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 printer can be inspected using the following function.
981 FILE *isl_printer_get_file(
982 __isl_keep isl_printer *printer);
984 The behavior of the printer can be modified in various ways
986 __isl_give isl_printer *isl_printer_set_output_format(
987 __isl_take isl_printer *p, int output_format);
988 __isl_give isl_printer *isl_printer_set_indent(
989 __isl_take isl_printer *p, int indent);
990 __isl_give isl_printer *isl_printer_indent(
991 __isl_take isl_printer *p, int indent);
992 __isl_give isl_printer *isl_printer_set_prefix(
993 __isl_take isl_printer *p, const char *prefix);
994 __isl_give isl_printer *isl_printer_set_suffix(
995 __isl_take isl_printer *p, const char *suffix);
997 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
998 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
999 and defaults to C<ISL_FORMAT_ISL>.
1000 Each line in the output is indented by C<indent> (set by
1001 C<isl_printer_set_indent>) spaces
1002 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1003 In the C<PolyLib> format output,
1004 the coefficients of the existentially quantified variables
1005 appear between those of the set variables and those
1007 The function C<isl_printer_indent> increases the indentation
1008 by the specified amount (which may be negative).
1010 To actually print something, use
1012 #include <isl/set.h>
1013 __isl_give isl_printer *isl_printer_print_basic_set(
1014 __isl_take isl_printer *printer,
1015 __isl_keep isl_basic_set *bset);
1016 __isl_give isl_printer *isl_printer_print_set(
1017 __isl_take isl_printer *printer,
1018 __isl_keep isl_set *set);
1020 #include <isl/map.h>
1021 __isl_give isl_printer *isl_printer_print_basic_map(
1022 __isl_take isl_printer *printer,
1023 __isl_keep isl_basic_map *bmap);
1024 __isl_give isl_printer *isl_printer_print_map(
1025 __isl_take isl_printer *printer,
1026 __isl_keep isl_map *map);
1028 #include <isl/union_set.h>
1029 __isl_give isl_printer *isl_printer_print_union_set(
1030 __isl_take isl_printer *p,
1031 __isl_keep isl_union_set *uset);
1033 #include <isl/union_map.h>
1034 __isl_give isl_printer *isl_printer_print_union_map(
1035 __isl_take isl_printer *p,
1036 __isl_keep isl_union_map *umap);
1038 When called on a file printer, the following function flushes
1039 the file. When called on a string printer, the buffer is cleared.
1041 __isl_give isl_printer *isl_printer_flush(
1042 __isl_take isl_printer *p);
1044 =head2 Creating New Sets and Relations
1046 C<isl> has functions for creating some standard sets and relations.
1050 =item * Empty sets and relations
1052 __isl_give isl_basic_set *isl_basic_set_empty(
1053 __isl_take isl_space *space);
1054 __isl_give isl_basic_map *isl_basic_map_empty(
1055 __isl_take isl_space *space);
1056 __isl_give isl_set *isl_set_empty(
1057 __isl_take isl_space *space);
1058 __isl_give isl_map *isl_map_empty(
1059 __isl_take isl_space *space);
1060 __isl_give isl_union_set *isl_union_set_empty(
1061 __isl_take isl_space *space);
1062 __isl_give isl_union_map *isl_union_map_empty(
1063 __isl_take isl_space *space);
1065 For C<isl_union_set>s and C<isl_union_map>s, the space
1066 is only used to specify the parameters.
1068 =item * Universe sets and relations
1070 __isl_give isl_basic_set *isl_basic_set_universe(
1071 __isl_take isl_space *space);
1072 __isl_give isl_basic_map *isl_basic_map_universe(
1073 __isl_take isl_space *space);
1074 __isl_give isl_set *isl_set_universe(
1075 __isl_take isl_space *space);
1076 __isl_give isl_map *isl_map_universe(
1077 __isl_take isl_space *space);
1078 __isl_give isl_union_set *isl_union_set_universe(
1079 __isl_take isl_union_set *uset);
1080 __isl_give isl_union_map *isl_union_map_universe(
1081 __isl_take isl_union_map *umap);
1083 The sets and relations constructed by the functions above
1084 contain all integer values, while those constructed by the
1085 functions below only contain non-negative values.
1087 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1088 __isl_take isl_space *space);
1089 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1090 __isl_take isl_space *space);
1091 __isl_give isl_set *isl_set_nat_universe(
1092 __isl_take isl_space *space);
1093 __isl_give isl_map *isl_map_nat_universe(
1094 __isl_take isl_space *space);
1096 =item * Identity relations
1098 __isl_give isl_basic_map *isl_basic_map_identity(
1099 __isl_take isl_space *space);
1100 __isl_give isl_map *isl_map_identity(
1101 __isl_take isl_space *space);
1103 The number of input and output dimensions in C<space> needs
1106 =item * Lexicographic order
1108 __isl_give isl_map *isl_map_lex_lt(
1109 __isl_take isl_space *set_space);
1110 __isl_give isl_map *isl_map_lex_le(
1111 __isl_take isl_space *set_space);
1112 __isl_give isl_map *isl_map_lex_gt(
1113 __isl_take isl_space *set_space);
1114 __isl_give isl_map *isl_map_lex_ge(
1115 __isl_take isl_space *set_space);
1116 __isl_give isl_map *isl_map_lex_lt_first(
1117 __isl_take isl_space *space, unsigned n);
1118 __isl_give isl_map *isl_map_lex_le_first(
1119 __isl_take isl_space *space, unsigned n);
1120 __isl_give isl_map *isl_map_lex_gt_first(
1121 __isl_take isl_space *space, unsigned n);
1122 __isl_give isl_map *isl_map_lex_ge_first(
1123 __isl_take isl_space *space, unsigned n);
1125 The first four functions take a space for a B<set>
1126 and return relations that express that the elements in the domain
1127 are lexicographically less
1128 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1129 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1130 than the elements in the range.
1131 The last four functions take a space for a map
1132 and return relations that express that the first C<n> dimensions
1133 in the domain are lexicographically less
1134 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1135 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1136 than the first C<n> dimensions in the range.
1140 A basic set or relation can be converted to a set or relation
1141 using the following functions.
1143 __isl_give isl_set *isl_set_from_basic_set(
1144 __isl_take isl_basic_set *bset);
1145 __isl_give isl_map *isl_map_from_basic_map(
1146 __isl_take isl_basic_map *bmap);
1148 Sets and relations can be converted to union sets and relations
1149 using the following functions.
1151 __isl_give isl_union_map *isl_union_map_from_map(
1152 __isl_take isl_map *map);
1153 __isl_give isl_union_set *isl_union_set_from_set(
1154 __isl_take isl_set *set);
1156 The inverse conversions below can only be used if the input
1157 union set or relation is known to contain elements in exactly one
1160 __isl_give isl_set *isl_set_from_union_set(
1161 __isl_take isl_union_set *uset);
1162 __isl_give isl_map *isl_map_from_union_map(
1163 __isl_take isl_union_map *umap);
1165 A zero-dimensional set can be constructed on a given parameter domain
1166 using the following function.
1168 __isl_give isl_set *isl_set_from_params(
1169 __isl_take isl_set *set);
1171 Sets and relations can be copied and freed again using the following
1174 __isl_give isl_basic_set *isl_basic_set_copy(
1175 __isl_keep isl_basic_set *bset);
1176 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1177 __isl_give isl_union_set *isl_union_set_copy(
1178 __isl_keep isl_union_set *uset);
1179 __isl_give isl_basic_map *isl_basic_map_copy(
1180 __isl_keep isl_basic_map *bmap);
1181 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1182 __isl_give isl_union_map *isl_union_map_copy(
1183 __isl_keep isl_union_map *umap);
1184 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1185 void isl_set_free(__isl_take isl_set *set);
1186 void *isl_union_set_free(__isl_take isl_union_set *uset);
1187 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1188 void isl_map_free(__isl_take isl_map *map);
1189 void *isl_union_map_free(__isl_take isl_union_map *umap);
1191 Other sets and relations can be constructed by starting
1192 from a universe set or relation, adding equality and/or
1193 inequality constraints and then projecting out the
1194 existentially quantified variables, if any.
1195 Constraints can be constructed, manipulated and
1196 added to (or removed from) (basic) sets and relations
1197 using the following functions.
1199 #include <isl/constraint.h>
1200 __isl_give isl_constraint *isl_equality_alloc(
1201 __isl_take isl_local_space *ls);
1202 __isl_give isl_constraint *isl_inequality_alloc(
1203 __isl_take isl_local_space *ls);
1204 __isl_give isl_constraint *isl_constraint_set_constant(
1205 __isl_take isl_constraint *constraint, isl_int v);
1206 __isl_give isl_constraint *isl_constraint_set_constant_si(
1207 __isl_take isl_constraint *constraint, int v);
1208 __isl_give isl_constraint *isl_constraint_set_coefficient(
1209 __isl_take isl_constraint *constraint,
1210 enum isl_dim_type type, int pos, isl_int v);
1211 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1212 __isl_take isl_constraint *constraint,
1213 enum isl_dim_type type, int pos, int v);
1214 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1215 __isl_take isl_basic_map *bmap,
1216 __isl_take isl_constraint *constraint);
1217 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1218 __isl_take isl_basic_set *bset,
1219 __isl_take isl_constraint *constraint);
1220 __isl_give isl_map *isl_map_add_constraint(
1221 __isl_take isl_map *map,
1222 __isl_take isl_constraint *constraint);
1223 __isl_give isl_set *isl_set_add_constraint(
1224 __isl_take isl_set *set,
1225 __isl_take isl_constraint *constraint);
1226 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1227 __isl_take isl_basic_set *bset,
1228 __isl_take isl_constraint *constraint);
1230 For example, to create a set containing the even integers
1231 between 10 and 42, you would use the following code.
1234 isl_local_space *ls;
1236 isl_basic_set *bset;
1238 space = isl_space_set_alloc(ctx, 0, 2);
1239 bset = isl_basic_set_universe(isl_space_copy(space));
1240 ls = isl_local_space_from_space(space);
1242 c = isl_equality_alloc(isl_local_space_copy(ls));
1243 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1244 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1245 bset = isl_basic_set_add_constraint(bset, c);
1247 c = isl_inequality_alloc(isl_local_space_copy(ls));
1248 c = isl_constraint_set_constant_si(c, -10);
1249 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1250 bset = isl_basic_set_add_constraint(bset, c);
1252 c = isl_inequality_alloc(ls);
1253 c = isl_constraint_set_constant_si(c, 42);
1254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1255 bset = isl_basic_set_add_constraint(bset, c);
1257 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1261 isl_basic_set *bset;
1262 bset = isl_basic_set_read_from_str(ctx,
1263 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1265 A basic set or relation can also be constructed from two matrices
1266 describing the equalities and the inequalities.
1268 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1269 __isl_take isl_space *space,
1270 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1271 enum isl_dim_type c1,
1272 enum isl_dim_type c2, enum isl_dim_type c3,
1273 enum isl_dim_type c4);
1274 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1275 __isl_take isl_space *space,
1276 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1277 enum isl_dim_type c1,
1278 enum isl_dim_type c2, enum isl_dim_type c3,
1279 enum isl_dim_type c4, enum isl_dim_type c5);
1281 The C<isl_dim_type> arguments indicate the order in which
1282 different kinds of variables appear in the input matrices
1283 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1284 C<isl_dim_set> and C<isl_dim_div> for sets and
1285 of C<isl_dim_cst>, C<isl_dim_param>,
1286 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1288 A (basic or union) set or relation can also be constructed from a
1289 (union) (piecewise) (multiple) affine expression
1290 or a list of affine expressions
1291 (See L<"Piecewise Quasi Affine Expressions"> and
1292 L<"Piecewise Multiple Quasi Affine Expressions">).
1294 __isl_give isl_basic_map *isl_basic_map_from_aff(
1295 __isl_take isl_aff *aff);
1296 __isl_give isl_map *isl_map_from_aff(
1297 __isl_take isl_aff *aff);
1298 __isl_give isl_set *isl_set_from_pw_aff(
1299 __isl_take isl_pw_aff *pwaff);
1300 __isl_give isl_map *isl_map_from_pw_aff(
1301 __isl_take isl_pw_aff *pwaff);
1302 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1303 __isl_take isl_space *domain_space,
1304 __isl_take isl_aff_list *list);
1305 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1306 __isl_take isl_multi_aff *maff)
1307 __isl_give isl_map *isl_map_from_multi_aff(
1308 __isl_take isl_multi_aff *maff)
1309 __isl_give isl_set *isl_set_from_pw_multi_aff(
1310 __isl_take isl_pw_multi_aff *pma);
1311 __isl_give isl_map *isl_map_from_pw_multi_aff(
1312 __isl_take isl_pw_multi_aff *pma);
1313 __isl_give isl_union_map *
1314 isl_union_map_from_union_pw_multi_aff(
1315 __isl_take isl_union_pw_multi_aff *upma);
1317 The C<domain_dim> argument describes the domain of the resulting
1318 basic relation. It is required because the C<list> may consist
1319 of zero affine expressions.
1321 =head2 Inspecting Sets and Relations
1323 Usually, the user should not have to care about the actual constraints
1324 of the sets and maps, but should instead apply the abstract operations
1325 explained in the following sections.
1326 Occasionally, however, it may be required to inspect the individual
1327 coefficients of the constraints. This section explains how to do so.
1328 In these cases, it may also be useful to have C<isl> compute
1329 an explicit representation of the existentially quantified variables.
1331 __isl_give isl_set *isl_set_compute_divs(
1332 __isl_take isl_set *set);
1333 __isl_give isl_map *isl_map_compute_divs(
1334 __isl_take isl_map *map);
1335 __isl_give isl_union_set *isl_union_set_compute_divs(
1336 __isl_take isl_union_set *uset);
1337 __isl_give isl_union_map *isl_union_map_compute_divs(
1338 __isl_take isl_union_map *umap);
1340 This explicit representation defines the existentially quantified
1341 variables as integer divisions of the other variables, possibly
1342 including earlier existentially quantified variables.
1343 An explicitly represented existentially quantified variable therefore
1344 has a unique value when the values of the other variables are known.
1345 If, furthermore, the same existentials, i.e., existentials
1346 with the same explicit representations, should appear in the
1347 same order in each of the disjuncts of a set or map, then the user should call
1348 either of the following functions.
1350 __isl_give isl_set *isl_set_align_divs(
1351 __isl_take isl_set *set);
1352 __isl_give isl_map *isl_map_align_divs(
1353 __isl_take isl_map *map);
1355 Alternatively, the existentially quantified variables can be removed
1356 using the following functions, which compute an overapproximation.
1358 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1359 __isl_take isl_basic_set *bset);
1360 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1361 __isl_take isl_basic_map *bmap);
1362 __isl_give isl_set *isl_set_remove_divs(
1363 __isl_take isl_set *set);
1364 __isl_give isl_map *isl_map_remove_divs(
1365 __isl_take isl_map *map);
1367 To iterate over all the sets or maps in a union set or map, use
1369 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1370 int (*fn)(__isl_take isl_set *set, void *user),
1372 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1373 int (*fn)(__isl_take isl_map *map, void *user),
1376 The number of sets or maps in a union set or map can be obtained
1379 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1380 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1382 To extract the set or map in a given space from a union, use
1384 __isl_give isl_set *isl_union_set_extract_set(
1385 __isl_keep isl_union_set *uset,
1386 __isl_take isl_space *space);
1387 __isl_give isl_map *isl_union_map_extract_map(
1388 __isl_keep isl_union_map *umap,
1389 __isl_take isl_space *space);
1391 To iterate over all the basic sets or maps in a set or map, use
1393 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1394 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1396 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1397 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1400 The callback function C<fn> should return 0 if successful and
1401 -1 if an error occurs. In the latter case, or if any other error
1402 occurs, the above functions will return -1.
1404 It should be noted that C<isl> does not guarantee that
1405 the basic sets or maps passed to C<fn> are disjoint.
1406 If this is required, then the user should call one of
1407 the following functions first.
1409 __isl_give isl_set *isl_set_make_disjoint(
1410 __isl_take isl_set *set);
1411 __isl_give isl_map *isl_map_make_disjoint(
1412 __isl_take isl_map *map);
1414 The number of basic sets in a set can be obtained
1417 int isl_set_n_basic_set(__isl_keep isl_set *set);
1419 To iterate over the constraints of a basic set or map, use
1421 #include <isl/constraint.h>
1423 int isl_basic_map_foreach_constraint(
1424 __isl_keep isl_basic_map *bmap,
1425 int (*fn)(__isl_take isl_constraint *c, void *user),
1427 void *isl_constraint_free(__isl_take isl_constraint *c);
1429 Again, the callback function C<fn> should return 0 if successful and
1430 -1 if an error occurs. In the latter case, or if any other error
1431 occurs, the above functions will return -1.
1432 The constraint C<c> represents either an equality or an inequality.
1433 Use the following function to find out whether a constraint
1434 represents an equality. If not, it represents an inequality.
1436 int isl_constraint_is_equality(
1437 __isl_keep isl_constraint *constraint);
1439 The coefficients of the constraints can be inspected using
1440 the following functions.
1442 void isl_constraint_get_constant(
1443 __isl_keep isl_constraint *constraint, isl_int *v);
1444 void isl_constraint_get_coefficient(
1445 __isl_keep isl_constraint *constraint,
1446 enum isl_dim_type type, int pos, isl_int *v);
1447 int isl_constraint_involves_dims(
1448 __isl_keep isl_constraint *constraint,
1449 enum isl_dim_type type, unsigned first, unsigned n);
1451 The explicit representations of the existentially quantified
1452 variables can be inspected using the following function.
1453 Note that the user is only allowed to use this function
1454 if the inspected set or map is the result of a call
1455 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1456 The existentially quantified variable is equal to the floor
1457 of the returned affine expression. The affine expression
1458 itself can be inspected using the functions in
1459 L<"Piecewise Quasi Affine Expressions">.
1461 __isl_give isl_aff *isl_constraint_get_div(
1462 __isl_keep isl_constraint *constraint, int pos);
1464 To obtain the constraints of a basic set or map in matrix
1465 form, use the following functions.
1467 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1468 __isl_keep isl_basic_set *bset,
1469 enum isl_dim_type c1, enum isl_dim_type c2,
1470 enum isl_dim_type c3, enum isl_dim_type c4);
1471 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1472 __isl_keep isl_basic_set *bset,
1473 enum isl_dim_type c1, enum isl_dim_type c2,
1474 enum isl_dim_type c3, enum isl_dim_type c4);
1475 __isl_give isl_mat *isl_basic_map_equalities_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);
1480 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1481 __isl_keep isl_basic_map *bmap,
1482 enum isl_dim_type c1,
1483 enum isl_dim_type c2, enum isl_dim_type c3,
1484 enum isl_dim_type c4, enum isl_dim_type c5);
1486 The C<isl_dim_type> arguments dictate the order in which
1487 different kinds of variables appear in the resulting matrix
1488 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1489 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1491 The number of parameters, input, output or set dimensions can
1492 be obtained using the following functions.
1494 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1495 enum isl_dim_type type);
1496 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1497 enum isl_dim_type type);
1498 unsigned isl_set_dim(__isl_keep isl_set *set,
1499 enum isl_dim_type type);
1500 unsigned isl_map_dim(__isl_keep isl_map *map,
1501 enum isl_dim_type type);
1503 To check whether the description of a set or relation depends
1504 on one or more given dimensions, it is not necessary to iterate over all
1505 constraints. Instead the following functions can be used.
1507 int isl_basic_set_involves_dims(
1508 __isl_keep isl_basic_set *bset,
1509 enum isl_dim_type type, unsigned first, unsigned n);
1510 int isl_set_involves_dims(__isl_keep isl_set *set,
1511 enum isl_dim_type type, unsigned first, unsigned n);
1512 int isl_basic_map_involves_dims(
1513 __isl_keep isl_basic_map *bmap,
1514 enum isl_dim_type type, unsigned first, unsigned n);
1515 int isl_map_involves_dims(__isl_keep isl_map *map,
1516 enum isl_dim_type type, unsigned first, unsigned n);
1518 Similarly, the following functions can be used to check whether
1519 a given dimension is involved in any lower or upper bound.
1521 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1522 enum isl_dim_type type, unsigned pos);
1523 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1524 enum isl_dim_type type, unsigned pos);
1526 The identifiers or names of the domain and range spaces of a set
1527 or relation can be read off or set using the following functions.
1529 __isl_give isl_set *isl_set_set_tuple_id(
1530 __isl_take isl_set *set, __isl_take isl_id *id);
1531 __isl_give isl_set *isl_set_reset_tuple_id(
1532 __isl_take isl_set *set);
1533 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1534 __isl_give isl_id *isl_set_get_tuple_id(
1535 __isl_keep isl_set *set);
1536 __isl_give isl_map *isl_map_set_tuple_id(
1537 __isl_take isl_map *map, enum isl_dim_type type,
1538 __isl_take isl_id *id);
1539 __isl_give isl_map *isl_map_reset_tuple_id(
1540 __isl_take isl_map *map, enum isl_dim_type type);
1541 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1542 enum isl_dim_type type);
1543 __isl_give isl_id *isl_map_get_tuple_id(
1544 __isl_keep isl_map *map, enum isl_dim_type type);
1546 const char *isl_basic_set_get_tuple_name(
1547 __isl_keep isl_basic_set *bset);
1548 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1549 __isl_take isl_basic_set *set, const char *s);
1550 const char *isl_set_get_tuple_name(
1551 __isl_keep isl_set *set);
1552 const char *isl_basic_map_get_tuple_name(
1553 __isl_keep isl_basic_map *bmap,
1554 enum isl_dim_type type);
1555 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1556 __isl_take isl_basic_map *bmap,
1557 enum isl_dim_type type, const char *s);
1558 const char *isl_map_get_tuple_name(
1559 __isl_keep isl_map *map,
1560 enum isl_dim_type type);
1562 As with C<isl_space_get_tuple_name>, the value returned points to
1563 an internal data structure.
1564 The identifiers, positions or names of individual dimensions can be
1565 read off using the following functions.
1567 __isl_give isl_set *isl_set_set_dim_id(
1568 __isl_take isl_set *set, enum isl_dim_type type,
1569 unsigned pos, __isl_take isl_id *id);
1570 int isl_set_has_dim_id(__isl_keep isl_set *set,
1571 enum isl_dim_type type, unsigned pos);
1572 __isl_give isl_id *isl_set_get_dim_id(
1573 __isl_keep isl_set *set, enum isl_dim_type type,
1575 int isl_basic_map_has_dim_id(
1576 __isl_keep isl_basic_map *bmap,
1577 enum isl_dim_type type, unsigned pos);
1578 __isl_give isl_map *isl_map_set_dim_id(
1579 __isl_take isl_map *map, enum isl_dim_type type,
1580 unsigned pos, __isl_take isl_id *id);
1581 int isl_map_has_dim_id(__isl_keep isl_map *map,
1582 enum isl_dim_type type, unsigned pos);
1583 __isl_give isl_id *isl_map_get_dim_id(
1584 __isl_keep isl_map *map, enum isl_dim_type type,
1587 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1588 enum isl_dim_type type, __isl_keep isl_id *id);
1589 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1590 enum isl_dim_type type, __isl_keep isl_id *id);
1591 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1592 enum isl_dim_type type, const char *name);
1593 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1594 enum isl_dim_type type, const char *name);
1596 const char *isl_constraint_get_dim_name(
1597 __isl_keep isl_constraint *constraint,
1598 enum isl_dim_type type, unsigned pos);
1599 const char *isl_basic_set_get_dim_name(
1600 __isl_keep isl_basic_set *bset,
1601 enum isl_dim_type type, unsigned pos);
1602 int isl_set_has_dim_name(__isl_keep isl_set *set,
1603 enum isl_dim_type type, unsigned pos);
1604 const char *isl_set_get_dim_name(
1605 __isl_keep isl_set *set,
1606 enum isl_dim_type type, unsigned pos);
1607 const char *isl_basic_map_get_dim_name(
1608 __isl_keep isl_basic_map *bmap,
1609 enum isl_dim_type type, unsigned pos);
1610 const char *isl_map_get_dim_name(
1611 __isl_keep isl_map *map,
1612 enum isl_dim_type type, unsigned pos);
1614 These functions are mostly useful to obtain the identifiers, positions
1615 or names of the parameters. Identifiers of individual dimensions are
1616 essentially only useful for printing. They are ignored by all other
1617 operations and may not be preserved across those operations.
1621 =head3 Unary Properties
1627 The following functions test whether the given set or relation
1628 contains any integer points. The ``plain'' variants do not perform
1629 any computations, but simply check if the given set or relation
1630 is already known to be empty.
1632 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1633 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1634 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1635 int isl_set_is_empty(__isl_keep isl_set *set);
1636 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1637 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1638 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1639 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1640 int isl_map_is_empty(__isl_keep isl_map *map);
1641 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1643 =item * Universality
1645 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1646 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1647 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1649 =item * Single-valuedness
1651 int isl_map_plain_is_single_valued(
1652 __isl_keep isl_map *map);
1653 int isl_map_is_single_valued(__isl_keep isl_map *map);
1654 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1658 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1659 int isl_map_is_injective(__isl_keep isl_map *map);
1660 int isl_union_map_plain_is_injective(
1661 __isl_keep isl_union_map *umap);
1662 int isl_union_map_is_injective(
1663 __isl_keep isl_union_map *umap);
1667 int isl_map_is_bijective(__isl_keep isl_map *map);
1668 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1672 int isl_basic_map_plain_is_fixed(
1673 __isl_keep isl_basic_map *bmap,
1674 enum isl_dim_type type, unsigned pos,
1676 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1677 enum isl_dim_type type, unsigned pos,
1679 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1680 enum isl_dim_type type, unsigned pos,
1683 Check if the relation obviously lies on a hyperplane where the given dimension
1684 has a fixed value and if so, return that value in C<*val>.
1688 To check whether a set is a parameter domain, use this function:
1690 int isl_set_is_params(__isl_keep isl_set *set);
1691 int isl_union_set_is_params(
1692 __isl_keep isl_union_set *uset);
1696 The following functions check whether the domain of the given
1697 (basic) set is a wrapped relation.
1699 int isl_basic_set_is_wrapping(
1700 __isl_keep isl_basic_set *bset);
1701 int isl_set_is_wrapping(__isl_keep isl_set *set);
1703 =item * Internal Product
1705 int isl_basic_map_can_zip(
1706 __isl_keep isl_basic_map *bmap);
1707 int isl_map_can_zip(__isl_keep isl_map *map);
1709 Check whether the product of domain and range of the given relation
1711 i.e., whether both domain and range are nested relations.
1715 int isl_basic_map_can_curry(
1716 __isl_keep isl_basic_map *bmap);
1717 int isl_map_can_curry(__isl_keep isl_map *map);
1719 Check whether the domain of the (basic) relation is a wrapped relation.
1723 =head3 Binary Properties
1729 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1730 __isl_keep isl_set *set2);
1731 int isl_set_is_equal(__isl_keep isl_set *set1,
1732 __isl_keep isl_set *set2);
1733 int isl_union_set_is_equal(
1734 __isl_keep isl_union_set *uset1,
1735 __isl_keep isl_union_set *uset2);
1736 int isl_basic_map_is_equal(
1737 __isl_keep isl_basic_map *bmap1,
1738 __isl_keep isl_basic_map *bmap2);
1739 int isl_map_is_equal(__isl_keep isl_map *map1,
1740 __isl_keep isl_map *map2);
1741 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1742 __isl_keep isl_map *map2);
1743 int isl_union_map_is_equal(
1744 __isl_keep isl_union_map *umap1,
1745 __isl_keep isl_union_map *umap2);
1747 =item * Disjointness
1749 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1750 __isl_keep isl_set *set2);
1754 int isl_basic_set_is_subset(
1755 __isl_keep isl_basic_set *bset1,
1756 __isl_keep isl_basic_set *bset2);
1757 int isl_set_is_subset(__isl_keep isl_set *set1,
1758 __isl_keep isl_set *set2);
1759 int isl_set_is_strict_subset(
1760 __isl_keep isl_set *set1,
1761 __isl_keep isl_set *set2);
1762 int isl_union_set_is_subset(
1763 __isl_keep isl_union_set *uset1,
1764 __isl_keep isl_union_set *uset2);
1765 int isl_union_set_is_strict_subset(
1766 __isl_keep isl_union_set *uset1,
1767 __isl_keep isl_union_set *uset2);
1768 int isl_basic_map_is_subset(
1769 __isl_keep isl_basic_map *bmap1,
1770 __isl_keep isl_basic_map *bmap2);
1771 int isl_basic_map_is_strict_subset(
1772 __isl_keep isl_basic_map *bmap1,
1773 __isl_keep isl_basic_map *bmap2);
1774 int isl_map_is_subset(
1775 __isl_keep isl_map *map1,
1776 __isl_keep isl_map *map2);
1777 int isl_map_is_strict_subset(
1778 __isl_keep isl_map *map1,
1779 __isl_keep isl_map *map2);
1780 int isl_union_map_is_subset(
1781 __isl_keep isl_union_map *umap1,
1782 __isl_keep isl_union_map *umap2);
1783 int isl_union_map_is_strict_subset(
1784 __isl_keep isl_union_map *umap1,
1785 __isl_keep isl_union_map *umap2);
1789 =head2 Unary Operations
1795 __isl_give isl_set *isl_set_complement(
1796 __isl_take isl_set *set);
1797 __isl_give isl_map *isl_map_complement(
1798 __isl_take isl_map *map);
1802 __isl_give isl_basic_map *isl_basic_map_reverse(
1803 __isl_take isl_basic_map *bmap);
1804 __isl_give isl_map *isl_map_reverse(
1805 __isl_take isl_map *map);
1806 __isl_give isl_union_map *isl_union_map_reverse(
1807 __isl_take isl_union_map *umap);
1811 __isl_give isl_basic_set *isl_basic_set_project_out(
1812 __isl_take isl_basic_set *bset,
1813 enum isl_dim_type type, unsigned first, unsigned n);
1814 __isl_give isl_basic_map *isl_basic_map_project_out(
1815 __isl_take isl_basic_map *bmap,
1816 enum isl_dim_type type, unsigned first, unsigned n);
1817 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1819 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 __isl_give isl_basic_set *isl_basic_set_params(
1822 __isl_take isl_basic_set *bset);
1823 __isl_give isl_basic_set *isl_basic_map_domain(
1824 __isl_take isl_basic_map *bmap);
1825 __isl_give isl_basic_set *isl_basic_map_range(
1826 __isl_take isl_basic_map *bmap);
1827 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1828 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1829 __isl_give isl_set *isl_map_domain(
1830 __isl_take isl_map *bmap);
1831 __isl_give isl_set *isl_map_range(
1832 __isl_take isl_map *map);
1833 __isl_give isl_set *isl_union_set_params(
1834 __isl_take isl_union_set *uset);
1835 __isl_give isl_set *isl_union_map_params(
1836 __isl_take isl_union_map *umap);
1837 __isl_give isl_union_set *isl_union_map_domain(
1838 __isl_take isl_union_map *umap);
1839 __isl_give isl_union_set *isl_union_map_range(
1840 __isl_take isl_union_map *umap);
1842 __isl_give isl_basic_map *isl_basic_map_domain_map(
1843 __isl_take isl_basic_map *bmap);
1844 __isl_give isl_basic_map *isl_basic_map_range_map(
1845 __isl_take isl_basic_map *bmap);
1846 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1847 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1848 __isl_give isl_union_map *isl_union_map_domain_map(
1849 __isl_take isl_union_map *umap);
1850 __isl_give isl_union_map *isl_union_map_range_map(
1851 __isl_take isl_union_map *umap);
1853 The functions above construct a (basic, regular or union) relation
1854 that maps (a wrapped version of) the input relation to its domain or range.
1858 __isl_give isl_set *isl_set_eliminate(
1859 __isl_take isl_set *set, enum isl_dim_type type,
1860 unsigned first, unsigned n);
1861 __isl_give isl_basic_map *isl_basic_map_eliminate(
1862 __isl_take isl_basic_map *bmap,
1863 enum isl_dim_type type,
1864 unsigned first, unsigned n);
1865 __isl_give isl_map *isl_map_eliminate(
1866 __isl_take isl_map *map, enum isl_dim_type type,
1867 unsigned first, unsigned n);
1869 Eliminate the coefficients for the given dimensions from the constraints,
1870 without removing the dimensions.
1874 __isl_give isl_basic_set *isl_basic_set_fix(
1875 __isl_take isl_basic_set *bset,
1876 enum isl_dim_type type, unsigned pos,
1878 __isl_give isl_basic_set *isl_basic_set_fix_si(
1879 __isl_take isl_basic_set *bset,
1880 enum isl_dim_type type, unsigned pos, int value);
1881 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1882 enum isl_dim_type type, unsigned pos,
1884 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1885 enum isl_dim_type type, unsigned pos, int value);
1886 __isl_give isl_basic_map *isl_basic_map_fix_si(
1887 __isl_take isl_basic_map *bmap,
1888 enum isl_dim_type type, unsigned pos, int value);
1889 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1890 enum isl_dim_type type, unsigned pos, int value);
1892 Intersect the set or relation with the hyperplane where the given
1893 dimension has the fixed given value.
1895 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1896 __isl_take isl_basic_map *bmap,
1897 enum isl_dim_type type, unsigned pos, int value);
1898 __isl_give isl_set *isl_set_lower_bound(
1899 __isl_take isl_set *set,
1900 enum isl_dim_type type, unsigned pos,
1902 __isl_give isl_set *isl_set_lower_bound_si(
1903 __isl_take isl_set *set,
1904 enum isl_dim_type type, unsigned pos, int value);
1905 __isl_give isl_map *isl_map_lower_bound_si(
1906 __isl_take isl_map *map,
1907 enum isl_dim_type type, unsigned pos, int value);
1908 __isl_give isl_set *isl_set_upper_bound(
1909 __isl_take isl_set *set,
1910 enum isl_dim_type type, unsigned pos,
1912 __isl_give isl_set *isl_set_upper_bound_si(
1913 __isl_take isl_set *set,
1914 enum isl_dim_type type, unsigned pos, int value);
1915 __isl_give isl_map *isl_map_upper_bound_si(
1916 __isl_take isl_map *map,
1917 enum isl_dim_type type, unsigned pos, int value);
1919 Intersect the set or relation with the half-space where the given
1920 dimension has a value bounded by the fixed given value.
1922 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1923 enum isl_dim_type type1, int pos1,
1924 enum isl_dim_type type2, int pos2);
1925 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1926 enum isl_dim_type type1, int pos1,
1927 enum isl_dim_type type2, int pos2);
1929 Intersect the set or relation with the hyperplane where the given
1930 dimensions are equal to each other.
1932 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1933 enum isl_dim_type type1, int pos1,
1934 enum isl_dim_type type2, int pos2);
1936 Intersect the relation with the hyperplane where the given
1937 dimensions have opposite values.
1939 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1940 enum isl_dim_type type1, int pos1,
1941 enum isl_dim_type type2, int pos2);
1943 Intersect the relation with the half-space where the given
1944 dimensions satisfy the given ordering.
1948 __isl_give isl_map *isl_set_identity(
1949 __isl_take isl_set *set);
1950 __isl_give isl_union_map *isl_union_set_identity(
1951 __isl_take isl_union_set *uset);
1953 Construct an identity relation on the given (union) set.
1957 __isl_give isl_basic_set *isl_basic_map_deltas(
1958 __isl_take isl_basic_map *bmap);
1959 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1960 __isl_give isl_union_set *isl_union_map_deltas(
1961 __isl_take isl_union_map *umap);
1963 These functions return a (basic) set containing the differences
1964 between image elements and corresponding domain elements in the input.
1966 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1967 __isl_take isl_basic_map *bmap);
1968 __isl_give isl_map *isl_map_deltas_map(
1969 __isl_take isl_map *map);
1970 __isl_give isl_union_map *isl_union_map_deltas_map(
1971 __isl_take isl_union_map *umap);
1973 The functions above construct a (basic, regular or union) relation
1974 that maps (a wrapped version of) the input relation to its delta set.
1978 Simplify the representation of a set or relation by trying
1979 to combine pairs of basic sets or relations into a single
1980 basic set or relation.
1982 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1983 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1984 __isl_give isl_union_set *isl_union_set_coalesce(
1985 __isl_take isl_union_set *uset);
1986 __isl_give isl_union_map *isl_union_map_coalesce(
1987 __isl_take isl_union_map *umap);
1989 One of the methods for combining pairs of basic sets or relations
1990 can result in coefficients that are much larger than those that appear
1991 in the constraints of the input. By default, the coefficients are
1992 not allowed to grow larger, but this can be changed by unsetting
1993 the following option.
1995 int isl_options_set_coalesce_bounded_wrapping(
1996 isl_ctx *ctx, int val);
1997 int isl_options_get_coalesce_bounded_wrapping(
2000 =item * Detecting equalities
2002 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2003 __isl_take isl_basic_set *bset);
2004 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2005 __isl_take isl_basic_map *bmap);
2006 __isl_give isl_set *isl_set_detect_equalities(
2007 __isl_take isl_set *set);
2008 __isl_give isl_map *isl_map_detect_equalities(
2009 __isl_take isl_map *map);
2010 __isl_give isl_union_set *isl_union_set_detect_equalities(
2011 __isl_take isl_union_set *uset);
2012 __isl_give isl_union_map *isl_union_map_detect_equalities(
2013 __isl_take isl_union_map *umap);
2015 Simplify the representation of a set or relation by detecting implicit
2018 =item * Removing redundant constraints
2020 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2021 __isl_take isl_basic_set *bset);
2022 __isl_give isl_set *isl_set_remove_redundancies(
2023 __isl_take isl_set *set);
2024 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2025 __isl_take isl_basic_map *bmap);
2026 __isl_give isl_map *isl_map_remove_redundancies(
2027 __isl_take isl_map *map);
2031 __isl_give isl_basic_set *isl_set_convex_hull(
2032 __isl_take isl_set *set);
2033 __isl_give isl_basic_map *isl_map_convex_hull(
2034 __isl_take isl_map *map);
2036 If the input set or relation has any existentially quantified
2037 variables, then the result of these operations is currently undefined.
2041 __isl_give isl_basic_set *isl_set_simple_hull(
2042 __isl_take isl_set *set);
2043 __isl_give isl_basic_map *isl_map_simple_hull(
2044 __isl_take isl_map *map);
2045 __isl_give isl_union_map *isl_union_map_simple_hull(
2046 __isl_take isl_union_map *umap);
2048 These functions compute a single basic set or relation
2049 that contains the whole input set or relation.
2050 In particular, the output is described by translates
2051 of the constraints describing the basic sets or relations in the input.
2055 (See \autoref{s:simple hull}.)
2061 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2062 __isl_take isl_basic_set *bset);
2063 __isl_give isl_basic_set *isl_set_affine_hull(
2064 __isl_take isl_set *set);
2065 __isl_give isl_union_set *isl_union_set_affine_hull(
2066 __isl_take isl_union_set *uset);
2067 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2068 __isl_take isl_basic_map *bmap);
2069 __isl_give isl_basic_map *isl_map_affine_hull(
2070 __isl_take isl_map *map);
2071 __isl_give isl_union_map *isl_union_map_affine_hull(
2072 __isl_take isl_union_map *umap);
2074 In case of union sets and relations, the affine hull is computed
2077 =item * Polyhedral hull
2079 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2080 __isl_take isl_set *set);
2081 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2082 __isl_take isl_map *map);
2083 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2084 __isl_take isl_union_set *uset);
2085 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2086 __isl_take isl_union_map *umap);
2088 These functions compute a single basic set or relation
2089 not involving any existentially quantified variables
2090 that contains the whole input set or relation.
2091 In case of union sets and relations, the polyhedral hull is computed
2096 __isl_give isl_basic_set *isl_basic_set_sample(
2097 __isl_take isl_basic_set *bset);
2098 __isl_give isl_basic_set *isl_set_sample(
2099 __isl_take isl_set *set);
2100 __isl_give isl_basic_map *isl_basic_map_sample(
2101 __isl_take isl_basic_map *bmap);
2102 __isl_give isl_basic_map *isl_map_sample(
2103 __isl_take isl_map *map);
2105 If the input (basic) set or relation is non-empty, then return
2106 a singleton subset of the input. Otherwise, return an empty set.
2108 =item * Optimization
2110 #include <isl/ilp.h>
2111 enum isl_lp_result isl_basic_set_max(
2112 __isl_keep isl_basic_set *bset,
2113 __isl_keep isl_aff *obj, isl_int *opt)
2114 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2115 __isl_keep isl_aff *obj, isl_int *opt);
2116 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2117 __isl_keep isl_aff *obj, isl_int *opt);
2119 Compute the minimum or maximum of the integer affine expression C<obj>
2120 over the points in C<set>, returning the result in C<opt>.
2121 The return value may be one of C<isl_lp_error>,
2122 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2124 =item * Parametric optimization
2126 __isl_give isl_pw_aff *isl_set_dim_min(
2127 __isl_take isl_set *set, int pos);
2128 __isl_give isl_pw_aff *isl_set_dim_max(
2129 __isl_take isl_set *set, int pos);
2130 __isl_give isl_pw_aff *isl_map_dim_max(
2131 __isl_take isl_map *map, int pos);
2133 Compute the minimum or maximum of the given set or output dimension
2134 as a function of the parameters (and input dimensions), but independently
2135 of the other set or output dimensions.
2136 For lexicographic optimization, see L<"Lexicographic Optimization">.
2140 The following functions compute either the set of (rational) coefficient
2141 values of valid constraints for the given set or the set of (rational)
2142 values satisfying the constraints with coefficients from the given set.
2143 Internally, these two sets of functions perform essentially the
2144 same operations, except that the set of coefficients is assumed to
2145 be a cone, while the set of values may be any polyhedron.
2146 The current implementation is based on the Farkas lemma and
2147 Fourier-Motzkin elimination, but this may change or be made optional
2148 in future. In particular, future implementations may use different
2149 dualization algorithms or skip the elimination step.
2151 __isl_give isl_basic_set *isl_basic_set_coefficients(
2152 __isl_take isl_basic_set *bset);
2153 __isl_give isl_basic_set *isl_set_coefficients(
2154 __isl_take isl_set *set);
2155 __isl_give isl_union_set *isl_union_set_coefficients(
2156 __isl_take isl_union_set *bset);
2157 __isl_give isl_basic_set *isl_basic_set_solutions(
2158 __isl_take isl_basic_set *bset);
2159 __isl_give isl_basic_set *isl_set_solutions(
2160 __isl_take isl_set *set);
2161 __isl_give isl_union_set *isl_union_set_solutions(
2162 __isl_take isl_union_set *bset);
2166 __isl_give isl_map *isl_map_fixed_power(
2167 __isl_take isl_map *map, isl_int exp);
2168 __isl_give isl_union_map *isl_union_map_fixed_power(
2169 __isl_take isl_union_map *umap, isl_int exp);
2171 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2172 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2173 of C<map> is computed.
2175 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2177 __isl_give isl_union_map *isl_union_map_power(
2178 __isl_take isl_union_map *umap, int *exact);
2180 Compute a parametric representation for all positive powers I<k> of C<map>.
2181 The result maps I<k> to a nested relation corresponding to the
2182 I<k>th power of C<map>.
2183 The result may be an overapproximation. If the result is known to be exact,
2184 then C<*exact> is set to C<1>.
2186 =item * Transitive closure
2188 __isl_give isl_map *isl_map_transitive_closure(
2189 __isl_take isl_map *map, int *exact);
2190 __isl_give isl_union_map *isl_union_map_transitive_closure(
2191 __isl_take isl_union_map *umap, int *exact);
2193 Compute the transitive closure of C<map>.
2194 The result may be an overapproximation. If the result is known to be exact,
2195 then C<*exact> is set to C<1>.
2197 =item * Reaching path lengths
2199 __isl_give isl_map *isl_map_reaching_path_lengths(
2200 __isl_take isl_map *map, int *exact);
2202 Compute a relation that maps each element in the range of C<map>
2203 to the lengths of all paths composed of edges in C<map> that
2204 end up in the given element.
2205 The result may be an overapproximation. If the result is known to be exact,
2206 then C<*exact> is set to C<1>.
2207 To compute the I<maximal> path length, the resulting relation
2208 should be postprocessed by C<isl_map_lexmax>.
2209 In particular, if the input relation is a dependence relation
2210 (mapping sources to sinks), then the maximal path length corresponds
2211 to the free schedule.
2212 Note, however, that C<isl_map_lexmax> expects the maximum to be
2213 finite, so if the path lengths are unbounded (possibly due to
2214 the overapproximation), then you will get an error message.
2218 __isl_give isl_basic_set *isl_basic_map_wrap(
2219 __isl_take isl_basic_map *bmap);
2220 __isl_give isl_set *isl_map_wrap(
2221 __isl_take isl_map *map);
2222 __isl_give isl_union_set *isl_union_map_wrap(
2223 __isl_take isl_union_map *umap);
2224 __isl_give isl_basic_map *isl_basic_set_unwrap(
2225 __isl_take isl_basic_set *bset);
2226 __isl_give isl_map *isl_set_unwrap(
2227 __isl_take isl_set *set);
2228 __isl_give isl_union_map *isl_union_set_unwrap(
2229 __isl_take isl_union_set *uset);
2233 Remove any internal structure of domain (and range) of the given
2234 set or relation. If there is any such internal structure in the input,
2235 then the name of the space is also removed.
2237 __isl_give isl_basic_set *isl_basic_set_flatten(
2238 __isl_take isl_basic_set *bset);
2239 __isl_give isl_set *isl_set_flatten(
2240 __isl_take isl_set *set);
2241 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2242 __isl_take isl_basic_map *bmap);
2243 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_map *isl_map_flatten_range(
2246 __isl_take isl_map *map);
2247 __isl_give isl_map *isl_map_flatten_domain(
2248 __isl_take isl_map *map);
2249 __isl_give isl_basic_map *isl_basic_map_flatten(
2250 __isl_take isl_basic_map *bmap);
2251 __isl_give isl_map *isl_map_flatten(
2252 __isl_take isl_map *map);
2254 __isl_give isl_map *isl_set_flatten_map(
2255 __isl_take isl_set *set);
2257 The function above constructs a relation
2258 that maps the input set to a flattened version of the set.
2262 Lift the input set to a space with extra dimensions corresponding
2263 to the existentially quantified variables in the input.
2264 In particular, the result lives in a wrapped map where the domain
2265 is the original space and the range corresponds to the original
2266 existentially quantified variables.
2268 __isl_give isl_basic_set *isl_basic_set_lift(
2269 __isl_take isl_basic_set *bset);
2270 __isl_give isl_set *isl_set_lift(
2271 __isl_take isl_set *set);
2272 __isl_give isl_union_set *isl_union_set_lift(
2273 __isl_take isl_union_set *uset);
2275 Given a local space that contains the existentially quantified
2276 variables of a set, a basic relation that, when applied to
2277 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2278 can be constructed using the following function.
2280 #include <isl/local_space.h>
2281 __isl_give isl_basic_map *isl_local_space_lifting(
2282 __isl_take isl_local_space *ls);
2284 =item * Internal Product
2286 __isl_give isl_basic_map *isl_basic_map_zip(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_map *isl_map_zip(
2289 __isl_take isl_map *map);
2290 __isl_give isl_union_map *isl_union_map_zip(
2291 __isl_take isl_union_map *umap);
2293 Given a relation with nested relations for domain and range,
2294 interchange the range of the domain with the domain of the range.
2298 __isl_give isl_basic_map *isl_basic_map_curry(
2299 __isl_take isl_basic_map *bmap);
2300 __isl_give isl_map *isl_map_curry(
2301 __isl_take isl_map *map);
2302 __isl_give isl_union_map *isl_union_map_curry(
2303 __isl_take isl_union_map *umap);
2305 Given a relation with a nested relation for domain,
2306 move the range of the nested relation out of the domain
2307 and use it as the domain of a nested relation in the range,
2308 with the original range as range of this nested relation.
2310 =item * Aligning parameters
2312 __isl_give isl_set *isl_set_align_params(
2313 __isl_take isl_set *set,
2314 __isl_take isl_space *model);
2315 __isl_give isl_map *isl_map_align_params(
2316 __isl_take isl_map *map,
2317 __isl_take isl_space *model);
2319 Change the order of the parameters of the given set or relation
2320 such that the first parameters match those of C<model>.
2321 This may involve the introduction of extra parameters.
2322 All parameters need to be named.
2324 =item * Dimension manipulation
2326 __isl_give isl_set *isl_set_add_dims(
2327 __isl_take isl_set *set,
2328 enum isl_dim_type type, unsigned n);
2329 __isl_give isl_map *isl_map_add_dims(
2330 __isl_take isl_map *map,
2331 enum isl_dim_type type, unsigned n);
2332 __isl_give isl_set *isl_set_insert_dims(
2333 __isl_take isl_set *set,
2334 enum isl_dim_type type, unsigned pos, unsigned n);
2335 __isl_give isl_map *isl_map_insert_dims(
2336 __isl_take isl_map *map,
2337 enum isl_dim_type type, unsigned pos, unsigned n);
2338 __isl_give isl_basic_set *isl_basic_set_move_dims(
2339 __isl_take isl_basic_set *bset,
2340 enum isl_dim_type dst_type, unsigned dst_pos,
2341 enum isl_dim_type src_type, unsigned src_pos,
2343 __isl_give isl_basic_map *isl_basic_map_move_dims(
2344 __isl_take isl_basic_map *bmap,
2345 enum isl_dim_type dst_type, unsigned dst_pos,
2346 enum isl_dim_type src_type, unsigned src_pos,
2348 __isl_give isl_set *isl_set_move_dims(
2349 __isl_take isl_set *set,
2350 enum isl_dim_type dst_type, unsigned dst_pos,
2351 enum isl_dim_type src_type, unsigned src_pos,
2353 __isl_give isl_map *isl_map_move_dims(
2354 __isl_take isl_map *map,
2355 enum isl_dim_type dst_type, unsigned dst_pos,
2356 enum isl_dim_type src_type, unsigned src_pos,
2359 It is usually not advisable to directly change the (input or output)
2360 space of a set or a relation as this removes the name and the internal
2361 structure of the space. However, the above functions can be useful
2362 to add new parameters, assuming
2363 C<isl_set_align_params> and C<isl_map_align_params>
2368 =head2 Binary Operations
2370 The two arguments of a binary operation not only need to live
2371 in the same C<isl_ctx>, they currently also need to have
2372 the same (number of) parameters.
2374 =head3 Basic Operations
2378 =item * Intersection
2380 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2381 __isl_take isl_basic_set *bset1,
2382 __isl_take isl_basic_set *bset2);
2383 __isl_give isl_basic_set *isl_basic_set_intersect(
2384 __isl_take isl_basic_set *bset1,
2385 __isl_take isl_basic_set *bset2);
2386 __isl_give isl_set *isl_set_intersect_params(
2387 __isl_take isl_set *set,
2388 __isl_take isl_set *params);
2389 __isl_give isl_set *isl_set_intersect(
2390 __isl_take isl_set *set1,
2391 __isl_take isl_set *set2);
2392 __isl_give isl_union_set *isl_union_set_intersect_params(
2393 __isl_take isl_union_set *uset,
2394 __isl_take isl_set *set);
2395 __isl_give isl_union_map *isl_union_map_intersect_params(
2396 __isl_take isl_union_map *umap,
2397 __isl_take isl_set *set);
2398 __isl_give isl_union_set *isl_union_set_intersect(
2399 __isl_take isl_union_set *uset1,
2400 __isl_take isl_union_set *uset2);
2401 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2402 __isl_take isl_basic_map *bmap,
2403 __isl_take isl_basic_set *bset);
2404 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2405 __isl_take isl_basic_map *bmap,
2406 __isl_take isl_basic_set *bset);
2407 __isl_give isl_basic_map *isl_basic_map_intersect(
2408 __isl_take isl_basic_map *bmap1,
2409 __isl_take isl_basic_map *bmap2);
2410 __isl_give isl_map *isl_map_intersect_params(
2411 __isl_take isl_map *map,
2412 __isl_take isl_set *params);
2413 __isl_give isl_map *isl_map_intersect_domain(
2414 __isl_take isl_map *map,
2415 __isl_take isl_set *set);
2416 __isl_give isl_map *isl_map_intersect_range(
2417 __isl_take isl_map *map,
2418 __isl_take isl_set *set);
2419 __isl_give isl_map *isl_map_intersect(
2420 __isl_take isl_map *map1,
2421 __isl_take isl_map *map2);
2422 __isl_give isl_union_map *isl_union_map_intersect_domain(
2423 __isl_take isl_union_map *umap,
2424 __isl_take isl_union_set *uset);
2425 __isl_give isl_union_map *isl_union_map_intersect_range(
2426 __isl_take isl_union_map *umap,
2427 __isl_take isl_union_set *uset);
2428 __isl_give isl_union_map *isl_union_map_intersect(
2429 __isl_take isl_union_map *umap1,
2430 __isl_take isl_union_map *umap2);
2434 __isl_give isl_set *isl_basic_set_union(
2435 __isl_take isl_basic_set *bset1,
2436 __isl_take isl_basic_set *bset2);
2437 __isl_give isl_map *isl_basic_map_union(
2438 __isl_take isl_basic_map *bmap1,
2439 __isl_take isl_basic_map *bmap2);
2440 __isl_give isl_set *isl_set_union(
2441 __isl_take isl_set *set1,
2442 __isl_take isl_set *set2);
2443 __isl_give isl_map *isl_map_union(
2444 __isl_take isl_map *map1,
2445 __isl_take isl_map *map2);
2446 __isl_give isl_union_set *isl_union_set_union(
2447 __isl_take isl_union_set *uset1,
2448 __isl_take isl_union_set *uset2);
2449 __isl_give isl_union_map *isl_union_map_union(
2450 __isl_take isl_union_map *umap1,
2451 __isl_take isl_union_map *umap2);
2453 =item * Set difference
2455 __isl_give isl_set *isl_set_subtract(
2456 __isl_take isl_set *set1,
2457 __isl_take isl_set *set2);
2458 __isl_give isl_map *isl_map_subtract(
2459 __isl_take isl_map *map1,
2460 __isl_take isl_map *map2);
2461 __isl_give isl_map *isl_map_subtract_domain(
2462 __isl_take isl_map *map,
2463 __isl_take isl_set *dom);
2464 __isl_give isl_map *isl_map_subtract_range(
2465 __isl_take isl_map *map,
2466 __isl_take isl_set *dom);
2467 __isl_give isl_union_set *isl_union_set_subtract(
2468 __isl_take isl_union_set *uset1,
2469 __isl_take isl_union_set *uset2);
2470 __isl_give isl_union_map *isl_union_map_subtract(
2471 __isl_take isl_union_map *umap1,
2472 __isl_take isl_union_map *umap2);
2476 __isl_give isl_basic_set *isl_basic_set_apply(
2477 __isl_take isl_basic_set *bset,
2478 __isl_take isl_basic_map *bmap);
2479 __isl_give isl_set *isl_set_apply(
2480 __isl_take isl_set *set,
2481 __isl_take isl_map *map);
2482 __isl_give isl_union_set *isl_union_set_apply(
2483 __isl_take isl_union_set *uset,
2484 __isl_take isl_union_map *umap);
2485 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2486 __isl_take isl_basic_map *bmap1,
2487 __isl_take isl_basic_map *bmap2);
2488 __isl_give isl_basic_map *isl_basic_map_apply_range(
2489 __isl_take isl_basic_map *bmap1,
2490 __isl_take isl_basic_map *bmap2);
2491 __isl_give isl_map *isl_map_apply_domain(
2492 __isl_take isl_map *map1,
2493 __isl_take isl_map *map2);
2494 __isl_give isl_union_map *isl_union_map_apply_domain(
2495 __isl_take isl_union_map *umap1,
2496 __isl_take isl_union_map *umap2);
2497 __isl_give isl_map *isl_map_apply_range(
2498 __isl_take isl_map *map1,
2499 __isl_take isl_map *map2);
2500 __isl_give isl_union_map *isl_union_map_apply_range(
2501 __isl_take isl_union_map *umap1,
2502 __isl_take isl_union_map *umap2);
2504 =item * Cartesian Product
2506 __isl_give isl_set *isl_set_product(
2507 __isl_take isl_set *set1,
2508 __isl_take isl_set *set2);
2509 __isl_give isl_union_set *isl_union_set_product(
2510 __isl_take isl_union_set *uset1,
2511 __isl_take isl_union_set *uset2);
2512 __isl_give isl_basic_map *isl_basic_map_domain_product(
2513 __isl_take isl_basic_map *bmap1,
2514 __isl_take isl_basic_map *bmap2);
2515 __isl_give isl_basic_map *isl_basic_map_range_product(
2516 __isl_take isl_basic_map *bmap1,
2517 __isl_take isl_basic_map *bmap2);
2518 __isl_give isl_map *isl_map_domain_product(
2519 __isl_take isl_map *map1,
2520 __isl_take isl_map *map2);
2521 __isl_give isl_map *isl_map_range_product(
2522 __isl_take isl_map *map1,
2523 __isl_take isl_map *map2);
2524 __isl_give isl_union_map *isl_union_map_range_product(
2525 __isl_take isl_union_map *umap1,
2526 __isl_take isl_union_map *umap2);
2527 __isl_give isl_map *isl_map_product(
2528 __isl_take isl_map *map1,
2529 __isl_take isl_map *map2);
2530 __isl_give isl_union_map *isl_union_map_product(
2531 __isl_take isl_union_map *umap1,
2532 __isl_take isl_union_map *umap2);
2534 The above functions compute the cross product of the given
2535 sets or relations. The domains and ranges of the results
2536 are wrapped maps between domains and ranges of the inputs.
2537 To obtain a ``flat'' product, use the following functions
2540 __isl_give isl_basic_set *isl_basic_set_flat_product(
2541 __isl_take isl_basic_set *bset1,
2542 __isl_take isl_basic_set *bset2);
2543 __isl_give isl_set *isl_set_flat_product(
2544 __isl_take isl_set *set1,
2545 __isl_take isl_set *set2);
2546 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2547 __isl_take isl_basic_map *bmap1,
2548 __isl_take isl_basic_map *bmap2);
2549 __isl_give isl_map *isl_map_flat_domain_product(
2550 __isl_take isl_map *map1,
2551 __isl_take isl_map *map2);
2552 __isl_give isl_map *isl_map_flat_range_product(
2553 __isl_take isl_map *map1,
2554 __isl_take isl_map *map2);
2555 __isl_give isl_union_map *isl_union_map_flat_range_product(
2556 __isl_take isl_union_map *umap1,
2557 __isl_take isl_union_map *umap2);
2558 __isl_give isl_basic_map *isl_basic_map_flat_product(
2559 __isl_take isl_basic_map *bmap1,
2560 __isl_take isl_basic_map *bmap2);
2561 __isl_give isl_map *isl_map_flat_product(
2562 __isl_take isl_map *map1,
2563 __isl_take isl_map *map2);
2565 =item * Simplification
2567 __isl_give isl_basic_set *isl_basic_set_gist(
2568 __isl_take isl_basic_set *bset,
2569 __isl_take isl_basic_set *context);
2570 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2571 __isl_take isl_set *context);
2572 __isl_give isl_set *isl_set_gist_params(
2573 __isl_take isl_set *set,
2574 __isl_take isl_set *context);
2575 __isl_give isl_union_set *isl_union_set_gist(
2576 __isl_take isl_union_set *uset,
2577 __isl_take isl_union_set *context);
2578 __isl_give isl_union_set *isl_union_set_gist_params(
2579 __isl_take isl_union_set *uset,
2580 __isl_take isl_set *set);
2581 __isl_give isl_basic_map *isl_basic_map_gist(
2582 __isl_take isl_basic_map *bmap,
2583 __isl_take isl_basic_map *context);
2584 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2585 __isl_take isl_map *context);
2586 __isl_give isl_map *isl_map_gist_params(
2587 __isl_take isl_map *map,
2588 __isl_take isl_set *context);
2589 __isl_give isl_map *isl_map_gist_domain(
2590 __isl_take isl_map *map,
2591 __isl_take isl_set *context);
2592 __isl_give isl_map *isl_map_gist_range(
2593 __isl_take isl_map *map,
2594 __isl_take isl_set *context);
2595 __isl_give isl_union_map *isl_union_map_gist(
2596 __isl_take isl_union_map *umap,
2597 __isl_take isl_union_map *context);
2598 __isl_give isl_union_map *isl_union_map_gist_params(
2599 __isl_take isl_union_map *umap,
2600 __isl_take isl_set *set);
2601 __isl_give isl_union_map *isl_union_map_gist_domain(
2602 __isl_take isl_union_map *umap,
2603 __isl_take isl_union_set *uset);
2604 __isl_give isl_union_map *isl_union_map_gist_range(
2605 __isl_take isl_union_map *umap,
2606 __isl_take isl_union_set *uset);
2608 The gist operation returns a set or relation that has the
2609 same intersection with the context as the input set or relation.
2610 Any implicit equality in the intersection is made explicit in the result,
2611 while all inequalities that are redundant with respect to the intersection
2613 In case of union sets and relations, the gist operation is performed
2618 =head3 Lexicographic Optimization
2620 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2621 the following functions
2622 compute a set that contains the lexicographic minimum or maximum
2623 of the elements in C<set> (or C<bset>) for those values of the parameters
2624 that satisfy C<dom>.
2625 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2626 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2628 In other words, the union of the parameter values
2629 for which the result is non-empty and of C<*empty>
2632 __isl_give isl_set *isl_basic_set_partial_lexmin(
2633 __isl_take isl_basic_set *bset,
2634 __isl_take isl_basic_set *dom,
2635 __isl_give isl_set **empty);
2636 __isl_give isl_set *isl_basic_set_partial_lexmax(
2637 __isl_take isl_basic_set *bset,
2638 __isl_take isl_basic_set *dom,
2639 __isl_give isl_set **empty);
2640 __isl_give isl_set *isl_set_partial_lexmin(
2641 __isl_take isl_set *set, __isl_take isl_set *dom,
2642 __isl_give isl_set **empty);
2643 __isl_give isl_set *isl_set_partial_lexmax(
2644 __isl_take isl_set *set, __isl_take isl_set *dom,
2645 __isl_give isl_set **empty);
2647 Given a (basic) set C<set> (or C<bset>), the following functions simply
2648 return a set containing the lexicographic minimum or maximum
2649 of the elements in C<set> (or C<bset>).
2650 In case of union sets, the optimum is computed per space.
2652 __isl_give isl_set *isl_basic_set_lexmin(
2653 __isl_take isl_basic_set *bset);
2654 __isl_give isl_set *isl_basic_set_lexmax(
2655 __isl_take isl_basic_set *bset);
2656 __isl_give isl_set *isl_set_lexmin(
2657 __isl_take isl_set *set);
2658 __isl_give isl_set *isl_set_lexmax(
2659 __isl_take isl_set *set);
2660 __isl_give isl_union_set *isl_union_set_lexmin(
2661 __isl_take isl_union_set *uset);
2662 __isl_give isl_union_set *isl_union_set_lexmax(
2663 __isl_take isl_union_set *uset);
2665 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2666 the following functions
2667 compute a relation that maps each element of C<dom>
2668 to the single lexicographic minimum or maximum
2669 of the elements that are associated to that same
2670 element in C<map> (or C<bmap>).
2671 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2672 that contains the elements in C<dom> that do not map
2673 to any elements in C<map> (or C<bmap>).
2674 In other words, the union of the domain of the result and of C<*empty>
2677 __isl_give isl_map *isl_basic_map_partial_lexmax(
2678 __isl_take isl_basic_map *bmap,
2679 __isl_take isl_basic_set *dom,
2680 __isl_give isl_set **empty);
2681 __isl_give isl_map *isl_basic_map_partial_lexmin(
2682 __isl_take isl_basic_map *bmap,
2683 __isl_take isl_basic_set *dom,
2684 __isl_give isl_set **empty);
2685 __isl_give isl_map *isl_map_partial_lexmax(
2686 __isl_take isl_map *map, __isl_take isl_set *dom,
2687 __isl_give isl_set **empty);
2688 __isl_give isl_map *isl_map_partial_lexmin(
2689 __isl_take isl_map *map, __isl_take isl_set *dom,
2690 __isl_give isl_set **empty);
2692 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2693 return a map mapping each element in the domain of
2694 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2695 of all elements associated to that element.
2696 In case of union relations, the optimum is computed per space.
2698 __isl_give isl_map *isl_basic_map_lexmin(
2699 __isl_take isl_basic_map *bmap);
2700 __isl_give isl_map *isl_basic_map_lexmax(
2701 __isl_take isl_basic_map *bmap);
2702 __isl_give isl_map *isl_map_lexmin(
2703 __isl_take isl_map *map);
2704 __isl_give isl_map *isl_map_lexmax(
2705 __isl_take isl_map *map);
2706 __isl_give isl_union_map *isl_union_map_lexmin(
2707 __isl_take isl_union_map *umap);
2708 __isl_give isl_union_map *isl_union_map_lexmax(
2709 __isl_take isl_union_map *umap);
2711 The following functions return their result in the form of
2712 a piecewise multi-affine expression
2713 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2714 but are otherwise equivalent to the corresponding functions
2715 returning a basic set or relation.
2717 __isl_give isl_pw_multi_aff *
2718 isl_basic_map_lexmin_pw_multi_aff(
2719 __isl_take isl_basic_map *bmap);
2720 __isl_give isl_pw_multi_aff *
2721 isl_basic_set_partial_lexmin_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_set_partial_lexmax_pw_multi_aff(
2727 __isl_take isl_basic_set *bset,
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_lexmin_pw_multi_aff(
2732 __isl_take isl_basic_map *bmap,
2733 __isl_take isl_basic_set *dom,
2734 __isl_give isl_set **empty);
2735 __isl_give isl_pw_multi_aff *
2736 isl_basic_map_partial_lexmax_pw_multi_aff(
2737 __isl_take isl_basic_map *bmap,
2738 __isl_take isl_basic_set *dom,
2739 __isl_give isl_set **empty);
2743 Lists are defined over several element types, including
2744 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2745 Here we take lists of C<isl_set>s as an example.
2746 Lists can be created, copied and freed using the following functions.
2748 #include <isl/list.h>
2749 __isl_give isl_set_list *isl_set_list_from_set(
2750 __isl_take isl_set *el);
2751 __isl_give isl_set_list *isl_set_list_alloc(
2752 isl_ctx *ctx, int n);
2753 __isl_give isl_set_list *isl_set_list_copy(
2754 __isl_keep isl_set_list *list);
2755 __isl_give isl_set_list *isl_set_list_add(
2756 __isl_take isl_set_list *list,
2757 __isl_take isl_set *el);
2758 __isl_give isl_set_list *isl_set_list_concat(
2759 __isl_take isl_set_list *list1,
2760 __isl_take isl_set_list *list2);
2761 void *isl_set_list_free(__isl_take isl_set_list *list);
2763 C<isl_set_list_alloc> creates an empty list with a capacity for
2764 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2767 Lists can be inspected using the following functions.
2769 #include <isl/list.h>
2770 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2771 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2772 __isl_give isl_set *isl_set_list_get_set(
2773 __isl_keep isl_set_list *list, int index);
2774 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2775 int (*fn)(__isl_take isl_set *el, void *user),
2778 Lists can be printed using
2780 #include <isl/list.h>
2781 __isl_give isl_printer *isl_printer_print_set_list(
2782 __isl_take isl_printer *p,
2783 __isl_keep isl_set_list *list);
2787 Vectors can be created, copied and freed using the following functions.
2789 #include <isl/vec.h>
2790 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2792 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2793 void isl_vec_free(__isl_take isl_vec *vec);
2795 Note that the elements of a newly created vector may have arbitrary values.
2796 The elements can be changed and inspected using the following functions.
2798 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2799 int isl_vec_size(__isl_keep isl_vec *vec);
2800 int isl_vec_get_element(__isl_keep isl_vec *vec,
2801 int pos, isl_int *v);
2802 __isl_give isl_vec *isl_vec_set_element(
2803 __isl_take isl_vec *vec, int pos, isl_int v);
2804 __isl_give isl_vec *isl_vec_set_element_si(
2805 __isl_take isl_vec *vec, int pos, int v);
2806 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2808 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2811 C<isl_vec_get_element> will return a negative value if anything went wrong.
2812 In that case, the value of C<*v> is undefined.
2816 Matrices can be created, copied and freed using the following functions.
2818 #include <isl/mat.h>
2819 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2820 unsigned n_row, unsigned n_col);
2821 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2822 void isl_mat_free(__isl_take isl_mat *mat);
2824 Note that the elements of a newly created matrix may have arbitrary values.
2825 The elements can be changed and inspected using the following functions.
2827 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2828 int isl_mat_rows(__isl_keep isl_mat *mat);
2829 int isl_mat_cols(__isl_keep isl_mat *mat);
2830 int isl_mat_get_element(__isl_keep isl_mat *mat,
2831 int row, int col, isl_int *v);
2832 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2833 int row, int col, isl_int v);
2834 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2835 int row, int col, int v);
2837 C<isl_mat_get_element> will return a negative value if anything went wrong.
2838 In that case, the value of C<*v> is undefined.
2840 The following function can be used to compute the (right) inverse
2841 of a matrix, i.e., a matrix such that the product of the original
2842 and the inverse (in that order) is a multiple of the identity matrix.
2843 The input matrix is assumed to be of full row-rank.
2845 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2847 The following function can be used to compute the (right) kernel
2848 (or null space) of a matrix, i.e., a matrix such that the product of
2849 the original and the kernel (in that order) is the zero matrix.
2851 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2853 =head2 Piecewise Quasi Affine Expressions
2855 The zero quasi affine expression on a given domain can be created using
2857 __isl_give isl_aff *isl_aff_zero_on_domain(
2858 __isl_take isl_local_space *ls);
2860 Note that the space in which the resulting object lives is a map space
2861 with the given space as domain and a one-dimensional range.
2863 An empty piecewise quasi affine expression (one with no cells)
2864 or a piecewise quasi affine expression with a single cell can
2865 be created using the following functions.
2867 #include <isl/aff.h>
2868 __isl_give isl_pw_aff *isl_pw_aff_empty(
2869 __isl_take isl_space *space);
2870 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2871 __isl_take isl_set *set, __isl_take isl_aff *aff);
2872 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2873 __isl_take isl_aff *aff);
2875 A piecewise quasi affine expression that is equal to 1 on a set
2876 and 0 outside the set can be created using the following function.
2878 #include <isl/aff.h>
2879 __isl_give isl_pw_aff *isl_set_indicator_function(
2880 __isl_take isl_set *set);
2882 Quasi affine expressions can be copied and freed using
2884 #include <isl/aff.h>
2885 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2886 void *isl_aff_free(__isl_take isl_aff *aff);
2888 __isl_give isl_pw_aff *isl_pw_aff_copy(
2889 __isl_keep isl_pw_aff *pwaff);
2890 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2892 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2893 using the following function. The constraint is required to have
2894 a non-zero coefficient for the specified dimension.
2896 #include <isl/constraint.h>
2897 __isl_give isl_aff *isl_constraint_get_bound(
2898 __isl_keep isl_constraint *constraint,
2899 enum isl_dim_type type, int pos);
2901 The entire affine expression of the constraint can also be extracted
2902 using the following function.
2904 #include <isl/constraint.h>
2905 __isl_give isl_aff *isl_constraint_get_aff(
2906 __isl_keep isl_constraint *constraint);
2908 Conversely, an equality constraint equating
2909 the affine expression to zero or an inequality constraint enforcing
2910 the affine expression to be non-negative, can be constructed using
2912 __isl_give isl_constraint *isl_equality_from_aff(
2913 __isl_take isl_aff *aff);
2914 __isl_give isl_constraint *isl_inequality_from_aff(
2915 __isl_take isl_aff *aff);
2917 The expression can be inspected using
2919 #include <isl/aff.h>
2920 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2921 int isl_aff_dim(__isl_keep isl_aff *aff,
2922 enum isl_dim_type type);
2923 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2924 __isl_keep isl_aff *aff);
2925 __isl_give isl_local_space *isl_aff_get_local_space(
2926 __isl_keep isl_aff *aff);
2927 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2928 enum isl_dim_type type, unsigned pos);
2929 const char *isl_pw_aff_get_dim_name(
2930 __isl_keep isl_pw_aff *pa,
2931 enum isl_dim_type type, unsigned pos);
2932 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2933 enum isl_dim_type type, unsigned pos);
2934 __isl_give isl_id *isl_pw_aff_get_dim_id(
2935 __isl_keep isl_pw_aff *pa,
2936 enum isl_dim_type type, unsigned pos);
2937 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2939 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2940 enum isl_dim_type type, int pos, isl_int *v);
2941 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2943 __isl_give isl_aff *isl_aff_get_div(
2944 __isl_keep isl_aff *aff, int pos);
2946 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2947 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2948 int (*fn)(__isl_take isl_set *set,
2949 __isl_take isl_aff *aff,
2950 void *user), void *user);
2952 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2953 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2955 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2956 enum isl_dim_type type, unsigned first, unsigned n);
2957 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2958 enum isl_dim_type type, unsigned first, unsigned n);
2960 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2961 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2962 enum isl_dim_type type);
2963 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2965 It can be modified using
2967 #include <isl/aff.h>
2968 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2969 __isl_take isl_pw_aff *pwaff,
2970 enum isl_dim_type type, __isl_take isl_id *id);
2971 __isl_give isl_aff *isl_aff_set_dim_name(
2972 __isl_take isl_aff *aff, enum isl_dim_type type,
2973 unsigned pos, const char *s);
2974 __isl_give isl_aff *isl_aff_set_dim_id(
2975 __isl_take isl_aff *aff, enum isl_dim_type type,
2976 unsigned pos, __isl_take isl_id *id);
2977 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2978 __isl_take isl_pw_aff *pma,
2979 enum isl_dim_type type, unsigned pos,
2980 __isl_take isl_id *id);
2981 __isl_give isl_aff *isl_aff_set_constant(
2982 __isl_take isl_aff *aff, isl_int v);
2983 __isl_give isl_aff *isl_aff_set_constant_si(
2984 __isl_take isl_aff *aff, int v);
2985 __isl_give isl_aff *isl_aff_set_coefficient(
2986 __isl_take isl_aff *aff,
2987 enum isl_dim_type type, int pos, isl_int v);
2988 __isl_give isl_aff *isl_aff_set_coefficient_si(
2989 __isl_take isl_aff *aff,
2990 enum isl_dim_type type, int pos, int v);
2991 __isl_give isl_aff *isl_aff_set_denominator(
2992 __isl_take isl_aff *aff, isl_int v);
2994 __isl_give isl_aff *isl_aff_add_constant(
2995 __isl_take isl_aff *aff, isl_int v);
2996 __isl_give isl_aff *isl_aff_add_constant_si(
2997 __isl_take isl_aff *aff, int v);
2998 __isl_give isl_aff *isl_aff_add_coefficient(
2999 __isl_take isl_aff *aff,
3000 enum isl_dim_type type, int pos, isl_int v);
3001 __isl_give isl_aff *isl_aff_add_coefficient_si(
3002 __isl_take isl_aff *aff,
3003 enum isl_dim_type type, int pos, int v);
3005 __isl_give isl_aff *isl_aff_insert_dims(
3006 __isl_take isl_aff *aff,
3007 enum isl_dim_type type, unsigned first, unsigned n);
3008 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3009 __isl_take isl_pw_aff *pwaff,
3010 enum isl_dim_type type, unsigned first, unsigned n);
3011 __isl_give isl_aff *isl_aff_add_dims(
3012 __isl_take isl_aff *aff,
3013 enum isl_dim_type type, unsigned n);
3014 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3015 __isl_take isl_pw_aff *pwaff,
3016 enum isl_dim_type type, unsigned n);
3017 __isl_give isl_aff *isl_aff_drop_dims(
3018 __isl_take isl_aff *aff,
3019 enum isl_dim_type type, unsigned first, unsigned n);
3020 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3021 __isl_take isl_pw_aff *pwaff,
3022 enum isl_dim_type type, unsigned first, unsigned n);
3024 Note that the C<set_constant> and C<set_coefficient> functions
3025 set the I<numerator> of the constant or coefficient, while
3026 C<add_constant> and C<add_coefficient> add an integer value to
3027 the possibly rational constant or coefficient.
3029 To check whether an affine expressions is obviously zero
3030 or obviously equal to some other affine expression, use
3032 #include <isl/aff.h>
3033 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3034 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3035 __isl_keep isl_aff *aff2);
3036 int isl_pw_aff_plain_is_equal(
3037 __isl_keep isl_pw_aff *pwaff1,
3038 __isl_keep isl_pw_aff *pwaff2);
3042 #include <isl/aff.h>
3043 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3044 __isl_take isl_aff *aff2);
3045 __isl_give isl_pw_aff *isl_pw_aff_add(
3046 __isl_take isl_pw_aff *pwaff1,
3047 __isl_take isl_pw_aff *pwaff2);
3048 __isl_give isl_pw_aff *isl_pw_aff_min(
3049 __isl_take isl_pw_aff *pwaff1,
3050 __isl_take isl_pw_aff *pwaff2);
3051 __isl_give isl_pw_aff *isl_pw_aff_max(
3052 __isl_take isl_pw_aff *pwaff1,
3053 __isl_take isl_pw_aff *pwaff2);
3054 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3055 __isl_take isl_aff *aff2);
3056 __isl_give isl_pw_aff *isl_pw_aff_sub(
3057 __isl_take isl_pw_aff *pwaff1,
3058 __isl_take isl_pw_aff *pwaff2);
3059 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3060 __isl_give isl_pw_aff *isl_pw_aff_neg(
3061 __isl_take isl_pw_aff *pwaff);
3062 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3063 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3064 __isl_take isl_pw_aff *pwaff);
3065 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3066 __isl_give isl_pw_aff *isl_pw_aff_floor(
3067 __isl_take isl_pw_aff *pwaff);
3068 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3070 __isl_give isl_pw_aff *isl_pw_aff_mod(
3071 __isl_take isl_pw_aff *pwaff, isl_int mod);
3072 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3074 __isl_give isl_pw_aff *isl_pw_aff_scale(
3075 __isl_take isl_pw_aff *pwaff, isl_int f);
3076 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3078 __isl_give isl_aff *isl_aff_scale_down_ui(
3079 __isl_take isl_aff *aff, unsigned f);
3080 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3081 __isl_take isl_pw_aff *pwaff, isl_int f);
3083 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3084 __isl_take isl_pw_aff_list *list);
3085 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3086 __isl_take isl_pw_aff_list *list);
3088 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3089 __isl_take isl_pw_aff *pwqp);
3091 __isl_give isl_aff *isl_aff_align_params(
3092 __isl_take isl_aff *aff,
3093 __isl_take isl_space *model);
3094 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3095 __isl_take isl_pw_aff *pwaff,
3096 __isl_take isl_space *model);
3098 __isl_give isl_aff *isl_aff_project_domain_on_params(
3099 __isl_take isl_aff *aff);
3101 __isl_give isl_aff *isl_aff_gist_params(
3102 __isl_take isl_aff *aff,
3103 __isl_take isl_set *context);
3104 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3105 __isl_take isl_set *context);
3106 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3107 __isl_take isl_pw_aff *pwaff,
3108 __isl_take isl_set *context);
3109 __isl_give isl_pw_aff *isl_pw_aff_gist(
3110 __isl_take isl_pw_aff *pwaff,
3111 __isl_take isl_set *context);
3113 __isl_give isl_set *isl_pw_aff_domain(
3114 __isl_take isl_pw_aff *pwaff);
3115 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3116 __isl_take isl_pw_aff *pa,
3117 __isl_take isl_set *set);
3118 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3119 __isl_take isl_pw_aff *pa,
3120 __isl_take isl_set *set);
3122 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3123 __isl_take isl_aff *aff2);
3124 __isl_give isl_pw_aff *isl_pw_aff_mul(
3125 __isl_take isl_pw_aff *pwaff1,
3126 __isl_take isl_pw_aff *pwaff2);
3128 When multiplying two affine expressions, at least one of the two needs
3131 #include <isl/aff.h>
3132 __isl_give isl_basic_set *isl_aff_le_basic_set(
3133 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3134 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3135 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3136 __isl_give isl_set *isl_pw_aff_eq_set(
3137 __isl_take isl_pw_aff *pwaff1,
3138 __isl_take isl_pw_aff *pwaff2);
3139 __isl_give isl_set *isl_pw_aff_ne_set(
3140 __isl_take isl_pw_aff *pwaff1,
3141 __isl_take isl_pw_aff *pwaff2);
3142 __isl_give isl_set *isl_pw_aff_le_set(
3143 __isl_take isl_pw_aff *pwaff1,
3144 __isl_take isl_pw_aff *pwaff2);
3145 __isl_give isl_set *isl_pw_aff_lt_set(
3146 __isl_take isl_pw_aff *pwaff1,
3147 __isl_take isl_pw_aff *pwaff2);
3148 __isl_give isl_set *isl_pw_aff_ge_set(
3149 __isl_take isl_pw_aff *pwaff1,
3150 __isl_take isl_pw_aff *pwaff2);
3151 __isl_give isl_set *isl_pw_aff_gt_set(
3152 __isl_take isl_pw_aff *pwaff1,
3153 __isl_take isl_pw_aff *pwaff2);
3155 __isl_give isl_set *isl_pw_aff_list_eq_set(
3156 __isl_take isl_pw_aff_list *list1,
3157 __isl_take isl_pw_aff_list *list2);
3158 __isl_give isl_set *isl_pw_aff_list_ne_set(
3159 __isl_take isl_pw_aff_list *list1,
3160 __isl_take isl_pw_aff_list *list2);
3161 __isl_give isl_set *isl_pw_aff_list_le_set(
3162 __isl_take isl_pw_aff_list *list1,
3163 __isl_take isl_pw_aff_list *list2);
3164 __isl_give isl_set *isl_pw_aff_list_lt_set(
3165 __isl_take isl_pw_aff_list *list1,
3166 __isl_take isl_pw_aff_list *list2);
3167 __isl_give isl_set *isl_pw_aff_list_ge_set(
3168 __isl_take isl_pw_aff_list *list1,
3169 __isl_take isl_pw_aff_list *list2);
3170 __isl_give isl_set *isl_pw_aff_list_gt_set(
3171 __isl_take isl_pw_aff_list *list1,
3172 __isl_take isl_pw_aff_list *list2);
3174 The function C<isl_aff_ge_basic_set> returns a basic set
3175 containing those elements in the shared space
3176 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3177 The function C<isl_aff_ge_set> returns a set
3178 containing those elements in the shared domain
3179 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3180 The functions operating on C<isl_pw_aff_list> apply the corresponding
3181 C<isl_pw_aff> function to each pair of elements in the two lists.
3183 #include <isl/aff.h>
3184 __isl_give isl_set *isl_pw_aff_nonneg_set(
3185 __isl_take isl_pw_aff *pwaff);
3186 __isl_give isl_set *isl_pw_aff_zero_set(
3187 __isl_take isl_pw_aff *pwaff);
3188 __isl_give isl_set *isl_pw_aff_non_zero_set(
3189 __isl_take isl_pw_aff *pwaff);
3191 The function C<isl_pw_aff_nonneg_set> returns a set
3192 containing those elements in the domain
3193 of C<pwaff> where C<pwaff> is non-negative.
3195 #include <isl/aff.h>
3196 __isl_give isl_pw_aff *isl_pw_aff_cond(
3197 __isl_take isl_pw_aff *cond,
3198 __isl_take isl_pw_aff *pwaff_true,
3199 __isl_take isl_pw_aff *pwaff_false);
3201 The function C<isl_pw_aff_cond> performs a conditional operator
3202 and returns an expression that is equal to C<pwaff_true>
3203 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3204 where C<cond> is zero.
3206 #include <isl/aff.h>
3207 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3208 __isl_take isl_pw_aff *pwaff1,
3209 __isl_take isl_pw_aff *pwaff2);
3210 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3211 __isl_take isl_pw_aff *pwaff1,
3212 __isl_take isl_pw_aff *pwaff2);
3213 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3214 __isl_take isl_pw_aff *pwaff1,
3215 __isl_take isl_pw_aff *pwaff2);
3217 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3218 expression with a domain that is the union of those of C<pwaff1> and
3219 C<pwaff2> and such that on each cell, the quasi-affine expression is
3220 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3221 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3222 associated expression is the defined one.
3224 An expression can be read from input using
3226 #include <isl/aff.h>
3227 __isl_give isl_aff *isl_aff_read_from_str(
3228 isl_ctx *ctx, const char *str);
3229 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3230 isl_ctx *ctx, const char *str);
3232 An expression can be printed using
3234 #include <isl/aff.h>
3235 __isl_give isl_printer *isl_printer_print_aff(
3236 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3238 __isl_give isl_printer *isl_printer_print_pw_aff(
3239 __isl_take isl_printer *p,
3240 __isl_keep isl_pw_aff *pwaff);
3242 =head2 Piecewise Multiple Quasi Affine Expressions
3244 An C<isl_multi_aff> object represents a sequence of
3245 zero or more affine expressions, all defined on the same domain space.
3247 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3250 #include <isl/aff.h>
3251 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3252 __isl_take isl_space *space,
3253 __isl_take isl_aff_list *list);
3255 An empty piecewise multiple quasi affine expression (one with no cells),
3256 the zero piecewise multiple quasi affine expression (with value zero
3257 for each output dimension),
3258 a piecewise multiple quasi affine expression with a single cell (with
3259 either a universe or a specified domain) or
3260 a zero-dimensional piecewise multiple quasi affine expression
3262 can be created using the following functions.
3264 #include <isl/aff.h>
3265 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3266 __isl_take isl_space *space);
3267 __isl_give isl_multi_aff *isl_multi_aff_zero(
3268 __isl_take isl_space *space);
3269 __isl_give isl_pw_multi_aff *
3270 isl_pw_multi_aff_from_multi_aff(
3271 __isl_take isl_multi_aff *ma);
3272 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3273 __isl_take isl_set *set,
3274 __isl_take isl_multi_aff *maff);
3275 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3276 __isl_take isl_set *set);
3278 __isl_give isl_union_pw_multi_aff *
3279 isl_union_pw_multi_aff_empty(
3280 __isl_take isl_space *space);
3281 __isl_give isl_union_pw_multi_aff *
3282 isl_union_pw_multi_aff_add_pw_multi_aff(
3283 __isl_take isl_union_pw_multi_aff *upma,
3284 __isl_take isl_pw_multi_aff *pma);
3285 __isl_give isl_union_pw_multi_aff *
3286 isl_union_pw_multi_aff_from_domain(
3287 __isl_take isl_union_set *uset);
3289 A piecewise multiple quasi affine expression can also be initialized
3290 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3291 and the C<isl_map> is single-valued.
3293 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3294 __isl_take isl_set *set);
3295 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3296 __isl_take isl_map *map);
3298 Multiple quasi affine expressions can be copied and freed using
3300 #include <isl/aff.h>
3301 __isl_give isl_multi_aff *isl_multi_aff_copy(
3302 __isl_keep isl_multi_aff *maff);
3303 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3305 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3306 __isl_keep isl_pw_multi_aff *pma);
3307 void *isl_pw_multi_aff_free(
3308 __isl_take isl_pw_multi_aff *pma);
3310 __isl_give isl_union_pw_multi_aff *
3311 isl_union_pw_multi_aff_copy(
3312 __isl_keep isl_union_pw_multi_aff *upma);
3313 void *isl_union_pw_multi_aff_free(
3314 __isl_take isl_union_pw_multi_aff *upma);
3316 The expression can be inspected using
3318 #include <isl/aff.h>
3319 isl_ctx *isl_multi_aff_get_ctx(
3320 __isl_keep isl_multi_aff *maff);
3321 isl_ctx *isl_pw_multi_aff_get_ctx(
3322 __isl_keep isl_pw_multi_aff *pma);
3323 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3324 __isl_keep isl_union_pw_multi_aff *upma);
3325 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3326 enum isl_dim_type type);
3327 unsigned isl_pw_multi_aff_dim(
3328 __isl_keep isl_pw_multi_aff *pma,
3329 enum isl_dim_type type);
3330 __isl_give isl_aff *isl_multi_aff_get_aff(
3331 __isl_keep isl_multi_aff *multi, int pos);
3332 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3333 __isl_keep isl_pw_multi_aff *pma, int pos);
3334 const char *isl_pw_multi_aff_get_dim_name(
3335 __isl_keep isl_pw_multi_aff *pma,
3336 enum isl_dim_type type, unsigned pos);
3337 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3338 __isl_keep isl_pw_multi_aff *pma,
3339 enum isl_dim_type type, unsigned pos);
3340 const char *isl_multi_aff_get_tuple_name(
3341 __isl_keep isl_multi_aff *multi,
3342 enum isl_dim_type type);
3343 const char *isl_pw_multi_aff_get_tuple_name(
3344 __isl_keep isl_pw_multi_aff *pma,
3345 enum isl_dim_type type);
3346 int isl_pw_multi_aff_has_tuple_id(
3347 __isl_keep isl_pw_multi_aff *pma,
3348 enum isl_dim_type type);
3349 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3350 __isl_keep isl_pw_multi_aff *pma,
3351 enum isl_dim_type type);
3353 int isl_pw_multi_aff_foreach_piece(
3354 __isl_keep isl_pw_multi_aff *pma,
3355 int (*fn)(__isl_take isl_set *set,
3356 __isl_take isl_multi_aff *maff,
3357 void *user), void *user);
3359 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3360 __isl_keep isl_union_pw_multi_aff *upma,
3361 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3362 void *user), void *user);
3364 It can be modified using
3366 #include <isl/aff.h>
3367 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3368 __isl_take isl_multi_aff *multi, int pos,
3369 __isl_take isl_aff *aff);
3370 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3371 __isl_take isl_multi_aff *maff,
3372 enum isl_dim_type type, unsigned pos, const char *s);
3373 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3374 __isl_take isl_multi_aff *maff,
3375 enum isl_dim_type type, __isl_take isl_id *id);
3376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3377 __isl_take isl_pw_multi_aff *pma,
3378 enum isl_dim_type type, __isl_take isl_id *id);
3380 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3381 __isl_take isl_multi_aff *maff,
3382 enum isl_dim_type type, unsigned first, unsigned n);
3384 To check whether two multiple affine expressions are
3385 obviously equal to each other, use
3387 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3388 __isl_keep isl_multi_aff *maff2);
3389 int isl_pw_multi_aff_plain_is_equal(
3390 __isl_keep isl_pw_multi_aff *pma1,
3391 __isl_keep isl_pw_multi_aff *pma2);
3395 #include <isl/aff.h>
3396 __isl_give isl_multi_aff *isl_multi_aff_add(
3397 __isl_take isl_multi_aff *maff1,
3398 __isl_take isl_multi_aff *maff2);
3399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3400 __isl_take isl_pw_multi_aff *pma1,
3401 __isl_take isl_pw_multi_aff *pma2);
3402 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3403 __isl_take isl_union_pw_multi_aff *upma1,
3404 __isl_take isl_union_pw_multi_aff *upma2);
3405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3406 __isl_take isl_pw_multi_aff *pma1,
3407 __isl_take isl_pw_multi_aff *pma2);
3408 __isl_give isl_multi_aff *isl_multi_aff_scale(
3409 __isl_take isl_multi_aff *maff,
3411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3412 __isl_take isl_pw_multi_aff *pma,
3413 __isl_take isl_set *set);
3414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3415 __isl_take isl_pw_multi_aff *pma,
3416 __isl_take isl_set *set);
3417 __isl_give isl_multi_aff *isl_multi_aff_lift(
3418 __isl_take isl_multi_aff *maff,
3419 __isl_give isl_local_space **ls);
3420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3421 __isl_take isl_pw_multi_aff *pma);
3422 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3423 __isl_take isl_multi_aff *maff,
3424 __isl_take isl_set *context);
3425 __isl_give isl_multi_aff *isl_multi_aff_gist(
3426 __isl_take isl_multi_aff *maff,
3427 __isl_take isl_set *context);
3428 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3429 __isl_take isl_pw_multi_aff *pma,
3430 __isl_take isl_set *set);
3431 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3432 __isl_take isl_pw_multi_aff *pma,
3433 __isl_take isl_set *set);
3434 __isl_give isl_set *isl_pw_multi_aff_domain(
3435 __isl_take isl_pw_multi_aff *pma);
3436 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3437 __isl_take isl_union_pw_multi_aff *upma);
3438 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3439 __isl_take isl_multi_aff *ma1,
3440 __isl_take isl_multi_aff *ma2);
3441 __isl_give isl_pw_multi_aff *
3442 isl_pw_multi_aff_flat_range_product(
3443 __isl_take isl_pw_multi_aff *pma1,
3444 __isl_take isl_pw_multi_aff *pma2);
3445 __isl_give isl_union_pw_multi_aff *
3446 isl_union_pw_multi_aff_flat_range_product(
3447 __isl_take isl_union_pw_multi_aff *upma1,
3448 __isl_take isl_union_pw_multi_aff *upma2);
3450 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3451 then it is assigned the local space that lies at the basis of
3452 the lifting applied.
3454 An expression can be read from input using
3456 #include <isl/aff.h>
3457 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3458 isl_ctx *ctx, const char *str);
3459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3460 isl_ctx *ctx, const char *str);
3462 An expression can be printed using
3464 #include <isl/aff.h>
3465 __isl_give isl_printer *isl_printer_print_multi_aff(
3466 __isl_take isl_printer *p,
3467 __isl_keep isl_multi_aff *maff);
3468 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3469 __isl_take isl_printer *p,
3470 __isl_keep isl_pw_multi_aff *pma);
3471 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3472 __isl_take isl_printer *p,
3473 __isl_keep isl_union_pw_multi_aff *upma);
3477 Points are elements of a set. They can be used to construct
3478 simple sets (boxes) or they can be used to represent the
3479 individual elements of a set.
3480 The zero point (the origin) can be created using
3482 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3484 The coordinates of a point can be inspected, set and changed
3487 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3488 enum isl_dim_type type, int pos, isl_int *v);
3489 __isl_give isl_point *isl_point_set_coordinate(
3490 __isl_take isl_point *pnt,
3491 enum isl_dim_type type, int pos, isl_int v);
3493 __isl_give isl_point *isl_point_add_ui(
3494 __isl_take isl_point *pnt,
3495 enum isl_dim_type type, int pos, unsigned val);
3496 __isl_give isl_point *isl_point_sub_ui(
3497 __isl_take isl_point *pnt,
3498 enum isl_dim_type type, int pos, unsigned val);
3500 Other properties can be obtained using
3502 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3504 Points can be copied or freed using
3506 __isl_give isl_point *isl_point_copy(
3507 __isl_keep isl_point *pnt);
3508 void isl_point_free(__isl_take isl_point *pnt);
3510 A singleton set can be created from a point using
3512 __isl_give isl_basic_set *isl_basic_set_from_point(
3513 __isl_take isl_point *pnt);
3514 __isl_give isl_set *isl_set_from_point(
3515 __isl_take isl_point *pnt);
3517 and a box can be created from two opposite extremal points using
3519 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3520 __isl_take isl_point *pnt1,
3521 __isl_take isl_point *pnt2);
3522 __isl_give isl_set *isl_set_box_from_points(
3523 __isl_take isl_point *pnt1,
3524 __isl_take isl_point *pnt2);
3526 All elements of a B<bounded> (union) set can be enumerated using
3527 the following functions.
3529 int isl_set_foreach_point(__isl_keep isl_set *set,
3530 int (*fn)(__isl_take isl_point *pnt, void *user),
3532 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3533 int (*fn)(__isl_take isl_point *pnt, void *user),
3536 The function C<fn> is called for each integer point in
3537 C<set> with as second argument the last argument of
3538 the C<isl_set_foreach_point> call. The function C<fn>
3539 should return C<0> on success and C<-1> on failure.
3540 In the latter case, C<isl_set_foreach_point> will stop
3541 enumerating and return C<-1> as well.
3542 If the enumeration is performed successfully and to completion,
3543 then C<isl_set_foreach_point> returns C<0>.
3545 To obtain a single point of a (basic) set, use
3547 __isl_give isl_point *isl_basic_set_sample_point(
3548 __isl_take isl_basic_set *bset);
3549 __isl_give isl_point *isl_set_sample_point(
3550 __isl_take isl_set *set);
3552 If C<set> does not contain any (integer) points, then the
3553 resulting point will be ``void'', a property that can be
3556 int isl_point_is_void(__isl_keep isl_point *pnt);
3558 =head2 Piecewise Quasipolynomials
3560 A piecewise quasipolynomial is a particular kind of function that maps
3561 a parametric point to a rational value.
3562 More specifically, a quasipolynomial is a polynomial expression in greatest
3563 integer parts of affine expressions of parameters and variables.
3564 A piecewise quasipolynomial is a subdivision of a given parametric
3565 domain into disjoint cells with a quasipolynomial associated to
3566 each cell. The value of the piecewise quasipolynomial at a given
3567 point is the value of the quasipolynomial associated to the cell
3568 that contains the point. Outside of the union of cells,
3569 the value is assumed to be zero.
3570 For example, the piecewise quasipolynomial
3572 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3574 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3575 A given piecewise quasipolynomial has a fixed domain dimension.
3576 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3577 defined over different domains.
3578 Piecewise quasipolynomials are mainly used by the C<barvinok>
3579 library for representing the number of elements in a parametric set or map.
3580 For example, the piecewise quasipolynomial above represents
3581 the number of points in the map
3583 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3585 =head3 Input and Output
3587 Piecewise quasipolynomials can be read from input using
3589 __isl_give isl_union_pw_qpolynomial *
3590 isl_union_pw_qpolynomial_read_from_str(
3591 isl_ctx *ctx, const char *str);
3593 Quasipolynomials and piecewise quasipolynomials can be printed
3594 using the following functions.
3596 __isl_give isl_printer *isl_printer_print_qpolynomial(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_qpolynomial *qp);
3600 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3601 __isl_take isl_printer *p,
3602 __isl_keep isl_pw_qpolynomial *pwqp);
3604 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3605 __isl_take isl_printer *p,
3606 __isl_keep isl_union_pw_qpolynomial *upwqp);
3608 The output format of the printer
3609 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3610 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3612 In case of printing in C<ISL_FORMAT_C>, the user may want
3613 to set the names of all dimensions
3615 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3616 __isl_take isl_qpolynomial *qp,
3617 enum isl_dim_type type, unsigned pos,
3619 __isl_give isl_pw_qpolynomial *
3620 isl_pw_qpolynomial_set_dim_name(
3621 __isl_take isl_pw_qpolynomial *pwqp,
3622 enum isl_dim_type type, unsigned pos,
3625 =head3 Creating New (Piecewise) Quasipolynomials
3627 Some simple quasipolynomials can be created using the following functions.
3628 More complicated quasipolynomials can be created by applying
3629 operations such as addition and multiplication
3630 on the resulting quasipolynomials
3632 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3633 __isl_take isl_space *domain);
3634 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3635 __isl_take isl_space *domain);
3636 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3637 __isl_take isl_space *domain);
3638 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3639 __isl_take isl_space *domain);
3640 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3641 __isl_take isl_space *domain);
3642 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3643 __isl_take isl_space *domain,
3644 const isl_int n, const isl_int d);
3645 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3646 __isl_take isl_space *domain,
3647 enum isl_dim_type type, unsigned pos);
3648 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3649 __isl_take isl_aff *aff);
3651 Note that the space in which a quasipolynomial lives is a map space
3652 with a one-dimensional range. The C<domain> argument in some of
3653 the functions above corresponds to the domain of this map space.
3655 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3656 with a single cell can be created using the following functions.
3657 Multiple of these single cell piecewise quasipolynomials can
3658 be combined to create more complicated piecewise quasipolynomials.
3660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3661 __isl_take isl_space *space);
3662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3663 __isl_take isl_set *set,
3664 __isl_take isl_qpolynomial *qp);
3665 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3666 __isl_take isl_qpolynomial *qp);
3667 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3668 __isl_take isl_pw_aff *pwaff);
3670 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3671 __isl_take isl_space *space);
3672 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3673 __isl_take isl_pw_qpolynomial *pwqp);
3674 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3675 __isl_take isl_union_pw_qpolynomial *upwqp,
3676 __isl_take isl_pw_qpolynomial *pwqp);
3678 Quasipolynomials can be copied and freed again using the following
3681 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3682 __isl_keep isl_qpolynomial *qp);
3683 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3685 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3686 __isl_keep isl_pw_qpolynomial *pwqp);
3687 void *isl_pw_qpolynomial_free(
3688 __isl_take isl_pw_qpolynomial *pwqp);
3690 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3691 __isl_keep isl_union_pw_qpolynomial *upwqp);
3692 void *isl_union_pw_qpolynomial_free(
3693 __isl_take isl_union_pw_qpolynomial *upwqp);
3695 =head3 Inspecting (Piecewise) Quasipolynomials
3697 To iterate over all piecewise quasipolynomials in a union
3698 piecewise quasipolynomial, use the following function
3700 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3701 __isl_keep isl_union_pw_qpolynomial *upwqp,
3702 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3705 To extract the piecewise quasipolynomial in a given space from a union, use
3707 __isl_give isl_pw_qpolynomial *
3708 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3709 __isl_keep isl_union_pw_qpolynomial *upwqp,
3710 __isl_take isl_space *space);
3712 To iterate over the cells in a piecewise quasipolynomial,
3713 use either of the following two functions
3715 int isl_pw_qpolynomial_foreach_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);
3720 int isl_pw_qpolynomial_foreach_lifted_piece(
3721 __isl_keep isl_pw_qpolynomial *pwqp,
3722 int (*fn)(__isl_take isl_set *set,
3723 __isl_take isl_qpolynomial *qp,
3724 void *user), void *user);
3726 As usual, the function C<fn> should return C<0> on success
3727 and C<-1> on failure. The difference between
3728 C<isl_pw_qpolynomial_foreach_piece> and
3729 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3730 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3731 compute unique representations for all existentially quantified
3732 variables and then turn these existentially quantified variables
3733 into extra set variables, adapting the associated quasipolynomial
3734 accordingly. This means that the C<set> passed to C<fn>
3735 will not have any existentially quantified variables, but that
3736 the dimensions of the sets may be different for different
3737 invocations of C<fn>.
3739 To iterate over all terms in a quasipolynomial,
3742 int isl_qpolynomial_foreach_term(
3743 __isl_keep isl_qpolynomial *qp,
3744 int (*fn)(__isl_take isl_term *term,
3745 void *user), void *user);
3747 The terms themselves can be inspected and freed using
3750 unsigned isl_term_dim(__isl_keep isl_term *term,
3751 enum isl_dim_type type);
3752 void isl_term_get_num(__isl_keep isl_term *term,
3754 void isl_term_get_den(__isl_keep isl_term *term,
3756 int isl_term_get_exp(__isl_keep isl_term *term,
3757 enum isl_dim_type type, unsigned pos);
3758 __isl_give isl_aff *isl_term_get_div(
3759 __isl_keep isl_term *term, unsigned pos);
3760 void isl_term_free(__isl_take isl_term *term);
3762 Each term is a product of parameters, set variables and
3763 integer divisions. The function C<isl_term_get_exp>
3764 returns the exponent of a given dimensions in the given term.
3765 The C<isl_int>s in the arguments of C<isl_term_get_num>
3766 and C<isl_term_get_den> need to have been initialized
3767 using C<isl_int_init> before calling these functions.
3769 =head3 Properties of (Piecewise) Quasipolynomials
3771 To check whether a quasipolynomial is actually a constant,
3772 use the following function.
3774 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3775 isl_int *n, isl_int *d);
3777 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3778 then the numerator and denominator of the constant
3779 are returned in C<*n> and C<*d>, respectively.
3781 To check whether two union piecewise quasipolynomials are
3782 obviously equal, use
3784 int isl_union_pw_qpolynomial_plain_is_equal(
3785 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3786 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3788 =head3 Operations on (Piecewise) Quasipolynomials
3790 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3791 __isl_take isl_qpolynomial *qp, isl_int v);
3792 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3793 __isl_take isl_qpolynomial *qp);
3794 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3795 __isl_take isl_qpolynomial *qp1,
3796 __isl_take isl_qpolynomial *qp2);
3797 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3798 __isl_take isl_qpolynomial *qp1,
3799 __isl_take isl_qpolynomial *qp2);
3800 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3801 __isl_take isl_qpolynomial *qp1,
3802 __isl_take isl_qpolynomial *qp2);
3803 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3804 __isl_take isl_qpolynomial *qp, unsigned exponent);
3806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3807 __isl_take isl_pw_qpolynomial *pwqp1,
3808 __isl_take isl_pw_qpolynomial *pwqp2);
3809 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3810 __isl_take isl_pw_qpolynomial *pwqp1,
3811 __isl_take isl_pw_qpolynomial *pwqp2);
3812 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3813 __isl_take isl_pw_qpolynomial *pwqp1,
3814 __isl_take isl_pw_qpolynomial *pwqp2);
3815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3816 __isl_take isl_pw_qpolynomial *pwqp);
3817 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3818 __isl_take isl_pw_qpolynomial *pwqp1,
3819 __isl_take isl_pw_qpolynomial *pwqp2);
3820 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3821 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3823 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3824 __isl_take isl_union_pw_qpolynomial *upwqp1,
3825 __isl_take isl_union_pw_qpolynomial *upwqp2);
3826 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3827 __isl_take isl_union_pw_qpolynomial *upwqp1,
3828 __isl_take isl_union_pw_qpolynomial *upwqp2);
3829 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3830 __isl_take isl_union_pw_qpolynomial *upwqp1,
3831 __isl_take isl_union_pw_qpolynomial *upwqp2);
3833 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3834 __isl_take isl_pw_qpolynomial *pwqp,
3835 __isl_take isl_point *pnt);
3837 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3838 __isl_take isl_union_pw_qpolynomial *upwqp,
3839 __isl_take isl_point *pnt);
3841 __isl_give isl_set *isl_pw_qpolynomial_domain(
3842 __isl_take isl_pw_qpolynomial *pwqp);
3843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3844 __isl_take isl_pw_qpolynomial *pwpq,
3845 __isl_take isl_set *set);
3846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3847 __isl_take isl_pw_qpolynomial *pwpq,
3848 __isl_take isl_set *set);
3850 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3851 __isl_take isl_union_pw_qpolynomial *upwqp);
3852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3853 __isl_take isl_union_pw_qpolynomial *upwpq,
3854 __isl_take isl_union_set *uset);
3855 __isl_give isl_union_pw_qpolynomial *
3856 isl_union_pw_qpolynomial_intersect_params(
3857 __isl_take isl_union_pw_qpolynomial *upwpq,
3858 __isl_take isl_set *set);
3860 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3861 __isl_take isl_qpolynomial *qp,
3862 __isl_take isl_space *model);
3864 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3865 __isl_take isl_qpolynomial *qp);
3866 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3867 __isl_take isl_pw_qpolynomial *pwqp);
3869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3870 __isl_take isl_union_pw_qpolynomial *upwqp);
3872 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3873 __isl_take isl_qpolynomial *qp,
3874 __isl_take isl_set *context);
3875 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3876 __isl_take isl_qpolynomial *qp,
3877 __isl_take isl_set *context);
3879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3880 __isl_take isl_pw_qpolynomial *pwqp,
3881 __isl_take isl_set *context);
3882 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3883 __isl_take isl_pw_qpolynomial *pwqp,
3884 __isl_take isl_set *context);
3886 __isl_give isl_union_pw_qpolynomial *
3887 isl_union_pw_qpolynomial_gist_params(
3888 __isl_take isl_union_pw_qpolynomial *upwqp,
3889 __isl_take isl_set *context);
3890 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3891 __isl_take isl_union_pw_qpolynomial *upwqp,
3892 __isl_take isl_union_set *context);
3894 The gist operation applies the gist operation to each of
3895 the cells in the domain of the input piecewise quasipolynomial.
3896 The context is also exploited
3897 to simplify the quasipolynomials associated to each cell.
3899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3900 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3901 __isl_give isl_union_pw_qpolynomial *
3902 isl_union_pw_qpolynomial_to_polynomial(
3903 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3905 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3906 the polynomial will be an overapproximation. If C<sign> is negative,
3907 it will be an underapproximation. If C<sign> is zero, the approximation
3908 will lie somewhere in between.
3910 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3912 A piecewise quasipolynomial reduction is a piecewise
3913 reduction (or fold) of quasipolynomials.
3914 In particular, the reduction can be maximum or a minimum.
3915 The objects are mainly used to represent the result of
3916 an upper or lower bound on a quasipolynomial over its domain,
3917 i.e., as the result of the following function.
3919 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3920 __isl_take isl_pw_qpolynomial *pwqp,
3921 enum isl_fold type, int *tight);
3923 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3924 __isl_take isl_union_pw_qpolynomial *upwqp,
3925 enum isl_fold type, int *tight);
3927 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3928 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3929 is the returned bound is known be tight, i.e., for each value
3930 of the parameters there is at least
3931 one element in the domain that reaches the bound.
3932 If the domain of C<pwqp> is not wrapping, then the bound is computed
3933 over all elements in that domain and the result has a purely parametric
3934 domain. If the domain of C<pwqp> is wrapping, then the bound is
3935 computed over the range of the wrapped relation. The domain of the
3936 wrapped relation becomes the domain of the result.
3938 A (piecewise) quasipolynomial reduction can be copied or freed using the
3939 following functions.
3941 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3942 __isl_keep isl_qpolynomial_fold *fold);
3943 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3944 __isl_keep isl_pw_qpolynomial_fold *pwf);
3945 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3946 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3947 void isl_qpolynomial_fold_free(
3948 __isl_take isl_qpolynomial_fold *fold);
3949 void *isl_pw_qpolynomial_fold_free(
3950 __isl_take isl_pw_qpolynomial_fold *pwf);
3951 void *isl_union_pw_qpolynomial_fold_free(
3952 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3954 =head3 Printing Piecewise Quasipolynomial Reductions
3956 Piecewise quasipolynomial reductions can be printed
3957 using the following function.
3959 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3960 __isl_take isl_printer *p,
3961 __isl_keep isl_pw_qpolynomial_fold *pwf);
3962 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3963 __isl_take isl_printer *p,
3964 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3966 For C<isl_printer_print_pw_qpolynomial_fold>,
3967 output format of the printer
3968 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3969 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3970 output format of the printer
3971 needs to be set to C<ISL_FORMAT_ISL>.
3972 In case of printing in C<ISL_FORMAT_C>, the user may want
3973 to set the names of all dimensions
3975 __isl_give isl_pw_qpolynomial_fold *
3976 isl_pw_qpolynomial_fold_set_dim_name(
3977 __isl_take isl_pw_qpolynomial_fold *pwf,
3978 enum isl_dim_type type, unsigned pos,
3981 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3983 To iterate over all piecewise quasipolynomial reductions in a union
3984 piecewise quasipolynomial reduction, use the following function
3986 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3987 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3988 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3989 void *user), void *user);
3991 To iterate over the cells in a piecewise quasipolynomial reduction,
3992 use either of the following two functions
3994 int isl_pw_qpolynomial_fold_foreach_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);
3999 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4000 __isl_keep isl_pw_qpolynomial_fold *pwf,
4001 int (*fn)(__isl_take isl_set *set,
4002 __isl_take isl_qpolynomial_fold *fold,
4003 void *user), void *user);
4005 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4006 of the difference between these two functions.
4008 To iterate over all quasipolynomials in a reduction, use
4010 int isl_qpolynomial_fold_foreach_qpolynomial(
4011 __isl_keep isl_qpolynomial_fold *fold,
4012 int (*fn)(__isl_take isl_qpolynomial *qp,
4013 void *user), void *user);
4015 =head3 Properties of Piecewise Quasipolynomial Reductions
4017 To check whether two union piecewise quasipolynomial reductions are
4018 obviously equal, use
4020 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4021 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4022 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4024 =head3 Operations on Piecewise Quasipolynomial Reductions
4026 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4027 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4029 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4030 __isl_take isl_pw_qpolynomial_fold *pwf1,
4031 __isl_take isl_pw_qpolynomial_fold *pwf2);
4033 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4034 __isl_take isl_pw_qpolynomial_fold *pwf1,
4035 __isl_take isl_pw_qpolynomial_fold *pwf2);
4037 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4038 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4039 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4041 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4042 __isl_take isl_pw_qpolynomial_fold *pwf,
4043 __isl_take isl_point *pnt);
4045 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4046 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4047 __isl_take isl_point *pnt);
4049 __isl_give isl_pw_qpolynomial_fold *
4050 sl_pw_qpolynomial_fold_intersect_params(
4051 __isl_take isl_pw_qpolynomial_fold *pwf,
4052 __isl_take isl_set *set);
4054 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4055 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4056 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4057 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4058 __isl_take isl_union_set *uset);
4059 __isl_give isl_union_pw_qpolynomial_fold *
4060 isl_union_pw_qpolynomial_fold_intersect_params(
4061 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4062 __isl_take isl_set *set);
4064 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4065 __isl_take isl_pw_qpolynomial_fold *pwf);
4067 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4068 __isl_take isl_pw_qpolynomial_fold *pwf);
4070 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4071 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4073 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4074 __isl_take isl_qpolynomial_fold *fold,
4075 __isl_take isl_set *context);
4076 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4077 __isl_take isl_qpolynomial_fold *fold,
4078 __isl_take isl_set *context);
4080 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4081 __isl_take isl_pw_qpolynomial_fold *pwf,
4082 __isl_take isl_set *context);
4083 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4084 __isl_take isl_pw_qpolynomial_fold *pwf,
4085 __isl_take isl_set *context);
4087 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4088 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4089 __isl_take isl_union_set *context);
4090 __isl_give isl_union_pw_qpolynomial_fold *
4091 isl_union_pw_qpolynomial_fold_gist_params(
4092 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4093 __isl_take isl_set *context);
4095 The gist operation applies the gist operation to each of
4096 the cells in the domain of the input piecewise quasipolynomial reduction.
4097 In future, the operation will also exploit the context
4098 to simplify the quasipolynomial reductions associated to each cell.
4100 __isl_give isl_pw_qpolynomial_fold *
4101 isl_set_apply_pw_qpolynomial_fold(
4102 __isl_take isl_set *set,
4103 __isl_take isl_pw_qpolynomial_fold *pwf,
4105 __isl_give isl_pw_qpolynomial_fold *
4106 isl_map_apply_pw_qpolynomial_fold(
4107 __isl_take isl_map *map,
4108 __isl_take isl_pw_qpolynomial_fold *pwf,
4110 __isl_give isl_union_pw_qpolynomial_fold *
4111 isl_union_set_apply_union_pw_qpolynomial_fold(
4112 __isl_take isl_union_set *uset,
4113 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4115 __isl_give isl_union_pw_qpolynomial_fold *
4116 isl_union_map_apply_union_pw_qpolynomial_fold(
4117 __isl_take isl_union_map *umap,
4118 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4121 The functions taking a map
4122 compose the given map with the given piecewise quasipolynomial reduction.
4123 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4124 over all elements in the intersection of the range of the map
4125 and the domain of the piecewise quasipolynomial reduction
4126 as a function of an element in the domain of the map.
4127 The functions taking a set compute a bound over all elements in the
4128 intersection of the set and the domain of the
4129 piecewise quasipolynomial reduction.
4131 =head2 Dependence Analysis
4133 C<isl> contains specialized functionality for performing
4134 array dataflow analysis. That is, given a I<sink> access relation
4135 and a collection of possible I<source> access relations,
4136 C<isl> can compute relations that describe
4137 for each iteration of the sink access, which iteration
4138 of which of the source access relations was the last
4139 to access the same data element before the given iteration
4141 The resulting dependence relations map source iterations
4142 to the corresponding sink iterations.
4143 To compute standard flow dependences, the sink should be
4144 a read, while the sources should be writes.
4145 If any of the source accesses are marked as being I<may>
4146 accesses, then there will be a dependence from the last
4147 I<must> access B<and> from any I<may> access that follows
4148 this last I<must> access.
4149 In particular, if I<all> sources are I<may> accesses,
4150 then memory based dependence analysis is performed.
4151 If, on the other hand, all sources are I<must> accesses,
4152 then value based dependence analysis is performed.
4154 #include <isl/flow.h>
4156 typedef int (*isl_access_level_before)(void *first, void *second);
4158 __isl_give isl_access_info *isl_access_info_alloc(
4159 __isl_take isl_map *sink,
4160 void *sink_user, isl_access_level_before fn,
4162 __isl_give isl_access_info *isl_access_info_add_source(
4163 __isl_take isl_access_info *acc,
4164 __isl_take isl_map *source, int must,
4166 void isl_access_info_free(__isl_take isl_access_info *acc);
4168 __isl_give isl_flow *isl_access_info_compute_flow(
4169 __isl_take isl_access_info *acc);
4171 int isl_flow_foreach(__isl_keep isl_flow *deps,
4172 int (*fn)(__isl_take isl_map *dep, int must,
4173 void *dep_user, void *user),
4175 __isl_give isl_map *isl_flow_get_no_source(
4176 __isl_keep isl_flow *deps, int must);
4177 void isl_flow_free(__isl_take isl_flow *deps);
4179 The function C<isl_access_info_compute_flow> performs the actual
4180 dependence analysis. The other functions are used to construct
4181 the input for this function or to read off the output.
4183 The input is collected in an C<isl_access_info>, which can
4184 be created through a call to C<isl_access_info_alloc>.
4185 The arguments to this functions are the sink access relation
4186 C<sink>, a token C<sink_user> used to identify the sink
4187 access to the user, a callback function for specifying the
4188 relative order of source and sink accesses, and the number
4189 of source access relations that will be added.
4190 The callback function has type C<int (*)(void *first, void *second)>.
4191 The function is called with two user supplied tokens identifying
4192 either a source or the sink and it should return the shared nesting
4193 level and the relative order of the two accesses.
4194 In particular, let I<n> be the number of loops shared by
4195 the two accesses. If C<first> precedes C<second> textually,
4196 then the function should return I<2 * n + 1>; otherwise,
4197 it should return I<2 * n>.
4198 The sources can be added to the C<isl_access_info> by performing
4199 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4200 C<must> indicates whether the source is a I<must> access
4201 or a I<may> access. Note that a multi-valued access relation
4202 should only be marked I<must> if every iteration in the domain
4203 of the relation accesses I<all> elements in its image.
4204 The C<source_user> token is again used to identify
4205 the source access. The range of the source access relation
4206 C<source> should have the same dimension as the range
4207 of the sink access relation.
4208 The C<isl_access_info_free> function should usually not be
4209 called explicitly, because it is called implicitly by
4210 C<isl_access_info_compute_flow>.
4212 The result of the dependence analysis is collected in an
4213 C<isl_flow>. There may be elements of
4214 the sink access for which no preceding source access could be
4215 found or for which all preceding sources are I<may> accesses.
4216 The relations containing these elements can be obtained through
4217 calls to C<isl_flow_get_no_source>, the first with C<must> set
4218 and the second with C<must> unset.
4219 In the case of standard flow dependence analysis,
4220 with the sink a read and the sources I<must> writes,
4221 the first relation corresponds to the reads from uninitialized
4222 array elements and the second relation is empty.
4223 The actual flow dependences can be extracted using
4224 C<isl_flow_foreach>. This function will call the user-specified
4225 callback function C<fn> for each B<non-empty> dependence between
4226 a source and the sink. The callback function is called
4227 with four arguments, the actual flow dependence relation
4228 mapping source iterations to sink iterations, a boolean that
4229 indicates whether it is a I<must> or I<may> dependence, a token
4230 identifying the source and an additional C<void *> with value
4231 equal to the third argument of the C<isl_flow_foreach> call.
4232 A dependence is marked I<must> if it originates from a I<must>
4233 source and if it is not followed by any I<may> sources.
4235 After finishing with an C<isl_flow>, the user should call
4236 C<isl_flow_free> to free all associated memory.
4238 A higher-level interface to dependence analysis is provided
4239 by the following function.
4241 #include <isl/flow.h>
4243 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4244 __isl_take isl_union_map *must_source,
4245 __isl_take isl_union_map *may_source,
4246 __isl_take isl_union_map *schedule,
4247 __isl_give isl_union_map **must_dep,
4248 __isl_give isl_union_map **may_dep,
4249 __isl_give isl_union_map **must_no_source,
4250 __isl_give isl_union_map **may_no_source);
4252 The arrays are identified by the tuple names of the ranges
4253 of the accesses. The iteration domains by the tuple names
4254 of the domains of the accesses and of the schedule.
4255 The relative order of the iteration domains is given by the
4256 schedule. The relations returned through C<must_no_source>
4257 and C<may_no_source> are subsets of C<sink>.
4258 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4259 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4260 any of the other arguments is treated as an error.
4262 =head3 Interaction with Dependence Analysis
4264 During the dependence analysis, we frequently need to perform
4265 the following operation. Given a relation between sink iterations
4266 and potential soure iterations from a particular source domain,
4267 what is the last potential source iteration corresponding to each
4268 sink iteration. It can sometimes be convenient to adjust
4269 the set of potential source iterations before or after each such operation.
4270 The prototypical example is fuzzy array dataflow analysis,
4271 where we need to analyze if, based on data-dependent constraints,
4272 the sink iteration can ever be executed without one or more of
4273 the corresponding potential source iterations being executed.
4274 If so, we can introduce extra parameters and select an unknown
4275 but fixed source iteration from the potential source iterations.
4276 To be able to perform such manipulations, C<isl> provides the following
4279 #include <isl/flow.h>
4281 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4282 __isl_keep isl_map *source_map,
4283 __isl_keep isl_set *sink, void *source_user,
4285 __isl_give isl_access_info *isl_access_info_set_restrict(
4286 __isl_take isl_access_info *acc,
4287 isl_access_restrict fn, void *user);
4289 The function C<isl_access_info_set_restrict> should be called
4290 before calling C<isl_access_info_compute_flow> and registers a callback function
4291 that will be called any time C<isl> is about to compute the last
4292 potential source. The first argument is the (reverse) proto-dependence,
4293 mapping sink iterations to potential source iterations.
4294 The second argument represents the sink iterations for which
4295 we want to compute the last source iteration.
4296 The third argument is the token corresponding to the source
4297 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4298 The callback is expected to return a restriction on either the input or
4299 the output of the operation computing the last potential source.
4300 If the input needs to be restricted then restrictions are needed
4301 for both the source and the sink iterations. The sink iterations
4302 and the potential source iterations will be intersected with these sets.
4303 If the output needs to be restricted then only a restriction on the source
4304 iterations is required.
4305 If any error occurs, the callback should return C<NULL>.
4306 An C<isl_restriction> object can be created and freed using the following
4309 #include <isl/flow.h>
4311 __isl_give isl_restriction *isl_restriction_input(
4312 __isl_take isl_set *source_restr,
4313 __isl_take isl_set *sink_restr);
4314 __isl_give isl_restriction *isl_restriction_output(
4315 __isl_take isl_set *source_restr);
4316 __isl_give isl_restriction *isl_restriction_none(
4317 __isl_keep isl_map *source_map);
4318 __isl_give isl_restriction *isl_restriction_empty(
4319 __isl_keep isl_map *source_map);
4320 void *isl_restriction_free(
4321 __isl_take isl_restriction *restr);
4323 C<isl_restriction_none> and C<isl_restriction_empty> are special
4324 cases of C<isl_restriction_input>. C<isl_restriction_none>
4325 is essentially equivalent to
4327 isl_restriction_input(isl_set_universe(
4328 isl_space_range(isl_map_get_space(source_map))),
4330 isl_space_domain(isl_map_get_space(source_map))));
4332 whereas C<isl_restriction_empty> is essentially equivalent to
4334 isl_restriction_input(isl_set_empty(
4335 isl_space_range(isl_map_get_space(source_map))),
4337 isl_space_domain(isl_map_get_space(source_map))));
4341 B<The functionality described in this section is fairly new
4342 and may be subject to change.>
4344 The following function can be used to compute a schedule
4345 for a union of domains.
4346 By default, the algorithm used to construct the schedule is similar
4347 to that of C<Pluto>.
4348 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4350 The generated schedule respects all C<validity> dependences.
4351 That is, all dependence distances over these dependences in the
4352 scheduled space are lexicographically positive.
4353 The default algorithm tries to minimize the dependence distances over
4354 C<proximity> dependences.
4355 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4356 for groups of domains where the dependence distances have only
4357 non-negative values.
4358 When using Feautrier's algorithm, the C<proximity> dependence
4359 distances are only minimized during the extension to a
4360 full-dimensional schedule.
4362 #include <isl/schedule.h>
4363 __isl_give isl_schedule *isl_union_set_compute_schedule(
4364 __isl_take isl_union_set *domain,
4365 __isl_take isl_union_map *validity,
4366 __isl_take isl_union_map *proximity);
4367 void *isl_schedule_free(__isl_take isl_schedule *sched);
4369 A mapping from the domains to the scheduled space can be obtained
4370 from an C<isl_schedule> using the following function.
4372 __isl_give isl_union_map *isl_schedule_get_map(
4373 __isl_keep isl_schedule *sched);
4375 A representation of the schedule can be printed using
4377 __isl_give isl_printer *isl_printer_print_schedule(
4378 __isl_take isl_printer *p,
4379 __isl_keep isl_schedule *schedule);
4381 A representation of the schedule as a forest of bands can be obtained
4382 using the following function.
4384 __isl_give isl_band_list *isl_schedule_get_band_forest(
4385 __isl_keep isl_schedule *schedule);
4387 The list can be manipulated as explained in L<"Lists">.
4388 The bands inside the list can be copied and freed using the following
4391 #include <isl/band.h>
4392 __isl_give isl_band *isl_band_copy(
4393 __isl_keep isl_band *band);
4394 void *isl_band_free(__isl_take isl_band *band);
4396 Each band contains zero or more scheduling dimensions.
4397 These are referred to as the members of the band.
4398 The section of the schedule that corresponds to the band is
4399 referred to as the partial schedule of the band.
4400 For those nodes that participate in a band, the outer scheduling
4401 dimensions form the prefix schedule, while the inner scheduling
4402 dimensions form the suffix schedule.
4403 That is, if we take a cut of the band forest, then the union of
4404 the concatenations of the prefix, partial and suffix schedules of
4405 each band in the cut is equal to the entire schedule (modulo
4406 some possible padding at the end with zero scheduling dimensions).
4407 The properties of a band can be inspected using the following functions.
4409 #include <isl/band.h>
4410 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4412 int isl_band_has_children(__isl_keep isl_band *band);
4413 __isl_give isl_band_list *isl_band_get_children(
4414 __isl_keep isl_band *band);
4416 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4417 __isl_keep isl_band *band);
4418 __isl_give isl_union_map *isl_band_get_partial_schedule(
4419 __isl_keep isl_band *band);
4420 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4421 __isl_keep isl_band *band);
4423 int isl_band_n_member(__isl_keep isl_band *band);
4424 int isl_band_member_is_zero_distance(
4425 __isl_keep isl_band *band, int pos);
4427 Note that a scheduling dimension is considered to be ``zero
4428 distance'' if it does not carry any proximity dependences
4430 That is, if the dependence distances of the proximity
4431 dependences are all zero in that direction (for fixed
4432 iterations of outer bands).
4434 A representation of the band can be printed using
4436 #include <isl/band.h>
4437 __isl_give isl_printer *isl_printer_print_band(
4438 __isl_take isl_printer *p,
4439 __isl_keep isl_band *band);
4443 #include <isl/schedule.h>
4444 int isl_options_set_schedule_max_coefficient(
4445 isl_ctx *ctx, int val);
4446 int isl_options_get_schedule_max_coefficient(
4448 int isl_options_set_schedule_max_constant_term(
4449 isl_ctx *ctx, int val);
4450 int isl_options_get_schedule_max_constant_term(
4452 int isl_options_set_schedule_maximize_band_depth(
4453 isl_ctx *ctx, int val);
4454 int isl_options_get_schedule_maximize_band_depth(
4456 int isl_options_set_schedule_outer_zero_distance(
4457 isl_ctx *ctx, int val);
4458 int isl_options_get_schedule_outer_zero_distance(
4460 int isl_options_set_schedule_split_scaled(
4461 isl_ctx *ctx, int val);
4462 int isl_options_get_schedule_split_scaled(
4464 int isl_options_set_schedule_algorithm(
4465 isl_ctx *ctx, int val);
4466 int isl_options_get_schedule_algorithm(
4472 =item * schedule_max_coefficient
4474 This option enforces that the coefficients for variable and parameter
4475 dimensions in the calculated schedule are not larger than the specified value.
4476 This option can significantly increase the speed of the scheduling calculation
4477 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4478 this option does not introduce bounds on the variable or parameter
4481 =item * schedule_max_constant_term
4483 This option enforces that the constant coefficients in the calculated schedule
4484 are not larger than the maximal constant term. This option can significantly
4485 increase the speed of the scheduling calculation and may also prevent fusing of
4486 unrelated dimensions. A value of -1 means that this option does not introduce
4487 bounds on the constant coefficients.
4489 =item * schedule_maximize_band_depth
4491 If this option is set, we do not split bands at the point
4492 where we detect splitting is necessary. Instead, we
4493 backtrack and split bands as early as possible. This
4494 reduces the number of splits and maximizes the width of
4495 the bands. Wider bands give more possibilities for tiling.
4497 =item * schedule_outer_zero_distance
4499 If this option is set, then we try to construct schedules
4500 where the outermost scheduling dimension in each band
4501 results in a zero dependence distance over the proximity
4504 =item * schedule_split_scaled
4506 If this option is set, then we try to construct schedules in which the
4507 constant term is split off from the linear part if the linear parts of
4508 the scheduling rows for all nodes in the graphs have a common non-trivial
4510 The constant term is then placed in a separate band and the linear
4513 =item * schedule_algorithm
4515 Selects the scheduling algorithm to be used.
4516 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4517 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4521 =head2 Parametric Vertex Enumeration
4523 The parametric vertex enumeration described in this section
4524 is mainly intended to be used internally and by the C<barvinok>
4527 #include <isl/vertices.h>
4528 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4529 __isl_keep isl_basic_set *bset);
4531 The function C<isl_basic_set_compute_vertices> performs the
4532 actual computation of the parametric vertices and the chamber
4533 decomposition and store the result in an C<isl_vertices> object.
4534 This information can be queried by either iterating over all
4535 the vertices or iterating over all the chambers or cells
4536 and then iterating over all vertices that are active on the chamber.
4538 int isl_vertices_foreach_vertex(
4539 __isl_keep isl_vertices *vertices,
4540 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4543 int isl_vertices_foreach_cell(
4544 __isl_keep isl_vertices *vertices,
4545 int (*fn)(__isl_take isl_cell *cell, void *user),
4547 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4548 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4551 Other operations that can be performed on an C<isl_vertices> object are
4554 isl_ctx *isl_vertices_get_ctx(
4555 __isl_keep isl_vertices *vertices);
4556 int isl_vertices_get_n_vertices(
4557 __isl_keep isl_vertices *vertices);
4558 void isl_vertices_free(__isl_take isl_vertices *vertices);
4560 Vertices can be inspected and destroyed using the following functions.
4562 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4563 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4564 __isl_give isl_basic_set *isl_vertex_get_domain(
4565 __isl_keep isl_vertex *vertex);
4566 __isl_give isl_basic_set *isl_vertex_get_expr(
4567 __isl_keep isl_vertex *vertex);
4568 void isl_vertex_free(__isl_take isl_vertex *vertex);
4570 C<isl_vertex_get_expr> returns a singleton parametric set describing
4571 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4573 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4574 B<rational> basic sets, so they should mainly be used for inspection
4575 and should not be mixed with integer sets.
4577 Chambers can be inspected and destroyed using the following functions.
4579 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4580 __isl_give isl_basic_set *isl_cell_get_domain(
4581 __isl_keep isl_cell *cell);
4582 void isl_cell_free(__isl_take isl_cell *cell);
4586 Although C<isl> is mainly meant to be used as a library,
4587 it also contains some basic applications that use some
4588 of the functionality of C<isl>.
4589 The input may be specified in either the L<isl format>
4590 or the L<PolyLib format>.
4592 =head2 C<isl_polyhedron_sample>
4594 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4595 an integer element of the polyhedron, if there is any.
4596 The first column in the output is the denominator and is always
4597 equal to 1. If the polyhedron contains no integer points,
4598 then a vector of length zero is printed.
4602 C<isl_pip> takes the same input as the C<example> program
4603 from the C<piplib> distribution, i.e., a set of constraints
4604 on the parameters, a line containing only -1 and finally a set
4605 of constraints on a parametric polyhedron.
4606 The coefficients of the parameters appear in the last columns
4607 (but before the final constant column).
4608 The output is the lexicographic minimum of the parametric polyhedron.
4609 As C<isl> currently does not have its own output format, the output
4610 is just a dump of the internal state.
4612 =head2 C<isl_polyhedron_minimize>
4614 C<isl_polyhedron_minimize> computes the minimum of some linear
4615 or affine objective function over the integer points in a polyhedron.
4616 If an affine objective function
4617 is given, then the constant should appear in the last column.
4619 =head2 C<isl_polytope_scan>
4621 Given a polytope, C<isl_polytope_scan> prints
4622 all integer points in the polytope.