The result of the dependence analysis is collected in an
3280 C<isl_flow>. There may be elements of
3281 the sink access for which no preceding source access could be
3282 found or for which all preceding sources are I<may> accesses.
3283 The relations containing these elements can be obtained through
3284 calls to C<isl_flow_get_no_source>, the first with C<must> set
3285 and the second with C<must> unset.
3286 In the case of standard flow dependence analysis,
3287 with the sink a read and the sources I<must> writes,
3288 the first relation corresponds to the reads from uninitialized
3289 array elements and the second relation is empty.
3290 The actual flow dependences can be extracted using
3291 C<isl_flow_foreach>. This function will call the user-specified
3292 callback function C<fn> for each B<non-empty> dependence between
3293 a source and the sink. The callback function is called
3294 with four arguments, the actual flow dependence relation
3295 mapping source iterations to sink iterations, a boolean that
3296 indicates whether it is a I<must> or I<may> dependence, a token
3297 identifying the source and an additional C<void *> with value
3298 equal to the third argument of the C<isl_flow_foreach> call.
3299 A dependence is marked I<must> if it originates from a I<must>
3300 source and if it is not followed by any I<may> sources.
3302 After finishing with an C<isl_flow>, the user should call
3303 C<isl_flow_free> to free all associated memory.
3305 A higher-level interface to dependence analysis is provided
3306 by the following function.
3308 #include <isl/flow.h>
3310 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3311 __isl_take isl_union_map *must_source,
3312 __isl_take isl_union_map *may_source,
3313 __isl_take isl_union_map *schedule,
3314 __isl_give isl_union_map **must_dep,
3315 __isl_give isl_union_map **may_dep,
3316 __isl_give isl_union_map **must_no_source,
3317 __isl_give isl_union_map **may_no_source);
3319 The arrays are identified by the tuple names of the ranges
3320 of the accesses. The iteration domains by the tuple names
3321 of the domains of the accesses and of the schedule.
3322 The relative order of the iteration domains is given by the
3323 schedule. The relations returned through C<must_no_source>
3324 and C<may_no_source> are subsets of C<sink>.
3325 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3326 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3327 any of the other arguments is treated as an error.
3331 B<The functionality described in this section is fairly new
3332 and may be subject to change.>
3334 The following function can be used to compute a schedule
3335 for a union of domains. The generated schedule respects
3336 all C<validity> dependences. That is, all dependence distances
3337 over these dependences in the scheduled space are lexicographically
3338 positive. The generated schedule schedule also tries to minimize
3339 the dependence distances over C<proximity> dependences.
3340 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3341 for groups of domains where the dependence distances have only
3342 non-negative values.
3343 The algorithm used to construct the schedule is similar to that
3346 #include <isl/schedule.h>
3347 __isl_give isl_schedule *isl_union_set_compute_schedule(
3348 __isl_take isl_union_set *domain,
3349 __isl_take isl_union_map *validity,
3350 __isl_take isl_union_map *proximity);
3351 void *isl_schedule_free(__isl_take isl_schedule *sched);
3353 A mapping from the domains to the scheduled space can be obtained
3354 from an C<isl_schedule> using the following function.
3356 __isl_give isl_union_map *isl_schedule_get_map(
3357 __isl_keep isl_schedule *sched);
3359 A representation of the schedule can be printed using
3361 __isl_give isl_printer *isl_printer_print_schedule(
3362 __isl_take isl_printer *p,
3363 __isl_keep isl_schedule *schedule);
3365 A representation of the schedule as a forest of bands can be obtained
3366 using the following function.
3368 __isl_give isl_band_list *isl_schedule_get_band_forest(
3369 __isl_keep isl_schedule *schedule);
3371 The list can be manipulated as explained in L<"Lists">.
3372 The bands inside the list can be copied and freed using the following
3375 #include <isl/band.h>
3376 __isl_give isl_band *isl_band_copy(
3377 __isl_keep isl_band *band);
3378 void *isl_band_free(__isl_take isl_band *band);
3380 Each band contains zero or more scheduling dimensions.
3381 These are referred to as the members of the band.
3382 The section of the schedule that corresponds to the band is
3383 referred to as the partial schedule of the band.
3384 For those nodes that participate in a band, the outer scheduling
3385 dimensions form the prefix schedule, while the inner scheduling
3386 dimensions form the suffix schedule.
3387 That is, if we take a cut of the band forest, then the union of
3388 the concatenations of the prefix, partial and suffix schedules of
3389 each band in the cut is equal to the entire schedule (modulo
3390 some possible padding at the end with zero scheduling dimensions).
3391 The properties of a band can be inspected using the following functions.
3393 #include <isl/band.h>
3394 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3396 int isl_band_has_children(__isl_keep isl_band *band);
3397 __isl_give isl_band_list *isl_band_get_children(
3398 __isl_keep isl_band *band);
3400 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3401 __isl_keep isl_band *band);
3402 __isl_give isl_union_map *isl_band_get_partial_schedule(
3403 __isl_keep isl_band *band);
3404 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3405 __isl_keep isl_band *band);
3407 int isl_band_n_member(__isl_keep isl_band *band);
3408 int isl_band_member_is_zero_distance(
3409 __isl_keep isl_band *band, int pos);
3411 Note that a scheduling dimension is considered to be ``zero
3412 distance'' if it does not carry any proximity dependences
3414 That is, if the dependence distances of the proximity
3415 dependences are all zero in that direction (for fixed
3416 iterations of outer bands).
3418 A representation of the band can be printed using
3420 #include <isl/band.h>
3421 __isl_give isl_printer *isl_printer_print_band(
3422 __isl_take isl_printer *p,
3423 __isl_keep isl_band *band);
3425 =head2 Parametric Vertex Enumeration
3427 The parametric vertex enumeration described in this section
3428 is mainly intended to be used internally and by the C<barvinok>
3431 #include <isl/vertices.h>
3432 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3433 __isl_keep isl_basic_set *bset);
3435 The function C<isl_basic_set_compute_vertices> performs the
3436 actual computation of the parametric vertices and the chamber
3437 decomposition and store the result in an C<isl_vertices> object.
3438 This information can be queried by either iterating over all
3439 the vertices or iterating over all the chambers or cells
3440 and then iterating over all vertices that are active on the chamber.
3442 int isl_vertices_foreach_vertex(
3443 __isl_keep isl_vertices *vertices,
3444 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3447 int isl_vertices_foreach_cell(
3448 __isl_keep isl_vertices *vertices,
3449 int (*fn)(__isl_take isl_cell *cell, void *user),
3451 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3452 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3455 Other operations that can be performed on an C<isl_vertices> object are
3458 isl_ctx *isl_vertices_get_ctx(
3459 __isl_keep isl_vertices *vertices);
3460 int isl_vertices_get_n_vertices(
3461 __isl_keep isl_vertices *vertices);
3462 void isl_vertices_free(__isl_take isl_vertices *vertices);
3464 Vertices can be inspected and destroyed using the following functions.
3466 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3467 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3468 __isl_give isl_basic_set *isl_vertex_get_domain(
3469 __isl_keep isl_vertex *vertex);
3470 __isl_give isl_basic_set *isl_vertex_get_expr(
3471 __isl_keep isl_vertex *vertex);
3472 void isl_vertex_free(__isl_take isl_vertex *vertex);
3474 C<isl_vertex_get_expr> returns a singleton parametric set describing
3475 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3477 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3478 B<rational> basic sets, so they should mainly be used for inspection
3479 and should not be mixed with integer sets.
3481 Chambers can be inspected and destroyed using the following functions.
3483 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3484 __isl_give isl_basic_set *isl_cell_get_domain(
3485 __isl_keep isl_cell *cell);
3486 void isl_cell_free(__isl_take isl_cell *cell);
3490 Although C<isl> is mainly meant to be used as a library,
3491 it also contains some basic applications that use some
3492 of the functionality of C<isl>.
3493 The input may be specified in either the L<isl format>
3494 or the L<PolyLib format>.
3496 =head2 C<isl_polyhedron_sample>
3498 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3499 an integer element of the polyhedron, if there is any.
3500 The first column in the output is the denominator and is always
3501 equal to 1. If the polyhedron contains no integer points,
3502 then a vector of length zero is printed.
3506 C<isl_pip> takes the same input as the C<example> program
3507 from the C<piplib> distribution, i.e., a set of constraints
3508 on the parameters, a line containing only -1 and finally a set
3509 of constraints on a parametric polyhedron.
3510 The coefficients of the parameters appear in the last columns
3511 (but before the final constant column).
3512 The output is the lexicographic minimum of the parametric polyhedron.
3513 As C<isl> currently does not have its own output format, the output
3514 is just a dump of the internal state.
3516 =head2 C<isl_polyhedron_minimize>
3518 C<isl_polyhedron_minimize> computes the minimum of some linear
3519 or affine objective function over the integer points in a polyhedron.
3520 If an affine objective function
3521 is given, then the constant should appear in the last column.
3523 =head2 C<isl_polytope_scan>
3525 Given a polytope, C<isl_polytope_scan> prints
3526 all integer points in the polytope.