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>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
167 The source of C<isl> can be obtained either as a tarball
168 or from the git repository. Both are available from
169 L<http://freshmeat.net/projects/isl/>.
170 The installation process depends on how you obtained
173 =head2 Installation from the git repository
177 =item 1 Clone or update the repository
179 The first time the source is obtained, you need to clone
182 git clone git://repo.or.cz/isl.git
184 To obtain updates, you need to pull in the latest changes
188 =item 2 Generate C<configure>
194 After performing the above steps, continue
195 with the L<Common installation instructions>.
197 =head2 Common installation instructions
201 =item 1 Obtain C<GMP>
203 Building C<isl> requires C<GMP>, including its headers files.
204 Your distribution may not provide these header files by default
205 and you may need to install a package called C<gmp-devel> or something
206 similar. Alternatively, C<GMP> can be built from
207 source, available from L<http://gmplib.org/>.
211 C<isl> uses the standard C<autoconf> C<configure> script.
216 optionally followed by some configure options.
217 A complete list of options can be obtained by running
221 Below we discuss some of the more common options.
223 C<isl> can optionally use C<piplib>, but no
224 C<piplib> functionality is currently used by default.
225 The C<--with-piplib> option can
226 be used to specify which C<piplib>
227 library to use, either an installed version (C<system>),
228 an externally built version (C<build>)
229 or no version (C<no>). The option C<build> is mostly useful
230 in C<configure> scripts of larger projects that bundle both C<isl>
237 Installation prefix for C<isl>
239 =item C<--with-gmp-prefix>
241 Installation prefix for C<GMP> (architecture-independent files).
243 =item C<--with-gmp-exec-prefix>
245 Installation prefix for C<GMP> (architecture-dependent files).
247 =item C<--with-piplib>
249 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
251 =item C<--with-piplib-prefix>
253 Installation prefix for C<system> C<piplib> (architecture-independent files).
255 =item C<--with-piplib-exec-prefix>
257 Installation prefix for C<system> C<piplib> (architecture-dependent files).
259 =item C<--with-piplib-builddir>
261 Location where C<build> C<piplib> was built.
269 =item 4 Install (optional)
277 =head2 Initialization
279 All manipulations of integer sets and relations occur within
280 the context of an C<isl_ctx>.
281 A given C<isl_ctx> can only be used within a single thread.
282 All arguments of a function are required to have been allocated
283 within the same context.
284 There are currently no functions available for moving an object
285 from one C<isl_ctx> to another C<isl_ctx>. This means that
286 there is currently no way of safely moving an object from one
287 thread to another, unless the whole C<isl_ctx> is moved.
289 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
290 freed using C<isl_ctx_free>.
291 All objects allocated within an C<isl_ctx> should be freed
292 before the C<isl_ctx> itself is freed.
294 isl_ctx *isl_ctx_alloc();
295 void isl_ctx_free(isl_ctx *ctx);
299 All operations on integers, mainly the coefficients
300 of the constraints describing the sets and relations,
301 are performed in exact integer arithmetic using C<GMP>.
302 However, to allow future versions of C<isl> to optionally
303 support fixed integer arithmetic, all calls to C<GMP>
304 are wrapped inside C<isl> specific macros.
305 The basic type is C<isl_int> and the operations below
306 are available on this type.
307 The meanings of these operations are essentially the same
308 as their C<GMP> C<mpz_> counterparts.
309 As always with C<GMP> types, C<isl_int>s need to be
310 initialized with C<isl_int_init> before they can be used
311 and they need to be released with C<isl_int_clear>
313 The user should not assume that an C<isl_int> is represented
314 as a C<mpz_t>, but should instead explicitly convert between
315 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
316 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
320 =item isl_int_init(i)
322 =item isl_int_clear(i)
324 =item isl_int_set(r,i)
326 =item isl_int_set_si(r,i)
328 =item isl_int_set_gmp(r,g)
330 =item isl_int_get_gmp(i,g)
332 =item isl_int_abs(r,i)
334 =item isl_int_neg(r,i)
336 =item isl_int_swap(i,j)
338 =item isl_int_swap_or_set(i,j)
340 =item isl_int_add_ui(r,i,j)
342 =item isl_int_sub_ui(r,i,j)
344 =item isl_int_add(r,i,j)
346 =item isl_int_sub(r,i,j)
348 =item isl_int_mul(r,i,j)
350 =item isl_int_mul_ui(r,i,j)
352 =item isl_int_addmul(r,i,j)
354 =item isl_int_submul(r,i,j)
356 =item isl_int_gcd(r,i,j)
358 =item isl_int_lcm(r,i,j)
360 =item isl_int_divexact(r,i,j)
362 =item isl_int_cdiv_q(r,i,j)
364 =item isl_int_fdiv_q(r,i,j)
366 =item isl_int_fdiv_r(r,i,j)
368 =item isl_int_fdiv_q_ui(r,i,j)
370 =item isl_int_read(r,s)
372 =item isl_int_print(out,i,width)
376 =item isl_int_cmp(i,j)
378 =item isl_int_cmp_si(i,si)
380 =item isl_int_eq(i,j)
382 =item isl_int_ne(i,j)
384 =item isl_int_lt(i,j)
386 =item isl_int_le(i,j)
388 =item isl_int_gt(i,j)
390 =item isl_int_ge(i,j)
392 =item isl_int_abs_eq(i,j)
394 =item isl_int_abs_ne(i,j)
396 =item isl_int_abs_lt(i,j)
398 =item isl_int_abs_gt(i,j)
400 =item isl_int_abs_ge(i,j)
402 =item isl_int_is_zero(i)
404 =item isl_int_is_one(i)
406 =item isl_int_is_negone(i)
408 =item isl_int_is_pos(i)
410 =item isl_int_is_neg(i)
412 =item isl_int_is_nonpos(i)
414 =item isl_int_is_nonneg(i)
416 =item isl_int_is_divisible_by(i,j)
420 =head2 Sets and Relations
422 C<isl> uses six types of objects for representing sets and relations,
423 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
424 C<isl_union_set> and C<isl_union_map>.
425 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
426 can be described as a conjunction of affine constraints, while
427 C<isl_set> and C<isl_map> represent unions of
428 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
429 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
430 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
431 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
432 where spaces are considered different if they have a different number
433 of dimensions and/or different names (see L<"Spaces">).
434 The difference between sets and relations (maps) is that sets have
435 one set of variables, while relations have two sets of variables,
436 input variables and output variables.
438 =head2 Memory Management
440 Since a high-level operation on sets and/or relations usually involves
441 several substeps and since the user is usually not interested in
442 the intermediate results, most functions that return a new object
443 will also release all the objects passed as arguments.
444 If the user still wants to use one or more of these arguments
445 after the function call, she should pass along a copy of the
446 object rather than the object itself.
447 The user is then responsible for making sure that the original
448 object gets used somewhere else or is explicitly freed.
450 The arguments and return values of all documented functions are
451 annotated to make clear which arguments are released and which
452 arguments are preserved. In particular, the following annotations
459 C<__isl_give> means that a new object is returned.
460 The user should make sure that the returned pointer is
461 used exactly once as a value for an C<__isl_take> argument.
462 In between, it can be used as a value for as many
463 C<__isl_keep> arguments as the user likes.
464 There is one exception, and that is the case where the
465 pointer returned is C<NULL>. Is this case, the user
466 is free to use it as an C<__isl_take> argument or not.
470 C<__isl_take> means that the object the argument points to
471 is taken over by the function and may no longer be used
472 by the user as an argument to any other function.
473 The pointer value must be one returned by a function
474 returning an C<__isl_give> pointer.
475 If the user passes in a C<NULL> value, then this will
476 be treated as an error in the sense that the function will
477 not perform its usual operation. However, it will still
478 make sure that all the other C<__isl_take> arguments
483 C<__isl_keep> means that the function will only use the object
484 temporarily. After the function has finished, the user
485 can still use it as an argument to other functions.
486 A C<NULL> value will be treated in the same way as
487 a C<NULL> value for an C<__isl_take> argument.
491 =head2 Error Handling
493 C<isl> supports different ways to react in case a runtime error is triggered.
494 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
495 with two maps that have incompatible spaces. There are three possible ways
496 to react on error: to warn, to continue or to abort.
498 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
499 the last error in the corresponding C<isl_ctx> and the function in which the
500 error was triggered returns C<NULL>. An error does not corrupt internal state,
501 such that isl can continue to be used. C<isl> also provides functions to
502 read the last error and to reset the memory that stores the last error. The
503 last error is only stored for information purposes. Its presence does not
504 change the behavior of C<isl>. Hence, resetting an error is not required to
505 continue to use isl, but only to observe new errors.
508 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
509 void isl_ctx_reset_error(isl_ctx *ctx);
511 Another option is to continue on error. This is similar to warn on error mode,
512 except that C<isl> does not print any warning. This allows a program to
513 implement its own error reporting.
515 The last option is to directly abort the execution of the program from within
516 the isl library. This makes it obviously impossible to recover from an error,
517 but it allows to directly spot the error location. By aborting on error,
518 debuggers break at the location the error occurred and can provide a stack
519 trace. Other tools that automatically provide stack traces on abort or that do
520 not want to continue execution after an error was triggered may also prefer to
523 The on error behavior of isl can be specified by calling
524 C<isl_options_set_on_error> or by setting the command line option
525 C<--isl-on-error>. Valid arguments for the function call are
526 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
527 choices for the command line option are C<warn>, C<continue> and C<abort>.
528 It is also possible to query the current error mode.
530 #include <isl/options.h>
531 int isl_options_set_on_error(isl_ctx *ctx, int val);
532 int isl_options_get_on_error(isl_ctx *ctx);
536 Identifiers are used to identify both individual dimensions
537 and tuples of dimensions. They consist of a name and an optional
538 pointer. Identifiers with the same name but different pointer values
539 are considered to be distinct.
540 Identifiers can be constructed, copied, freed, inspected and printed
541 using the following functions.
544 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
545 __isl_keep const char *name, void *user);
546 __isl_give isl_id *isl_id_copy(isl_id *id);
547 void *isl_id_free(__isl_take isl_id *id);
549 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
550 void *isl_id_get_user(__isl_keep isl_id *id);
551 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
553 __isl_give isl_printer *isl_printer_print_id(
554 __isl_take isl_printer *p, __isl_keep isl_id *id);
556 Note that C<isl_id_get_name> returns a pointer to some internal
557 data structure, so the result can only be used while the
558 corresponding C<isl_id> is alive.
562 Whenever a new set or relation is created from scratch,
563 the space in which it lives needs to be specified using an C<isl_space>.
565 #include <isl/space.h>
566 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
567 unsigned nparam, unsigned n_in, unsigned n_out);
568 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
570 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
571 unsigned nparam, unsigned dim);
572 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
573 void isl_space_free(__isl_take isl_space *space);
574 unsigned isl_space_dim(__isl_keep isl_space *space,
575 enum isl_dim_type type);
577 The space used for creating a parameter domain
578 needs to be created using C<isl_space_params_alloc>.
579 For other sets, the space
580 needs to be created using C<isl_space_set_alloc>, while
581 for a relation, the space
582 needs to be created using C<isl_space_alloc>.
583 C<isl_space_dim> can be used
584 to find out the number of dimensions of each type in
585 a space, where type may be
586 C<isl_dim_param>, C<isl_dim_in> (only for relations),
587 C<isl_dim_out> (only for relations), C<isl_dim_set>
588 (only for sets) or C<isl_dim_all>.
590 To check whether a given space is that of a set or a map
591 or whether it is a parameter space, use these functions:
593 #include <isl/space.h>
594 int isl_space_is_params(__isl_keep isl_space *space);
595 int isl_space_is_set(__isl_keep isl_space *space);
597 It is often useful to create objects that live in the
598 same space as some other object. This can be accomplished
599 by creating the new objects
600 (see L<Creating New Sets and Relations> or
601 L<Creating New (Piecewise) Quasipolynomials>) based on the space
602 of the original object.
605 __isl_give isl_space *isl_basic_set_get_space(
606 __isl_keep isl_basic_set *bset);
607 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
609 #include <isl/union_set.h>
610 __isl_give isl_space *isl_union_set_get_space(
611 __isl_keep isl_union_set *uset);
614 __isl_give isl_space *isl_basic_map_get_space(
615 __isl_keep isl_basic_map *bmap);
616 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
618 #include <isl/union_map.h>
619 __isl_give isl_space *isl_union_map_get_space(
620 __isl_keep isl_union_map *umap);
622 #include <isl/constraint.h>
623 __isl_give isl_space *isl_constraint_get_space(
624 __isl_keep isl_constraint *constraint);
626 #include <isl/polynomial.h>
627 __isl_give isl_space *isl_qpolynomial_get_domain_space(
628 __isl_keep isl_qpolynomial *qp);
629 __isl_give isl_space *isl_qpolynomial_get_space(
630 __isl_keep isl_qpolynomial *qp);
631 __isl_give isl_space *isl_qpolynomial_fold_get_space(
632 __isl_keep isl_qpolynomial_fold *fold);
633 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
634 __isl_keep isl_pw_qpolynomial *pwqp);
635 __isl_give isl_space *isl_pw_qpolynomial_get_space(
636 __isl_keep isl_pw_qpolynomial *pwqp);
637 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
638 __isl_keep isl_pw_qpolynomial_fold *pwf);
639 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
640 __isl_keep isl_pw_qpolynomial_fold *pwf);
641 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
642 __isl_keep isl_union_pw_qpolynomial *upwqp);
643 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
644 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
647 __isl_give isl_space *isl_aff_get_domain_space(
648 __isl_keep isl_aff *aff);
649 __isl_give isl_space *isl_aff_get_space(
650 __isl_keep isl_aff *aff);
651 __isl_give isl_space *isl_pw_aff_get_domain_space(
652 __isl_keep isl_pw_aff *pwaff);
653 __isl_give isl_space *isl_pw_aff_get_space(
654 __isl_keep isl_pw_aff *pwaff);
655 __isl_give isl_space *isl_multi_aff_get_space(
656 __isl_keep isl_multi_aff *maff);
657 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
658 __isl_keep isl_pw_multi_aff *pma);
659 __isl_give isl_space *isl_pw_multi_aff_get_space(
660 __isl_keep isl_pw_multi_aff *pma);
662 #include <isl/point.h>
663 __isl_give isl_space *isl_point_get_space(
664 __isl_keep isl_point *pnt);
666 The identifiers or names of the individual dimensions may be set or read off
667 using the following functions.
669 #include <isl/space.h>
670 __isl_give isl_space *isl_space_set_dim_id(
671 __isl_take isl_space *space,
672 enum isl_dim_type type, unsigned pos,
673 __isl_take isl_id *id);
674 int isl_space_has_dim_id(__isl_keep isl_space *space,
675 enum isl_dim_type type, unsigned pos);
676 __isl_give isl_id *isl_space_get_dim_id(
677 __isl_keep isl_space *space,
678 enum isl_dim_type type, unsigned pos);
679 __isl_give isl_space *isl_space_set_dim_name(
680 __isl_take isl_space *space,
681 enum isl_dim_type type, unsigned pos,
682 __isl_keep const char *name);
683 int isl_space_has_dim_name(__isl_keep isl_space *space,
684 enum isl_dim_type type, unsigned pos);
685 __isl_keep const char *isl_space_get_dim_name(
686 __isl_keep isl_space *space,
687 enum isl_dim_type type, unsigned pos);
689 Note that C<isl_space_get_name> returns a pointer to some internal
690 data structure, so the result can only be used while the
691 corresponding C<isl_space> is alive.
692 Also note that every function that operates on two sets or relations
693 requires that both arguments have the same parameters. This also
694 means that if one of the arguments has named parameters, then the
695 other needs to have named parameters too and the names need to match.
696 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
697 arguments may have different parameters (as long as they are named),
698 in which case the result will have as parameters the union of the parameters of
701 Given the identifier or name of a dimension (typically a parameter),
702 its position can be obtained from the following function.
704 #include <isl/space.h>
705 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
706 enum isl_dim_type type, __isl_keep isl_id *id);
707 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
708 enum isl_dim_type type, const char *name);
710 The identifiers or names of entire spaces may be set or read off
711 using the following functions.
713 #include <isl/space.h>
714 __isl_give isl_space *isl_space_set_tuple_id(
715 __isl_take isl_space *space,
716 enum isl_dim_type type, __isl_take isl_id *id);
717 __isl_give isl_space *isl_space_reset_tuple_id(
718 __isl_take isl_space *space, enum isl_dim_type type);
719 int isl_space_has_tuple_id(__isl_keep isl_space *space,
720 enum isl_dim_type type);
721 __isl_give isl_id *isl_space_get_tuple_id(
722 __isl_keep isl_space *space, enum isl_dim_type type);
723 __isl_give isl_space *isl_space_set_tuple_name(
724 __isl_take isl_space *space,
725 enum isl_dim_type type, const char *s);
726 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
727 enum isl_dim_type type);
729 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
730 or C<isl_dim_set>. As with C<isl_space_get_name>,
731 the C<isl_space_get_tuple_name> function returns a pointer to some internal
733 Binary operations require the corresponding spaces of their arguments
734 to have the same name.
736 Spaces can be nested. In particular, the domain of a set or
737 the domain or range of a relation can be a nested relation.
738 The following functions can be used to construct and deconstruct
741 #include <isl/space.h>
742 int isl_space_is_wrapping(__isl_keep isl_space *space);
743 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
744 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
746 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
747 be the space of a set, while that of
748 C<isl_space_wrap> should be the space of a relation.
749 Conversely, the output of C<isl_space_unwrap> is the space
750 of a relation, while that of C<isl_space_wrap> is the space of a set.
752 Spaces can be created from other spaces
753 using the following functions.
755 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
756 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
757 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
758 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
759 __isl_give isl_space *isl_space_params(
760 __isl_take isl_space *space);
761 __isl_give isl_space *isl_space_set_from_params(
762 __isl_take isl_space *space);
763 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
764 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
765 __isl_take isl_space *right);
766 __isl_give isl_space *isl_space_align_params(
767 __isl_take isl_space *space1, __isl_take isl_space *space2)
768 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
769 enum isl_dim_type type, unsigned pos, unsigned n);
770 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
771 enum isl_dim_type type, unsigned n);
772 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
773 enum isl_dim_type type, unsigned first, unsigned n);
774 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
775 enum isl_dim_type dst_type, unsigned dst_pos,
776 enum isl_dim_type src_type, unsigned src_pos,
778 __isl_give isl_space *isl_space_map_from_set(
779 __isl_take isl_space *space);
780 __isl_give isl_space *isl_space_map_from_domain_and_range(
781 __isl_take isl_space *domain,
782 __isl_take isl_space *range);
783 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
785 Note that if dimensions are added or removed from a space, then
786 the name and the internal structure are lost.
790 A local space is essentially a space with
791 zero or more existentially quantified variables.
792 The local space of a basic set or relation can be obtained
793 using the following functions.
796 __isl_give isl_local_space *isl_basic_set_get_local_space(
797 __isl_keep isl_basic_set *bset);
800 __isl_give isl_local_space *isl_basic_map_get_local_space(
801 __isl_keep isl_basic_map *bmap);
803 A new local space can be created from a space using
805 #include <isl/local_space.h>
806 __isl_give isl_local_space *isl_local_space_from_space(
807 __isl_take isl_space *space);
809 They can be inspected, modified, copied and freed using the following functions.
811 #include <isl/local_space.h>
812 isl_ctx *isl_local_space_get_ctx(
813 __isl_keep isl_local_space *ls);
814 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
815 int isl_local_space_dim(__isl_keep isl_local_space *ls,
816 enum isl_dim_type type);
817 const char *isl_local_space_get_dim_name(
818 __isl_keep isl_local_space *ls,
819 enum isl_dim_type type, unsigned pos);
820 __isl_give isl_local_space *isl_local_space_set_dim_name(
821 __isl_take isl_local_space *ls,
822 enum isl_dim_type type, unsigned pos, const char *s);
823 __isl_give isl_local_space *isl_local_space_set_dim_id(
824 __isl_take isl_local_space *ls,
825 enum isl_dim_type type, unsigned pos,
826 __isl_take isl_id *id);
827 __isl_give isl_space *isl_local_space_get_space(
828 __isl_keep isl_local_space *ls);
829 __isl_give isl_aff *isl_local_space_get_div(
830 __isl_keep isl_local_space *ls, int pos);
831 __isl_give isl_local_space *isl_local_space_copy(
832 __isl_keep isl_local_space *ls);
833 void *isl_local_space_free(__isl_take isl_local_space *ls);
835 Two local spaces can be compared using
837 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
838 __isl_keep isl_local_space *ls2);
840 Local spaces can be created from other local spaces
841 using the following functions.
843 __isl_give isl_local_space *isl_local_space_domain(
844 __isl_take isl_local_space *ls);
845 __isl_give isl_local_space *isl_local_space_range(
846 __isl_take isl_local_space *ls);
847 __isl_give isl_local_space *isl_local_space_from_domain(
848 __isl_take isl_local_space *ls);
849 __isl_give isl_local_space *isl_local_space_intersect(
850 __isl_take isl_local_space *ls1,
851 __isl_take isl_local_space *ls2);
852 __isl_give isl_local_space *isl_local_space_add_dims(
853 __isl_take isl_local_space *ls,
854 enum isl_dim_type type, unsigned n);
855 __isl_give isl_local_space *isl_local_space_insert_dims(
856 __isl_take isl_local_space *ls,
857 enum isl_dim_type type, unsigned first, unsigned n);
858 __isl_give isl_local_space *isl_local_space_drop_dims(
859 __isl_take isl_local_space *ls,
860 enum isl_dim_type type, unsigned first, unsigned n);
862 =head2 Input and Output
864 C<isl> supports its own input/output format, which is similar
865 to the C<Omega> format, but also supports the C<PolyLib> format
870 The C<isl> format is similar to that of C<Omega>, but has a different
871 syntax for describing the parameters and allows for the definition
872 of an existentially quantified variable as the integer division
873 of an affine expression.
874 For example, the set of integers C<i> between C<0> and C<n>
875 such that C<i % 10 <= 6> can be described as
877 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
880 A set or relation can have several disjuncts, separated
881 by the keyword C<or>. Each disjunct is either a conjunction
882 of constraints or a projection (C<exists>) of a conjunction
883 of constraints. The constraints are separated by the keyword
886 =head3 C<PolyLib> format
888 If the represented set is a union, then the first line
889 contains a single number representing the number of disjuncts.
890 Otherwise, a line containing the number C<1> is optional.
892 Each disjunct is represented by a matrix of constraints.
893 The first line contains two numbers representing
894 the number of rows and columns,
895 where the number of rows is equal to the number of constraints
896 and the number of columns is equal to two plus the number of variables.
897 The following lines contain the actual rows of the constraint matrix.
898 In each row, the first column indicates whether the constraint
899 is an equality (C<0>) or inequality (C<1>). The final column
900 corresponds to the constant term.
902 If the set is parametric, then the coefficients of the parameters
903 appear in the last columns before the constant column.
904 The coefficients of any existentially quantified variables appear
905 between those of the set variables and those of the parameters.
907 =head3 Extended C<PolyLib> format
909 The extended C<PolyLib> format is nearly identical to the
910 C<PolyLib> format. The only difference is that the line
911 containing the number of rows and columns of a constraint matrix
912 also contains four additional numbers:
913 the number of output dimensions, the number of input dimensions,
914 the number of local dimensions (i.e., the number of existentially
915 quantified variables) and the number of parameters.
916 For sets, the number of ``output'' dimensions is equal
917 to the number of set dimensions, while the number of ``input''
923 __isl_give isl_basic_set *isl_basic_set_read_from_file(
924 isl_ctx *ctx, FILE *input);
925 __isl_give isl_basic_set *isl_basic_set_read_from_str(
926 isl_ctx *ctx, const char *str);
927 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
929 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
933 __isl_give isl_basic_map *isl_basic_map_read_from_file(
934 isl_ctx *ctx, FILE *input);
935 __isl_give isl_basic_map *isl_basic_map_read_from_str(
936 isl_ctx *ctx, const char *str);
937 __isl_give isl_map *isl_map_read_from_file(
938 isl_ctx *ctx, FILE *input);
939 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
942 #include <isl/union_set.h>
943 __isl_give isl_union_set *isl_union_set_read_from_file(
944 isl_ctx *ctx, FILE *input);
945 __isl_give isl_union_set *isl_union_set_read_from_str(
946 isl_ctx *ctx, const char *str);
948 #include <isl/union_map.h>
949 __isl_give isl_union_map *isl_union_map_read_from_file(
950 isl_ctx *ctx, FILE *input);
951 __isl_give isl_union_map *isl_union_map_read_from_str(
952 isl_ctx *ctx, const char *str);
954 The input format is autodetected and may be either the C<PolyLib> format
955 or the C<isl> format.
959 Before anything can be printed, an C<isl_printer> needs to
962 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
964 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
965 void isl_printer_free(__isl_take isl_printer *printer);
966 __isl_give char *isl_printer_get_str(
967 __isl_keep isl_printer *printer);
969 The behavior of the printer can be modified in various ways
971 __isl_give isl_printer *isl_printer_set_output_format(
972 __isl_take isl_printer *p, int output_format);
973 __isl_give isl_printer *isl_printer_set_indent(
974 __isl_take isl_printer *p, int indent);
975 __isl_give isl_printer *isl_printer_indent(
976 __isl_take isl_printer *p, int indent);
977 __isl_give isl_printer *isl_printer_set_prefix(
978 __isl_take isl_printer *p, const char *prefix);
979 __isl_give isl_printer *isl_printer_set_suffix(
980 __isl_take isl_printer *p, const char *suffix);
982 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
983 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
984 and defaults to C<ISL_FORMAT_ISL>.
985 Each line in the output is indented by C<indent> (set by
986 C<isl_printer_set_indent>) spaces
987 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
988 In the C<PolyLib> format output,
989 the coefficients of the existentially quantified variables
990 appear between those of the set variables and those
992 The function C<isl_printer_indent> increases the indentation
993 by the specified amount (which may be negative).
995 To actually print something, use
998 __isl_give isl_printer *isl_printer_print_basic_set(
999 __isl_take isl_printer *printer,
1000 __isl_keep isl_basic_set *bset);
1001 __isl_give isl_printer *isl_printer_print_set(
1002 __isl_take isl_printer *printer,
1003 __isl_keep isl_set *set);
1005 #include <isl/map.h>
1006 __isl_give isl_printer *isl_printer_print_basic_map(
1007 __isl_take isl_printer *printer,
1008 __isl_keep isl_basic_map *bmap);
1009 __isl_give isl_printer *isl_printer_print_map(
1010 __isl_take isl_printer *printer,
1011 __isl_keep isl_map *map);
1013 #include <isl/union_set.h>
1014 __isl_give isl_printer *isl_printer_print_union_set(
1015 __isl_take isl_printer *p,
1016 __isl_keep isl_union_set *uset);
1018 #include <isl/union_map.h>
1019 __isl_give isl_printer *isl_printer_print_union_map(
1020 __isl_take isl_printer *p,
1021 __isl_keep isl_union_map *umap);
1023 When called on a file printer, the following function flushes
1024 the file. When called on a string printer, the buffer is cleared.
1026 __isl_give isl_printer *isl_printer_flush(
1027 __isl_take isl_printer *p);
1029 =head2 Creating New Sets and Relations
1031 C<isl> has functions for creating some standard sets and relations.
1035 =item * Empty sets and relations
1037 __isl_give isl_basic_set *isl_basic_set_empty(
1038 __isl_take isl_space *space);
1039 __isl_give isl_basic_map *isl_basic_map_empty(
1040 __isl_take isl_space *space);
1041 __isl_give isl_set *isl_set_empty(
1042 __isl_take isl_space *space);
1043 __isl_give isl_map *isl_map_empty(
1044 __isl_take isl_space *space);
1045 __isl_give isl_union_set *isl_union_set_empty(
1046 __isl_take isl_space *space);
1047 __isl_give isl_union_map *isl_union_map_empty(
1048 __isl_take isl_space *space);
1050 For C<isl_union_set>s and C<isl_union_map>s, the space
1051 is only used to specify the parameters.
1053 =item * Universe sets and relations
1055 __isl_give isl_basic_set *isl_basic_set_universe(
1056 __isl_take isl_space *space);
1057 __isl_give isl_basic_map *isl_basic_map_universe(
1058 __isl_take isl_space *space);
1059 __isl_give isl_set *isl_set_universe(
1060 __isl_take isl_space *space);
1061 __isl_give isl_map *isl_map_universe(
1062 __isl_take isl_space *space);
1063 __isl_give isl_union_set *isl_union_set_universe(
1064 __isl_take isl_union_set *uset);
1065 __isl_give isl_union_map *isl_union_map_universe(
1066 __isl_take isl_union_map *umap);
1068 The sets and relations constructed by the functions above
1069 contain all integer values, while those constructed by the
1070 functions below only contain non-negative values.
1072 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1073 __isl_take isl_space *space);
1074 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1075 __isl_take isl_space *space);
1076 __isl_give isl_set *isl_set_nat_universe(
1077 __isl_take isl_space *space);
1078 __isl_give isl_map *isl_map_nat_universe(
1079 __isl_take isl_space *space);
1081 =item * Identity relations
1083 __isl_give isl_basic_map *isl_basic_map_identity(
1084 __isl_take isl_space *space);
1085 __isl_give isl_map *isl_map_identity(
1086 __isl_take isl_space *space);
1088 The number of input and output dimensions in C<space> needs
1091 =item * Lexicographic order
1093 __isl_give isl_map *isl_map_lex_lt(
1094 __isl_take isl_space *set_space);
1095 __isl_give isl_map *isl_map_lex_le(
1096 __isl_take isl_space *set_space);
1097 __isl_give isl_map *isl_map_lex_gt(
1098 __isl_take isl_space *set_space);
1099 __isl_give isl_map *isl_map_lex_ge(
1100 __isl_take isl_space *set_space);
1101 __isl_give isl_map *isl_map_lex_lt_first(
1102 __isl_take isl_space *space, unsigned n);
1103 __isl_give isl_map *isl_map_lex_le_first(
1104 __isl_take isl_space *space, unsigned n);
1105 __isl_give isl_map *isl_map_lex_gt_first(
1106 __isl_take isl_space *space, unsigned n);
1107 __isl_give isl_map *isl_map_lex_ge_first(
1108 __isl_take isl_space *space, unsigned n);
1110 The first four functions take a space for a B<set>
1111 and return relations that express that the elements in the domain
1112 are lexicographically less
1113 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1114 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1115 than the elements in the range.
1116 The last four functions take a space for a map
1117 and return relations that express that the first C<n> dimensions
1118 in the domain are lexicographically less
1119 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1120 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1121 than the first C<n> dimensions in the range.
1125 A basic set or relation can be converted to a set or relation
1126 using the following functions.
1128 __isl_give isl_set *isl_set_from_basic_set(
1129 __isl_take isl_basic_set *bset);
1130 __isl_give isl_map *isl_map_from_basic_map(
1131 __isl_take isl_basic_map *bmap);
1133 Sets and relations can be converted to union sets and relations
1134 using the following functions.
1136 __isl_give isl_union_map *isl_union_map_from_map(
1137 __isl_take isl_map *map);
1138 __isl_give isl_union_set *isl_union_set_from_set(
1139 __isl_take isl_set *set);
1141 The inverse conversions below can only be used if the input
1142 union set or relation is known to contain elements in exactly one
1145 __isl_give isl_set *isl_set_from_union_set(
1146 __isl_take isl_union_set *uset);
1147 __isl_give isl_map *isl_map_from_union_map(
1148 __isl_take isl_union_map *umap);
1150 A zero-dimensional set can be constructed on a given parameter domain
1151 using the following function.
1153 __isl_give isl_set *isl_set_from_params(
1154 __isl_take isl_set *set);
1156 Sets and relations can be copied and freed again using the following
1159 __isl_give isl_basic_set *isl_basic_set_copy(
1160 __isl_keep isl_basic_set *bset);
1161 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1162 __isl_give isl_union_set *isl_union_set_copy(
1163 __isl_keep isl_union_set *uset);
1164 __isl_give isl_basic_map *isl_basic_map_copy(
1165 __isl_keep isl_basic_map *bmap);
1166 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1167 __isl_give isl_union_map *isl_union_map_copy(
1168 __isl_keep isl_union_map *umap);
1169 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1170 void isl_set_free(__isl_take isl_set *set);
1171 void *isl_union_set_free(__isl_take isl_union_set *uset);
1172 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1173 void isl_map_free(__isl_take isl_map *map);
1174 void *isl_union_map_free(__isl_take isl_union_map *umap);
1176 Other sets and relations can be constructed by starting
1177 from a universe set or relation, adding equality and/or
1178 inequality constraints and then projecting out the
1179 existentially quantified variables, if any.
1180 Constraints can be constructed, manipulated and
1181 added to (or removed from) (basic) sets and relations
1182 using the following functions.
1184 #include <isl/constraint.h>
1185 __isl_give isl_constraint *isl_equality_alloc(
1186 __isl_take isl_local_space *ls);
1187 __isl_give isl_constraint *isl_inequality_alloc(
1188 __isl_take isl_local_space *ls);
1189 __isl_give isl_constraint *isl_constraint_set_constant(
1190 __isl_take isl_constraint *constraint, isl_int v);
1191 __isl_give isl_constraint *isl_constraint_set_constant_si(
1192 __isl_take isl_constraint *constraint, int v);
1193 __isl_give isl_constraint *isl_constraint_set_coefficient(
1194 __isl_take isl_constraint *constraint,
1195 enum isl_dim_type type, int pos, isl_int v);
1196 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1197 __isl_take isl_constraint *constraint,
1198 enum isl_dim_type type, int pos, int v);
1199 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1200 __isl_take isl_basic_map *bmap,
1201 __isl_take isl_constraint *constraint);
1202 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1203 __isl_take isl_basic_set *bset,
1204 __isl_take isl_constraint *constraint);
1205 __isl_give isl_map *isl_map_add_constraint(
1206 __isl_take isl_map *map,
1207 __isl_take isl_constraint *constraint);
1208 __isl_give isl_set *isl_set_add_constraint(
1209 __isl_take isl_set *set,
1210 __isl_take isl_constraint *constraint);
1211 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1212 __isl_take isl_basic_set *bset,
1213 __isl_take isl_constraint *constraint);
1215 For example, to create a set containing the even integers
1216 between 10 and 42, you would use the following code.
1219 isl_local_space *ls;
1221 isl_basic_set *bset;
1223 space = isl_space_set_alloc(ctx, 0, 2);
1224 bset = isl_basic_set_universe(isl_space_copy(space));
1225 ls = isl_local_space_from_space(space);
1227 c = isl_equality_alloc(isl_local_space_copy(ls));
1228 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1229 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1230 bset = isl_basic_set_add_constraint(bset, c);
1232 c = isl_inequality_alloc(isl_local_space_copy(ls));
1233 c = isl_constraint_set_constant_si(c, -10);
1234 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1235 bset = isl_basic_set_add_constraint(bset, c);
1237 c = isl_inequality_alloc(ls);
1238 c = isl_constraint_set_constant_si(c, 42);
1239 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1240 bset = isl_basic_set_add_constraint(bset, c);
1242 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1246 isl_basic_set *bset;
1247 bset = isl_basic_set_read_from_str(ctx,
1248 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1250 A basic set or relation can also be constructed from two matrices
1251 describing the equalities and the inequalities.
1253 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1254 __isl_take isl_space *space,
1255 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1256 enum isl_dim_type c1,
1257 enum isl_dim_type c2, enum isl_dim_type c3,
1258 enum isl_dim_type c4);
1259 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1260 __isl_take isl_space *space,
1261 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1262 enum isl_dim_type c1,
1263 enum isl_dim_type c2, enum isl_dim_type c3,
1264 enum isl_dim_type c4, enum isl_dim_type c5);
1266 The C<isl_dim_type> arguments indicate the order in which
1267 different kinds of variables appear in the input matrices
1268 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1269 C<isl_dim_set> and C<isl_dim_div> for sets and
1270 of C<isl_dim_cst>, C<isl_dim_param>,
1271 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1273 A (basic) set or relation can also be constructed from a (piecewise)
1274 (multiple) affine expression
1275 or a list of affine expressions
1276 (See L<"Piecewise Quasi Affine Expressions"> and
1277 L<"Piecewise Multiple Quasi Affine Expressions">).
1279 __isl_give isl_basic_map *isl_basic_map_from_aff(
1280 __isl_take isl_aff *aff);
1281 __isl_give isl_set *isl_set_from_pw_aff(
1282 __isl_take isl_pw_aff *pwaff);
1283 __isl_give isl_map *isl_map_from_pw_aff(
1284 __isl_take isl_pw_aff *pwaff);
1285 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1286 __isl_take isl_space *domain_space,
1287 __isl_take isl_aff_list *list);
1288 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1289 __isl_take isl_multi_aff *maff)
1290 __isl_give isl_set *isl_set_from_pw_multi_aff(
1291 __isl_take isl_pw_multi_aff *pma);
1292 __isl_give isl_map *isl_map_from_pw_multi_aff(
1293 __isl_take isl_pw_multi_aff *pma);
1295 The C<domain_dim> argument describes the domain of the resulting
1296 basic relation. It is required because the C<list> may consist
1297 of zero affine expressions.
1299 =head2 Inspecting Sets and Relations
1301 Usually, the user should not have to care about the actual constraints
1302 of the sets and maps, but should instead apply the abstract operations
1303 explained in the following sections.
1304 Occasionally, however, it may be required to inspect the individual
1305 coefficients of the constraints. This section explains how to do so.
1306 In these cases, it may also be useful to have C<isl> compute
1307 an explicit representation of the existentially quantified variables.
1309 __isl_give isl_set *isl_set_compute_divs(
1310 __isl_take isl_set *set);
1311 __isl_give isl_map *isl_map_compute_divs(
1312 __isl_take isl_map *map);
1313 __isl_give isl_union_set *isl_union_set_compute_divs(
1314 __isl_take isl_union_set *uset);
1315 __isl_give isl_union_map *isl_union_map_compute_divs(
1316 __isl_take isl_union_map *umap);
1318 This explicit representation defines the existentially quantified
1319 variables as integer divisions of the other variables, possibly
1320 including earlier existentially quantified variables.
1321 An explicitly represented existentially quantified variable therefore
1322 has a unique value when the values of the other variables are known.
1323 If, furthermore, the same existentials, i.e., existentials
1324 with the same explicit representations, should appear in the
1325 same order in each of the disjuncts of a set or map, then the user should call
1326 either of the following functions.
1328 __isl_give isl_set *isl_set_align_divs(
1329 __isl_take isl_set *set);
1330 __isl_give isl_map *isl_map_align_divs(
1331 __isl_take isl_map *map);
1333 Alternatively, the existentially quantified variables can be removed
1334 using the following functions, which compute an overapproximation.
1336 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1337 __isl_take isl_basic_set *bset);
1338 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1339 __isl_take isl_basic_map *bmap);
1340 __isl_give isl_set *isl_set_remove_divs(
1341 __isl_take isl_set *set);
1342 __isl_give isl_map *isl_map_remove_divs(
1343 __isl_take isl_map *map);
1345 To iterate over all the sets or maps in a union set or map, use
1347 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1348 int (*fn)(__isl_take isl_set *set, void *user),
1350 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1351 int (*fn)(__isl_take isl_map *map, void *user),
1354 The number of sets or maps in a union set or map can be obtained
1357 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1358 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1360 To extract the set or map in a given space from a union, use
1362 __isl_give isl_set *isl_union_set_extract_set(
1363 __isl_keep isl_union_set *uset,
1364 __isl_take isl_space *space);
1365 __isl_give isl_map *isl_union_map_extract_map(
1366 __isl_keep isl_union_map *umap,
1367 __isl_take isl_space *space);
1369 To iterate over all the basic sets or maps in a set or map, use
1371 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1372 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1374 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1375 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1378 The callback function C<fn> should return 0 if successful and
1379 -1 if an error occurs. In the latter case, or if any other error
1380 occurs, the above functions will return -1.
1382 It should be noted that C<isl> does not guarantee that
1383 the basic sets or maps passed to C<fn> are disjoint.
1384 If this is required, then the user should call one of
1385 the following functions first.
1387 __isl_give isl_set *isl_set_make_disjoint(
1388 __isl_take isl_set *set);
1389 __isl_give isl_map *isl_map_make_disjoint(
1390 __isl_take isl_map *map);
1392 The number of basic sets in a set can be obtained
1395 int isl_set_n_basic_set(__isl_keep isl_set *set);
1397 To iterate over the constraints of a basic set or map, use
1399 #include <isl/constraint.h>
1401 int isl_basic_map_foreach_constraint(
1402 __isl_keep isl_basic_map *bmap,
1403 int (*fn)(__isl_take isl_constraint *c, void *user),
1405 void *isl_constraint_free(__isl_take isl_constraint *c);
1407 Again, the callback function C<fn> should return 0 if successful and
1408 -1 if an error occurs. In the latter case, or if any other error
1409 occurs, the above functions will return -1.
1410 The constraint C<c> represents either an equality or an inequality.
1411 Use the following function to find out whether a constraint
1412 represents an equality. If not, it represents an inequality.
1414 int isl_constraint_is_equality(
1415 __isl_keep isl_constraint *constraint);
1417 The coefficients of the constraints can be inspected using
1418 the following functions.
1420 void isl_constraint_get_constant(
1421 __isl_keep isl_constraint *constraint, isl_int *v);
1422 void isl_constraint_get_coefficient(
1423 __isl_keep isl_constraint *constraint,
1424 enum isl_dim_type type, int pos, isl_int *v);
1425 int isl_constraint_involves_dims(
1426 __isl_keep isl_constraint *constraint,
1427 enum isl_dim_type type, unsigned first, unsigned n);
1429 The explicit representations of the existentially quantified
1430 variables can be inspected using the following function.
1431 Note that the user is only allowed to use this function
1432 if the inspected set or map is the result of a call
1433 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1434 The existentially quantified variable is equal to the floor
1435 of the returned affine expression. The affine expression
1436 itself can be inspected using the functions in
1437 L<"Piecewise Quasi Affine Expressions">.
1439 __isl_give isl_aff *isl_constraint_get_div(
1440 __isl_keep isl_constraint *constraint, int pos);
1442 To obtain the constraints of a basic set or map in matrix
1443 form, use the following functions.
1445 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1446 __isl_keep isl_basic_set *bset,
1447 enum isl_dim_type c1, enum isl_dim_type c2,
1448 enum isl_dim_type c3, enum isl_dim_type c4);
1449 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1450 __isl_keep isl_basic_set *bset,
1451 enum isl_dim_type c1, enum isl_dim_type c2,
1452 enum isl_dim_type c3, enum isl_dim_type c4);
1453 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1454 __isl_keep isl_basic_map *bmap,
1455 enum isl_dim_type c1,
1456 enum isl_dim_type c2, enum isl_dim_type c3,
1457 enum isl_dim_type c4, enum isl_dim_type c5);
1458 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1459 __isl_keep isl_basic_map *bmap,
1460 enum isl_dim_type c1,
1461 enum isl_dim_type c2, enum isl_dim_type c3,
1462 enum isl_dim_type c4, enum isl_dim_type c5);
1464 The C<isl_dim_type> arguments dictate the order in which
1465 different kinds of variables appear in the resulting matrix
1466 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1467 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1469 The number of parameters, input, output or set dimensions can
1470 be obtained using the following functions.
1472 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1473 enum isl_dim_type type);
1474 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1475 enum isl_dim_type type);
1476 unsigned isl_set_dim(__isl_keep isl_set *set,
1477 enum isl_dim_type type);
1478 unsigned isl_map_dim(__isl_keep isl_map *map,
1479 enum isl_dim_type type);
1481 To check whether the description of a set or relation depends
1482 on one or more given dimensions, it is not necessary to iterate over all
1483 constraints. Instead the following functions can be used.
1485 int isl_basic_set_involves_dims(
1486 __isl_keep isl_basic_set *bset,
1487 enum isl_dim_type type, unsigned first, unsigned n);
1488 int isl_set_involves_dims(__isl_keep isl_set *set,
1489 enum isl_dim_type type, unsigned first, unsigned n);
1490 int isl_basic_map_involves_dims(
1491 __isl_keep isl_basic_map *bmap,
1492 enum isl_dim_type type, unsigned first, unsigned n);
1493 int isl_map_involves_dims(__isl_keep isl_map *map,
1494 enum isl_dim_type type, unsigned first, unsigned n);
1496 Similarly, the following functions can be used to check whether
1497 a given dimension is involved in any lower or upper bound.
1499 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1500 enum isl_dim_type type, unsigned pos);
1501 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1502 enum isl_dim_type type, unsigned pos);
1504 The identifiers or names of the domain and range spaces of a set
1505 or relation can be read off or set using the following functions.
1507 __isl_give isl_set *isl_set_set_tuple_id(
1508 __isl_take isl_set *set, __isl_take isl_id *id);
1509 __isl_give isl_set *isl_set_reset_tuple_id(
1510 __isl_take isl_set *set);
1511 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1512 __isl_give isl_id *isl_set_get_tuple_id(
1513 __isl_keep isl_set *set);
1514 __isl_give isl_map *isl_map_set_tuple_id(
1515 __isl_take isl_map *map, enum isl_dim_type type,
1516 __isl_take isl_id *id);
1517 __isl_give isl_map *isl_map_reset_tuple_id(
1518 __isl_take isl_map *map, enum isl_dim_type type);
1519 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1520 enum isl_dim_type type);
1521 __isl_give isl_id *isl_map_get_tuple_id(
1522 __isl_keep isl_map *map, enum isl_dim_type type);
1524 const char *isl_basic_set_get_tuple_name(
1525 __isl_keep isl_basic_set *bset);
1526 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1527 __isl_take isl_basic_set *set, const char *s);
1528 const char *isl_set_get_tuple_name(
1529 __isl_keep isl_set *set);
1530 const char *isl_basic_map_get_tuple_name(
1531 __isl_keep isl_basic_map *bmap,
1532 enum isl_dim_type type);
1533 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1534 __isl_take isl_basic_map *bmap,
1535 enum isl_dim_type type, const char *s);
1536 const char *isl_map_get_tuple_name(
1537 __isl_keep isl_map *map,
1538 enum isl_dim_type type);
1540 As with C<isl_space_get_tuple_name>, the value returned points to
1541 an internal data structure.
1542 The identifiers, positions or names of individual dimensions can be
1543 read off using the following functions.
1545 __isl_give isl_set *isl_set_set_dim_id(
1546 __isl_take isl_set *set, enum isl_dim_type type,
1547 unsigned pos, __isl_take isl_id *id);
1548 int isl_set_has_dim_id(__isl_keep isl_set *set,
1549 enum isl_dim_type type, unsigned pos);
1550 __isl_give isl_id *isl_set_get_dim_id(
1551 __isl_keep isl_set *set, enum isl_dim_type type,
1553 int isl_basic_map_has_dim_id(
1554 __isl_keep isl_basic_map *bmap,
1555 enum isl_dim_type type, unsigned pos);
1556 __isl_give isl_map *isl_map_set_dim_id(
1557 __isl_take isl_map *map, enum isl_dim_type type,
1558 unsigned pos, __isl_take isl_id *id);
1559 int isl_map_has_dim_id(__isl_keep isl_map *map,
1560 enum isl_dim_type type, unsigned pos);
1561 __isl_give isl_id *isl_map_get_dim_id(
1562 __isl_keep isl_map *map, enum isl_dim_type type,
1565 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1566 enum isl_dim_type type, __isl_keep isl_id *id);
1567 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1568 enum isl_dim_type type, __isl_keep isl_id *id);
1569 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1570 enum isl_dim_type type, const char *name);
1571 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1572 enum isl_dim_type type, const char *name);
1574 const char *isl_constraint_get_dim_name(
1575 __isl_keep isl_constraint *constraint,
1576 enum isl_dim_type type, unsigned pos);
1577 const char *isl_basic_set_get_dim_name(
1578 __isl_keep isl_basic_set *bset,
1579 enum isl_dim_type type, unsigned pos);
1580 int isl_set_has_dim_name(__isl_keep isl_set *set,
1581 enum isl_dim_type type, unsigned pos);
1582 const char *isl_set_get_dim_name(
1583 __isl_keep isl_set *set,
1584 enum isl_dim_type type, unsigned pos);
1585 const char *isl_basic_map_get_dim_name(
1586 __isl_keep isl_basic_map *bmap,
1587 enum isl_dim_type type, unsigned pos);
1588 const char *isl_map_get_dim_name(
1589 __isl_keep isl_map *map,
1590 enum isl_dim_type type, unsigned pos);
1592 These functions are mostly useful to obtain the identifiers, positions
1593 or names of the parameters. Identifiers of individual dimensions are
1594 essentially only useful for printing. They are ignored by all other
1595 operations and may not be preserved across those operations.
1599 =head3 Unary Properties
1605 The following functions test whether the given set or relation
1606 contains any integer points. The ``plain'' variants do not perform
1607 any computations, but simply check if the given set or relation
1608 is already known to be empty.
1610 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1611 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1612 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1613 int isl_set_is_empty(__isl_keep isl_set *set);
1614 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1615 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1616 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1617 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1618 int isl_map_is_empty(__isl_keep isl_map *map);
1619 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1621 =item * Universality
1623 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1624 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1625 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1627 =item * Single-valuedness
1629 int isl_map_plain_is_single_valued(
1630 __isl_keep isl_map *map);
1631 int isl_map_is_single_valued(__isl_keep isl_map *map);
1632 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1636 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1637 int isl_map_is_injective(__isl_keep isl_map *map);
1638 int isl_union_map_plain_is_injective(
1639 __isl_keep isl_union_map *umap);
1640 int isl_union_map_is_injective(
1641 __isl_keep isl_union_map *umap);
1645 int isl_map_is_bijective(__isl_keep isl_map *map);
1646 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1650 int isl_basic_map_plain_is_fixed(
1651 __isl_keep isl_basic_map *bmap,
1652 enum isl_dim_type type, unsigned pos,
1654 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1655 enum isl_dim_type type, unsigned pos,
1657 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1658 enum isl_dim_type type, unsigned pos,
1661 Check if the relation obviously lies on a hyperplane where the given dimension
1662 has a fixed value and if so, return that value in C<*val>.
1666 To check whether a set is a parameter domain, use this function:
1668 int isl_set_is_params(__isl_keep isl_set *set);
1669 int isl_union_set_is_params(
1670 __isl_keep isl_union_set *uset);
1674 The following functions check whether the domain of the given
1675 (basic) set is a wrapped relation.
1677 int isl_basic_set_is_wrapping(
1678 __isl_keep isl_basic_set *bset);
1679 int isl_set_is_wrapping(__isl_keep isl_set *set);
1681 =item * Internal Product
1683 int isl_basic_map_can_zip(
1684 __isl_keep isl_basic_map *bmap);
1685 int isl_map_can_zip(__isl_keep isl_map *map);
1687 Check whether the product of domain and range of the given relation
1689 i.e., whether both domain and range are nested relations.
1693 =head3 Binary Properties
1699 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1700 __isl_keep isl_set *set2);
1701 int isl_set_is_equal(__isl_keep isl_set *set1,
1702 __isl_keep isl_set *set2);
1703 int isl_union_set_is_equal(
1704 __isl_keep isl_union_set *uset1,
1705 __isl_keep isl_union_set *uset2);
1706 int isl_basic_map_is_equal(
1707 __isl_keep isl_basic_map *bmap1,
1708 __isl_keep isl_basic_map *bmap2);
1709 int isl_map_is_equal(__isl_keep isl_map *map1,
1710 __isl_keep isl_map *map2);
1711 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1712 __isl_keep isl_map *map2);
1713 int isl_union_map_is_equal(
1714 __isl_keep isl_union_map *umap1,
1715 __isl_keep isl_union_map *umap2);
1717 =item * Disjointness
1719 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1720 __isl_keep isl_set *set2);
1724 int isl_basic_set_is_subset(
1725 __isl_keep isl_basic_set *bset1,
1726 __isl_keep isl_basic_set *bset2);
1727 int isl_set_is_subset(__isl_keep isl_set *set1,
1728 __isl_keep isl_set *set2);
1729 int isl_set_is_strict_subset(
1730 __isl_keep isl_set *set1,
1731 __isl_keep isl_set *set2);
1732 int isl_union_set_is_subset(
1733 __isl_keep isl_union_set *uset1,
1734 __isl_keep isl_union_set *uset2);
1735 int isl_union_set_is_strict_subset(
1736 __isl_keep isl_union_set *uset1,
1737 __isl_keep isl_union_set *uset2);
1738 int isl_basic_map_is_subset(
1739 __isl_keep isl_basic_map *bmap1,
1740 __isl_keep isl_basic_map *bmap2);
1741 int isl_basic_map_is_strict_subset(
1742 __isl_keep isl_basic_map *bmap1,
1743 __isl_keep isl_basic_map *bmap2);
1744 int isl_map_is_subset(
1745 __isl_keep isl_map *map1,
1746 __isl_keep isl_map *map2);
1747 int isl_map_is_strict_subset(
1748 __isl_keep isl_map *map1,
1749 __isl_keep isl_map *map2);
1750 int isl_union_map_is_subset(
1751 __isl_keep isl_union_map *umap1,
1752 __isl_keep isl_union_map *umap2);
1753 int isl_union_map_is_strict_subset(
1754 __isl_keep isl_union_map *umap1,
1755 __isl_keep isl_union_map *umap2);
1759 =head2 Unary Operations
1765 __isl_give isl_set *isl_set_complement(
1766 __isl_take isl_set *set);
1767 __isl_give isl_map *isl_map_complement(
1768 __isl_take isl_map *map);
1772 __isl_give isl_basic_map *isl_basic_map_reverse(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_map *isl_map_reverse(
1775 __isl_take isl_map *map);
1776 __isl_give isl_union_map *isl_union_map_reverse(
1777 __isl_take isl_union_map *umap);
1781 __isl_give isl_basic_set *isl_basic_set_project_out(
1782 __isl_take isl_basic_set *bset,
1783 enum isl_dim_type type, unsigned first, unsigned n);
1784 __isl_give isl_basic_map *isl_basic_map_project_out(
1785 __isl_take isl_basic_map *bmap,
1786 enum isl_dim_type type, unsigned first, unsigned n);
1787 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1788 enum isl_dim_type type, unsigned first, unsigned n);
1789 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1790 enum isl_dim_type type, unsigned first, unsigned n);
1791 __isl_give isl_basic_set *isl_basic_set_params(
1792 __isl_take isl_basic_set *bset);
1793 __isl_give isl_basic_set *isl_basic_map_domain(
1794 __isl_take isl_basic_map *bmap);
1795 __isl_give isl_basic_set *isl_basic_map_range(
1796 __isl_take isl_basic_map *bmap);
1797 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1798 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1799 __isl_give isl_set *isl_map_domain(
1800 __isl_take isl_map *bmap);
1801 __isl_give isl_set *isl_map_range(
1802 __isl_take isl_map *map);
1803 __isl_give isl_set *isl_union_set_params(
1804 __isl_take isl_union_set *uset);
1805 __isl_give isl_set *isl_union_map_params(
1806 __isl_take isl_union_map *umap);
1807 __isl_give isl_union_set *isl_union_map_domain(
1808 __isl_take isl_union_map *umap);
1809 __isl_give isl_union_set *isl_union_map_range(
1810 __isl_take isl_union_map *umap);
1812 __isl_give isl_basic_map *isl_basic_map_domain_map(
1813 __isl_take isl_basic_map *bmap);
1814 __isl_give isl_basic_map *isl_basic_map_range_map(
1815 __isl_take isl_basic_map *bmap);
1816 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1817 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1818 __isl_give isl_union_map *isl_union_map_domain_map(
1819 __isl_take isl_union_map *umap);
1820 __isl_give isl_union_map *isl_union_map_range_map(
1821 __isl_take isl_union_map *umap);
1823 The functions above construct a (basic, regular or union) relation
1824 that maps (a wrapped version of) the input relation to its domain or range.
1828 __isl_give isl_set *isl_set_eliminate(
1829 __isl_take isl_set *set, enum isl_dim_type type,
1830 unsigned first, unsigned n);
1831 __isl_give isl_basic_map *isl_basic_map_eliminate(
1832 __isl_take isl_basic_map *bmap,
1833 enum isl_dim_type type,
1834 unsigned first, unsigned n);
1835 __isl_give isl_map *isl_map_eliminate(
1836 __isl_take isl_map *map, enum isl_dim_type type,
1837 unsigned first, unsigned n);
1839 Eliminate the coefficients for the given dimensions from the constraints,
1840 without removing the dimensions.
1844 __isl_give isl_basic_set *isl_basic_set_fix(
1845 __isl_take isl_basic_set *bset,
1846 enum isl_dim_type type, unsigned pos,
1848 __isl_give isl_basic_set *isl_basic_set_fix_si(
1849 __isl_take isl_basic_set *bset,
1850 enum isl_dim_type type, unsigned pos, int value);
1851 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1852 enum isl_dim_type type, unsigned pos,
1854 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1855 enum isl_dim_type type, unsigned pos, int value);
1856 __isl_give isl_basic_map *isl_basic_map_fix_si(
1857 __isl_take isl_basic_map *bmap,
1858 enum isl_dim_type type, unsigned pos, int value);
1859 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1860 enum isl_dim_type type, unsigned pos, int value);
1862 Intersect the set or relation with the hyperplane where the given
1863 dimension has the fixed given value.
1865 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1866 __isl_take isl_basic_map *bmap,
1867 enum isl_dim_type type, unsigned pos, int value);
1868 __isl_give isl_set *isl_set_lower_bound_si(
1869 __isl_take isl_set *set,
1870 enum isl_dim_type type, unsigned pos, int value);
1871 __isl_give isl_map *isl_map_lower_bound_si(
1872 __isl_take isl_map *map,
1873 enum isl_dim_type type, unsigned pos, int value);
1874 __isl_give isl_set *isl_set_upper_bound_si(
1875 __isl_take isl_set *set,
1876 enum isl_dim_type type, unsigned pos, int value);
1877 __isl_give isl_map *isl_map_upper_bound_si(
1878 __isl_take isl_map *map,
1879 enum isl_dim_type type, unsigned pos, int value);
1881 Intersect the set or relation with the half-space where the given
1882 dimension has a value bounded by the fixed given value.
1884 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1885 enum isl_dim_type type1, int pos1,
1886 enum isl_dim_type type2, int pos2);
1887 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1888 enum isl_dim_type type1, int pos1,
1889 enum isl_dim_type type2, int pos2);
1891 Intersect the set or relation with the hyperplane where the given
1892 dimensions are equal to each other.
1894 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1895 enum isl_dim_type type1, int pos1,
1896 enum isl_dim_type type2, int pos2);
1898 Intersect the relation with the hyperplane where the given
1899 dimensions have opposite values.
1903 __isl_give isl_map *isl_set_identity(
1904 __isl_take isl_set *set);
1905 __isl_give isl_union_map *isl_union_set_identity(
1906 __isl_take isl_union_set *uset);
1908 Construct an identity relation on the given (union) set.
1912 __isl_give isl_basic_set *isl_basic_map_deltas(
1913 __isl_take isl_basic_map *bmap);
1914 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1915 __isl_give isl_union_set *isl_union_map_deltas(
1916 __isl_take isl_union_map *umap);
1918 These functions return a (basic) set containing the differences
1919 between image elements and corresponding domain elements in the input.
1921 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1922 __isl_take isl_basic_map *bmap);
1923 __isl_give isl_map *isl_map_deltas_map(
1924 __isl_take isl_map *map);
1925 __isl_give isl_union_map *isl_union_map_deltas_map(
1926 __isl_take isl_union_map *umap);
1928 The functions above construct a (basic, regular or union) relation
1929 that maps (a wrapped version of) the input relation to its delta set.
1933 Simplify the representation of a set or relation by trying
1934 to combine pairs of basic sets or relations into a single
1935 basic set or relation.
1937 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1938 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1939 __isl_give isl_union_set *isl_union_set_coalesce(
1940 __isl_take isl_union_set *uset);
1941 __isl_give isl_union_map *isl_union_map_coalesce(
1942 __isl_take isl_union_map *umap);
1944 =item * Detecting equalities
1946 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1947 __isl_take isl_basic_set *bset);
1948 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1949 __isl_take isl_basic_map *bmap);
1950 __isl_give isl_set *isl_set_detect_equalities(
1951 __isl_take isl_set *set);
1952 __isl_give isl_map *isl_map_detect_equalities(
1953 __isl_take isl_map *map);
1954 __isl_give isl_union_set *isl_union_set_detect_equalities(
1955 __isl_take isl_union_set *uset);
1956 __isl_give isl_union_map *isl_union_map_detect_equalities(
1957 __isl_take isl_union_map *umap);
1959 Simplify the representation of a set or relation by detecting implicit
1962 =item * Removing redundant constraints
1964 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1965 __isl_take isl_basic_set *bset);
1966 __isl_give isl_set *isl_set_remove_redundancies(
1967 __isl_take isl_set *set);
1968 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1969 __isl_take isl_basic_map *bmap);
1970 __isl_give isl_map *isl_map_remove_redundancies(
1971 __isl_take isl_map *map);
1975 __isl_give isl_basic_set *isl_set_convex_hull(
1976 __isl_take isl_set *set);
1977 __isl_give isl_basic_map *isl_map_convex_hull(
1978 __isl_take isl_map *map);
1980 If the input set or relation has any existentially quantified
1981 variables, then the result of these operations is currently undefined.
1985 __isl_give isl_basic_set *isl_set_simple_hull(
1986 __isl_take isl_set *set);
1987 __isl_give isl_basic_map *isl_map_simple_hull(
1988 __isl_take isl_map *map);
1989 __isl_give isl_union_map *isl_union_map_simple_hull(
1990 __isl_take isl_union_map *umap);
1992 These functions compute a single basic set or relation
1993 that contains the whole input set or relation.
1994 In particular, the output is described by translates
1995 of the constraints describing the basic sets or relations in the input.
1999 (See \autoref{s:simple hull}.)
2005 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2006 __isl_take isl_basic_set *bset);
2007 __isl_give isl_basic_set *isl_set_affine_hull(
2008 __isl_take isl_set *set);
2009 __isl_give isl_union_set *isl_union_set_affine_hull(
2010 __isl_take isl_union_set *uset);
2011 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2012 __isl_take isl_basic_map *bmap);
2013 __isl_give isl_basic_map *isl_map_affine_hull(
2014 __isl_take isl_map *map);
2015 __isl_give isl_union_map *isl_union_map_affine_hull(
2016 __isl_take isl_union_map *umap);
2018 In case of union sets and relations, the affine hull is computed
2021 =item * Polyhedral hull
2023 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2024 __isl_take isl_set *set);
2025 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2026 __isl_take isl_map *map);
2027 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2028 __isl_take isl_union_set *uset);
2029 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2030 __isl_take isl_union_map *umap);
2032 These functions compute a single basic set or relation
2033 not involving any existentially quantified variables
2034 that contains the whole input set or relation.
2035 In case of union sets and relations, the polyhedral hull is computed
2040 __isl_give isl_basic_set *isl_basic_set_sample(
2041 __isl_take isl_basic_set *bset);
2042 __isl_give isl_basic_set *isl_set_sample(
2043 __isl_take isl_set *set);
2044 __isl_give isl_basic_map *isl_basic_map_sample(
2045 __isl_take isl_basic_map *bmap);
2046 __isl_give isl_basic_map *isl_map_sample(
2047 __isl_take isl_map *map);
2049 If the input (basic) set or relation is non-empty, then return
2050 a singleton subset of the input. Otherwise, return an empty set.
2052 =item * Optimization
2054 #include <isl/ilp.h>
2055 enum isl_lp_result isl_basic_set_max(
2056 __isl_keep isl_basic_set *bset,
2057 __isl_keep isl_aff *obj, isl_int *opt)
2058 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2059 __isl_keep isl_aff *obj, isl_int *opt);
2060 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2061 __isl_keep isl_aff *obj, isl_int *opt);
2063 Compute the minimum or maximum of the integer affine expression C<obj>
2064 over the points in C<set>, returning the result in C<opt>.
2065 The return value may be one of C<isl_lp_error>,
2066 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2068 =item * Parametric optimization
2070 __isl_give isl_pw_aff *isl_set_dim_min(
2071 __isl_take isl_set *set, int pos);
2072 __isl_give isl_pw_aff *isl_set_dim_max(
2073 __isl_take isl_set *set, int pos);
2074 __isl_give isl_pw_aff *isl_map_dim_max(
2075 __isl_take isl_map *map, int pos);
2077 Compute the minimum or maximum of the given set or output dimension
2078 as a function of the parameters (and input dimensions), but independently
2079 of the other set or output dimensions.
2080 For lexicographic optimization, see L<"Lexicographic Optimization">.
2084 The following functions compute either the set of (rational) coefficient
2085 values of valid constraints for the given set or the set of (rational)
2086 values satisfying the constraints with coefficients from the given set.
2087 Internally, these two sets of functions perform essentially the
2088 same operations, except that the set of coefficients is assumed to
2089 be a cone, while the set of values may be any polyhedron.
2090 The current implementation is based on the Farkas lemma and
2091 Fourier-Motzkin elimination, but this may change or be made optional
2092 in future. In particular, future implementations may use different
2093 dualization algorithms or skip the elimination step.
2095 __isl_give isl_basic_set *isl_basic_set_coefficients(
2096 __isl_take isl_basic_set *bset);
2097 __isl_give isl_basic_set *isl_set_coefficients(
2098 __isl_take isl_set *set);
2099 __isl_give isl_union_set *isl_union_set_coefficients(
2100 __isl_take isl_union_set *bset);
2101 __isl_give isl_basic_set *isl_basic_set_solutions(
2102 __isl_take isl_basic_set *bset);
2103 __isl_give isl_basic_set *isl_set_solutions(
2104 __isl_take isl_set *set);
2105 __isl_give isl_union_set *isl_union_set_solutions(
2106 __isl_take isl_union_set *bset);
2110 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2112 __isl_give isl_union_map *isl_union_map_power(
2113 __isl_take isl_union_map *umap, int *exact);
2115 Compute a parametric representation for all positive powers I<k> of C<map>.
2116 The result maps I<k> to a nested relation corresponding to the
2117 I<k>th power of C<map>.
2118 The result may be an overapproximation. If the result is known to be exact,
2119 then C<*exact> is set to C<1>.
2121 =item * Transitive closure
2123 __isl_give isl_map *isl_map_transitive_closure(
2124 __isl_take isl_map *map, int *exact);
2125 __isl_give isl_union_map *isl_union_map_transitive_closure(
2126 __isl_take isl_union_map *umap, int *exact);
2128 Compute the transitive closure of C<map>.
2129 The result may be an overapproximation. If the result is known to be exact,
2130 then C<*exact> is set to C<1>.
2132 =item * Reaching path lengths
2134 __isl_give isl_map *isl_map_reaching_path_lengths(
2135 __isl_take isl_map *map, int *exact);
2137 Compute a relation that maps each element in the range of C<map>
2138 to the lengths of all paths composed of edges in C<map> that
2139 end up in the given element.
2140 The result may be an overapproximation. If the result is known to be exact,
2141 then C<*exact> is set to C<1>.
2142 To compute the I<maximal> path length, the resulting relation
2143 should be postprocessed by C<isl_map_lexmax>.
2144 In particular, if the input relation is a dependence relation
2145 (mapping sources to sinks), then the maximal path length corresponds
2146 to the free schedule.
2147 Note, however, that C<isl_map_lexmax> expects the maximum to be
2148 finite, so if the path lengths are unbounded (possibly due to
2149 the overapproximation), then you will get an error message.
2153 __isl_give isl_basic_set *isl_basic_map_wrap(
2154 __isl_take isl_basic_map *bmap);
2155 __isl_give isl_set *isl_map_wrap(
2156 __isl_take isl_map *map);
2157 __isl_give isl_union_set *isl_union_map_wrap(
2158 __isl_take isl_union_map *umap);
2159 __isl_give isl_basic_map *isl_basic_set_unwrap(
2160 __isl_take isl_basic_set *bset);
2161 __isl_give isl_map *isl_set_unwrap(
2162 __isl_take isl_set *set);
2163 __isl_give isl_union_map *isl_union_set_unwrap(
2164 __isl_take isl_union_set *uset);
2168 Remove any internal structure of domain (and range) of the given
2169 set or relation. If there is any such internal structure in the input,
2170 then the name of the space is also removed.
2172 __isl_give isl_basic_set *isl_basic_set_flatten(
2173 __isl_take isl_basic_set *bset);
2174 __isl_give isl_set *isl_set_flatten(
2175 __isl_take isl_set *set);
2176 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2177 __isl_take isl_basic_map *bmap);
2178 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2179 __isl_take isl_basic_map *bmap);
2180 __isl_give isl_map *isl_map_flatten_range(
2181 __isl_take isl_map *map);
2182 __isl_give isl_map *isl_map_flatten_domain(
2183 __isl_take isl_map *map);
2184 __isl_give isl_basic_map *isl_basic_map_flatten(
2185 __isl_take isl_basic_map *bmap);
2186 __isl_give isl_map *isl_map_flatten(
2187 __isl_take isl_map *map);
2189 __isl_give isl_map *isl_set_flatten_map(
2190 __isl_take isl_set *set);
2192 The function above constructs a relation
2193 that maps the input set to a flattened version of the set.
2197 Lift the input set to a space with extra dimensions corresponding
2198 to the existentially quantified variables in the input.
2199 In particular, the result lives in a wrapped map where the domain
2200 is the original space and the range corresponds to the original
2201 existentially quantified variables.
2203 __isl_give isl_basic_set *isl_basic_set_lift(
2204 __isl_take isl_basic_set *bset);
2205 __isl_give isl_set *isl_set_lift(
2206 __isl_take isl_set *set);
2207 __isl_give isl_union_set *isl_union_set_lift(
2208 __isl_take isl_union_set *uset);
2210 Given a local space that contains the existentially quantified
2211 variables of a set, a basic relation that, when applied to
2212 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2213 can be constructed using the following function.
2215 #include <isl/local_space.h>
2216 __isl_give isl_basic_map *isl_local_space_lifting(
2217 __isl_take isl_local_space *ls);
2219 =item * Internal Product
2221 __isl_give isl_basic_map *isl_basic_map_zip(
2222 __isl_take isl_basic_map *bmap);
2223 __isl_give isl_map *isl_map_zip(
2224 __isl_take isl_map *map);
2225 __isl_give isl_union_map *isl_union_map_zip(
2226 __isl_take isl_union_map *umap);
2228 Given a relation with nested relations for domain and range,
2229 interchange the range of the domain with the domain of the range.
2231 =item * Aligning parameters
2233 __isl_give isl_set *isl_set_align_params(
2234 __isl_take isl_set *set,
2235 __isl_take isl_space *model);
2236 __isl_give isl_map *isl_map_align_params(
2237 __isl_take isl_map *map,
2238 __isl_take isl_space *model);
2240 Change the order of the parameters of the given set or relation
2241 such that the first parameters match those of C<model>.
2242 This may involve the introduction of extra parameters.
2243 All parameters need to be named.
2245 =item * Dimension manipulation
2247 __isl_give isl_set *isl_set_add_dims(
2248 __isl_take isl_set *set,
2249 enum isl_dim_type type, unsigned n);
2250 __isl_give isl_map *isl_map_add_dims(
2251 __isl_take isl_map *map,
2252 enum isl_dim_type type, unsigned n);
2253 __isl_give isl_set *isl_set_insert_dims(
2254 __isl_take isl_set *set,
2255 enum isl_dim_type type, unsigned pos, unsigned n);
2256 __isl_give isl_map *isl_map_insert_dims(
2257 __isl_take isl_map *map,
2258 enum isl_dim_type type, unsigned pos, unsigned n);
2259 __isl_give isl_basic_set *isl_basic_set_move_dims(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type dst_type, unsigned dst_pos,
2262 enum isl_dim_type src_type, unsigned src_pos,
2264 __isl_give isl_basic_map *isl_basic_map_move_dims(
2265 __isl_take isl_basic_map *bmap,
2266 enum isl_dim_type dst_type, unsigned dst_pos,
2267 enum isl_dim_type src_type, unsigned src_pos,
2269 __isl_give isl_set *isl_set_move_dims(
2270 __isl_take isl_set *set,
2271 enum isl_dim_type dst_type, unsigned dst_pos,
2272 enum isl_dim_type src_type, unsigned src_pos,
2274 __isl_give isl_map *isl_map_move_dims(
2275 __isl_take isl_map *map,
2276 enum isl_dim_type dst_type, unsigned dst_pos,
2277 enum isl_dim_type src_type, unsigned src_pos,
2280 It is usually not advisable to directly change the (input or output)
2281 space of a set or a relation as this removes the name and the internal
2282 structure of the space. However, the above functions can be useful
2283 to add new parameters, assuming
2284 C<isl_set_align_params> and C<isl_map_align_params>
2289 =head2 Binary Operations
2291 The two arguments of a binary operation not only need to live
2292 in the same C<isl_ctx>, they currently also need to have
2293 the same (number of) parameters.
2295 =head3 Basic Operations
2299 =item * Intersection
2301 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2302 __isl_take isl_basic_set *bset1,
2303 __isl_take isl_basic_set *bset2);
2304 __isl_give isl_basic_set *isl_basic_set_intersect(
2305 __isl_take isl_basic_set *bset1,
2306 __isl_take isl_basic_set *bset2);
2307 __isl_give isl_set *isl_set_intersect_params(
2308 __isl_take isl_set *set,
2309 __isl_take isl_set *params);
2310 __isl_give isl_set *isl_set_intersect(
2311 __isl_take isl_set *set1,
2312 __isl_take isl_set *set2);
2313 __isl_give isl_union_set *isl_union_set_intersect_params(
2314 __isl_take isl_union_set *uset,
2315 __isl_take isl_set *set);
2316 __isl_give isl_union_map *isl_union_map_intersect_params(
2317 __isl_take isl_union_map *umap,
2318 __isl_take isl_set *set);
2319 __isl_give isl_union_set *isl_union_set_intersect(
2320 __isl_take isl_union_set *uset1,
2321 __isl_take isl_union_set *uset2);
2322 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2323 __isl_take isl_basic_map *bmap,
2324 __isl_take isl_basic_set *bset);
2325 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2326 __isl_take isl_basic_map *bmap,
2327 __isl_take isl_basic_set *bset);
2328 __isl_give isl_basic_map *isl_basic_map_intersect(
2329 __isl_take isl_basic_map *bmap1,
2330 __isl_take isl_basic_map *bmap2);
2331 __isl_give isl_map *isl_map_intersect_params(
2332 __isl_take isl_map *map,
2333 __isl_take isl_set *params);
2334 __isl_give isl_map *isl_map_intersect_domain(
2335 __isl_take isl_map *map,
2336 __isl_take isl_set *set);
2337 __isl_give isl_map *isl_map_intersect_range(
2338 __isl_take isl_map *map,
2339 __isl_take isl_set *set);
2340 __isl_give isl_map *isl_map_intersect(
2341 __isl_take isl_map *map1,
2342 __isl_take isl_map *map2);
2343 __isl_give isl_union_map *isl_union_map_intersect_domain(
2344 __isl_take isl_union_map *umap,
2345 __isl_take isl_union_set *uset);
2346 __isl_give isl_union_map *isl_union_map_intersect_range(
2347 __isl_take isl_union_map *umap,
2348 __isl_take isl_union_set *uset);
2349 __isl_give isl_union_map *isl_union_map_intersect(
2350 __isl_take isl_union_map *umap1,
2351 __isl_take isl_union_map *umap2);
2355 __isl_give isl_set *isl_basic_set_union(
2356 __isl_take isl_basic_set *bset1,
2357 __isl_take isl_basic_set *bset2);
2358 __isl_give isl_map *isl_basic_map_union(
2359 __isl_take isl_basic_map *bmap1,
2360 __isl_take isl_basic_map *bmap2);
2361 __isl_give isl_set *isl_set_union(
2362 __isl_take isl_set *set1,
2363 __isl_take isl_set *set2);
2364 __isl_give isl_map *isl_map_union(
2365 __isl_take isl_map *map1,
2366 __isl_take isl_map *map2);
2367 __isl_give isl_union_set *isl_union_set_union(
2368 __isl_take isl_union_set *uset1,
2369 __isl_take isl_union_set *uset2);
2370 __isl_give isl_union_map *isl_union_map_union(
2371 __isl_take isl_union_map *umap1,
2372 __isl_take isl_union_map *umap2);
2374 =item * Set difference
2376 __isl_give isl_set *isl_set_subtract(
2377 __isl_take isl_set *set1,
2378 __isl_take isl_set *set2);
2379 __isl_give isl_map *isl_map_subtract(
2380 __isl_take isl_map *map1,
2381 __isl_take isl_map *map2);
2382 __isl_give isl_map *isl_map_subtract_domain(
2383 __isl_take isl_map *map,
2384 __isl_take isl_set *dom);
2385 __isl_give isl_map *isl_map_subtract_range(
2386 __isl_take isl_map *map,
2387 __isl_take isl_set *dom);
2388 __isl_give isl_union_set *isl_union_set_subtract(
2389 __isl_take isl_union_set *uset1,
2390 __isl_take isl_union_set *uset2);
2391 __isl_give isl_union_map *isl_union_map_subtract(
2392 __isl_take isl_union_map *umap1,
2393 __isl_take isl_union_map *umap2);
2397 __isl_give isl_basic_set *isl_basic_set_apply(
2398 __isl_take isl_basic_set *bset,
2399 __isl_take isl_basic_map *bmap);
2400 __isl_give isl_set *isl_set_apply(
2401 __isl_take isl_set *set,
2402 __isl_take isl_map *map);
2403 __isl_give isl_union_set *isl_union_set_apply(
2404 __isl_take isl_union_set *uset,
2405 __isl_take isl_union_map *umap);
2406 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2407 __isl_take isl_basic_map *bmap1,
2408 __isl_take isl_basic_map *bmap2);
2409 __isl_give isl_basic_map *isl_basic_map_apply_range(
2410 __isl_take isl_basic_map *bmap1,
2411 __isl_take isl_basic_map *bmap2);
2412 __isl_give isl_map *isl_map_apply_domain(
2413 __isl_take isl_map *map1,
2414 __isl_take isl_map *map2);
2415 __isl_give isl_union_map *isl_union_map_apply_domain(
2416 __isl_take isl_union_map *umap1,
2417 __isl_take isl_union_map *umap2);
2418 __isl_give isl_map *isl_map_apply_range(
2419 __isl_take isl_map *map1,
2420 __isl_take isl_map *map2);
2421 __isl_give isl_union_map *isl_union_map_apply_range(
2422 __isl_take isl_union_map *umap1,
2423 __isl_take isl_union_map *umap2);
2425 =item * Cartesian Product
2427 __isl_give isl_set *isl_set_product(
2428 __isl_take isl_set *set1,
2429 __isl_take isl_set *set2);
2430 __isl_give isl_union_set *isl_union_set_product(
2431 __isl_take isl_union_set *uset1,
2432 __isl_take isl_union_set *uset2);
2433 __isl_give isl_basic_map *isl_basic_map_domain_product(
2434 __isl_take isl_basic_map *bmap1,
2435 __isl_take isl_basic_map *bmap2);
2436 __isl_give isl_basic_map *isl_basic_map_range_product(
2437 __isl_take isl_basic_map *bmap1,
2438 __isl_take isl_basic_map *bmap2);
2439 __isl_give isl_map *isl_map_domain_product(
2440 __isl_take isl_map *map1,
2441 __isl_take isl_map *map2);
2442 __isl_give isl_map *isl_map_range_product(
2443 __isl_take isl_map *map1,
2444 __isl_take isl_map *map2);
2445 __isl_give isl_union_map *isl_union_map_range_product(
2446 __isl_take isl_union_map *umap1,
2447 __isl_take isl_union_map *umap2);
2448 __isl_give isl_map *isl_map_product(
2449 __isl_take isl_map *map1,
2450 __isl_take isl_map *map2);
2451 __isl_give isl_union_map *isl_union_map_product(
2452 __isl_take isl_union_map *umap1,
2453 __isl_take isl_union_map *umap2);
2455 The above functions compute the cross product of the given
2456 sets or relations. The domains and ranges of the results
2457 are wrapped maps between domains and ranges of the inputs.
2458 To obtain a ``flat'' product, use the following functions
2461 __isl_give isl_basic_set *isl_basic_set_flat_product(
2462 __isl_take isl_basic_set *bset1,
2463 __isl_take isl_basic_set *bset2);
2464 __isl_give isl_set *isl_set_flat_product(
2465 __isl_take isl_set *set1,
2466 __isl_take isl_set *set2);
2467 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2468 __isl_take isl_basic_map *bmap1,
2469 __isl_take isl_basic_map *bmap2);
2470 __isl_give isl_map *isl_map_flat_domain_product(
2471 __isl_take isl_map *map1,
2472 __isl_take isl_map *map2);
2473 __isl_give isl_map *isl_map_flat_range_product(
2474 __isl_take isl_map *map1,
2475 __isl_take isl_map *map2);
2476 __isl_give isl_union_map *isl_union_map_flat_range_product(
2477 __isl_take isl_union_map *umap1,
2478 __isl_take isl_union_map *umap2);
2479 __isl_give isl_basic_map *isl_basic_map_flat_product(
2480 __isl_take isl_basic_map *bmap1,
2481 __isl_take isl_basic_map *bmap2);
2482 __isl_give isl_map *isl_map_flat_product(
2483 __isl_take isl_map *map1,
2484 __isl_take isl_map *map2);
2486 =item * Simplification
2488 __isl_give isl_basic_set *isl_basic_set_gist(
2489 __isl_take isl_basic_set *bset,
2490 __isl_take isl_basic_set *context);
2491 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2492 __isl_take isl_set *context);
2493 __isl_give isl_set *isl_set_gist_params(
2494 __isl_take isl_set *set,
2495 __isl_take isl_set *context);
2496 __isl_give isl_union_set *isl_union_set_gist(
2497 __isl_take isl_union_set *uset,
2498 __isl_take isl_union_set *context);
2499 __isl_give isl_union_set *isl_union_set_gist_params(
2500 __isl_take isl_union_set *uset,
2501 __isl_take isl_set *set);
2502 __isl_give isl_basic_map *isl_basic_map_gist(
2503 __isl_take isl_basic_map *bmap,
2504 __isl_take isl_basic_map *context);
2505 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2506 __isl_take isl_map *context);
2507 __isl_give isl_map *isl_map_gist_params(
2508 __isl_take isl_map *map,
2509 __isl_take isl_set *context);
2510 __isl_give isl_map *isl_map_gist_domain(
2511 __isl_take isl_map *map,
2512 __isl_take isl_set *context);
2513 __isl_give isl_map *isl_map_gist_range(
2514 __isl_take isl_map *map,
2515 __isl_take isl_set *context);
2516 __isl_give isl_union_map *isl_union_map_gist(
2517 __isl_take isl_union_map *umap,
2518 __isl_take isl_union_map *context);
2519 __isl_give isl_union_map *isl_union_map_gist_params(
2520 __isl_take isl_union_map *umap,
2521 __isl_take isl_set *set);
2522 __isl_give isl_union_map *isl_union_map_gist_domain(
2523 __isl_take isl_union_map *umap,
2524 __isl_take isl_union_set *uset);
2525 __isl_give isl_union_map *isl_union_map_gist_range(
2526 __isl_take isl_union_map *umap,
2527 __isl_take isl_union_set *uset);
2529 The gist operation returns a set or relation that has the
2530 same intersection with the context as the input set or relation.
2531 Any implicit equality in the intersection is made explicit in the result,
2532 while all inequalities that are redundant with respect to the intersection
2534 In case of union sets and relations, the gist operation is performed
2539 =head3 Lexicographic Optimization
2541 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2542 the following functions
2543 compute a set that contains the lexicographic minimum or maximum
2544 of the elements in C<set> (or C<bset>) for those values of the parameters
2545 that satisfy C<dom>.
2546 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2547 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2549 In other words, the union of the parameter values
2550 for which the result is non-empty and of C<*empty>
2553 __isl_give isl_set *isl_basic_set_partial_lexmin(
2554 __isl_take isl_basic_set *bset,
2555 __isl_take isl_basic_set *dom,
2556 __isl_give isl_set **empty);
2557 __isl_give isl_set *isl_basic_set_partial_lexmax(
2558 __isl_take isl_basic_set *bset,
2559 __isl_take isl_basic_set *dom,
2560 __isl_give isl_set **empty);
2561 __isl_give isl_set *isl_set_partial_lexmin(
2562 __isl_take isl_set *set, __isl_take isl_set *dom,
2563 __isl_give isl_set **empty);
2564 __isl_give isl_set *isl_set_partial_lexmax(
2565 __isl_take isl_set *set, __isl_take isl_set *dom,
2566 __isl_give isl_set **empty);
2568 Given a (basic) set C<set> (or C<bset>), the following functions simply
2569 return a set containing the lexicographic minimum or maximum
2570 of the elements in C<set> (or C<bset>).
2571 In case of union sets, the optimum is computed per space.
2573 __isl_give isl_set *isl_basic_set_lexmin(
2574 __isl_take isl_basic_set *bset);
2575 __isl_give isl_set *isl_basic_set_lexmax(
2576 __isl_take isl_basic_set *bset);
2577 __isl_give isl_set *isl_set_lexmin(
2578 __isl_take isl_set *set);
2579 __isl_give isl_set *isl_set_lexmax(
2580 __isl_take isl_set *set);
2581 __isl_give isl_union_set *isl_union_set_lexmin(
2582 __isl_take isl_union_set *uset);
2583 __isl_give isl_union_set *isl_union_set_lexmax(
2584 __isl_take isl_union_set *uset);
2586 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2587 the following functions
2588 compute a relation that maps each element of C<dom>
2589 to the single lexicographic minimum or maximum
2590 of the elements that are associated to that same
2591 element in C<map> (or C<bmap>).
2592 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2593 that contains the elements in C<dom> that do not map
2594 to any elements in C<map> (or C<bmap>).
2595 In other words, the union of the domain of the result and of C<*empty>
2598 __isl_give isl_map *isl_basic_map_partial_lexmax(
2599 __isl_take isl_basic_map *bmap,
2600 __isl_take isl_basic_set *dom,
2601 __isl_give isl_set **empty);
2602 __isl_give isl_map *isl_basic_map_partial_lexmin(
2603 __isl_take isl_basic_map *bmap,
2604 __isl_take isl_basic_set *dom,
2605 __isl_give isl_set **empty);
2606 __isl_give isl_map *isl_map_partial_lexmax(
2607 __isl_take isl_map *map, __isl_take isl_set *dom,
2608 __isl_give isl_set **empty);
2609 __isl_give isl_map *isl_map_partial_lexmin(
2610 __isl_take isl_map *map, __isl_take isl_set *dom,
2611 __isl_give isl_set **empty);
2613 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2614 return a map mapping each element in the domain of
2615 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2616 of all elements associated to that element.
2617 In case of union relations, the optimum is computed per space.
2619 __isl_give isl_map *isl_basic_map_lexmin(
2620 __isl_take isl_basic_map *bmap);
2621 __isl_give isl_map *isl_basic_map_lexmax(
2622 __isl_take isl_basic_map *bmap);
2623 __isl_give isl_map *isl_map_lexmin(
2624 __isl_take isl_map *map);
2625 __isl_give isl_map *isl_map_lexmax(
2626 __isl_take isl_map *map);
2627 __isl_give isl_union_map *isl_union_map_lexmin(
2628 __isl_take isl_union_map *umap);
2629 __isl_give isl_union_map *isl_union_map_lexmax(
2630 __isl_take isl_union_map *umap);
2632 The following functions return their result in the form of
2633 a piecewise multi-affine expression
2634 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2635 but are otherwise equivalent to the corresponding functions
2636 returning a basic set or relation.
2638 __isl_give isl_pw_multi_aff *
2639 isl_basic_map_lexmin_pw_multi_aff(
2640 __isl_take isl_basic_map *bmap);
2641 __isl_give isl_pw_multi_aff *
2642 isl_basic_set_partial_lexmin_pw_multi_aff(
2643 __isl_take isl_basic_set *bset,
2644 __isl_take isl_basic_set *dom,
2645 __isl_give isl_set **empty);
2646 __isl_give isl_pw_multi_aff *
2647 isl_basic_set_partial_lexmax_pw_multi_aff(
2648 __isl_take isl_basic_set *bset,
2649 __isl_take isl_basic_set *dom,
2650 __isl_give isl_set **empty);
2651 __isl_give isl_pw_multi_aff *
2652 isl_basic_map_partial_lexmin_pw_multi_aff(
2653 __isl_take isl_basic_map *bmap,
2654 __isl_take isl_basic_set *dom,
2655 __isl_give isl_set **empty);
2656 __isl_give isl_pw_multi_aff *
2657 isl_basic_map_partial_lexmax_pw_multi_aff(
2658 __isl_take isl_basic_map *bmap,
2659 __isl_take isl_basic_set *dom,
2660 __isl_give isl_set **empty);
2664 Lists are defined over several element types, including
2665 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2666 Here we take lists of C<isl_set>s as an example.
2667 Lists can be created, copied and freed using the following functions.
2669 #include <isl/list.h>
2670 __isl_give isl_set_list *isl_set_list_from_set(
2671 __isl_take isl_set *el);
2672 __isl_give isl_set_list *isl_set_list_alloc(
2673 isl_ctx *ctx, int n);
2674 __isl_give isl_set_list *isl_set_list_copy(
2675 __isl_keep isl_set_list *list);
2676 __isl_give isl_set_list *isl_set_list_add(
2677 __isl_take isl_set_list *list,
2678 __isl_take isl_set *el);
2679 __isl_give isl_set_list *isl_set_list_concat(
2680 __isl_take isl_set_list *list1,
2681 __isl_take isl_set_list *list2);
2682 void *isl_set_list_free(__isl_take isl_set_list *list);
2684 C<isl_set_list_alloc> creates an empty list with a capacity for
2685 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2688 Lists can be inspected using the following functions.
2690 #include <isl/list.h>
2691 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2692 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2693 __isl_give isl_set *isl_set_list_get_set(
2694 __isl_keep isl_set_list *list, int index);
2695 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2696 int (*fn)(__isl_take isl_set *el, void *user),
2699 Lists can be printed using
2701 #include <isl/list.h>
2702 __isl_give isl_printer *isl_printer_print_set_list(
2703 __isl_take isl_printer *p,
2704 __isl_keep isl_set_list *list);
2708 Matrices can be created, copied and freed using the following functions.
2710 #include <isl/mat.h>
2711 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2712 unsigned n_row, unsigned n_col);
2713 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2714 void isl_mat_free(__isl_take isl_mat *mat);
2716 Note that the elements of a newly created matrix may have arbitrary values.
2717 The elements can be changed and inspected using the following functions.
2719 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2720 int isl_mat_rows(__isl_keep isl_mat *mat);
2721 int isl_mat_cols(__isl_keep isl_mat *mat);
2722 int isl_mat_get_element(__isl_keep isl_mat *mat,
2723 int row, int col, isl_int *v);
2724 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2725 int row, int col, isl_int v);
2726 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2727 int row, int col, int v);
2729 C<isl_mat_get_element> will return a negative value if anything went wrong.
2730 In that case, the value of C<*v> is undefined.
2732 The following function can be used to compute the (right) inverse
2733 of a matrix, i.e., a matrix such that the product of the original
2734 and the inverse (in that order) is a multiple of the identity matrix.
2735 The input matrix is assumed to be of full row-rank.
2737 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2739 The following function can be used to compute the (right) kernel
2740 (or null space) of a matrix, i.e., a matrix such that the product of
2741 the original and the kernel (in that order) is the zero matrix.
2743 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2745 =head2 Piecewise Quasi Affine Expressions
2747 The zero quasi affine expression on a given domain can be created using
2749 __isl_give isl_aff *isl_aff_zero_on_domain(
2750 __isl_take isl_local_space *ls);
2752 Note that the space in which the resulting object lives is a map space
2753 with the given space as domain and a one-dimensional range.
2755 An empty piecewise quasi affine expression (one with no cells)
2756 or a piecewise quasi affine expression with a single cell can
2757 be created using the following functions.
2759 #include <isl/aff.h>
2760 __isl_give isl_pw_aff *isl_pw_aff_empty(
2761 __isl_take isl_space *space);
2762 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2763 __isl_take isl_set *set, __isl_take isl_aff *aff);
2764 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2765 __isl_take isl_aff *aff);
2767 A piecewise quasi affine expression that is equal to 1 on a set
2768 and 0 outside the set can be created using the following function.
2770 #include <isl/aff.h>
2771 __isl_give isl_pw_aff *isl_set_indicator_function(
2772 __isl_take isl_set *set);
2774 Quasi affine expressions can be copied and freed using
2776 #include <isl/aff.h>
2777 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2778 void *isl_aff_free(__isl_take isl_aff *aff);
2780 __isl_give isl_pw_aff *isl_pw_aff_copy(
2781 __isl_keep isl_pw_aff *pwaff);
2782 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2784 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2785 using the following function. The constraint is required to have
2786 a non-zero coefficient for the specified dimension.
2788 #include <isl/constraint.h>
2789 __isl_give isl_aff *isl_constraint_get_bound(
2790 __isl_keep isl_constraint *constraint,
2791 enum isl_dim_type type, int pos);
2793 The entire affine expression of the constraint can also be extracted
2794 using the following function.
2796 #include <isl/constraint.h>
2797 __isl_give isl_aff *isl_constraint_get_aff(
2798 __isl_keep isl_constraint *constraint);
2800 Conversely, an equality constraint equating
2801 the affine expression to zero or an inequality constraint enforcing
2802 the affine expression to be non-negative, can be constructed using
2804 __isl_give isl_constraint *isl_equality_from_aff(
2805 __isl_take isl_aff *aff);
2806 __isl_give isl_constraint *isl_inequality_from_aff(
2807 __isl_take isl_aff *aff);
2809 The expression can be inspected using
2811 #include <isl/aff.h>
2812 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2813 int isl_aff_dim(__isl_keep isl_aff *aff,
2814 enum isl_dim_type type);
2815 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2816 __isl_keep isl_aff *aff);
2817 __isl_give isl_local_space *isl_aff_get_local_space(
2818 __isl_keep isl_aff *aff);
2819 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2820 enum isl_dim_type type, unsigned pos);
2821 const char *isl_pw_aff_get_dim_name(
2822 __isl_keep isl_pw_aff *pa,
2823 enum isl_dim_type type, unsigned pos);
2824 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2825 enum isl_dim_type type, unsigned pos);
2826 __isl_give isl_id *isl_pw_aff_get_dim_id(
2827 __isl_keep isl_pw_aff *pa,
2828 enum isl_dim_type type, unsigned pos);
2829 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2831 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2832 enum isl_dim_type type, int pos, isl_int *v);
2833 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2835 __isl_give isl_aff *isl_aff_get_div(
2836 __isl_keep isl_aff *aff, int pos);
2838 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2839 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2840 int (*fn)(__isl_take isl_set *set,
2841 __isl_take isl_aff *aff,
2842 void *user), void *user);
2844 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2845 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2847 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2848 enum isl_dim_type type, unsigned first, unsigned n);
2849 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2850 enum isl_dim_type type, unsigned first, unsigned n);
2852 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2853 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2854 enum isl_dim_type type);
2855 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2857 It can be modified using
2859 #include <isl/aff.h>
2860 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2861 __isl_take isl_pw_aff *pwaff,
2862 enum isl_dim_type type, __isl_take isl_id *id);
2863 __isl_give isl_aff *isl_aff_set_dim_name(
2864 __isl_take isl_aff *aff, enum isl_dim_type type,
2865 unsigned pos, const char *s);
2866 __isl_give isl_aff *isl_aff_set_dim_id(
2867 __isl_take isl_aff *aff, enum isl_dim_type type,
2868 unsigned pos, __isl_take isl_id *id);
2869 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2870 __isl_take isl_pw_aff *pma,
2871 enum isl_dim_type type, unsigned pos,
2872 __isl_take isl_id *id);
2873 __isl_give isl_aff *isl_aff_set_constant(
2874 __isl_take isl_aff *aff, isl_int v);
2875 __isl_give isl_aff *isl_aff_set_constant_si(
2876 __isl_take isl_aff *aff, int v);
2877 __isl_give isl_aff *isl_aff_set_coefficient(
2878 __isl_take isl_aff *aff,
2879 enum isl_dim_type type, int pos, isl_int v);
2880 __isl_give isl_aff *isl_aff_set_coefficient_si(
2881 __isl_take isl_aff *aff,
2882 enum isl_dim_type type, int pos, int v);
2883 __isl_give isl_aff *isl_aff_set_denominator(
2884 __isl_take isl_aff *aff, isl_int v);
2886 __isl_give isl_aff *isl_aff_add_constant(
2887 __isl_take isl_aff *aff, isl_int v);
2888 __isl_give isl_aff *isl_aff_add_constant_si(
2889 __isl_take isl_aff *aff, int v);
2890 __isl_give isl_aff *isl_aff_add_coefficient(
2891 __isl_take isl_aff *aff,
2892 enum isl_dim_type type, int pos, isl_int v);
2893 __isl_give isl_aff *isl_aff_add_coefficient_si(
2894 __isl_take isl_aff *aff,
2895 enum isl_dim_type type, int pos, int v);
2897 __isl_give isl_aff *isl_aff_insert_dims(
2898 __isl_take isl_aff *aff,
2899 enum isl_dim_type type, unsigned first, unsigned n);
2900 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2901 __isl_take isl_pw_aff *pwaff,
2902 enum isl_dim_type type, unsigned first, unsigned n);
2903 __isl_give isl_aff *isl_aff_add_dims(
2904 __isl_take isl_aff *aff,
2905 enum isl_dim_type type, unsigned n);
2906 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2907 __isl_take isl_pw_aff *pwaff,
2908 enum isl_dim_type type, unsigned n);
2909 __isl_give isl_aff *isl_aff_drop_dims(
2910 __isl_take isl_aff *aff,
2911 enum isl_dim_type type, unsigned first, unsigned n);
2912 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2913 __isl_take isl_pw_aff *pwaff,
2914 enum isl_dim_type type, unsigned first, unsigned n);
2916 Note that the C<set_constant> and C<set_coefficient> functions
2917 set the I<numerator> of the constant or coefficient, while
2918 C<add_constant> and C<add_coefficient> add an integer value to
2919 the possibly rational constant or coefficient.
2921 To check whether an affine expressions is obviously zero
2922 or obviously equal to some other affine expression, use
2924 #include <isl/aff.h>
2925 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2926 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2927 __isl_keep isl_aff *aff2);
2928 int isl_pw_aff_plain_is_equal(
2929 __isl_keep isl_pw_aff *pwaff1,
2930 __isl_keep isl_pw_aff *pwaff2);
2934 #include <isl/aff.h>
2935 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2936 __isl_take isl_aff *aff2);
2937 __isl_give isl_pw_aff *isl_pw_aff_add(
2938 __isl_take isl_pw_aff *pwaff1,
2939 __isl_take isl_pw_aff *pwaff2);
2940 __isl_give isl_pw_aff *isl_pw_aff_min(
2941 __isl_take isl_pw_aff *pwaff1,
2942 __isl_take isl_pw_aff *pwaff2);
2943 __isl_give isl_pw_aff *isl_pw_aff_max(
2944 __isl_take isl_pw_aff *pwaff1,
2945 __isl_take isl_pw_aff *pwaff2);
2946 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2947 __isl_take isl_aff *aff2);
2948 __isl_give isl_pw_aff *isl_pw_aff_sub(
2949 __isl_take isl_pw_aff *pwaff1,
2950 __isl_take isl_pw_aff *pwaff2);
2951 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2952 __isl_give isl_pw_aff *isl_pw_aff_neg(
2953 __isl_take isl_pw_aff *pwaff);
2954 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2955 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2956 __isl_take isl_pw_aff *pwaff);
2957 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2958 __isl_give isl_pw_aff *isl_pw_aff_floor(
2959 __isl_take isl_pw_aff *pwaff);
2960 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2962 __isl_give isl_pw_aff *isl_pw_aff_mod(
2963 __isl_take isl_pw_aff *pwaff, isl_int mod);
2964 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2966 __isl_give isl_pw_aff *isl_pw_aff_scale(
2967 __isl_take isl_pw_aff *pwaff, isl_int f);
2968 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2970 __isl_give isl_aff *isl_aff_scale_down_ui(
2971 __isl_take isl_aff *aff, unsigned f);
2972 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2973 __isl_take isl_pw_aff *pwaff, isl_int f);
2975 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2976 __isl_take isl_pw_aff_list *list);
2977 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2978 __isl_take isl_pw_aff_list *list);
2980 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2981 __isl_take isl_pw_aff *pwqp);
2983 __isl_give isl_aff *isl_aff_align_params(
2984 __isl_take isl_aff *aff,
2985 __isl_take isl_space *model);
2986 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2987 __isl_take isl_pw_aff *pwaff,
2988 __isl_take isl_space *model);
2990 __isl_give isl_aff *isl_aff_project_domain_on_params(
2991 __isl_take isl_aff *aff);
2993 __isl_give isl_aff *isl_aff_gist_params(
2994 __isl_take isl_aff *aff,
2995 __isl_take isl_set *context);
2996 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2997 __isl_take isl_set *context);
2998 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2999 __isl_take isl_pw_aff *pwaff,
3000 __isl_take isl_set *context);
3001 __isl_give isl_pw_aff *isl_pw_aff_gist(
3002 __isl_take isl_pw_aff *pwaff,
3003 __isl_take isl_set *context);
3005 __isl_give isl_set *isl_pw_aff_domain(
3006 __isl_take isl_pw_aff *pwaff);
3007 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3008 __isl_take isl_pw_aff *pa,
3009 __isl_take isl_set *set);
3010 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3011 __isl_take isl_pw_aff *pa,
3012 __isl_take isl_set *set);
3014 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3015 __isl_take isl_aff *aff2);
3016 __isl_give isl_pw_aff *isl_pw_aff_mul(
3017 __isl_take isl_pw_aff *pwaff1,
3018 __isl_take isl_pw_aff *pwaff2);
3020 When multiplying two affine expressions, at least one of the two needs
3023 #include <isl/aff.h>
3024 __isl_give isl_basic_set *isl_aff_le_basic_set(
3025 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3026 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3027 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3028 __isl_give isl_set *isl_pw_aff_eq_set(
3029 __isl_take isl_pw_aff *pwaff1,
3030 __isl_take isl_pw_aff *pwaff2);
3031 __isl_give isl_set *isl_pw_aff_ne_set(
3032 __isl_take isl_pw_aff *pwaff1,
3033 __isl_take isl_pw_aff *pwaff2);
3034 __isl_give isl_set *isl_pw_aff_le_set(
3035 __isl_take isl_pw_aff *pwaff1,
3036 __isl_take isl_pw_aff *pwaff2);
3037 __isl_give isl_set *isl_pw_aff_lt_set(
3038 __isl_take isl_pw_aff *pwaff1,
3039 __isl_take isl_pw_aff *pwaff2);
3040 __isl_give isl_set *isl_pw_aff_ge_set(
3041 __isl_take isl_pw_aff *pwaff1,
3042 __isl_take isl_pw_aff *pwaff2);
3043 __isl_give isl_set *isl_pw_aff_gt_set(
3044 __isl_take isl_pw_aff *pwaff1,
3045 __isl_take isl_pw_aff *pwaff2);
3047 __isl_give isl_set *isl_pw_aff_list_eq_set(
3048 __isl_take isl_pw_aff_list *list1,
3049 __isl_take isl_pw_aff_list *list2);
3050 __isl_give isl_set *isl_pw_aff_list_ne_set(
3051 __isl_take isl_pw_aff_list *list1,
3052 __isl_take isl_pw_aff_list *list2);
3053 __isl_give isl_set *isl_pw_aff_list_le_set(
3054 __isl_take isl_pw_aff_list *list1,
3055 __isl_take isl_pw_aff_list *list2);
3056 __isl_give isl_set *isl_pw_aff_list_lt_set(
3057 __isl_take isl_pw_aff_list *list1,
3058 __isl_take isl_pw_aff_list *list2);
3059 __isl_give isl_set *isl_pw_aff_list_ge_set(
3060 __isl_take isl_pw_aff_list *list1,
3061 __isl_take isl_pw_aff_list *list2);
3062 __isl_give isl_set *isl_pw_aff_list_gt_set(
3063 __isl_take isl_pw_aff_list *list1,
3064 __isl_take isl_pw_aff_list *list2);
3066 The function C<isl_aff_ge_basic_set> returns a basic set
3067 containing those elements in the shared space
3068 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3069 The function C<isl_aff_ge_set> returns a set
3070 containing those elements in the shared domain
3071 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3072 The functions operating on C<isl_pw_aff_list> apply the corresponding
3073 C<isl_pw_aff> function to each pair of elements in the two lists.
3075 #include <isl/aff.h>
3076 __isl_give isl_set *isl_pw_aff_nonneg_set(
3077 __isl_take isl_pw_aff *pwaff);
3078 __isl_give isl_set *isl_pw_aff_zero_set(
3079 __isl_take isl_pw_aff *pwaff);
3080 __isl_give isl_set *isl_pw_aff_non_zero_set(
3081 __isl_take isl_pw_aff *pwaff);
3083 The function C<isl_pw_aff_nonneg_set> returns a set
3084 containing those elements in the domain
3085 of C<pwaff> where C<pwaff> is non-negative.
3087 #include <isl/aff.h>
3088 __isl_give isl_pw_aff *isl_pw_aff_cond(
3089 __isl_take isl_set *cond,
3090 __isl_take isl_pw_aff *pwaff_true,
3091 __isl_take isl_pw_aff *pwaff_false);
3093 The function C<isl_pw_aff_cond> performs a conditional operator
3094 and returns an expression that is equal to C<pwaff_true>
3095 for elements in C<cond> and equal to C<pwaff_false> for elements
3098 #include <isl/aff.h>
3099 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3100 __isl_take isl_pw_aff *pwaff1,
3101 __isl_take isl_pw_aff *pwaff2);
3102 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3103 __isl_take isl_pw_aff *pwaff1,
3104 __isl_take isl_pw_aff *pwaff2);
3105 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3106 __isl_take isl_pw_aff *pwaff1,
3107 __isl_take isl_pw_aff *pwaff2);
3109 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3110 expression with a domain that is the union of those of C<pwaff1> and
3111 C<pwaff2> and such that on each cell, the quasi-affine expression is
3112 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3113 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3114 associated expression is the defined one.
3116 An expression can be read from input using
3118 #include <isl/aff.h>
3119 __isl_give isl_aff *isl_aff_read_from_str(
3120 isl_ctx *ctx, const char *str);
3121 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3122 isl_ctx *ctx, const char *str);
3124 An expression can be printed using
3126 #include <isl/aff.h>
3127 __isl_give isl_printer *isl_printer_print_aff(
3128 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3130 __isl_give isl_printer *isl_printer_print_pw_aff(
3131 __isl_take isl_printer *p,
3132 __isl_keep isl_pw_aff *pwaff);
3134 =head2 Piecewise Multiple Quasi Affine Expressions
3136 An C<isl_multi_aff> object represents a sequence of
3137 zero or more affine expressions, all defined on the same domain space.
3139 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3142 #include <isl/aff.h>
3143 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3144 __isl_take isl_space *space,
3145 __isl_take isl_aff_list *list);
3147 An empty piecewise multiple quasi affine expression (one with no cells) or
3148 a piecewise multiple quasi affine expression with a single cell can
3149 be created using the following functions.
3151 #include <isl/aff.h>
3152 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3153 __isl_take isl_space *space);
3154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3155 __isl_take isl_set *set,
3156 __isl_take isl_multi_aff *maff);
3158 A piecewise multiple quasi affine expression can also be initialized
3159 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3160 and the C<isl_map> is single-valued.
3162 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3163 __isl_take isl_set *set);
3164 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3165 __isl_take isl_map *map);
3167 Multiple quasi affine expressions can be copied and freed using
3169 #include <isl/aff.h>
3170 __isl_give isl_multi_aff *isl_multi_aff_copy(
3171 __isl_keep isl_multi_aff *maff);
3172 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3174 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3175 __isl_keep isl_pw_multi_aff *pma);
3176 void *isl_pw_multi_aff_free(
3177 __isl_take isl_pw_multi_aff *pma);
3179 The expression can be inspected using
3181 #include <isl/aff.h>
3182 isl_ctx *isl_multi_aff_get_ctx(
3183 __isl_keep isl_multi_aff *maff);
3184 isl_ctx *isl_pw_multi_aff_get_ctx(
3185 __isl_keep isl_pw_multi_aff *pma);
3186 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3187 enum isl_dim_type type);
3188 unsigned isl_pw_multi_aff_dim(
3189 __isl_keep isl_pw_multi_aff *pma,
3190 enum isl_dim_type type);
3191 __isl_give isl_aff *isl_multi_aff_get_aff(
3192 __isl_keep isl_multi_aff *multi, int pos);
3193 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3194 __isl_keep isl_pw_multi_aff *pma, int pos);
3195 const char *isl_pw_multi_aff_get_dim_name(
3196 __isl_keep isl_pw_multi_aff *pma,
3197 enum isl_dim_type type, unsigned pos);
3198 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3199 __isl_keep isl_pw_multi_aff *pma,
3200 enum isl_dim_type type, unsigned pos);
3201 const char *isl_multi_aff_get_tuple_name(
3202 __isl_keep isl_multi_aff *multi,
3203 enum isl_dim_type type);
3204 const char *isl_pw_multi_aff_get_tuple_name(
3205 __isl_keep isl_pw_multi_aff *pma,
3206 enum isl_dim_type type);
3207 int isl_pw_multi_aff_has_tuple_id(
3208 __isl_keep isl_pw_multi_aff *pma,
3209 enum isl_dim_type type);
3210 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3211 __isl_keep isl_pw_multi_aff *pma,
3212 enum isl_dim_type type);
3214 int isl_pw_multi_aff_foreach_piece(
3215 __isl_keep isl_pw_multi_aff *pma,
3216 int (*fn)(__isl_take isl_set *set,
3217 __isl_take isl_multi_aff *maff,
3218 void *user), void *user);
3220 It can be modified using
3222 #include <isl/aff.h>
3223 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3224 __isl_take isl_multi_aff *maff,
3225 enum isl_dim_type type, unsigned pos, const char *s);
3226 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3227 __isl_take isl_multi_aff *maff,
3228 enum isl_dim_type type, __isl_take isl_id *id);
3229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3230 __isl_take isl_pw_multi_aff *pma,
3231 enum isl_dim_type type, __isl_take isl_id *id);
3233 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3234 __isl_take isl_multi_aff *maff,
3235 enum isl_dim_type type, unsigned first, unsigned n);
3237 To check whether two multiple affine expressions are
3238 obviously equal to each other, use
3240 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3241 __isl_keep isl_multi_aff *maff2);
3242 int isl_pw_multi_aff_plain_is_equal(
3243 __isl_keep isl_pw_multi_aff *pma1,
3244 __isl_keep isl_pw_multi_aff *pma2);
3248 #include <isl/aff.h>
3249 __isl_give isl_multi_aff *isl_multi_aff_add(
3250 __isl_take isl_multi_aff *maff1,
3251 __isl_take isl_multi_aff *maff2);
3252 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3253 __isl_take isl_pw_multi_aff *pma1,
3254 __isl_take isl_pw_multi_aff *pma2);
3255 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3256 __isl_take isl_pw_multi_aff *pma1,
3257 __isl_take isl_pw_multi_aff *pma2);
3258 __isl_give isl_multi_aff *isl_multi_aff_scale(
3259 __isl_take isl_multi_aff *maff,
3261 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3262 __isl_take isl_pw_multi_aff *pma,
3263 __isl_take isl_set *set);
3264 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3265 __isl_take isl_pw_multi_aff *pma,
3266 __isl_take isl_set *set);
3267 __isl_give isl_multi_aff *isl_multi_aff_lift(
3268 __isl_take isl_multi_aff *maff,
3269 __isl_give isl_local_space **ls);
3270 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3271 __isl_take isl_pw_multi_aff *pma);
3272 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3273 __isl_take isl_multi_aff *maff,
3274 __isl_take isl_set *context);
3275 __isl_give isl_multi_aff *isl_multi_aff_gist(
3276 __isl_take isl_multi_aff *maff,
3277 __isl_take isl_set *context);
3278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3279 __isl_take isl_pw_multi_aff *pma,
3280 __isl_take isl_set *set);
3281 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3282 __isl_take isl_pw_multi_aff *pma,
3283 __isl_take isl_set *set);
3284 __isl_give isl_set *isl_pw_multi_aff_domain(
3285 __isl_take isl_pw_multi_aff *pma);
3287 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3288 then it is assigned the local space that lies at the basis of
3289 the lifting applied.
3291 An expression can be read from input using
3293 #include <isl/aff.h>
3294 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3295 isl_ctx *ctx, const char *str);
3296 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3297 isl_ctx *ctx, const char *str);
3299 An expression can be printed using
3301 #include <isl/aff.h>
3302 __isl_give isl_printer *isl_printer_print_multi_aff(
3303 __isl_take isl_printer *p,
3304 __isl_keep isl_multi_aff *maff);
3305 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3306 __isl_take isl_printer *p,
3307 __isl_keep isl_pw_multi_aff *pma);
3311 Points are elements of a set. They can be used to construct
3312 simple sets (boxes) or they can be used to represent the
3313 individual elements of a set.
3314 The zero point (the origin) can be created using
3316 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3318 The coordinates of a point can be inspected, set and changed
3321 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3322 enum isl_dim_type type, int pos, isl_int *v);
3323 __isl_give isl_point *isl_point_set_coordinate(
3324 __isl_take isl_point *pnt,
3325 enum isl_dim_type type, int pos, isl_int v);
3327 __isl_give isl_point *isl_point_add_ui(
3328 __isl_take isl_point *pnt,
3329 enum isl_dim_type type, int pos, unsigned val);
3330 __isl_give isl_point *isl_point_sub_ui(
3331 __isl_take isl_point *pnt,
3332 enum isl_dim_type type, int pos, unsigned val);
3334 Other properties can be obtained using
3336 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3338 Points can be copied or freed using
3340 __isl_give isl_point *isl_point_copy(
3341 __isl_keep isl_point *pnt);
3342 void isl_point_free(__isl_take isl_point *pnt);
3344 A singleton set can be created from a point using
3346 __isl_give isl_basic_set *isl_basic_set_from_point(
3347 __isl_take isl_point *pnt);
3348 __isl_give isl_set *isl_set_from_point(
3349 __isl_take isl_point *pnt);
3351 and a box can be created from two opposite extremal points using
3353 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3354 __isl_take isl_point *pnt1,
3355 __isl_take isl_point *pnt2);
3356 __isl_give isl_set *isl_set_box_from_points(
3357 __isl_take isl_point *pnt1,
3358 __isl_take isl_point *pnt2);
3360 All elements of a B<bounded> (union) set can be enumerated using
3361 the following functions.
3363 int isl_set_foreach_point(__isl_keep isl_set *set,
3364 int (*fn)(__isl_take isl_point *pnt, void *user),
3366 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3367 int (*fn)(__isl_take isl_point *pnt, void *user),
3370 The function C<fn> is called for each integer point in
3371 C<set> with as second argument the last argument of
3372 the C<isl_set_foreach_point> call. The function C<fn>
3373 should return C<0> on success and C<-1> on failure.
3374 In the latter case, C<isl_set_foreach_point> will stop
3375 enumerating and return C<-1> as well.
3376 If the enumeration is performed successfully and to completion,
3377 then C<isl_set_foreach_point> returns C<0>.
3379 To obtain a single point of a (basic) set, use
3381 __isl_give isl_point *isl_basic_set_sample_point(
3382 __isl_take isl_basic_set *bset);
3383 __isl_give isl_point *isl_set_sample_point(
3384 __isl_take isl_set *set);
3386 If C<set> does not contain any (integer) points, then the
3387 resulting point will be ``void'', a property that can be
3390 int isl_point_is_void(__isl_keep isl_point *pnt);
3392 =head2 Piecewise Quasipolynomials
3394 A piecewise quasipolynomial is a particular kind of function that maps
3395 a parametric point to a rational value.
3396 More specifically, a quasipolynomial is a polynomial expression in greatest
3397 integer parts of affine expressions of parameters and variables.
3398 A piecewise quasipolynomial is a subdivision of a given parametric
3399 domain into disjoint cells with a quasipolynomial associated to
3400 each cell. The value of the piecewise quasipolynomial at a given
3401 point is the value of the quasipolynomial associated to the cell
3402 that contains the point. Outside of the union of cells,
3403 the value is assumed to be zero.
3404 For example, the piecewise quasipolynomial
3406 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3408 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3409 A given piecewise quasipolynomial has a fixed domain dimension.
3410 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3411 defined over different domains.
3412 Piecewise quasipolynomials are mainly used by the C<barvinok>
3413 library for representing the number of elements in a parametric set or map.
3414 For example, the piecewise quasipolynomial above represents
3415 the number of points in the map
3417 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3419 =head3 Input and Output
3421 Piecewise quasipolynomials can be read from input using
3423 __isl_give isl_union_pw_qpolynomial *
3424 isl_union_pw_qpolynomial_read_from_str(
3425 isl_ctx *ctx, const char *str);
3427 Quasipolynomials and piecewise quasipolynomials can be printed
3428 using the following functions.
3430 __isl_give isl_printer *isl_printer_print_qpolynomial(
3431 __isl_take isl_printer *p,
3432 __isl_keep isl_qpolynomial *qp);
3434 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3435 __isl_take isl_printer *p,
3436 __isl_keep isl_pw_qpolynomial *pwqp);
3438 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3439 __isl_take isl_printer *p,
3440 __isl_keep isl_union_pw_qpolynomial *upwqp);
3442 The output format of the printer
3443 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3444 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3446 In case of printing in C<ISL_FORMAT_C>, the user may want
3447 to set the names of all dimensions
3449 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3450 __isl_take isl_qpolynomial *qp,
3451 enum isl_dim_type type, unsigned pos,
3453 __isl_give isl_pw_qpolynomial *
3454 isl_pw_qpolynomial_set_dim_name(
3455 __isl_take isl_pw_qpolynomial *pwqp,
3456 enum isl_dim_type type, unsigned pos,
3459 =head3 Creating New (Piecewise) Quasipolynomials
3461 Some simple quasipolynomials can be created using the following functions.
3462 More complicated quasipolynomials can be created by applying
3463 operations such as addition and multiplication
3464 on the resulting quasipolynomials
3466 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3467 __isl_take isl_space *domain);
3468 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3469 __isl_take isl_space *domain);
3470 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3471 __isl_take isl_space *domain);
3472 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3473 __isl_take isl_space *domain);
3474 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3475 __isl_take isl_space *domain);
3476 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3477 __isl_take isl_space *domain,
3478 const isl_int n, const isl_int d);
3479 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3480 __isl_take isl_space *domain,
3481 enum isl_dim_type type, unsigned pos);
3482 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3483 __isl_take isl_aff *aff);
3485 Note that the space in which a quasipolynomial lives is a map space
3486 with a one-dimensional range. The C<domain> argument in some of
3487 the functions above corresponds to the domain of this map space.
3489 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3490 with a single cell can be created using the following functions.
3491 Multiple of these single cell piecewise quasipolynomials can
3492 be combined to create more complicated piecewise quasipolynomials.
3494 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3495 __isl_take isl_space *space);
3496 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3497 __isl_take isl_set *set,
3498 __isl_take isl_qpolynomial *qp);
3499 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3500 __isl_take isl_qpolynomial *qp);
3501 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3502 __isl_take isl_pw_aff *pwaff);
3504 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3505 __isl_take isl_space *space);
3506 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3507 __isl_take isl_pw_qpolynomial *pwqp);
3508 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3509 __isl_take isl_union_pw_qpolynomial *upwqp,
3510 __isl_take isl_pw_qpolynomial *pwqp);
3512 Quasipolynomials can be copied and freed again using the following
3515 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3516 __isl_keep isl_qpolynomial *qp);
3517 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3520 __isl_keep isl_pw_qpolynomial *pwqp);
3521 void *isl_pw_qpolynomial_free(
3522 __isl_take isl_pw_qpolynomial *pwqp);
3524 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3525 __isl_keep isl_union_pw_qpolynomial *upwqp);
3526 void isl_union_pw_qpolynomial_free(
3527 __isl_take isl_union_pw_qpolynomial *upwqp);
3529 =head3 Inspecting (Piecewise) Quasipolynomials
3531 To iterate over all piecewise quasipolynomials in a union
3532 piecewise quasipolynomial, use the following function
3534 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3535 __isl_keep isl_union_pw_qpolynomial *upwqp,
3536 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3539 To extract the piecewise quasipolynomial in a given space from a union, use
3541 __isl_give isl_pw_qpolynomial *
3542 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3543 __isl_keep isl_union_pw_qpolynomial *upwqp,
3544 __isl_take isl_space *space);
3546 To iterate over the cells in a piecewise quasipolynomial,
3547 use either of the following two functions
3549 int isl_pw_qpolynomial_foreach_piece(
3550 __isl_keep isl_pw_qpolynomial *pwqp,
3551 int (*fn)(__isl_take isl_set *set,
3552 __isl_take isl_qpolynomial *qp,
3553 void *user), void *user);
3554 int isl_pw_qpolynomial_foreach_lifted_piece(
3555 __isl_keep isl_pw_qpolynomial *pwqp,
3556 int (*fn)(__isl_take isl_set *set,
3557 __isl_take isl_qpolynomial *qp,
3558 void *user), void *user);
3560 As usual, the function C<fn> should return C<0> on success
3561 and C<-1> on failure. The difference between
3562 C<isl_pw_qpolynomial_foreach_piece> and
3563 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3564 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3565 compute unique representations for all existentially quantified
3566 variables and then turn these existentially quantified variables
3567 into extra set variables, adapting the associated quasipolynomial
3568 accordingly. This means that the C<set> passed to C<fn>
3569 will not have any existentially quantified variables, but that
3570 the dimensions of the sets may be different for different
3571 invocations of C<fn>.
3573 To iterate over all terms in a quasipolynomial,
3576 int isl_qpolynomial_foreach_term(
3577 __isl_keep isl_qpolynomial *qp,
3578 int (*fn)(__isl_take isl_term *term,
3579 void *user), void *user);
3581 The terms themselves can be inspected and freed using
3584 unsigned isl_term_dim(__isl_keep isl_term *term,
3585 enum isl_dim_type type);
3586 void isl_term_get_num(__isl_keep isl_term *term,
3588 void isl_term_get_den(__isl_keep isl_term *term,
3590 int isl_term_get_exp(__isl_keep isl_term *term,
3591 enum isl_dim_type type, unsigned pos);
3592 __isl_give isl_aff *isl_term_get_div(
3593 __isl_keep isl_term *term, unsigned pos);
3594 void isl_term_free(__isl_take isl_term *term);
3596 Each term is a product of parameters, set variables and
3597 integer divisions. The function C<isl_term_get_exp>
3598 returns the exponent of a given dimensions in the given term.
3599 The C<isl_int>s in the arguments of C<isl_term_get_num>
3600 and C<isl_term_get_den> need to have been initialized
3601 using C<isl_int_init> before calling these functions.
3603 =head3 Properties of (Piecewise) Quasipolynomials
3605 To check whether a quasipolynomial is actually a constant,
3606 use the following function.
3608 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3609 isl_int *n, isl_int *d);
3611 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3612 then the numerator and denominator of the constant
3613 are returned in C<*n> and C<*d>, respectively.
3615 To check whether two union piecewise quasipolynomials are
3616 obviously equal, use
3618 int isl_union_pw_qpolynomial_plain_is_equal(
3619 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3620 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3622 =head3 Operations on (Piecewise) Quasipolynomials
3624 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3625 __isl_take isl_qpolynomial *qp, isl_int v);
3626 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3627 __isl_take isl_qpolynomial *qp);
3628 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3629 __isl_take isl_qpolynomial *qp1,
3630 __isl_take isl_qpolynomial *qp2);
3631 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3632 __isl_take isl_qpolynomial *qp1,
3633 __isl_take isl_qpolynomial *qp2);
3634 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3635 __isl_take isl_qpolynomial *qp1,
3636 __isl_take isl_qpolynomial *qp2);
3637 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3638 __isl_take isl_qpolynomial *qp, unsigned exponent);
3640 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3641 __isl_take isl_pw_qpolynomial *pwqp1,
3642 __isl_take isl_pw_qpolynomial *pwqp2);
3643 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3644 __isl_take isl_pw_qpolynomial *pwqp1,
3645 __isl_take isl_pw_qpolynomial *pwqp2);
3646 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3647 __isl_take isl_pw_qpolynomial *pwqp1,
3648 __isl_take isl_pw_qpolynomial *pwqp2);
3649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3650 __isl_take isl_pw_qpolynomial *pwqp);
3651 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3652 __isl_take isl_pw_qpolynomial *pwqp1,
3653 __isl_take isl_pw_qpolynomial *pwqp2);
3654 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3655 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3657 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3658 __isl_take isl_union_pw_qpolynomial *upwqp1,
3659 __isl_take isl_union_pw_qpolynomial *upwqp2);
3660 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3661 __isl_take isl_union_pw_qpolynomial *upwqp1,
3662 __isl_take isl_union_pw_qpolynomial *upwqp2);
3663 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3664 __isl_take isl_union_pw_qpolynomial *upwqp1,
3665 __isl_take isl_union_pw_qpolynomial *upwqp2);
3667 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3668 __isl_take isl_pw_qpolynomial *pwqp,
3669 __isl_take isl_point *pnt);
3671 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3672 __isl_take isl_union_pw_qpolynomial *upwqp,
3673 __isl_take isl_point *pnt);
3675 __isl_give isl_set *isl_pw_qpolynomial_domain(
3676 __isl_take isl_pw_qpolynomial *pwqp);
3677 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3678 __isl_take isl_pw_qpolynomial *pwpq,
3679 __isl_take isl_set *set);
3680 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3681 __isl_take isl_pw_qpolynomial *pwpq,
3682 __isl_take isl_set *set);
3684 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3685 __isl_take isl_union_pw_qpolynomial *upwqp);
3686 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3687 __isl_take isl_union_pw_qpolynomial *upwpq,
3688 __isl_take isl_union_set *uset);
3689 __isl_give isl_union_pw_qpolynomial *
3690 isl_union_pw_qpolynomial_intersect_params(
3691 __isl_take isl_union_pw_qpolynomial *upwpq,
3692 __isl_take isl_set *set);
3694 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3695 __isl_take isl_qpolynomial *qp,
3696 __isl_take isl_space *model);
3698 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3699 __isl_take isl_qpolynomial *qp);
3700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3701 __isl_take isl_pw_qpolynomial *pwqp);
3703 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3704 __isl_take isl_union_pw_qpolynomial *upwqp);
3706 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3707 __isl_take isl_qpolynomial *qp,
3708 __isl_take isl_set *context);
3709 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3710 __isl_take isl_qpolynomial *qp,
3711 __isl_take isl_set *context);
3713 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3714 __isl_take isl_pw_qpolynomial *pwqp,
3715 __isl_take isl_set *context);
3716 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3717 __isl_take isl_pw_qpolynomial *pwqp,
3718 __isl_take isl_set *context);
3720 __isl_give isl_union_pw_qpolynomial *
3721 isl_union_pw_qpolynomial_gist_params(
3722 __isl_take isl_union_pw_qpolynomial *upwqp,
3723 __isl_take isl_set *context);
3724 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3725 __isl_take isl_union_pw_qpolynomial *upwqp,
3726 __isl_take isl_union_set *context);
3728 The gist operation applies the gist operation to each of
3729 the cells in the domain of the input piecewise quasipolynomial.
3730 The context is also exploited
3731 to simplify the quasipolynomials associated to each cell.
3733 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3734 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3735 __isl_give isl_union_pw_qpolynomial *
3736 isl_union_pw_qpolynomial_to_polynomial(
3737 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3739 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3740 the polynomial will be an overapproximation. If C<sign> is negative,
3741 it will be an underapproximation. If C<sign> is zero, the approximation
3742 will lie somewhere in between.
3744 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3746 A piecewise quasipolynomial reduction is a piecewise
3747 reduction (or fold) of quasipolynomials.
3748 In particular, the reduction can be maximum or a minimum.
3749 The objects are mainly used to represent the result of
3750 an upper or lower bound on a quasipolynomial over its domain,
3751 i.e., as the result of the following function.
3753 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3754 __isl_take isl_pw_qpolynomial *pwqp,
3755 enum isl_fold type, int *tight);
3757 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3758 __isl_take isl_union_pw_qpolynomial *upwqp,
3759 enum isl_fold type, int *tight);
3761 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3762 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3763 is the returned bound is known be tight, i.e., for each value
3764 of the parameters there is at least
3765 one element in the domain that reaches the bound.
3766 If the domain of C<pwqp> is not wrapping, then the bound is computed
3767 over all elements in that domain and the result has a purely parametric
3768 domain. If the domain of C<pwqp> is wrapping, then the bound is
3769 computed over the range of the wrapped relation. The domain of the
3770 wrapped relation becomes the domain of the result.
3772 A (piecewise) quasipolynomial reduction can be copied or freed using the
3773 following functions.
3775 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3776 __isl_keep isl_qpolynomial_fold *fold);
3777 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3778 __isl_keep isl_pw_qpolynomial_fold *pwf);
3779 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3780 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3781 void isl_qpolynomial_fold_free(
3782 __isl_take isl_qpolynomial_fold *fold);
3783 void *isl_pw_qpolynomial_fold_free(
3784 __isl_take isl_pw_qpolynomial_fold *pwf);
3785 void isl_union_pw_qpolynomial_fold_free(
3786 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3788 =head3 Printing Piecewise Quasipolynomial Reductions
3790 Piecewise quasipolynomial reductions can be printed
3791 using the following function.
3793 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3794 __isl_take isl_printer *p,
3795 __isl_keep isl_pw_qpolynomial_fold *pwf);
3796 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3797 __isl_take isl_printer *p,
3798 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3800 For C<isl_printer_print_pw_qpolynomial_fold>,
3801 output format of the printer
3802 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3803 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3804 output format of the printer
3805 needs to be set to C<ISL_FORMAT_ISL>.
3806 In case of printing in C<ISL_FORMAT_C>, the user may want
3807 to set the names of all dimensions
3809 __isl_give isl_pw_qpolynomial_fold *
3810 isl_pw_qpolynomial_fold_set_dim_name(
3811 __isl_take isl_pw_qpolynomial_fold *pwf,
3812 enum isl_dim_type type, unsigned pos,
3815 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3817 To iterate over all piecewise quasipolynomial reductions in a union
3818 piecewise quasipolynomial reduction, use the following function
3820 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3821 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3822 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3823 void *user), void *user);
3825 To iterate over the cells in a piecewise quasipolynomial reduction,
3826 use either of the following two functions
3828 int isl_pw_qpolynomial_fold_foreach_piece(
3829 __isl_keep isl_pw_qpolynomial_fold *pwf,
3830 int (*fn)(__isl_take isl_set *set,
3831 __isl_take isl_qpolynomial_fold *fold,
3832 void *user), void *user);
3833 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3834 __isl_keep isl_pw_qpolynomial_fold *pwf,
3835 int (*fn)(__isl_take isl_set *set,
3836 __isl_take isl_qpolynomial_fold *fold,
3837 void *user), void *user);
3839 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3840 of the difference between these two functions.
3842 To iterate over all quasipolynomials in a reduction, use
3844 int isl_qpolynomial_fold_foreach_qpolynomial(
3845 __isl_keep isl_qpolynomial_fold *fold,
3846 int (*fn)(__isl_take isl_qpolynomial *qp,
3847 void *user), void *user);
3849 =head3 Properties of Piecewise Quasipolynomial Reductions
3851 To check whether two union piecewise quasipolynomial reductions are
3852 obviously equal, use
3854 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3855 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3856 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3858 =head3 Operations on Piecewise Quasipolynomial Reductions
3860 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3861 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3863 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3864 __isl_take isl_pw_qpolynomial_fold *pwf1,
3865 __isl_take isl_pw_qpolynomial_fold *pwf2);
3867 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3868 __isl_take isl_pw_qpolynomial_fold *pwf1,
3869 __isl_take isl_pw_qpolynomial_fold *pwf2);
3871 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3872 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3873 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3875 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3876 __isl_take isl_pw_qpolynomial_fold *pwf,
3877 __isl_take isl_point *pnt);
3879 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3880 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3881 __isl_take isl_point *pnt);
3883 __isl_give isl_pw_qpolynomial_fold *
3884 sl_pw_qpolynomial_fold_intersect_params(
3885 __isl_take isl_pw_qpolynomial_fold *pwf,
3886 __isl_take isl_set *set);
3888 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3889 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3890 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3891 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3892 __isl_take isl_union_set *uset);
3893 __isl_give isl_union_pw_qpolynomial_fold *
3894 isl_union_pw_qpolynomial_fold_intersect_params(
3895 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3896 __isl_take isl_set *set);
3898 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3899 __isl_take isl_pw_qpolynomial_fold *pwf);
3901 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3902 __isl_take isl_pw_qpolynomial_fold *pwf);
3904 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3905 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3907 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3908 __isl_take isl_qpolynomial_fold *fold,
3909 __isl_take isl_set *context);
3910 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3911 __isl_take isl_qpolynomial_fold *fold,
3912 __isl_take isl_set *context);
3914 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3915 __isl_take isl_pw_qpolynomial_fold *pwf,
3916 __isl_take isl_set *context);
3917 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3918 __isl_take isl_pw_qpolynomial_fold *pwf,
3919 __isl_take isl_set *context);
3921 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3922 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3923 __isl_take isl_union_set *context);
3924 __isl_give isl_union_pw_qpolynomial_fold *
3925 isl_union_pw_qpolynomial_fold_gist_params(
3926 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3927 __isl_take isl_set *context);
3929 The gist operation applies the gist operation to each of
3930 the cells in the domain of the input piecewise quasipolynomial reduction.
3931 In future, the operation will also exploit the context
3932 to simplify the quasipolynomial reductions associated to each cell.
3934 __isl_give isl_pw_qpolynomial_fold *
3935 isl_set_apply_pw_qpolynomial_fold(
3936 __isl_take isl_set *set,
3937 __isl_take isl_pw_qpolynomial_fold *pwf,
3939 __isl_give isl_pw_qpolynomial_fold *
3940 isl_map_apply_pw_qpolynomial_fold(
3941 __isl_take isl_map *map,
3942 __isl_take isl_pw_qpolynomial_fold *pwf,
3944 __isl_give isl_union_pw_qpolynomial_fold *
3945 isl_union_set_apply_union_pw_qpolynomial_fold(
3946 __isl_take isl_union_set *uset,
3947 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3949 __isl_give isl_union_pw_qpolynomial_fold *
3950 isl_union_map_apply_union_pw_qpolynomial_fold(
3951 __isl_take isl_union_map *umap,
3952 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3955 The functions taking a map
3956 compose the given map with the given piecewise quasipolynomial reduction.
3957 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3958 over all elements in the intersection of the range of the map
3959 and the domain of the piecewise quasipolynomial reduction
3960 as a function of an element in the domain of the map.
3961 The functions taking a set compute a bound over all elements in the
3962 intersection of the set and the domain of the
3963 piecewise quasipolynomial reduction.
3965 =head2 Dependence Analysis
3967 C<isl> contains specialized functionality for performing
3968 array dataflow analysis. That is, given a I<sink> access relation
3969 and a collection of possible I<source> access relations,
3970 C<isl> can compute relations that describe
3971 for each iteration of the sink access, which iteration
3972 of which of the source access relations was the last
3973 to access the same data element before the given iteration
3975 The resulting dependence relations map source iterations
3976 to the corresponding sink iterations.
3977 To compute standard flow dependences, the sink should be
3978 a read, while the sources should be writes.
3979 If any of the source accesses are marked as being I<may>
3980 accesses, then there will be a dependence from the last
3981 I<must> access B<and> from any I<may> access that follows
3982 this last I<must> access.
3983 In particular, if I<all> sources are I<may> accesses,
3984 then memory based dependence analysis is performed.
3985 If, on the other hand, all sources are I<must> accesses,
3986 then value based dependence analysis is performed.
3988 #include <isl/flow.h>
3990 typedef int (*isl_access_level_before)(void *first, void *second);
3992 __isl_give isl_access_info *isl_access_info_alloc(
3993 __isl_take isl_map *sink,
3994 void *sink_user, isl_access_level_before fn,
3996 __isl_give isl_access_info *isl_access_info_add_source(
3997 __isl_take isl_access_info *acc,
3998 __isl_take isl_map *source, int must,
4000 void isl_access_info_free(__isl_take isl_access_info *acc);
4002 __isl_give isl_flow *isl_access_info_compute_flow(
4003 __isl_take isl_access_info *acc);
4005 int isl_flow_foreach(__isl_keep isl_flow *deps,
4006 int (*fn)(__isl_take isl_map *dep, int must,
4007 void *dep_user, void *user),
4009 __isl_give isl_map *isl_flow_get_no_source(
4010 __isl_keep isl_flow *deps, int must);
4011 void isl_flow_free(__isl_take isl_flow *deps);
4013 The function C<isl_access_info_compute_flow> performs the actual
4014 dependence analysis. The other functions are used to construct
4015 the input for this function or to read off the output.
4017 The input is collected in an C<isl_access_info>, which can
4018 be created through a call to C<isl_access_info_alloc>.
4019 The arguments to this functions are the sink access relation
4020 C<sink>, a token C<sink_user> used to identify the sink
4021 access to the user, a callback function for specifying the
4022 relative order of source and sink accesses, and the number
4023 of source access relations that will be added.
4024 The callback function has type C<int (*)(void *first, void *second)>.
4025 The function is called with two user supplied tokens identifying
4026 either a source or the sink and it should return the shared nesting
4027 level and the relative order of the two accesses.
4028 In particular, let I<n> be the number of loops shared by
4029 the two accesses. If C<first> precedes C<second> textually,
4030 then the function should return I<2 * n + 1>; otherwise,
4031 it should return I<2 * n>.
4032 The sources can be added to the C<isl_access_info> by performing
4033 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4034 C<must> indicates whether the source is a I<must> access
4035 or a I<may> access. Note that a multi-valued access relation
4036 should only be marked I<must> if every iteration in the domain
4037 of the relation accesses I<all> elements in its image.
4038 The C<source_user> token is again used to identify
4039 the source access. The range of the source access relation
4040 C<source> should have the same dimension as the range
4041 of the sink access relation.
4042 The C<isl_access_info_free> function should usually not be
4043 called explicitly, because it is called implicitly by
4044 C<isl_access_info_compute_flow>.
4046 The result of the dependence analysis is collected in an
4047 C<isl_flow>. There may be elements of
4048 the sink access for which no preceding source access could be
4049 found or for which all preceding sources are I<may> accesses.
4050 The relations containing these elements can be obtained through
4051 calls to C<isl_flow_get_no_source>, the first with C<must> set
4052 and the second with C<must> unset.
4053 In the case of standard flow dependence analysis,
4054 with the sink a read and the sources I<must> writes,
4055 the first relation corresponds to the reads from uninitialized
4056 array elements and the second relation is empty.
4057 The actual flow dependences can be extracted using
4058 C<isl_flow_foreach>. This function will call the user-specified
4059 callback function C<fn> for each B<non-empty> dependence between
4060 a source and the sink. The callback function is called
4061 with four arguments, the actual flow dependence relation
4062 mapping source iterations to sink iterations, a boolean that
4063 indicates whether it is a I<must> or I<may> dependence, a token
4064 identifying the source and an additional C<void *> with value
4065 equal to the third argument of the C<isl_flow_foreach> call.
4066 A dependence is marked I<must> if it originates from a I<must>
4067 source and if it is not followed by any I<may> sources.
4069 After finishing with an C<isl_flow>, the user should call
4070 C<isl_flow_free> to free all associated memory.
4072 A higher-level interface to dependence analysis is provided
4073 by the following function.
4075 #include <isl/flow.h>
4077 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4078 __isl_take isl_union_map *must_source,
4079 __isl_take isl_union_map *may_source,
4080 __isl_take isl_union_map *schedule,
4081 __isl_give isl_union_map **must_dep,
4082 __isl_give isl_union_map **may_dep,
4083 __isl_give isl_union_map **must_no_source,
4084 __isl_give isl_union_map **may_no_source);
4086 The arrays are identified by the tuple names of the ranges
4087 of the accesses. The iteration domains by the tuple names
4088 of the domains of the accesses and of the schedule.
4089 The relative order of the iteration domains is given by the
4090 schedule. The relations returned through C<must_no_source>
4091 and C<may_no_source> are subsets of C<sink>.
4092 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4093 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4094 any of the other arguments is treated as an error.
4096 =head3 Interaction with Dependence Analysis
4098 During the dependence analysis, we frequently need to perform
4099 the following operation. Given a relation between sink iterations
4100 and potential soure iterations from a particular source domain,
4101 what is the last potential source iteration corresponding to each
4102 sink iteration. It can sometimes be convenient to adjust
4103 the set of potential source iterations before each such operation.
4104 The prototypical example is fuzzy array dataflow analysis,
4105 where we need to analyze if, based on data-dependent constraints,
4106 the sink iteration can ever be executed without one or more of
4107 the corresponding potential source iterations being executed.
4108 If so, we can introduce extra parameters and select an unknown
4109 but fixed source iteration from the potential source iterations.
4110 To be able to perform such manipulations, C<isl> provides the following
4113 #include <isl/flow.h>
4115 typedef __isl_give isl_set *(*isl_access_restrict_sources)(
4116 __isl_take isl_map *source_map,
4117 void *sink_user, void *source_user);
4118 __isl_give isl_access_info *
4119 isl_access_info_set_restrict_sources(
4120 __isl_take isl_access_info *acc,
4121 isl_access_restrict_sources fn);
4123 The function C<isl_access_info_set_restrict_sources> should be called
4124 before C<isl_access_info_compute_flow> and registers a callback function
4125 that will be called any time C<isl> is about to compute the last
4126 potential source. The first argument is the (reverse) proto-dependence,
4127 mapping sink iterations to potential source iterations.
4128 The other two arguments are the tokens corresponding to the sink
4129 and the source. The callback is expected to return a set
4130 that restricts the source iterations. The potential source iterations
4131 will be intersected with this set. If no restrictions are required
4132 for a given C<source_map>, then the callback should return
4135 isl_space_range(isl_map_get_space(source_map)));
4137 If any error occurs, the callback should return C<NULL>.
4141 B<The functionality described in this section is fairly new
4142 and may be subject to change.>
4144 The following function can be used to compute a schedule
4145 for a union of domains.
4146 By default, the algorithm used to construct the schedule is similar
4147 to that of C<Pluto>.
4148 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4150 The generated schedule respects all C<validity> dependences.
4151 That is, all dependence distances over these dependences in the
4152 scheduled space are lexicographically positive.
4153 The default algorithm tries to minimize the dependence distances over
4154 C<proximity> dependences.
4155 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4156 for groups of domains where the dependence distances have only
4157 non-negative values.
4158 When using Feautrier's algorithm, the C<proximity> dependence
4159 distances are only minimized during the extension to a
4160 full-dimensional schedule.
4162 #include <isl/schedule.h>
4163 __isl_give isl_schedule *isl_union_set_compute_schedule(
4164 __isl_take isl_union_set *domain,
4165 __isl_take isl_union_map *validity,
4166 __isl_take isl_union_map *proximity);
4167 void *isl_schedule_free(__isl_take isl_schedule *sched);
4169 A mapping from the domains to the scheduled space can be obtained
4170 from an C<isl_schedule> using the following function.
4172 __isl_give isl_union_map *isl_schedule_get_map(
4173 __isl_keep isl_schedule *sched);
4175 A representation of the schedule can be printed using
4177 __isl_give isl_printer *isl_printer_print_schedule(
4178 __isl_take isl_printer *p,
4179 __isl_keep isl_schedule *schedule);
4181 A representation of the schedule as a forest of bands can be obtained
4182 using the following function.
4184 __isl_give isl_band_list *isl_schedule_get_band_forest(
4185 __isl_keep isl_schedule *schedule);
4187 The list can be manipulated as explained in L<"Lists">.
4188 The bands inside the list can be copied and freed using the following
4191 #include <isl/band.h>
4192 __isl_give isl_band *isl_band_copy(
4193 __isl_keep isl_band *band);
4194 void *isl_band_free(__isl_take isl_band *band);
4196 Each band contains zero or more scheduling dimensions.
4197 These are referred to as the members of the band.
4198 The section of the schedule that corresponds to the band is
4199 referred to as the partial schedule of the band.
4200 For those nodes that participate in a band, the outer scheduling
4201 dimensions form the prefix schedule, while the inner scheduling
4202 dimensions form the suffix schedule.
4203 That is, if we take a cut of the band forest, then the union of
4204 the concatenations of the prefix, partial and suffix schedules of
4205 each band in the cut is equal to the entire schedule (modulo
4206 some possible padding at the end with zero scheduling dimensions).
4207 The properties of a band can be inspected using the following functions.
4209 #include <isl/band.h>
4210 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4212 int isl_band_has_children(__isl_keep isl_band *band);
4213 __isl_give isl_band_list *isl_band_get_children(
4214 __isl_keep isl_band *band);
4216 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4217 __isl_keep isl_band *band);
4218 __isl_give isl_union_map *isl_band_get_partial_schedule(
4219 __isl_keep isl_band *band);
4220 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4221 __isl_keep isl_band *band);
4223 int isl_band_n_member(__isl_keep isl_band *band);
4224 int isl_band_member_is_zero_distance(
4225 __isl_keep isl_band *band, int pos);
4227 Note that a scheduling dimension is considered to be ``zero
4228 distance'' if it does not carry any proximity dependences
4230 That is, if the dependence distances of the proximity
4231 dependences are all zero in that direction (for fixed
4232 iterations of outer bands).
4234 A representation of the band can be printed using
4236 #include <isl/band.h>
4237 __isl_give isl_printer *isl_printer_print_band(
4238 __isl_take isl_printer *p,
4239 __isl_keep isl_band *band);
4243 #include <isl/schedule.h>
4244 int isl_options_set_schedule_max_coefficient(
4245 isl_ctx *ctx, int val);
4246 int isl_options_get_schedule_max_coefficient(
4248 int isl_options_set_schedule_max_constant_term(
4249 isl_ctx *ctx, int val);
4250 int isl_options_get_schedule_max_constant_term(
4252 int isl_options_set_schedule_maximize_band_depth(
4253 isl_ctx *ctx, int val);
4254 int isl_options_get_schedule_maximize_band_depth(
4256 int isl_options_set_schedule_outer_zero_distance(
4257 isl_ctx *ctx, int val);
4258 int isl_options_get_schedule_outer_zero_distance(
4260 int isl_options_set_schedule_split_scaled(
4261 isl_ctx *ctx, int val);
4262 int isl_options_get_schedule_split_scaled(
4264 int isl_options_set_schedule_algorithm(
4265 isl_ctx *ctx, int val);
4266 int isl_options_get_schedule_algorithm(
4272 =item * schedule_max_coefficient
4274 This option enforces that the coefficients for variable and parameter
4275 dimensions in the calculated schedule are not larger than the specified value.
4276 This option can significantly increase the speed of the scheduling calculation
4277 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4278 this option does not introduce bounds on the variable or parameter
4281 =item * schedule_max_constant_term
4283 This option enforces that the constant coefficients in the calculated schedule
4284 are not larger than the maximal constant term. This option can significantly
4285 increase the speed of the scheduling calculation and may also prevent fusing of
4286 unrelated dimensions. A value of -1 means that this option does not introduce
4287 bounds on the constant coefficients.
4289 =item * schedule_maximize_band_depth
4291 If this option is set, we do not split bands at the point
4292 where we detect splitting is necessary. Instead, we
4293 backtrack and split bands as early as possible. This
4294 reduces the number of splits and maximizes the width of
4295 the bands. Wider bands give more possibilities for tiling.
4297 =item * schedule_outer_zero_distance
4299 If this option is set, then we try to construct schedules
4300 where the outermost scheduling dimension in each band
4301 results in a zero dependence distance over the proximity
4304 =item * schedule_split_scaled
4306 If this option is set, then we try to construct schedules in which the
4307 constant term is split off from the linear part if the linear parts of
4308 the scheduling rows for all nodes in the graphs have a common non-trivial
4310 The constant term is then placed in a separate band and the linear
4313 =item * schedule_algorithm
4315 Selects the scheduling algorithm to be used.
4316 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4317 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4321 =head2 Parametric Vertex Enumeration
4323 The parametric vertex enumeration described in this section
4324 is mainly intended to be used internally and by the C<barvinok>
4327 #include <isl/vertices.h>
4328 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4329 __isl_keep isl_basic_set *bset);
4331 The function C<isl_basic_set_compute_vertices> performs the
4332 actual computation of the parametric vertices and the chamber
4333 decomposition and store the result in an C<isl_vertices> object.
4334 This information can be queried by either iterating over all
4335 the vertices or iterating over all the chambers or cells
4336 and then iterating over all vertices that are active on the chamber.
4338 int isl_vertices_foreach_vertex(
4339 __isl_keep isl_vertices *vertices,
4340 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4343 int isl_vertices_foreach_cell(
4344 __isl_keep isl_vertices *vertices,
4345 int (*fn)(__isl_take isl_cell *cell, void *user),
4347 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4348 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4351 Other operations that can be performed on an C<isl_vertices> object are
4354 isl_ctx *isl_vertices_get_ctx(
4355 __isl_keep isl_vertices *vertices);
4356 int isl_vertices_get_n_vertices(
4357 __isl_keep isl_vertices *vertices);
4358 void isl_vertices_free(__isl_take isl_vertices *vertices);
4360 Vertices can be inspected and destroyed using the following functions.
4362 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4363 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4364 __isl_give isl_basic_set *isl_vertex_get_domain(
4365 __isl_keep isl_vertex *vertex);
4366 __isl_give isl_basic_set *isl_vertex_get_expr(
4367 __isl_keep isl_vertex *vertex);
4368 void isl_vertex_free(__isl_take isl_vertex *vertex);
4370 C<isl_vertex_get_expr> returns a singleton parametric set describing
4371 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4373 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4374 B<rational> basic sets, so they should mainly be used for inspection
4375 and should not be mixed with integer sets.
4377 Chambers can be inspected and destroyed using the following functions.
4379 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4380 __isl_give isl_basic_set *isl_cell_get_domain(
4381 __isl_keep isl_cell *cell);
4382 void isl_cell_free(__isl_take isl_cell *cell);
4386 Although C<isl> is mainly meant to be used as a library,
4387 it also contains some basic applications that use some
4388 of the functionality of C<isl>.
4389 The input may be specified in either the L<isl format>
4390 or the L<PolyLib format>.
4392 =head2 C<isl_polyhedron_sample>
4394 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4395 an integer element of the polyhedron, if there is any.
4396 The first column in the output is the denominator and is always
4397 equal to 1. If the polyhedron contains no integer points,
4398 then a vector of length zero is printed.
4402 C<isl_pip> takes the same input as the C<example> program
4403 from the C<piplib> distribution, i.e., a set of constraints
4404 on the parameters, a line containing only -1 and finally a set
4405 of constraints on a parametric polyhedron.
4406 The coefficients of the parameters appear in the last columns
4407 (but before the final constant column).
4408 The output is the lexicographic minimum of the parametric polyhedron.
4409 As C<isl> currently does not have its own output format, the output
4410 is just a dump of the internal state.
4412 =head2 C<isl_polyhedron_minimize>
4414 C<isl_polyhedron_minimize> computes the minimum of some linear
4415 or affine objective function over the integer points in a polyhedron.
4416 If an affine objective function
4417 is given, then the constant should appear in the last column.
4419 =head2 C<isl_polytope_scan>
4421 Given a polytope, C<isl_polytope_scan> prints
4422 all integer points in the polytope.