3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
145 =item * The C<nparam> argument has been removed from
146 C<isl_map_read_from_str> and similar functions.
147 When reading input in the original PolyLib format,
148 the result will have no parameters.
149 If parameters are expected, the caller may want to perform
150 dimension manipulation on the result.
156 The source of C<isl> can be obtained either as a tarball
157 or from the git repository. Both are available from
158 L<http://freshmeat.net/projects/isl/>.
159 The installation process depends on how you obtained
162 =head2 Installation from the git repository
166 =item 1 Clone or update the repository
168 The first time the source is obtained, you need to clone
171 git clone git://repo.or.cz/isl.git
173 To obtain updates, you need to pull in the latest changes
177 =item 2 Generate C<configure>
183 After performing the above steps, continue
184 with the L<Common installation instructions>.
186 =head2 Common installation instructions
190 =item 1 Obtain C<GMP>
192 Building C<isl> requires C<GMP>, including its headers files.
193 Your distribution may not provide these header files by default
194 and you may need to install a package called C<gmp-devel> or something
195 similar. Alternatively, C<GMP> can be built from
196 source, available from L<http://gmplib.org/>.
200 C<isl> uses the standard C<autoconf> C<configure> script.
205 optionally followed by some configure options.
206 A complete list of options can be obtained by running
210 Below we discuss some of the more common options.
212 C<isl> can optionally use C<piplib>, but no
213 C<piplib> functionality is currently used by default.
214 The C<--with-piplib> option can
215 be used to specify which C<piplib>
216 library to use, either an installed version (C<system>),
217 an externally built version (C<build>)
218 or no version (C<no>). The option C<build> is mostly useful
219 in C<configure> scripts of larger projects that bundle both C<isl>
226 Installation prefix for C<isl>
228 =item C<--with-gmp-prefix>
230 Installation prefix for C<GMP> (architecture-independent files).
232 =item C<--with-gmp-exec-prefix>
234 Installation prefix for C<GMP> (architecture-dependent files).
236 =item C<--with-piplib>
238 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
240 =item C<--with-piplib-prefix>
242 Installation prefix for C<system> C<piplib> (architecture-independent files).
244 =item C<--with-piplib-exec-prefix>
246 Installation prefix for C<system> C<piplib> (architecture-dependent files).
248 =item C<--with-piplib-builddir>
250 Location where C<build> C<piplib> was built.
258 =item 4 Install (optional)
266 =head2 Initialization
268 All manipulations of integer sets and relations occur within
269 the context of an C<isl_ctx>.
270 A given C<isl_ctx> can only be used within a single thread.
271 All arguments of a function are required to have been allocated
272 within the same context.
273 There are currently no functions available for moving an object
274 from one C<isl_ctx> to another C<isl_ctx>. This means that
275 there is currently no way of safely moving an object from one
276 thread to another, unless the whole C<isl_ctx> is moved.
278 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
279 freed using C<isl_ctx_free>.
280 All objects allocated within an C<isl_ctx> should be freed
281 before the C<isl_ctx> itself is freed.
283 isl_ctx *isl_ctx_alloc();
284 void isl_ctx_free(isl_ctx *ctx);
288 All operations on integers, mainly the coefficients
289 of the constraints describing the sets and relations,
290 are performed in exact integer arithmetic using C<GMP>.
291 However, to allow future versions of C<isl> to optionally
292 support fixed integer arithmetic, all calls to C<GMP>
293 are wrapped inside C<isl> specific macros.
294 The basic type is C<isl_int> and the operations below
295 are available on this type.
296 The meanings of these operations are essentially the same
297 as their C<GMP> C<mpz_> counterparts.
298 As always with C<GMP> types, C<isl_int>s need to be
299 initialized with C<isl_int_init> before they can be used
300 and they need to be released with C<isl_int_clear>
302 The user should not assume that an C<isl_int> is represented
303 as a C<mpz_t>, but should instead explicitly convert between
304 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
305 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
309 =item isl_int_init(i)
311 =item isl_int_clear(i)
313 =item isl_int_set(r,i)
315 =item isl_int_set_si(r,i)
317 =item isl_int_set_gmp(r,g)
319 =item isl_int_get_gmp(i,g)
321 =item isl_int_abs(r,i)
323 =item isl_int_neg(r,i)
325 =item isl_int_swap(i,j)
327 =item isl_int_swap_or_set(i,j)
329 =item isl_int_add_ui(r,i,j)
331 =item isl_int_sub_ui(r,i,j)
333 =item isl_int_add(r,i,j)
335 =item isl_int_sub(r,i,j)
337 =item isl_int_mul(r,i,j)
339 =item isl_int_mul_ui(r,i,j)
341 =item isl_int_addmul(r,i,j)
343 =item isl_int_submul(r,i,j)
345 =item isl_int_gcd(r,i,j)
347 =item isl_int_lcm(r,i,j)
349 =item isl_int_divexact(r,i,j)
351 =item isl_int_cdiv_q(r,i,j)
353 =item isl_int_fdiv_q(r,i,j)
355 =item isl_int_fdiv_r(r,i,j)
357 =item isl_int_fdiv_q_ui(r,i,j)
359 =item isl_int_read(r,s)
361 =item isl_int_print(out,i,width)
365 =item isl_int_cmp(i,j)
367 =item isl_int_cmp_si(i,si)
369 =item isl_int_eq(i,j)
371 =item isl_int_ne(i,j)
373 =item isl_int_lt(i,j)
375 =item isl_int_le(i,j)
377 =item isl_int_gt(i,j)
379 =item isl_int_ge(i,j)
381 =item isl_int_abs_eq(i,j)
383 =item isl_int_abs_ne(i,j)
385 =item isl_int_abs_lt(i,j)
387 =item isl_int_abs_gt(i,j)
389 =item isl_int_abs_ge(i,j)
391 =item isl_int_is_zero(i)
393 =item isl_int_is_one(i)
395 =item isl_int_is_negone(i)
397 =item isl_int_is_pos(i)
399 =item isl_int_is_neg(i)
401 =item isl_int_is_nonpos(i)
403 =item isl_int_is_nonneg(i)
405 =item isl_int_is_divisible_by(i,j)
409 =head2 Sets and Relations
411 C<isl> uses six types of objects for representing sets and relations,
412 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
413 C<isl_union_set> and C<isl_union_map>.
414 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
415 can be described as a conjunction of affine constraints, while
416 C<isl_set> and C<isl_map> represent unions of
417 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
418 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
419 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
420 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
421 where spaces are considered different if they have a different number
422 of dimensions and/or different names (see L<"Spaces">).
423 The difference between sets and relations (maps) is that sets have
424 one set of variables, while relations have two sets of variables,
425 input variables and output variables.
427 =head2 Memory Management
429 Since a high-level operation on sets and/or relations usually involves
430 several substeps and since the user is usually not interested in
431 the intermediate results, most functions that return a new object
432 will also release all the objects passed as arguments.
433 If the user still wants to use one or more of these arguments
434 after the function call, she should pass along a copy of the
435 object rather than the object itself.
436 The user is then responsible for making sure that the original
437 object gets used somewhere else or is explicitly freed.
439 The arguments and return values of all documented functions are
440 annotated to make clear which arguments are released and which
441 arguments are preserved. In particular, the following annotations
448 C<__isl_give> means that a new object is returned.
449 The user should make sure that the returned pointer is
450 used exactly once as a value for an C<__isl_take> argument.
451 In between, it can be used as a value for as many
452 C<__isl_keep> arguments as the user likes.
453 There is one exception, and that is the case where the
454 pointer returned is C<NULL>. Is this case, the user
455 is free to use it as an C<__isl_take> argument or not.
459 C<__isl_take> means that the object the argument points to
460 is taken over by the function and may no longer be used
461 by the user as an argument to any other function.
462 The pointer value must be one returned by a function
463 returning an C<__isl_give> pointer.
464 If the user passes in a C<NULL> value, then this will
465 be treated as an error in the sense that the function will
466 not perform its usual operation. However, it will still
467 make sure that all the other C<__isl_take> arguments
472 C<__isl_keep> means that the function will only use the object
473 temporarily. After the function has finished, the user
474 can still use it as an argument to other functions.
475 A C<NULL> value will be treated in the same way as
476 a C<NULL> value for an C<__isl_take> argument.
482 Identifiers are used to identify both individual dimensions
483 and tuples of dimensions. They consist of a name and an optional
484 pointer. Identifiers with the same name but different pointer values
485 are considered to be distinct.
486 Identifiers can be constructed, copied, freed, inspected and printed
487 using the following functions.
490 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
491 __isl_keep const char *name, void *user);
492 __isl_give isl_id *isl_id_copy(isl_id *id);
493 void *isl_id_free(__isl_take isl_id *id);
495 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
496 void *isl_id_get_user(__isl_keep isl_id *id);
497 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
499 __isl_give isl_printer *isl_printer_print_id(
500 __isl_take isl_printer *p, __isl_keep isl_id *id);
502 Note that C<isl_id_get_name> returns a pointer to some internal
503 data structure, so the result can only be used while the
504 corresponding C<isl_id> is alive.
508 Whenever a new set or relation is created from scratch,
509 the space in which it lives needs to be specified using an C<isl_space>.
511 #include <isl/space.h>
512 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
513 unsigned nparam, unsigned n_in, unsigned n_out);
514 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
516 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
517 unsigned nparam, unsigned dim);
518 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
519 void isl_space_free(__isl_take isl_space *space);
520 unsigned isl_space_dim(__isl_keep isl_space *space,
521 enum isl_dim_type type);
523 The space used for creating a parameter domain
524 needs to be created using C<isl_space_params_alloc>.
525 For other sets, the space
526 needs to be created using C<isl_space_set_alloc>, while
527 for a relation, the space
528 needs to be created using C<isl_space_alloc>.
529 C<isl_space_dim> can be used
530 to find out the number of dimensions of each type in
531 a space, where type may be
532 C<isl_dim_param>, C<isl_dim_in> (only for relations),
533 C<isl_dim_out> (only for relations), C<isl_dim_set>
534 (only for sets) or C<isl_dim_all>.
536 To check whether a given space is that of a set or a map
537 or whether it is a parameter space, use these functions:
539 #include <isl/space.h>
540 int isl_space_is_params(__isl_keep isl_space *space);
541 int isl_space_is_set(__isl_keep isl_space *space);
543 It is often useful to create objects that live in the
544 same space as some other object. This can be accomplished
545 by creating the new objects
546 (see L<Creating New Sets and Relations> or
547 L<Creating New (Piecewise) Quasipolynomials>) based on the space
548 of the original object.
551 __isl_give isl_space *isl_basic_set_get_space(
552 __isl_keep isl_basic_set *bset);
553 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
555 #include <isl/union_set.h>
556 __isl_give isl_space *isl_union_set_get_space(
557 __isl_keep isl_union_set *uset);
560 __isl_give isl_space *isl_basic_map_get_space(
561 __isl_keep isl_basic_map *bmap);
562 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
564 #include <isl/union_map.h>
565 __isl_give isl_space *isl_union_map_get_space(
566 __isl_keep isl_union_map *umap);
568 #include <isl/constraint.h>
569 __isl_give isl_space *isl_constraint_get_space(
570 __isl_keep isl_constraint *constraint);
572 #include <isl/polynomial.h>
573 __isl_give isl_space *isl_qpolynomial_get_domain_space(
574 __isl_keep isl_qpolynomial *qp);
575 __isl_give isl_space *isl_qpolynomial_get_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_fold_get_space(
578 __isl_keep isl_qpolynomial_fold *fold);
579 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
580 __isl_keep isl_pw_qpolynomial *pwqp);
581 __isl_give isl_space *isl_pw_qpolynomial_get_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
584 __isl_keep isl_pw_qpolynomial_fold *pwf);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
588 __isl_keep isl_union_pw_qpolynomial *upwqp);
589 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
590 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
593 __isl_give isl_space *isl_aff_get_domain_space(
594 __isl_keep isl_aff *aff);
595 __isl_give isl_space *isl_aff_get_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_pw_aff_get_domain_space(
598 __isl_keep isl_pw_aff *pwaff);
599 __isl_give isl_space *isl_pw_aff_get_space(
600 __isl_keep isl_pw_aff *pwaff);
601 __isl_give isl_space *isl_multi_aff_get_space(
602 __isl_keep isl_multi_aff *maff);
603 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
604 __isl_keep isl_pw_multi_aff *pma);
605 __isl_give isl_space *isl_pw_multi_aff_get_space(
606 __isl_keep isl_pw_multi_aff *pma);
608 #include <isl/point.h>
609 __isl_give isl_space *isl_point_get_space(
610 __isl_keep isl_point *pnt);
612 The identifiers or names of the individual dimensions may be set or read off
613 using the following functions.
615 #include <isl/space.h>
616 __isl_give isl_space *isl_space_set_dim_id(
617 __isl_take isl_space *space,
618 enum isl_dim_type type, unsigned pos,
619 __isl_take isl_id *id);
620 int isl_space_has_dim_id(__isl_keep isl_space *space,
621 enum isl_dim_type type, unsigned pos);
622 __isl_give isl_id *isl_space_get_dim_id(
623 __isl_keep isl_space *space,
624 enum isl_dim_type type, unsigned pos);
625 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
626 enum isl_dim_type type, unsigned pos,
627 __isl_keep const char *name);
628 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
629 enum isl_dim_type type, unsigned pos);
631 Note that C<isl_space_get_name> returns a pointer to some internal
632 data structure, so the result can only be used while the
633 corresponding C<isl_space> is alive.
634 Also note that every function that operates on two sets or relations
635 requires that both arguments have the same parameters. This also
636 means that if one of the arguments has named parameters, then the
637 other needs to have named parameters too and the names need to match.
638 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
639 arguments may have different parameters (as long as they are named),
640 in which case the result will have as parameters the union of the parameters of
643 Given the identifier or name of a dimension (typically a parameter),
644 its position can be obtained from the following function.
646 #include <isl/space.h>
647 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
648 enum isl_dim_type type, __isl_keep isl_id *id);
649 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
650 enum isl_dim_type type, const char *name);
652 The identifiers or names of entire spaces may be set or read off
653 using the following functions.
655 #include <isl/space.h>
656 __isl_give isl_space *isl_space_set_tuple_id(
657 __isl_take isl_space *space,
658 enum isl_dim_type type, __isl_take isl_id *id);
659 __isl_give isl_space *isl_space_reset_tuple_id(
660 __isl_take isl_space *space, enum isl_dim_type type);
661 int isl_space_has_tuple_id(__isl_keep isl_space *space,
662 enum isl_dim_type type);
663 __isl_give isl_id *isl_space_get_tuple_id(
664 __isl_keep isl_space *space, enum isl_dim_type type);
665 __isl_give isl_space *isl_space_set_tuple_name(
666 __isl_take isl_space *space,
667 enum isl_dim_type type, const char *s);
668 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
669 enum isl_dim_type type);
671 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
672 or C<isl_dim_set>. As with C<isl_space_get_name>,
673 the C<isl_space_get_tuple_name> function returns a pointer to some internal
675 Binary operations require the corresponding spaces of their arguments
676 to have the same name.
678 Spaces can be nested. In particular, the domain of a set or
679 the domain or range of a relation can be a nested relation.
680 The following functions can be used to construct and deconstruct
683 #include <isl/space.h>
684 int isl_space_is_wrapping(__isl_keep isl_space *space);
685 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
686 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
688 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
689 be the space of a set, while that of
690 C<isl_space_wrap> should be the space of a relation.
691 Conversely, the output of C<isl_space_unwrap> is the space
692 of a relation, while that of C<isl_space_wrap> is the space of a set.
694 Spaces can be created from other spaces
695 using the following functions.
697 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
698 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
699 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
701 __isl_give isl_space *isl_space_params(
702 __isl_take isl_space *space);
703 __isl_give isl_space *isl_space_set_from_params(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
706 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
707 __isl_take isl_space *right);
708 __isl_give isl_space *isl_space_align_params(
709 __isl_take isl_space *space1, __isl_take isl_space *space2)
710 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
711 enum isl_dim_type type, unsigned pos, unsigned n);
712 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
713 enum isl_dim_type type, unsigned n);
714 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
715 enum isl_dim_type type, unsigned first, unsigned n);
716 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
717 enum isl_dim_type dst_type, unsigned dst_pos,
718 enum isl_dim_type src_type, unsigned src_pos,
720 __isl_give isl_space *isl_space_map_from_set(
721 __isl_take isl_space *space);
722 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
724 Note that if dimensions are added or removed from a space, then
725 the name and the internal structure are lost.
729 A local space is essentially a space with
730 zero or more existentially quantified variables.
731 The local space of a basic set or relation can be obtained
732 using the following functions.
735 __isl_give isl_local_space *isl_basic_set_get_local_space(
736 __isl_keep isl_basic_set *bset);
739 __isl_give isl_local_space *isl_basic_map_get_local_space(
740 __isl_keep isl_basic_map *bmap);
742 A new local space can be created from a space using
744 #include <isl/local_space.h>
745 __isl_give isl_local_space *isl_local_space_from_space(
746 __isl_take isl_space *space);
748 They can be inspected, modified, copied and freed using the following functions.
750 #include <isl/local_space.h>
751 isl_ctx *isl_local_space_get_ctx(
752 __isl_keep isl_local_space *ls);
753 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
754 int isl_local_space_dim(__isl_keep isl_local_space *ls,
755 enum isl_dim_type type);
756 const char *isl_local_space_get_dim_name(
757 __isl_keep isl_local_space *ls,
758 enum isl_dim_type type, unsigned pos);
759 __isl_give isl_local_space *isl_local_space_set_dim_name(
760 __isl_take isl_local_space *ls,
761 enum isl_dim_type type, unsigned pos, const char *s);
762 __isl_give isl_local_space *isl_local_space_set_dim_id(
763 __isl_take isl_local_space *ls,
764 enum isl_dim_type type, unsigned pos,
765 __isl_take isl_id *id);
766 __isl_give isl_space *isl_local_space_get_space(
767 __isl_keep isl_local_space *ls);
768 __isl_give isl_aff *isl_local_space_get_div(
769 __isl_keep isl_local_space *ls, int pos);
770 __isl_give isl_local_space *isl_local_space_copy(
771 __isl_keep isl_local_space *ls);
772 void *isl_local_space_free(__isl_take isl_local_space *ls);
774 Two local spaces can be compared using
776 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
777 __isl_keep isl_local_space *ls2);
779 Local spaces can be created from other local spaces
780 using the following functions.
782 __isl_give isl_local_space *isl_local_space_domain(
783 __isl_take isl_local_space *ls);
784 __isl_give isl_local_space *isl_local_space_from_domain(
785 __isl_take isl_local_space *ls);
786 __isl_give isl_local_space *isl_local_space_intersect(
787 __isl_take isl_local_space *ls1,
788 __isl_take isl_local_space *ls2);
789 __isl_give isl_local_space *isl_local_space_add_dims(
790 __isl_take isl_local_space *ls,
791 enum isl_dim_type type, unsigned n);
792 __isl_give isl_local_space *isl_local_space_insert_dims(
793 __isl_take isl_local_space *ls,
794 enum isl_dim_type type, unsigned first, unsigned n);
795 __isl_give isl_local_space *isl_local_space_drop_dims(
796 __isl_take isl_local_space *ls,
797 enum isl_dim_type type, unsigned first, unsigned n);
799 =head2 Input and Output
801 C<isl> supports its own input/output format, which is similar
802 to the C<Omega> format, but also supports the C<PolyLib> format
807 The C<isl> format is similar to that of C<Omega>, but has a different
808 syntax for describing the parameters and allows for the definition
809 of an existentially quantified variable as the integer division
810 of an affine expression.
811 For example, the set of integers C<i> between C<0> and C<n>
812 such that C<i % 10 <= 6> can be described as
814 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
817 A set or relation can have several disjuncts, separated
818 by the keyword C<or>. Each disjunct is either a conjunction
819 of constraints or a projection (C<exists>) of a conjunction
820 of constraints. The constraints are separated by the keyword
823 =head3 C<PolyLib> format
825 If the represented set is a union, then the first line
826 contains a single number representing the number of disjuncts.
827 Otherwise, a line containing the number C<1> is optional.
829 Each disjunct is represented by a matrix of constraints.
830 The first line contains two numbers representing
831 the number of rows and columns,
832 where the number of rows is equal to the number of constraints
833 and the number of columns is equal to two plus the number of variables.
834 The following lines contain the actual rows of the constraint matrix.
835 In each row, the first column indicates whether the constraint
836 is an equality (C<0>) or inequality (C<1>). The final column
837 corresponds to the constant term.
839 If the set is parametric, then the coefficients of the parameters
840 appear in the last columns before the constant column.
841 The coefficients of any existentially quantified variables appear
842 between those of the set variables and those of the parameters.
844 =head3 Extended C<PolyLib> format
846 The extended C<PolyLib> format is nearly identical to the
847 C<PolyLib> format. The only difference is that the line
848 containing the number of rows and columns of a constraint matrix
849 also contains four additional numbers:
850 the number of output dimensions, the number of input dimensions,
851 the number of local dimensions (i.e., the number of existentially
852 quantified variables) and the number of parameters.
853 For sets, the number of ``output'' dimensions is equal
854 to the number of set dimensions, while the number of ``input''
860 __isl_give isl_basic_set *isl_basic_set_read_from_file(
861 isl_ctx *ctx, FILE *input);
862 __isl_give isl_basic_set *isl_basic_set_read_from_str(
863 isl_ctx *ctx, const char *str);
864 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
866 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
870 __isl_give isl_basic_map *isl_basic_map_read_from_file(
871 isl_ctx *ctx, FILE *input);
872 __isl_give isl_basic_map *isl_basic_map_read_from_str(
873 isl_ctx *ctx, const char *str);
874 __isl_give isl_map *isl_map_read_from_file(
875 isl_ctx *ctx, FILE *input);
876 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
879 #include <isl/union_set.h>
880 __isl_give isl_union_set *isl_union_set_read_from_file(
881 isl_ctx *ctx, FILE *input);
882 __isl_give isl_union_set *isl_union_set_read_from_str(
883 isl_ctx *ctx, const char *str);
885 #include <isl/union_map.h>
886 __isl_give isl_union_map *isl_union_map_read_from_file(
887 isl_ctx *ctx, FILE *input);
888 __isl_give isl_union_map *isl_union_map_read_from_str(
889 isl_ctx *ctx, const char *str);
891 The input format is autodetected and may be either the C<PolyLib> format
892 or the C<isl> format.
896 Before anything can be printed, an C<isl_printer> needs to
899 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
901 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
902 void isl_printer_free(__isl_take isl_printer *printer);
903 __isl_give char *isl_printer_get_str(
904 __isl_keep isl_printer *printer);
906 The behavior of the printer can be modified in various ways
908 __isl_give isl_printer *isl_printer_set_output_format(
909 __isl_take isl_printer *p, int output_format);
910 __isl_give isl_printer *isl_printer_set_indent(
911 __isl_take isl_printer *p, int indent);
912 __isl_give isl_printer *isl_printer_indent(
913 __isl_take isl_printer *p, int indent);
914 __isl_give isl_printer *isl_printer_set_prefix(
915 __isl_take isl_printer *p, const char *prefix);
916 __isl_give isl_printer *isl_printer_set_suffix(
917 __isl_take isl_printer *p, const char *suffix);
919 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
920 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
921 and defaults to C<ISL_FORMAT_ISL>.
922 Each line in the output is indented by C<indent> (set by
923 C<isl_printer_set_indent>) spaces
924 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
925 In the C<PolyLib> format output,
926 the coefficients of the existentially quantified variables
927 appear between those of the set variables and those
929 The function C<isl_printer_indent> increases the indentation
930 by the specified amount (which may be negative).
932 To actually print something, use
935 __isl_give isl_printer *isl_printer_print_basic_set(
936 __isl_take isl_printer *printer,
937 __isl_keep isl_basic_set *bset);
938 __isl_give isl_printer *isl_printer_print_set(
939 __isl_take isl_printer *printer,
940 __isl_keep isl_set *set);
943 __isl_give isl_printer *isl_printer_print_basic_map(
944 __isl_take isl_printer *printer,
945 __isl_keep isl_basic_map *bmap);
946 __isl_give isl_printer *isl_printer_print_map(
947 __isl_take isl_printer *printer,
948 __isl_keep isl_map *map);
950 #include <isl/union_set.h>
951 __isl_give isl_printer *isl_printer_print_union_set(
952 __isl_take isl_printer *p,
953 __isl_keep isl_union_set *uset);
955 #include <isl/union_map.h>
956 __isl_give isl_printer *isl_printer_print_union_map(
957 __isl_take isl_printer *p,
958 __isl_keep isl_union_map *umap);
960 When called on a file printer, the following function flushes
961 the file. When called on a string printer, the buffer is cleared.
963 __isl_give isl_printer *isl_printer_flush(
964 __isl_take isl_printer *p);
966 =head2 Creating New Sets and Relations
968 C<isl> has functions for creating some standard sets and relations.
972 =item * Empty sets and relations
974 __isl_give isl_basic_set *isl_basic_set_empty(
975 __isl_take isl_space *space);
976 __isl_give isl_basic_map *isl_basic_map_empty(
977 __isl_take isl_space *space);
978 __isl_give isl_set *isl_set_empty(
979 __isl_take isl_space *space);
980 __isl_give isl_map *isl_map_empty(
981 __isl_take isl_space *space);
982 __isl_give isl_union_set *isl_union_set_empty(
983 __isl_take isl_space *space);
984 __isl_give isl_union_map *isl_union_map_empty(
985 __isl_take isl_space *space);
987 For C<isl_union_set>s and C<isl_union_map>s, the space
988 is only used to specify the parameters.
990 =item * Universe sets and relations
992 __isl_give isl_basic_set *isl_basic_set_universe(
993 __isl_take isl_space *space);
994 __isl_give isl_basic_map *isl_basic_map_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_set *isl_set_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_map *isl_map_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_union_set *isl_union_set_universe(
1001 __isl_take isl_union_set *uset);
1002 __isl_give isl_union_map *isl_union_map_universe(
1003 __isl_take isl_union_map *umap);
1005 The sets and relations constructed by the functions above
1006 contain all integer values, while those constructed by the
1007 functions below only contain non-negative values.
1009 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1010 __isl_take isl_space *space);
1011 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1012 __isl_take isl_space *space);
1013 __isl_give isl_set *isl_set_nat_universe(
1014 __isl_take isl_space *space);
1015 __isl_give isl_map *isl_map_nat_universe(
1016 __isl_take isl_space *space);
1018 =item * Identity relations
1020 __isl_give isl_basic_map *isl_basic_map_identity(
1021 __isl_take isl_space *space);
1022 __isl_give isl_map *isl_map_identity(
1023 __isl_take isl_space *space);
1025 The number of input and output dimensions in C<space> needs
1028 =item * Lexicographic order
1030 __isl_give isl_map *isl_map_lex_lt(
1031 __isl_take isl_space *set_space);
1032 __isl_give isl_map *isl_map_lex_le(
1033 __isl_take isl_space *set_space);
1034 __isl_give isl_map *isl_map_lex_gt(
1035 __isl_take isl_space *set_space);
1036 __isl_give isl_map *isl_map_lex_ge(
1037 __isl_take isl_space *set_space);
1038 __isl_give isl_map *isl_map_lex_lt_first(
1039 __isl_take isl_space *space, unsigned n);
1040 __isl_give isl_map *isl_map_lex_le_first(
1041 __isl_take isl_space *space, unsigned n);
1042 __isl_give isl_map *isl_map_lex_gt_first(
1043 __isl_take isl_space *space, unsigned n);
1044 __isl_give isl_map *isl_map_lex_ge_first(
1045 __isl_take isl_space *space, unsigned n);
1047 The first four functions take a space for a B<set>
1048 and return relations that express that the elements in the domain
1049 are lexicographically less
1050 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1051 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1052 than the elements in the range.
1053 The last four functions take a space for a map
1054 and return relations that express that the first C<n> dimensions
1055 in the domain are lexicographically less
1056 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1057 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1058 than the first C<n> dimensions in the range.
1062 A basic set or relation can be converted to a set or relation
1063 using the following functions.
1065 __isl_give isl_set *isl_set_from_basic_set(
1066 __isl_take isl_basic_set *bset);
1067 __isl_give isl_map *isl_map_from_basic_map(
1068 __isl_take isl_basic_map *bmap);
1070 Sets and relations can be converted to union sets and relations
1071 using the following functions.
1073 __isl_give isl_union_map *isl_union_map_from_map(
1074 __isl_take isl_map *map);
1075 __isl_give isl_union_set *isl_union_set_from_set(
1076 __isl_take isl_set *set);
1078 The inverse conversions below can only be used if the input
1079 union set or relation is known to contain elements in exactly one
1082 __isl_give isl_set *isl_set_from_union_set(
1083 __isl_take isl_union_set *uset);
1084 __isl_give isl_map *isl_map_from_union_map(
1085 __isl_take isl_union_map *umap);
1087 A zero-dimensional set can be constructed on a given parameter domain
1088 using the following function.
1090 __isl_give isl_set *isl_set_from_params(
1091 __isl_take isl_set *set);
1093 Sets and relations can be copied and freed again using the following
1096 __isl_give isl_basic_set *isl_basic_set_copy(
1097 __isl_keep isl_basic_set *bset);
1098 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1099 __isl_give isl_union_set *isl_union_set_copy(
1100 __isl_keep isl_union_set *uset);
1101 __isl_give isl_basic_map *isl_basic_map_copy(
1102 __isl_keep isl_basic_map *bmap);
1103 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1104 __isl_give isl_union_map *isl_union_map_copy(
1105 __isl_keep isl_union_map *umap);
1106 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1107 void isl_set_free(__isl_take isl_set *set);
1108 void *isl_union_set_free(__isl_take isl_union_set *uset);
1109 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1110 void isl_map_free(__isl_take isl_map *map);
1111 void *isl_union_map_free(__isl_take isl_union_map *umap);
1113 Other sets and relations can be constructed by starting
1114 from a universe set or relation, adding equality and/or
1115 inequality constraints and then projecting out the
1116 existentially quantified variables, if any.
1117 Constraints can be constructed, manipulated and
1118 added to (or removed from) (basic) sets and relations
1119 using the following functions.
1121 #include <isl/constraint.h>
1122 __isl_give isl_constraint *isl_equality_alloc(
1123 __isl_take isl_local_space *ls);
1124 __isl_give isl_constraint *isl_inequality_alloc(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_constraint *isl_constraint_set_constant(
1127 __isl_take isl_constraint *constraint, isl_int v);
1128 __isl_give isl_constraint *isl_constraint_set_constant_si(
1129 __isl_take isl_constraint *constraint, int v);
1130 __isl_give isl_constraint *isl_constraint_set_coefficient(
1131 __isl_take isl_constraint *constraint,
1132 enum isl_dim_type type, int pos, isl_int v);
1133 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1134 __isl_take isl_constraint *constraint,
1135 enum isl_dim_type type, int pos, int v);
1136 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1137 __isl_take isl_basic_map *bmap,
1138 __isl_take isl_constraint *constraint);
1139 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1140 __isl_take isl_basic_set *bset,
1141 __isl_take isl_constraint *constraint);
1142 __isl_give isl_map *isl_map_add_constraint(
1143 __isl_take isl_map *map,
1144 __isl_take isl_constraint *constraint);
1145 __isl_give isl_set *isl_set_add_constraint(
1146 __isl_take isl_set *set,
1147 __isl_take isl_constraint *constraint);
1148 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1149 __isl_take isl_basic_set *bset,
1150 __isl_take isl_constraint *constraint);
1152 For example, to create a set containing the even integers
1153 between 10 and 42, you would use the following code.
1156 isl_local_space *ls;
1158 isl_basic_set *bset;
1160 space = isl_space_set_alloc(ctx, 0, 2);
1161 bset = isl_basic_set_universe(isl_space_copy(space));
1162 ls = isl_local_space_from_space(space);
1164 c = isl_equality_alloc(isl_local_space_copy(ls));
1165 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1166 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1167 bset = isl_basic_set_add_constraint(bset, c);
1169 c = isl_inequality_alloc(isl_local_space_copy(ls));
1170 c = isl_constraint_set_constant_si(c, -10);
1171 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1172 bset = isl_basic_set_add_constraint(bset, c);
1174 c = isl_inequality_alloc(ls);
1175 c = isl_constraint_set_constant_si(c, 42);
1176 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1177 bset = isl_basic_set_add_constraint(bset, c);
1179 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1183 isl_basic_set *bset;
1184 bset = isl_basic_set_read_from_str(ctx,
1185 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1187 A basic set or relation can also be constructed from two matrices
1188 describing the equalities and the inequalities.
1190 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1191 __isl_take isl_space *space,
1192 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1193 enum isl_dim_type c1,
1194 enum isl_dim_type c2, enum isl_dim_type c3,
1195 enum isl_dim_type c4);
1196 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1197 __isl_take isl_space *space,
1198 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1199 enum isl_dim_type c1,
1200 enum isl_dim_type c2, enum isl_dim_type c3,
1201 enum isl_dim_type c4, enum isl_dim_type c5);
1203 The C<isl_dim_type> arguments indicate the order in which
1204 different kinds of variables appear in the input matrices
1205 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1206 C<isl_dim_set> and C<isl_dim_div> for sets and
1207 of C<isl_dim_cst>, C<isl_dim_param>,
1208 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1210 A (basic) set or relation can also be constructed from a (piecewise)
1211 (multiple) affine expression
1212 or a list of affine expressions
1213 (See L<"Piecewise Quasi Affine Expressions"> and
1214 L<"Piecewise Multiple Quasi Affine Expressions">).
1216 __isl_give isl_basic_map *isl_basic_map_from_aff(
1217 __isl_take isl_aff *aff);
1218 __isl_give isl_set *isl_set_from_pw_aff(
1219 __isl_take isl_pw_aff *pwaff);
1220 __isl_give isl_map *isl_map_from_pw_aff(
1221 __isl_take isl_pw_aff *pwaff);
1222 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1223 __isl_take isl_space *domain_space,
1224 __isl_take isl_aff_list *list);
1225 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1226 __isl_take isl_multi_aff *maff)
1227 __isl_give isl_set *isl_set_from_pw_multi_aff(
1228 __isl_take isl_pw_multi_aff *pma);
1229 __isl_give isl_map *isl_map_from_pw_multi_aff(
1230 __isl_take isl_pw_multi_aff *pma);
1232 The C<domain_dim> argument describes the domain of the resulting
1233 basic relation. It is required because the C<list> may consist
1234 of zero affine expressions.
1236 =head2 Inspecting Sets and Relations
1238 Usually, the user should not have to care about the actual constraints
1239 of the sets and maps, but should instead apply the abstract operations
1240 explained in the following sections.
1241 Occasionally, however, it may be required to inspect the individual
1242 coefficients of the constraints. This section explains how to do so.
1243 In these cases, it may also be useful to have C<isl> compute
1244 an explicit representation of the existentially quantified variables.
1246 __isl_give isl_set *isl_set_compute_divs(
1247 __isl_take isl_set *set);
1248 __isl_give isl_map *isl_map_compute_divs(
1249 __isl_take isl_map *map);
1250 __isl_give isl_union_set *isl_union_set_compute_divs(
1251 __isl_take isl_union_set *uset);
1252 __isl_give isl_union_map *isl_union_map_compute_divs(
1253 __isl_take isl_union_map *umap);
1255 This explicit representation defines the existentially quantified
1256 variables as integer divisions of the other variables, possibly
1257 including earlier existentially quantified variables.
1258 An explicitly represented existentially quantified variable therefore
1259 has a unique value when the values of the other variables are known.
1260 If, furthermore, the same existentials, i.e., existentials
1261 with the same explicit representations, should appear in the
1262 same order in each of the disjuncts of a set or map, then the user should call
1263 either of the following functions.
1265 __isl_give isl_set *isl_set_align_divs(
1266 __isl_take isl_set *set);
1267 __isl_give isl_map *isl_map_align_divs(
1268 __isl_take isl_map *map);
1270 Alternatively, the existentially quantified variables can be removed
1271 using the following functions, which compute an overapproximation.
1273 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1274 __isl_take isl_basic_set *bset);
1275 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1276 __isl_take isl_basic_map *bmap);
1277 __isl_give isl_set *isl_set_remove_divs(
1278 __isl_take isl_set *set);
1279 __isl_give isl_map *isl_map_remove_divs(
1280 __isl_take isl_map *map);
1282 To iterate over all the sets or maps in a union set or map, use
1284 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1285 int (*fn)(__isl_take isl_set *set, void *user),
1287 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1288 int (*fn)(__isl_take isl_map *map, void *user),
1291 The number of sets or maps in a union set or map can be obtained
1294 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1295 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1297 To extract the set or map in a given space from a union, use
1299 __isl_give isl_set *isl_union_set_extract_set(
1300 __isl_keep isl_union_set *uset,
1301 __isl_take isl_space *space);
1302 __isl_give isl_map *isl_union_map_extract_map(
1303 __isl_keep isl_union_map *umap,
1304 __isl_take isl_space *space);
1306 To iterate over all the basic sets or maps in a set or map, use
1308 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1309 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1311 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1312 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1315 The callback function C<fn> should return 0 if successful and
1316 -1 if an error occurs. In the latter case, or if any other error
1317 occurs, the above functions will return -1.
1319 It should be noted that C<isl> does not guarantee that
1320 the basic sets or maps passed to C<fn> are disjoint.
1321 If this is required, then the user should call one of
1322 the following functions first.
1324 __isl_give isl_set *isl_set_make_disjoint(
1325 __isl_take isl_set *set);
1326 __isl_give isl_map *isl_map_make_disjoint(
1327 __isl_take isl_map *map);
1329 The number of basic sets in a set can be obtained
1332 int isl_set_n_basic_set(__isl_keep isl_set *set);
1334 To iterate over the constraints of a basic set or map, use
1336 #include <isl/constraint.h>
1338 int isl_basic_map_foreach_constraint(
1339 __isl_keep isl_basic_map *bmap,
1340 int (*fn)(__isl_take isl_constraint *c, void *user),
1342 void *isl_constraint_free(__isl_take isl_constraint *c);
1344 Again, the callback function C<fn> should return 0 if successful and
1345 -1 if an error occurs. In the latter case, or if any other error
1346 occurs, the above functions will return -1.
1347 The constraint C<c> represents either an equality or an inequality.
1348 Use the following function to find out whether a constraint
1349 represents an equality. If not, it represents an inequality.
1351 int isl_constraint_is_equality(
1352 __isl_keep isl_constraint *constraint);
1354 The coefficients of the constraints can be inspected using
1355 the following functions.
1357 void isl_constraint_get_constant(
1358 __isl_keep isl_constraint *constraint, isl_int *v);
1359 void isl_constraint_get_coefficient(
1360 __isl_keep isl_constraint *constraint,
1361 enum isl_dim_type type, int pos, isl_int *v);
1362 int isl_constraint_involves_dims(
1363 __isl_keep isl_constraint *constraint,
1364 enum isl_dim_type type, unsigned first, unsigned n);
1366 The explicit representations of the existentially quantified
1367 variables can be inspected using the following function.
1368 Note that the user is only allowed to use this function
1369 if the inspected set or map is the result of a call
1370 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1371 The existentially quantified variable is equal to the floor
1372 of the returned affine expression. The affine expression
1373 itself can be inspected using the functions in
1374 L<"Piecewise Quasi Affine Expressions">.
1376 __isl_give isl_aff *isl_constraint_get_div(
1377 __isl_keep isl_constraint *constraint, int pos);
1379 To obtain the constraints of a basic set or map in matrix
1380 form, use the following functions.
1382 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1383 __isl_keep isl_basic_set *bset,
1384 enum isl_dim_type c1, enum isl_dim_type c2,
1385 enum isl_dim_type c3, enum isl_dim_type c4);
1386 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1387 __isl_keep isl_basic_set *bset,
1388 enum isl_dim_type c1, enum isl_dim_type c2,
1389 enum isl_dim_type c3, enum isl_dim_type c4);
1390 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1391 __isl_keep isl_basic_map *bmap,
1392 enum isl_dim_type c1,
1393 enum isl_dim_type c2, enum isl_dim_type c3,
1394 enum isl_dim_type c4, enum isl_dim_type c5);
1395 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1396 __isl_keep isl_basic_map *bmap,
1397 enum isl_dim_type c1,
1398 enum isl_dim_type c2, enum isl_dim_type c3,
1399 enum isl_dim_type c4, enum isl_dim_type c5);
1401 The C<isl_dim_type> arguments dictate the order in which
1402 different kinds of variables appear in the resulting matrix
1403 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1404 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1406 The number of parameters, input, output or set dimensions can
1407 be obtained using the following functions.
1409 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1410 enum isl_dim_type type);
1411 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1412 enum isl_dim_type type);
1413 unsigned isl_set_dim(__isl_keep isl_set *set,
1414 enum isl_dim_type type);
1415 unsigned isl_map_dim(__isl_keep isl_map *map,
1416 enum isl_dim_type type);
1418 To check whether the description of a set or relation depends
1419 on one or more given dimensions, it is not necessary to iterate over all
1420 constraints. Instead the following functions can be used.
1422 int isl_basic_set_involves_dims(
1423 __isl_keep isl_basic_set *bset,
1424 enum isl_dim_type type, unsigned first, unsigned n);
1425 int isl_set_involves_dims(__isl_keep isl_set *set,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 int isl_basic_map_involves_dims(
1428 __isl_keep isl_basic_map *bmap,
1429 enum isl_dim_type type, unsigned first, unsigned n);
1430 int isl_map_involves_dims(__isl_keep isl_map *map,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1433 Similarly, the following functions can be used to check whether
1434 a given dimension is involved in any lower or upper bound.
1436 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1437 enum isl_dim_type type, unsigned pos);
1438 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1439 enum isl_dim_type type, unsigned pos);
1441 The identifiers or names of the domain and range spaces of a set
1442 or relation can be read off or set using the following functions.
1444 __isl_give isl_set *isl_set_set_tuple_id(
1445 __isl_take isl_set *set, __isl_take isl_id *id);
1446 __isl_give isl_set *isl_set_reset_tuple_id(
1447 __isl_take isl_set *set);
1448 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1449 __isl_give isl_id *isl_set_get_tuple_id(
1450 __isl_keep isl_set *set);
1451 __isl_give isl_map *isl_map_set_tuple_id(
1452 __isl_take isl_map *map, enum isl_dim_type type,
1453 __isl_take isl_id *id);
1454 __isl_give isl_map *isl_map_reset_tuple_id(
1455 __isl_take isl_map *map, enum isl_dim_type type);
1456 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1457 enum isl_dim_type type);
1458 __isl_give isl_id *isl_map_get_tuple_id(
1459 __isl_keep isl_map *map, enum isl_dim_type type);
1461 const char *isl_basic_set_get_tuple_name(
1462 __isl_keep isl_basic_set *bset);
1463 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1464 __isl_take isl_basic_set *set, const char *s);
1465 const char *isl_set_get_tuple_name(
1466 __isl_keep isl_set *set);
1467 const char *isl_basic_map_get_tuple_name(
1468 __isl_keep isl_basic_map *bmap,
1469 enum isl_dim_type type);
1470 const char *isl_map_get_tuple_name(
1471 __isl_keep isl_map *map,
1472 enum isl_dim_type type);
1474 As with C<isl_space_get_tuple_name>, the value returned points to
1475 an internal data structure.
1476 The identifiers, positions or names of individual dimensions can be
1477 read off using the following functions.
1479 __isl_give isl_set *isl_set_set_dim_id(
1480 __isl_take isl_set *set, enum isl_dim_type type,
1481 unsigned pos, __isl_take isl_id *id);
1482 int isl_set_has_dim_id(__isl_keep isl_set *set,
1483 enum isl_dim_type type, unsigned pos);
1484 __isl_give isl_id *isl_set_get_dim_id(
1485 __isl_keep isl_set *set, enum isl_dim_type type,
1487 int isl_basic_map_has_dim_id(
1488 __isl_keep isl_basic_map *bmap,
1489 enum isl_dim_type type, unsigned pos);
1490 __isl_give isl_map *isl_map_set_dim_id(
1491 __isl_take isl_map *map, enum isl_dim_type type,
1492 unsigned pos, __isl_take isl_id *id);
1493 int isl_map_has_dim_id(__isl_keep isl_map *map,
1494 enum isl_dim_type type, unsigned pos);
1495 __isl_give isl_id *isl_map_get_dim_id(
1496 __isl_keep isl_map *map, enum isl_dim_type type,
1499 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1500 enum isl_dim_type type, __isl_keep isl_id *id);
1501 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1502 enum isl_dim_type type, __isl_keep isl_id *id);
1503 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1504 enum isl_dim_type type, const char *name);
1506 const char *isl_constraint_get_dim_name(
1507 __isl_keep isl_constraint *constraint,
1508 enum isl_dim_type type, unsigned pos);
1509 const char *isl_basic_set_get_dim_name(
1510 __isl_keep isl_basic_set *bset,
1511 enum isl_dim_type type, unsigned pos);
1512 const char *isl_set_get_dim_name(
1513 __isl_keep isl_set *set,
1514 enum isl_dim_type type, unsigned pos);
1515 const char *isl_basic_map_get_dim_name(
1516 __isl_keep isl_basic_map *bmap,
1517 enum isl_dim_type type, unsigned pos);
1518 const char *isl_map_get_dim_name(
1519 __isl_keep isl_map *map,
1520 enum isl_dim_type type, unsigned pos);
1522 These functions are mostly useful to obtain the identifiers, positions
1523 or names of the parameters. Identifiers of individual dimensions are
1524 essentially only useful for printing. They are ignored by all other
1525 operations and may not be preserved across those operations.
1529 =head3 Unary Properties
1535 The following functions test whether the given set or relation
1536 contains any integer points. The ``plain'' variants do not perform
1537 any computations, but simply check if the given set or relation
1538 is already known to be empty.
1540 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1541 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1542 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1543 int isl_set_is_empty(__isl_keep isl_set *set);
1544 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1545 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1546 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1547 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1548 int isl_map_is_empty(__isl_keep isl_map *map);
1549 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1551 =item * Universality
1553 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1554 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1555 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1557 =item * Single-valuedness
1559 int isl_map_is_single_valued(__isl_keep isl_map *map);
1560 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1564 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1565 int isl_map_is_injective(__isl_keep isl_map *map);
1566 int isl_union_map_plain_is_injective(
1567 __isl_keep isl_union_map *umap);
1568 int isl_union_map_is_injective(
1569 __isl_keep isl_union_map *umap);
1573 int isl_map_is_bijective(__isl_keep isl_map *map);
1574 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1578 int isl_basic_map_plain_is_fixed(
1579 __isl_keep isl_basic_map *bmap,
1580 enum isl_dim_type type, unsigned pos,
1582 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1583 enum isl_dim_type type, unsigned pos,
1585 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1586 enum isl_dim_type type, unsigned pos,
1589 Check if the relation obviously lies on a hyperplane where the given dimension
1590 has a fixed value and if so, return that value in C<*val>.
1594 To check whether a set is a parameter domain, use this function:
1596 int isl_set_is_params(__isl_keep isl_set *set);
1600 The following functions check whether the domain of the given
1601 (basic) set is a wrapped relation.
1603 int isl_basic_set_is_wrapping(
1604 __isl_keep isl_basic_set *bset);
1605 int isl_set_is_wrapping(__isl_keep isl_set *set);
1607 =item * Internal Product
1609 int isl_basic_map_can_zip(
1610 __isl_keep isl_basic_map *bmap);
1611 int isl_map_can_zip(__isl_keep isl_map *map);
1613 Check whether the product of domain and range of the given relation
1615 i.e., whether both domain and range are nested relations.
1619 =head3 Binary Properties
1625 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1626 __isl_keep isl_set *set2);
1627 int isl_set_is_equal(__isl_keep isl_set *set1,
1628 __isl_keep isl_set *set2);
1629 int isl_union_set_is_equal(
1630 __isl_keep isl_union_set *uset1,
1631 __isl_keep isl_union_set *uset2);
1632 int isl_basic_map_is_equal(
1633 __isl_keep isl_basic_map *bmap1,
1634 __isl_keep isl_basic_map *bmap2);
1635 int isl_map_is_equal(__isl_keep isl_map *map1,
1636 __isl_keep isl_map *map2);
1637 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1638 __isl_keep isl_map *map2);
1639 int isl_union_map_is_equal(
1640 __isl_keep isl_union_map *umap1,
1641 __isl_keep isl_union_map *umap2);
1643 =item * Disjointness
1645 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1646 __isl_keep isl_set *set2);
1650 int isl_set_is_subset(__isl_keep isl_set *set1,
1651 __isl_keep isl_set *set2);
1652 int isl_set_is_strict_subset(
1653 __isl_keep isl_set *set1,
1654 __isl_keep isl_set *set2);
1655 int isl_union_set_is_subset(
1656 __isl_keep isl_union_set *uset1,
1657 __isl_keep isl_union_set *uset2);
1658 int isl_union_set_is_strict_subset(
1659 __isl_keep isl_union_set *uset1,
1660 __isl_keep isl_union_set *uset2);
1661 int isl_basic_map_is_subset(
1662 __isl_keep isl_basic_map *bmap1,
1663 __isl_keep isl_basic_map *bmap2);
1664 int isl_basic_map_is_strict_subset(
1665 __isl_keep isl_basic_map *bmap1,
1666 __isl_keep isl_basic_map *bmap2);
1667 int isl_map_is_subset(
1668 __isl_keep isl_map *map1,
1669 __isl_keep isl_map *map2);
1670 int isl_map_is_strict_subset(
1671 __isl_keep isl_map *map1,
1672 __isl_keep isl_map *map2);
1673 int isl_union_map_is_subset(
1674 __isl_keep isl_union_map *umap1,
1675 __isl_keep isl_union_map *umap2);
1676 int isl_union_map_is_strict_subset(
1677 __isl_keep isl_union_map *umap1,
1678 __isl_keep isl_union_map *umap2);
1682 =head2 Unary Operations
1688 __isl_give isl_set *isl_set_complement(
1689 __isl_take isl_set *set);
1693 __isl_give isl_basic_map *isl_basic_map_reverse(
1694 __isl_take isl_basic_map *bmap);
1695 __isl_give isl_map *isl_map_reverse(
1696 __isl_take isl_map *map);
1697 __isl_give isl_union_map *isl_union_map_reverse(
1698 __isl_take isl_union_map *umap);
1702 __isl_give isl_basic_set *isl_basic_set_project_out(
1703 __isl_take isl_basic_set *bset,
1704 enum isl_dim_type type, unsigned first, unsigned n);
1705 __isl_give isl_basic_map *isl_basic_map_project_out(
1706 __isl_take isl_basic_map *bmap,
1707 enum isl_dim_type type, unsigned first, unsigned n);
1708 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1709 enum isl_dim_type type, unsigned first, unsigned n);
1710 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1711 enum isl_dim_type type, unsigned first, unsigned n);
1712 __isl_give isl_basic_set *isl_basic_set_params(
1713 __isl_take isl_basic_set *bset);
1714 __isl_give isl_basic_set *isl_basic_map_domain(
1715 __isl_take isl_basic_map *bmap);
1716 __isl_give isl_basic_set *isl_basic_map_range(
1717 __isl_take isl_basic_map *bmap);
1718 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1719 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1720 __isl_give isl_set *isl_map_domain(
1721 __isl_take isl_map *bmap);
1722 __isl_give isl_set *isl_map_range(
1723 __isl_take isl_map *map);
1724 __isl_give isl_union_set *isl_union_map_domain(
1725 __isl_take isl_union_map *umap);
1726 __isl_give isl_union_set *isl_union_map_range(
1727 __isl_take isl_union_map *umap);
1729 __isl_give isl_basic_map *isl_basic_map_domain_map(
1730 __isl_take isl_basic_map *bmap);
1731 __isl_give isl_basic_map *isl_basic_map_range_map(
1732 __isl_take isl_basic_map *bmap);
1733 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1734 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1735 __isl_give isl_union_map *isl_union_map_domain_map(
1736 __isl_take isl_union_map *umap);
1737 __isl_give isl_union_map *isl_union_map_range_map(
1738 __isl_take isl_union_map *umap);
1740 The functions above construct a (basic, regular or union) relation
1741 that maps (a wrapped version of) the input relation to its domain or range.
1745 __isl_give isl_set *isl_set_eliminate(
1746 __isl_take isl_set *set, enum isl_dim_type type,
1747 unsigned first, unsigned n);
1748 __isl_give isl_basic_map *isl_basic_map_eliminate(
1749 __isl_take isl_basic_map *bmap,
1750 enum isl_dim_type type,
1751 unsigned first, unsigned n);
1753 Eliminate the coefficients for the given dimensions from the constraints,
1754 without removing the dimensions.
1758 __isl_give isl_basic_set *isl_basic_set_fix(
1759 __isl_take isl_basic_set *bset,
1760 enum isl_dim_type type, unsigned pos,
1762 __isl_give isl_basic_set *isl_basic_set_fix_si(
1763 __isl_take isl_basic_set *bset,
1764 enum isl_dim_type type, unsigned pos, int value);
1765 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1766 enum isl_dim_type type, unsigned pos,
1768 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1769 enum isl_dim_type type, unsigned pos, int value);
1770 __isl_give isl_basic_map *isl_basic_map_fix_si(
1771 __isl_take isl_basic_map *bmap,
1772 enum isl_dim_type type, unsigned pos, int value);
1773 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1774 enum isl_dim_type type, unsigned pos, int value);
1776 Intersect the set or relation with the hyperplane where the given
1777 dimension has the fixed given value.
1779 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1780 enum isl_dim_type type1, int pos1,
1781 enum isl_dim_type type2, int pos2);
1782 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1783 enum isl_dim_type type1, int pos1,
1784 enum isl_dim_type type2, int pos2);
1786 Intersect the set or relation with the hyperplane where the given
1787 dimensions are equal to each other.
1789 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1790 enum isl_dim_type type1, int pos1,
1791 enum isl_dim_type type2, int pos2);
1793 Intersect the relation with the hyperplane where the given
1794 dimensions have opposite values.
1798 __isl_give isl_map *isl_set_identity(
1799 __isl_take isl_set *set);
1800 __isl_give isl_union_map *isl_union_set_identity(
1801 __isl_take isl_union_set *uset);
1803 Construct an identity relation on the given (union) set.
1807 __isl_give isl_basic_set *isl_basic_map_deltas(
1808 __isl_take isl_basic_map *bmap);
1809 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1810 __isl_give isl_union_set *isl_union_map_deltas(
1811 __isl_take isl_union_map *umap);
1813 These functions return a (basic) set containing the differences
1814 between image elements and corresponding domain elements in the input.
1816 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1817 __isl_take isl_basic_map *bmap);
1818 __isl_give isl_map *isl_map_deltas_map(
1819 __isl_take isl_map *map);
1820 __isl_give isl_union_map *isl_union_map_deltas_map(
1821 __isl_take isl_union_map *umap);
1823 The functions above construct a (basic, regular or union) relation
1824 that maps (a wrapped version of) the input relation to its delta set.
1828 Simplify the representation of a set or relation by trying
1829 to combine pairs of basic sets or relations into a single
1830 basic set or relation.
1832 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1833 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1834 __isl_give isl_union_set *isl_union_set_coalesce(
1835 __isl_take isl_union_set *uset);
1836 __isl_give isl_union_map *isl_union_map_coalesce(
1837 __isl_take isl_union_map *umap);
1839 =item * Detecting equalities
1841 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1842 __isl_take isl_basic_set *bset);
1843 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1844 __isl_take isl_basic_map *bmap);
1845 __isl_give isl_set *isl_set_detect_equalities(
1846 __isl_take isl_set *set);
1847 __isl_give isl_map *isl_map_detect_equalities(
1848 __isl_take isl_map *map);
1849 __isl_give isl_union_set *isl_union_set_detect_equalities(
1850 __isl_take isl_union_set *uset);
1851 __isl_give isl_union_map *isl_union_map_detect_equalities(
1852 __isl_take isl_union_map *umap);
1854 Simplify the representation of a set or relation by detecting implicit
1857 =item * Removing redundant constraints
1859 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1860 __isl_take isl_basic_set *bset);
1861 __isl_give isl_set *isl_set_remove_redundancies(
1862 __isl_take isl_set *set);
1863 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1864 __isl_take isl_basic_map *bmap);
1865 __isl_give isl_map *isl_map_remove_redundancies(
1866 __isl_take isl_map *map);
1870 __isl_give isl_basic_set *isl_set_convex_hull(
1871 __isl_take isl_set *set);
1872 __isl_give isl_basic_map *isl_map_convex_hull(
1873 __isl_take isl_map *map);
1875 If the input set or relation has any existentially quantified
1876 variables, then the result of these operations is currently undefined.
1880 __isl_give isl_basic_set *isl_set_simple_hull(
1881 __isl_take isl_set *set);
1882 __isl_give isl_basic_map *isl_map_simple_hull(
1883 __isl_take isl_map *map);
1884 __isl_give isl_union_map *isl_union_map_simple_hull(
1885 __isl_take isl_union_map *umap);
1887 These functions compute a single basic set or relation
1888 that contains the whole input set or relation.
1889 In particular, the output is described by translates
1890 of the constraints describing the basic sets or relations in the input.
1894 (See \autoref{s:simple hull}.)
1900 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1901 __isl_take isl_basic_set *bset);
1902 __isl_give isl_basic_set *isl_set_affine_hull(
1903 __isl_take isl_set *set);
1904 __isl_give isl_union_set *isl_union_set_affine_hull(
1905 __isl_take isl_union_set *uset);
1906 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1907 __isl_take isl_basic_map *bmap);
1908 __isl_give isl_basic_map *isl_map_affine_hull(
1909 __isl_take isl_map *map);
1910 __isl_give isl_union_map *isl_union_map_affine_hull(
1911 __isl_take isl_union_map *umap);
1913 In case of union sets and relations, the affine hull is computed
1916 =item * Polyhedral hull
1918 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1919 __isl_take isl_set *set);
1920 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1921 __isl_take isl_map *map);
1922 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1923 __isl_take isl_union_set *uset);
1924 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1925 __isl_take isl_union_map *umap);
1927 These functions compute a single basic set or relation
1928 not involving any existentially quantified variables
1929 that contains the whole input set or relation.
1930 In case of union sets and relations, the polyhedral hull is computed
1933 =item * Optimization
1935 #include <isl/ilp.h>
1936 enum isl_lp_result isl_basic_set_max(
1937 __isl_keep isl_basic_set *bset,
1938 __isl_keep isl_aff *obj, isl_int *opt)
1939 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1940 __isl_keep isl_aff *obj, isl_int *opt);
1941 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1942 __isl_keep isl_aff *obj, isl_int *opt);
1944 Compute the minimum or maximum of the integer affine expression C<obj>
1945 over the points in C<set>, returning the result in C<opt>.
1946 The return value may be one of C<isl_lp_error>,
1947 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1949 =item * Parametric optimization
1951 __isl_give isl_pw_aff *isl_set_dim_min(
1952 __isl_take isl_set *set, int pos);
1953 __isl_give isl_pw_aff *isl_set_dim_max(
1954 __isl_take isl_set *set, int pos);
1955 __isl_give isl_pw_aff *isl_map_dim_max(
1956 __isl_take isl_map *map, int pos);
1958 Compute the minimum or maximum of the given set or output dimension
1959 as a function of the parameters (and input dimensions), but independently
1960 of the other set or output dimensions.
1961 For lexicographic optimization, see L<"Lexicographic Optimization">.
1965 The following functions compute either the set of (rational) coefficient
1966 values of valid constraints for the given set or the set of (rational)
1967 values satisfying the constraints with coefficients from the given set.
1968 Internally, these two sets of functions perform essentially the
1969 same operations, except that the set of coefficients is assumed to
1970 be a cone, while the set of values may be any polyhedron.
1971 The current implementation is based on the Farkas lemma and
1972 Fourier-Motzkin elimination, but this may change or be made optional
1973 in future. In particular, future implementations may use different
1974 dualization algorithms or skip the elimination step.
1976 __isl_give isl_basic_set *isl_basic_set_coefficients(
1977 __isl_take isl_basic_set *bset);
1978 __isl_give isl_basic_set *isl_set_coefficients(
1979 __isl_take isl_set *set);
1980 __isl_give isl_union_set *isl_union_set_coefficients(
1981 __isl_take isl_union_set *bset);
1982 __isl_give isl_basic_set *isl_basic_set_solutions(
1983 __isl_take isl_basic_set *bset);
1984 __isl_give isl_basic_set *isl_set_solutions(
1985 __isl_take isl_set *set);
1986 __isl_give isl_union_set *isl_union_set_solutions(
1987 __isl_take isl_union_set *bset);
1991 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1993 __isl_give isl_union_map *isl_union_map_power(
1994 __isl_take isl_union_map *umap, int *exact);
1996 Compute a parametric representation for all positive powers I<k> of C<map>.
1997 The result maps I<k> to a nested relation corresponding to the
1998 I<k>th power of C<map>.
1999 The result may be an overapproximation. If the result is known to be exact,
2000 then C<*exact> is set to C<1>.
2002 =item * Transitive closure
2004 __isl_give isl_map *isl_map_transitive_closure(
2005 __isl_take isl_map *map, int *exact);
2006 __isl_give isl_union_map *isl_union_map_transitive_closure(
2007 __isl_take isl_union_map *umap, int *exact);
2009 Compute the transitive closure of C<map>.
2010 The result may be an overapproximation. If the result is known to be exact,
2011 then C<*exact> is set to C<1>.
2013 =item * Reaching path lengths
2015 __isl_give isl_map *isl_map_reaching_path_lengths(
2016 __isl_take isl_map *map, int *exact);
2018 Compute a relation that maps each element in the range of C<map>
2019 to the lengths of all paths composed of edges in C<map> that
2020 end up in the given element.
2021 The result may be an overapproximation. If the result is known to be exact,
2022 then C<*exact> is set to C<1>.
2023 To compute the I<maximal> path length, the resulting relation
2024 should be postprocessed by C<isl_map_lexmax>.
2025 In particular, if the input relation is a dependence relation
2026 (mapping sources to sinks), then the maximal path length corresponds
2027 to the free schedule.
2028 Note, however, that C<isl_map_lexmax> expects the maximum to be
2029 finite, so if the path lengths are unbounded (possibly due to
2030 the overapproximation), then you will get an error message.
2034 __isl_give isl_basic_set *isl_basic_map_wrap(
2035 __isl_take isl_basic_map *bmap);
2036 __isl_give isl_set *isl_map_wrap(
2037 __isl_take isl_map *map);
2038 __isl_give isl_union_set *isl_union_map_wrap(
2039 __isl_take isl_union_map *umap);
2040 __isl_give isl_basic_map *isl_basic_set_unwrap(
2041 __isl_take isl_basic_set *bset);
2042 __isl_give isl_map *isl_set_unwrap(
2043 __isl_take isl_set *set);
2044 __isl_give isl_union_map *isl_union_set_unwrap(
2045 __isl_take isl_union_set *uset);
2049 Remove any internal structure of domain (and range) of the given
2050 set or relation. If there is any such internal structure in the input,
2051 then the name of the space is also removed.
2053 __isl_give isl_basic_set *isl_basic_set_flatten(
2054 __isl_take isl_basic_set *bset);
2055 __isl_give isl_set *isl_set_flatten(
2056 __isl_take isl_set *set);
2057 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2058 __isl_take isl_basic_map *bmap);
2059 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2060 __isl_take isl_basic_map *bmap);
2061 __isl_give isl_map *isl_map_flatten_range(
2062 __isl_take isl_map *map);
2063 __isl_give isl_map *isl_map_flatten_domain(
2064 __isl_take isl_map *map);
2065 __isl_give isl_basic_map *isl_basic_map_flatten(
2066 __isl_take isl_basic_map *bmap);
2067 __isl_give isl_map *isl_map_flatten(
2068 __isl_take isl_map *map);
2070 __isl_give isl_map *isl_set_flatten_map(
2071 __isl_take isl_set *set);
2073 The function above constructs a relation
2074 that maps the input set to a flattened version of the set.
2078 Lift the input set to a space with extra dimensions corresponding
2079 to the existentially quantified variables in the input.
2080 In particular, the result lives in a wrapped map where the domain
2081 is the original space and the range corresponds to the original
2082 existentially quantified variables.
2084 __isl_give isl_basic_set *isl_basic_set_lift(
2085 __isl_take isl_basic_set *bset);
2086 __isl_give isl_set *isl_set_lift(
2087 __isl_take isl_set *set);
2088 __isl_give isl_union_set *isl_union_set_lift(
2089 __isl_take isl_union_set *uset);
2091 =item * Internal Product
2093 __isl_give isl_basic_map *isl_basic_map_zip(
2094 __isl_take isl_basic_map *bmap);
2095 __isl_give isl_map *isl_map_zip(
2096 __isl_take isl_map *map);
2097 __isl_give isl_union_map *isl_union_map_zip(
2098 __isl_take isl_union_map *umap);
2100 Given a relation with nested relations for domain and range,
2101 interchange the range of the domain with the domain of the range.
2103 =item * Aligning parameters
2105 __isl_give isl_set *isl_set_align_params(
2106 __isl_take isl_set *set,
2107 __isl_take isl_space *model);
2108 __isl_give isl_map *isl_map_align_params(
2109 __isl_take isl_map *map,
2110 __isl_take isl_space *model);
2112 Change the order of the parameters of the given set or relation
2113 such that the first parameters match those of C<model>.
2114 This may involve the introduction of extra parameters.
2115 All parameters need to be named.
2117 =item * Dimension manipulation
2119 __isl_give isl_set *isl_set_add_dims(
2120 __isl_take isl_set *set,
2121 enum isl_dim_type type, unsigned n);
2122 __isl_give isl_map *isl_map_add_dims(
2123 __isl_take isl_map *map,
2124 enum isl_dim_type type, unsigned n);
2125 __isl_give isl_set *isl_set_insert_dims(
2126 __isl_take isl_set *set,
2127 enum isl_dim_type type, unsigned pos, unsigned n);
2128 __isl_give isl_map *isl_map_insert_dims(
2129 __isl_take isl_map *map,
2130 enum isl_dim_type type, unsigned pos, unsigned n);
2131 __isl_give isl_basic_set *isl_basic_set_move_dims(
2132 __isl_take isl_basic_set *bset,
2133 enum isl_dim_type dst_type, unsigned dst_pos,
2134 enum isl_dim_type src_type, unsigned src_pos,
2136 __isl_give isl_basic_map *isl_basic_map_move_dims(
2137 __isl_take isl_basic_map *bmap,
2138 enum isl_dim_type dst_type, unsigned dst_pos,
2139 enum isl_dim_type src_type, unsigned src_pos,
2141 __isl_give isl_set *isl_set_move_dims(
2142 __isl_take isl_set *set,
2143 enum isl_dim_type dst_type, unsigned dst_pos,
2144 enum isl_dim_type src_type, unsigned src_pos,
2146 __isl_give isl_map *isl_map_move_dims(
2147 __isl_take isl_map *map,
2148 enum isl_dim_type dst_type, unsigned dst_pos,
2149 enum isl_dim_type src_type, unsigned src_pos,
2152 It is usually not advisable to directly change the (input or output)
2153 space of a set or a relation as this removes the name and the internal
2154 structure of the space. However, the above functions can be useful
2155 to add new parameters, assuming
2156 C<isl_set_align_params> and C<isl_map_align_params>
2161 =head2 Binary Operations
2163 The two arguments of a binary operation not only need to live
2164 in the same C<isl_ctx>, they currently also need to have
2165 the same (number of) parameters.
2167 =head3 Basic Operations
2171 =item * Intersection
2173 __isl_give isl_basic_set *isl_basic_set_intersect(
2174 __isl_take isl_basic_set *bset1,
2175 __isl_take isl_basic_set *bset2);
2176 __isl_give isl_set *isl_set_intersect_params(
2177 __isl_take isl_set *set,
2178 __isl_take isl_set *params);
2179 __isl_give isl_set *isl_set_intersect(
2180 __isl_take isl_set *set1,
2181 __isl_take isl_set *set2);
2182 __isl_give isl_union_set *isl_union_set_intersect(
2183 __isl_take isl_union_set *uset1,
2184 __isl_take isl_union_set *uset2);
2185 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2186 __isl_take isl_basic_map *bmap,
2187 __isl_take isl_basic_set *bset);
2188 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2189 __isl_take isl_basic_map *bmap,
2190 __isl_take isl_basic_set *bset);
2191 __isl_give isl_basic_map *isl_basic_map_intersect(
2192 __isl_take isl_basic_map *bmap1,
2193 __isl_take isl_basic_map *bmap2);
2194 __isl_give isl_map *isl_map_intersect_params(
2195 __isl_take isl_map *map,
2196 __isl_take isl_set *params);
2197 __isl_give isl_map *isl_map_intersect_domain(
2198 __isl_take isl_map *map,
2199 __isl_take isl_set *set);
2200 __isl_give isl_map *isl_map_intersect_range(
2201 __isl_take isl_map *map,
2202 __isl_take isl_set *set);
2203 __isl_give isl_map *isl_map_intersect(
2204 __isl_take isl_map *map1,
2205 __isl_take isl_map *map2);
2206 __isl_give isl_union_map *isl_union_map_intersect_domain(
2207 __isl_take isl_union_map *umap,
2208 __isl_take isl_union_set *uset);
2209 __isl_give isl_union_map *isl_union_map_intersect_range(
2210 __isl_take isl_union_map *umap,
2211 __isl_take isl_union_set *uset);
2212 __isl_give isl_union_map *isl_union_map_intersect(
2213 __isl_take isl_union_map *umap1,
2214 __isl_take isl_union_map *umap2);
2218 __isl_give isl_set *isl_basic_set_union(
2219 __isl_take isl_basic_set *bset1,
2220 __isl_take isl_basic_set *bset2);
2221 __isl_give isl_map *isl_basic_map_union(
2222 __isl_take isl_basic_map *bmap1,
2223 __isl_take isl_basic_map *bmap2);
2224 __isl_give isl_set *isl_set_union(
2225 __isl_take isl_set *set1,
2226 __isl_take isl_set *set2);
2227 __isl_give isl_map *isl_map_union(
2228 __isl_take isl_map *map1,
2229 __isl_take isl_map *map2);
2230 __isl_give isl_union_set *isl_union_set_union(
2231 __isl_take isl_union_set *uset1,
2232 __isl_take isl_union_set *uset2);
2233 __isl_give isl_union_map *isl_union_map_union(
2234 __isl_take isl_union_map *umap1,
2235 __isl_take isl_union_map *umap2);
2237 =item * Set difference
2239 __isl_give isl_set *isl_set_subtract(
2240 __isl_take isl_set *set1,
2241 __isl_take isl_set *set2);
2242 __isl_give isl_map *isl_map_subtract(
2243 __isl_take isl_map *map1,
2244 __isl_take isl_map *map2);
2245 __isl_give isl_union_set *isl_union_set_subtract(
2246 __isl_take isl_union_set *uset1,
2247 __isl_take isl_union_set *uset2);
2248 __isl_give isl_union_map *isl_union_map_subtract(
2249 __isl_take isl_union_map *umap1,
2250 __isl_take isl_union_map *umap2);
2254 __isl_give isl_basic_set *isl_basic_set_apply(
2255 __isl_take isl_basic_set *bset,
2256 __isl_take isl_basic_map *bmap);
2257 __isl_give isl_set *isl_set_apply(
2258 __isl_take isl_set *set,
2259 __isl_take isl_map *map);
2260 __isl_give isl_union_set *isl_union_set_apply(
2261 __isl_take isl_union_set *uset,
2262 __isl_take isl_union_map *umap);
2263 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2264 __isl_take isl_basic_map *bmap1,
2265 __isl_take isl_basic_map *bmap2);
2266 __isl_give isl_basic_map *isl_basic_map_apply_range(
2267 __isl_take isl_basic_map *bmap1,
2268 __isl_take isl_basic_map *bmap2);
2269 __isl_give isl_map *isl_map_apply_domain(
2270 __isl_take isl_map *map1,
2271 __isl_take isl_map *map2);
2272 __isl_give isl_union_map *isl_union_map_apply_domain(
2273 __isl_take isl_union_map *umap1,
2274 __isl_take isl_union_map *umap2);
2275 __isl_give isl_map *isl_map_apply_range(
2276 __isl_take isl_map *map1,
2277 __isl_take isl_map *map2);
2278 __isl_give isl_union_map *isl_union_map_apply_range(
2279 __isl_take isl_union_map *umap1,
2280 __isl_take isl_union_map *umap2);
2282 =item * Cartesian Product
2284 __isl_give isl_set *isl_set_product(
2285 __isl_take isl_set *set1,
2286 __isl_take isl_set *set2);
2287 __isl_give isl_union_set *isl_union_set_product(
2288 __isl_take isl_union_set *uset1,
2289 __isl_take isl_union_set *uset2);
2290 __isl_give isl_basic_map *isl_basic_map_domain_product(
2291 __isl_take isl_basic_map *bmap1,
2292 __isl_take isl_basic_map *bmap2);
2293 __isl_give isl_basic_map *isl_basic_map_range_product(
2294 __isl_take isl_basic_map *bmap1,
2295 __isl_take isl_basic_map *bmap2);
2296 __isl_give isl_map *isl_map_domain_product(
2297 __isl_take isl_map *map1,
2298 __isl_take isl_map *map2);
2299 __isl_give isl_map *isl_map_range_product(
2300 __isl_take isl_map *map1,
2301 __isl_take isl_map *map2);
2302 __isl_give isl_union_map *isl_union_map_range_product(
2303 __isl_take isl_union_map *umap1,
2304 __isl_take isl_union_map *umap2);
2305 __isl_give isl_map *isl_map_product(
2306 __isl_take isl_map *map1,
2307 __isl_take isl_map *map2);
2308 __isl_give isl_union_map *isl_union_map_product(
2309 __isl_take isl_union_map *umap1,
2310 __isl_take isl_union_map *umap2);
2312 The above functions compute the cross product of the given
2313 sets or relations. The domains and ranges of the results
2314 are wrapped maps between domains and ranges of the inputs.
2315 To obtain a ``flat'' product, use the following functions
2318 __isl_give isl_basic_set *isl_basic_set_flat_product(
2319 __isl_take isl_basic_set *bset1,
2320 __isl_take isl_basic_set *bset2);
2321 __isl_give isl_set *isl_set_flat_product(
2322 __isl_take isl_set *set1,
2323 __isl_take isl_set *set2);
2324 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2325 __isl_take isl_basic_map *bmap1,
2326 __isl_take isl_basic_map *bmap2);
2327 __isl_give isl_map *isl_map_flat_domain_product(
2328 __isl_take isl_map *map1,
2329 __isl_take isl_map *map2);
2330 __isl_give isl_map *isl_map_flat_range_product(
2331 __isl_take isl_map *map1,
2332 __isl_take isl_map *map2);
2333 __isl_give isl_union_map *isl_union_map_flat_range_product(
2334 __isl_take isl_union_map *umap1,
2335 __isl_take isl_union_map *umap2);
2336 __isl_give isl_basic_map *isl_basic_map_flat_product(
2337 __isl_take isl_basic_map *bmap1,
2338 __isl_take isl_basic_map *bmap2);
2339 __isl_give isl_map *isl_map_flat_product(
2340 __isl_take isl_map *map1,
2341 __isl_take isl_map *map2);
2343 =item * Simplification
2345 __isl_give isl_basic_set *isl_basic_set_gist(
2346 __isl_take isl_basic_set *bset,
2347 __isl_take isl_basic_set *context);
2348 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2349 __isl_take isl_set *context);
2350 __isl_give isl_set *isl_set_gist_params(
2351 __isl_take isl_set *set,
2352 __isl_take isl_set *context);
2353 __isl_give isl_union_set *isl_union_set_gist(
2354 __isl_take isl_union_set *uset,
2355 __isl_take isl_union_set *context);
2356 __isl_give isl_basic_map *isl_basic_map_gist(
2357 __isl_take isl_basic_map *bmap,
2358 __isl_take isl_basic_map *context);
2359 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2360 __isl_take isl_map *context);
2361 __isl_give isl_map *isl_map_gist_params(
2362 __isl_take isl_map *map,
2363 __isl_take isl_set *context);
2364 __isl_give isl_union_map *isl_union_map_gist(
2365 __isl_take isl_union_map *umap,
2366 __isl_take isl_union_map *context);
2368 The gist operation returns a set or relation that has the
2369 same intersection with the context as the input set or relation.
2370 Any implicit equality in the intersection is made explicit in the result,
2371 while all inequalities that are redundant with respect to the intersection
2373 In case of union sets and relations, the gist operation is performed
2378 =head3 Lexicographic Optimization
2380 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2381 the following functions
2382 compute a set that contains the lexicographic minimum or maximum
2383 of the elements in C<set> (or C<bset>) for those values of the parameters
2384 that satisfy C<dom>.
2385 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2386 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2388 In other words, the union of the parameter values
2389 for which the result is non-empty and of C<*empty>
2392 __isl_give isl_set *isl_basic_set_partial_lexmin(
2393 __isl_take isl_basic_set *bset,
2394 __isl_take isl_basic_set *dom,
2395 __isl_give isl_set **empty);
2396 __isl_give isl_set *isl_basic_set_partial_lexmax(
2397 __isl_take isl_basic_set *bset,
2398 __isl_take isl_basic_set *dom,
2399 __isl_give isl_set **empty);
2400 __isl_give isl_set *isl_set_partial_lexmin(
2401 __isl_take isl_set *set, __isl_take isl_set *dom,
2402 __isl_give isl_set **empty);
2403 __isl_give isl_set *isl_set_partial_lexmax(
2404 __isl_take isl_set *set, __isl_take isl_set *dom,
2405 __isl_give isl_set **empty);
2407 Given a (basic) set C<set> (or C<bset>), the following functions simply
2408 return a set containing the lexicographic minimum or maximum
2409 of the elements in C<set> (or C<bset>).
2410 In case of union sets, the optimum is computed per space.
2412 __isl_give isl_set *isl_basic_set_lexmin(
2413 __isl_take isl_basic_set *bset);
2414 __isl_give isl_set *isl_basic_set_lexmax(
2415 __isl_take isl_basic_set *bset);
2416 __isl_give isl_set *isl_set_lexmin(
2417 __isl_take isl_set *set);
2418 __isl_give isl_set *isl_set_lexmax(
2419 __isl_take isl_set *set);
2420 __isl_give isl_union_set *isl_union_set_lexmin(
2421 __isl_take isl_union_set *uset);
2422 __isl_give isl_union_set *isl_union_set_lexmax(
2423 __isl_take isl_union_set *uset);
2425 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2426 the following functions
2427 compute a relation that maps each element of C<dom>
2428 to the single lexicographic minimum or maximum
2429 of the elements that are associated to that same
2430 element in C<map> (or C<bmap>).
2431 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2432 that contains the elements in C<dom> that do not map
2433 to any elements in C<map> (or C<bmap>).
2434 In other words, the union of the domain of the result and of C<*empty>
2437 __isl_give isl_map *isl_basic_map_partial_lexmax(
2438 __isl_take isl_basic_map *bmap,
2439 __isl_take isl_basic_set *dom,
2440 __isl_give isl_set **empty);
2441 __isl_give isl_map *isl_basic_map_partial_lexmin(
2442 __isl_take isl_basic_map *bmap,
2443 __isl_take isl_basic_set *dom,
2444 __isl_give isl_set **empty);
2445 __isl_give isl_map *isl_map_partial_lexmax(
2446 __isl_take isl_map *map, __isl_take isl_set *dom,
2447 __isl_give isl_set **empty);
2448 __isl_give isl_map *isl_map_partial_lexmin(
2449 __isl_take isl_map *map, __isl_take isl_set *dom,
2450 __isl_give isl_set **empty);
2452 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2453 return a map mapping each element in the domain of
2454 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2455 of all elements associated to that element.
2456 In case of union relations, the optimum is computed per space.
2458 __isl_give isl_map *isl_basic_map_lexmin(
2459 __isl_take isl_basic_map *bmap);
2460 __isl_give isl_map *isl_basic_map_lexmax(
2461 __isl_take isl_basic_map *bmap);
2462 __isl_give isl_map *isl_map_lexmin(
2463 __isl_take isl_map *map);
2464 __isl_give isl_map *isl_map_lexmax(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_map *isl_union_map_lexmin(
2467 __isl_take isl_union_map *umap);
2468 __isl_give isl_union_map *isl_union_map_lexmax(
2469 __isl_take isl_union_map *umap);
2471 The following functions return their result in the form of
2472 a piecewise multi-affine expression
2473 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2474 but are otherwise equivalent to the corresponding functions
2475 returning a basic set or relation.
2477 __isl_give isl_pw_multi_aff *
2478 isl_basic_map_lexmin_pw_multi_aff(
2479 __isl_take isl_basic_map *bmap);
2480 __isl_give isl_pw_multi_aff *
2481 isl_basic_set_partial_lexmin_pw_multi_aff(
2482 __isl_take isl_basic_set *bset,
2483 __isl_take isl_basic_set *dom,
2484 __isl_give isl_set **empty);
2485 __isl_give isl_pw_multi_aff *
2486 isl_basic_set_partial_lexmax_pw_multi_aff(
2487 __isl_take isl_basic_set *bset,
2488 __isl_take isl_basic_set *dom,
2489 __isl_give isl_set **empty);
2490 __isl_give isl_pw_multi_aff *
2491 isl_basic_map_partial_lexmin_pw_multi_aff(
2492 __isl_take isl_basic_map *bmap,
2493 __isl_take isl_basic_set *dom,
2494 __isl_give isl_set **empty);
2495 __isl_give isl_pw_multi_aff *
2496 isl_basic_map_partial_lexmax_pw_multi_aff(
2497 __isl_take isl_basic_map *bmap,
2498 __isl_take isl_basic_set *dom,
2499 __isl_give isl_set **empty);
2503 Lists are defined over several element types, including
2504 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2505 Here we take lists of C<isl_set>s as an example.
2506 Lists can be created, copied and freed using the following functions.
2508 #include <isl/list.h>
2509 __isl_give isl_set_list *isl_set_list_from_set(
2510 __isl_take isl_set *el);
2511 __isl_give isl_set_list *isl_set_list_alloc(
2512 isl_ctx *ctx, int n);
2513 __isl_give isl_set_list *isl_set_list_copy(
2514 __isl_keep isl_set_list *list);
2515 __isl_give isl_set_list *isl_set_list_add(
2516 __isl_take isl_set_list *list,
2517 __isl_take isl_set *el);
2518 __isl_give isl_set_list *isl_set_list_concat(
2519 __isl_take isl_set_list *list1,
2520 __isl_take isl_set_list *list2);
2521 void *isl_set_list_free(__isl_take isl_set_list *list);
2523 C<isl_set_list_alloc> creates an empty list with a capacity for
2524 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2527 Lists can be inspected using the following functions.
2529 #include <isl/list.h>
2530 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2531 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2532 __isl_give isl_set *isl_set_list_get_set(
2533 __isl_keep isl_set_list *list, int index);
2534 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2535 int (*fn)(__isl_take isl_set *el, void *user),
2538 Lists can be printed using
2540 #include <isl/list.h>
2541 __isl_give isl_printer *isl_printer_print_set_list(
2542 __isl_take isl_printer *p,
2543 __isl_keep isl_set_list *list);
2547 Matrices can be created, copied and freed using the following functions.
2549 #include <isl/mat.h>
2550 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2551 unsigned n_row, unsigned n_col);
2552 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2553 void isl_mat_free(__isl_take isl_mat *mat);
2555 Note that the elements of a newly created matrix may have arbitrary values.
2556 The elements can be changed and inspected using the following functions.
2558 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2559 int isl_mat_rows(__isl_keep isl_mat *mat);
2560 int isl_mat_cols(__isl_keep isl_mat *mat);
2561 int isl_mat_get_element(__isl_keep isl_mat *mat,
2562 int row, int col, isl_int *v);
2563 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2564 int row, int col, isl_int v);
2565 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2566 int row, int col, int v);
2568 C<isl_mat_get_element> will return a negative value if anything went wrong.
2569 In that case, the value of C<*v> is undefined.
2571 The following function can be used to compute the (right) inverse
2572 of a matrix, i.e., a matrix such that the product of the original
2573 and the inverse (in that order) is a multiple of the identity matrix.
2574 The input matrix is assumed to be of full row-rank.
2576 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2578 The following function can be used to compute the (right) kernel
2579 (or null space) of a matrix, i.e., a matrix such that the product of
2580 the original and the kernel (in that order) is the zero matrix.
2582 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2584 =head2 Piecewise Quasi Affine Expressions
2586 The zero quasi affine expression on a given domain can be created using
2588 __isl_give isl_aff *isl_aff_zero_on_domain(
2589 __isl_take isl_local_space *ls);
2591 Note that the space in which the resulting object lives is a map space
2592 with the given space as domain and a one-dimensional range.
2594 An empty piecewise quasi affine expression (one with no cells)
2595 or a piecewise quasi affine expression with a single cell can
2596 be created using the following functions.
2598 #include <isl/aff.h>
2599 __isl_give isl_pw_aff *isl_pw_aff_empty(
2600 __isl_take isl_space *space);
2601 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2602 __isl_take isl_set *set, __isl_take isl_aff *aff);
2603 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2604 __isl_take isl_aff *aff);
2606 Quasi affine expressions can be copied and freed using
2608 #include <isl/aff.h>
2609 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2610 void *isl_aff_free(__isl_take isl_aff *aff);
2612 __isl_give isl_pw_aff *isl_pw_aff_copy(
2613 __isl_keep isl_pw_aff *pwaff);
2614 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2616 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2617 using the following function. The constraint is required to have
2618 a non-zero coefficient for the specified dimension.
2620 #include <isl/constraint.h>
2621 __isl_give isl_aff *isl_constraint_get_bound(
2622 __isl_keep isl_constraint *constraint,
2623 enum isl_dim_type type, int pos);
2625 The entire affine expression of the constraint can also be extracted
2626 using the following function.
2628 #include <isl/constraint.h>
2629 __isl_give isl_aff *isl_constraint_get_aff(
2630 __isl_keep isl_constraint *constraint);
2632 Conversely, an equality constraint equating
2633 the affine expression to zero or an inequality constraint enforcing
2634 the affine expression to be non-negative, can be constructed using
2636 __isl_give isl_constraint *isl_equality_from_aff(
2637 __isl_take isl_aff *aff);
2638 __isl_give isl_constraint *isl_inequality_from_aff(
2639 __isl_take isl_aff *aff);
2641 The expression can be inspected using
2643 #include <isl/aff.h>
2644 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2645 int isl_aff_dim(__isl_keep isl_aff *aff,
2646 enum isl_dim_type type);
2647 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2648 __isl_keep isl_aff *aff);
2649 __isl_give isl_local_space *isl_aff_get_local_space(
2650 __isl_keep isl_aff *aff);
2651 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2652 enum isl_dim_type type, unsigned pos);
2653 const char *isl_pw_aff_get_dim_name(
2654 __isl_keep isl_pw_aff *pa,
2655 enum isl_dim_type type, unsigned pos);
2656 __isl_give isl_id *isl_pw_aff_get_dim_id(
2657 __isl_keep isl_pw_aff *pa,
2658 enum isl_dim_type type, unsigned pos);
2659 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2661 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2662 enum isl_dim_type type, int pos, isl_int *v);
2663 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2665 __isl_give isl_aff *isl_aff_get_div(
2666 __isl_keep isl_aff *aff, int pos);
2668 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2669 int (*fn)(__isl_take isl_set *set,
2670 __isl_take isl_aff *aff,
2671 void *user), void *user);
2673 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2674 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2676 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2677 enum isl_dim_type type, unsigned first, unsigned n);
2678 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2679 enum isl_dim_type type, unsigned first, unsigned n);
2681 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2682 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2683 enum isl_dim_type type);
2684 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2686 It can be modified using
2688 #include <isl/aff.h>
2689 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2690 __isl_take isl_pw_aff *pwaff,
2691 enum isl_dim_type type, __isl_take isl_id *id);
2692 __isl_give isl_aff *isl_aff_set_dim_name(
2693 __isl_take isl_aff *aff, enum isl_dim_type type,
2694 unsigned pos, const char *s);
2695 __isl_give isl_aff *isl_aff_set_dim_id(
2696 __isl_take isl_aff *aff, enum isl_dim_type type,
2697 unsigned pos, __isl_take isl_id *id);
2698 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2699 __isl_take isl_pw_aff *pma,
2700 enum isl_dim_type type, unsigned pos,
2701 __isl_take isl_id *id);
2702 __isl_give isl_aff *isl_aff_set_constant(
2703 __isl_take isl_aff *aff, isl_int v);
2704 __isl_give isl_aff *isl_aff_set_constant_si(
2705 __isl_take isl_aff *aff, int v);
2706 __isl_give isl_aff *isl_aff_set_coefficient(
2707 __isl_take isl_aff *aff,
2708 enum isl_dim_type type, int pos, isl_int v);
2709 __isl_give isl_aff *isl_aff_set_coefficient_si(
2710 __isl_take isl_aff *aff,
2711 enum isl_dim_type type, int pos, int v);
2712 __isl_give isl_aff *isl_aff_set_denominator(
2713 __isl_take isl_aff *aff, isl_int v);
2715 __isl_give isl_aff *isl_aff_add_constant(
2716 __isl_take isl_aff *aff, isl_int v);
2717 __isl_give isl_aff *isl_aff_add_constant_si(
2718 __isl_take isl_aff *aff, int v);
2719 __isl_give isl_aff *isl_aff_add_coefficient(
2720 __isl_take isl_aff *aff,
2721 enum isl_dim_type type, int pos, isl_int v);
2722 __isl_give isl_aff *isl_aff_add_coefficient_si(
2723 __isl_take isl_aff *aff,
2724 enum isl_dim_type type, int pos, int v);
2726 __isl_give isl_aff *isl_aff_insert_dims(
2727 __isl_take isl_aff *aff,
2728 enum isl_dim_type type, unsigned first, unsigned n);
2729 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2730 __isl_take isl_pw_aff *pwaff,
2731 enum isl_dim_type type, unsigned first, unsigned n);
2732 __isl_give isl_aff *isl_aff_add_dims(
2733 __isl_take isl_aff *aff,
2734 enum isl_dim_type type, unsigned n);
2735 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2736 __isl_take isl_pw_aff *pwaff,
2737 enum isl_dim_type type, unsigned n);
2738 __isl_give isl_aff *isl_aff_drop_dims(
2739 __isl_take isl_aff *aff,
2740 enum isl_dim_type type, unsigned first, unsigned n);
2741 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2742 __isl_take isl_pw_aff *pwaff,
2743 enum isl_dim_type type, unsigned first, unsigned n);
2745 Note that the C<set_constant> and C<set_coefficient> functions
2746 set the I<numerator> of the constant or coefficient, while
2747 C<add_constant> and C<add_coefficient> add an integer value to
2748 the possibly rational constant or coefficient.
2750 To check whether an affine expressions is obviously zero
2751 or obviously equal to some other affine expression, use
2753 #include <isl/aff.h>
2754 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2755 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2756 __isl_keep isl_aff *aff2);
2757 int isl_pw_aff_plain_is_equal(
2758 __isl_keep isl_pw_aff *pwaff1,
2759 __isl_keep isl_pw_aff *pwaff2);
2763 #include <isl/aff.h>
2764 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2765 __isl_take isl_aff *aff2);
2766 __isl_give isl_pw_aff *isl_pw_aff_add(
2767 __isl_take isl_pw_aff *pwaff1,
2768 __isl_take isl_pw_aff *pwaff2);
2769 __isl_give isl_pw_aff *isl_pw_aff_min(
2770 __isl_take isl_pw_aff *pwaff1,
2771 __isl_take isl_pw_aff *pwaff2);
2772 __isl_give isl_pw_aff *isl_pw_aff_max(
2773 __isl_take isl_pw_aff *pwaff1,
2774 __isl_take isl_pw_aff *pwaff2);
2775 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2776 __isl_take isl_aff *aff2);
2777 __isl_give isl_pw_aff *isl_pw_aff_sub(
2778 __isl_take isl_pw_aff *pwaff1,
2779 __isl_take isl_pw_aff *pwaff2);
2780 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2781 __isl_give isl_pw_aff *isl_pw_aff_neg(
2782 __isl_take isl_pw_aff *pwaff);
2783 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2784 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2785 __isl_take isl_pw_aff *pwaff);
2786 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2787 __isl_give isl_pw_aff *isl_pw_aff_floor(
2788 __isl_take isl_pw_aff *pwaff);
2789 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2791 __isl_give isl_pw_aff *isl_pw_aff_mod(
2792 __isl_take isl_pw_aff *pwaff, isl_int mod);
2793 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2795 __isl_give isl_pw_aff *isl_pw_aff_scale(
2796 __isl_take isl_pw_aff *pwaff, isl_int f);
2797 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2799 __isl_give isl_aff *isl_aff_scale_down_ui(
2800 __isl_take isl_aff *aff, unsigned f);
2801 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2802 __isl_take isl_pw_aff *pwaff, isl_int f);
2804 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2805 __isl_take isl_pw_aff_list *list);
2806 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2807 __isl_take isl_pw_aff_list *list);
2809 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2810 __isl_take isl_pw_aff *pwqp);
2812 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2813 __isl_take isl_pw_aff *pwaff,
2814 __isl_take isl_space *model);
2816 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2817 __isl_take isl_set *context);
2818 __isl_give isl_pw_aff *isl_pw_aff_gist(
2819 __isl_take isl_pw_aff *pwaff,
2820 __isl_take isl_set *context);
2822 __isl_give isl_set *isl_pw_aff_domain(
2823 __isl_take isl_pw_aff *pwaff);
2824 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2825 __isl_take isl_pw_aff *pa,
2826 __isl_take isl_set *set);
2828 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2829 __isl_take isl_aff *aff2);
2830 __isl_give isl_pw_aff *isl_pw_aff_mul(
2831 __isl_take isl_pw_aff *pwaff1,
2832 __isl_take isl_pw_aff *pwaff2);
2834 When multiplying two affine expressions, at least one of the two needs
2837 #include <isl/aff.h>
2838 __isl_give isl_basic_set *isl_aff_le_basic_set(
2839 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2840 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2841 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2842 __isl_give isl_set *isl_pw_aff_eq_set(
2843 __isl_take isl_pw_aff *pwaff1,
2844 __isl_take isl_pw_aff *pwaff2);
2845 __isl_give isl_set *isl_pw_aff_ne_set(
2846 __isl_take isl_pw_aff *pwaff1,
2847 __isl_take isl_pw_aff *pwaff2);
2848 __isl_give isl_set *isl_pw_aff_le_set(
2849 __isl_take isl_pw_aff *pwaff1,
2850 __isl_take isl_pw_aff *pwaff2);
2851 __isl_give isl_set *isl_pw_aff_lt_set(
2852 __isl_take isl_pw_aff *pwaff1,
2853 __isl_take isl_pw_aff *pwaff2);
2854 __isl_give isl_set *isl_pw_aff_ge_set(
2855 __isl_take isl_pw_aff *pwaff1,
2856 __isl_take isl_pw_aff *pwaff2);
2857 __isl_give isl_set *isl_pw_aff_gt_set(
2858 __isl_take isl_pw_aff *pwaff1,
2859 __isl_take isl_pw_aff *pwaff2);
2861 __isl_give isl_set *isl_pw_aff_list_eq_set(
2862 __isl_take isl_pw_aff_list *list1,
2863 __isl_take isl_pw_aff_list *list2);
2864 __isl_give isl_set *isl_pw_aff_list_ne_set(
2865 __isl_take isl_pw_aff_list *list1,
2866 __isl_take isl_pw_aff_list *list2);
2867 __isl_give isl_set *isl_pw_aff_list_le_set(
2868 __isl_take isl_pw_aff_list *list1,
2869 __isl_take isl_pw_aff_list *list2);
2870 __isl_give isl_set *isl_pw_aff_list_lt_set(
2871 __isl_take isl_pw_aff_list *list1,
2872 __isl_take isl_pw_aff_list *list2);
2873 __isl_give isl_set *isl_pw_aff_list_ge_set(
2874 __isl_take isl_pw_aff_list *list1,
2875 __isl_take isl_pw_aff_list *list2);
2876 __isl_give isl_set *isl_pw_aff_list_gt_set(
2877 __isl_take isl_pw_aff_list *list1,
2878 __isl_take isl_pw_aff_list *list2);
2880 The function C<isl_aff_ge_basic_set> returns a basic set
2881 containing those elements in the shared space
2882 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2883 The function C<isl_aff_ge_set> returns a set
2884 containing those elements in the shared domain
2885 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2886 The functions operating on C<isl_pw_aff_list> apply the corresponding
2887 C<isl_pw_aff> function to each pair of elements in the two lists.
2889 #include <isl/aff.h>
2890 __isl_give isl_set *isl_pw_aff_nonneg_set(
2891 __isl_take isl_pw_aff *pwaff);
2892 __isl_give isl_set *isl_pw_aff_zero_set(
2893 __isl_take isl_pw_aff *pwaff);
2894 __isl_give isl_set *isl_pw_aff_non_zero_set(
2895 __isl_take isl_pw_aff *pwaff);
2897 The function C<isl_pw_aff_nonneg_set> returns a set
2898 containing those elements in the domain
2899 of C<pwaff> where C<pwaff> is non-negative.
2901 #include <isl/aff.h>
2902 __isl_give isl_pw_aff *isl_pw_aff_cond(
2903 __isl_take isl_set *cond,
2904 __isl_take isl_pw_aff *pwaff_true,
2905 __isl_take isl_pw_aff *pwaff_false);
2907 The function C<isl_pw_aff_cond> performs a conditional operator
2908 and returns an expression that is equal to C<pwaff_true>
2909 for elements in C<cond> and equal to C<pwaff_false> for elements
2912 #include <isl/aff.h>
2913 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2914 __isl_take isl_pw_aff *pwaff1,
2915 __isl_take isl_pw_aff *pwaff2);
2916 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2917 __isl_take isl_pw_aff *pwaff1,
2918 __isl_take isl_pw_aff *pwaff2);
2920 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2921 expression with a domain that is the union of those of C<pwaff1> and
2922 C<pwaff2> and such that on each cell, the quasi-affine expression is
2923 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2924 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2925 associated expression is the defined one.
2927 An expression can be read from input using
2929 #include <isl/aff.h>
2930 __isl_give isl_aff *isl_aff_read_from_str(
2931 isl_ctx *ctx, const char *str);
2932 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
2933 isl_ctx *ctx, const char *str);
2935 An expression can be printed using
2937 #include <isl/aff.h>
2938 __isl_give isl_printer *isl_printer_print_aff(
2939 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2941 __isl_give isl_printer *isl_printer_print_pw_aff(
2942 __isl_take isl_printer *p,
2943 __isl_keep isl_pw_aff *pwaff);
2945 =head2 Piecewise Multiple Quasi Affine Expressions
2947 An C<isl_multi_aff> object represents a sequence of
2948 zero or more affine expressions, all defined on the same domain space.
2950 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
2953 #include <isl/aff.h>
2954 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2955 __isl_take isl_space *space,
2956 __isl_take isl_aff_list *list);
2958 An empty piecewise multiple quasi affine expression (one with no cells) or
2959 a piecewise multiple quasi affine expression with a single cell can
2960 be created using the following functions.
2962 #include <isl/aff.h>
2963 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2964 __isl_take isl_space *space);
2965 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2966 __isl_take isl_set *set,
2967 __isl_take isl_multi_aff *maff);
2969 A piecewise multiple quasi affine expression can also be initialized
2970 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
2971 and the C<isl_map> is single-valued.
2973 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
2974 __isl_take isl_set *set);
2975 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
2976 __isl_take isl_map *map);
2978 Multiple quasi affine expressions can be copied and freed using
2980 #include <isl/aff.h>
2981 __isl_give isl_multi_aff *isl_multi_aff_copy(
2982 __isl_keep isl_multi_aff *maff);
2983 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
2985 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2986 __isl_keep isl_pw_multi_aff *pma);
2987 void *isl_pw_multi_aff_free(
2988 __isl_take isl_pw_multi_aff *pma);
2990 The expression can be inspected using
2992 #include <isl/aff.h>
2993 isl_ctx *isl_multi_aff_get_ctx(
2994 __isl_keep isl_multi_aff *maff);
2995 isl_ctx *isl_pw_multi_aff_get_ctx(
2996 __isl_keep isl_pw_multi_aff *pma);
2997 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
2998 enum isl_dim_type type);
2999 unsigned isl_pw_multi_aff_dim(
3000 __isl_keep isl_pw_multi_aff *pma,
3001 enum isl_dim_type type);
3002 __isl_give isl_aff *isl_multi_aff_get_aff(
3003 __isl_keep isl_multi_aff *multi, int pos);
3004 const char *isl_pw_multi_aff_get_dim_name(
3005 __isl_keep isl_pw_multi_aff *pma,
3006 enum isl_dim_type type, unsigned pos);
3007 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3008 __isl_keep isl_pw_multi_aff *pma,
3009 enum isl_dim_type type, unsigned pos);
3010 const char *isl_multi_aff_get_tuple_name(
3011 __isl_keep isl_multi_aff *multi,
3012 enum isl_dim_type type);
3013 const char *isl_pw_multi_aff_get_tuple_name(
3014 __isl_keep isl_pw_multi_aff *pma,
3015 enum isl_dim_type type);
3016 int isl_pw_multi_aff_has_tuple_id(
3017 __isl_keep isl_pw_multi_aff *pma,
3018 enum isl_dim_type type);
3019 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3020 __isl_keep isl_pw_multi_aff *pma,
3021 enum isl_dim_type type);
3023 int isl_pw_multi_aff_foreach_piece(
3024 __isl_keep isl_pw_multi_aff *pma,
3025 int (*fn)(__isl_take isl_set *set,
3026 __isl_take isl_multi_aff *maff,
3027 void *user), void *user);
3029 It can be modified using
3031 #include <isl/aff.h>
3032 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3033 __isl_take isl_multi_aff *maff,
3034 enum isl_dim_type type, unsigned pos, const char *s);
3035 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3036 __isl_take isl_pw_multi_aff *pma,
3037 enum isl_dim_type type, __isl_take isl_id *id);
3039 To check whether two multiple affine expressions are
3040 obviously equal to each other, use
3042 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3043 __isl_keep isl_multi_aff *maff2);
3044 int isl_pw_multi_aff_plain_is_equal(
3045 __isl_keep isl_pw_multi_aff *pma1,
3046 __isl_keep isl_pw_multi_aff *pma2);
3050 #include <isl/aff.h>
3051 __isl_give isl_multi_aff *isl_multi_aff_add(
3052 __isl_take isl_multi_aff *maff1,
3053 __isl_take isl_multi_aff *maff2);
3054 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3055 __isl_take isl_pw_multi_aff *pma1,
3056 __isl_take isl_pw_multi_aff *pma2);
3057 __isl_give isl_multi_aff *isl_multi_aff_scale(
3058 __isl_take isl_multi_aff *maff,
3060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3061 __isl_take isl_pw_multi_aff *pma,
3062 __isl_take isl_set *set);
3063 __isl_give isl_multi_aff *isl_multi_aff_gist(
3064 __isl_take isl_multi_aff *maff,
3065 __isl_take isl_set *context);
3067 An expression can be read from input using
3069 #include <isl/aff.h>
3070 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3071 isl_ctx *ctx, const char *str);
3072 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3073 isl_ctx *ctx, const char *str);
3075 An expression can be printed using
3077 #include <isl/aff.h>
3078 __isl_give isl_printer *isl_printer_print_multi_aff(
3079 __isl_take isl_printer *p,
3080 __isl_keep isl_multi_aff *maff);
3081 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3082 __isl_take isl_printer *p,
3083 __isl_keep isl_pw_multi_aff *pma);
3087 Points are elements of a set. They can be used to construct
3088 simple sets (boxes) or they can be used to represent the
3089 individual elements of a set.
3090 The zero point (the origin) can be created using
3092 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3094 The coordinates of a point can be inspected, set and changed
3097 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
3098 enum isl_dim_type type, int pos, isl_int *v);
3099 __isl_give isl_point *isl_point_set_coordinate(
3100 __isl_take isl_point *pnt,
3101 enum isl_dim_type type, int pos, isl_int v);
3103 __isl_give isl_point *isl_point_add_ui(
3104 __isl_take isl_point *pnt,
3105 enum isl_dim_type type, int pos, unsigned val);
3106 __isl_give isl_point *isl_point_sub_ui(
3107 __isl_take isl_point *pnt,
3108 enum isl_dim_type type, int pos, unsigned val);
3110 Other properties can be obtained using
3112 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3114 Points can be copied or freed using
3116 __isl_give isl_point *isl_point_copy(
3117 __isl_keep isl_point *pnt);
3118 void isl_point_free(__isl_take isl_point *pnt);
3120 A singleton set can be created from a point using
3122 __isl_give isl_basic_set *isl_basic_set_from_point(
3123 __isl_take isl_point *pnt);
3124 __isl_give isl_set *isl_set_from_point(
3125 __isl_take isl_point *pnt);
3127 and a box can be created from two opposite extremal points using
3129 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3130 __isl_take isl_point *pnt1,
3131 __isl_take isl_point *pnt2);
3132 __isl_give isl_set *isl_set_box_from_points(
3133 __isl_take isl_point *pnt1,
3134 __isl_take isl_point *pnt2);
3136 All elements of a B<bounded> (union) set can be enumerated using
3137 the following functions.
3139 int isl_set_foreach_point(__isl_keep isl_set *set,
3140 int (*fn)(__isl_take isl_point *pnt, void *user),
3142 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3143 int (*fn)(__isl_take isl_point *pnt, void *user),
3146 The function C<fn> is called for each integer point in
3147 C<set> with as second argument the last argument of
3148 the C<isl_set_foreach_point> call. The function C<fn>
3149 should return C<0> on success and C<-1> on failure.
3150 In the latter case, C<isl_set_foreach_point> will stop
3151 enumerating and return C<-1> as well.
3152 If the enumeration is performed successfully and to completion,
3153 then C<isl_set_foreach_point> returns C<0>.
3155 To obtain a single point of a (basic) set, use
3157 __isl_give isl_point *isl_basic_set_sample_point(
3158 __isl_take isl_basic_set *bset);
3159 __isl_give isl_point *isl_set_sample_point(
3160 __isl_take isl_set *set);
3162 If C<set> does not contain any (integer) points, then the
3163 resulting point will be ``void'', a property that can be
3166 int isl_point_is_void(__isl_keep isl_point *pnt);
3168 =head2 Piecewise Quasipolynomials
3170 A piecewise quasipolynomial is a particular kind of function that maps
3171 a parametric point to a rational value.
3172 More specifically, a quasipolynomial is a polynomial expression in greatest
3173 integer parts of affine expressions of parameters and variables.
3174 A piecewise quasipolynomial is a subdivision of a given parametric
3175 domain into disjoint cells with a quasipolynomial associated to
3176 each cell. The value of the piecewise quasipolynomial at a given
3177 point is the value of the quasipolynomial associated to the cell
3178 that contains the point. Outside of the union of cells,
3179 the value is assumed to be zero.
3180 For example, the piecewise quasipolynomial
3182 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3184 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3185 A given piecewise quasipolynomial has a fixed domain dimension.
3186 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3187 defined over different domains.
3188 Piecewise quasipolynomials are mainly used by the C<barvinok>
3189 library for representing the number of elements in a parametric set or map.
3190 For example, the piecewise quasipolynomial above represents
3191 the number of points in the map
3193 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3195 =head3 Printing (Piecewise) Quasipolynomials
3197 Quasipolynomials and piecewise quasipolynomials can be printed
3198 using the following functions.
3200 __isl_give isl_printer *isl_printer_print_qpolynomial(
3201 __isl_take isl_printer *p,
3202 __isl_keep isl_qpolynomial *qp);
3204 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3205 __isl_take isl_printer *p,
3206 __isl_keep isl_pw_qpolynomial *pwqp);
3208 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3209 __isl_take isl_printer *p,
3210 __isl_keep isl_union_pw_qpolynomial *upwqp);
3212 The output format of the printer
3213 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3214 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3216 In case of printing in C<ISL_FORMAT_C>, the user may want
3217 to set the names of all dimensions
3219 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3220 __isl_take isl_qpolynomial *qp,
3221 enum isl_dim_type type, unsigned pos,
3223 __isl_give isl_pw_qpolynomial *
3224 isl_pw_qpolynomial_set_dim_name(
3225 __isl_take isl_pw_qpolynomial *pwqp,
3226 enum isl_dim_type type, unsigned pos,
3229 =head3 Creating New (Piecewise) Quasipolynomials
3231 Some simple quasipolynomials can be created using the following functions.
3232 More complicated quasipolynomials can be created by applying
3233 operations such as addition and multiplication
3234 on the resulting quasipolynomials
3236 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3237 __isl_take isl_space *domain);
3238 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3239 __isl_take isl_space *domain);
3240 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3241 __isl_take isl_space *domain);
3242 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3243 __isl_take isl_space *domain);
3244 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3245 __isl_take isl_space *domain);
3246 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3247 __isl_take isl_space *domain,
3248 const isl_int n, const isl_int d);
3249 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3250 __isl_take isl_space *domain,
3251 enum isl_dim_type type, unsigned pos);
3252 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3253 __isl_take isl_aff *aff);
3255 Note that the space in which a quasipolynomial lives is a map space
3256 with a one-dimensional range. The C<domain> argument in some of
3257 the functions above corresponds to the domain of this map space.
3259 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3260 with a single cell can be created using the following functions.
3261 Multiple of these single cell piecewise quasipolynomials can
3262 be combined to create more complicated piecewise quasipolynomials.
3264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3265 __isl_take isl_space *space);
3266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3267 __isl_take isl_set *set,
3268 __isl_take isl_qpolynomial *qp);
3269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3270 __isl_take isl_qpolynomial *qp);
3271 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3272 __isl_take isl_pw_aff *pwaff);
3274 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3275 __isl_take isl_space *space);
3276 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3277 __isl_take isl_pw_qpolynomial *pwqp);
3278 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3279 __isl_take isl_union_pw_qpolynomial *upwqp,
3280 __isl_take isl_pw_qpolynomial *pwqp);
3282 Quasipolynomials can be copied and freed again using the following
3285 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3286 __isl_keep isl_qpolynomial *qp);
3287 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3289 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3290 __isl_keep isl_pw_qpolynomial *pwqp);
3291 void *isl_pw_qpolynomial_free(
3292 __isl_take isl_pw_qpolynomial *pwqp);
3294 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3295 __isl_keep isl_union_pw_qpolynomial *upwqp);
3296 void isl_union_pw_qpolynomial_free(
3297 __isl_take isl_union_pw_qpolynomial *upwqp);
3299 =head3 Inspecting (Piecewise) Quasipolynomials
3301 To iterate over all piecewise quasipolynomials in a union
3302 piecewise quasipolynomial, use the following function
3304 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3305 __isl_keep isl_union_pw_qpolynomial *upwqp,
3306 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3309 To extract the piecewise quasipolynomial in a given space from a union, use
3311 __isl_give isl_pw_qpolynomial *
3312 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3313 __isl_keep isl_union_pw_qpolynomial *upwqp,
3314 __isl_take isl_space *space);
3316 To iterate over the cells in a piecewise quasipolynomial,
3317 use either of the following two functions
3319 int isl_pw_qpolynomial_foreach_piece(
3320 __isl_keep isl_pw_qpolynomial *pwqp,
3321 int (*fn)(__isl_take isl_set *set,
3322 __isl_take isl_qpolynomial *qp,
3323 void *user), void *user);
3324 int isl_pw_qpolynomial_foreach_lifted_piece(
3325 __isl_keep isl_pw_qpolynomial *pwqp,
3326 int (*fn)(__isl_take isl_set *set,
3327 __isl_take isl_qpolynomial *qp,
3328 void *user), void *user);
3330 As usual, the function C<fn> should return C<0> on success
3331 and C<-1> on failure. The difference between
3332 C<isl_pw_qpolynomial_foreach_piece> and
3333 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3334 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3335 compute unique representations for all existentially quantified
3336 variables and then turn these existentially quantified variables
3337 into extra set variables, adapting the associated quasipolynomial
3338 accordingly. This means that the C<set> passed to C<fn>
3339 will not have any existentially quantified variables, but that
3340 the dimensions of the sets may be different for different
3341 invocations of C<fn>.
3343 To iterate over all terms in a quasipolynomial,
3346 int isl_qpolynomial_foreach_term(
3347 __isl_keep isl_qpolynomial *qp,
3348 int (*fn)(__isl_take isl_term *term,
3349 void *user), void *user);
3351 The terms themselves can be inspected and freed using
3354 unsigned isl_term_dim(__isl_keep isl_term *term,
3355 enum isl_dim_type type);
3356 void isl_term_get_num(__isl_keep isl_term *term,
3358 void isl_term_get_den(__isl_keep isl_term *term,
3360 int isl_term_get_exp(__isl_keep isl_term *term,
3361 enum isl_dim_type type, unsigned pos);
3362 __isl_give isl_aff *isl_term_get_div(
3363 __isl_keep isl_term *term, unsigned pos);
3364 void isl_term_free(__isl_take isl_term *term);
3366 Each term is a product of parameters, set variables and
3367 integer divisions. The function C<isl_term_get_exp>
3368 returns the exponent of a given dimensions in the given term.
3369 The C<isl_int>s in the arguments of C<isl_term_get_num>
3370 and C<isl_term_get_den> need to have been initialized
3371 using C<isl_int_init> before calling these functions.
3373 =head3 Properties of (Piecewise) Quasipolynomials
3375 To check whether a quasipolynomial is actually a constant,
3376 use the following function.
3378 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3379 isl_int *n, isl_int *d);
3381 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3382 then the numerator and denominator of the constant
3383 are returned in C<*n> and C<*d>, respectively.
3385 To check whether two union piecewise quasipolynomials are
3386 obviously equal, use
3388 int isl_union_pw_qpolynomial_plain_is_equal(
3389 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3390 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3392 =head3 Operations on (Piecewise) Quasipolynomials
3394 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3395 __isl_take isl_qpolynomial *qp, isl_int v);
3396 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3397 __isl_take isl_qpolynomial *qp);
3398 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3399 __isl_take isl_qpolynomial *qp1,
3400 __isl_take isl_qpolynomial *qp2);
3401 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3402 __isl_take isl_qpolynomial *qp1,
3403 __isl_take isl_qpolynomial *qp2);
3404 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3405 __isl_take isl_qpolynomial *qp1,
3406 __isl_take isl_qpolynomial *qp2);
3407 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3408 __isl_take isl_qpolynomial *qp, unsigned exponent);
3410 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3411 __isl_take isl_pw_qpolynomial *pwqp1,
3412 __isl_take isl_pw_qpolynomial *pwqp2);
3413 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3414 __isl_take isl_pw_qpolynomial *pwqp1,
3415 __isl_take isl_pw_qpolynomial *pwqp2);
3416 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3417 __isl_take isl_pw_qpolynomial *pwqp1,
3418 __isl_take isl_pw_qpolynomial *pwqp2);
3419 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3420 __isl_take isl_pw_qpolynomial *pwqp);
3421 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3422 __isl_take isl_pw_qpolynomial *pwqp1,
3423 __isl_take isl_pw_qpolynomial *pwqp2);
3424 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3425 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3427 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3428 __isl_take isl_union_pw_qpolynomial *upwqp1,
3429 __isl_take isl_union_pw_qpolynomial *upwqp2);
3430 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3431 __isl_take isl_union_pw_qpolynomial *upwqp1,
3432 __isl_take isl_union_pw_qpolynomial *upwqp2);
3433 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3434 __isl_take isl_union_pw_qpolynomial *upwqp1,
3435 __isl_take isl_union_pw_qpolynomial *upwqp2);
3437 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3438 __isl_take isl_pw_qpolynomial *pwqp,
3439 __isl_take isl_point *pnt);
3441 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3442 __isl_take isl_union_pw_qpolynomial *upwqp,
3443 __isl_take isl_point *pnt);
3445 __isl_give isl_set *isl_pw_qpolynomial_domain(
3446 __isl_take isl_pw_qpolynomial *pwqp);
3447 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3448 __isl_take isl_pw_qpolynomial *pwpq,
3449 __isl_take isl_set *set);
3451 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3452 __isl_take isl_union_pw_qpolynomial *upwqp);
3453 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3454 __isl_take isl_union_pw_qpolynomial *upwpq,
3455 __isl_take isl_union_set *uset);
3457 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3458 __isl_take isl_qpolynomial *qp,
3459 __isl_take isl_space *model);
3461 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3462 __isl_take isl_qpolynomial *qp);
3463 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3464 __isl_take isl_pw_qpolynomial *pwqp);
3466 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3467 __isl_take isl_union_pw_qpolynomial *upwqp);
3469 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3470 __isl_take isl_qpolynomial *qp,
3471 __isl_take isl_set *context);
3473 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3474 __isl_take isl_pw_qpolynomial *pwqp,
3475 __isl_take isl_set *context);
3477 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3478 __isl_take isl_union_pw_qpolynomial *upwqp,
3479 __isl_take isl_union_set *context);
3481 The gist operation applies the gist operation to each of
3482 the cells in the domain of the input piecewise quasipolynomial.
3483 The context is also exploited
3484 to simplify the quasipolynomials associated to each cell.
3486 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3487 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3488 __isl_give isl_union_pw_qpolynomial *
3489 isl_union_pw_qpolynomial_to_polynomial(
3490 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3492 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3493 the polynomial will be an overapproximation. If C<sign> is negative,
3494 it will be an underapproximation. If C<sign> is zero, the approximation
3495 will lie somewhere in between.
3497 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3499 A piecewise quasipolynomial reduction is a piecewise
3500 reduction (or fold) of quasipolynomials.
3501 In particular, the reduction can be maximum or a minimum.
3502 The objects are mainly used to represent the result of
3503 an upper or lower bound on a quasipolynomial over its domain,
3504 i.e., as the result of the following function.
3506 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3507 __isl_take isl_pw_qpolynomial *pwqp,
3508 enum isl_fold type, int *tight);
3510 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3511 __isl_take isl_union_pw_qpolynomial *upwqp,
3512 enum isl_fold type, int *tight);
3514 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3515 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3516 is the returned bound is known be tight, i.e., for each value
3517 of the parameters there is at least
3518 one element in the domain that reaches the bound.
3519 If the domain of C<pwqp> is not wrapping, then the bound is computed
3520 over all elements in that domain and the result has a purely parametric
3521 domain. If the domain of C<pwqp> is wrapping, then the bound is
3522 computed over the range of the wrapped relation. The domain of the
3523 wrapped relation becomes the domain of the result.
3525 A (piecewise) quasipolynomial reduction can be copied or freed using the
3526 following functions.
3528 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3529 __isl_keep isl_qpolynomial_fold *fold);
3530 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3531 __isl_keep isl_pw_qpolynomial_fold *pwf);
3532 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3533 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3534 void isl_qpolynomial_fold_free(
3535 __isl_take isl_qpolynomial_fold *fold);
3536 void *isl_pw_qpolynomial_fold_free(
3537 __isl_take isl_pw_qpolynomial_fold *pwf);
3538 void isl_union_pw_qpolynomial_fold_free(
3539 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3541 =head3 Printing Piecewise Quasipolynomial Reductions
3543 Piecewise quasipolynomial reductions can be printed
3544 using the following function.
3546 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3547 __isl_take isl_printer *p,
3548 __isl_keep isl_pw_qpolynomial_fold *pwf);
3549 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3550 __isl_take isl_printer *p,
3551 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3553 For C<isl_printer_print_pw_qpolynomial_fold>,
3554 output format of the printer
3555 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3556 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3557 output format of the printer
3558 needs to be set to C<ISL_FORMAT_ISL>.
3559 In case of printing in C<ISL_FORMAT_C>, the user may want
3560 to set the names of all dimensions
3562 __isl_give isl_pw_qpolynomial_fold *
3563 isl_pw_qpolynomial_fold_set_dim_name(
3564 __isl_take isl_pw_qpolynomial_fold *pwf,
3565 enum isl_dim_type type, unsigned pos,
3568 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3570 To iterate over all piecewise quasipolynomial reductions in a union
3571 piecewise quasipolynomial reduction, use the following function
3573 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3574 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3575 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3576 void *user), void *user);
3578 To iterate over the cells in a piecewise quasipolynomial reduction,
3579 use either of the following two functions
3581 int isl_pw_qpolynomial_fold_foreach_piece(
3582 __isl_keep isl_pw_qpolynomial_fold *pwf,
3583 int (*fn)(__isl_take isl_set *set,
3584 __isl_take isl_qpolynomial_fold *fold,
3585 void *user), void *user);
3586 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3587 __isl_keep isl_pw_qpolynomial_fold *pwf,
3588 int (*fn)(__isl_take isl_set *set,
3589 __isl_take isl_qpolynomial_fold *fold,
3590 void *user), void *user);
3592 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3593 of the difference between these two functions.
3595 To iterate over all quasipolynomials in a reduction, use
3597 int isl_qpolynomial_fold_foreach_qpolynomial(
3598 __isl_keep isl_qpolynomial_fold *fold,
3599 int (*fn)(__isl_take isl_qpolynomial *qp,
3600 void *user), void *user);
3602 =head3 Properties of Piecewise Quasipolynomial Reductions
3604 To check whether two union piecewise quasipolynomial reductions are
3605 obviously equal, use
3607 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3608 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3609 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3611 =head3 Operations on Piecewise Quasipolynomial Reductions
3613 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3614 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3616 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3617 __isl_take isl_pw_qpolynomial_fold *pwf1,
3618 __isl_take isl_pw_qpolynomial_fold *pwf2);
3620 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3621 __isl_take isl_pw_qpolynomial_fold *pwf1,
3622 __isl_take isl_pw_qpolynomial_fold *pwf2);
3624 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3625 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3626 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3628 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3629 __isl_take isl_pw_qpolynomial_fold *pwf,
3630 __isl_take isl_point *pnt);
3632 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3633 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3634 __isl_take isl_point *pnt);
3636 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3637 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3638 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3639 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3640 __isl_take isl_union_set *uset);
3642 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3643 __isl_take isl_pw_qpolynomial_fold *pwf);
3645 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3646 __isl_take isl_pw_qpolynomial_fold *pwf);
3648 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3649 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3651 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3652 __isl_take isl_pw_qpolynomial_fold *pwf,
3653 __isl_take isl_set *context);
3655 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3656 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3657 __isl_take isl_union_set *context);
3659 The gist operation applies the gist operation to each of
3660 the cells in the domain of the input piecewise quasipolynomial reduction.
3661 In future, the operation will also exploit the context
3662 to simplify the quasipolynomial reductions associated to each cell.
3664 __isl_give isl_pw_qpolynomial_fold *
3665 isl_set_apply_pw_qpolynomial_fold(
3666 __isl_take isl_set *set,
3667 __isl_take isl_pw_qpolynomial_fold *pwf,
3669 __isl_give isl_pw_qpolynomial_fold *
3670 isl_map_apply_pw_qpolynomial_fold(
3671 __isl_take isl_map *map,
3672 __isl_take isl_pw_qpolynomial_fold *pwf,
3674 __isl_give isl_union_pw_qpolynomial_fold *
3675 isl_union_set_apply_union_pw_qpolynomial_fold(
3676 __isl_take isl_union_set *uset,
3677 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3679 __isl_give isl_union_pw_qpolynomial_fold *
3680 isl_union_map_apply_union_pw_qpolynomial_fold(
3681 __isl_take isl_union_map *umap,
3682 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3685 The functions taking a map
3686 compose the given map with the given piecewise quasipolynomial reduction.
3687 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3688 over all elements in the intersection of the range of the map
3689 and the domain of the piecewise quasipolynomial reduction
3690 as a function of an element in the domain of the map.
3691 The functions taking a set compute a bound over all elements in the
3692 intersection of the set and the domain of the
3693 piecewise quasipolynomial reduction.
3695 =head2 Dependence Analysis
3697 C<isl> contains specialized functionality for performing
3698 array dataflow analysis. That is, given a I<sink> access relation
3699 and a collection of possible I<source> access relations,
3700 C<isl> can compute relations that describe
3701 for each iteration of the sink access, which iteration
3702 of which of the source access relations was the last
3703 to access the same data element before the given iteration
3705 To compute standard flow dependences, the sink should be
3706 a read, while the sources should be writes.
3707 If any of the source accesses are marked as being I<may>
3708 accesses, then there will be a dependence to the last
3709 I<must> access B<and> to any I<may> access that follows
3710 this last I<must> access.
3711 In particular, if I<all> sources are I<may> accesses,
3712 then memory based dependence analysis is performed.
3713 If, on the other hand, all sources are I<must> accesses,
3714 then value based dependence analysis is performed.
3716 #include <isl/flow.h>
3718 typedef int (*isl_access_level_before)(void *first, void *second);
3720 __isl_give isl_access_info *isl_access_info_alloc(
3721 __isl_take isl_map *sink,
3722 void *sink_user, isl_access_level_before fn,
3724 __isl_give isl_access_info *isl_access_info_add_source(
3725 __isl_take isl_access_info *acc,
3726 __isl_take isl_map *source, int must,
3728 void isl_access_info_free(__isl_take isl_access_info *acc);
3730 __isl_give isl_flow *isl_access_info_compute_flow(
3731 __isl_take isl_access_info *acc);
3733 int isl_flow_foreach(__isl_keep isl_flow *deps,
3734 int (*fn)(__isl_take isl_map *dep, int must,
3735 void *dep_user, void *user),
3737 __isl_give isl_map *isl_flow_get_no_source(
3738 __isl_keep isl_flow *deps, int must);
3739 void isl_flow_free(__isl_take isl_flow *deps);
3741 The function C<isl_access_info_compute_flow> performs the actual
3742 dependence analysis. The other functions are used to construct
3743 the input for this function or to read off the output.
3745 The input is collected in an C<isl_access_info>, which can
3746 be created through a call to C<isl_access_info_alloc>.
3747 The arguments to this functions are the sink access relation
3748 C<sink>, a token C<sink_user> used to identify the sink
3749 access to the user, a callback function for specifying the
3750 relative order of source and sink accesses, and the number
3751 of source access relations that will be added.
3752 The callback function has type C<int (*)(void *first, void *second)>.
3753 The function is called with two user supplied tokens identifying
3754 either a source or the sink and it should return the shared nesting
3755 level and the relative order of the two accesses.
3756 In particular, let I<n> be the number of loops shared by
3757 the two accesses. If C<first> precedes C<second> textually,
3758 then the function should return I<2 * n + 1>; otherwise,
3759 it should return I<2 * n>.
3760 The sources can be added to the C<isl_access_info> by performing
3761 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3762 C<must> indicates whether the source is a I<must> access
3763 or a I<may> access. Note that a multi-valued access relation
3764 should only be marked I<must> if every iteration in the domain
3765 of the relation accesses I<all> elements in its image.
3766 The C<source_user> token is again used to identify
3767 the source access. The range of the source access relation
3768 C<source> should have the same dimension as the range
3769 of the sink access relation.
3770 The C<isl_access_info_free> function should usually not be
3771 called explicitly, because it is called implicitly by
3772 C<isl_access_info_compute_flow>.
3774 The result of the dependence analysis is collected in an
3775 C<isl_flow>. There may be elements of
3776 the sink access for which no preceding source access could be
3777 found or for which all preceding sources are I<may> accesses.
3778 The relations containing these elements can be obtained through
3779 calls to C<isl_flow_get_no_source>, the first with C<must> set
3780 and the second with C<must> unset.
3781 In the case of standard flow dependence analysis,
3782 with the sink a read and the sources I<must> writes,
3783 the first relation corresponds to the reads from uninitialized
3784 array elements and the second relation is empty.
3785 The actual flow dependences can be extracted using
3786 C<isl_flow_foreach>. This function will call the user-specified
3787 callback function C<fn> for each B<non-empty> dependence between
3788 a source and the sink. The callback function is called
3789 with four arguments, the actual flow dependence relation
3790 mapping source iterations to sink iterations, a boolean that
3791 indicates whether it is a I<must> or I<may> dependence, a token
3792 identifying the source and an additional C<void *> with value
3793 equal to the third argument of the C<isl_flow_foreach> call.
3794 A dependence is marked I<must> if it originates from a I<must>
3795 source and if it is not followed by any I<may> sources.
3797 After finishing with an C<isl_flow>, the user should call
3798 C<isl_flow_free> to free all associated memory.
3800 A higher-level interface to dependence analysis is provided
3801 by the following function.
3803 #include <isl/flow.h>
3805 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3806 __isl_take isl_union_map *must_source,
3807 __isl_take isl_union_map *may_source,
3808 __isl_take isl_union_map *schedule,
3809 __isl_give isl_union_map **must_dep,
3810 __isl_give isl_union_map **may_dep,
3811 __isl_give isl_union_map **must_no_source,
3812 __isl_give isl_union_map **may_no_source);
3814 The arrays are identified by the tuple names of the ranges
3815 of the accesses. The iteration domains by the tuple names
3816 of the domains of the accesses and of the schedule.
3817 The relative order of the iteration domains is given by the
3818 schedule. The relations returned through C<must_no_source>
3819 and C<may_no_source> are subsets of C<sink>.
3820 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3821 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3822 any of the other arguments is treated as an error.
3826 B<The functionality described in this section is fairly new
3827 and may be subject to change.>
3829 The following function can be used to compute a schedule
3830 for a union of domains. The generated schedule respects
3831 all C<validity> dependences. That is, all dependence distances
3832 over these dependences in the scheduled space are lexicographically
3833 positive. The generated schedule schedule also tries to minimize
3834 the dependence distances over C<proximity> dependences.
3835 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3836 for groups of domains where the dependence distances have only
3837 non-negative values.
3838 The algorithm used to construct the schedule is similar to that
3841 #include <isl/schedule.h>
3842 __isl_give isl_schedule *isl_union_set_compute_schedule(
3843 __isl_take isl_union_set *domain,
3844 __isl_take isl_union_map *validity,
3845 __isl_take isl_union_map *proximity);
3846 void *isl_schedule_free(__isl_take isl_schedule *sched);
3848 A mapping from the domains to the scheduled space can be obtained
3849 from an C<isl_schedule> using the following function.
3851 __isl_give isl_union_map *isl_schedule_get_map(
3852 __isl_keep isl_schedule *sched);
3854 A representation of the schedule can be printed using
3856 __isl_give isl_printer *isl_printer_print_schedule(
3857 __isl_take isl_printer *p,
3858 __isl_keep isl_schedule *schedule);
3860 A representation of the schedule as a forest of bands can be obtained
3861 using the following function.
3863 __isl_give isl_band_list *isl_schedule_get_band_forest(
3864 __isl_keep isl_schedule *schedule);
3866 The list can be manipulated as explained in L<"Lists">.
3867 The bands inside the list can be copied and freed using the following
3870 #include <isl/band.h>
3871 __isl_give isl_band *isl_band_copy(
3872 __isl_keep isl_band *band);
3873 void *isl_band_free(__isl_take isl_band *band);
3875 Each band contains zero or more scheduling dimensions.
3876 These are referred to as the members of the band.
3877 The section of the schedule that corresponds to the band is
3878 referred to as the partial schedule of the band.
3879 For those nodes that participate in a band, the outer scheduling
3880 dimensions form the prefix schedule, while the inner scheduling
3881 dimensions form the suffix schedule.
3882 That is, if we take a cut of the band forest, then the union of
3883 the concatenations of the prefix, partial and suffix schedules of
3884 each band in the cut is equal to the entire schedule (modulo
3885 some possible padding at the end with zero scheduling dimensions).
3886 The properties of a band can be inspected using the following functions.
3888 #include <isl/band.h>
3889 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3891 int isl_band_has_children(__isl_keep isl_band *band);
3892 __isl_give isl_band_list *isl_band_get_children(
3893 __isl_keep isl_band *band);
3895 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3896 __isl_keep isl_band *band);
3897 __isl_give isl_union_map *isl_band_get_partial_schedule(
3898 __isl_keep isl_band *band);
3899 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3900 __isl_keep isl_band *band);
3902 int isl_band_n_member(__isl_keep isl_band *band);
3903 int isl_band_member_is_zero_distance(
3904 __isl_keep isl_band *band, int pos);
3906 Note that a scheduling dimension is considered to be ``zero
3907 distance'' if it does not carry any proximity dependences
3909 That is, if the dependence distances of the proximity
3910 dependences are all zero in that direction (for fixed
3911 iterations of outer bands).
3913 A representation of the band can be printed using
3915 #include <isl/band.h>
3916 __isl_give isl_printer *isl_printer_print_band(
3917 __isl_take isl_printer *p,
3918 __isl_keep isl_band *band);
3920 =head2 Parametric Vertex Enumeration
3922 The parametric vertex enumeration described in this section
3923 is mainly intended to be used internally and by the C<barvinok>
3926 #include <isl/vertices.h>
3927 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3928 __isl_keep isl_basic_set *bset);
3930 The function C<isl_basic_set_compute_vertices> performs the
3931 actual computation of the parametric vertices and the chamber
3932 decomposition and store the result in an C<isl_vertices> object.
3933 This information can be queried by either iterating over all
3934 the vertices or iterating over all the chambers or cells
3935 and then iterating over all vertices that are active on the chamber.
3937 int isl_vertices_foreach_vertex(
3938 __isl_keep isl_vertices *vertices,
3939 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3942 int isl_vertices_foreach_cell(
3943 __isl_keep isl_vertices *vertices,
3944 int (*fn)(__isl_take isl_cell *cell, void *user),
3946 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3947 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3950 Other operations that can be performed on an C<isl_vertices> object are
3953 isl_ctx *isl_vertices_get_ctx(
3954 __isl_keep isl_vertices *vertices);
3955 int isl_vertices_get_n_vertices(
3956 __isl_keep isl_vertices *vertices);
3957 void isl_vertices_free(__isl_take isl_vertices *vertices);
3959 Vertices can be inspected and destroyed using the following functions.
3961 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3962 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3963 __isl_give isl_basic_set *isl_vertex_get_domain(
3964 __isl_keep isl_vertex *vertex);
3965 __isl_give isl_basic_set *isl_vertex_get_expr(
3966 __isl_keep isl_vertex *vertex);
3967 void isl_vertex_free(__isl_take isl_vertex *vertex);
3969 C<isl_vertex_get_expr> returns a singleton parametric set describing
3970 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3972 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3973 B<rational> basic sets, so they should mainly be used for inspection
3974 and should not be mixed with integer sets.
3976 Chambers can be inspected and destroyed using the following functions.
3978 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3979 __isl_give isl_basic_set *isl_cell_get_domain(
3980 __isl_keep isl_cell *cell);
3981 void isl_cell_free(__isl_take isl_cell *cell);
3985 Although C<isl> is mainly meant to be used as a library,
3986 it also contains some basic applications that use some
3987 of the functionality of C<isl>.
3988 The input may be specified in either the L<isl format>
3989 or the L<PolyLib format>.
3991 =head2 C<isl_polyhedron_sample>
3993 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3994 an integer element of the polyhedron, if there is any.
3995 The first column in the output is the denominator and is always
3996 equal to 1. If the polyhedron contains no integer points,
3997 then a vector of length zero is printed.
4001 C<isl_pip> takes the same input as the C<example> program
4002 from the C<piplib> distribution, i.e., a set of constraints
4003 on the parameters, a line containing only -1 and finally a set
4004 of constraints on a parametric polyhedron.
4005 The coefficients of the parameters appear in the last columns
4006 (but before the final constant column).
4007 The output is the lexicographic minimum of the parametric polyhedron.
4008 As C<isl> currently does not have its own output format, the output
4009 is just a dump of the internal state.
4011 =head2 C<isl_polyhedron_minimize>
4013 C<isl_polyhedron_minimize> computes the minimum of some linear
4014 or affine objective function over the integer points in a polyhedron.
4015 If an affine objective function
4016 is given, then the constant should appear in the last column.
4018 =head2 C<isl_polytope_scan>
4020 Given a polytope, C<isl_polytope_scan> prints
4021 all integer points in the polytope.