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);
602 #include <isl/point.h>
603 __isl_give isl_space *isl_point_get_space(
604 __isl_keep isl_point *pnt);
606 The identifiers or names of the individual dimensions may be set or read off
607 using the following functions.
609 #include <isl/space.h>
610 __isl_give isl_space *isl_space_set_dim_id(
611 __isl_take isl_space *space,
612 enum isl_dim_type type, unsigned pos,
613 __isl_take isl_id *id);
614 int isl_space_has_dim_id(__isl_keep isl_space *space,
615 enum isl_dim_type type, unsigned pos);
616 __isl_give isl_id *isl_space_get_dim_id(
617 __isl_keep isl_space *space,
618 enum isl_dim_type type, unsigned pos);
619 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_keep const char *name);
622 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
625 Note that C<isl_space_get_name> returns a pointer to some internal
626 data structure, so the result can only be used while the
627 corresponding C<isl_space> is alive.
628 Also note that every function that operates on two sets or relations
629 requires that both arguments have the same parameters. This also
630 means that if one of the arguments has named parameters, then the
631 other needs to have named parameters too and the names need to match.
632 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
633 arguments may have different parameters (as long as they are named),
634 in which case the result will have as parameters the union of the parameters of
637 Given the identifier of a dimension (typically a parameter),
638 its position can be obtained from the following function.
640 #include <isl/space.h>
641 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
642 enum isl_dim_type type, __isl_keep isl_id *id);
644 The identifiers or names of entire spaces may be set or read off
645 using the following functions.
647 #include <isl/space.h>
648 __isl_give isl_space *isl_space_set_tuple_id(
649 __isl_take isl_space *space,
650 enum isl_dim_type type, __isl_take isl_id *id);
651 __isl_give isl_space *isl_space_reset_tuple_id(
652 __isl_take isl_space *space, enum isl_dim_type type);
653 int isl_space_has_tuple_id(__isl_keep isl_space *space,
654 enum isl_dim_type type);
655 __isl_give isl_id *isl_space_get_tuple_id(
656 __isl_keep isl_space *space, enum isl_dim_type type);
657 __isl_give isl_space *isl_space_set_tuple_name(
658 __isl_take isl_space *space,
659 enum isl_dim_type type, const char *s);
660 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
661 enum isl_dim_type type);
663 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
664 or C<isl_dim_set>. As with C<isl_space_get_name>,
665 the C<isl_space_get_tuple_name> function returns a pointer to some internal
667 Binary operations require the corresponding spaces of their arguments
668 to have the same name.
670 Spaces can be nested. In particular, the domain of a set or
671 the domain or range of a relation can be a nested relation.
672 The following functions can be used to construct and deconstruct
675 #include <isl/space.h>
676 int isl_space_is_wrapping(__isl_keep isl_space *space);
677 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
678 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
680 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
681 be the space of a set, while that of
682 C<isl_space_wrap> should be the space of a relation.
683 Conversely, the output of C<isl_space_unwrap> is the space
684 of a relation, while that of C<isl_space_wrap> is the space of a set.
686 Spaces can be created from other spaces
687 using the following functions.
689 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
690 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
691 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
692 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
693 __isl_give isl_space *isl_space_params(
694 __isl_take isl_space *space);
695 __isl_give isl_space *isl_space_set_from_params(
696 __isl_take isl_space *space);
697 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
698 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
699 __isl_take isl_space *right);
700 __isl_give isl_space *isl_space_align_params(
701 __isl_take isl_space *space1, __isl_take isl_space *space2)
702 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
703 enum isl_dim_type type, unsigned pos, unsigned n);
704 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned n);
706 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned first, unsigned n);
708 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
709 enum isl_dim_type dst_type, unsigned dst_pos,
710 enum isl_dim_type src_type, unsigned src_pos,
712 __isl_give isl_space *isl_space_map_from_set(
713 __isl_take isl_space *space);
714 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
716 Note that if dimensions are added or removed from a space, then
717 the name and the internal structure are lost.
721 A local space is essentially a space with
722 zero or more existentially quantified variables.
723 The local space of a basic set or relation can be obtained
724 using the following functions.
727 __isl_give isl_local_space *isl_basic_set_get_local_space(
728 __isl_keep isl_basic_set *bset);
731 __isl_give isl_local_space *isl_basic_map_get_local_space(
732 __isl_keep isl_basic_map *bmap);
734 A new local space can be created from a space using
736 #include <isl/local_space.h>
737 __isl_give isl_local_space *isl_local_space_from_space(
738 __isl_take isl_space *space);
740 They can be inspected, copied and freed using the following functions.
742 #include <isl/local_space.h>
743 isl_ctx *isl_local_space_get_ctx(
744 __isl_keep isl_local_space *ls);
745 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
746 int isl_local_space_dim(__isl_keep isl_local_space *ls,
747 enum isl_dim_type type);
748 const char *isl_local_space_get_dim_name(
749 __isl_keep isl_local_space *ls,
750 enum isl_dim_type type, unsigned pos);
751 __isl_give isl_local_space *isl_local_space_set_dim_name(
752 __isl_take isl_local_space *ls,
753 enum isl_dim_type type, unsigned pos, const char *s);
754 __isl_give isl_space *isl_local_space_get_space(
755 __isl_keep isl_local_space *ls);
756 __isl_give isl_aff *isl_local_space_get_div(
757 __isl_keep isl_local_space *ls, int pos);
758 __isl_give isl_local_space *isl_local_space_copy(
759 __isl_keep isl_local_space *ls);
760 void *isl_local_space_free(__isl_take isl_local_space *ls);
762 Two local spaces can be compared using
764 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
765 __isl_keep isl_local_space *ls2);
767 Local spaces can be created from other local spaces
768 using the following functions.
770 __isl_give isl_local_space *isl_local_space_domain(
771 __isl_take isl_local_space *ls);
772 __isl_give isl_local_space *isl_local_space_from_domain(
773 __isl_take isl_local_space *ls);
774 __isl_give isl_local_space *isl_local_space_add_dims(
775 __isl_take isl_local_space *ls,
776 enum isl_dim_type type, unsigned n);
777 __isl_give isl_local_space *isl_local_space_insert_dims(
778 __isl_take isl_local_space *ls,
779 enum isl_dim_type type, unsigned first, unsigned n);
780 __isl_give isl_local_space *isl_local_space_drop_dims(
781 __isl_take isl_local_space *ls,
782 enum isl_dim_type type, unsigned first, unsigned n);
784 =head2 Input and Output
786 C<isl> supports its own input/output format, which is similar
787 to the C<Omega> format, but also supports the C<PolyLib> format
792 The C<isl> format is similar to that of C<Omega>, but has a different
793 syntax for describing the parameters and allows for the definition
794 of an existentially quantified variable as the integer division
795 of an affine expression.
796 For example, the set of integers C<i> between C<0> and C<n>
797 such that C<i % 10 <= 6> can be described as
799 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
802 A set or relation can have several disjuncts, separated
803 by the keyword C<or>. Each disjunct is either a conjunction
804 of constraints or a projection (C<exists>) of a conjunction
805 of constraints. The constraints are separated by the keyword
808 =head3 C<PolyLib> format
810 If the represented set is a union, then the first line
811 contains a single number representing the number of disjuncts.
812 Otherwise, a line containing the number C<1> is optional.
814 Each disjunct is represented by a matrix of constraints.
815 The first line contains two numbers representing
816 the number of rows and columns,
817 where the number of rows is equal to the number of constraints
818 and the number of columns is equal to two plus the number of variables.
819 The following lines contain the actual rows of the constraint matrix.
820 In each row, the first column indicates whether the constraint
821 is an equality (C<0>) or inequality (C<1>). The final column
822 corresponds to the constant term.
824 If the set is parametric, then the coefficients of the parameters
825 appear in the last columns before the constant column.
826 The coefficients of any existentially quantified variables appear
827 between those of the set variables and those of the parameters.
829 =head3 Extended C<PolyLib> format
831 The extended C<PolyLib> format is nearly identical to the
832 C<PolyLib> format. The only difference is that the line
833 containing the number of rows and columns of a constraint matrix
834 also contains four additional numbers:
835 the number of output dimensions, the number of input dimensions,
836 the number of local dimensions (i.e., the number of existentially
837 quantified variables) and the number of parameters.
838 For sets, the number of ``output'' dimensions is equal
839 to the number of set dimensions, while the number of ``input''
845 __isl_give isl_basic_set *isl_basic_set_read_from_file(
846 isl_ctx *ctx, FILE *input);
847 __isl_give isl_basic_set *isl_basic_set_read_from_str(
848 isl_ctx *ctx, const char *str);
849 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
851 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
855 __isl_give isl_basic_map *isl_basic_map_read_from_file(
856 isl_ctx *ctx, FILE *input);
857 __isl_give isl_basic_map *isl_basic_map_read_from_str(
858 isl_ctx *ctx, const char *str);
859 __isl_give isl_map *isl_map_read_from_file(
860 isl_ctx *ctx, FILE *input);
861 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
864 #include <isl/union_set.h>
865 __isl_give isl_union_set *isl_union_set_read_from_file(
866 isl_ctx *ctx, FILE *input);
867 __isl_give isl_union_set *isl_union_set_read_from_str(
868 isl_ctx *ctx, const char *str);
870 #include <isl/union_map.h>
871 __isl_give isl_union_map *isl_union_map_read_from_file(
872 isl_ctx *ctx, FILE *input);
873 __isl_give isl_union_map *isl_union_map_read_from_str(
874 isl_ctx *ctx, const char *str);
876 The input format is autodetected and may be either the C<PolyLib> format
877 or the C<isl> format.
881 Before anything can be printed, an C<isl_printer> needs to
884 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
886 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
887 void isl_printer_free(__isl_take isl_printer *printer);
888 __isl_give char *isl_printer_get_str(
889 __isl_keep isl_printer *printer);
891 The behavior of the printer can be modified in various ways
893 __isl_give isl_printer *isl_printer_set_output_format(
894 __isl_take isl_printer *p, int output_format);
895 __isl_give isl_printer *isl_printer_set_indent(
896 __isl_take isl_printer *p, int indent);
897 __isl_give isl_printer *isl_printer_indent(
898 __isl_take isl_printer *p, int indent);
899 __isl_give isl_printer *isl_printer_set_prefix(
900 __isl_take isl_printer *p, const char *prefix);
901 __isl_give isl_printer *isl_printer_set_suffix(
902 __isl_take isl_printer *p, const char *suffix);
904 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
905 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
906 and defaults to C<ISL_FORMAT_ISL>.
907 Each line in the output is indented by C<indent> (set by
908 C<isl_printer_set_indent>) spaces
909 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
910 In the C<PolyLib> format output,
911 the coefficients of the existentially quantified variables
912 appear between those of the set variables and those
914 The function C<isl_printer_indent> increases the indentation
915 by the specified amount (which may be negative).
917 To actually print something, use
920 __isl_give isl_printer *isl_printer_print_basic_set(
921 __isl_take isl_printer *printer,
922 __isl_keep isl_basic_set *bset);
923 __isl_give isl_printer *isl_printer_print_set(
924 __isl_take isl_printer *printer,
925 __isl_keep isl_set *set);
928 __isl_give isl_printer *isl_printer_print_basic_map(
929 __isl_take isl_printer *printer,
930 __isl_keep isl_basic_map *bmap);
931 __isl_give isl_printer *isl_printer_print_map(
932 __isl_take isl_printer *printer,
933 __isl_keep isl_map *map);
935 #include <isl/union_set.h>
936 __isl_give isl_printer *isl_printer_print_union_set(
937 __isl_take isl_printer *p,
938 __isl_keep isl_union_set *uset);
940 #include <isl/union_map.h>
941 __isl_give isl_printer *isl_printer_print_union_map(
942 __isl_take isl_printer *p,
943 __isl_keep isl_union_map *umap);
945 When called on a file printer, the following function flushes
946 the file. When called on a string printer, the buffer is cleared.
948 __isl_give isl_printer *isl_printer_flush(
949 __isl_take isl_printer *p);
951 =head2 Creating New Sets and Relations
953 C<isl> has functions for creating some standard sets and relations.
957 =item * Empty sets and relations
959 __isl_give isl_basic_set *isl_basic_set_empty(
960 __isl_take isl_space *space);
961 __isl_give isl_basic_map *isl_basic_map_empty(
962 __isl_take isl_space *space);
963 __isl_give isl_set *isl_set_empty(
964 __isl_take isl_space *space);
965 __isl_give isl_map *isl_map_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_union_set *isl_union_set_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_union_map *isl_union_map_empty(
970 __isl_take isl_space *space);
972 For C<isl_union_set>s and C<isl_union_map>s, the space
973 is only used to specify the parameters.
975 =item * Universe sets and relations
977 __isl_give isl_basic_set *isl_basic_set_universe(
978 __isl_take isl_space *space);
979 __isl_give isl_basic_map *isl_basic_map_universe(
980 __isl_take isl_space *space);
981 __isl_give isl_set *isl_set_universe(
982 __isl_take isl_space *space);
983 __isl_give isl_map *isl_map_universe(
984 __isl_take isl_space *space);
985 __isl_give isl_union_set *isl_union_set_universe(
986 __isl_take isl_union_set *uset);
987 __isl_give isl_union_map *isl_union_map_universe(
988 __isl_take isl_union_map *umap);
990 The sets and relations constructed by the functions above
991 contain all integer values, while those constructed by the
992 functions below only contain non-negative values.
994 __isl_give isl_basic_set *isl_basic_set_nat_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_nat_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_nat_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_nat_universe(
1001 __isl_take isl_space *space);
1003 =item * Identity relations
1005 __isl_give isl_basic_map *isl_basic_map_identity(
1006 __isl_take isl_space *space);
1007 __isl_give isl_map *isl_map_identity(
1008 __isl_take isl_space *space);
1010 The number of input and output dimensions in C<space> needs
1013 =item * Lexicographic order
1015 __isl_give isl_map *isl_map_lex_lt(
1016 __isl_take isl_space *set_space);
1017 __isl_give isl_map *isl_map_lex_le(
1018 __isl_take isl_space *set_space);
1019 __isl_give isl_map *isl_map_lex_gt(
1020 __isl_take isl_space *set_space);
1021 __isl_give isl_map *isl_map_lex_ge(
1022 __isl_take isl_space *set_space);
1023 __isl_give isl_map *isl_map_lex_lt_first(
1024 __isl_take isl_space *space, unsigned n);
1025 __isl_give isl_map *isl_map_lex_le_first(
1026 __isl_take isl_space *space, unsigned n);
1027 __isl_give isl_map *isl_map_lex_gt_first(
1028 __isl_take isl_space *space, unsigned n);
1029 __isl_give isl_map *isl_map_lex_ge_first(
1030 __isl_take isl_space *space, unsigned n);
1032 The first four functions take a space for a B<set>
1033 and return relations that express that the elements in the domain
1034 are lexicographically less
1035 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1036 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1037 than the elements in the range.
1038 The last four functions take a space for a map
1039 and return relations that express that the first C<n> dimensions
1040 in the domain are lexicographically less
1041 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1042 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1043 than the first C<n> dimensions in the range.
1047 A basic set or relation can be converted to a set or relation
1048 using the following functions.
1050 __isl_give isl_set *isl_set_from_basic_set(
1051 __isl_take isl_basic_set *bset);
1052 __isl_give isl_map *isl_map_from_basic_map(
1053 __isl_take isl_basic_map *bmap);
1055 Sets and relations can be converted to union sets and relations
1056 using the following functions.
1058 __isl_give isl_union_map *isl_union_map_from_map(
1059 __isl_take isl_map *map);
1060 __isl_give isl_union_set *isl_union_set_from_set(
1061 __isl_take isl_set *set);
1063 The inverse conversions below can only be used if the input
1064 union set or relation is known to contain elements in exactly one
1067 __isl_give isl_set *isl_set_from_union_set(
1068 __isl_take isl_union_set *uset);
1069 __isl_give isl_map *isl_map_from_union_map(
1070 __isl_take isl_union_map *umap);
1072 A zero-dimensional set can be constructed on a given parameter domain
1073 using the following function.
1075 __isl_give isl_set *isl_set_from_params(
1076 __isl_take isl_set *set);
1078 Sets and relations can be copied and freed again using the following
1081 __isl_give isl_basic_set *isl_basic_set_copy(
1082 __isl_keep isl_basic_set *bset);
1083 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1084 __isl_give isl_union_set *isl_union_set_copy(
1085 __isl_keep isl_union_set *uset);
1086 __isl_give isl_basic_map *isl_basic_map_copy(
1087 __isl_keep isl_basic_map *bmap);
1088 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1089 __isl_give isl_union_map *isl_union_map_copy(
1090 __isl_keep isl_union_map *umap);
1091 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1092 void isl_set_free(__isl_take isl_set *set);
1093 void *isl_union_set_free(__isl_take isl_union_set *uset);
1094 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1095 void isl_map_free(__isl_take isl_map *map);
1096 void *isl_union_map_free(__isl_take isl_union_map *umap);
1098 Other sets and relations can be constructed by starting
1099 from a universe set or relation, adding equality and/or
1100 inequality constraints and then projecting out the
1101 existentially quantified variables, if any.
1102 Constraints can be constructed, manipulated and
1103 added to (or removed from) (basic) sets and relations
1104 using the following functions.
1106 #include <isl/constraint.h>
1107 __isl_give isl_constraint *isl_equality_alloc(
1108 __isl_take isl_local_space *ls);
1109 __isl_give isl_constraint *isl_inequality_alloc(
1110 __isl_take isl_local_space *ls);
1111 __isl_give isl_constraint *isl_constraint_set_constant(
1112 __isl_take isl_constraint *constraint, isl_int v);
1113 __isl_give isl_constraint *isl_constraint_set_constant_si(
1114 __isl_take isl_constraint *constraint, int v);
1115 __isl_give isl_constraint *isl_constraint_set_coefficient(
1116 __isl_take isl_constraint *constraint,
1117 enum isl_dim_type type, int pos, isl_int v);
1118 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1119 __isl_take isl_constraint *constraint,
1120 enum isl_dim_type type, int pos, int v);
1121 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1122 __isl_take isl_basic_map *bmap,
1123 __isl_take isl_constraint *constraint);
1124 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1125 __isl_take isl_basic_set *bset,
1126 __isl_take isl_constraint *constraint);
1127 __isl_give isl_map *isl_map_add_constraint(
1128 __isl_take isl_map *map,
1129 __isl_take isl_constraint *constraint);
1130 __isl_give isl_set *isl_set_add_constraint(
1131 __isl_take isl_set *set,
1132 __isl_take isl_constraint *constraint);
1133 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1134 __isl_take isl_basic_set *bset,
1135 __isl_take isl_constraint *constraint);
1137 For example, to create a set containing the even integers
1138 between 10 and 42, you would use the following code.
1141 isl_local_space *ls;
1143 isl_basic_set *bset;
1145 space = isl_space_set_alloc(ctx, 0, 2);
1146 bset = isl_basic_set_universe(isl_space_copy(space));
1147 ls = isl_local_space_from_space(space);
1149 c = isl_equality_alloc(isl_local_space_copy(ls));
1150 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1151 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1152 bset = isl_basic_set_add_constraint(bset, c);
1154 c = isl_inequality_alloc(isl_local_space_copy(ls));
1155 c = isl_constraint_set_constant_si(c, -10);
1156 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1157 bset = isl_basic_set_add_constraint(bset, c);
1159 c = isl_inequality_alloc(ls);
1160 c = isl_constraint_set_constant_si(c, 42);
1161 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1162 bset = isl_basic_set_add_constraint(bset, c);
1164 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1168 isl_basic_set *bset;
1169 bset = isl_basic_set_read_from_str(ctx,
1170 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1172 A basic set or relation can also be constructed from two matrices
1173 describing the equalities and the inequalities.
1175 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1176 __isl_take isl_space *space,
1177 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1178 enum isl_dim_type c1,
1179 enum isl_dim_type c2, enum isl_dim_type c3,
1180 enum isl_dim_type c4);
1181 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1182 __isl_take isl_space *space,
1183 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1184 enum isl_dim_type c1,
1185 enum isl_dim_type c2, enum isl_dim_type c3,
1186 enum isl_dim_type c4, enum isl_dim_type c5);
1188 The C<isl_dim_type> arguments indicate the order in which
1189 different kinds of variables appear in the input matrices
1190 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1191 C<isl_dim_set> and C<isl_dim_div> for sets and
1192 of C<isl_dim_cst>, C<isl_dim_param>,
1193 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1195 A (basic) set or relation can also be constructed from a (piecewise)
1197 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1199 __isl_give isl_basic_map *isl_basic_map_from_aff(
1200 __isl_take isl_aff *aff);
1201 __isl_give isl_set *isl_set_from_pw_aff(
1202 __isl_take isl_pw_aff *pwaff);
1203 __isl_give isl_map *isl_map_from_pw_aff(
1204 __isl_take isl_pw_aff *pwaff);
1205 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1206 __isl_take isl_space *domain_space,
1207 __isl_take isl_aff_list *list);
1209 The C<domain_dim> argument describes the domain of the resulting
1210 basic relation. It is required because the C<list> may consist
1211 of zero affine expressions.
1213 =head2 Inspecting Sets and Relations
1215 Usually, the user should not have to care about the actual constraints
1216 of the sets and maps, but should instead apply the abstract operations
1217 explained in the following sections.
1218 Occasionally, however, it may be required to inspect the individual
1219 coefficients of the constraints. This section explains how to do so.
1220 In these cases, it may also be useful to have C<isl> compute
1221 an explicit representation of the existentially quantified variables.
1223 __isl_give isl_set *isl_set_compute_divs(
1224 __isl_take isl_set *set);
1225 __isl_give isl_map *isl_map_compute_divs(
1226 __isl_take isl_map *map);
1227 __isl_give isl_union_set *isl_union_set_compute_divs(
1228 __isl_take isl_union_set *uset);
1229 __isl_give isl_union_map *isl_union_map_compute_divs(
1230 __isl_take isl_union_map *umap);
1232 This explicit representation defines the existentially quantified
1233 variables as integer divisions of the other variables, possibly
1234 including earlier existentially quantified variables.
1235 An explicitly represented existentially quantified variable therefore
1236 has a unique value when the values of the other variables are known.
1237 If, furthermore, the same existentials, i.e., existentials
1238 with the same explicit representations, should appear in the
1239 same order in each of the disjuncts of a set or map, then the user should call
1240 either of the following functions.
1242 __isl_give isl_set *isl_set_align_divs(
1243 __isl_take isl_set *set);
1244 __isl_give isl_map *isl_map_align_divs(
1245 __isl_take isl_map *map);
1247 Alternatively, the existentially quantified variables can be removed
1248 using the following functions, which compute an overapproximation.
1250 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1251 __isl_take isl_basic_set *bset);
1252 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1253 __isl_take isl_basic_map *bmap);
1254 __isl_give isl_set *isl_set_remove_divs(
1255 __isl_take isl_set *set);
1256 __isl_give isl_map *isl_map_remove_divs(
1257 __isl_take isl_map *map);
1259 To iterate over all the sets or maps in a union set or map, use
1261 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1262 int (*fn)(__isl_take isl_set *set, void *user),
1264 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1265 int (*fn)(__isl_take isl_map *map, void *user),
1268 The number of sets or maps in a union set or map can be obtained
1271 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1272 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1274 To extract the set or map in a given space from a union, use
1276 __isl_give isl_set *isl_union_set_extract_set(
1277 __isl_keep isl_union_set *uset,
1278 __isl_take isl_space *space);
1279 __isl_give isl_map *isl_union_map_extract_map(
1280 __isl_keep isl_union_map *umap,
1281 __isl_take isl_space *space);
1283 To iterate over all the basic sets or maps in a set or map, use
1285 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1286 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1288 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1289 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1292 The callback function C<fn> should return 0 if successful and
1293 -1 if an error occurs. In the latter case, or if any other error
1294 occurs, the above functions will return -1.
1296 It should be noted that C<isl> does not guarantee that
1297 the basic sets or maps passed to C<fn> are disjoint.
1298 If this is required, then the user should call one of
1299 the following functions first.
1301 __isl_give isl_set *isl_set_make_disjoint(
1302 __isl_take isl_set *set);
1303 __isl_give isl_map *isl_map_make_disjoint(
1304 __isl_take isl_map *map);
1306 The number of basic sets in a set can be obtained
1309 int isl_set_n_basic_set(__isl_keep isl_set *set);
1311 To iterate over the constraints of a basic set or map, use
1313 #include <isl/constraint.h>
1315 int isl_basic_map_foreach_constraint(
1316 __isl_keep isl_basic_map *bmap,
1317 int (*fn)(__isl_take isl_constraint *c, void *user),
1319 void *isl_constraint_free(__isl_take isl_constraint *c);
1321 Again, the callback function C<fn> should return 0 if successful and
1322 -1 if an error occurs. In the latter case, or if any other error
1323 occurs, the above functions will return -1.
1324 The constraint C<c> represents either an equality or an inequality.
1325 Use the following function to find out whether a constraint
1326 represents an equality. If not, it represents an inequality.
1328 int isl_constraint_is_equality(
1329 __isl_keep isl_constraint *constraint);
1331 The coefficients of the constraints can be inspected using
1332 the following functions.
1334 void isl_constraint_get_constant(
1335 __isl_keep isl_constraint *constraint, isl_int *v);
1336 void isl_constraint_get_coefficient(
1337 __isl_keep isl_constraint *constraint,
1338 enum isl_dim_type type, int pos, isl_int *v);
1339 int isl_constraint_involves_dims(
1340 __isl_keep isl_constraint *constraint,
1341 enum isl_dim_type type, unsigned first, unsigned n);
1343 The explicit representations of the existentially quantified
1344 variables can be inspected using the following function.
1345 Note that the user is only allowed to use this function
1346 if the inspected set or map is the result of a call
1347 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1348 The existentially quantified variable is equal to the floor
1349 of the returned affine expression. The affine expression
1350 itself can be inspected using the functions in
1351 L<"Piecewise Quasi Affine Expressions">.
1353 __isl_give isl_aff *isl_constraint_get_div(
1354 __isl_keep isl_constraint *constraint, int pos);
1356 To obtain the constraints of a basic set or map in matrix
1357 form, use the following functions.
1359 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1360 __isl_keep isl_basic_set *bset,
1361 enum isl_dim_type c1, enum isl_dim_type c2,
1362 enum isl_dim_type c3, enum isl_dim_type c4);
1363 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1364 __isl_keep isl_basic_set *bset,
1365 enum isl_dim_type c1, enum isl_dim_type c2,
1366 enum isl_dim_type c3, enum isl_dim_type c4);
1367 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1368 __isl_keep isl_basic_map *bmap,
1369 enum isl_dim_type c1,
1370 enum isl_dim_type c2, enum isl_dim_type c3,
1371 enum isl_dim_type c4, enum isl_dim_type c5);
1372 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1373 __isl_keep isl_basic_map *bmap,
1374 enum isl_dim_type c1,
1375 enum isl_dim_type c2, enum isl_dim_type c3,
1376 enum isl_dim_type c4, enum isl_dim_type c5);
1378 The C<isl_dim_type> arguments dictate the order in which
1379 different kinds of variables appear in the resulting matrix
1380 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1381 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1383 The number of parameters, input, output or set dimensions can
1384 be obtained using the following functions.
1386 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1387 enum isl_dim_type type);
1388 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1389 enum isl_dim_type type);
1390 unsigned isl_set_dim(__isl_keep isl_set *set,
1391 enum isl_dim_type type);
1392 unsigned isl_map_dim(__isl_keep isl_map *map,
1393 enum isl_dim_type type);
1395 To check whether the description of a set or relation depends
1396 on one or more given dimensions, it is not necessary to iterate over all
1397 constraints. Instead the following functions can be used.
1399 int isl_basic_set_involves_dims(
1400 __isl_keep isl_basic_set *bset,
1401 enum isl_dim_type type, unsigned first, unsigned n);
1402 int isl_set_involves_dims(__isl_keep isl_set *set,
1403 enum isl_dim_type type, unsigned first, unsigned n);
1404 int isl_basic_map_involves_dims(
1405 __isl_keep isl_basic_map *bmap,
1406 enum isl_dim_type type, unsigned first, unsigned n);
1407 int isl_map_involves_dims(__isl_keep isl_map *map,
1408 enum isl_dim_type type, unsigned first, unsigned n);
1410 Similarly, the following functions can be used to check whether
1411 a given dimension is involved in any lower or upper bound.
1413 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1414 enum isl_dim_type type, unsigned pos);
1415 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1416 enum isl_dim_type type, unsigned pos);
1418 The identifiers or names of the domain and range spaces of a set
1419 or relation can be read off or set using the following functions.
1421 __isl_give isl_set *isl_set_set_tuple_id(
1422 __isl_take isl_set *set, __isl_take isl_id *id);
1423 __isl_give isl_set *isl_set_reset_tuple_id(
1424 __isl_take isl_set *set);
1425 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1426 __isl_give isl_id *isl_set_get_tuple_id(
1427 __isl_keep isl_set *set);
1428 __isl_give isl_map *isl_map_set_tuple_id(
1429 __isl_take isl_map *map, enum isl_dim_type type,
1430 __isl_take isl_id *id);
1431 __isl_give isl_map *isl_map_reset_tuple_id(
1432 __isl_take isl_map *map, enum isl_dim_type type);
1433 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1434 enum isl_dim_type type);
1435 __isl_give isl_id *isl_map_get_tuple_id(
1436 __isl_keep isl_map *map, enum isl_dim_type type);
1438 const char *isl_basic_set_get_tuple_name(
1439 __isl_keep isl_basic_set *bset);
1440 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1441 __isl_take isl_basic_set *set, const char *s);
1442 const char *isl_set_get_tuple_name(
1443 __isl_keep isl_set *set);
1444 const char *isl_basic_map_get_tuple_name(
1445 __isl_keep isl_basic_map *bmap,
1446 enum isl_dim_type type);
1447 const char *isl_map_get_tuple_name(
1448 __isl_keep isl_map *map,
1449 enum isl_dim_type type);
1451 As with C<isl_space_get_tuple_name>, the value returned points to
1452 an internal data structure.
1453 The identifiers, positions or names of individual dimensions can be
1454 read off using the following functions.
1456 __isl_give isl_set *isl_set_set_dim_id(
1457 __isl_take isl_set *set, enum isl_dim_type type,
1458 unsigned pos, __isl_take isl_id *id);
1459 int isl_set_has_dim_id(__isl_keep isl_set *set,
1460 enum isl_dim_type type, unsigned pos);
1461 __isl_give isl_id *isl_set_get_dim_id(
1462 __isl_keep isl_set *set, enum isl_dim_type type,
1464 __isl_give isl_map *isl_map_set_dim_id(
1465 __isl_take isl_map *map, enum isl_dim_type type,
1466 unsigned pos, __isl_take isl_id *id);
1467 int isl_map_has_dim_id(__isl_keep isl_map *map,
1468 enum isl_dim_type type, unsigned pos);
1469 __isl_give isl_id *isl_map_get_dim_id(
1470 __isl_keep isl_map *map, enum isl_dim_type type,
1473 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1474 enum isl_dim_type type, __isl_keep isl_id *id);
1475 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1476 enum isl_dim_type type, __isl_keep isl_id *id);
1478 const char *isl_constraint_get_dim_name(
1479 __isl_keep isl_constraint *constraint,
1480 enum isl_dim_type type, unsigned pos);
1481 const char *isl_basic_set_get_dim_name(
1482 __isl_keep isl_basic_set *bset,
1483 enum isl_dim_type type, unsigned pos);
1484 const char *isl_set_get_dim_name(
1485 __isl_keep isl_set *set,
1486 enum isl_dim_type type, unsigned pos);
1487 const char *isl_basic_map_get_dim_name(
1488 __isl_keep isl_basic_map *bmap,
1489 enum isl_dim_type type, unsigned pos);
1490 const char *isl_map_get_dim_name(
1491 __isl_keep isl_map *map,
1492 enum isl_dim_type type, unsigned pos);
1494 These functions are mostly useful to obtain the identifiers, positions
1495 or names of the parameters. Identifiers of individual dimensions are
1496 essentially only useful for printing. They are ignored by all other
1497 operations and may not be preserved across those operations.
1501 =head3 Unary Properties
1507 The following functions test whether the given set or relation
1508 contains any integer points. The ``plain'' variants do not perform
1509 any computations, but simply check if the given set or relation
1510 is already known to be empty.
1512 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1513 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1514 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1515 int isl_set_is_empty(__isl_keep isl_set *set);
1516 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1517 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1518 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1519 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1520 int isl_map_is_empty(__isl_keep isl_map *map);
1521 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1523 =item * Universality
1525 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1526 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1527 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1529 =item * Single-valuedness
1531 int isl_map_is_single_valued(__isl_keep isl_map *map);
1532 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1536 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1537 int isl_map_is_injective(__isl_keep isl_map *map);
1538 int isl_union_map_plain_is_injective(
1539 __isl_keep isl_union_map *umap);
1540 int isl_union_map_is_injective(
1541 __isl_keep isl_union_map *umap);
1545 int isl_map_is_bijective(__isl_keep isl_map *map);
1546 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1550 int isl_basic_map_plain_is_fixed(
1551 __isl_keep isl_basic_map *bmap,
1552 enum isl_dim_type type, unsigned pos,
1554 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1555 enum isl_dim_type type, unsigned pos,
1558 Check if the relation obviously lies on a hyperplane where the given dimension
1559 has a fixed value and if so, return that value in C<*val>.
1563 To check whether a set is a parameter domain, use this function:
1565 int isl_set_is_params(__isl_keep isl_set *set);
1569 The following functions check whether the domain of the given
1570 (basic) set is a wrapped relation.
1572 int isl_basic_set_is_wrapping(
1573 __isl_keep isl_basic_set *bset);
1574 int isl_set_is_wrapping(__isl_keep isl_set *set);
1576 =item * Internal Product
1578 int isl_basic_map_can_zip(
1579 __isl_keep isl_basic_map *bmap);
1580 int isl_map_can_zip(__isl_keep isl_map *map);
1582 Check whether the product of domain and range of the given relation
1584 i.e., whether both domain and range are nested relations.
1588 =head3 Binary Properties
1594 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1595 __isl_keep isl_set *set2);
1596 int isl_set_is_equal(__isl_keep isl_set *set1,
1597 __isl_keep isl_set *set2);
1598 int isl_union_set_is_equal(
1599 __isl_keep isl_union_set *uset1,
1600 __isl_keep isl_union_set *uset2);
1601 int isl_basic_map_is_equal(
1602 __isl_keep isl_basic_map *bmap1,
1603 __isl_keep isl_basic_map *bmap2);
1604 int isl_map_is_equal(__isl_keep isl_map *map1,
1605 __isl_keep isl_map *map2);
1606 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1607 __isl_keep isl_map *map2);
1608 int isl_union_map_is_equal(
1609 __isl_keep isl_union_map *umap1,
1610 __isl_keep isl_union_map *umap2);
1612 =item * Disjointness
1614 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1615 __isl_keep isl_set *set2);
1619 int isl_set_is_subset(__isl_keep isl_set *set1,
1620 __isl_keep isl_set *set2);
1621 int isl_set_is_strict_subset(
1622 __isl_keep isl_set *set1,
1623 __isl_keep isl_set *set2);
1624 int isl_union_set_is_subset(
1625 __isl_keep isl_union_set *uset1,
1626 __isl_keep isl_union_set *uset2);
1627 int isl_union_set_is_strict_subset(
1628 __isl_keep isl_union_set *uset1,
1629 __isl_keep isl_union_set *uset2);
1630 int isl_basic_map_is_subset(
1631 __isl_keep isl_basic_map *bmap1,
1632 __isl_keep isl_basic_map *bmap2);
1633 int isl_basic_map_is_strict_subset(
1634 __isl_keep isl_basic_map *bmap1,
1635 __isl_keep isl_basic_map *bmap2);
1636 int isl_map_is_subset(
1637 __isl_keep isl_map *map1,
1638 __isl_keep isl_map *map2);
1639 int isl_map_is_strict_subset(
1640 __isl_keep isl_map *map1,
1641 __isl_keep isl_map *map2);
1642 int isl_union_map_is_subset(
1643 __isl_keep isl_union_map *umap1,
1644 __isl_keep isl_union_map *umap2);
1645 int isl_union_map_is_strict_subset(
1646 __isl_keep isl_union_map *umap1,
1647 __isl_keep isl_union_map *umap2);
1651 =head2 Unary Operations
1657 __isl_give isl_set *isl_set_complement(
1658 __isl_take isl_set *set);
1662 __isl_give isl_basic_map *isl_basic_map_reverse(
1663 __isl_take isl_basic_map *bmap);
1664 __isl_give isl_map *isl_map_reverse(
1665 __isl_take isl_map *map);
1666 __isl_give isl_union_map *isl_union_map_reverse(
1667 __isl_take isl_union_map *umap);
1671 __isl_give isl_basic_set *isl_basic_set_project_out(
1672 __isl_take isl_basic_set *bset,
1673 enum isl_dim_type type, unsigned first, unsigned n);
1674 __isl_give isl_basic_map *isl_basic_map_project_out(
1675 __isl_take isl_basic_map *bmap,
1676 enum isl_dim_type type, unsigned first, unsigned n);
1677 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1678 enum isl_dim_type type, unsigned first, unsigned n);
1679 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1680 enum isl_dim_type type, unsigned first, unsigned n);
1681 __isl_give isl_basic_set *isl_basic_set_params(
1682 __isl_take isl_basic_set *bset);
1683 __isl_give isl_basic_set *isl_basic_map_domain(
1684 __isl_take isl_basic_map *bmap);
1685 __isl_give isl_basic_set *isl_basic_map_range(
1686 __isl_take isl_basic_map *bmap);
1687 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1688 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1689 __isl_give isl_set *isl_map_domain(
1690 __isl_take isl_map *bmap);
1691 __isl_give isl_set *isl_map_range(
1692 __isl_take isl_map *map);
1693 __isl_give isl_union_set *isl_union_map_domain(
1694 __isl_take isl_union_map *umap);
1695 __isl_give isl_union_set *isl_union_map_range(
1696 __isl_take isl_union_map *umap);
1698 __isl_give isl_basic_map *isl_basic_map_domain_map(
1699 __isl_take isl_basic_map *bmap);
1700 __isl_give isl_basic_map *isl_basic_map_range_map(
1701 __isl_take isl_basic_map *bmap);
1702 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1703 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1704 __isl_give isl_union_map *isl_union_map_domain_map(
1705 __isl_take isl_union_map *umap);
1706 __isl_give isl_union_map *isl_union_map_range_map(
1707 __isl_take isl_union_map *umap);
1709 The functions above construct a (basic, regular or union) relation
1710 that maps (a wrapped version of) the input relation to its domain or range.
1714 __isl_give isl_set *isl_set_eliminate(
1715 __isl_take isl_set *set, enum isl_dim_type type,
1716 unsigned first, unsigned n);
1718 Eliminate the coefficients for the given dimensions from the constraints,
1719 without removing the dimensions.
1723 __isl_give isl_basic_set *isl_basic_set_fix(
1724 __isl_take isl_basic_set *bset,
1725 enum isl_dim_type type, unsigned pos,
1727 __isl_give isl_basic_set *isl_basic_set_fix_si(
1728 __isl_take isl_basic_set *bset,
1729 enum isl_dim_type type, unsigned pos, int value);
1730 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1731 enum isl_dim_type type, unsigned pos,
1733 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1734 enum isl_dim_type type, unsigned pos, int value);
1735 __isl_give isl_basic_map *isl_basic_map_fix_si(
1736 __isl_take isl_basic_map *bmap,
1737 enum isl_dim_type type, unsigned pos, int value);
1738 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1739 enum isl_dim_type type, unsigned pos, int value);
1741 Intersect the set or relation with the hyperplane where the given
1742 dimension has the fixed given value.
1744 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1745 enum isl_dim_type type1, int pos1,
1746 enum isl_dim_type type2, int pos2);
1747 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1748 enum isl_dim_type type1, int pos1,
1749 enum isl_dim_type type2, int pos2);
1751 Intersect the set or relation with the hyperplane where the given
1752 dimensions are equal to each other.
1754 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1755 enum isl_dim_type type1, int pos1,
1756 enum isl_dim_type type2, int pos2);
1758 Intersect the relation with the hyperplane where the given
1759 dimensions have opposite values.
1763 __isl_give isl_map *isl_set_identity(
1764 __isl_take isl_set *set);
1765 __isl_give isl_union_map *isl_union_set_identity(
1766 __isl_take isl_union_set *uset);
1768 Construct an identity relation on the given (union) set.
1772 __isl_give isl_basic_set *isl_basic_map_deltas(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1775 __isl_give isl_union_set *isl_union_map_deltas(
1776 __isl_take isl_union_map *umap);
1778 These functions return a (basic) set containing the differences
1779 between image elements and corresponding domain elements in the input.
1781 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1782 __isl_take isl_basic_map *bmap);
1783 __isl_give isl_map *isl_map_deltas_map(
1784 __isl_take isl_map *map);
1785 __isl_give isl_union_map *isl_union_map_deltas_map(
1786 __isl_take isl_union_map *umap);
1788 The functions above construct a (basic, regular or union) relation
1789 that maps (a wrapped version of) the input relation to its delta set.
1793 Simplify the representation of a set or relation by trying
1794 to combine pairs of basic sets or relations into a single
1795 basic set or relation.
1797 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1798 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1799 __isl_give isl_union_set *isl_union_set_coalesce(
1800 __isl_take isl_union_set *uset);
1801 __isl_give isl_union_map *isl_union_map_coalesce(
1802 __isl_take isl_union_map *umap);
1804 =item * Detecting equalities
1806 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1807 __isl_take isl_basic_set *bset);
1808 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1809 __isl_take isl_basic_map *bmap);
1810 __isl_give isl_set *isl_set_detect_equalities(
1811 __isl_take isl_set *set);
1812 __isl_give isl_map *isl_map_detect_equalities(
1813 __isl_take isl_map *map);
1814 __isl_give isl_union_set *isl_union_set_detect_equalities(
1815 __isl_take isl_union_set *uset);
1816 __isl_give isl_union_map *isl_union_map_detect_equalities(
1817 __isl_take isl_union_map *umap);
1819 Simplify the representation of a set or relation by detecting implicit
1822 =item * Removing redundant constraints
1824 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1825 __isl_take isl_basic_set *bset);
1826 __isl_give isl_set *isl_set_remove_redundancies(
1827 __isl_take isl_set *set);
1828 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_give isl_map *isl_map_remove_redundancies(
1831 __isl_take isl_map *map);
1835 __isl_give isl_basic_set *isl_set_convex_hull(
1836 __isl_take isl_set *set);
1837 __isl_give isl_basic_map *isl_map_convex_hull(
1838 __isl_take isl_map *map);
1840 If the input set or relation has any existentially quantified
1841 variables, then the result of these operations is currently undefined.
1845 __isl_give isl_basic_set *isl_set_simple_hull(
1846 __isl_take isl_set *set);
1847 __isl_give isl_basic_map *isl_map_simple_hull(
1848 __isl_take isl_map *map);
1849 __isl_give isl_union_map *isl_union_map_simple_hull(
1850 __isl_take isl_union_map *umap);
1852 These functions compute a single basic set or relation
1853 that contains the whole input set or relation.
1854 In particular, the output is described by translates
1855 of the constraints describing the basic sets or relations in the input.
1859 (See \autoref{s:simple hull}.)
1865 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1866 __isl_take isl_basic_set *bset);
1867 __isl_give isl_basic_set *isl_set_affine_hull(
1868 __isl_take isl_set *set);
1869 __isl_give isl_union_set *isl_union_set_affine_hull(
1870 __isl_take isl_union_set *uset);
1871 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1872 __isl_take isl_basic_map *bmap);
1873 __isl_give isl_basic_map *isl_map_affine_hull(
1874 __isl_take isl_map *map);
1875 __isl_give isl_union_map *isl_union_map_affine_hull(
1876 __isl_take isl_union_map *umap);
1878 In case of union sets and relations, the affine hull is computed
1881 =item * Polyhedral hull
1883 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1884 __isl_take isl_set *set);
1885 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1886 __isl_take isl_map *map);
1887 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1888 __isl_take isl_union_set *uset);
1889 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1890 __isl_take isl_union_map *umap);
1892 These functions compute a single basic set or relation
1893 not involving any existentially quantified variables
1894 that contains the whole input set or relation.
1895 In case of union sets and relations, the polyhedral hull is computed
1898 =item * Optimization
1900 #include <isl/ilp.h>
1901 enum isl_lp_result isl_basic_set_max(
1902 __isl_keep isl_basic_set *bset,
1903 __isl_keep isl_aff *obj, isl_int *opt)
1904 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1905 __isl_keep isl_aff *obj, isl_int *opt);
1906 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1907 __isl_keep isl_aff *obj, isl_int *opt);
1909 Compute the minimum or maximum of the integer affine expression C<obj>
1910 over the points in C<set>, returning the result in C<opt>.
1911 The return value may be one of C<isl_lp_error>,
1912 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1914 =item * Parametric optimization
1916 __isl_give isl_pw_aff *isl_set_dim_min(
1917 __isl_take isl_set *set, int pos);
1918 __isl_give isl_pw_aff *isl_set_dim_max(
1919 __isl_take isl_set *set, int pos);
1921 Compute the minimum or maximum of the given set dimension as a function of the
1922 parameters, but independently of the other set dimensions.
1923 For lexicographic optimization, see L<"Lexicographic Optimization">.
1927 The following functions compute either the set of (rational) coefficient
1928 values of valid constraints for the given set or the set of (rational)
1929 values satisfying the constraints with coefficients from the given set.
1930 Internally, these two sets of functions perform essentially the
1931 same operations, except that the set of coefficients is assumed to
1932 be a cone, while the set of values may be any polyhedron.
1933 The current implementation is based on the Farkas lemma and
1934 Fourier-Motzkin elimination, but this may change or be made optional
1935 in future. In particular, future implementations may use different
1936 dualization algorithms or skip the elimination step.
1938 __isl_give isl_basic_set *isl_basic_set_coefficients(
1939 __isl_take isl_basic_set *bset);
1940 __isl_give isl_basic_set *isl_set_coefficients(
1941 __isl_take isl_set *set);
1942 __isl_give isl_union_set *isl_union_set_coefficients(
1943 __isl_take isl_union_set *bset);
1944 __isl_give isl_basic_set *isl_basic_set_solutions(
1945 __isl_take isl_basic_set *bset);
1946 __isl_give isl_basic_set *isl_set_solutions(
1947 __isl_take isl_set *set);
1948 __isl_give isl_union_set *isl_union_set_solutions(
1949 __isl_take isl_union_set *bset);
1953 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1955 __isl_give isl_union_map *isl_union_map_power(
1956 __isl_take isl_union_map *umap, int *exact);
1958 Compute a parametric representation for all positive powers I<k> of C<map>.
1959 The result maps I<k> to a nested relation corresponding to the
1960 I<k>th power of C<map>.
1961 The result may be an overapproximation. If the result is known to be exact,
1962 then C<*exact> is set to C<1>.
1964 =item * Transitive closure
1966 __isl_give isl_map *isl_map_transitive_closure(
1967 __isl_take isl_map *map, int *exact);
1968 __isl_give isl_union_map *isl_union_map_transitive_closure(
1969 __isl_take isl_union_map *umap, int *exact);
1971 Compute the transitive closure of C<map>.
1972 The result may be an overapproximation. If the result is known to be exact,
1973 then C<*exact> is set to C<1>.
1975 =item * Reaching path lengths
1977 __isl_give isl_map *isl_map_reaching_path_lengths(
1978 __isl_take isl_map *map, int *exact);
1980 Compute a relation that maps each element in the range of C<map>
1981 to the lengths of all paths composed of edges in C<map> that
1982 end up in the given element.
1983 The result may be an overapproximation. If the result is known to be exact,
1984 then C<*exact> is set to C<1>.
1985 To compute the I<maximal> path length, the resulting relation
1986 should be postprocessed by C<isl_map_lexmax>.
1987 In particular, if the input relation is a dependence relation
1988 (mapping sources to sinks), then the maximal path length corresponds
1989 to the free schedule.
1990 Note, however, that C<isl_map_lexmax> expects the maximum to be
1991 finite, so if the path lengths are unbounded (possibly due to
1992 the overapproximation), then you will get an error message.
1996 __isl_give isl_basic_set *isl_basic_map_wrap(
1997 __isl_take isl_basic_map *bmap);
1998 __isl_give isl_set *isl_map_wrap(
1999 __isl_take isl_map *map);
2000 __isl_give isl_union_set *isl_union_map_wrap(
2001 __isl_take isl_union_map *umap);
2002 __isl_give isl_basic_map *isl_basic_set_unwrap(
2003 __isl_take isl_basic_set *bset);
2004 __isl_give isl_map *isl_set_unwrap(
2005 __isl_take isl_set *set);
2006 __isl_give isl_union_map *isl_union_set_unwrap(
2007 __isl_take isl_union_set *uset);
2011 Remove any internal structure of domain (and range) of the given
2012 set or relation. If there is any such internal structure in the input,
2013 then the name of the space is also removed.
2015 __isl_give isl_basic_set *isl_basic_set_flatten(
2016 __isl_take isl_basic_set *bset);
2017 __isl_give isl_set *isl_set_flatten(
2018 __isl_take isl_set *set);
2019 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2020 __isl_take isl_basic_map *bmap);
2021 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2022 __isl_take isl_basic_map *bmap);
2023 __isl_give isl_map *isl_map_flatten_range(
2024 __isl_take isl_map *map);
2025 __isl_give isl_map *isl_map_flatten_domain(
2026 __isl_take isl_map *map);
2027 __isl_give isl_basic_map *isl_basic_map_flatten(
2028 __isl_take isl_basic_map *bmap);
2029 __isl_give isl_map *isl_map_flatten(
2030 __isl_take isl_map *map);
2032 __isl_give isl_map *isl_set_flatten_map(
2033 __isl_take isl_set *set);
2035 The function above constructs a relation
2036 that maps the input set to a flattened version of the set.
2040 Lift the input set to a space with extra dimensions corresponding
2041 to the existentially quantified variables in the input.
2042 In particular, the result lives in a wrapped map where the domain
2043 is the original space and the range corresponds to the original
2044 existentially quantified variables.
2046 __isl_give isl_basic_set *isl_basic_set_lift(
2047 __isl_take isl_basic_set *bset);
2048 __isl_give isl_set *isl_set_lift(
2049 __isl_take isl_set *set);
2050 __isl_give isl_union_set *isl_union_set_lift(
2051 __isl_take isl_union_set *uset);
2053 =item * Internal Product
2055 __isl_give isl_basic_map *isl_basic_map_zip(
2056 __isl_take isl_basic_map *bmap);
2057 __isl_give isl_map *isl_map_zip(
2058 __isl_take isl_map *map);
2059 __isl_give isl_union_map *isl_union_map_zip(
2060 __isl_take isl_union_map *umap);
2062 Given a relation with nested relations for domain and range,
2063 interchange the range of the domain with the domain of the range.
2065 =item * Aligning parameters
2067 __isl_give isl_set *isl_set_align_params(
2068 __isl_take isl_set *set,
2069 __isl_take isl_space *model);
2070 __isl_give isl_map *isl_map_align_params(
2071 __isl_take isl_map *map,
2072 __isl_take isl_space *model);
2074 Change the order of the parameters of the given set or relation
2075 such that the first parameters match those of C<model>.
2076 This may involve the introduction of extra parameters.
2077 All parameters need to be named.
2079 =item * Dimension manipulation
2081 __isl_give isl_set *isl_set_add_dims(
2082 __isl_take isl_set *set,
2083 enum isl_dim_type type, unsigned n);
2084 __isl_give isl_map *isl_map_add_dims(
2085 __isl_take isl_map *map,
2086 enum isl_dim_type type, unsigned n);
2087 __isl_give isl_set *isl_set_insert_dims(
2088 __isl_take isl_set *set,
2089 enum isl_dim_type type, unsigned pos, unsigned n);
2090 __isl_give isl_map *isl_map_insert_dims(
2091 __isl_take isl_map *map,
2092 enum isl_dim_type type, unsigned pos, unsigned n);
2093 __isl_give isl_basic_set *isl_basic_set_move_dims(
2094 __isl_take isl_basic_set *bset,
2095 enum isl_dim_type dst_type, unsigned dst_pos,
2096 enum isl_dim_type src_type, unsigned src_pos,
2098 __isl_give isl_basic_map *isl_basic_map_move_dims(
2099 __isl_take isl_basic_map *bmap,
2100 enum isl_dim_type dst_type, unsigned dst_pos,
2101 enum isl_dim_type src_type, unsigned src_pos,
2103 __isl_give isl_set *isl_set_move_dims(
2104 __isl_take isl_set *set,
2105 enum isl_dim_type dst_type, unsigned dst_pos,
2106 enum isl_dim_type src_type, unsigned src_pos,
2108 __isl_give isl_map *isl_map_move_dims(
2109 __isl_take isl_map *map,
2110 enum isl_dim_type dst_type, unsigned dst_pos,
2111 enum isl_dim_type src_type, unsigned src_pos,
2114 It is usually not advisable to directly change the (input or output)
2115 space of a set or a relation as this removes the name and the internal
2116 structure of the space. However, the above functions can be useful
2117 to add new parameters, assuming
2118 C<isl_set_align_params> and C<isl_map_align_params>
2123 =head2 Binary Operations
2125 The two arguments of a binary operation not only need to live
2126 in the same C<isl_ctx>, they currently also need to have
2127 the same (number of) parameters.
2129 =head3 Basic Operations
2133 =item * Intersection
2135 __isl_give isl_basic_set *isl_basic_set_intersect(
2136 __isl_take isl_basic_set *bset1,
2137 __isl_take isl_basic_set *bset2);
2138 __isl_give isl_set *isl_set_intersect_params(
2139 __isl_take isl_set *set,
2140 __isl_take isl_set *params);
2141 __isl_give isl_set *isl_set_intersect(
2142 __isl_take isl_set *set1,
2143 __isl_take isl_set *set2);
2144 __isl_give isl_union_set *isl_union_set_intersect(
2145 __isl_take isl_union_set *uset1,
2146 __isl_take isl_union_set *uset2);
2147 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2148 __isl_take isl_basic_map *bmap,
2149 __isl_take isl_basic_set *bset);
2150 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2151 __isl_take isl_basic_map *bmap,
2152 __isl_take isl_basic_set *bset);
2153 __isl_give isl_basic_map *isl_basic_map_intersect(
2154 __isl_take isl_basic_map *bmap1,
2155 __isl_take isl_basic_map *bmap2);
2156 __isl_give isl_map *isl_map_intersect_params(
2157 __isl_take isl_map *map,
2158 __isl_take isl_set *params);
2159 __isl_give isl_map *isl_map_intersect_domain(
2160 __isl_take isl_map *map,
2161 __isl_take isl_set *set);
2162 __isl_give isl_map *isl_map_intersect_range(
2163 __isl_take isl_map *map,
2164 __isl_take isl_set *set);
2165 __isl_give isl_map *isl_map_intersect(
2166 __isl_take isl_map *map1,
2167 __isl_take isl_map *map2);
2168 __isl_give isl_union_map *isl_union_map_intersect_domain(
2169 __isl_take isl_union_map *umap,
2170 __isl_take isl_union_set *uset);
2171 __isl_give isl_union_map *isl_union_map_intersect_range(
2172 __isl_take isl_union_map *umap,
2173 __isl_take isl_union_set *uset);
2174 __isl_give isl_union_map *isl_union_map_intersect(
2175 __isl_take isl_union_map *umap1,
2176 __isl_take isl_union_map *umap2);
2180 __isl_give isl_set *isl_basic_set_union(
2181 __isl_take isl_basic_set *bset1,
2182 __isl_take isl_basic_set *bset2);
2183 __isl_give isl_map *isl_basic_map_union(
2184 __isl_take isl_basic_map *bmap1,
2185 __isl_take isl_basic_map *bmap2);
2186 __isl_give isl_set *isl_set_union(
2187 __isl_take isl_set *set1,
2188 __isl_take isl_set *set2);
2189 __isl_give isl_map *isl_map_union(
2190 __isl_take isl_map *map1,
2191 __isl_take isl_map *map2);
2192 __isl_give isl_union_set *isl_union_set_union(
2193 __isl_take isl_union_set *uset1,
2194 __isl_take isl_union_set *uset2);
2195 __isl_give isl_union_map *isl_union_map_union(
2196 __isl_take isl_union_map *umap1,
2197 __isl_take isl_union_map *umap2);
2199 =item * Set difference
2201 __isl_give isl_set *isl_set_subtract(
2202 __isl_take isl_set *set1,
2203 __isl_take isl_set *set2);
2204 __isl_give isl_map *isl_map_subtract(
2205 __isl_take isl_map *map1,
2206 __isl_take isl_map *map2);
2207 __isl_give isl_union_set *isl_union_set_subtract(
2208 __isl_take isl_union_set *uset1,
2209 __isl_take isl_union_set *uset2);
2210 __isl_give isl_union_map *isl_union_map_subtract(
2211 __isl_take isl_union_map *umap1,
2212 __isl_take isl_union_map *umap2);
2216 __isl_give isl_basic_set *isl_basic_set_apply(
2217 __isl_take isl_basic_set *bset,
2218 __isl_take isl_basic_map *bmap);
2219 __isl_give isl_set *isl_set_apply(
2220 __isl_take isl_set *set,
2221 __isl_take isl_map *map);
2222 __isl_give isl_union_set *isl_union_set_apply(
2223 __isl_take isl_union_set *uset,
2224 __isl_take isl_union_map *umap);
2225 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2226 __isl_take isl_basic_map *bmap1,
2227 __isl_take isl_basic_map *bmap2);
2228 __isl_give isl_basic_map *isl_basic_map_apply_range(
2229 __isl_take isl_basic_map *bmap1,
2230 __isl_take isl_basic_map *bmap2);
2231 __isl_give isl_map *isl_map_apply_domain(
2232 __isl_take isl_map *map1,
2233 __isl_take isl_map *map2);
2234 __isl_give isl_union_map *isl_union_map_apply_domain(
2235 __isl_take isl_union_map *umap1,
2236 __isl_take isl_union_map *umap2);
2237 __isl_give isl_map *isl_map_apply_range(
2238 __isl_take isl_map *map1,
2239 __isl_take isl_map *map2);
2240 __isl_give isl_union_map *isl_union_map_apply_range(
2241 __isl_take isl_union_map *umap1,
2242 __isl_take isl_union_map *umap2);
2244 =item * Cartesian Product
2246 __isl_give isl_set *isl_set_product(
2247 __isl_take isl_set *set1,
2248 __isl_take isl_set *set2);
2249 __isl_give isl_union_set *isl_union_set_product(
2250 __isl_take isl_union_set *uset1,
2251 __isl_take isl_union_set *uset2);
2252 __isl_give isl_basic_map *isl_basic_map_domain_product(
2253 __isl_take isl_basic_map *bmap1,
2254 __isl_take isl_basic_map *bmap2);
2255 __isl_give isl_basic_map *isl_basic_map_range_product(
2256 __isl_take isl_basic_map *bmap1,
2257 __isl_take isl_basic_map *bmap2);
2258 __isl_give isl_map *isl_map_domain_product(
2259 __isl_take isl_map *map1,
2260 __isl_take isl_map *map2);
2261 __isl_give isl_map *isl_map_range_product(
2262 __isl_take isl_map *map1,
2263 __isl_take isl_map *map2);
2264 __isl_give isl_union_map *isl_union_map_range_product(
2265 __isl_take isl_union_map *umap1,
2266 __isl_take isl_union_map *umap2);
2267 __isl_give isl_map *isl_map_product(
2268 __isl_take isl_map *map1,
2269 __isl_take isl_map *map2);
2270 __isl_give isl_union_map *isl_union_map_product(
2271 __isl_take isl_union_map *umap1,
2272 __isl_take isl_union_map *umap2);
2274 The above functions compute the cross product of the given
2275 sets or relations. The domains and ranges of the results
2276 are wrapped maps between domains and ranges of the inputs.
2277 To obtain a ``flat'' product, use the following functions
2280 __isl_give isl_basic_set *isl_basic_set_flat_product(
2281 __isl_take isl_basic_set *bset1,
2282 __isl_take isl_basic_set *bset2);
2283 __isl_give isl_set *isl_set_flat_product(
2284 __isl_take isl_set *set1,
2285 __isl_take isl_set *set2);
2286 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2287 __isl_take isl_basic_map *bmap1,
2288 __isl_take isl_basic_map *bmap2);
2289 __isl_give isl_map *isl_map_flat_domain_product(
2290 __isl_take isl_map *map1,
2291 __isl_take isl_map *map2);
2292 __isl_give isl_map *isl_map_flat_range_product(
2293 __isl_take isl_map *map1,
2294 __isl_take isl_map *map2);
2295 __isl_give isl_union_map *isl_union_map_flat_range_product(
2296 __isl_take isl_union_map *umap1,
2297 __isl_take isl_union_map *umap2);
2298 __isl_give isl_basic_map *isl_basic_map_flat_product(
2299 __isl_take isl_basic_map *bmap1,
2300 __isl_take isl_basic_map *bmap2);
2301 __isl_give isl_map *isl_map_flat_product(
2302 __isl_take isl_map *map1,
2303 __isl_take isl_map *map2);
2305 =item * Simplification
2307 __isl_give isl_basic_set *isl_basic_set_gist(
2308 __isl_take isl_basic_set *bset,
2309 __isl_take isl_basic_set *context);
2310 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2311 __isl_take isl_set *context);
2312 __isl_give isl_set *isl_set_gist_params(
2313 __isl_take isl_set *set,
2314 __isl_take isl_set *context);
2315 __isl_give isl_union_set *isl_union_set_gist(
2316 __isl_take isl_union_set *uset,
2317 __isl_take isl_union_set *context);
2318 __isl_give isl_basic_map *isl_basic_map_gist(
2319 __isl_take isl_basic_map *bmap,
2320 __isl_take isl_basic_map *context);
2321 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2322 __isl_take isl_map *context);
2323 __isl_give isl_map *isl_map_gist_params(
2324 __isl_take isl_map *map,
2325 __isl_take isl_set *context);
2326 __isl_give isl_union_map *isl_union_map_gist(
2327 __isl_take isl_union_map *umap,
2328 __isl_take isl_union_map *context);
2330 The gist operation returns a set or relation that has the
2331 same intersection with the context as the input set or relation.
2332 Any implicit equality in the intersection is made explicit in the result,
2333 while all inequalities that are redundant with respect to the intersection
2335 In case of union sets and relations, the gist operation is performed
2340 =head3 Lexicographic Optimization
2342 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2343 the following functions
2344 compute a set that contains the lexicographic minimum or maximum
2345 of the elements in C<set> (or C<bset>) for those values of the parameters
2346 that satisfy C<dom>.
2347 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2348 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2350 In other words, the union of the parameter values
2351 for which the result is non-empty and of C<*empty>
2354 __isl_give isl_set *isl_basic_set_partial_lexmin(
2355 __isl_take isl_basic_set *bset,
2356 __isl_take isl_basic_set *dom,
2357 __isl_give isl_set **empty);
2358 __isl_give isl_set *isl_basic_set_partial_lexmax(
2359 __isl_take isl_basic_set *bset,
2360 __isl_take isl_basic_set *dom,
2361 __isl_give isl_set **empty);
2362 __isl_give isl_set *isl_set_partial_lexmin(
2363 __isl_take isl_set *set, __isl_take isl_set *dom,
2364 __isl_give isl_set **empty);
2365 __isl_give isl_set *isl_set_partial_lexmax(
2366 __isl_take isl_set *set, __isl_take isl_set *dom,
2367 __isl_give isl_set **empty);
2369 Given a (basic) set C<set> (or C<bset>), the following functions simply
2370 return a set containing the lexicographic minimum or maximum
2371 of the elements in C<set> (or C<bset>).
2372 In case of union sets, the optimum is computed per space.
2374 __isl_give isl_set *isl_basic_set_lexmin(
2375 __isl_take isl_basic_set *bset);
2376 __isl_give isl_set *isl_basic_set_lexmax(
2377 __isl_take isl_basic_set *bset);
2378 __isl_give isl_set *isl_set_lexmin(
2379 __isl_take isl_set *set);
2380 __isl_give isl_set *isl_set_lexmax(
2381 __isl_take isl_set *set);
2382 __isl_give isl_union_set *isl_union_set_lexmin(
2383 __isl_take isl_union_set *uset);
2384 __isl_give isl_union_set *isl_union_set_lexmax(
2385 __isl_take isl_union_set *uset);
2387 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2388 the following functions
2389 compute a relation that maps each element of C<dom>
2390 to the single lexicographic minimum or maximum
2391 of the elements that are associated to that same
2392 element in C<map> (or C<bmap>).
2393 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2394 that contains the elements in C<dom> that do not map
2395 to any elements in C<map> (or C<bmap>).
2396 In other words, the union of the domain of the result and of C<*empty>
2399 __isl_give isl_map *isl_basic_map_partial_lexmax(
2400 __isl_take isl_basic_map *bmap,
2401 __isl_take isl_basic_set *dom,
2402 __isl_give isl_set **empty);
2403 __isl_give isl_map *isl_basic_map_partial_lexmin(
2404 __isl_take isl_basic_map *bmap,
2405 __isl_take isl_basic_set *dom,
2406 __isl_give isl_set **empty);
2407 __isl_give isl_map *isl_map_partial_lexmax(
2408 __isl_take isl_map *map, __isl_take isl_set *dom,
2409 __isl_give isl_set **empty);
2410 __isl_give isl_map *isl_map_partial_lexmin(
2411 __isl_take isl_map *map, __isl_take isl_set *dom,
2412 __isl_give isl_set **empty);
2414 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2415 return a map mapping each element in the domain of
2416 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2417 of all elements associated to that element.
2418 In case of union relations, the optimum is computed per space.
2420 __isl_give isl_map *isl_basic_map_lexmin(
2421 __isl_take isl_basic_map *bmap);
2422 __isl_give isl_map *isl_basic_map_lexmax(
2423 __isl_take isl_basic_map *bmap);
2424 __isl_give isl_map *isl_map_lexmin(
2425 __isl_take isl_map *map);
2426 __isl_give isl_map *isl_map_lexmax(
2427 __isl_take isl_map *map);
2428 __isl_give isl_union_map *isl_union_map_lexmin(
2429 __isl_take isl_union_map *umap);
2430 __isl_give isl_union_map *isl_union_map_lexmax(
2431 __isl_take isl_union_map *umap);
2435 Lists are defined over several element types, including
2436 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2437 Here we take lists of C<isl_set>s as an example.
2438 Lists can be created, copied and freed using the following functions.
2440 #include <isl/list.h>
2441 __isl_give isl_set_list *isl_set_list_from_set(
2442 __isl_take isl_set *el);
2443 __isl_give isl_set_list *isl_set_list_alloc(
2444 isl_ctx *ctx, int n);
2445 __isl_give isl_set_list *isl_set_list_copy(
2446 __isl_keep isl_set_list *list);
2447 __isl_give isl_set_list *isl_set_list_add(
2448 __isl_take isl_set_list *list,
2449 __isl_take isl_set *el);
2450 __isl_give isl_set_list *isl_set_list_concat(
2451 __isl_take isl_set_list *list1,
2452 __isl_take isl_set_list *list2);
2453 void *isl_set_list_free(__isl_take isl_set_list *list);
2455 C<isl_set_list_alloc> creates an empty list with a capacity for
2456 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2459 Lists can be inspected using the following functions.
2461 #include <isl/list.h>
2462 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2463 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2464 __isl_give isl_set *isl_set_list_get_set(
2465 __isl_keep isl_set_list *list, int index);
2466 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2467 int (*fn)(__isl_take isl_set *el, void *user),
2470 Lists can be printed using
2472 #include <isl/list.h>
2473 __isl_give isl_printer *isl_printer_print_set_list(
2474 __isl_take isl_printer *p,
2475 __isl_keep isl_set_list *list);
2479 Matrices can be created, copied and freed using the following functions.
2481 #include <isl/mat.h>
2482 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2483 unsigned n_row, unsigned n_col);
2484 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2485 void isl_mat_free(__isl_take isl_mat *mat);
2487 Note that the elements of a newly created matrix may have arbitrary values.
2488 The elements can be changed and inspected using the following functions.
2490 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2491 int isl_mat_rows(__isl_keep isl_mat *mat);
2492 int isl_mat_cols(__isl_keep isl_mat *mat);
2493 int isl_mat_get_element(__isl_keep isl_mat *mat,
2494 int row, int col, isl_int *v);
2495 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2496 int row, int col, isl_int v);
2497 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2498 int row, int col, int v);
2500 C<isl_mat_get_element> will return a negative value if anything went wrong.
2501 In that case, the value of C<*v> is undefined.
2503 The following function can be used to compute the (right) inverse
2504 of a matrix, i.e., a matrix such that the product of the original
2505 and the inverse (in that order) is a multiple of the identity matrix.
2506 The input matrix is assumed to be of full row-rank.
2508 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2510 The following function can be used to compute the (right) kernel
2511 (or null space) of a matrix, i.e., a matrix such that the product of
2512 the original and the kernel (in that order) is the zero matrix.
2514 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2516 =head2 Piecewise Quasi Affine Expressions
2518 The zero quasi affine expression on a given domain can be created using
2520 __isl_give isl_aff *isl_aff_zero_on_domain(
2521 __isl_take isl_local_space *ls);
2523 Note that the space in which the resulting object lives is a map space
2524 with the given space as domain and a one-dimensional range.
2526 An empty piecewise quasi affine expression (one with no cells)
2527 or a piecewise quasi affine expression with a single cell can
2528 be created using the following functions.
2530 #include <isl/aff.h>
2531 __isl_give isl_pw_aff *isl_pw_aff_empty(
2532 __isl_take isl_space *space);
2533 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2534 __isl_take isl_set *set, __isl_take isl_aff *aff);
2535 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2536 __isl_take isl_aff *aff);
2538 Quasi affine expressions can be copied and freed using
2540 #include <isl/aff.h>
2541 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2542 void *isl_aff_free(__isl_take isl_aff *aff);
2544 __isl_give isl_pw_aff *isl_pw_aff_copy(
2545 __isl_keep isl_pw_aff *pwaff);
2546 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2548 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2549 using the following function. The constraint is required to have
2550 a non-zero coefficient for the specified dimension.
2552 #include <isl/constraint.h>
2553 __isl_give isl_aff *isl_constraint_get_bound(
2554 __isl_keep isl_constraint *constraint,
2555 enum isl_dim_type type, int pos);
2557 The entire affine expression of the constraint can also be extracted
2558 using the following function.
2560 #include <isl/constraint.h>
2561 __isl_give isl_aff *isl_constraint_get_aff(
2562 __isl_keep isl_constraint *constraint);
2564 Conversely, an equality constraint equating
2565 the affine expression to zero or an inequality constraint enforcing
2566 the affine expression to be non-negative, can be constructed using
2568 __isl_give isl_constraint *isl_equality_from_aff(
2569 __isl_take isl_aff *aff);
2570 __isl_give isl_constraint *isl_inequality_from_aff(
2571 __isl_take isl_aff *aff);
2573 The expression can be inspected using
2575 #include <isl/aff.h>
2576 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2577 int isl_aff_dim(__isl_keep isl_aff *aff,
2578 enum isl_dim_type type);
2579 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2580 __isl_keep isl_aff *aff);
2581 __isl_give isl_local_space *isl_aff_get_local_space(
2582 __isl_keep isl_aff *aff);
2583 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2584 enum isl_dim_type type, unsigned pos);
2585 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2587 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2588 enum isl_dim_type type, int pos, isl_int *v);
2589 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2591 __isl_give isl_aff *isl_aff_get_div(
2592 __isl_keep isl_aff *aff, int pos);
2594 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2595 int (*fn)(__isl_take isl_set *set,
2596 __isl_take isl_aff *aff,
2597 void *user), void *user);
2599 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2600 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2602 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2603 enum isl_dim_type type, unsigned first, unsigned n);
2604 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2605 enum isl_dim_type type, unsigned first, unsigned n);
2607 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2608 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2609 enum isl_dim_type type);
2610 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2612 It can be modified using
2614 #include <isl/aff.h>
2615 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2616 __isl_take isl_pw_aff *pwaff,
2617 __isl_take isl_id *id);
2618 __isl_give isl_aff *isl_aff_set_dim_name(
2619 __isl_take isl_aff *aff, enum isl_dim_type type,
2620 unsigned pos, const char *s);
2621 __isl_give isl_aff *isl_aff_set_constant(
2622 __isl_take isl_aff *aff, isl_int v);
2623 __isl_give isl_aff *isl_aff_set_constant_si(
2624 __isl_take isl_aff *aff, int v);
2625 __isl_give isl_aff *isl_aff_set_coefficient(
2626 __isl_take isl_aff *aff,
2627 enum isl_dim_type type, int pos, isl_int v);
2628 __isl_give isl_aff *isl_aff_set_coefficient_si(
2629 __isl_take isl_aff *aff,
2630 enum isl_dim_type type, int pos, int v);
2631 __isl_give isl_aff *isl_aff_set_denominator(
2632 __isl_take isl_aff *aff, isl_int v);
2634 __isl_give isl_aff *isl_aff_add_constant(
2635 __isl_take isl_aff *aff, isl_int v);
2636 __isl_give isl_aff *isl_aff_add_constant_si(
2637 __isl_take isl_aff *aff, int v);
2638 __isl_give isl_aff *isl_aff_add_coefficient(
2639 __isl_take isl_aff *aff,
2640 enum isl_dim_type type, int pos, isl_int v);
2641 __isl_give isl_aff *isl_aff_add_coefficient_si(
2642 __isl_take isl_aff *aff,
2643 enum isl_dim_type type, int pos, int v);
2645 __isl_give isl_aff *isl_aff_insert_dims(
2646 __isl_take isl_aff *aff,
2647 enum isl_dim_type type, unsigned first, unsigned n);
2648 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2649 __isl_take isl_pw_aff *pwaff,
2650 enum isl_dim_type type, unsigned first, unsigned n);
2651 __isl_give isl_aff *isl_aff_add_dims(
2652 __isl_take isl_aff *aff,
2653 enum isl_dim_type type, unsigned n);
2654 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2655 __isl_take isl_pw_aff *pwaff,
2656 enum isl_dim_type type, unsigned n);
2657 __isl_give isl_aff *isl_aff_drop_dims(
2658 __isl_take isl_aff *aff,
2659 enum isl_dim_type type, unsigned first, unsigned n);
2660 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2661 __isl_take isl_pw_aff *pwaff,
2662 enum isl_dim_type type, unsigned first, unsigned n);
2664 Note that the C<set_constant> and C<set_coefficient> functions
2665 set the I<numerator> of the constant or coefficient, while
2666 C<add_constant> and C<add_coefficient> add an integer value to
2667 the possibly rational constant or coefficient.
2669 To check whether an affine expressions is obviously zero
2670 or obviously equal to some other affine expression, use
2672 #include <isl/aff.h>
2673 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2674 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2675 __isl_keep isl_aff *aff2);
2679 #include <isl/aff.h>
2680 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2681 __isl_take isl_aff *aff2);
2682 __isl_give isl_pw_aff *isl_pw_aff_add(
2683 __isl_take isl_pw_aff *pwaff1,
2684 __isl_take isl_pw_aff *pwaff2);
2685 __isl_give isl_pw_aff *isl_pw_aff_min(
2686 __isl_take isl_pw_aff *pwaff1,
2687 __isl_take isl_pw_aff *pwaff2);
2688 __isl_give isl_pw_aff *isl_pw_aff_max(
2689 __isl_take isl_pw_aff *pwaff1,
2690 __isl_take isl_pw_aff *pwaff2);
2691 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2692 __isl_take isl_aff *aff2);
2693 __isl_give isl_pw_aff *isl_pw_aff_sub(
2694 __isl_take isl_pw_aff *pwaff1,
2695 __isl_take isl_pw_aff *pwaff2);
2696 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2697 __isl_give isl_pw_aff *isl_pw_aff_neg(
2698 __isl_take isl_pw_aff *pwaff);
2699 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2700 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2701 __isl_take isl_pw_aff *pwaff);
2702 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2703 __isl_give isl_pw_aff *isl_pw_aff_floor(
2704 __isl_take isl_pw_aff *pwaff);
2705 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2707 __isl_give isl_pw_aff *isl_pw_aff_mod(
2708 __isl_take isl_pw_aff *pwaff, isl_int mod);
2709 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2711 __isl_give isl_pw_aff *isl_pw_aff_scale(
2712 __isl_take isl_pw_aff *pwaff, isl_int f);
2713 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2715 __isl_give isl_aff *isl_aff_scale_down_ui(
2716 __isl_take isl_aff *aff, unsigned f);
2717 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2718 __isl_take isl_pw_aff *pwaff, isl_int f);
2720 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2721 __isl_take isl_pw_aff_list *list);
2722 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2723 __isl_take isl_pw_aff_list *list);
2725 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2726 __isl_take isl_pw_aff *pwqp);
2728 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2729 __isl_take isl_pw_aff *pwaff,
2730 __isl_take isl_space *model);
2732 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2733 __isl_take isl_set *context);
2734 __isl_give isl_pw_aff *isl_pw_aff_gist(
2735 __isl_take isl_pw_aff *pwaff,
2736 __isl_take isl_set *context);
2738 __isl_give isl_set *isl_pw_aff_domain(
2739 __isl_take isl_pw_aff *pwaff);
2741 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2742 __isl_take isl_aff *aff2);
2743 __isl_give isl_pw_aff *isl_pw_aff_mul(
2744 __isl_take isl_pw_aff *pwaff1,
2745 __isl_take isl_pw_aff *pwaff2);
2747 When multiplying two affine expressions, at least one of the two needs
2750 #include <isl/aff.h>
2751 __isl_give isl_basic_set *isl_aff_le_basic_set(
2752 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2753 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2754 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2755 __isl_give isl_set *isl_pw_aff_eq_set(
2756 __isl_take isl_pw_aff *pwaff1,
2757 __isl_take isl_pw_aff *pwaff2);
2758 __isl_give isl_set *isl_pw_aff_ne_set(
2759 __isl_take isl_pw_aff *pwaff1,
2760 __isl_take isl_pw_aff *pwaff2);
2761 __isl_give isl_set *isl_pw_aff_le_set(
2762 __isl_take isl_pw_aff *pwaff1,
2763 __isl_take isl_pw_aff *pwaff2);
2764 __isl_give isl_set *isl_pw_aff_lt_set(
2765 __isl_take isl_pw_aff *pwaff1,
2766 __isl_take isl_pw_aff *pwaff2);
2767 __isl_give isl_set *isl_pw_aff_ge_set(
2768 __isl_take isl_pw_aff *pwaff1,
2769 __isl_take isl_pw_aff *pwaff2);
2770 __isl_give isl_set *isl_pw_aff_gt_set(
2771 __isl_take isl_pw_aff *pwaff1,
2772 __isl_take isl_pw_aff *pwaff2);
2774 __isl_give isl_set *isl_pw_aff_list_eq_set(
2775 __isl_take isl_pw_aff_list *list1,
2776 __isl_take isl_pw_aff_list *list2);
2777 __isl_give isl_set *isl_pw_aff_list_ne_set(
2778 __isl_take isl_pw_aff_list *list1,
2779 __isl_take isl_pw_aff_list *list2);
2780 __isl_give isl_set *isl_pw_aff_list_le_set(
2781 __isl_take isl_pw_aff_list *list1,
2782 __isl_take isl_pw_aff_list *list2);
2783 __isl_give isl_set *isl_pw_aff_list_lt_set(
2784 __isl_take isl_pw_aff_list *list1,
2785 __isl_take isl_pw_aff_list *list2);
2786 __isl_give isl_set *isl_pw_aff_list_ge_set(
2787 __isl_take isl_pw_aff_list *list1,
2788 __isl_take isl_pw_aff_list *list2);
2789 __isl_give isl_set *isl_pw_aff_list_gt_set(
2790 __isl_take isl_pw_aff_list *list1,
2791 __isl_take isl_pw_aff_list *list2);
2793 The function C<isl_aff_ge_basic_set> returns a basic set
2794 containing those elements in the shared space
2795 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2796 The function C<isl_aff_ge_set> returns a set
2797 containing those elements in the shared domain
2798 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2799 The functions operating on C<isl_pw_aff_list> apply the corresponding
2800 C<isl_pw_aff> function to each pair of elements in the two lists.
2802 #include <isl/aff.h>
2803 __isl_give isl_set *isl_pw_aff_nonneg_set(
2804 __isl_take isl_pw_aff *pwaff);
2805 __isl_give isl_set *isl_pw_aff_zero_set(
2806 __isl_take isl_pw_aff *pwaff);
2807 __isl_give isl_set *isl_pw_aff_non_zero_set(
2808 __isl_take isl_pw_aff *pwaff);
2810 The function C<isl_pw_aff_nonneg_set> returns a set
2811 containing those elements in the domain
2812 of C<pwaff> where C<pwaff> is non-negative.
2814 #include <isl/aff.h>
2815 __isl_give isl_pw_aff *isl_pw_aff_cond(
2816 __isl_take isl_set *cond,
2817 __isl_take isl_pw_aff *pwaff_true,
2818 __isl_take isl_pw_aff *pwaff_false);
2820 The function C<isl_pw_aff_cond> performs a conditional operator
2821 and returns an expression that is equal to C<pwaff_true>
2822 for elements in C<cond> and equal to C<pwaff_false> for elements
2825 #include <isl/aff.h>
2826 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2827 __isl_take isl_pw_aff *pwaff1,
2828 __isl_take isl_pw_aff *pwaff2);
2829 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2830 __isl_take isl_pw_aff *pwaff1,
2831 __isl_take isl_pw_aff *pwaff2);
2833 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2834 expression with a domain that is the union of those of C<pwaff1> and
2835 C<pwaff2> and such that on each cell, the quasi-affine expression is
2836 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2837 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2838 associated expression is the defined one.
2840 An expression can be printed using
2842 #include <isl/aff.h>
2843 __isl_give isl_printer *isl_printer_print_aff(
2844 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2846 __isl_give isl_printer *isl_printer_print_pw_aff(
2847 __isl_take isl_printer *p,
2848 __isl_keep isl_pw_aff *pwaff);
2852 Points are elements of a set. They can be used to construct
2853 simple sets (boxes) or they can be used to represent the
2854 individual elements of a set.
2855 The zero point (the origin) can be created using
2857 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2859 The coordinates of a point can be inspected, set and changed
2862 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2863 enum isl_dim_type type, int pos, isl_int *v);
2864 __isl_give isl_point *isl_point_set_coordinate(
2865 __isl_take isl_point *pnt,
2866 enum isl_dim_type type, int pos, isl_int v);
2868 __isl_give isl_point *isl_point_add_ui(
2869 __isl_take isl_point *pnt,
2870 enum isl_dim_type type, int pos, unsigned val);
2871 __isl_give isl_point *isl_point_sub_ui(
2872 __isl_take isl_point *pnt,
2873 enum isl_dim_type type, int pos, unsigned val);
2875 Other properties can be obtained using
2877 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2879 Points can be copied or freed using
2881 __isl_give isl_point *isl_point_copy(
2882 __isl_keep isl_point *pnt);
2883 void isl_point_free(__isl_take isl_point *pnt);
2885 A singleton set can be created from a point using
2887 __isl_give isl_basic_set *isl_basic_set_from_point(
2888 __isl_take isl_point *pnt);
2889 __isl_give isl_set *isl_set_from_point(
2890 __isl_take isl_point *pnt);
2892 and a box can be created from two opposite extremal points using
2894 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2895 __isl_take isl_point *pnt1,
2896 __isl_take isl_point *pnt2);
2897 __isl_give isl_set *isl_set_box_from_points(
2898 __isl_take isl_point *pnt1,
2899 __isl_take isl_point *pnt2);
2901 All elements of a B<bounded> (union) set can be enumerated using
2902 the following functions.
2904 int isl_set_foreach_point(__isl_keep isl_set *set,
2905 int (*fn)(__isl_take isl_point *pnt, void *user),
2907 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2908 int (*fn)(__isl_take isl_point *pnt, void *user),
2911 The function C<fn> is called for each integer point in
2912 C<set> with as second argument the last argument of
2913 the C<isl_set_foreach_point> call. The function C<fn>
2914 should return C<0> on success and C<-1> on failure.
2915 In the latter case, C<isl_set_foreach_point> will stop
2916 enumerating and return C<-1> as well.
2917 If the enumeration is performed successfully and to completion,
2918 then C<isl_set_foreach_point> returns C<0>.
2920 To obtain a single point of a (basic) set, use
2922 __isl_give isl_point *isl_basic_set_sample_point(
2923 __isl_take isl_basic_set *bset);
2924 __isl_give isl_point *isl_set_sample_point(
2925 __isl_take isl_set *set);
2927 If C<set> does not contain any (integer) points, then the
2928 resulting point will be ``void'', a property that can be
2931 int isl_point_is_void(__isl_keep isl_point *pnt);
2933 =head2 Piecewise Quasipolynomials
2935 A piecewise quasipolynomial is a particular kind of function that maps
2936 a parametric point to a rational value.
2937 More specifically, a quasipolynomial is a polynomial expression in greatest
2938 integer parts of affine expressions of parameters and variables.
2939 A piecewise quasipolynomial is a subdivision of a given parametric
2940 domain into disjoint cells with a quasipolynomial associated to
2941 each cell. The value of the piecewise quasipolynomial at a given
2942 point is the value of the quasipolynomial associated to the cell
2943 that contains the point. Outside of the union of cells,
2944 the value is assumed to be zero.
2945 For example, the piecewise quasipolynomial
2947 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2949 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2950 A given piecewise quasipolynomial has a fixed domain dimension.
2951 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2952 defined over different domains.
2953 Piecewise quasipolynomials are mainly used by the C<barvinok>
2954 library for representing the number of elements in a parametric set or map.
2955 For example, the piecewise quasipolynomial above represents
2956 the number of points in the map
2958 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2960 =head3 Printing (Piecewise) Quasipolynomials
2962 Quasipolynomials and piecewise quasipolynomials can be printed
2963 using the following functions.
2965 __isl_give isl_printer *isl_printer_print_qpolynomial(
2966 __isl_take isl_printer *p,
2967 __isl_keep isl_qpolynomial *qp);
2969 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2970 __isl_take isl_printer *p,
2971 __isl_keep isl_pw_qpolynomial *pwqp);
2973 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2974 __isl_take isl_printer *p,
2975 __isl_keep isl_union_pw_qpolynomial *upwqp);
2977 The output format of the printer
2978 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2979 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2981 In case of printing in C<ISL_FORMAT_C>, the user may want
2982 to set the names of all dimensions
2984 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2985 __isl_take isl_qpolynomial *qp,
2986 enum isl_dim_type type, unsigned pos,
2988 __isl_give isl_pw_qpolynomial *
2989 isl_pw_qpolynomial_set_dim_name(
2990 __isl_take isl_pw_qpolynomial *pwqp,
2991 enum isl_dim_type type, unsigned pos,
2994 =head3 Creating New (Piecewise) Quasipolynomials
2996 Some simple quasipolynomials can be created using the following functions.
2997 More complicated quasipolynomials can be created by applying
2998 operations such as addition and multiplication
2999 on the resulting quasipolynomials
3001 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3002 __isl_take isl_space *domain);
3003 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3004 __isl_take isl_space *domain);
3005 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3006 __isl_take isl_space *domain);
3007 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3008 __isl_take isl_space *domain);
3009 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3010 __isl_take isl_space *domain);
3011 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3012 __isl_take isl_space *domain,
3013 const isl_int n, const isl_int d);
3014 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3015 __isl_take isl_space *domain,
3016 enum isl_dim_type type, unsigned pos);
3017 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3018 __isl_take isl_aff *aff);
3020 Note that the space in which a quasipolynomial lives is a map space
3021 with a one-dimensional range. The C<domain> argument in some of
3022 the functions above corresponds to the domain of this map space.
3024 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3025 with a single cell can be created using the following functions.
3026 Multiple of these single cell piecewise quasipolynomials can
3027 be combined to create more complicated piecewise quasipolynomials.
3029 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3030 __isl_take isl_space *space);
3031 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3032 __isl_take isl_set *set,
3033 __isl_take isl_qpolynomial *qp);
3034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3035 __isl_take isl_qpolynomial *qp);
3036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3037 __isl_take isl_pw_aff *pwaff);
3039 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3040 __isl_take isl_space *space);
3041 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3042 __isl_take isl_pw_qpolynomial *pwqp);
3043 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3044 __isl_take isl_union_pw_qpolynomial *upwqp,
3045 __isl_take isl_pw_qpolynomial *pwqp);
3047 Quasipolynomials can be copied and freed again using the following
3050 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3051 __isl_keep isl_qpolynomial *qp);
3052 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3054 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3055 __isl_keep isl_pw_qpolynomial *pwqp);
3056 void *isl_pw_qpolynomial_free(
3057 __isl_take isl_pw_qpolynomial *pwqp);
3059 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3060 __isl_keep isl_union_pw_qpolynomial *upwqp);
3061 void isl_union_pw_qpolynomial_free(
3062 __isl_take isl_union_pw_qpolynomial *upwqp);
3064 =head3 Inspecting (Piecewise) Quasipolynomials
3066 To iterate over all piecewise quasipolynomials in a union
3067 piecewise quasipolynomial, use the following function
3069 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3070 __isl_keep isl_union_pw_qpolynomial *upwqp,
3071 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3074 To extract the piecewise quasipolynomial in a given space from a union, use
3076 __isl_give isl_pw_qpolynomial *
3077 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3078 __isl_keep isl_union_pw_qpolynomial *upwqp,
3079 __isl_take isl_space *space);
3081 To iterate over the cells in a piecewise quasipolynomial,
3082 use either of the following two functions
3084 int isl_pw_qpolynomial_foreach_piece(
3085 __isl_keep isl_pw_qpolynomial *pwqp,
3086 int (*fn)(__isl_take isl_set *set,
3087 __isl_take isl_qpolynomial *qp,
3088 void *user), void *user);
3089 int isl_pw_qpolynomial_foreach_lifted_piece(
3090 __isl_keep isl_pw_qpolynomial *pwqp,
3091 int (*fn)(__isl_take isl_set *set,
3092 __isl_take isl_qpolynomial *qp,
3093 void *user), void *user);
3095 As usual, the function C<fn> should return C<0> on success
3096 and C<-1> on failure. The difference between
3097 C<isl_pw_qpolynomial_foreach_piece> and
3098 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3099 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3100 compute unique representations for all existentially quantified
3101 variables and then turn these existentially quantified variables
3102 into extra set variables, adapting the associated quasipolynomial
3103 accordingly. This means that the C<set> passed to C<fn>
3104 will not have any existentially quantified variables, but that
3105 the dimensions of the sets may be different for different
3106 invocations of C<fn>.
3108 To iterate over all terms in a quasipolynomial,
3111 int isl_qpolynomial_foreach_term(
3112 __isl_keep isl_qpolynomial *qp,
3113 int (*fn)(__isl_take isl_term *term,
3114 void *user), void *user);
3116 The terms themselves can be inspected and freed using
3119 unsigned isl_term_dim(__isl_keep isl_term *term,
3120 enum isl_dim_type type);
3121 void isl_term_get_num(__isl_keep isl_term *term,
3123 void isl_term_get_den(__isl_keep isl_term *term,
3125 int isl_term_get_exp(__isl_keep isl_term *term,
3126 enum isl_dim_type type, unsigned pos);
3127 __isl_give isl_aff *isl_term_get_div(
3128 __isl_keep isl_term *term, unsigned pos);
3129 void isl_term_free(__isl_take isl_term *term);
3131 Each term is a product of parameters, set variables and
3132 integer divisions. The function C<isl_term_get_exp>
3133 returns the exponent of a given dimensions in the given term.
3134 The C<isl_int>s in the arguments of C<isl_term_get_num>
3135 and C<isl_term_get_den> need to have been initialized
3136 using C<isl_int_init> before calling these functions.
3138 =head3 Properties of (Piecewise) Quasipolynomials
3140 To check whether a quasipolynomial is actually a constant,
3141 use the following function.
3143 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3144 isl_int *n, isl_int *d);
3146 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3147 then the numerator and denominator of the constant
3148 are returned in C<*n> and C<*d>, respectively.
3150 To check whether two union piecewise quasipolynomials are
3151 obviously equal, use
3153 int isl_union_pw_qpolynomial_plain_is_equal(
3154 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3155 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3157 =head3 Operations on (Piecewise) Quasipolynomials
3159 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3160 __isl_take isl_qpolynomial *qp, isl_int v);
3161 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3162 __isl_take isl_qpolynomial *qp);
3163 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3164 __isl_take isl_qpolynomial *qp1,
3165 __isl_take isl_qpolynomial *qp2);
3166 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3167 __isl_take isl_qpolynomial *qp1,
3168 __isl_take isl_qpolynomial *qp2);
3169 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3170 __isl_take isl_qpolynomial *qp1,
3171 __isl_take isl_qpolynomial *qp2);
3172 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3173 __isl_take isl_qpolynomial *qp, unsigned exponent);
3175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3176 __isl_take isl_pw_qpolynomial *pwqp1,
3177 __isl_take isl_pw_qpolynomial *pwqp2);
3178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3179 __isl_take isl_pw_qpolynomial *pwqp1,
3180 __isl_take isl_pw_qpolynomial *pwqp2);
3181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3182 __isl_take isl_pw_qpolynomial *pwqp1,
3183 __isl_take isl_pw_qpolynomial *pwqp2);
3184 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3185 __isl_take isl_pw_qpolynomial *pwqp);
3186 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3187 __isl_take isl_pw_qpolynomial *pwqp1,
3188 __isl_take isl_pw_qpolynomial *pwqp2);
3189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3190 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3192 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3193 __isl_take isl_union_pw_qpolynomial *upwqp1,
3194 __isl_take isl_union_pw_qpolynomial *upwqp2);
3195 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3196 __isl_take isl_union_pw_qpolynomial *upwqp1,
3197 __isl_take isl_union_pw_qpolynomial *upwqp2);
3198 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3199 __isl_take isl_union_pw_qpolynomial *upwqp1,
3200 __isl_take isl_union_pw_qpolynomial *upwqp2);
3202 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3203 __isl_take isl_pw_qpolynomial *pwqp,
3204 __isl_take isl_point *pnt);
3206 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3207 __isl_take isl_union_pw_qpolynomial *upwqp,
3208 __isl_take isl_point *pnt);
3210 __isl_give isl_set *isl_pw_qpolynomial_domain(
3211 __isl_take isl_pw_qpolynomial *pwqp);
3212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3213 __isl_take isl_pw_qpolynomial *pwpq,
3214 __isl_take isl_set *set);
3216 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3217 __isl_take isl_union_pw_qpolynomial *upwqp);
3218 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3219 __isl_take isl_union_pw_qpolynomial *upwpq,
3220 __isl_take isl_union_set *uset);
3222 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3223 __isl_take isl_qpolynomial *qp,
3224 __isl_take isl_space *model);
3226 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3227 __isl_take isl_qpolynomial *qp);
3228 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3229 __isl_take isl_pw_qpolynomial *pwqp);
3231 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3232 __isl_take isl_union_pw_qpolynomial *upwqp);
3234 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3235 __isl_take isl_qpolynomial *qp,
3236 __isl_take isl_set *context);
3238 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3239 __isl_take isl_pw_qpolynomial *pwqp,
3240 __isl_take isl_set *context);
3242 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3243 __isl_take isl_union_pw_qpolynomial *upwqp,
3244 __isl_take isl_union_set *context);
3246 The gist operation applies the gist operation to each of
3247 the cells in the domain of the input piecewise quasipolynomial.
3248 The context is also exploited
3249 to simplify the quasipolynomials associated to each cell.
3251 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3252 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3253 __isl_give isl_union_pw_qpolynomial *
3254 isl_union_pw_qpolynomial_to_polynomial(
3255 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3257 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3258 the polynomial will be an overapproximation. If C<sign> is negative,
3259 it will be an underapproximation. If C<sign> is zero, the approximation
3260 will lie somewhere in between.
3262 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3264 A piecewise quasipolynomial reduction is a piecewise
3265 reduction (or fold) of quasipolynomials.
3266 In particular, the reduction can be maximum or a minimum.
3267 The objects are mainly used to represent the result of
3268 an upper or lower bound on a quasipolynomial over its domain,
3269 i.e., as the result of the following function.
3271 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3272 __isl_take isl_pw_qpolynomial *pwqp,
3273 enum isl_fold type, int *tight);
3275 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3276 __isl_take isl_union_pw_qpolynomial *upwqp,
3277 enum isl_fold type, int *tight);
3279 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3280 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3281 is the returned bound is known be tight, i.e., for each value
3282 of the parameters there is at least
3283 one element in the domain that reaches the bound.
3284 If the domain of C<pwqp> is not wrapping, then the bound is computed
3285 over all elements in that domain and the result has a purely parametric
3286 domain. If the domain of C<pwqp> is wrapping, then the bound is
3287 computed over the range of the wrapped relation. The domain of the
3288 wrapped relation becomes the domain of the result.
3290 A (piecewise) quasipolynomial reduction can be copied or freed using the
3291 following functions.
3293 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3294 __isl_keep isl_qpolynomial_fold *fold);
3295 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3296 __isl_keep isl_pw_qpolynomial_fold *pwf);
3297 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3298 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3299 void isl_qpolynomial_fold_free(
3300 __isl_take isl_qpolynomial_fold *fold);
3301 void *isl_pw_qpolynomial_fold_free(
3302 __isl_take isl_pw_qpolynomial_fold *pwf);
3303 void isl_union_pw_qpolynomial_fold_free(
3304 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3306 =head3 Printing Piecewise Quasipolynomial Reductions
3308 Piecewise quasipolynomial reductions can be printed
3309 using the following function.
3311 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3312 __isl_take isl_printer *p,
3313 __isl_keep isl_pw_qpolynomial_fold *pwf);
3314 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3315 __isl_take isl_printer *p,
3316 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3318 For C<isl_printer_print_pw_qpolynomial_fold>,
3319 output format of the printer
3320 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3321 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3322 output format of the printer
3323 needs to be set to C<ISL_FORMAT_ISL>.
3324 In case of printing in C<ISL_FORMAT_C>, the user may want
3325 to set the names of all dimensions
3327 __isl_give isl_pw_qpolynomial_fold *
3328 isl_pw_qpolynomial_fold_set_dim_name(
3329 __isl_take isl_pw_qpolynomial_fold *pwf,
3330 enum isl_dim_type type, unsigned pos,
3333 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3335 To iterate over all piecewise quasipolynomial reductions in a union
3336 piecewise quasipolynomial reduction, use the following function
3338 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3339 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3340 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3341 void *user), void *user);
3343 To iterate over the cells in a piecewise quasipolynomial reduction,
3344 use either of the following two functions
3346 int isl_pw_qpolynomial_fold_foreach_piece(
3347 __isl_keep isl_pw_qpolynomial_fold *pwf,
3348 int (*fn)(__isl_take isl_set *set,
3349 __isl_take isl_qpolynomial_fold *fold,
3350 void *user), void *user);
3351 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3352 __isl_keep isl_pw_qpolynomial_fold *pwf,
3353 int (*fn)(__isl_take isl_set *set,
3354 __isl_take isl_qpolynomial_fold *fold,
3355 void *user), void *user);
3357 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3358 of the difference between these two functions.
3360 To iterate over all quasipolynomials in a reduction, use
3362 int isl_qpolynomial_fold_foreach_qpolynomial(
3363 __isl_keep isl_qpolynomial_fold *fold,
3364 int (*fn)(__isl_take isl_qpolynomial *qp,
3365 void *user), void *user);
3367 =head3 Properties of Piecewise Quasipolynomial Reductions
3369 To check whether two union piecewise quasipolynomial reductions are
3370 obviously equal, use
3372 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3373 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3374 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3376 =head3 Operations on Piecewise Quasipolynomial Reductions
3378 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3379 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3381 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3382 __isl_take isl_pw_qpolynomial_fold *pwf1,
3383 __isl_take isl_pw_qpolynomial_fold *pwf2);
3385 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3386 __isl_take isl_pw_qpolynomial_fold *pwf1,
3387 __isl_take isl_pw_qpolynomial_fold *pwf2);
3389 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3390 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3391 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3393 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3394 __isl_take isl_pw_qpolynomial_fold *pwf,
3395 __isl_take isl_point *pnt);
3397 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3398 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3399 __isl_take isl_point *pnt);
3401 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3402 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3403 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3404 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3405 __isl_take isl_union_set *uset);
3407 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3408 __isl_take isl_pw_qpolynomial_fold *pwf);
3410 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3411 __isl_take isl_pw_qpolynomial_fold *pwf);
3413 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3414 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3416 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3417 __isl_take isl_pw_qpolynomial_fold *pwf,
3418 __isl_take isl_set *context);
3420 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3421 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3422 __isl_take isl_union_set *context);
3424 The gist operation applies the gist operation to each of
3425 the cells in the domain of the input piecewise quasipolynomial reduction.
3426 In future, the operation will also exploit the context
3427 to simplify the quasipolynomial reductions associated to each cell.
3429 __isl_give isl_pw_qpolynomial_fold *
3430 isl_set_apply_pw_qpolynomial_fold(
3431 __isl_take isl_set *set,
3432 __isl_take isl_pw_qpolynomial_fold *pwf,
3434 __isl_give isl_pw_qpolynomial_fold *
3435 isl_map_apply_pw_qpolynomial_fold(
3436 __isl_take isl_map *map,
3437 __isl_take isl_pw_qpolynomial_fold *pwf,
3439 __isl_give isl_union_pw_qpolynomial_fold *
3440 isl_union_set_apply_union_pw_qpolynomial_fold(
3441 __isl_take isl_union_set *uset,
3442 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3444 __isl_give isl_union_pw_qpolynomial_fold *
3445 isl_union_map_apply_union_pw_qpolynomial_fold(
3446 __isl_take isl_union_map *umap,
3447 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3450 The functions taking a map
3451 compose the given map with the given piecewise quasipolynomial reduction.
3452 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3453 over all elements in the intersection of the range of the map
3454 and the domain of the piecewise quasipolynomial reduction
3455 as a function of an element in the domain of the map.
3456 The functions taking a set compute a bound over all elements in the
3457 intersection of the set and the domain of the
3458 piecewise quasipolynomial reduction.
3460 =head2 Dependence Analysis
3462 C<isl> contains specialized functionality for performing
3463 array dataflow analysis. That is, given a I<sink> access relation
3464 and a collection of possible I<source> access relations,
3465 C<isl> can compute relations that describe
3466 for each iteration of the sink access, which iteration
3467 of which of the source access relations was the last
3468 to access the same data element before the given iteration
3470 To compute standard flow dependences, the sink should be
3471 a read, while the sources should be writes.
3472 If any of the source accesses are marked as being I<may>
3473 accesses, then there will be a dependence to the last
3474 I<must> access B<and> to any I<may> access that follows
3475 this last I<must> access.
3476 In particular, if I<all> sources are I<may> accesses,
3477 then memory based dependence analysis is performed.
3478 If, on the other hand, all sources are I<must> accesses,
3479 then value based dependence analysis is performed.
3481 #include <isl/flow.h>
3483 typedef int (*isl_access_level_before)(void *first, void *second);
3485 __isl_give isl_access_info *isl_access_info_alloc(
3486 __isl_take isl_map *sink,
3487 void *sink_user, isl_access_level_before fn,
3489 __isl_give isl_access_info *isl_access_info_add_source(
3490 __isl_take isl_access_info *acc,
3491 __isl_take isl_map *source, int must,
3493 void isl_access_info_free(__isl_take isl_access_info *acc);
3495 __isl_give isl_flow *isl_access_info_compute_flow(
3496 __isl_take isl_access_info *acc);
3498 int isl_flow_foreach(__isl_keep isl_flow *deps,
3499 int (*fn)(__isl_take isl_map *dep, int must,
3500 void *dep_user, void *user),
3502 __isl_give isl_map *isl_flow_get_no_source(
3503 __isl_keep isl_flow *deps, int must);
3504 void isl_flow_free(__isl_take isl_flow *deps);
3506 The function C<isl_access_info_compute_flow> performs the actual
3507 dependence analysis. The other functions are used to construct
3508 the input for this function or to read off the output.
3510 The input is collected in an C<isl_access_info>, which can
3511 be created through a call to C<isl_access_info_alloc>.
3512 The arguments to this functions are the sink access relation
3513 C<sink>, a token C<sink_user> used to identify the sink
3514 access to the user, a callback function for specifying the
3515 relative order of source and sink accesses, and the number
3516 of source access relations that will be added.
3517 The callback function has type C<int (*)(void *first, void *second)>.
3518 The function is called with two user supplied tokens identifying
3519 either a source or the sink and it should return the shared nesting
3520 level and the relative order of the two accesses.
3521 In particular, let I<n> be the number of loops shared by
3522 the two accesses. If C<first> precedes C<second> textually,
3523 then the function should return I<2 * n + 1>; otherwise,
3524 it should return I<2 * n>.
3525 The sources can be added to the C<isl_access_info> by performing
3526 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3527 C<must> indicates whether the source is a I<must> access
3528 or a I<may> access. Note that a multi-valued access relation
3529 should only be marked I<must> if every iteration in the domain
3530 of the relation accesses I<all> elements in its image.
3531 The C<source_user> token is again used to identify
3532 the source access. The range of the source access relation
3533 C<source> should have the same dimension as the range
3534 of the sink access relation.
3535 The C<isl_access_info_free> function should usually not be
3536 called explicitly, because it is called implicitly by
3537 C<isl_access_info_compute_flow>.
3539 The result of the dependence analysis is collected in an
3540 C<isl_flow>. There may be elements of
3541 the sink access for which no preceding source access could be
3542 found or for which all preceding sources are I<may> accesses.
3543 The relations containing these elements can be obtained through
3544 calls to C<isl_flow_get_no_source>, the first with C<must> set
3545 and the second with C<must> unset.
3546 In the case of standard flow dependence analysis,
3547 with the sink a read and the sources I<must> writes,
3548 the first relation corresponds to the reads from uninitialized
3549 array elements and the second relation is empty.
3550 The actual flow dependences can be extracted using
3551 C<isl_flow_foreach>. This function will call the user-specified
3552 callback function C<fn> for each B<non-empty> dependence between
3553 a source and the sink. The callback function is called
3554 with four arguments, the actual flow dependence relation
3555 mapping source iterations to sink iterations, a boolean that
3556 indicates whether it is a I<must> or I<may> dependence, a token
3557 identifying the source and an additional C<void *> with value
3558 equal to the third argument of the C<isl_flow_foreach> call.
3559 A dependence is marked I<must> if it originates from a I<must>
3560 source and if it is not followed by any I<may> sources.
3562 After finishing with an C<isl_flow>, the user should call
3563 C<isl_flow_free> to free all associated memory.
3565 A higher-level interface to dependence analysis is provided
3566 by the following function.
3568 #include <isl/flow.h>
3570 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3571 __isl_take isl_union_map *must_source,
3572 __isl_take isl_union_map *may_source,
3573 __isl_take isl_union_map *schedule,
3574 __isl_give isl_union_map **must_dep,
3575 __isl_give isl_union_map **may_dep,
3576 __isl_give isl_union_map **must_no_source,
3577 __isl_give isl_union_map **may_no_source);
3579 The arrays are identified by the tuple names of the ranges
3580 of the accesses. The iteration domains by the tuple names
3581 of the domains of the accesses and of the schedule.
3582 The relative order of the iteration domains is given by the
3583 schedule. The relations returned through C<must_no_source>
3584 and C<may_no_source> are subsets of C<sink>.
3585 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3586 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3587 any of the other arguments is treated as an error.
3591 B<The functionality described in this section is fairly new
3592 and may be subject to change.>
3594 The following function can be used to compute a schedule
3595 for a union of domains. The generated schedule respects
3596 all C<validity> dependences. That is, all dependence distances
3597 over these dependences in the scheduled space are lexicographically
3598 positive. The generated schedule schedule also tries to minimize
3599 the dependence distances over C<proximity> dependences.
3600 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3601 for groups of domains where the dependence distances have only
3602 non-negative values.
3603 The algorithm used to construct the schedule is similar to that
3606 #include <isl/schedule.h>
3607 __isl_give isl_schedule *isl_union_set_compute_schedule(
3608 __isl_take isl_union_set *domain,
3609 __isl_take isl_union_map *validity,
3610 __isl_take isl_union_map *proximity);
3611 void *isl_schedule_free(__isl_take isl_schedule *sched);
3613 A mapping from the domains to the scheduled space can be obtained
3614 from an C<isl_schedule> using the following function.
3616 __isl_give isl_union_map *isl_schedule_get_map(
3617 __isl_keep isl_schedule *sched);
3619 A representation of the schedule can be printed using
3621 __isl_give isl_printer *isl_printer_print_schedule(
3622 __isl_take isl_printer *p,
3623 __isl_keep isl_schedule *schedule);
3625 A representation of the schedule as a forest of bands can be obtained
3626 using the following function.
3628 __isl_give isl_band_list *isl_schedule_get_band_forest(
3629 __isl_keep isl_schedule *schedule);
3631 The list can be manipulated as explained in L<"Lists">.
3632 The bands inside the list can be copied and freed using the following
3635 #include <isl/band.h>
3636 __isl_give isl_band *isl_band_copy(
3637 __isl_keep isl_band *band);
3638 void *isl_band_free(__isl_take isl_band *band);
3640 Each band contains zero or more scheduling dimensions.
3641 These are referred to as the members of the band.
3642 The section of the schedule that corresponds to the band is
3643 referred to as the partial schedule of the band.
3644 For those nodes that participate in a band, the outer scheduling
3645 dimensions form the prefix schedule, while the inner scheduling
3646 dimensions form the suffix schedule.
3647 That is, if we take a cut of the band forest, then the union of
3648 the concatenations of the prefix, partial and suffix schedules of
3649 each band in the cut is equal to the entire schedule (modulo
3650 some possible padding at the end with zero scheduling dimensions).
3651 The properties of a band can be inspected using the following functions.
3653 #include <isl/band.h>
3654 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3656 int isl_band_has_children(__isl_keep isl_band *band);
3657 __isl_give isl_band_list *isl_band_get_children(
3658 __isl_keep isl_band *band);
3660 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3661 __isl_keep isl_band *band);
3662 __isl_give isl_union_map *isl_band_get_partial_schedule(
3663 __isl_keep isl_band *band);
3664 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3665 __isl_keep isl_band *band);
3667 int isl_band_n_member(__isl_keep isl_band *band);
3668 int isl_band_member_is_zero_distance(
3669 __isl_keep isl_band *band, int pos);
3671 Note that a scheduling dimension is considered to be ``zero
3672 distance'' if it does not carry any proximity dependences
3674 That is, if the dependence distances of the proximity
3675 dependences are all zero in that direction (for fixed
3676 iterations of outer bands).
3678 A representation of the band can be printed using
3680 #include <isl/band.h>
3681 __isl_give isl_printer *isl_printer_print_band(
3682 __isl_take isl_printer *p,
3683 __isl_keep isl_band *band);
3685 =head2 Parametric Vertex Enumeration
3687 The parametric vertex enumeration described in this section
3688 is mainly intended to be used internally and by the C<barvinok>
3691 #include <isl/vertices.h>
3692 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3693 __isl_keep isl_basic_set *bset);
3695 The function C<isl_basic_set_compute_vertices> performs the
3696 actual computation of the parametric vertices and the chamber
3697 decomposition and store the result in an C<isl_vertices> object.
3698 This information can be queried by either iterating over all
3699 the vertices or iterating over all the chambers or cells
3700 and then iterating over all vertices that are active on the chamber.
3702 int isl_vertices_foreach_vertex(
3703 __isl_keep isl_vertices *vertices,
3704 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3707 int isl_vertices_foreach_cell(
3708 __isl_keep isl_vertices *vertices,
3709 int (*fn)(__isl_take isl_cell *cell, void *user),
3711 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3712 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3715 Other operations that can be performed on an C<isl_vertices> object are
3718 isl_ctx *isl_vertices_get_ctx(
3719 __isl_keep isl_vertices *vertices);
3720 int isl_vertices_get_n_vertices(
3721 __isl_keep isl_vertices *vertices);
3722 void isl_vertices_free(__isl_take isl_vertices *vertices);
3724 Vertices can be inspected and destroyed using the following functions.
3726 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3727 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3728 __isl_give isl_basic_set *isl_vertex_get_domain(
3729 __isl_keep isl_vertex *vertex);
3730 __isl_give isl_basic_set *isl_vertex_get_expr(
3731 __isl_keep isl_vertex *vertex);
3732 void isl_vertex_free(__isl_take isl_vertex *vertex);
3734 C<isl_vertex_get_expr> returns a singleton parametric set describing
3735 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3737 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3738 B<rational> basic sets, so they should mainly be used for inspection
3739 and should not be mixed with integer sets.
3741 Chambers can be inspected and destroyed using the following functions.
3743 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3744 __isl_give isl_basic_set *isl_cell_get_domain(
3745 __isl_keep isl_cell *cell);
3746 void isl_cell_free(__isl_take isl_cell *cell);
3750 Although C<isl> is mainly meant to be used as a library,
3751 it also contains some basic applications that use some
3752 of the functionality of C<isl>.
3753 The input may be specified in either the L<isl format>
3754 or the L<PolyLib format>.
3756 =head2 C<isl_polyhedron_sample>
3758 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3759 an integer element of the polyhedron, if there is any.
3760 The first column in the output is the denominator and is always
3761 equal to 1. If the polyhedron contains no integer points,
3762 then a vector of length zero is printed.
3766 C<isl_pip> takes the same input as the C<example> program
3767 from the C<piplib> distribution, i.e., a set of constraints
3768 on the parameters, a line containing only -1 and finally a set
3769 of constraints on a parametric polyhedron.
3770 The coefficients of the parameters appear in the last columns
3771 (but before the final constant column).
3772 The output is the lexicographic minimum of the parametric polyhedron.
3773 As C<isl> currently does not have its own output format, the output
3774 is just a dump of the internal state.
3776 =head2 C<isl_polyhedron_minimize>
3778 C<isl_polyhedron_minimize> computes the minimum of some linear
3779 or affine objective function over the integer points in a polyhedron.
3780 If an affine objective function
3781 is given, then the constant should appear in the last column.
3783 =head2 C<isl_polytope_scan>
3785 Given a polytope, C<isl_polytope_scan> prints
3786 all integer points in the polytope.