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.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
737 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
738 or C<isl_dim_set>. As with C<isl_space_get_name>,
739 the C<isl_space_get_tuple_name> function returns a pointer to some internal
741 Binary operations require the corresponding spaces of their arguments
742 to have the same name.
744 Spaces can be nested. In particular, the domain of a set or
745 the domain or range of a relation can be a nested relation.
746 The following functions can be used to construct and deconstruct
749 #include <isl/space.h>
750 int isl_space_is_wrapping(__isl_keep isl_space *space);
751 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
752 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
754 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
755 be the space of a set, while that of
756 C<isl_space_wrap> should be the space of a relation.
757 Conversely, the output of C<isl_space_unwrap> is the space
758 of a relation, while that of C<isl_space_wrap> is the space of a set.
760 Spaces can be created from other spaces
761 using the following functions.
763 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
764 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
765 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_params(
768 __isl_take isl_space *space);
769 __isl_give isl_space *isl_space_set_from_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
772 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
773 __isl_take isl_space *right);
774 __isl_give isl_space *isl_space_align_params(
775 __isl_take isl_space *space1, __isl_take isl_space *space2)
776 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
777 enum isl_dim_type type, unsigned pos, unsigned n);
778 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned n);
780 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned first, unsigned n);
782 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
783 enum isl_dim_type dst_type, unsigned dst_pos,
784 enum isl_dim_type src_type, unsigned src_pos,
786 __isl_give isl_space *isl_space_map_from_set(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_map_from_domain_and_range(
789 __isl_take isl_space *domain,
790 __isl_take isl_space *range);
791 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
792 __isl_give isl_space *isl_space_curry(
793 __isl_take isl_space *space);
795 Note that if dimensions are added or removed from a space, then
796 the name and the internal structure are lost.
800 A local space is essentially a space with
801 zero or more existentially quantified variables.
802 The local space of a basic set or relation can be obtained
803 using the following functions.
806 __isl_give isl_local_space *isl_basic_set_get_local_space(
807 __isl_keep isl_basic_set *bset);
810 __isl_give isl_local_space *isl_basic_map_get_local_space(
811 __isl_keep isl_basic_map *bmap);
813 A new local space can be created from a space using
815 #include <isl/local_space.h>
816 __isl_give isl_local_space *isl_local_space_from_space(
817 __isl_take isl_space *space);
819 They can be inspected, modified, copied and freed using the following functions.
821 #include <isl/local_space.h>
822 isl_ctx *isl_local_space_get_ctx(
823 __isl_keep isl_local_space *ls);
824 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
825 int isl_local_space_dim(__isl_keep isl_local_space *ls,
826 enum isl_dim_type type);
827 const char *isl_local_space_get_dim_name(
828 __isl_keep isl_local_space *ls,
829 enum isl_dim_type type, unsigned pos);
830 __isl_give isl_local_space *isl_local_space_set_dim_name(
831 __isl_take isl_local_space *ls,
832 enum isl_dim_type type, unsigned pos, const char *s);
833 __isl_give isl_local_space *isl_local_space_set_dim_id(
834 __isl_take isl_local_space *ls,
835 enum isl_dim_type type, unsigned pos,
836 __isl_take isl_id *id);
837 __isl_give isl_space *isl_local_space_get_space(
838 __isl_keep isl_local_space *ls);
839 __isl_give isl_aff *isl_local_space_get_div(
840 __isl_keep isl_local_space *ls, int pos);
841 __isl_give isl_local_space *isl_local_space_copy(
842 __isl_keep isl_local_space *ls);
843 void *isl_local_space_free(__isl_take isl_local_space *ls);
845 Two local spaces can be compared using
847 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
848 __isl_keep isl_local_space *ls2);
850 Local spaces can be created from other local spaces
851 using the following functions.
853 __isl_give isl_local_space *isl_local_space_domain(
854 __isl_take isl_local_space *ls);
855 __isl_give isl_local_space *isl_local_space_range(
856 __isl_take isl_local_space *ls);
857 __isl_give isl_local_space *isl_local_space_from_domain(
858 __isl_take isl_local_space *ls);
859 __isl_give isl_local_space *isl_local_space_intersect(
860 __isl_take isl_local_space *ls1,
861 __isl_take isl_local_space *ls2);
862 __isl_give isl_local_space *isl_local_space_add_dims(
863 __isl_take isl_local_space *ls,
864 enum isl_dim_type type, unsigned n);
865 __isl_give isl_local_space *isl_local_space_insert_dims(
866 __isl_take isl_local_space *ls,
867 enum isl_dim_type type, unsigned first, unsigned n);
868 __isl_give isl_local_space *isl_local_space_drop_dims(
869 __isl_take isl_local_space *ls,
870 enum isl_dim_type type, unsigned first, unsigned n);
872 =head2 Input and Output
874 C<isl> supports its own input/output format, which is similar
875 to the C<Omega> format, but also supports the C<PolyLib> format
880 The C<isl> format is similar to that of C<Omega>, but has a different
881 syntax for describing the parameters and allows for the definition
882 of an existentially quantified variable as the integer division
883 of an affine expression.
884 For example, the set of integers C<i> between C<0> and C<n>
885 such that C<i % 10 <= 6> can be described as
887 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
890 A set or relation can have several disjuncts, separated
891 by the keyword C<or>. Each disjunct is either a conjunction
892 of constraints or a projection (C<exists>) of a conjunction
893 of constraints. The constraints are separated by the keyword
896 =head3 C<PolyLib> format
898 If the represented set is a union, then the first line
899 contains a single number representing the number of disjuncts.
900 Otherwise, a line containing the number C<1> is optional.
902 Each disjunct is represented by a matrix of constraints.
903 The first line contains two numbers representing
904 the number of rows and columns,
905 where the number of rows is equal to the number of constraints
906 and the number of columns is equal to two plus the number of variables.
907 The following lines contain the actual rows of the constraint matrix.
908 In each row, the first column indicates whether the constraint
909 is an equality (C<0>) or inequality (C<1>). The final column
910 corresponds to the constant term.
912 If the set is parametric, then the coefficients of the parameters
913 appear in the last columns before the constant column.
914 The coefficients of any existentially quantified variables appear
915 between those of the set variables and those of the parameters.
917 =head3 Extended C<PolyLib> format
919 The extended C<PolyLib> format is nearly identical to the
920 C<PolyLib> format. The only difference is that the line
921 containing the number of rows and columns of a constraint matrix
922 also contains four additional numbers:
923 the number of output dimensions, the number of input dimensions,
924 the number of local dimensions (i.e., the number of existentially
925 quantified variables) and the number of parameters.
926 For sets, the number of ``output'' dimensions is equal
927 to the number of set dimensions, while the number of ``input''
933 __isl_give isl_basic_set *isl_basic_set_read_from_file(
934 isl_ctx *ctx, FILE *input);
935 __isl_give isl_basic_set *isl_basic_set_read_from_str(
936 isl_ctx *ctx, const char *str);
937 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
939 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
943 __isl_give isl_basic_map *isl_basic_map_read_from_file(
944 isl_ctx *ctx, FILE *input);
945 __isl_give isl_basic_map *isl_basic_map_read_from_str(
946 isl_ctx *ctx, const char *str);
947 __isl_give isl_map *isl_map_read_from_file(
948 isl_ctx *ctx, FILE *input);
949 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
952 #include <isl/union_set.h>
953 __isl_give isl_union_set *isl_union_set_read_from_file(
954 isl_ctx *ctx, FILE *input);
955 __isl_give isl_union_set *isl_union_set_read_from_str(
956 isl_ctx *ctx, const char *str);
958 #include <isl/union_map.h>
959 __isl_give isl_union_map *isl_union_map_read_from_file(
960 isl_ctx *ctx, FILE *input);
961 __isl_give isl_union_map *isl_union_map_read_from_str(
962 isl_ctx *ctx, const char *str);
964 The input format is autodetected and may be either the C<PolyLib> format
965 or the C<isl> format.
969 Before anything can be printed, an C<isl_printer> needs to
972 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
974 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
975 void isl_printer_free(__isl_take isl_printer *printer);
976 __isl_give char *isl_printer_get_str(
977 __isl_keep isl_printer *printer);
979 The behavior of the printer can be modified in various ways
981 __isl_give isl_printer *isl_printer_set_output_format(
982 __isl_take isl_printer *p, int output_format);
983 __isl_give isl_printer *isl_printer_set_indent(
984 __isl_take isl_printer *p, int indent);
985 __isl_give isl_printer *isl_printer_indent(
986 __isl_take isl_printer *p, int indent);
987 __isl_give isl_printer *isl_printer_set_prefix(
988 __isl_take isl_printer *p, const char *prefix);
989 __isl_give isl_printer *isl_printer_set_suffix(
990 __isl_take isl_printer *p, const char *suffix);
992 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
993 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
994 and defaults to C<ISL_FORMAT_ISL>.
995 Each line in the output is indented by C<indent> (set by
996 C<isl_printer_set_indent>) spaces
997 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
998 In the C<PolyLib> format output,
999 the coefficients of the existentially quantified variables
1000 appear between those of the set variables and those
1002 The function C<isl_printer_indent> increases the indentation
1003 by the specified amount (which may be negative).
1005 To actually print something, use
1007 #include <isl/set.h>
1008 __isl_give isl_printer *isl_printer_print_basic_set(
1009 __isl_take isl_printer *printer,
1010 __isl_keep isl_basic_set *bset);
1011 __isl_give isl_printer *isl_printer_print_set(
1012 __isl_take isl_printer *printer,
1013 __isl_keep isl_set *set);
1015 #include <isl/map.h>
1016 __isl_give isl_printer *isl_printer_print_basic_map(
1017 __isl_take isl_printer *printer,
1018 __isl_keep isl_basic_map *bmap);
1019 __isl_give isl_printer *isl_printer_print_map(
1020 __isl_take isl_printer *printer,
1021 __isl_keep isl_map *map);
1023 #include <isl/union_set.h>
1024 __isl_give isl_printer *isl_printer_print_union_set(
1025 __isl_take isl_printer *p,
1026 __isl_keep isl_union_set *uset);
1028 #include <isl/union_map.h>
1029 __isl_give isl_printer *isl_printer_print_union_map(
1030 __isl_take isl_printer *p,
1031 __isl_keep isl_union_map *umap);
1033 When called on a file printer, the following function flushes
1034 the file. When called on a string printer, the buffer is cleared.
1036 __isl_give isl_printer *isl_printer_flush(
1037 __isl_take isl_printer *p);
1039 =head2 Creating New Sets and Relations
1041 C<isl> has functions for creating some standard sets and relations.
1045 =item * Empty sets and relations
1047 __isl_give isl_basic_set *isl_basic_set_empty(
1048 __isl_take isl_space *space);
1049 __isl_give isl_basic_map *isl_basic_map_empty(
1050 __isl_take isl_space *space);
1051 __isl_give isl_set *isl_set_empty(
1052 __isl_take isl_space *space);
1053 __isl_give isl_map *isl_map_empty(
1054 __isl_take isl_space *space);
1055 __isl_give isl_union_set *isl_union_set_empty(
1056 __isl_take isl_space *space);
1057 __isl_give isl_union_map *isl_union_map_empty(
1058 __isl_take isl_space *space);
1060 For C<isl_union_set>s and C<isl_union_map>s, the space
1061 is only used to specify the parameters.
1063 =item * Universe sets and relations
1065 __isl_give isl_basic_set *isl_basic_set_universe(
1066 __isl_take isl_space *space);
1067 __isl_give isl_basic_map *isl_basic_map_universe(
1068 __isl_take isl_space *space);
1069 __isl_give isl_set *isl_set_universe(
1070 __isl_take isl_space *space);
1071 __isl_give isl_map *isl_map_universe(
1072 __isl_take isl_space *space);
1073 __isl_give isl_union_set *isl_union_set_universe(
1074 __isl_take isl_union_set *uset);
1075 __isl_give isl_union_map *isl_union_map_universe(
1076 __isl_take isl_union_map *umap);
1078 The sets and relations constructed by the functions above
1079 contain all integer values, while those constructed by the
1080 functions below only contain non-negative values.
1082 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1083 __isl_take isl_space *space);
1084 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1085 __isl_take isl_space *space);
1086 __isl_give isl_set *isl_set_nat_universe(
1087 __isl_take isl_space *space);
1088 __isl_give isl_map *isl_map_nat_universe(
1089 __isl_take isl_space *space);
1091 =item * Identity relations
1093 __isl_give isl_basic_map *isl_basic_map_identity(
1094 __isl_take isl_space *space);
1095 __isl_give isl_map *isl_map_identity(
1096 __isl_take isl_space *space);
1098 The number of input and output dimensions in C<space> needs
1101 =item * Lexicographic order
1103 __isl_give isl_map *isl_map_lex_lt(
1104 __isl_take isl_space *set_space);
1105 __isl_give isl_map *isl_map_lex_le(
1106 __isl_take isl_space *set_space);
1107 __isl_give isl_map *isl_map_lex_gt(
1108 __isl_take isl_space *set_space);
1109 __isl_give isl_map *isl_map_lex_ge(
1110 __isl_take isl_space *set_space);
1111 __isl_give isl_map *isl_map_lex_lt_first(
1112 __isl_take isl_space *space, unsigned n);
1113 __isl_give isl_map *isl_map_lex_le_first(
1114 __isl_take isl_space *space, unsigned n);
1115 __isl_give isl_map *isl_map_lex_gt_first(
1116 __isl_take isl_space *space, unsigned n);
1117 __isl_give isl_map *isl_map_lex_ge_first(
1118 __isl_take isl_space *space, unsigned n);
1120 The first four functions take a space for a B<set>
1121 and return relations that express that the elements in the domain
1122 are lexicographically less
1123 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1124 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1125 than the elements in the range.
1126 The last four functions take a space for a map
1127 and return relations that express that the first C<n> dimensions
1128 in the domain are lexicographically less
1129 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1130 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1131 than the first C<n> dimensions in the range.
1135 A basic set or relation can be converted to a set or relation
1136 using the following functions.
1138 __isl_give isl_set *isl_set_from_basic_set(
1139 __isl_take isl_basic_set *bset);
1140 __isl_give isl_map *isl_map_from_basic_map(
1141 __isl_take isl_basic_map *bmap);
1143 Sets and relations can be converted to union sets and relations
1144 using the following functions.
1146 __isl_give isl_union_map *isl_union_map_from_map(
1147 __isl_take isl_map *map);
1148 __isl_give isl_union_set *isl_union_set_from_set(
1149 __isl_take isl_set *set);
1151 The inverse conversions below can only be used if the input
1152 union set or relation is known to contain elements in exactly one
1155 __isl_give isl_set *isl_set_from_union_set(
1156 __isl_take isl_union_set *uset);
1157 __isl_give isl_map *isl_map_from_union_map(
1158 __isl_take isl_union_map *umap);
1160 A zero-dimensional set can be constructed on a given parameter domain
1161 using the following function.
1163 __isl_give isl_set *isl_set_from_params(
1164 __isl_take isl_set *set);
1166 Sets and relations can be copied and freed again using the following
1169 __isl_give isl_basic_set *isl_basic_set_copy(
1170 __isl_keep isl_basic_set *bset);
1171 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1172 __isl_give isl_union_set *isl_union_set_copy(
1173 __isl_keep isl_union_set *uset);
1174 __isl_give isl_basic_map *isl_basic_map_copy(
1175 __isl_keep isl_basic_map *bmap);
1176 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1177 __isl_give isl_union_map *isl_union_map_copy(
1178 __isl_keep isl_union_map *umap);
1179 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1180 void isl_set_free(__isl_take isl_set *set);
1181 void *isl_union_set_free(__isl_take isl_union_set *uset);
1182 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1183 void isl_map_free(__isl_take isl_map *map);
1184 void *isl_union_map_free(__isl_take isl_union_map *umap);
1186 Other sets and relations can be constructed by starting
1187 from a universe set or relation, adding equality and/or
1188 inequality constraints and then projecting out the
1189 existentially quantified variables, if any.
1190 Constraints can be constructed, manipulated and
1191 added to (or removed from) (basic) sets and relations
1192 using the following functions.
1194 #include <isl/constraint.h>
1195 __isl_give isl_constraint *isl_equality_alloc(
1196 __isl_take isl_local_space *ls);
1197 __isl_give isl_constraint *isl_inequality_alloc(
1198 __isl_take isl_local_space *ls);
1199 __isl_give isl_constraint *isl_constraint_set_constant(
1200 __isl_take isl_constraint *constraint, isl_int v);
1201 __isl_give isl_constraint *isl_constraint_set_constant_si(
1202 __isl_take isl_constraint *constraint, int v);
1203 __isl_give isl_constraint *isl_constraint_set_coefficient(
1204 __isl_take isl_constraint *constraint,
1205 enum isl_dim_type type, int pos, isl_int v);
1206 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1207 __isl_take isl_constraint *constraint,
1208 enum isl_dim_type type, int pos, int v);
1209 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1210 __isl_take isl_basic_map *bmap,
1211 __isl_take isl_constraint *constraint);
1212 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1213 __isl_take isl_basic_set *bset,
1214 __isl_take isl_constraint *constraint);
1215 __isl_give isl_map *isl_map_add_constraint(
1216 __isl_take isl_map *map,
1217 __isl_take isl_constraint *constraint);
1218 __isl_give isl_set *isl_set_add_constraint(
1219 __isl_take isl_set *set,
1220 __isl_take isl_constraint *constraint);
1221 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1222 __isl_take isl_basic_set *bset,
1223 __isl_take isl_constraint *constraint);
1225 For example, to create a set containing the even integers
1226 between 10 and 42, you would use the following code.
1229 isl_local_space *ls;
1231 isl_basic_set *bset;
1233 space = isl_space_set_alloc(ctx, 0, 2);
1234 bset = isl_basic_set_universe(isl_space_copy(space));
1235 ls = isl_local_space_from_space(space);
1237 c = isl_equality_alloc(isl_local_space_copy(ls));
1238 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1239 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1240 bset = isl_basic_set_add_constraint(bset, c);
1242 c = isl_inequality_alloc(isl_local_space_copy(ls));
1243 c = isl_constraint_set_constant_si(c, -10);
1244 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1245 bset = isl_basic_set_add_constraint(bset, c);
1247 c = isl_inequality_alloc(ls);
1248 c = isl_constraint_set_constant_si(c, 42);
1249 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1250 bset = isl_basic_set_add_constraint(bset, c);
1252 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1256 isl_basic_set *bset;
1257 bset = isl_basic_set_read_from_str(ctx,
1258 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1260 A basic set or relation can also be constructed from two matrices
1261 describing the equalities and the inequalities.
1263 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1264 __isl_take isl_space *space,
1265 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1266 enum isl_dim_type c1,
1267 enum isl_dim_type c2, enum isl_dim_type c3,
1268 enum isl_dim_type c4);
1269 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1270 __isl_take isl_space *space,
1271 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1272 enum isl_dim_type c1,
1273 enum isl_dim_type c2, enum isl_dim_type c3,
1274 enum isl_dim_type c4, enum isl_dim_type c5);
1276 The C<isl_dim_type> arguments indicate the order in which
1277 different kinds of variables appear in the input matrices
1278 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1279 C<isl_dim_set> and C<isl_dim_div> for sets and
1280 of C<isl_dim_cst>, C<isl_dim_param>,
1281 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1283 A (basic or union) set or relation can also be constructed from a
1284 (union) (piecewise) (multiple) affine expression
1285 or a list of affine expressions
1286 (See L<"Piecewise Quasi Affine Expressions"> and
1287 L<"Piecewise Multiple Quasi Affine Expressions">).
1289 __isl_give isl_basic_map *isl_basic_map_from_aff(
1290 __isl_take isl_aff *aff);
1291 __isl_give isl_map *isl_map_from_aff(
1292 __isl_take isl_aff *aff);
1293 __isl_give isl_set *isl_set_from_pw_aff(
1294 __isl_take isl_pw_aff *pwaff);
1295 __isl_give isl_map *isl_map_from_pw_aff(
1296 __isl_take isl_pw_aff *pwaff);
1297 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1298 __isl_take isl_space *domain_space,
1299 __isl_take isl_aff_list *list);
1300 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1301 __isl_take isl_multi_aff *maff)
1302 __isl_give isl_map *isl_map_from_multi_aff(
1303 __isl_take isl_multi_aff *maff)
1304 __isl_give isl_set *isl_set_from_pw_multi_aff(
1305 __isl_take isl_pw_multi_aff *pma);
1306 __isl_give isl_map *isl_map_from_pw_multi_aff(
1307 __isl_take isl_pw_multi_aff *pma);
1308 __isl_give isl_union_map *
1309 isl_union_map_from_union_pw_multi_aff(
1310 __isl_take isl_union_pw_multi_aff *upma);
1312 The C<domain_dim> argument describes the domain of the resulting
1313 basic relation. It is required because the C<list> may consist
1314 of zero affine expressions.
1316 =head2 Inspecting Sets and Relations
1318 Usually, the user should not have to care about the actual constraints
1319 of the sets and maps, but should instead apply the abstract operations
1320 explained in the following sections.
1321 Occasionally, however, it may be required to inspect the individual
1322 coefficients of the constraints. This section explains how to do so.
1323 In these cases, it may also be useful to have C<isl> compute
1324 an explicit representation of the existentially quantified variables.
1326 __isl_give isl_set *isl_set_compute_divs(
1327 __isl_take isl_set *set);
1328 __isl_give isl_map *isl_map_compute_divs(
1329 __isl_take isl_map *map);
1330 __isl_give isl_union_set *isl_union_set_compute_divs(
1331 __isl_take isl_union_set *uset);
1332 __isl_give isl_union_map *isl_union_map_compute_divs(
1333 __isl_take isl_union_map *umap);
1335 This explicit representation defines the existentially quantified
1336 variables as integer divisions of the other variables, possibly
1337 including earlier existentially quantified variables.
1338 An explicitly represented existentially quantified variable therefore
1339 has a unique value when the values of the other variables are known.
1340 If, furthermore, the same existentials, i.e., existentials
1341 with the same explicit representations, should appear in the
1342 same order in each of the disjuncts of a set or map, then the user should call
1343 either of the following functions.
1345 __isl_give isl_set *isl_set_align_divs(
1346 __isl_take isl_set *set);
1347 __isl_give isl_map *isl_map_align_divs(
1348 __isl_take isl_map *map);
1350 Alternatively, the existentially quantified variables can be removed
1351 using the following functions, which compute an overapproximation.
1353 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1356 __isl_take isl_basic_map *bmap);
1357 __isl_give isl_set *isl_set_remove_divs(
1358 __isl_take isl_set *set);
1359 __isl_give isl_map *isl_map_remove_divs(
1360 __isl_take isl_map *map);
1362 To iterate over all the sets or maps in a union set or map, use
1364 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1365 int (*fn)(__isl_take isl_set *set, void *user),
1367 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1368 int (*fn)(__isl_take isl_map *map, void *user),
1371 The number of sets or maps in a union set or map can be obtained
1374 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1375 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1377 To extract the set or map in a given space from a union, use
1379 __isl_give isl_set *isl_union_set_extract_set(
1380 __isl_keep isl_union_set *uset,
1381 __isl_take isl_space *space);
1382 __isl_give isl_map *isl_union_map_extract_map(
1383 __isl_keep isl_union_map *umap,
1384 __isl_take isl_space *space);
1386 To iterate over all the basic sets or maps in a set or map, use
1388 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1389 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1391 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1392 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1395 The callback function C<fn> should return 0 if successful and
1396 -1 if an error occurs. In the latter case, or if any other error
1397 occurs, the above functions will return -1.
1399 It should be noted that C<isl> does not guarantee that
1400 the basic sets or maps passed to C<fn> are disjoint.
1401 If this is required, then the user should call one of
1402 the following functions first.
1404 __isl_give isl_set *isl_set_make_disjoint(
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_make_disjoint(
1407 __isl_take isl_map *map);
1409 The number of basic sets in a set can be obtained
1412 int isl_set_n_basic_set(__isl_keep isl_set *set);
1414 To iterate over the constraints of a basic set or map, use
1416 #include <isl/constraint.h>
1418 int isl_basic_map_foreach_constraint(
1419 __isl_keep isl_basic_map *bmap,
1420 int (*fn)(__isl_take isl_constraint *c, void *user),
1422 void *isl_constraint_free(__isl_take isl_constraint *c);
1424 Again, the callback function C<fn> should return 0 if successful and
1425 -1 if an error occurs. In the latter case, or if any other error
1426 occurs, the above functions will return -1.
1427 The constraint C<c> represents either an equality or an inequality.
1428 Use the following function to find out whether a constraint
1429 represents an equality. If not, it represents an inequality.
1431 int isl_constraint_is_equality(
1432 __isl_keep isl_constraint *constraint);
1434 The coefficients of the constraints can be inspected using
1435 the following functions.
1437 void isl_constraint_get_constant(
1438 __isl_keep isl_constraint *constraint, isl_int *v);
1439 void isl_constraint_get_coefficient(
1440 __isl_keep isl_constraint *constraint,
1441 enum isl_dim_type type, int pos, isl_int *v);
1442 int isl_constraint_involves_dims(
1443 __isl_keep isl_constraint *constraint,
1444 enum isl_dim_type type, unsigned first, unsigned n);
1446 The explicit representations of the existentially quantified
1447 variables can be inspected using the following function.
1448 Note that the user is only allowed to use this function
1449 if the inspected set or map is the result of a call
1450 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1451 The existentially quantified variable is equal to the floor
1452 of the returned affine expression. The affine expression
1453 itself can be inspected using the functions in
1454 L<"Piecewise Quasi Affine Expressions">.
1456 __isl_give isl_aff *isl_constraint_get_div(
1457 __isl_keep isl_constraint *constraint, int pos);
1459 To obtain the constraints of a basic set or map in matrix
1460 form, use the following functions.
1462 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1463 __isl_keep isl_basic_set *bset,
1464 enum isl_dim_type c1, enum isl_dim_type c2,
1465 enum isl_dim_type c3, enum isl_dim_type c4);
1466 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1467 __isl_keep isl_basic_set *bset,
1468 enum isl_dim_type c1, enum isl_dim_type c2,
1469 enum isl_dim_type c3, enum isl_dim_type c4);
1470 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1471 __isl_keep isl_basic_map *bmap,
1472 enum isl_dim_type c1,
1473 enum isl_dim_type c2, enum isl_dim_type c3,
1474 enum isl_dim_type c4, enum isl_dim_type c5);
1475 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1476 __isl_keep isl_basic_map *bmap,
1477 enum isl_dim_type c1,
1478 enum isl_dim_type c2, enum isl_dim_type c3,
1479 enum isl_dim_type c4, enum isl_dim_type c5);
1481 The C<isl_dim_type> arguments dictate the order in which
1482 different kinds of variables appear in the resulting matrix
1483 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1484 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1486 The number of parameters, input, output or set dimensions can
1487 be obtained using the following functions.
1489 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1490 enum isl_dim_type type);
1491 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1492 enum isl_dim_type type);
1493 unsigned isl_set_dim(__isl_keep isl_set *set,
1494 enum isl_dim_type type);
1495 unsigned isl_map_dim(__isl_keep isl_map *map,
1496 enum isl_dim_type type);
1498 To check whether the description of a set or relation depends
1499 on one or more given dimensions, it is not necessary to iterate over all
1500 constraints. Instead the following functions can be used.
1502 int isl_basic_set_involves_dims(
1503 __isl_keep isl_basic_set *bset,
1504 enum isl_dim_type type, unsigned first, unsigned n);
1505 int isl_set_involves_dims(__isl_keep isl_set *set,
1506 enum isl_dim_type type, unsigned first, unsigned n);
1507 int isl_basic_map_involves_dims(
1508 __isl_keep isl_basic_map *bmap,
1509 enum isl_dim_type type, unsigned first, unsigned n);
1510 int isl_map_involves_dims(__isl_keep isl_map *map,
1511 enum isl_dim_type type, unsigned first, unsigned n);
1513 Similarly, the following functions can be used to check whether
1514 a given dimension is involved in any lower or upper bound.
1516 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1517 enum isl_dim_type type, unsigned pos);
1518 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1519 enum isl_dim_type type, unsigned pos);
1521 The identifiers or names of the domain and range spaces of a set
1522 or relation can be read off or set using the following functions.
1524 __isl_give isl_set *isl_set_set_tuple_id(
1525 __isl_take isl_set *set, __isl_take isl_id *id);
1526 __isl_give isl_set *isl_set_reset_tuple_id(
1527 __isl_take isl_set *set);
1528 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1529 __isl_give isl_id *isl_set_get_tuple_id(
1530 __isl_keep isl_set *set);
1531 __isl_give isl_map *isl_map_set_tuple_id(
1532 __isl_take isl_map *map, enum isl_dim_type type,
1533 __isl_take isl_id *id);
1534 __isl_give isl_map *isl_map_reset_tuple_id(
1535 __isl_take isl_map *map, enum isl_dim_type type);
1536 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1537 enum isl_dim_type type);
1538 __isl_give isl_id *isl_map_get_tuple_id(
1539 __isl_keep isl_map *map, enum isl_dim_type type);
1541 const char *isl_basic_set_get_tuple_name(
1542 __isl_keep isl_basic_set *bset);
1543 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1544 __isl_take isl_basic_set *set, const char *s);
1545 const char *isl_set_get_tuple_name(
1546 __isl_keep isl_set *set);
1547 const char *isl_basic_map_get_tuple_name(
1548 __isl_keep isl_basic_map *bmap,
1549 enum isl_dim_type type);
1550 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1551 __isl_take isl_basic_map *bmap,
1552 enum isl_dim_type type, const char *s);
1553 const char *isl_map_get_tuple_name(
1554 __isl_keep isl_map *map,
1555 enum isl_dim_type type);
1557 As with C<isl_space_get_tuple_name>, the value returned points to
1558 an internal data structure.
1559 The identifiers, positions or names of individual dimensions can be
1560 read off using the following functions.
1562 __isl_give isl_set *isl_set_set_dim_id(
1563 __isl_take isl_set *set, enum isl_dim_type type,
1564 unsigned pos, __isl_take isl_id *id);
1565 int isl_set_has_dim_id(__isl_keep isl_set *set,
1566 enum isl_dim_type type, unsigned pos);
1567 __isl_give isl_id *isl_set_get_dim_id(
1568 __isl_keep isl_set *set, enum isl_dim_type type,
1570 int isl_basic_map_has_dim_id(
1571 __isl_keep isl_basic_map *bmap,
1572 enum isl_dim_type type, unsigned pos);
1573 __isl_give isl_map *isl_map_set_dim_id(
1574 __isl_take isl_map *map, enum isl_dim_type type,
1575 unsigned pos, __isl_take isl_id *id);
1576 int isl_map_has_dim_id(__isl_keep isl_map *map,
1577 enum isl_dim_type type, unsigned pos);
1578 __isl_give isl_id *isl_map_get_dim_id(
1579 __isl_keep isl_map *map, enum isl_dim_type type,
1582 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1583 enum isl_dim_type type, __isl_keep isl_id *id);
1584 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1585 enum isl_dim_type type, __isl_keep isl_id *id);
1586 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1587 enum isl_dim_type type, const char *name);
1588 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1589 enum isl_dim_type type, const char *name);
1591 const char *isl_constraint_get_dim_name(
1592 __isl_keep isl_constraint *constraint,
1593 enum isl_dim_type type, unsigned pos);
1594 const char *isl_basic_set_get_dim_name(
1595 __isl_keep isl_basic_set *bset,
1596 enum isl_dim_type type, unsigned pos);
1597 int isl_set_has_dim_name(__isl_keep isl_set *set,
1598 enum isl_dim_type type, unsigned pos);
1599 const char *isl_set_get_dim_name(
1600 __isl_keep isl_set *set,
1601 enum isl_dim_type type, unsigned pos);
1602 const char *isl_basic_map_get_dim_name(
1603 __isl_keep isl_basic_map *bmap,
1604 enum isl_dim_type type, unsigned pos);
1605 const char *isl_map_get_dim_name(
1606 __isl_keep isl_map *map,
1607 enum isl_dim_type type, unsigned pos);
1609 These functions are mostly useful to obtain the identifiers, positions
1610 or names of the parameters. Identifiers of individual dimensions are
1611 essentially only useful for printing. They are ignored by all other
1612 operations and may not be preserved across those operations.
1616 =head3 Unary Properties
1622 The following functions test whether the given set or relation
1623 contains any integer points. The ``plain'' variants do not perform
1624 any computations, but simply check if the given set or relation
1625 is already known to be empty.
1627 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1628 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1629 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1630 int isl_set_is_empty(__isl_keep isl_set *set);
1631 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1632 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1633 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1634 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1635 int isl_map_is_empty(__isl_keep isl_map *map);
1636 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1638 =item * Universality
1640 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1641 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1642 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1644 =item * Single-valuedness
1646 int isl_map_plain_is_single_valued(
1647 __isl_keep isl_map *map);
1648 int isl_map_is_single_valued(__isl_keep isl_map *map);
1649 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1653 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1654 int isl_map_is_injective(__isl_keep isl_map *map);
1655 int isl_union_map_plain_is_injective(
1656 __isl_keep isl_union_map *umap);
1657 int isl_union_map_is_injective(
1658 __isl_keep isl_union_map *umap);
1662 int isl_map_is_bijective(__isl_keep isl_map *map);
1663 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1667 int isl_basic_map_plain_is_fixed(
1668 __isl_keep isl_basic_map *bmap,
1669 enum isl_dim_type type, unsigned pos,
1671 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1672 enum isl_dim_type type, unsigned pos,
1674 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1675 enum isl_dim_type type, unsigned pos,
1678 Check if the relation obviously lies on a hyperplane where the given dimension
1679 has a fixed value and if so, return that value in C<*val>.
1683 To check whether a set is a parameter domain, use this function:
1685 int isl_set_is_params(__isl_keep isl_set *set);
1686 int isl_union_set_is_params(
1687 __isl_keep isl_union_set *uset);
1691 The following functions check whether the domain of the given
1692 (basic) set is a wrapped relation.
1694 int isl_basic_set_is_wrapping(
1695 __isl_keep isl_basic_set *bset);
1696 int isl_set_is_wrapping(__isl_keep isl_set *set);
1698 =item * Internal Product
1700 int isl_basic_map_can_zip(
1701 __isl_keep isl_basic_map *bmap);
1702 int isl_map_can_zip(__isl_keep isl_map *map);
1704 Check whether the product of domain and range of the given relation
1706 i.e., whether both domain and range are nested relations.
1710 int isl_basic_map_can_curry(
1711 __isl_keep isl_basic_map *bmap);
1712 int isl_map_can_curry(__isl_keep isl_map *map);
1714 Check whether the domain of the (basic) relation is a wrapped relation.
1718 =head3 Binary Properties
1724 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1725 __isl_keep isl_set *set2);
1726 int isl_set_is_equal(__isl_keep isl_set *set1,
1727 __isl_keep isl_set *set2);
1728 int isl_union_set_is_equal(
1729 __isl_keep isl_union_set *uset1,
1730 __isl_keep isl_union_set *uset2);
1731 int isl_basic_map_is_equal(
1732 __isl_keep isl_basic_map *bmap1,
1733 __isl_keep isl_basic_map *bmap2);
1734 int isl_map_is_equal(__isl_keep isl_map *map1,
1735 __isl_keep isl_map *map2);
1736 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1737 __isl_keep isl_map *map2);
1738 int isl_union_map_is_equal(
1739 __isl_keep isl_union_map *umap1,
1740 __isl_keep isl_union_map *umap2);
1742 =item * Disjointness
1744 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1745 __isl_keep isl_set *set2);
1749 int isl_basic_set_is_subset(
1750 __isl_keep isl_basic_set *bset1,
1751 __isl_keep isl_basic_set *bset2);
1752 int isl_set_is_subset(__isl_keep isl_set *set1,
1753 __isl_keep isl_set *set2);
1754 int isl_set_is_strict_subset(
1755 __isl_keep isl_set *set1,
1756 __isl_keep isl_set *set2);
1757 int isl_union_set_is_subset(
1758 __isl_keep isl_union_set *uset1,
1759 __isl_keep isl_union_set *uset2);
1760 int isl_union_set_is_strict_subset(
1761 __isl_keep isl_union_set *uset1,
1762 __isl_keep isl_union_set *uset2);
1763 int isl_basic_map_is_subset(
1764 __isl_keep isl_basic_map *bmap1,
1765 __isl_keep isl_basic_map *bmap2);
1766 int isl_basic_map_is_strict_subset(
1767 __isl_keep isl_basic_map *bmap1,
1768 __isl_keep isl_basic_map *bmap2);
1769 int isl_map_is_subset(
1770 __isl_keep isl_map *map1,
1771 __isl_keep isl_map *map2);
1772 int isl_map_is_strict_subset(
1773 __isl_keep isl_map *map1,
1774 __isl_keep isl_map *map2);
1775 int isl_union_map_is_subset(
1776 __isl_keep isl_union_map *umap1,
1777 __isl_keep isl_union_map *umap2);
1778 int isl_union_map_is_strict_subset(
1779 __isl_keep isl_union_map *umap1,
1780 __isl_keep isl_union_map *umap2);
1784 =head2 Unary Operations
1790 __isl_give isl_set *isl_set_complement(
1791 __isl_take isl_set *set);
1792 __isl_give isl_map *isl_map_complement(
1793 __isl_take isl_map *map);
1797 __isl_give isl_basic_map *isl_basic_map_reverse(
1798 __isl_take isl_basic_map *bmap);
1799 __isl_give isl_map *isl_map_reverse(
1800 __isl_take isl_map *map);
1801 __isl_give isl_union_map *isl_union_map_reverse(
1802 __isl_take isl_union_map *umap);
1806 __isl_give isl_basic_set *isl_basic_set_project_out(
1807 __isl_take isl_basic_set *bset,
1808 enum isl_dim_type type, unsigned first, unsigned n);
1809 __isl_give isl_basic_map *isl_basic_map_project_out(
1810 __isl_take isl_basic_map *bmap,
1811 enum isl_dim_type type, unsigned first, unsigned n);
1812 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1813 enum isl_dim_type type, unsigned first, unsigned n);
1814 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1815 enum isl_dim_type type, unsigned first, unsigned n);
1816 __isl_give isl_basic_set *isl_basic_set_params(
1817 __isl_take isl_basic_set *bset);
1818 __isl_give isl_basic_set *isl_basic_map_domain(
1819 __isl_take isl_basic_map *bmap);
1820 __isl_give isl_basic_set *isl_basic_map_range(
1821 __isl_take isl_basic_map *bmap);
1822 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1823 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1824 __isl_give isl_set *isl_map_domain(
1825 __isl_take isl_map *bmap);
1826 __isl_give isl_set *isl_map_range(
1827 __isl_take isl_map *map);
1828 __isl_give isl_set *isl_union_set_params(
1829 __isl_take isl_union_set *uset);
1830 __isl_give isl_set *isl_union_map_params(
1831 __isl_take isl_union_map *umap);
1832 __isl_give isl_union_set *isl_union_map_domain(
1833 __isl_take isl_union_map *umap);
1834 __isl_give isl_union_set *isl_union_map_range(
1835 __isl_take isl_union_map *umap);
1837 __isl_give isl_basic_map *isl_basic_map_domain_map(
1838 __isl_take isl_basic_map *bmap);
1839 __isl_give isl_basic_map *isl_basic_map_range_map(
1840 __isl_take isl_basic_map *bmap);
1841 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1842 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1843 __isl_give isl_union_map *isl_union_map_domain_map(
1844 __isl_take isl_union_map *umap);
1845 __isl_give isl_union_map *isl_union_map_range_map(
1846 __isl_take isl_union_map *umap);
1848 The functions above construct a (basic, regular or union) relation
1849 that maps (a wrapped version of) the input relation to its domain or range.
1853 __isl_give isl_set *isl_set_eliminate(
1854 __isl_take isl_set *set, enum isl_dim_type type,
1855 unsigned first, unsigned n);
1856 __isl_give isl_basic_map *isl_basic_map_eliminate(
1857 __isl_take isl_basic_map *bmap,
1858 enum isl_dim_type type,
1859 unsigned first, unsigned n);
1860 __isl_give isl_map *isl_map_eliminate(
1861 __isl_take isl_map *map, enum isl_dim_type type,
1862 unsigned first, unsigned n);
1864 Eliminate the coefficients for the given dimensions from the constraints,
1865 without removing the dimensions.
1869 __isl_give isl_basic_set *isl_basic_set_fix(
1870 __isl_take isl_basic_set *bset,
1871 enum isl_dim_type type, unsigned pos,
1873 __isl_give isl_basic_set *isl_basic_set_fix_si(
1874 __isl_take isl_basic_set *bset,
1875 enum isl_dim_type type, unsigned pos, int value);
1876 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1877 enum isl_dim_type type, unsigned pos,
1879 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1880 enum isl_dim_type type, unsigned pos, int value);
1881 __isl_give isl_basic_map *isl_basic_map_fix_si(
1882 __isl_take isl_basic_map *bmap,
1883 enum isl_dim_type type, unsigned pos, int value);
1884 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1885 enum isl_dim_type type, unsigned pos, int value);
1887 Intersect the set or relation with the hyperplane where the given
1888 dimension has the fixed given value.
1890 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1891 __isl_take isl_basic_map *bmap,
1892 enum isl_dim_type type, unsigned pos, int value);
1893 __isl_give isl_set *isl_set_lower_bound(
1894 __isl_take isl_set *set,
1895 enum isl_dim_type type, unsigned pos,
1897 __isl_give isl_set *isl_set_lower_bound_si(
1898 __isl_take isl_set *set,
1899 enum isl_dim_type type, unsigned pos, int value);
1900 __isl_give isl_map *isl_map_lower_bound_si(
1901 __isl_take isl_map *map,
1902 enum isl_dim_type type, unsigned pos, int value);
1903 __isl_give isl_set *isl_set_upper_bound(
1904 __isl_take isl_set *set,
1905 enum isl_dim_type type, unsigned pos,
1907 __isl_give isl_set *isl_set_upper_bound_si(
1908 __isl_take isl_set *set,
1909 enum isl_dim_type type, unsigned pos, int value);
1910 __isl_give isl_map *isl_map_upper_bound_si(
1911 __isl_take isl_map *map,
1912 enum isl_dim_type type, unsigned pos, int value);
1914 Intersect the set or relation with the half-space where the given
1915 dimension has a value bounded by the fixed given value.
1917 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1918 enum isl_dim_type type1, int pos1,
1919 enum isl_dim_type type2, int pos2);
1920 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1921 enum isl_dim_type type1, int pos1,
1922 enum isl_dim_type type2, int pos2);
1924 Intersect the set or relation with the hyperplane where the given
1925 dimensions are equal to each other.
1927 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1928 enum isl_dim_type type1, int pos1,
1929 enum isl_dim_type type2, int pos2);
1931 Intersect the relation with the hyperplane where the given
1932 dimensions have opposite values.
1934 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1935 enum isl_dim_type type1, int pos1,
1936 enum isl_dim_type type2, int pos2);
1938 Intersect the relation with the half-space where the given
1939 dimensions satisfy the given ordering.
1943 __isl_give isl_map *isl_set_identity(
1944 __isl_take isl_set *set);
1945 __isl_give isl_union_map *isl_union_set_identity(
1946 __isl_take isl_union_set *uset);
1948 Construct an identity relation on the given (union) set.
1952 __isl_give isl_basic_set *isl_basic_map_deltas(
1953 __isl_take isl_basic_map *bmap);
1954 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1955 __isl_give isl_union_set *isl_union_map_deltas(
1956 __isl_take isl_union_map *umap);
1958 These functions return a (basic) set containing the differences
1959 between image elements and corresponding domain elements in the input.
1961 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1962 __isl_take isl_basic_map *bmap);
1963 __isl_give isl_map *isl_map_deltas_map(
1964 __isl_take isl_map *map);
1965 __isl_give isl_union_map *isl_union_map_deltas_map(
1966 __isl_take isl_union_map *umap);
1968 The functions above construct a (basic, regular or union) relation
1969 that maps (a wrapped version of) the input relation to its delta set.
1973 Simplify the representation of a set or relation by trying
1974 to combine pairs of basic sets or relations into a single
1975 basic set or relation.
1977 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1978 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1979 __isl_give isl_union_set *isl_union_set_coalesce(
1980 __isl_take isl_union_set *uset);
1981 __isl_give isl_union_map *isl_union_map_coalesce(
1982 __isl_take isl_union_map *umap);
1984 One of the methods for combining pairs of basic sets or relations
1985 can result in coefficients that are much larger than those that appear
1986 in the constraints of the input. By default, the coefficients are
1987 not allowed to grow larger, but this can be changed by unsetting
1988 the following option.
1990 int isl_options_set_coalesce_bounded_wrapping(
1991 isl_ctx *ctx, int val);
1992 int isl_options_get_coalesce_bounded_wrapping(
1995 =item * Detecting equalities
1997 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1998 __isl_take isl_basic_set *bset);
1999 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2000 __isl_take isl_basic_map *bmap);
2001 __isl_give isl_set *isl_set_detect_equalities(
2002 __isl_take isl_set *set);
2003 __isl_give isl_map *isl_map_detect_equalities(
2004 __isl_take isl_map *map);
2005 __isl_give isl_union_set *isl_union_set_detect_equalities(
2006 __isl_take isl_union_set *uset);
2007 __isl_give isl_union_map *isl_union_map_detect_equalities(
2008 __isl_take isl_union_map *umap);
2010 Simplify the representation of a set or relation by detecting implicit
2013 =item * Removing redundant constraints
2015 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2016 __isl_take isl_basic_set *bset);
2017 __isl_give isl_set *isl_set_remove_redundancies(
2018 __isl_take isl_set *set);
2019 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2020 __isl_take isl_basic_map *bmap);
2021 __isl_give isl_map *isl_map_remove_redundancies(
2022 __isl_take isl_map *map);
2026 __isl_give isl_basic_set *isl_set_convex_hull(
2027 __isl_take isl_set *set);
2028 __isl_give isl_basic_map *isl_map_convex_hull(
2029 __isl_take isl_map *map);
2031 If the input set or relation has any existentially quantified
2032 variables, then the result of these operations is currently undefined.
2036 __isl_give isl_basic_set *isl_set_simple_hull(
2037 __isl_take isl_set *set);
2038 __isl_give isl_basic_map *isl_map_simple_hull(
2039 __isl_take isl_map *map);
2040 __isl_give isl_union_map *isl_union_map_simple_hull(
2041 __isl_take isl_union_map *umap);
2043 These functions compute a single basic set or relation
2044 that contains the whole input set or relation.
2045 In particular, the output is described by translates
2046 of the constraints describing the basic sets or relations in the input.
2050 (See \autoref{s:simple hull}.)
2056 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2057 __isl_take isl_basic_set *bset);
2058 __isl_give isl_basic_set *isl_set_affine_hull(
2059 __isl_take isl_set *set);
2060 __isl_give isl_union_set *isl_union_set_affine_hull(
2061 __isl_take isl_union_set *uset);
2062 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2063 __isl_take isl_basic_map *bmap);
2064 __isl_give isl_basic_map *isl_map_affine_hull(
2065 __isl_take isl_map *map);
2066 __isl_give isl_union_map *isl_union_map_affine_hull(
2067 __isl_take isl_union_map *umap);
2069 In case of union sets and relations, the affine hull is computed
2072 =item * Polyhedral hull
2074 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2075 __isl_take isl_set *set);
2076 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2079 __isl_take isl_union_set *uset);
2080 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2081 __isl_take isl_union_map *umap);
2083 These functions compute a single basic set or relation
2084 not involving any existentially quantified variables
2085 that contains the whole input set or relation.
2086 In case of union sets and relations, the polyhedral hull is computed
2091 __isl_give isl_basic_set *isl_basic_set_sample(
2092 __isl_take isl_basic_set *bset);
2093 __isl_give isl_basic_set *isl_set_sample(
2094 __isl_take isl_set *set);
2095 __isl_give isl_basic_map *isl_basic_map_sample(
2096 __isl_take isl_basic_map *bmap);
2097 __isl_give isl_basic_map *isl_map_sample(
2098 __isl_take isl_map *map);
2100 If the input (basic) set or relation is non-empty, then return
2101 a singleton subset of the input. Otherwise, return an empty set.
2103 =item * Optimization
2105 #include <isl/ilp.h>
2106 enum isl_lp_result isl_basic_set_max(
2107 __isl_keep isl_basic_set *bset,
2108 __isl_keep isl_aff *obj, isl_int *opt)
2109 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2110 __isl_keep isl_aff *obj, isl_int *opt);
2111 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2112 __isl_keep isl_aff *obj, isl_int *opt);
2114 Compute the minimum or maximum of the integer affine expression C<obj>
2115 over the points in C<set>, returning the result in C<opt>.
2116 The return value may be one of C<isl_lp_error>,
2117 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2119 =item * Parametric optimization
2121 __isl_give isl_pw_aff *isl_set_dim_min(
2122 __isl_take isl_set *set, int pos);
2123 __isl_give isl_pw_aff *isl_set_dim_max(
2124 __isl_take isl_set *set, int pos);
2125 __isl_give isl_pw_aff *isl_map_dim_max(
2126 __isl_take isl_map *map, int pos);
2128 Compute the minimum or maximum of the given set or output dimension
2129 as a function of the parameters (and input dimensions), but independently
2130 of the other set or output dimensions.
2131 For lexicographic optimization, see L<"Lexicographic Optimization">.
2135 The following functions compute either the set of (rational) coefficient
2136 values of valid constraints for the given set or the set of (rational)
2137 values satisfying the constraints with coefficients from the given set.
2138 Internally, these two sets of functions perform essentially the
2139 same operations, except that the set of coefficients is assumed to
2140 be a cone, while the set of values may be any polyhedron.
2141 The current implementation is based on the Farkas lemma and
2142 Fourier-Motzkin elimination, but this may change or be made optional
2143 in future. In particular, future implementations may use different
2144 dualization algorithms or skip the elimination step.
2146 __isl_give isl_basic_set *isl_basic_set_coefficients(
2147 __isl_take isl_basic_set *bset);
2148 __isl_give isl_basic_set *isl_set_coefficients(
2149 __isl_take isl_set *set);
2150 __isl_give isl_union_set *isl_union_set_coefficients(
2151 __isl_take isl_union_set *bset);
2152 __isl_give isl_basic_set *isl_basic_set_solutions(
2153 __isl_take isl_basic_set *bset);
2154 __isl_give isl_basic_set *isl_set_solutions(
2155 __isl_take isl_set *set);
2156 __isl_give isl_union_set *isl_union_set_solutions(
2157 __isl_take isl_union_set *bset);
2161 __isl_give isl_map *isl_map_fixed_power(
2162 __isl_take isl_map *map, isl_int exp);
2163 __isl_give isl_union_map *isl_union_map_fixed_power(
2164 __isl_take isl_union_map *umap, isl_int exp);
2166 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2167 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2168 of C<map> is computed.
2170 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2172 __isl_give isl_union_map *isl_union_map_power(
2173 __isl_take isl_union_map *umap, int *exact);
2175 Compute a parametric representation for all positive powers I<k> of C<map>.
2176 The result maps I<k> to a nested relation corresponding to the
2177 I<k>th power of C<map>.
2178 The result may be an overapproximation. If the result is known to be exact,
2179 then C<*exact> is set to C<1>.
2181 =item * Transitive closure
2183 __isl_give isl_map *isl_map_transitive_closure(
2184 __isl_take isl_map *map, int *exact);
2185 __isl_give isl_union_map *isl_union_map_transitive_closure(
2186 __isl_take isl_union_map *umap, int *exact);
2188 Compute the transitive closure of C<map>.
2189 The result may be an overapproximation. If the result is known to be exact,
2190 then C<*exact> is set to C<1>.
2192 =item * Reaching path lengths
2194 __isl_give isl_map *isl_map_reaching_path_lengths(
2195 __isl_take isl_map *map, int *exact);
2197 Compute a relation that maps each element in the range of C<map>
2198 to the lengths of all paths composed of edges in C<map> that
2199 end up in the given element.
2200 The result may be an overapproximation. If the result is known to be exact,
2201 then C<*exact> is set to C<1>.
2202 To compute the I<maximal> path length, the resulting relation
2203 should be postprocessed by C<isl_map_lexmax>.
2204 In particular, if the input relation is a dependence relation
2205 (mapping sources to sinks), then the maximal path length corresponds
2206 to the free schedule.
2207 Note, however, that C<isl_map_lexmax> expects the maximum to be
2208 finite, so if the path lengths are unbounded (possibly due to
2209 the overapproximation), then you will get an error message.
2213 __isl_give isl_basic_set *isl_basic_map_wrap(
2214 __isl_take isl_basic_map *bmap);
2215 __isl_give isl_set *isl_map_wrap(
2216 __isl_take isl_map *map);
2217 __isl_give isl_union_set *isl_union_map_wrap(
2218 __isl_take isl_union_map *umap);
2219 __isl_give isl_basic_map *isl_basic_set_unwrap(
2220 __isl_take isl_basic_set *bset);
2221 __isl_give isl_map *isl_set_unwrap(
2222 __isl_take isl_set *set);
2223 __isl_give isl_union_map *isl_union_set_unwrap(
2224 __isl_take isl_union_set *uset);
2228 Remove any internal structure of domain (and range) of the given
2229 set or relation. If there is any such internal structure in the input,
2230 then the name of the space is also removed.
2232 __isl_give isl_basic_set *isl_basic_set_flatten(
2233 __isl_take isl_basic_set *bset);
2234 __isl_give isl_set *isl_set_flatten(
2235 __isl_take isl_set *set);
2236 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2237 __isl_take isl_basic_map *bmap);
2238 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_give isl_map *isl_map_flatten_range(
2241 __isl_take isl_map *map);
2242 __isl_give isl_map *isl_map_flatten_domain(
2243 __isl_take isl_map *map);
2244 __isl_give isl_basic_map *isl_basic_map_flatten(
2245 __isl_take isl_basic_map *bmap);
2246 __isl_give isl_map *isl_map_flatten(
2247 __isl_take isl_map *map);
2249 __isl_give isl_map *isl_set_flatten_map(
2250 __isl_take isl_set *set);
2252 The function above constructs a relation
2253 that maps the input set to a flattened version of the set.
2257 Lift the input set to a space with extra dimensions corresponding
2258 to the existentially quantified variables in the input.
2259 In particular, the result lives in a wrapped map where the domain
2260 is the original space and the range corresponds to the original
2261 existentially quantified variables.
2263 __isl_give isl_basic_set *isl_basic_set_lift(
2264 __isl_take isl_basic_set *bset);
2265 __isl_give isl_set *isl_set_lift(
2266 __isl_take isl_set *set);
2267 __isl_give isl_union_set *isl_union_set_lift(
2268 __isl_take isl_union_set *uset);
2270 Given a local space that contains the existentially quantified
2271 variables of a set, a basic relation that, when applied to
2272 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2273 can be constructed using the following function.
2275 #include <isl/local_space.h>
2276 __isl_give isl_basic_map *isl_local_space_lifting(
2277 __isl_take isl_local_space *ls);
2279 =item * Internal Product
2281 __isl_give isl_basic_map *isl_basic_map_zip(
2282 __isl_take isl_basic_map *bmap);
2283 __isl_give isl_map *isl_map_zip(
2284 __isl_take isl_map *map);
2285 __isl_give isl_union_map *isl_union_map_zip(
2286 __isl_take isl_union_map *umap);
2288 Given a relation with nested relations for domain and range,
2289 interchange the range of the domain with the domain of the range.
2293 __isl_give isl_basic_map *isl_basic_map_curry(
2294 __isl_take isl_basic_map *bmap);
2295 __isl_give isl_map *isl_map_curry(
2296 __isl_take isl_map *map);
2297 __isl_give isl_union_map *isl_union_map_curry(
2298 __isl_take isl_union_map *umap);
2300 Given a relation with a nested relation for domain,
2301 move the range of the nested relation out of the domain
2302 and use it as the domain of a nested relation in the range,
2303 with the original range as range of this nested relation.
2305 =item * Aligning parameters
2307 __isl_give isl_set *isl_set_align_params(
2308 __isl_take isl_set *set,
2309 __isl_take isl_space *model);
2310 __isl_give isl_map *isl_map_align_params(
2311 __isl_take isl_map *map,
2312 __isl_take isl_space *model);
2314 Change the order of the parameters of the given set or relation
2315 such that the first parameters match those of C<model>.
2316 This may involve the introduction of extra parameters.
2317 All parameters need to be named.
2319 =item * Dimension manipulation
2321 __isl_give isl_set *isl_set_add_dims(
2322 __isl_take isl_set *set,
2323 enum isl_dim_type type, unsigned n);
2324 __isl_give isl_map *isl_map_add_dims(
2325 __isl_take isl_map *map,
2326 enum isl_dim_type type, unsigned n);
2327 __isl_give isl_set *isl_set_insert_dims(
2328 __isl_take isl_set *set,
2329 enum isl_dim_type type, unsigned pos, unsigned n);
2330 __isl_give isl_map *isl_map_insert_dims(
2331 __isl_take isl_map *map,
2332 enum isl_dim_type type, unsigned pos, unsigned n);
2333 __isl_give isl_basic_set *isl_basic_set_move_dims(
2334 __isl_take isl_basic_set *bset,
2335 enum isl_dim_type dst_type, unsigned dst_pos,
2336 enum isl_dim_type src_type, unsigned src_pos,
2338 __isl_give isl_basic_map *isl_basic_map_move_dims(
2339 __isl_take isl_basic_map *bmap,
2340 enum isl_dim_type dst_type, unsigned dst_pos,
2341 enum isl_dim_type src_type, unsigned src_pos,
2343 __isl_give isl_set *isl_set_move_dims(
2344 __isl_take isl_set *set,
2345 enum isl_dim_type dst_type, unsigned dst_pos,
2346 enum isl_dim_type src_type, unsigned src_pos,
2348 __isl_give isl_map *isl_map_move_dims(
2349 __isl_take isl_map *map,
2350 enum isl_dim_type dst_type, unsigned dst_pos,
2351 enum isl_dim_type src_type, unsigned src_pos,
2354 It is usually not advisable to directly change the (input or output)
2355 space of a set or a relation as this removes the name and the internal
2356 structure of the space. However, the above functions can be useful
2357 to add new parameters, assuming
2358 C<isl_set_align_params> and C<isl_map_align_params>
2363 =head2 Binary Operations
2365 The two arguments of a binary operation not only need to live
2366 in the same C<isl_ctx>, they currently also need to have
2367 the same (number of) parameters.
2369 =head3 Basic Operations
2373 =item * Intersection
2375 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2376 __isl_take isl_basic_set *bset1,
2377 __isl_take isl_basic_set *bset2);
2378 __isl_give isl_basic_set *isl_basic_set_intersect(
2379 __isl_take isl_basic_set *bset1,
2380 __isl_take isl_basic_set *bset2);
2381 __isl_give isl_set *isl_set_intersect_params(
2382 __isl_take isl_set *set,
2383 __isl_take isl_set *params);
2384 __isl_give isl_set *isl_set_intersect(
2385 __isl_take isl_set *set1,
2386 __isl_take isl_set *set2);
2387 __isl_give isl_union_set *isl_union_set_intersect_params(
2388 __isl_take isl_union_set *uset,
2389 __isl_take isl_set *set);
2390 __isl_give isl_union_map *isl_union_map_intersect_params(
2391 __isl_take isl_union_map *umap,
2392 __isl_take isl_set *set);
2393 __isl_give isl_union_set *isl_union_set_intersect(
2394 __isl_take isl_union_set *uset1,
2395 __isl_take isl_union_set *uset2);
2396 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2397 __isl_take isl_basic_map *bmap,
2398 __isl_take isl_basic_set *bset);
2399 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2400 __isl_take isl_basic_map *bmap,
2401 __isl_take isl_basic_set *bset);
2402 __isl_give isl_basic_map *isl_basic_map_intersect(
2403 __isl_take isl_basic_map *bmap1,
2404 __isl_take isl_basic_map *bmap2);
2405 __isl_give isl_map *isl_map_intersect_params(
2406 __isl_take isl_map *map,
2407 __isl_take isl_set *params);
2408 __isl_give isl_map *isl_map_intersect_domain(
2409 __isl_take isl_map *map,
2410 __isl_take isl_set *set);
2411 __isl_give isl_map *isl_map_intersect_range(
2412 __isl_take isl_map *map,
2413 __isl_take isl_set *set);
2414 __isl_give isl_map *isl_map_intersect(
2415 __isl_take isl_map *map1,
2416 __isl_take isl_map *map2);
2417 __isl_give isl_union_map *isl_union_map_intersect_domain(
2418 __isl_take isl_union_map *umap,
2419 __isl_take isl_union_set *uset);
2420 __isl_give isl_union_map *isl_union_map_intersect_range(
2421 __isl_take isl_union_map *umap,
2422 __isl_take isl_union_set *uset);
2423 __isl_give isl_union_map *isl_union_map_intersect(
2424 __isl_take isl_union_map *umap1,
2425 __isl_take isl_union_map *umap2);
2429 __isl_give isl_set *isl_basic_set_union(
2430 __isl_take isl_basic_set *bset1,
2431 __isl_take isl_basic_set *bset2);
2432 __isl_give isl_map *isl_basic_map_union(
2433 __isl_take isl_basic_map *bmap1,
2434 __isl_take isl_basic_map *bmap2);
2435 __isl_give isl_set *isl_set_union(
2436 __isl_take isl_set *set1,
2437 __isl_take isl_set *set2);
2438 __isl_give isl_map *isl_map_union(
2439 __isl_take isl_map *map1,
2440 __isl_take isl_map *map2);
2441 __isl_give isl_union_set *isl_union_set_union(
2442 __isl_take isl_union_set *uset1,
2443 __isl_take isl_union_set *uset2);
2444 __isl_give isl_union_map *isl_union_map_union(
2445 __isl_take isl_union_map *umap1,
2446 __isl_take isl_union_map *umap2);
2448 =item * Set difference
2450 __isl_give isl_set *isl_set_subtract(
2451 __isl_take isl_set *set1,
2452 __isl_take isl_set *set2);
2453 __isl_give isl_map *isl_map_subtract(
2454 __isl_take isl_map *map1,
2455 __isl_take isl_map *map2);
2456 __isl_give isl_map *isl_map_subtract_domain(
2457 __isl_take isl_map *map,
2458 __isl_take isl_set *dom);
2459 __isl_give isl_map *isl_map_subtract_range(
2460 __isl_take isl_map *map,
2461 __isl_take isl_set *dom);
2462 __isl_give isl_union_set *isl_union_set_subtract(
2463 __isl_take isl_union_set *uset1,
2464 __isl_take isl_union_set *uset2);
2465 __isl_give isl_union_map *isl_union_map_subtract(
2466 __isl_take isl_union_map *umap1,
2467 __isl_take isl_union_map *umap2);
2471 __isl_give isl_basic_set *isl_basic_set_apply(
2472 __isl_take isl_basic_set *bset,
2473 __isl_take isl_basic_map *bmap);
2474 __isl_give isl_set *isl_set_apply(
2475 __isl_take isl_set *set,
2476 __isl_take isl_map *map);
2477 __isl_give isl_union_set *isl_union_set_apply(
2478 __isl_take isl_union_set *uset,
2479 __isl_take isl_union_map *umap);
2480 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2481 __isl_take isl_basic_map *bmap1,
2482 __isl_take isl_basic_map *bmap2);
2483 __isl_give isl_basic_map *isl_basic_map_apply_range(
2484 __isl_take isl_basic_map *bmap1,
2485 __isl_take isl_basic_map *bmap2);
2486 __isl_give isl_map *isl_map_apply_domain(
2487 __isl_take isl_map *map1,
2488 __isl_take isl_map *map2);
2489 __isl_give isl_union_map *isl_union_map_apply_domain(
2490 __isl_take isl_union_map *umap1,
2491 __isl_take isl_union_map *umap2);
2492 __isl_give isl_map *isl_map_apply_range(
2493 __isl_take isl_map *map1,
2494 __isl_take isl_map *map2);
2495 __isl_give isl_union_map *isl_union_map_apply_range(
2496 __isl_take isl_union_map *umap1,
2497 __isl_take isl_union_map *umap2);
2499 =item * Cartesian Product
2501 __isl_give isl_set *isl_set_product(
2502 __isl_take isl_set *set1,
2503 __isl_take isl_set *set2);
2504 __isl_give isl_union_set *isl_union_set_product(
2505 __isl_take isl_union_set *uset1,
2506 __isl_take isl_union_set *uset2);
2507 __isl_give isl_basic_map *isl_basic_map_domain_product(
2508 __isl_take isl_basic_map *bmap1,
2509 __isl_take isl_basic_map *bmap2);
2510 __isl_give isl_basic_map *isl_basic_map_range_product(
2511 __isl_take isl_basic_map *bmap1,
2512 __isl_take isl_basic_map *bmap2);
2513 __isl_give isl_map *isl_map_domain_product(
2514 __isl_take isl_map *map1,
2515 __isl_take isl_map *map2);
2516 __isl_give isl_map *isl_map_range_product(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2519 __isl_give isl_union_map *isl_union_map_range_product(
2520 __isl_take isl_union_map *umap1,
2521 __isl_take isl_union_map *umap2);
2522 __isl_give isl_map *isl_map_product(
2523 __isl_take isl_map *map1,
2524 __isl_take isl_map *map2);
2525 __isl_give isl_union_map *isl_union_map_product(
2526 __isl_take isl_union_map *umap1,
2527 __isl_take isl_union_map *umap2);
2529 The above functions compute the cross product of the given
2530 sets or relations. The domains and ranges of the results
2531 are wrapped maps between domains and ranges of the inputs.
2532 To obtain a ``flat'' product, use the following functions
2535 __isl_give isl_basic_set *isl_basic_set_flat_product(
2536 __isl_take isl_basic_set *bset1,
2537 __isl_take isl_basic_set *bset2);
2538 __isl_give isl_set *isl_set_flat_product(
2539 __isl_take isl_set *set1,
2540 __isl_take isl_set *set2);
2541 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2542 __isl_take isl_basic_map *bmap1,
2543 __isl_take isl_basic_map *bmap2);
2544 __isl_give isl_map *isl_map_flat_domain_product(
2545 __isl_take isl_map *map1,
2546 __isl_take isl_map *map2);
2547 __isl_give isl_map *isl_map_flat_range_product(
2548 __isl_take isl_map *map1,
2549 __isl_take isl_map *map2);
2550 __isl_give isl_union_map *isl_union_map_flat_range_product(
2551 __isl_take isl_union_map *umap1,
2552 __isl_take isl_union_map *umap2);
2553 __isl_give isl_basic_map *isl_basic_map_flat_product(
2554 __isl_take isl_basic_map *bmap1,
2555 __isl_take isl_basic_map *bmap2);
2556 __isl_give isl_map *isl_map_flat_product(
2557 __isl_take isl_map *map1,
2558 __isl_take isl_map *map2);
2560 =item * Simplification
2562 __isl_give isl_basic_set *isl_basic_set_gist(
2563 __isl_take isl_basic_set *bset,
2564 __isl_take isl_basic_set *context);
2565 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2566 __isl_take isl_set *context);
2567 __isl_give isl_set *isl_set_gist_params(
2568 __isl_take isl_set *set,
2569 __isl_take isl_set *context);
2570 __isl_give isl_union_set *isl_union_set_gist(
2571 __isl_take isl_union_set *uset,
2572 __isl_take isl_union_set *context);
2573 __isl_give isl_union_set *isl_union_set_gist_params(
2574 __isl_take isl_union_set *uset,
2575 __isl_take isl_set *set);
2576 __isl_give isl_basic_map *isl_basic_map_gist(
2577 __isl_take isl_basic_map *bmap,
2578 __isl_take isl_basic_map *context);
2579 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2580 __isl_take isl_map *context);
2581 __isl_give isl_map *isl_map_gist_params(
2582 __isl_take isl_map *map,
2583 __isl_take isl_set *context);
2584 __isl_give isl_map *isl_map_gist_domain(
2585 __isl_take isl_map *map,
2586 __isl_take isl_set *context);
2587 __isl_give isl_map *isl_map_gist_range(
2588 __isl_take isl_map *map,
2589 __isl_take isl_set *context);
2590 __isl_give isl_union_map *isl_union_map_gist(
2591 __isl_take isl_union_map *umap,
2592 __isl_take isl_union_map *context);
2593 __isl_give isl_union_map *isl_union_map_gist_params(
2594 __isl_take isl_union_map *umap,
2595 __isl_take isl_set *set);
2596 __isl_give isl_union_map *isl_union_map_gist_domain(
2597 __isl_take isl_union_map *umap,
2598 __isl_take isl_union_set *uset);
2599 __isl_give isl_union_map *isl_union_map_gist_range(
2600 __isl_take isl_union_map *umap,
2601 __isl_take isl_union_set *uset);
2603 The gist operation returns a set or relation that has the
2604 same intersection with the context as the input set or relation.
2605 Any implicit equality in the intersection is made explicit in the result,
2606 while all inequalities that are redundant with respect to the intersection
2608 In case of union sets and relations, the gist operation is performed
2613 =head3 Lexicographic Optimization
2615 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2616 the following functions
2617 compute a set that contains the lexicographic minimum or maximum
2618 of the elements in C<set> (or C<bset>) for those values of the parameters
2619 that satisfy C<dom>.
2620 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2621 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2623 In other words, the union of the parameter values
2624 for which the result is non-empty and of C<*empty>
2627 __isl_give isl_set *isl_basic_set_partial_lexmin(
2628 __isl_take isl_basic_set *bset,
2629 __isl_take isl_basic_set *dom,
2630 __isl_give isl_set **empty);
2631 __isl_give isl_set *isl_basic_set_partial_lexmax(
2632 __isl_take isl_basic_set *bset,
2633 __isl_take isl_basic_set *dom,
2634 __isl_give isl_set **empty);
2635 __isl_give isl_set *isl_set_partial_lexmin(
2636 __isl_take isl_set *set, __isl_take isl_set *dom,
2637 __isl_give isl_set **empty);
2638 __isl_give isl_set *isl_set_partial_lexmax(
2639 __isl_take isl_set *set, __isl_take isl_set *dom,
2640 __isl_give isl_set **empty);
2642 Given a (basic) set C<set> (or C<bset>), the following functions simply
2643 return a set containing the lexicographic minimum or maximum
2644 of the elements in C<set> (or C<bset>).
2645 In case of union sets, the optimum is computed per space.
2647 __isl_give isl_set *isl_basic_set_lexmin(
2648 __isl_take isl_basic_set *bset);
2649 __isl_give isl_set *isl_basic_set_lexmax(
2650 __isl_take isl_basic_set *bset);
2651 __isl_give isl_set *isl_set_lexmin(
2652 __isl_take isl_set *set);
2653 __isl_give isl_set *isl_set_lexmax(
2654 __isl_take isl_set *set);
2655 __isl_give isl_union_set *isl_union_set_lexmin(
2656 __isl_take isl_union_set *uset);
2657 __isl_give isl_union_set *isl_union_set_lexmax(
2658 __isl_take isl_union_set *uset);
2660 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2661 the following functions
2662 compute a relation that maps each element of C<dom>
2663 to the single lexicographic minimum or maximum
2664 of the elements that are associated to that same
2665 element in C<map> (or C<bmap>).
2666 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2667 that contains the elements in C<dom> that do not map
2668 to any elements in C<map> (or C<bmap>).
2669 In other words, the union of the domain of the result and of C<*empty>
2672 __isl_give isl_map *isl_basic_map_partial_lexmax(
2673 __isl_take isl_basic_map *bmap,
2674 __isl_take isl_basic_set *dom,
2675 __isl_give isl_set **empty);
2676 __isl_give isl_map *isl_basic_map_partial_lexmin(
2677 __isl_take isl_basic_map *bmap,
2678 __isl_take isl_basic_set *dom,
2679 __isl_give isl_set **empty);
2680 __isl_give isl_map *isl_map_partial_lexmax(
2681 __isl_take isl_map *map, __isl_take isl_set *dom,
2682 __isl_give isl_set **empty);
2683 __isl_give isl_map *isl_map_partial_lexmin(
2684 __isl_take isl_map *map, __isl_take isl_set *dom,
2685 __isl_give isl_set **empty);
2687 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2688 return a map mapping each element in the domain of
2689 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2690 of all elements associated to that element.
2691 In case of union relations, the optimum is computed per space.
2693 __isl_give isl_map *isl_basic_map_lexmin(
2694 __isl_take isl_basic_map *bmap);
2695 __isl_give isl_map *isl_basic_map_lexmax(
2696 __isl_take isl_basic_map *bmap);
2697 __isl_give isl_map *isl_map_lexmin(
2698 __isl_take isl_map *map);
2699 __isl_give isl_map *isl_map_lexmax(
2700 __isl_take isl_map *map);
2701 __isl_give isl_union_map *isl_union_map_lexmin(
2702 __isl_take isl_union_map *umap);
2703 __isl_give isl_union_map *isl_union_map_lexmax(
2704 __isl_take isl_union_map *umap);
2706 The following functions return their result in the form of
2707 a piecewise multi-affine expression
2708 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2709 but are otherwise equivalent to the corresponding functions
2710 returning a basic set or relation.
2712 __isl_give isl_pw_multi_aff *
2713 isl_basic_map_lexmin_pw_multi_aff(
2714 __isl_take isl_basic_map *bmap);
2715 __isl_give isl_pw_multi_aff *
2716 isl_basic_set_partial_lexmin_pw_multi_aff(
2717 __isl_take isl_basic_set *bset,
2718 __isl_take isl_basic_set *dom,
2719 __isl_give isl_set **empty);
2720 __isl_give isl_pw_multi_aff *
2721 isl_basic_set_partial_lexmax_pw_multi_aff(
2722 __isl_take isl_basic_set *bset,
2723 __isl_take isl_basic_set *dom,
2724 __isl_give isl_set **empty);
2725 __isl_give isl_pw_multi_aff *
2726 isl_basic_map_partial_lexmin_pw_multi_aff(
2727 __isl_take isl_basic_map *bmap,
2728 __isl_take isl_basic_set *dom,
2729 __isl_give isl_set **empty);
2730 __isl_give isl_pw_multi_aff *
2731 isl_basic_map_partial_lexmax_pw_multi_aff(
2732 __isl_take isl_basic_map *bmap,
2733 __isl_take isl_basic_set *dom,
2734 __isl_give isl_set **empty);
2738 Lists are defined over several element types, including
2739 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2740 Here we take lists of C<isl_set>s as an example.
2741 Lists can be created, copied and freed using the following functions.
2743 #include <isl/list.h>
2744 __isl_give isl_set_list *isl_set_list_from_set(
2745 __isl_take isl_set *el);
2746 __isl_give isl_set_list *isl_set_list_alloc(
2747 isl_ctx *ctx, int n);
2748 __isl_give isl_set_list *isl_set_list_copy(
2749 __isl_keep isl_set_list *list);
2750 __isl_give isl_set_list *isl_set_list_add(
2751 __isl_take isl_set_list *list,
2752 __isl_take isl_set *el);
2753 __isl_give isl_set_list *isl_set_list_concat(
2754 __isl_take isl_set_list *list1,
2755 __isl_take isl_set_list *list2);
2756 void *isl_set_list_free(__isl_take isl_set_list *list);
2758 C<isl_set_list_alloc> creates an empty list with a capacity for
2759 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2762 Lists can be inspected using the following functions.
2764 #include <isl/list.h>
2765 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2766 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2767 __isl_give isl_set *isl_set_list_get_set(
2768 __isl_keep isl_set_list *list, int index);
2769 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2770 int (*fn)(__isl_take isl_set *el, void *user),
2773 Lists can be printed using
2775 #include <isl/list.h>
2776 __isl_give isl_printer *isl_printer_print_set_list(
2777 __isl_take isl_printer *p,
2778 __isl_keep isl_set_list *list);
2782 Vectors can be created, copied and freed using the following functions.
2784 #include <isl/vec.h>
2785 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2787 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2788 void isl_vec_free(__isl_take isl_vec *vec);
2790 Note that the elements of a newly created vector may have arbitrary values.
2791 The elements can be changed and inspected using the following functions.
2793 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2794 int isl_vec_size(__isl_keep isl_vec *vec);
2795 int isl_vec_get_element(__isl_keep isl_vec *vec,
2796 int pos, isl_int *v);
2797 __isl_give isl_vec *isl_vec_set_element(
2798 __isl_take isl_vec *vec, int pos, isl_int v);
2799 __isl_give isl_vec *isl_vec_set_element_si(
2800 __isl_take isl_vec *vec, int pos, int v);
2801 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2803 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2806 C<isl_vec_get_element> will return a negative value if anything went wrong.
2807 In that case, the value of C<*v> is undefined.
2811 Matrices can be created, copied and freed using the following functions.
2813 #include <isl/mat.h>
2814 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2815 unsigned n_row, unsigned n_col);
2816 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2817 void isl_mat_free(__isl_take isl_mat *mat);
2819 Note that the elements of a newly created matrix may have arbitrary values.
2820 The elements can be changed and inspected using the following functions.
2822 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2823 int isl_mat_rows(__isl_keep isl_mat *mat);
2824 int isl_mat_cols(__isl_keep isl_mat *mat);
2825 int isl_mat_get_element(__isl_keep isl_mat *mat,
2826 int row, int col, isl_int *v);
2827 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2828 int row, int col, isl_int v);
2829 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2830 int row, int col, int v);
2832 C<isl_mat_get_element> will return a negative value if anything went wrong.
2833 In that case, the value of C<*v> is undefined.
2835 The following function can be used to compute the (right) inverse
2836 of a matrix, i.e., a matrix such that the product of the original
2837 and the inverse (in that order) is a multiple of the identity matrix.
2838 The input matrix is assumed to be of full row-rank.
2840 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2842 The following function can be used to compute the (right) kernel
2843 (or null space) of a matrix, i.e., a matrix such that the product of
2844 the original and the kernel (in that order) is the zero matrix.
2846 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2848 =head2 Piecewise Quasi Affine Expressions
2850 The zero quasi affine expression on a given domain can be created using
2852 __isl_give isl_aff *isl_aff_zero_on_domain(
2853 __isl_take isl_local_space *ls);
2855 Note that the space in which the resulting object lives is a map space
2856 with the given space as domain and a one-dimensional range.
2858 An empty piecewise quasi affine expression (one with no cells)
2859 or a piecewise quasi affine expression with a single cell can
2860 be created using the following functions.
2862 #include <isl/aff.h>
2863 __isl_give isl_pw_aff *isl_pw_aff_empty(
2864 __isl_take isl_space *space);
2865 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2866 __isl_take isl_set *set, __isl_take isl_aff *aff);
2867 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2868 __isl_take isl_aff *aff);
2870 A piecewise quasi affine expression that is equal to 1 on a set
2871 and 0 outside the set can be created using the following function.
2873 #include <isl/aff.h>
2874 __isl_give isl_pw_aff *isl_set_indicator_function(
2875 __isl_take isl_set *set);
2877 Quasi affine expressions can be copied and freed using
2879 #include <isl/aff.h>
2880 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2881 void *isl_aff_free(__isl_take isl_aff *aff);
2883 __isl_give isl_pw_aff *isl_pw_aff_copy(
2884 __isl_keep isl_pw_aff *pwaff);
2885 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2887 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2888 using the following function. The constraint is required to have
2889 a non-zero coefficient for the specified dimension.
2891 #include <isl/constraint.h>
2892 __isl_give isl_aff *isl_constraint_get_bound(
2893 __isl_keep isl_constraint *constraint,
2894 enum isl_dim_type type, int pos);
2896 The entire affine expression of the constraint can also be extracted
2897 using the following function.
2899 #include <isl/constraint.h>
2900 __isl_give isl_aff *isl_constraint_get_aff(
2901 __isl_keep isl_constraint *constraint);
2903 Conversely, an equality constraint equating
2904 the affine expression to zero or an inequality constraint enforcing
2905 the affine expression to be non-negative, can be constructed using
2907 __isl_give isl_constraint *isl_equality_from_aff(
2908 __isl_take isl_aff *aff);
2909 __isl_give isl_constraint *isl_inequality_from_aff(
2910 __isl_take isl_aff *aff);
2912 The expression can be inspected using
2914 #include <isl/aff.h>
2915 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2916 int isl_aff_dim(__isl_keep isl_aff *aff,
2917 enum isl_dim_type type);
2918 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2919 __isl_keep isl_aff *aff);
2920 __isl_give isl_local_space *isl_aff_get_local_space(
2921 __isl_keep isl_aff *aff);
2922 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2923 enum isl_dim_type type, unsigned pos);
2924 const char *isl_pw_aff_get_dim_name(
2925 __isl_keep isl_pw_aff *pa,
2926 enum isl_dim_type type, unsigned pos);
2927 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2928 enum isl_dim_type type, unsigned pos);
2929 __isl_give isl_id *isl_pw_aff_get_dim_id(
2930 __isl_keep isl_pw_aff *pa,
2931 enum isl_dim_type type, unsigned pos);
2932 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2934 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2935 enum isl_dim_type type, int pos, isl_int *v);
2936 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2938 __isl_give isl_aff *isl_aff_get_div(
2939 __isl_keep isl_aff *aff, int pos);
2941 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2942 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2943 int (*fn)(__isl_take isl_set *set,
2944 __isl_take isl_aff *aff,
2945 void *user), void *user);
2947 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2948 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2950 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2951 enum isl_dim_type type, unsigned first, unsigned n);
2952 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2953 enum isl_dim_type type, unsigned first, unsigned n);
2955 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2956 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2957 enum isl_dim_type type);
2958 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2960 It can be modified using
2962 #include <isl/aff.h>
2963 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2964 __isl_take isl_pw_aff *pwaff,
2965 enum isl_dim_type type, __isl_take isl_id *id);
2966 __isl_give isl_aff *isl_aff_set_dim_name(
2967 __isl_take isl_aff *aff, enum isl_dim_type type,
2968 unsigned pos, const char *s);
2969 __isl_give isl_aff *isl_aff_set_dim_id(
2970 __isl_take isl_aff *aff, enum isl_dim_type type,
2971 unsigned pos, __isl_take isl_id *id);
2972 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2973 __isl_take isl_pw_aff *pma,
2974 enum isl_dim_type type, unsigned pos,
2975 __isl_take isl_id *id);
2976 __isl_give isl_aff *isl_aff_set_constant(
2977 __isl_take isl_aff *aff, isl_int v);
2978 __isl_give isl_aff *isl_aff_set_constant_si(
2979 __isl_take isl_aff *aff, int v);
2980 __isl_give isl_aff *isl_aff_set_coefficient(
2981 __isl_take isl_aff *aff,
2982 enum isl_dim_type type, int pos, isl_int v);
2983 __isl_give isl_aff *isl_aff_set_coefficient_si(
2984 __isl_take isl_aff *aff,
2985 enum isl_dim_type type, int pos, int v);
2986 __isl_give isl_aff *isl_aff_set_denominator(
2987 __isl_take isl_aff *aff, isl_int v);
2989 __isl_give isl_aff *isl_aff_add_constant(
2990 __isl_take isl_aff *aff, isl_int v);
2991 __isl_give isl_aff *isl_aff_add_constant_si(
2992 __isl_take isl_aff *aff, int v);
2993 __isl_give isl_aff *isl_aff_add_coefficient(
2994 __isl_take isl_aff *aff,
2995 enum isl_dim_type type, int pos, isl_int v);
2996 __isl_give isl_aff *isl_aff_add_coefficient_si(
2997 __isl_take isl_aff *aff,
2998 enum isl_dim_type type, int pos, int v);
3000 __isl_give isl_aff *isl_aff_insert_dims(
3001 __isl_take isl_aff *aff,
3002 enum isl_dim_type type, unsigned first, unsigned n);
3003 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3004 __isl_take isl_pw_aff *pwaff,
3005 enum isl_dim_type type, unsigned first, unsigned n);
3006 __isl_give isl_aff *isl_aff_add_dims(
3007 __isl_take isl_aff *aff,
3008 enum isl_dim_type type, unsigned n);
3009 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3010 __isl_take isl_pw_aff *pwaff,
3011 enum isl_dim_type type, unsigned n);
3012 __isl_give isl_aff *isl_aff_drop_dims(
3013 __isl_take isl_aff *aff,
3014 enum isl_dim_type type, unsigned first, unsigned n);
3015 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3016 __isl_take isl_pw_aff *pwaff,
3017 enum isl_dim_type type, unsigned first, unsigned n);
3019 Note that the C<set_constant> and C<set_coefficient> functions
3020 set the I<numerator> of the constant or coefficient, while
3021 C<add_constant> and C<add_coefficient> add an integer value to
3022 the possibly rational constant or coefficient.
3024 To check whether an affine expressions is obviously zero
3025 or obviously equal to some other affine expression, use
3027 #include <isl/aff.h>
3028 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3029 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3030 __isl_keep isl_aff *aff2);
3031 int isl_pw_aff_plain_is_equal(
3032 __isl_keep isl_pw_aff *pwaff1,
3033 __isl_keep isl_pw_aff *pwaff2);
3037 #include <isl/aff.h>
3038 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3039 __isl_take isl_aff *aff2);
3040 __isl_give isl_pw_aff *isl_pw_aff_add(
3041 __isl_take isl_pw_aff *pwaff1,
3042 __isl_take isl_pw_aff *pwaff2);
3043 __isl_give isl_pw_aff *isl_pw_aff_min(
3044 __isl_take isl_pw_aff *pwaff1,
3045 __isl_take isl_pw_aff *pwaff2);
3046 __isl_give isl_pw_aff *isl_pw_aff_max(
3047 __isl_take isl_pw_aff *pwaff1,
3048 __isl_take isl_pw_aff *pwaff2);
3049 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3050 __isl_take isl_aff *aff2);
3051 __isl_give isl_pw_aff *isl_pw_aff_sub(
3052 __isl_take isl_pw_aff *pwaff1,
3053 __isl_take isl_pw_aff *pwaff2);
3054 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3055 __isl_give isl_pw_aff *isl_pw_aff_neg(
3056 __isl_take isl_pw_aff *pwaff);
3057 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3058 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3059 __isl_take isl_pw_aff *pwaff);
3060 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3061 __isl_give isl_pw_aff *isl_pw_aff_floor(
3062 __isl_take isl_pw_aff *pwaff);
3063 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3065 __isl_give isl_pw_aff *isl_pw_aff_mod(
3066 __isl_take isl_pw_aff *pwaff, isl_int mod);
3067 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3069 __isl_give isl_pw_aff *isl_pw_aff_scale(
3070 __isl_take isl_pw_aff *pwaff, isl_int f);
3071 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3073 __isl_give isl_aff *isl_aff_scale_down_ui(
3074 __isl_take isl_aff *aff, unsigned f);
3075 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3076 __isl_take isl_pw_aff *pwaff, isl_int f);
3078 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3079 __isl_take isl_pw_aff_list *list);
3080 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3081 __isl_take isl_pw_aff_list *list);
3083 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3084 __isl_take isl_pw_aff *pwqp);
3086 __isl_give isl_aff *isl_aff_align_params(
3087 __isl_take isl_aff *aff,
3088 __isl_take isl_space *model);
3089 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3090 __isl_take isl_pw_aff *pwaff,
3091 __isl_take isl_space *model);
3093 __isl_give isl_aff *isl_aff_project_domain_on_params(
3094 __isl_take isl_aff *aff);
3096 __isl_give isl_aff *isl_aff_gist_params(
3097 __isl_take isl_aff *aff,
3098 __isl_take isl_set *context);
3099 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3100 __isl_take isl_set *context);
3101 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3102 __isl_take isl_pw_aff *pwaff,
3103 __isl_take isl_set *context);
3104 __isl_give isl_pw_aff *isl_pw_aff_gist(
3105 __isl_take isl_pw_aff *pwaff,
3106 __isl_take isl_set *context);
3108 __isl_give isl_set *isl_pw_aff_domain(
3109 __isl_take isl_pw_aff *pwaff);
3110 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3111 __isl_take isl_pw_aff *pa,
3112 __isl_take isl_set *set);
3113 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3114 __isl_take isl_pw_aff *pa,
3115 __isl_take isl_set *set);
3117 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3118 __isl_take isl_aff *aff2);
3119 __isl_give isl_pw_aff *isl_pw_aff_mul(
3120 __isl_take isl_pw_aff *pwaff1,
3121 __isl_take isl_pw_aff *pwaff2);
3123 When multiplying two affine expressions, at least one of the two needs
3126 #include <isl/aff.h>
3127 __isl_give isl_basic_set *isl_aff_le_basic_set(
3128 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3129 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3130 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3131 __isl_give isl_set *isl_pw_aff_eq_set(
3132 __isl_take isl_pw_aff *pwaff1,
3133 __isl_take isl_pw_aff *pwaff2);
3134 __isl_give isl_set *isl_pw_aff_ne_set(
3135 __isl_take isl_pw_aff *pwaff1,
3136 __isl_take isl_pw_aff *pwaff2);
3137 __isl_give isl_set *isl_pw_aff_le_set(
3138 __isl_take isl_pw_aff *pwaff1,
3139 __isl_take isl_pw_aff *pwaff2);
3140 __isl_give isl_set *isl_pw_aff_lt_set(
3141 __isl_take isl_pw_aff *pwaff1,
3142 __isl_take isl_pw_aff *pwaff2);
3143 __isl_give isl_set *isl_pw_aff_ge_set(
3144 __isl_take isl_pw_aff *pwaff1,
3145 __isl_take isl_pw_aff *pwaff2);
3146 __isl_give isl_set *isl_pw_aff_gt_set(
3147 __isl_take isl_pw_aff *pwaff1,
3148 __isl_take isl_pw_aff *pwaff2);
3150 __isl_give isl_set *isl_pw_aff_list_eq_set(
3151 __isl_take isl_pw_aff_list *list1,
3152 __isl_take isl_pw_aff_list *list2);
3153 __isl_give isl_set *isl_pw_aff_list_ne_set(
3154 __isl_take isl_pw_aff_list *list1,
3155 __isl_take isl_pw_aff_list *list2);
3156 __isl_give isl_set *isl_pw_aff_list_le_set(
3157 __isl_take isl_pw_aff_list *list1,
3158 __isl_take isl_pw_aff_list *list2);
3159 __isl_give isl_set *isl_pw_aff_list_lt_set(
3160 __isl_take isl_pw_aff_list *list1,
3161 __isl_take isl_pw_aff_list *list2);
3162 __isl_give isl_set *isl_pw_aff_list_ge_set(
3163 __isl_take isl_pw_aff_list *list1,
3164 __isl_take isl_pw_aff_list *list2);
3165 __isl_give isl_set *isl_pw_aff_list_gt_set(
3166 __isl_take isl_pw_aff_list *list1,
3167 __isl_take isl_pw_aff_list *list2);
3169 The function C<isl_aff_ge_basic_set> returns a basic set
3170 containing those elements in the shared space
3171 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3172 The function C<isl_aff_ge_set> returns a set
3173 containing those elements in the shared domain
3174 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3175 The functions operating on C<isl_pw_aff_list> apply the corresponding
3176 C<isl_pw_aff> function to each pair of elements in the two lists.
3178 #include <isl/aff.h>
3179 __isl_give isl_set *isl_pw_aff_nonneg_set(
3180 __isl_take isl_pw_aff *pwaff);
3181 __isl_give isl_set *isl_pw_aff_zero_set(
3182 __isl_take isl_pw_aff *pwaff);
3183 __isl_give isl_set *isl_pw_aff_non_zero_set(
3184 __isl_take isl_pw_aff *pwaff);
3186 The function C<isl_pw_aff_nonneg_set> returns a set
3187 containing those elements in the domain
3188 of C<pwaff> where C<pwaff> is non-negative.
3190 #include <isl/aff.h>
3191 __isl_give isl_pw_aff *isl_pw_aff_cond(
3192 __isl_take isl_pw_aff *cond,
3193 __isl_take isl_pw_aff *pwaff_true,
3194 __isl_take isl_pw_aff *pwaff_false);
3196 The function C<isl_pw_aff_cond> performs a conditional operator
3197 and returns an expression that is equal to C<pwaff_true>
3198 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3199 where C<cond> is zero.
3201 #include <isl/aff.h>
3202 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3203 __isl_take isl_pw_aff *pwaff1,
3204 __isl_take isl_pw_aff *pwaff2);
3205 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3206 __isl_take isl_pw_aff *pwaff1,
3207 __isl_take isl_pw_aff *pwaff2);
3208 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3209 __isl_take isl_pw_aff *pwaff1,
3210 __isl_take isl_pw_aff *pwaff2);
3212 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3213 expression with a domain that is the union of those of C<pwaff1> and
3214 C<pwaff2> and such that on each cell, the quasi-affine expression is
3215 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3216 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3217 associated expression is the defined one.
3219 An expression can be read from input using
3221 #include <isl/aff.h>
3222 __isl_give isl_aff *isl_aff_read_from_str(
3223 isl_ctx *ctx, const char *str);
3224 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3225 isl_ctx *ctx, const char *str);
3227 An expression can be printed using
3229 #include <isl/aff.h>
3230 __isl_give isl_printer *isl_printer_print_aff(
3231 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3233 __isl_give isl_printer *isl_printer_print_pw_aff(
3234 __isl_take isl_printer *p,
3235 __isl_keep isl_pw_aff *pwaff);
3237 =head2 Piecewise Multiple Quasi Affine Expressions
3239 An C<isl_multi_aff> object represents a sequence of
3240 zero or more affine expressions, all defined on the same domain space.
3242 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3245 #include <isl/aff.h>
3246 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3247 __isl_take isl_space *space,
3248 __isl_take isl_aff_list *list);
3250 An empty piecewise multiple quasi affine expression (one with no cells),
3251 the zero piecewise multiple quasi affine expression (with value zero
3252 for each output dimension),
3253 a piecewise multiple quasi affine expression with a single cell (with
3254 either a universe or a specified domain) or
3255 a zero-dimensional piecewise multiple quasi affine expression
3257 can be created using the following functions.
3259 #include <isl/aff.h>
3260 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3261 __isl_take isl_space *space);
3262 __isl_give isl_multi_aff *isl_multi_aff_zero(
3263 __isl_take isl_space *space);
3264 __isl_give isl_pw_multi_aff *
3265 isl_pw_multi_aff_from_multi_aff(
3266 __isl_take isl_multi_aff *ma);
3267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3268 __isl_take isl_set *set,
3269 __isl_take isl_multi_aff *maff);
3270 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3271 __isl_take isl_set *set);
3273 __isl_give isl_union_pw_multi_aff *
3274 isl_union_pw_multi_aff_empty(
3275 __isl_take isl_space *space);
3276 __isl_give isl_union_pw_multi_aff *
3277 isl_union_pw_multi_aff_add_pw_multi_aff(
3278 __isl_take isl_union_pw_multi_aff *upma,
3279 __isl_take isl_pw_multi_aff *pma);
3280 __isl_give isl_union_pw_multi_aff *
3281 isl_union_pw_multi_aff_from_domain(
3282 __isl_take isl_union_set *uset);
3284 A piecewise multiple quasi affine expression can also be initialized
3285 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3286 and the C<isl_map> is single-valued.
3288 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3289 __isl_take isl_set *set);
3290 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3291 __isl_take isl_map *map);
3293 Multiple quasi affine expressions can be copied and freed using
3295 #include <isl/aff.h>
3296 __isl_give isl_multi_aff *isl_multi_aff_copy(
3297 __isl_keep isl_multi_aff *maff);
3298 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3301 __isl_keep isl_pw_multi_aff *pma);
3302 void *isl_pw_multi_aff_free(
3303 __isl_take isl_pw_multi_aff *pma);
3305 __isl_give isl_union_pw_multi_aff *
3306 isl_union_pw_multi_aff_copy(
3307 __isl_keep isl_union_pw_multi_aff *upma);
3308 void *isl_union_pw_multi_aff_free(
3309 __isl_take isl_union_pw_multi_aff *upma);
3311 The expression can be inspected using
3313 #include <isl/aff.h>
3314 isl_ctx *isl_multi_aff_get_ctx(
3315 __isl_keep isl_multi_aff *maff);
3316 isl_ctx *isl_pw_multi_aff_get_ctx(
3317 __isl_keep isl_pw_multi_aff *pma);
3318 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3319 __isl_keep isl_union_pw_multi_aff *upma);
3320 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3321 enum isl_dim_type type);
3322 unsigned isl_pw_multi_aff_dim(
3323 __isl_keep isl_pw_multi_aff *pma,
3324 enum isl_dim_type type);
3325 __isl_give isl_aff *isl_multi_aff_get_aff(
3326 __isl_keep isl_multi_aff *multi, int pos);
3327 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3328 __isl_keep isl_pw_multi_aff *pma, int pos);
3329 const char *isl_pw_multi_aff_get_dim_name(
3330 __isl_keep isl_pw_multi_aff *pma,
3331 enum isl_dim_type type, unsigned pos);
3332 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3333 __isl_keep isl_pw_multi_aff *pma,
3334 enum isl_dim_type type, unsigned pos);
3335 const char *isl_multi_aff_get_tuple_name(
3336 __isl_keep isl_multi_aff *multi,
3337 enum isl_dim_type type);
3338 const char *isl_pw_multi_aff_get_tuple_name(
3339 __isl_keep isl_pw_multi_aff *pma,
3340 enum isl_dim_type type);
3341 int isl_pw_multi_aff_has_tuple_id(
3342 __isl_keep isl_pw_multi_aff *pma,
3343 enum isl_dim_type type);
3344 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3345 __isl_keep isl_pw_multi_aff *pma,
3346 enum isl_dim_type type);
3348 int isl_pw_multi_aff_foreach_piece(
3349 __isl_keep isl_pw_multi_aff *pma,
3350 int (*fn)(__isl_take isl_set *set,
3351 __isl_take isl_multi_aff *maff,
3352 void *user), void *user);
3354 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3355 __isl_keep isl_union_pw_multi_aff *upma,
3356 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3357 void *user), void *user);
3359 It can be modified using
3361 #include <isl/aff.h>
3362 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3363 __isl_take isl_multi_aff *multi, int pos,
3364 __isl_take isl_aff *aff);
3365 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3366 __isl_take isl_multi_aff *maff,
3367 enum isl_dim_type type, unsigned pos, const char *s);
3368 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3369 __isl_take isl_multi_aff *maff,
3370 enum isl_dim_type type, __isl_take isl_id *id);
3371 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3372 __isl_take isl_pw_multi_aff *pma,
3373 enum isl_dim_type type, __isl_take isl_id *id);
3375 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3376 __isl_take isl_multi_aff *maff,
3377 enum isl_dim_type type, unsigned first, unsigned n);
3379 To check whether two multiple affine expressions are
3380 obviously equal to each other, use
3382 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3383 __isl_keep isl_multi_aff *maff2);
3384 int isl_pw_multi_aff_plain_is_equal(
3385 __isl_keep isl_pw_multi_aff *pma1,
3386 __isl_keep isl_pw_multi_aff *pma2);
3390 #include <isl/aff.h>
3391 __isl_give isl_multi_aff *isl_multi_aff_add(
3392 __isl_take isl_multi_aff *maff1,
3393 __isl_take isl_multi_aff *maff2);
3394 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3395 __isl_take isl_pw_multi_aff *pma1,
3396 __isl_take isl_pw_multi_aff *pma2);
3397 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3398 __isl_take isl_union_pw_multi_aff *upma1,
3399 __isl_take isl_union_pw_multi_aff *upma2);
3400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3401 __isl_take isl_pw_multi_aff *pma1,
3402 __isl_take isl_pw_multi_aff *pma2);
3403 __isl_give isl_multi_aff *isl_multi_aff_scale(
3404 __isl_take isl_multi_aff *maff,
3406 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3407 __isl_take isl_pw_multi_aff *pma,
3408 __isl_take isl_set *set);
3409 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3410 __isl_take isl_pw_multi_aff *pma,
3411 __isl_take isl_set *set);
3412 __isl_give isl_multi_aff *isl_multi_aff_lift(
3413 __isl_take isl_multi_aff *maff,
3414 __isl_give isl_local_space **ls);
3415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3416 __isl_take isl_pw_multi_aff *pma);
3417 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3418 __isl_take isl_multi_aff *maff,
3419 __isl_take isl_set *context);
3420 __isl_give isl_multi_aff *isl_multi_aff_gist(
3421 __isl_take isl_multi_aff *maff,
3422 __isl_take isl_set *context);
3423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3424 __isl_take isl_pw_multi_aff *pma,
3425 __isl_take isl_set *set);
3426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3427 __isl_take isl_pw_multi_aff *pma,
3428 __isl_take isl_set *set);
3429 __isl_give isl_set *isl_pw_multi_aff_domain(
3430 __isl_take isl_pw_multi_aff *pma);
3431 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3432 __isl_take isl_union_pw_multi_aff *upma);
3433 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3434 __isl_take isl_multi_aff *ma1,
3435 __isl_take isl_multi_aff *ma2);
3436 __isl_give isl_pw_multi_aff *
3437 isl_pw_multi_aff_flat_range_product(
3438 __isl_take isl_pw_multi_aff *pma1,
3439 __isl_take isl_pw_multi_aff *pma2);
3440 __isl_give isl_union_pw_multi_aff *
3441 isl_union_pw_multi_aff_flat_range_product(
3442 __isl_take isl_union_pw_multi_aff *upma1,
3443 __isl_take isl_union_pw_multi_aff *upma2);
3445 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3446 then it is assigned the local space that lies at the basis of
3447 the lifting applied.
3449 An expression can be read from input using
3451 #include <isl/aff.h>
3452 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3453 isl_ctx *ctx, const char *str);
3454 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3455 isl_ctx *ctx, const char *str);
3457 An expression can be printed using
3459 #include <isl/aff.h>
3460 __isl_give isl_printer *isl_printer_print_multi_aff(
3461 __isl_take isl_printer *p,
3462 __isl_keep isl_multi_aff *maff);
3463 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3464 __isl_take isl_printer *p,
3465 __isl_keep isl_pw_multi_aff *pma);
3466 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3467 __isl_take isl_printer *p,
3468 __isl_keep isl_union_pw_multi_aff *upma);
3472 Points are elements of a set. They can be used to construct
3473 simple sets (boxes) or they can be used to represent the
3474 individual elements of a set.
3475 The zero point (the origin) can be created using
3477 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3479 The coordinates of a point can be inspected, set and changed
3482 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3483 enum isl_dim_type type, int pos, isl_int *v);
3484 __isl_give isl_point *isl_point_set_coordinate(
3485 __isl_take isl_point *pnt,
3486 enum isl_dim_type type, int pos, isl_int v);
3488 __isl_give isl_point *isl_point_add_ui(
3489 __isl_take isl_point *pnt,
3490 enum isl_dim_type type, int pos, unsigned val);
3491 __isl_give isl_point *isl_point_sub_ui(
3492 __isl_take isl_point *pnt,
3493 enum isl_dim_type type, int pos, unsigned val);
3495 Other properties can be obtained using
3497 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3499 Points can be copied or freed using
3501 __isl_give isl_point *isl_point_copy(
3502 __isl_keep isl_point *pnt);
3503 void isl_point_free(__isl_take isl_point *pnt);
3505 A singleton set can be created from a point using
3507 __isl_give isl_basic_set *isl_basic_set_from_point(
3508 __isl_take isl_point *pnt);
3509 __isl_give isl_set *isl_set_from_point(
3510 __isl_take isl_point *pnt);
3512 and a box can be created from two opposite extremal points using
3514 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3515 __isl_take isl_point *pnt1,
3516 __isl_take isl_point *pnt2);
3517 __isl_give isl_set *isl_set_box_from_points(
3518 __isl_take isl_point *pnt1,
3519 __isl_take isl_point *pnt2);
3521 All elements of a B<bounded> (union) set can be enumerated using
3522 the following functions.
3524 int isl_set_foreach_point(__isl_keep isl_set *set,
3525 int (*fn)(__isl_take isl_point *pnt, void *user),
3527 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3528 int (*fn)(__isl_take isl_point *pnt, void *user),
3531 The function C<fn> is called for each integer point in
3532 C<set> with as second argument the last argument of
3533 the C<isl_set_foreach_point> call. The function C<fn>
3534 should return C<0> on success and C<-1> on failure.
3535 In the latter case, C<isl_set_foreach_point> will stop
3536 enumerating and return C<-1> as well.
3537 If the enumeration is performed successfully and to completion,
3538 then C<isl_set_foreach_point> returns C<0>.
3540 To obtain a single point of a (basic) set, use
3542 __isl_give isl_point *isl_basic_set_sample_point(
3543 __isl_take isl_basic_set *bset);
3544 __isl_give isl_point *isl_set_sample_point(
3545 __isl_take isl_set *set);
3547 If C<set> does not contain any (integer) points, then the
3548 resulting point will be ``void'', a property that can be
3551 int isl_point_is_void(__isl_keep isl_point *pnt);
3553 =head2 Piecewise Quasipolynomials
3555 A piecewise quasipolynomial is a particular kind of function that maps
3556 a parametric point to a rational value.
3557 More specifically, a quasipolynomial is a polynomial expression in greatest
3558 integer parts of affine expressions of parameters and variables.
3559 A piecewise quasipolynomial is a subdivision of a given parametric
3560 domain into disjoint cells with a quasipolynomial associated to
3561 each cell. The value of the piecewise quasipolynomial at a given
3562 point is the value of the quasipolynomial associated to the cell
3563 that contains the point. Outside of the union of cells,
3564 the value is assumed to be zero.
3565 For example, the piecewise quasipolynomial
3567 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3569 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3570 A given piecewise quasipolynomial has a fixed domain dimension.
3571 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3572 defined over different domains.
3573 Piecewise quasipolynomials are mainly used by the C<barvinok>
3574 library for representing the number of elements in a parametric set or map.
3575 For example, the piecewise quasipolynomial above represents
3576 the number of points in the map
3578 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3580 =head3 Input and Output
3582 Piecewise quasipolynomials can be read from input using
3584 __isl_give isl_union_pw_qpolynomial *
3585 isl_union_pw_qpolynomial_read_from_str(
3586 isl_ctx *ctx, const char *str);
3588 Quasipolynomials and piecewise quasipolynomials can be printed
3589 using the following functions.
3591 __isl_give isl_printer *isl_printer_print_qpolynomial(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_qpolynomial *qp);
3595 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3596 __isl_take isl_printer *p,
3597 __isl_keep isl_pw_qpolynomial *pwqp);
3599 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3600 __isl_take isl_printer *p,
3601 __isl_keep isl_union_pw_qpolynomial *upwqp);
3603 The output format of the printer
3604 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3605 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3607 In case of printing in C<ISL_FORMAT_C>, the user may want
3608 to set the names of all dimensions
3610 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3611 __isl_take isl_qpolynomial *qp,
3612 enum isl_dim_type type, unsigned pos,
3614 __isl_give isl_pw_qpolynomial *
3615 isl_pw_qpolynomial_set_dim_name(
3616 __isl_take isl_pw_qpolynomial *pwqp,
3617 enum isl_dim_type type, unsigned pos,
3620 =head3 Creating New (Piecewise) Quasipolynomials
3622 Some simple quasipolynomials can be created using the following functions.
3623 More complicated quasipolynomials can be created by applying
3624 operations such as addition and multiplication
3625 on the resulting quasipolynomials
3627 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3628 __isl_take isl_space *domain);
3629 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3630 __isl_take isl_space *domain);
3631 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3632 __isl_take isl_space *domain);
3633 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3634 __isl_take isl_space *domain);
3635 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3636 __isl_take isl_space *domain);
3637 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3638 __isl_take isl_space *domain,
3639 const isl_int n, const isl_int d);
3640 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3641 __isl_take isl_space *domain,
3642 enum isl_dim_type type, unsigned pos);
3643 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3644 __isl_take isl_aff *aff);
3646 Note that the space in which a quasipolynomial lives is a map space
3647 with a one-dimensional range. The C<domain> argument in some of
3648 the functions above corresponds to the domain of this map space.
3650 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3651 with a single cell can be created using the following functions.
3652 Multiple of these single cell piecewise quasipolynomials can
3653 be combined to create more complicated piecewise quasipolynomials.
3655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3656 __isl_take isl_space *space);
3657 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3658 __isl_take isl_set *set,
3659 __isl_take isl_qpolynomial *qp);
3660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3661 __isl_take isl_qpolynomial *qp);
3662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3663 __isl_take isl_pw_aff *pwaff);
3665 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3666 __isl_take isl_space *space);
3667 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3668 __isl_take isl_pw_qpolynomial *pwqp);
3669 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3670 __isl_take isl_union_pw_qpolynomial *upwqp,
3671 __isl_take isl_pw_qpolynomial *pwqp);
3673 Quasipolynomials can be copied and freed again using the following
3676 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3677 __isl_keep isl_qpolynomial *qp);
3678 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3680 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3681 __isl_keep isl_pw_qpolynomial *pwqp);
3682 void *isl_pw_qpolynomial_free(
3683 __isl_take isl_pw_qpolynomial *pwqp);
3685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3686 __isl_keep isl_union_pw_qpolynomial *upwqp);
3687 void *isl_union_pw_qpolynomial_free(
3688 __isl_take isl_union_pw_qpolynomial *upwqp);
3690 =head3 Inspecting (Piecewise) Quasipolynomials
3692 To iterate over all piecewise quasipolynomials in a union
3693 piecewise quasipolynomial, use the following function
3695 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3696 __isl_keep isl_union_pw_qpolynomial *upwqp,
3697 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3700 To extract the piecewise quasipolynomial in a given space from a union, use
3702 __isl_give isl_pw_qpolynomial *
3703 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3704 __isl_keep isl_union_pw_qpolynomial *upwqp,
3705 __isl_take isl_space *space);
3707 To iterate over the cells in a piecewise quasipolynomial,
3708 use either of the following two functions
3710 int isl_pw_qpolynomial_foreach_piece(
3711 __isl_keep isl_pw_qpolynomial *pwqp,
3712 int (*fn)(__isl_take isl_set *set,
3713 __isl_take isl_qpolynomial *qp,
3714 void *user), void *user);
3715 int isl_pw_qpolynomial_foreach_lifted_piece(
3716 __isl_keep isl_pw_qpolynomial *pwqp,
3717 int (*fn)(__isl_take isl_set *set,
3718 __isl_take isl_qpolynomial *qp,
3719 void *user), void *user);
3721 As usual, the function C<fn> should return C<0> on success
3722 and C<-1> on failure. The difference between
3723 C<isl_pw_qpolynomial_foreach_piece> and
3724 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3725 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3726 compute unique representations for all existentially quantified
3727 variables and then turn these existentially quantified variables
3728 into extra set variables, adapting the associated quasipolynomial
3729 accordingly. This means that the C<set> passed to C<fn>
3730 will not have any existentially quantified variables, but that
3731 the dimensions of the sets may be different for different
3732 invocations of C<fn>.
3734 To iterate over all terms in a quasipolynomial,
3737 int isl_qpolynomial_foreach_term(
3738 __isl_keep isl_qpolynomial *qp,
3739 int (*fn)(__isl_take isl_term *term,
3740 void *user), void *user);
3742 The terms themselves can be inspected and freed using
3745 unsigned isl_term_dim(__isl_keep isl_term *term,
3746 enum isl_dim_type type);
3747 void isl_term_get_num(__isl_keep isl_term *term,
3749 void isl_term_get_den(__isl_keep isl_term *term,
3751 int isl_term_get_exp(__isl_keep isl_term *term,
3752 enum isl_dim_type type, unsigned pos);
3753 __isl_give isl_aff *isl_term_get_div(
3754 __isl_keep isl_term *term, unsigned pos);
3755 void isl_term_free(__isl_take isl_term *term);
3757 Each term is a product of parameters, set variables and
3758 integer divisions. The function C<isl_term_get_exp>
3759 returns the exponent of a given dimensions in the given term.
3760 The C<isl_int>s in the arguments of C<isl_term_get_num>
3761 and C<isl_term_get_den> need to have been initialized
3762 using C<isl_int_init> before calling these functions.
3764 =head3 Properties of (Piecewise) Quasipolynomials
3766 To check whether a quasipolynomial is actually a constant,
3767 use the following function.
3769 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3770 isl_int *n, isl_int *d);
3772 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3773 then the numerator and denominator of the constant
3774 are returned in C<*n> and C<*d>, respectively.
3776 To check whether two union piecewise quasipolynomials are
3777 obviously equal, use
3779 int isl_union_pw_qpolynomial_plain_is_equal(
3780 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3781 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3783 =head3 Operations on (Piecewise) Quasipolynomials
3785 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3786 __isl_take isl_qpolynomial *qp, isl_int v);
3787 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3788 __isl_take isl_qpolynomial *qp);
3789 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3790 __isl_take isl_qpolynomial *qp1,
3791 __isl_take isl_qpolynomial *qp2);
3792 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3793 __isl_take isl_qpolynomial *qp1,
3794 __isl_take isl_qpolynomial *qp2);
3795 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3796 __isl_take isl_qpolynomial *qp1,
3797 __isl_take isl_qpolynomial *qp2);
3798 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3799 __isl_take isl_qpolynomial *qp, unsigned exponent);
3801 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3802 __isl_take isl_pw_qpolynomial *pwqp1,
3803 __isl_take isl_pw_qpolynomial *pwqp2);
3804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3805 __isl_take isl_pw_qpolynomial *pwqp1,
3806 __isl_take isl_pw_qpolynomial *pwqp2);
3807 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3808 __isl_take isl_pw_qpolynomial *pwqp1,
3809 __isl_take isl_pw_qpolynomial *pwqp2);
3810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3811 __isl_take isl_pw_qpolynomial *pwqp);
3812 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3813 __isl_take isl_pw_qpolynomial *pwqp1,
3814 __isl_take isl_pw_qpolynomial *pwqp2);
3815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3816 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3819 __isl_take isl_union_pw_qpolynomial *upwqp1,
3820 __isl_take isl_union_pw_qpolynomial *upwqp2);
3821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3822 __isl_take isl_union_pw_qpolynomial *upwqp1,
3823 __isl_take isl_union_pw_qpolynomial *upwqp2);
3824 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3825 __isl_take isl_union_pw_qpolynomial *upwqp1,
3826 __isl_take isl_union_pw_qpolynomial *upwqp2);
3828 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3829 __isl_take isl_pw_qpolynomial *pwqp,
3830 __isl_take isl_point *pnt);
3832 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3833 __isl_take isl_union_pw_qpolynomial *upwqp,
3834 __isl_take isl_point *pnt);
3836 __isl_give isl_set *isl_pw_qpolynomial_domain(
3837 __isl_take isl_pw_qpolynomial *pwqp);
3838 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3839 __isl_take isl_pw_qpolynomial *pwpq,
3840 __isl_take isl_set *set);
3841 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3842 __isl_take isl_pw_qpolynomial *pwpq,
3843 __isl_take isl_set *set);
3845 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3846 __isl_take isl_union_pw_qpolynomial *upwqp);
3847 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3848 __isl_take isl_union_pw_qpolynomial *upwpq,
3849 __isl_take isl_union_set *uset);
3850 __isl_give isl_union_pw_qpolynomial *
3851 isl_union_pw_qpolynomial_intersect_params(
3852 __isl_take isl_union_pw_qpolynomial *upwpq,
3853 __isl_take isl_set *set);
3855 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3856 __isl_take isl_qpolynomial *qp,
3857 __isl_take isl_space *model);
3859 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3860 __isl_take isl_qpolynomial *qp);
3861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3862 __isl_take isl_pw_qpolynomial *pwqp);
3864 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3865 __isl_take isl_union_pw_qpolynomial *upwqp);
3867 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3868 __isl_take isl_qpolynomial *qp,
3869 __isl_take isl_set *context);
3870 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3871 __isl_take isl_qpolynomial *qp,
3872 __isl_take isl_set *context);
3874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3875 __isl_take isl_pw_qpolynomial *pwqp,
3876 __isl_take isl_set *context);
3877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3878 __isl_take isl_pw_qpolynomial *pwqp,
3879 __isl_take isl_set *context);
3881 __isl_give isl_union_pw_qpolynomial *
3882 isl_union_pw_qpolynomial_gist_params(
3883 __isl_take isl_union_pw_qpolynomial *upwqp,
3884 __isl_take isl_set *context);
3885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3886 __isl_take isl_union_pw_qpolynomial *upwqp,
3887 __isl_take isl_union_set *context);
3889 The gist operation applies the gist operation to each of
3890 the cells in the domain of the input piecewise quasipolynomial.
3891 The context is also exploited
3892 to simplify the quasipolynomials associated to each cell.
3894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3895 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3896 __isl_give isl_union_pw_qpolynomial *
3897 isl_union_pw_qpolynomial_to_polynomial(
3898 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3900 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3901 the polynomial will be an overapproximation. If C<sign> is negative,
3902 it will be an underapproximation. If C<sign> is zero, the approximation
3903 will lie somewhere in between.
3905 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3907 A piecewise quasipolynomial reduction is a piecewise
3908 reduction (or fold) of quasipolynomials.
3909 In particular, the reduction can be maximum or a minimum.
3910 The objects are mainly used to represent the result of
3911 an upper or lower bound on a quasipolynomial over its domain,
3912 i.e., as the result of the following function.
3914 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3915 __isl_take isl_pw_qpolynomial *pwqp,
3916 enum isl_fold type, int *tight);
3918 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3919 __isl_take isl_union_pw_qpolynomial *upwqp,
3920 enum isl_fold type, int *tight);
3922 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3923 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3924 is the returned bound is known be tight, i.e., for each value
3925 of the parameters there is at least
3926 one element in the domain that reaches the bound.
3927 If the domain of C<pwqp> is not wrapping, then the bound is computed
3928 over all elements in that domain and the result has a purely parametric
3929 domain. If the domain of C<pwqp> is wrapping, then the bound is
3930 computed over the range of the wrapped relation. The domain of the
3931 wrapped relation becomes the domain of the result.
3933 A (piecewise) quasipolynomial reduction can be copied or freed using the
3934 following functions.
3936 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3937 __isl_keep isl_qpolynomial_fold *fold);
3938 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3939 __isl_keep isl_pw_qpolynomial_fold *pwf);
3940 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3941 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3942 void isl_qpolynomial_fold_free(
3943 __isl_take isl_qpolynomial_fold *fold);
3944 void *isl_pw_qpolynomial_fold_free(
3945 __isl_take isl_pw_qpolynomial_fold *pwf);
3946 void *isl_union_pw_qpolynomial_fold_free(
3947 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3949 =head3 Printing Piecewise Quasipolynomial Reductions
3951 Piecewise quasipolynomial reductions can be printed
3952 using the following function.
3954 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3955 __isl_take isl_printer *p,
3956 __isl_keep isl_pw_qpolynomial_fold *pwf);
3957 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3958 __isl_take isl_printer *p,
3959 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3961 For C<isl_printer_print_pw_qpolynomial_fold>,
3962 output format of the printer
3963 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3964 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3965 output format of the printer
3966 needs to be set to C<ISL_FORMAT_ISL>.
3967 In case of printing in C<ISL_FORMAT_C>, the user may want
3968 to set the names of all dimensions
3970 __isl_give isl_pw_qpolynomial_fold *
3971 isl_pw_qpolynomial_fold_set_dim_name(
3972 __isl_take isl_pw_qpolynomial_fold *pwf,
3973 enum isl_dim_type type, unsigned pos,
3976 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3978 To iterate over all piecewise quasipolynomial reductions in a union
3979 piecewise quasipolynomial reduction, use the following function
3981 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3982 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3983 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3984 void *user), void *user);
3986 To iterate over the cells in a piecewise quasipolynomial reduction,
3987 use either of the following two functions
3989 int isl_pw_qpolynomial_fold_foreach_piece(
3990 __isl_keep isl_pw_qpolynomial_fold *pwf,
3991 int (*fn)(__isl_take isl_set *set,
3992 __isl_take isl_qpolynomial_fold *fold,
3993 void *user), void *user);
3994 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3995 __isl_keep isl_pw_qpolynomial_fold *pwf,
3996 int (*fn)(__isl_take isl_set *set,
3997 __isl_take isl_qpolynomial_fold *fold,
3998 void *user), void *user);
4000 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4001 of the difference between these two functions.
4003 To iterate over all quasipolynomials in a reduction, use
4005 int isl_qpolynomial_fold_foreach_qpolynomial(
4006 __isl_keep isl_qpolynomial_fold *fold,
4007 int (*fn)(__isl_take isl_qpolynomial *qp,
4008 void *user), void *user);
4010 =head3 Properties of Piecewise Quasipolynomial Reductions
4012 To check whether two union piecewise quasipolynomial reductions are
4013 obviously equal, use
4015 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4016 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4017 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4019 =head3 Operations on Piecewise Quasipolynomial Reductions
4021 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4022 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4024 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4025 __isl_take isl_pw_qpolynomial_fold *pwf1,
4026 __isl_take isl_pw_qpolynomial_fold *pwf2);
4028 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4029 __isl_take isl_pw_qpolynomial_fold *pwf1,
4030 __isl_take isl_pw_qpolynomial_fold *pwf2);
4032 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4033 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4034 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4036 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4037 __isl_take isl_pw_qpolynomial_fold *pwf,
4038 __isl_take isl_point *pnt);
4040 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4041 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4042 __isl_take isl_point *pnt);
4044 __isl_give isl_pw_qpolynomial_fold *
4045 sl_pw_qpolynomial_fold_intersect_params(
4046 __isl_take isl_pw_qpolynomial_fold *pwf,
4047 __isl_take isl_set *set);
4049 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4050 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4051 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4052 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4053 __isl_take isl_union_set *uset);
4054 __isl_give isl_union_pw_qpolynomial_fold *
4055 isl_union_pw_qpolynomial_fold_intersect_params(
4056 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4057 __isl_take isl_set *set);
4059 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4060 __isl_take isl_pw_qpolynomial_fold *pwf);
4062 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4063 __isl_take isl_pw_qpolynomial_fold *pwf);
4065 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4066 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4068 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4069 __isl_take isl_qpolynomial_fold *fold,
4070 __isl_take isl_set *context);
4071 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4072 __isl_take isl_qpolynomial_fold *fold,
4073 __isl_take isl_set *context);
4075 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4076 __isl_take isl_pw_qpolynomial_fold *pwf,
4077 __isl_take isl_set *context);
4078 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4079 __isl_take isl_pw_qpolynomial_fold *pwf,
4080 __isl_take isl_set *context);
4082 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4083 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4084 __isl_take isl_union_set *context);
4085 __isl_give isl_union_pw_qpolynomial_fold *
4086 isl_union_pw_qpolynomial_fold_gist_params(
4087 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4088 __isl_take isl_set *context);
4090 The gist operation applies the gist operation to each of
4091 the cells in the domain of the input piecewise quasipolynomial reduction.
4092 In future, the operation will also exploit the context
4093 to simplify the quasipolynomial reductions associated to each cell.
4095 __isl_give isl_pw_qpolynomial_fold *
4096 isl_set_apply_pw_qpolynomial_fold(
4097 __isl_take isl_set *set,
4098 __isl_take isl_pw_qpolynomial_fold *pwf,
4100 __isl_give isl_pw_qpolynomial_fold *
4101 isl_map_apply_pw_qpolynomial_fold(
4102 __isl_take isl_map *map,
4103 __isl_take isl_pw_qpolynomial_fold *pwf,
4105 __isl_give isl_union_pw_qpolynomial_fold *
4106 isl_union_set_apply_union_pw_qpolynomial_fold(
4107 __isl_take isl_union_set *uset,
4108 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4110 __isl_give isl_union_pw_qpolynomial_fold *
4111 isl_union_map_apply_union_pw_qpolynomial_fold(
4112 __isl_take isl_union_map *umap,
4113 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4116 The functions taking a map
4117 compose the given map with the given piecewise quasipolynomial reduction.
4118 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4119 over all elements in the intersection of the range of the map
4120 and the domain of the piecewise quasipolynomial reduction
4121 as a function of an element in the domain of the map.
4122 The functions taking a set compute a bound over all elements in the
4123 intersection of the set and the domain of the
4124 piecewise quasipolynomial reduction.
4126 =head2 Dependence Analysis
4128 C<isl> contains specialized functionality for performing
4129 array dataflow analysis. That is, given a I<sink> access relation
4130 and a collection of possible I<source> access relations,
4131 C<isl> can compute relations that describe
4132 for each iteration of the sink access, which iteration
4133 of which of the source access relations was the last
4134 to access the same data element before the given iteration
4136 The resulting dependence relations map source iterations
4137 to the corresponding sink iterations.
4138 To compute standard flow dependences, the sink should be
4139 a read, while the sources should be writes.
4140 If any of the source accesses are marked as being I<may>
4141 accesses, then there will be a dependence from the last
4142 I<must> access B<and> from any I<may> access that follows
4143 this last I<must> access.
4144 In particular, if I<all> sources are I<may> accesses,
4145 then memory based dependence analysis is performed.
4146 If, on the other hand, all sources are I<must> accesses,
4147 then value based dependence analysis is performed.
4149 #include <isl/flow.h>
4151 typedef int (*isl_access_level_before)(void *first, void *second);
4153 __isl_give isl_access_info *isl_access_info_alloc(
4154 __isl_take isl_map *sink,
4155 void *sink_user, isl_access_level_before fn,
4157 __isl_give isl_access_info *isl_access_info_add_source(
4158 __isl_take isl_access_info *acc,
4159 __isl_take isl_map *source, int must,
4161 void isl_access_info_free(__isl_take isl_access_info *acc);
4163 __isl_give isl_flow *isl_access_info_compute_flow(
4164 __isl_take isl_access_info *acc);
4166 int isl_flow_foreach(__isl_keep isl_flow *deps,
4167 int (*fn)(__isl_take isl_map *dep, int must,
4168 void *dep_user, void *user),
4170 __isl_give isl_map *isl_flow_get_no_source(
4171 __isl_keep isl_flow *deps, int must);
4172 void isl_flow_free(__isl_take isl_flow *deps);
4174 The function C<isl_access_info_compute_flow> performs the actual
4175 dependence analysis. The other functions are used to construct
4176 the input for this function or to read off the output.
4178 The input is collected in an C<isl_access_info>, which can
4179 be created through a call to C<isl_access_info_alloc>.
4180 The arguments to this functions are the sink access relation
4181 C<sink>, a token C<sink_user> used to identify the sink
4182 access to the user, a callback function for specifying the
4183 relative order of source and sink accesses, and the number
4184 of source access relations that will be added.
4185 The callback function has type C<int (*)(void *first, void *second)>.
4186 The function is called with two user supplied tokens identifying
4187 either a source or the sink and it should return the shared nesting
4188 level and the relative order of the two accesses.
4189 In particular, let I<n> be the number of loops shared by
4190 the two accesses. If C<first> precedes C<second> textually,
4191 then the function should return I<2 * n + 1>; otherwise,
4192 it should return I<2 * n>.
4193 The sources can be added to the C<isl_access_info> by performing
4194 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4195 C<must> indicates whether the source is a I<must> access
4196 or a I<may> access. Note that a multi-valued access relation
4197 should only be marked I<must> if every iteration in the domain
4198 of the relation accesses I<all> elements in its image.
4199 The C<source_user> token is again used to identify
4200 the source access. The range of the source access relation
4201 C<source> should have the same dimension as the range
4202 of the sink access relation.
4203 The C<isl_access_info_free> function should usually not be
4204 called explicitly, because it is called implicitly by
4205 C<isl_access_info_compute_flow>.
4207 The result of the dependence analysis is collected in an
4208 C<isl_flow>. There may be elements of
4209 the sink access for which no preceding source access could be
4210 found or for which all preceding sources are I<may> accesses.
4211 The relations containing these elements can be obtained through
4212 calls to C<isl_flow_get_no_source>, the first with C<must> set
4213 and the second with C<must> unset.
4214 In the case of standard flow dependence analysis,
4215 with the sink a read and the sources I<must> writes,
4216 the first relation corresponds to the reads from uninitialized
4217 array elements and the second relation is empty.
4218 The actual flow dependences can be extracted using
4219 C<isl_flow_foreach>. This function will call the user-specified
4220 callback function C<fn> for each B<non-empty> dependence between
4221 a source and the sink. The callback function is called
4222 with four arguments, the actual flow dependence relation
4223 mapping source iterations to sink iterations, a boolean that
4224 indicates whether it is a I<must> or I<may> dependence, a token
4225 identifying the source and an additional C<void *> with value
4226 equal to the third argument of the C<isl_flow_foreach> call.
4227 A dependence is marked I<must> if it originates from a I<must>
4228 source and if it is not followed by any I<may> sources.
4230 After finishing with an C<isl_flow>, the user should call
4231 C<isl_flow_free> to free all associated memory.
4233 A higher-level interface to dependence analysis is provided
4234 by the following function.
4236 #include <isl/flow.h>
4238 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4239 __isl_take isl_union_map *must_source,
4240 __isl_take isl_union_map *may_source,
4241 __isl_take isl_union_map *schedule,
4242 __isl_give isl_union_map **must_dep,
4243 __isl_give isl_union_map **may_dep,
4244 __isl_give isl_union_map **must_no_source,
4245 __isl_give isl_union_map **may_no_source);
4247 The arrays are identified by the tuple names of the ranges
4248 of the accesses. The iteration domains by the tuple names
4249 of the domains of the accesses and of the schedule.
4250 The relative order of the iteration domains is given by the
4251 schedule. The relations returned through C<must_no_source>
4252 and C<may_no_source> are subsets of C<sink>.
4253 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4254 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4255 any of the other arguments is treated as an error.
4257 =head3 Interaction with Dependence Analysis
4259 During the dependence analysis, we frequently need to perform
4260 the following operation. Given a relation between sink iterations
4261 and potential soure iterations from a particular source domain,
4262 what is the last potential source iteration corresponding to each
4263 sink iteration. It can sometimes be convenient to adjust
4264 the set of potential source iterations before or after each such operation.
4265 The prototypical example is fuzzy array dataflow analysis,
4266 where we need to analyze if, based on data-dependent constraints,
4267 the sink iteration can ever be executed without one or more of
4268 the corresponding potential source iterations being executed.
4269 If so, we can introduce extra parameters and select an unknown
4270 but fixed source iteration from the potential source iterations.
4271 To be able to perform such manipulations, C<isl> provides the following
4274 #include <isl/flow.h>
4276 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4277 __isl_keep isl_map *source_map,
4278 __isl_keep isl_set *sink, void *source_user,
4280 __isl_give isl_access_info *isl_access_info_set_restrict(
4281 __isl_take isl_access_info *acc,
4282 isl_access_restrict fn, void *user);
4284 The function C<isl_access_info_set_restrict> should be called
4285 before calling C<isl_access_info_compute_flow> and registers a callback function
4286 that will be called any time C<isl> is about to compute the last
4287 potential source. The first argument is the (reverse) proto-dependence,
4288 mapping sink iterations to potential source iterations.
4289 The second argument represents the sink iterations for which
4290 we want to compute the last source iteration.
4291 The third argument is the token corresponding to the source
4292 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4293 The callback is expected to return a restriction on either the input or
4294 the output of the operation computing the last potential source.
4295 If the input needs to be restricted then restrictions are needed
4296 for both the source and the sink iterations. The sink iterations
4297 and the potential source iterations will be intersected with these sets.
4298 If the output needs to be restricted then only a restriction on the source
4299 iterations is required.
4300 If any error occurs, the callback should return C<NULL>.
4301 An C<isl_restriction> object can be created and freed using the following
4304 #include <isl/flow.h>
4306 __isl_give isl_restriction *isl_restriction_input(
4307 __isl_take isl_set *source_restr,
4308 __isl_take isl_set *sink_restr);
4309 __isl_give isl_restriction *isl_restriction_output(
4310 __isl_take isl_set *source_restr);
4311 __isl_give isl_restriction *isl_restriction_none(
4312 __isl_keep isl_map *source_map);
4313 __isl_give isl_restriction *isl_restriction_empty(
4314 __isl_keep isl_map *source_map);
4315 void *isl_restriction_free(
4316 __isl_take isl_restriction *restr);
4318 C<isl_restriction_none> and C<isl_restriction_empty> are special
4319 cases of C<isl_restriction_input>. C<isl_restriction_none>
4320 is essentially equivalent to
4322 isl_restriction_input(isl_set_universe(
4323 isl_space_range(isl_map_get_space(source_map))),
4325 isl_space_domain(isl_map_get_space(source_map))));
4327 whereas C<isl_restriction_empty> is essentially equivalent to
4329 isl_restriction_input(isl_set_empty(
4330 isl_space_range(isl_map_get_space(source_map))),
4332 isl_space_domain(isl_map_get_space(source_map))));
4336 B<The functionality described in this section is fairly new
4337 and may be subject to change.>
4339 The following function can be used to compute a schedule
4340 for a union of domains.
4341 By default, the algorithm used to construct the schedule is similar
4342 to that of C<Pluto>.
4343 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4345 The generated schedule respects all C<validity> dependences.
4346 That is, all dependence distances over these dependences in the
4347 scheduled space are lexicographically positive.
4348 The default algorithm tries to minimize the dependence distances over
4349 C<proximity> dependences.
4350 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4351 for groups of domains where the dependence distances have only
4352 non-negative values.
4353 When using Feautrier's algorithm, the C<proximity> dependence
4354 distances are only minimized during the extension to a
4355 full-dimensional schedule.
4357 #include <isl/schedule.h>
4358 __isl_give isl_schedule *isl_union_set_compute_schedule(
4359 __isl_take isl_union_set *domain,
4360 __isl_take isl_union_map *validity,
4361 __isl_take isl_union_map *proximity);
4362 void *isl_schedule_free(__isl_take isl_schedule *sched);
4364 A mapping from the domains to the scheduled space can be obtained
4365 from an C<isl_schedule> using the following function.
4367 __isl_give isl_union_map *isl_schedule_get_map(
4368 __isl_keep isl_schedule *sched);
4370 A representation of the schedule can be printed using
4372 __isl_give isl_printer *isl_printer_print_schedule(
4373 __isl_take isl_printer *p,
4374 __isl_keep isl_schedule *schedule);
4376 A representation of the schedule as a forest of bands can be obtained
4377 using the following function.
4379 __isl_give isl_band_list *isl_schedule_get_band_forest(
4380 __isl_keep isl_schedule *schedule);
4382 The list can be manipulated as explained in L<"Lists">.
4383 The bands inside the list can be copied and freed using the following
4386 #include <isl/band.h>
4387 __isl_give isl_band *isl_band_copy(
4388 __isl_keep isl_band *band);
4389 void *isl_band_free(__isl_take isl_band *band);
4391 Each band contains zero or more scheduling dimensions.
4392 These are referred to as the members of the band.
4393 The section of the schedule that corresponds to the band is
4394 referred to as the partial schedule of the band.
4395 For those nodes that participate in a band, the outer scheduling
4396 dimensions form the prefix schedule, while the inner scheduling
4397 dimensions form the suffix schedule.
4398 That is, if we take a cut of the band forest, then the union of
4399 the concatenations of the prefix, partial and suffix schedules of
4400 each band in the cut is equal to the entire schedule (modulo
4401 some possible padding at the end with zero scheduling dimensions).
4402 The properties of a band can be inspected using the following functions.
4404 #include <isl/band.h>
4405 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4407 int isl_band_has_children(__isl_keep isl_band *band);
4408 __isl_give isl_band_list *isl_band_get_children(
4409 __isl_keep isl_band *band);
4411 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4412 __isl_keep isl_band *band);
4413 __isl_give isl_union_map *isl_band_get_partial_schedule(
4414 __isl_keep isl_band *band);
4415 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4416 __isl_keep isl_band *band);
4418 int isl_band_n_member(__isl_keep isl_band *band);
4419 int isl_band_member_is_zero_distance(
4420 __isl_keep isl_band *band, int pos);
4422 Note that a scheduling dimension is considered to be ``zero
4423 distance'' if it does not carry any proximity dependences
4425 That is, if the dependence distances of the proximity
4426 dependences are all zero in that direction (for fixed
4427 iterations of outer bands).
4429 A representation of the band can be printed using
4431 #include <isl/band.h>
4432 __isl_give isl_printer *isl_printer_print_band(
4433 __isl_take isl_printer *p,
4434 __isl_keep isl_band *band);
4438 #include <isl/schedule.h>
4439 int isl_options_set_schedule_max_coefficient(
4440 isl_ctx *ctx, int val);
4441 int isl_options_get_schedule_max_coefficient(
4443 int isl_options_set_schedule_max_constant_term(
4444 isl_ctx *ctx, int val);
4445 int isl_options_get_schedule_max_constant_term(
4447 int isl_options_set_schedule_maximize_band_depth(
4448 isl_ctx *ctx, int val);
4449 int isl_options_get_schedule_maximize_band_depth(
4451 int isl_options_set_schedule_outer_zero_distance(
4452 isl_ctx *ctx, int val);
4453 int isl_options_get_schedule_outer_zero_distance(
4455 int isl_options_set_schedule_split_scaled(
4456 isl_ctx *ctx, int val);
4457 int isl_options_get_schedule_split_scaled(
4459 int isl_options_set_schedule_algorithm(
4460 isl_ctx *ctx, int val);
4461 int isl_options_get_schedule_algorithm(
4467 =item * schedule_max_coefficient
4469 This option enforces that the coefficients for variable and parameter
4470 dimensions in the calculated schedule are not larger than the specified value.
4471 This option can significantly increase the speed of the scheduling calculation
4472 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4473 this option does not introduce bounds on the variable or parameter
4476 =item * schedule_max_constant_term
4478 This option enforces that the constant coefficients in the calculated schedule
4479 are not larger than the maximal constant term. This option can significantly
4480 increase the speed of the scheduling calculation and may also prevent fusing of
4481 unrelated dimensions. A value of -1 means that this option does not introduce
4482 bounds on the constant coefficients.
4484 =item * schedule_maximize_band_depth
4486 If this option is set, we do not split bands at the point
4487 where we detect splitting is necessary. Instead, we
4488 backtrack and split bands as early as possible. This
4489 reduces the number of splits and maximizes the width of
4490 the bands. Wider bands give more possibilities for tiling.
4492 =item * schedule_outer_zero_distance
4494 If this option is set, then we try to construct schedules
4495 where the outermost scheduling dimension in each band
4496 results in a zero dependence distance over the proximity
4499 =item * schedule_split_scaled
4501 If this option is set, then we try to construct schedules in which the
4502 constant term is split off from the linear part if the linear parts of
4503 the scheduling rows for all nodes in the graphs have a common non-trivial
4505 The constant term is then placed in a separate band and the linear
4508 =item * schedule_algorithm
4510 Selects the scheduling algorithm to be used.
4511 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4512 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4516 =head2 Parametric Vertex Enumeration
4518 The parametric vertex enumeration described in this section
4519 is mainly intended to be used internally and by the C<barvinok>
4522 #include <isl/vertices.h>
4523 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4524 __isl_keep isl_basic_set *bset);
4526 The function C<isl_basic_set_compute_vertices> performs the
4527 actual computation of the parametric vertices and the chamber
4528 decomposition and store the result in an C<isl_vertices> object.
4529 This information can be queried by either iterating over all
4530 the vertices or iterating over all the chambers or cells
4531 and then iterating over all vertices that are active on the chamber.
4533 int isl_vertices_foreach_vertex(
4534 __isl_keep isl_vertices *vertices,
4535 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4538 int isl_vertices_foreach_cell(
4539 __isl_keep isl_vertices *vertices,
4540 int (*fn)(__isl_take isl_cell *cell, void *user),
4542 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4543 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4546 Other operations that can be performed on an C<isl_vertices> object are
4549 isl_ctx *isl_vertices_get_ctx(
4550 __isl_keep isl_vertices *vertices);
4551 int isl_vertices_get_n_vertices(
4552 __isl_keep isl_vertices *vertices);
4553 void isl_vertices_free(__isl_take isl_vertices *vertices);
4555 Vertices can be inspected and destroyed using the following functions.
4557 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4558 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4559 __isl_give isl_basic_set *isl_vertex_get_domain(
4560 __isl_keep isl_vertex *vertex);
4561 __isl_give isl_basic_set *isl_vertex_get_expr(
4562 __isl_keep isl_vertex *vertex);
4563 void isl_vertex_free(__isl_take isl_vertex *vertex);
4565 C<isl_vertex_get_expr> returns a singleton parametric set describing
4566 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4568 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4569 B<rational> basic sets, so they should mainly be used for inspection
4570 and should not be mixed with integer sets.
4572 Chambers can be inspected and destroyed using the following functions.
4574 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4575 __isl_give isl_basic_set *isl_cell_get_domain(
4576 __isl_keep isl_cell *cell);
4577 void isl_cell_free(__isl_take isl_cell *cell);
4581 Although C<isl> is mainly meant to be used as a library,
4582 it also contains some basic applications that use some
4583 of the functionality of C<isl>.
4584 The input may be specified in either the L<isl format>
4585 or the L<PolyLib format>.
4587 =head2 C<isl_polyhedron_sample>
4589 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4590 an integer element of the polyhedron, if there is any.
4591 The first column in the output is the denominator and is always
4592 equal to 1. If the polyhedron contains no integer points,
4593 then a vector of length zero is printed.
4597 C<isl_pip> takes the same input as the C<example> program
4598 from the C<piplib> distribution, i.e., a set of constraints
4599 on the parameters, a line containing only -1 and finally a set
4600 of constraints on a parametric polyhedron.
4601 The coefficients of the parameters appear in the last columns
4602 (but before the final constant column).
4603 The output is the lexicographic minimum of the parametric polyhedron.
4604 As C<isl> currently does not have its own output format, the output
4605 is just a dump of the internal state.
4607 =head2 C<isl_polyhedron_minimize>
4609 C<isl_polyhedron_minimize> computes the minimum of some linear
4610 or affine objective function over the integer points in a polyhedron.
4611 If an affine objective function
4612 is given, then the constant should appear in the last column.
4614 =head2 C<isl_polytope_scan>
4616 Given a polytope, C<isl_polytope_scan> prints
4617 all integer points in the polytope.