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 int isl_space_has_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
736 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
737 enum isl_dim_type type);
739 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
740 or C<isl_dim_set>. As with C<isl_space_get_name>,
741 the C<isl_space_get_tuple_name> function returns a pointer to some internal
743 Binary operations require the corresponding spaces of their arguments
744 to have the same name.
746 Spaces can be nested. In particular, the domain of a set or
747 the domain or range of a relation can be a nested relation.
748 The following functions can be used to construct and deconstruct
751 #include <isl/space.h>
752 int isl_space_is_wrapping(__isl_keep isl_space *space);
753 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
754 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
756 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
757 be the space of a set, while that of
758 C<isl_space_wrap> should be the space of a relation.
759 Conversely, the output of C<isl_space_unwrap> is the space
760 of a relation, while that of C<isl_space_wrap> is the space of a set.
762 Spaces can be created from other spaces
763 using the following functions.
765 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
768 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_set_from_params(
772 __isl_take isl_space *space);
773 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
774 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
775 __isl_take isl_space *right);
776 __isl_give isl_space *isl_space_align_params(
777 __isl_take isl_space *space1, __isl_take isl_space *space2)
778 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned pos, unsigned n);
780 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned n);
782 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
783 enum isl_dim_type type, unsigned first, unsigned n);
784 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
785 enum isl_dim_type dst_type, unsigned dst_pos,
786 enum isl_dim_type src_type, unsigned src_pos,
788 __isl_give isl_space *isl_space_map_from_set(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_map_from_domain_and_range(
791 __isl_take isl_space *domain,
792 __isl_take isl_space *range);
793 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
794 __isl_give isl_space *isl_space_curry(
795 __isl_take isl_space *space);
797 Note that if dimensions are added or removed from a space, then
798 the name and the internal structure are lost.
802 A local space is essentially a space with
803 zero or more existentially quantified variables.
804 The local space of a basic set or relation can be obtained
805 using the following functions.
808 __isl_give isl_local_space *isl_basic_set_get_local_space(
809 __isl_keep isl_basic_set *bset);
812 __isl_give isl_local_space *isl_basic_map_get_local_space(
813 __isl_keep isl_basic_map *bmap);
815 A new local space can be created from a space using
817 #include <isl/local_space.h>
818 __isl_give isl_local_space *isl_local_space_from_space(
819 __isl_take isl_space *space);
821 They can be inspected, modified, copied and freed using the following functions.
823 #include <isl/local_space.h>
824 isl_ctx *isl_local_space_get_ctx(
825 __isl_keep isl_local_space *ls);
826 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
827 int isl_local_space_dim(__isl_keep isl_local_space *ls,
828 enum isl_dim_type type);
829 const char *isl_local_space_get_dim_name(
830 __isl_keep isl_local_space *ls,
831 enum isl_dim_type type, unsigned pos);
832 __isl_give isl_local_space *isl_local_space_set_dim_name(
833 __isl_take isl_local_space *ls,
834 enum isl_dim_type type, unsigned pos, const char *s);
835 __isl_give isl_local_space *isl_local_space_set_dim_id(
836 __isl_take isl_local_space *ls,
837 enum isl_dim_type type, unsigned pos,
838 __isl_take isl_id *id);
839 __isl_give isl_space *isl_local_space_get_space(
840 __isl_keep isl_local_space *ls);
841 __isl_give isl_aff *isl_local_space_get_div(
842 __isl_keep isl_local_space *ls, int pos);
843 __isl_give isl_local_space *isl_local_space_copy(
844 __isl_keep isl_local_space *ls);
845 void *isl_local_space_free(__isl_take isl_local_space *ls);
847 Two local spaces can be compared using
849 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
850 __isl_keep isl_local_space *ls2);
852 Local spaces can be created from other local spaces
853 using the following functions.
855 __isl_give isl_local_space *isl_local_space_domain(
856 __isl_take isl_local_space *ls);
857 __isl_give isl_local_space *isl_local_space_range(
858 __isl_take isl_local_space *ls);
859 __isl_give isl_local_space *isl_local_space_from_domain(
860 __isl_take isl_local_space *ls);
861 __isl_give isl_local_space *isl_local_space_intersect(
862 __isl_take isl_local_space *ls1,
863 __isl_take isl_local_space *ls2);
864 __isl_give isl_local_space *isl_local_space_add_dims(
865 __isl_take isl_local_space *ls,
866 enum isl_dim_type type, unsigned n);
867 __isl_give isl_local_space *isl_local_space_insert_dims(
868 __isl_take isl_local_space *ls,
869 enum isl_dim_type type, unsigned first, unsigned n);
870 __isl_give isl_local_space *isl_local_space_drop_dims(
871 __isl_take isl_local_space *ls,
872 enum isl_dim_type type, unsigned first, unsigned n);
874 =head2 Input and Output
876 C<isl> supports its own input/output format, which is similar
877 to the C<Omega> format, but also supports the C<PolyLib> format
882 The C<isl> format is similar to that of C<Omega>, but has a different
883 syntax for describing the parameters and allows for the definition
884 of an existentially quantified variable as the integer division
885 of an affine expression.
886 For example, the set of integers C<i> between C<0> and C<n>
887 such that C<i % 10 <= 6> can be described as
889 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
892 A set or relation can have several disjuncts, separated
893 by the keyword C<or>. Each disjunct is either a conjunction
894 of constraints or a projection (C<exists>) of a conjunction
895 of constraints. The constraints are separated by the keyword
898 =head3 C<PolyLib> format
900 If the represented set is a union, then the first line
901 contains a single number representing the number of disjuncts.
902 Otherwise, a line containing the number C<1> is optional.
904 Each disjunct is represented by a matrix of constraints.
905 The first line contains two numbers representing
906 the number of rows and columns,
907 where the number of rows is equal to the number of constraints
908 and the number of columns is equal to two plus the number of variables.
909 The following lines contain the actual rows of the constraint matrix.
910 In each row, the first column indicates whether the constraint
911 is an equality (C<0>) or inequality (C<1>). The final column
912 corresponds to the constant term.
914 If the set is parametric, then the coefficients of the parameters
915 appear in the last columns before the constant column.
916 The coefficients of any existentially quantified variables appear
917 between those of the set variables and those of the parameters.
919 =head3 Extended C<PolyLib> format
921 The extended C<PolyLib> format is nearly identical to the
922 C<PolyLib> format. The only difference is that the line
923 containing the number of rows and columns of a constraint matrix
924 also contains four additional numbers:
925 the number of output dimensions, the number of input dimensions,
926 the number of local dimensions (i.e., the number of existentially
927 quantified variables) and the number of parameters.
928 For sets, the number of ``output'' dimensions is equal
929 to the number of set dimensions, while the number of ``input''
935 __isl_give isl_basic_set *isl_basic_set_read_from_file(
936 isl_ctx *ctx, FILE *input);
937 __isl_give isl_basic_set *isl_basic_set_read_from_str(
938 isl_ctx *ctx, const char *str);
939 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
941 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
945 __isl_give isl_basic_map *isl_basic_map_read_from_file(
946 isl_ctx *ctx, FILE *input);
947 __isl_give isl_basic_map *isl_basic_map_read_from_str(
948 isl_ctx *ctx, const char *str);
949 __isl_give isl_map *isl_map_read_from_file(
950 isl_ctx *ctx, FILE *input);
951 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
954 #include <isl/union_set.h>
955 __isl_give isl_union_set *isl_union_set_read_from_file(
956 isl_ctx *ctx, FILE *input);
957 __isl_give isl_union_set *isl_union_set_read_from_str(
958 isl_ctx *ctx, const char *str);
960 #include <isl/union_map.h>
961 __isl_give isl_union_map *isl_union_map_read_from_file(
962 isl_ctx *ctx, FILE *input);
963 __isl_give isl_union_map *isl_union_map_read_from_str(
964 isl_ctx *ctx, const char *str);
966 The input format is autodetected and may be either the C<PolyLib> format
967 or the C<isl> format.
971 Before anything can be printed, an C<isl_printer> needs to
974 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
976 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
977 void isl_printer_free(__isl_take isl_printer *printer);
978 __isl_give char *isl_printer_get_str(
979 __isl_keep isl_printer *printer);
981 The printer can be inspected using the following function.
983 FILE *isl_printer_get_file(
984 __isl_keep isl_printer *printer);
986 The behavior of the printer can be modified in various ways
988 __isl_give isl_printer *isl_printer_set_output_format(
989 __isl_take isl_printer *p, int output_format);
990 __isl_give isl_printer *isl_printer_set_indent(
991 __isl_take isl_printer *p, int indent);
992 __isl_give isl_printer *isl_printer_indent(
993 __isl_take isl_printer *p, int indent);
994 __isl_give isl_printer *isl_printer_set_prefix(
995 __isl_take isl_printer *p, const char *prefix);
996 __isl_give isl_printer *isl_printer_set_suffix(
997 __isl_take isl_printer *p, const char *suffix);
999 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1000 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1001 and defaults to C<ISL_FORMAT_ISL>.
1002 Each line in the output is indented by C<indent> (set by
1003 C<isl_printer_set_indent>) spaces
1004 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1005 In the C<PolyLib> format output,
1006 the coefficients of the existentially quantified variables
1007 appear between those of the set variables and those
1009 The function C<isl_printer_indent> increases the indentation
1010 by the specified amount (which may be negative).
1012 To actually print something, use
1014 #include <isl/set.h>
1015 __isl_give isl_printer *isl_printer_print_basic_set(
1016 __isl_take isl_printer *printer,
1017 __isl_keep isl_basic_set *bset);
1018 __isl_give isl_printer *isl_printer_print_set(
1019 __isl_take isl_printer *printer,
1020 __isl_keep isl_set *set);
1022 #include <isl/map.h>
1023 __isl_give isl_printer *isl_printer_print_basic_map(
1024 __isl_take isl_printer *printer,
1025 __isl_keep isl_basic_map *bmap);
1026 __isl_give isl_printer *isl_printer_print_map(
1027 __isl_take isl_printer *printer,
1028 __isl_keep isl_map *map);
1030 #include <isl/union_set.h>
1031 __isl_give isl_printer *isl_printer_print_union_set(
1032 __isl_take isl_printer *p,
1033 __isl_keep isl_union_set *uset);
1035 #include <isl/union_map.h>
1036 __isl_give isl_printer *isl_printer_print_union_map(
1037 __isl_take isl_printer *p,
1038 __isl_keep isl_union_map *umap);
1040 When called on a file printer, the following function flushes
1041 the file. When called on a string printer, the buffer is cleared.
1043 __isl_give isl_printer *isl_printer_flush(
1044 __isl_take isl_printer *p);
1046 =head2 Creating New Sets and Relations
1048 C<isl> has functions for creating some standard sets and relations.
1052 =item * Empty sets and relations
1054 __isl_give isl_basic_set *isl_basic_set_empty(
1055 __isl_take isl_space *space);
1056 __isl_give isl_basic_map *isl_basic_map_empty(
1057 __isl_take isl_space *space);
1058 __isl_give isl_set *isl_set_empty(
1059 __isl_take isl_space *space);
1060 __isl_give isl_map *isl_map_empty(
1061 __isl_take isl_space *space);
1062 __isl_give isl_union_set *isl_union_set_empty(
1063 __isl_take isl_space *space);
1064 __isl_give isl_union_map *isl_union_map_empty(
1065 __isl_take isl_space *space);
1067 For C<isl_union_set>s and C<isl_union_map>s, the space
1068 is only used to specify the parameters.
1070 =item * Universe sets and relations
1072 __isl_give isl_basic_set *isl_basic_set_universe(
1073 __isl_take isl_space *space);
1074 __isl_give isl_basic_map *isl_basic_map_universe(
1075 __isl_take isl_space *space);
1076 __isl_give isl_set *isl_set_universe(
1077 __isl_take isl_space *space);
1078 __isl_give isl_map *isl_map_universe(
1079 __isl_take isl_space *space);
1080 __isl_give isl_union_set *isl_union_set_universe(
1081 __isl_take isl_union_set *uset);
1082 __isl_give isl_union_map *isl_union_map_universe(
1083 __isl_take isl_union_map *umap);
1085 The sets and relations constructed by the functions above
1086 contain all integer values, while those constructed by the
1087 functions below only contain non-negative values.
1089 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1090 __isl_take isl_space *space);
1091 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1092 __isl_take isl_space *space);
1093 __isl_give isl_set *isl_set_nat_universe(
1094 __isl_take isl_space *space);
1095 __isl_give isl_map *isl_map_nat_universe(
1096 __isl_take isl_space *space);
1098 =item * Identity relations
1100 __isl_give isl_basic_map *isl_basic_map_identity(
1101 __isl_take isl_space *space);
1102 __isl_give isl_map *isl_map_identity(
1103 __isl_take isl_space *space);
1105 The number of input and output dimensions in C<space> needs
1108 =item * Lexicographic order
1110 __isl_give isl_map *isl_map_lex_lt(
1111 __isl_take isl_space *set_space);
1112 __isl_give isl_map *isl_map_lex_le(
1113 __isl_take isl_space *set_space);
1114 __isl_give isl_map *isl_map_lex_gt(
1115 __isl_take isl_space *set_space);
1116 __isl_give isl_map *isl_map_lex_ge(
1117 __isl_take isl_space *set_space);
1118 __isl_give isl_map *isl_map_lex_lt_first(
1119 __isl_take isl_space *space, unsigned n);
1120 __isl_give isl_map *isl_map_lex_le_first(
1121 __isl_take isl_space *space, unsigned n);
1122 __isl_give isl_map *isl_map_lex_gt_first(
1123 __isl_take isl_space *space, unsigned n);
1124 __isl_give isl_map *isl_map_lex_ge_first(
1125 __isl_take isl_space *space, unsigned n);
1127 The first four functions take a space for a B<set>
1128 and return relations that express that the elements in the domain
1129 are lexicographically less
1130 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1131 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1132 than the elements in the range.
1133 The last four functions take a space for a map
1134 and return relations that express that the first C<n> dimensions
1135 in the domain are lexicographically less
1136 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1137 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1138 than the first C<n> dimensions in the range.
1142 A basic set or relation can be converted to a set or relation
1143 using the following functions.
1145 __isl_give isl_set *isl_set_from_basic_set(
1146 __isl_take isl_basic_set *bset);
1147 __isl_give isl_map *isl_map_from_basic_map(
1148 __isl_take isl_basic_map *bmap);
1150 Sets and relations can be converted to union sets and relations
1151 using the following functions.
1153 __isl_give isl_union_map *isl_union_map_from_map(
1154 __isl_take isl_map *map);
1155 __isl_give isl_union_set *isl_union_set_from_set(
1156 __isl_take isl_set *set);
1158 The inverse conversions below can only be used if the input
1159 union set or relation is known to contain elements in exactly one
1162 __isl_give isl_set *isl_set_from_union_set(
1163 __isl_take isl_union_set *uset);
1164 __isl_give isl_map *isl_map_from_union_map(
1165 __isl_take isl_union_map *umap);
1167 A zero-dimensional set can be constructed on a given parameter domain
1168 using the following function.
1170 __isl_give isl_set *isl_set_from_params(
1171 __isl_take isl_set *set);
1173 Sets and relations can be copied and freed again using the following
1176 __isl_give isl_basic_set *isl_basic_set_copy(
1177 __isl_keep isl_basic_set *bset);
1178 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1179 __isl_give isl_union_set *isl_union_set_copy(
1180 __isl_keep isl_union_set *uset);
1181 __isl_give isl_basic_map *isl_basic_map_copy(
1182 __isl_keep isl_basic_map *bmap);
1183 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1184 __isl_give isl_union_map *isl_union_map_copy(
1185 __isl_keep isl_union_map *umap);
1186 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1187 void isl_set_free(__isl_take isl_set *set);
1188 void *isl_union_set_free(__isl_take isl_union_set *uset);
1189 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1190 void isl_map_free(__isl_take isl_map *map);
1191 void *isl_union_map_free(__isl_take isl_union_map *umap);
1193 Other sets and relations can be constructed by starting
1194 from a universe set or relation, adding equality and/or
1195 inequality constraints and then projecting out the
1196 existentially quantified variables, if any.
1197 Constraints can be constructed, manipulated and
1198 added to (or removed from) (basic) sets and relations
1199 using the following functions.
1201 #include <isl/constraint.h>
1202 __isl_give isl_constraint *isl_equality_alloc(
1203 __isl_take isl_local_space *ls);
1204 __isl_give isl_constraint *isl_inequality_alloc(
1205 __isl_take isl_local_space *ls);
1206 __isl_give isl_constraint *isl_constraint_set_constant(
1207 __isl_take isl_constraint *constraint, isl_int v);
1208 __isl_give isl_constraint *isl_constraint_set_constant_si(
1209 __isl_take isl_constraint *constraint, int v);
1210 __isl_give isl_constraint *isl_constraint_set_coefficient(
1211 __isl_take isl_constraint *constraint,
1212 enum isl_dim_type type, int pos, isl_int v);
1213 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1214 __isl_take isl_constraint *constraint,
1215 enum isl_dim_type type, int pos, int v);
1216 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1217 __isl_take isl_basic_map *bmap,
1218 __isl_take isl_constraint *constraint);
1219 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1220 __isl_take isl_basic_set *bset,
1221 __isl_take isl_constraint *constraint);
1222 __isl_give isl_map *isl_map_add_constraint(
1223 __isl_take isl_map *map,
1224 __isl_take isl_constraint *constraint);
1225 __isl_give isl_set *isl_set_add_constraint(
1226 __isl_take isl_set *set,
1227 __isl_take isl_constraint *constraint);
1228 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1229 __isl_take isl_basic_set *bset,
1230 __isl_take isl_constraint *constraint);
1232 For example, to create a set containing the even integers
1233 between 10 and 42, you would use the following code.
1236 isl_local_space *ls;
1238 isl_basic_set *bset;
1240 space = isl_space_set_alloc(ctx, 0, 2);
1241 bset = isl_basic_set_universe(isl_space_copy(space));
1242 ls = isl_local_space_from_space(space);
1244 c = isl_equality_alloc(isl_local_space_copy(ls));
1245 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1246 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1247 bset = isl_basic_set_add_constraint(bset, c);
1249 c = isl_inequality_alloc(isl_local_space_copy(ls));
1250 c = isl_constraint_set_constant_si(c, -10);
1251 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1252 bset = isl_basic_set_add_constraint(bset, c);
1254 c = isl_inequality_alloc(ls);
1255 c = isl_constraint_set_constant_si(c, 42);
1256 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1257 bset = isl_basic_set_add_constraint(bset, c);
1259 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1263 isl_basic_set *bset;
1264 bset = isl_basic_set_read_from_str(ctx,
1265 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1267 A basic set or relation can also be constructed from two matrices
1268 describing the equalities and the inequalities.
1270 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1271 __isl_take isl_space *space,
1272 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1273 enum isl_dim_type c1,
1274 enum isl_dim_type c2, enum isl_dim_type c3,
1275 enum isl_dim_type c4);
1276 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1277 __isl_take isl_space *space,
1278 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1279 enum isl_dim_type c1,
1280 enum isl_dim_type c2, enum isl_dim_type c3,
1281 enum isl_dim_type c4, enum isl_dim_type c5);
1283 The C<isl_dim_type> arguments indicate the order in which
1284 different kinds of variables appear in the input matrices
1285 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1286 C<isl_dim_set> and C<isl_dim_div> for sets and
1287 of C<isl_dim_cst>, C<isl_dim_param>,
1288 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1290 A (basic or union) set or relation can also be constructed from a
1291 (union) (piecewise) (multiple) affine expression
1292 or a list of affine expressions
1293 (See L<"Piecewise Quasi Affine Expressions"> and
1294 L<"Piecewise Multiple Quasi Affine Expressions">).
1296 __isl_give isl_basic_map *isl_basic_map_from_aff(
1297 __isl_take isl_aff *aff);
1298 __isl_give isl_map *isl_map_from_aff(
1299 __isl_take isl_aff *aff);
1300 __isl_give isl_set *isl_set_from_pw_aff(
1301 __isl_take isl_pw_aff *pwaff);
1302 __isl_give isl_map *isl_map_from_pw_aff(
1303 __isl_take isl_pw_aff *pwaff);
1304 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1305 __isl_take isl_space *domain_space,
1306 __isl_take isl_aff_list *list);
1307 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1308 __isl_take isl_multi_aff *maff)
1309 __isl_give isl_map *isl_map_from_multi_aff(
1310 __isl_take isl_multi_aff *maff)
1311 __isl_give isl_set *isl_set_from_pw_multi_aff(
1312 __isl_take isl_pw_multi_aff *pma);
1313 __isl_give isl_map *isl_map_from_pw_multi_aff(
1314 __isl_take isl_pw_multi_aff *pma);
1315 __isl_give isl_union_map *
1316 isl_union_map_from_union_pw_multi_aff(
1317 __isl_take isl_union_pw_multi_aff *upma);
1319 The C<domain_dim> argument describes the domain of the resulting
1320 basic relation. It is required because the C<list> may consist
1321 of zero affine expressions.
1323 =head2 Inspecting Sets and Relations
1325 Usually, the user should not have to care about the actual constraints
1326 of the sets and maps, but should instead apply the abstract operations
1327 explained in the following sections.
1328 Occasionally, however, it may be required to inspect the individual
1329 coefficients of the constraints. This section explains how to do so.
1330 In these cases, it may also be useful to have C<isl> compute
1331 an explicit representation of the existentially quantified variables.
1333 __isl_give isl_set *isl_set_compute_divs(
1334 __isl_take isl_set *set);
1335 __isl_give isl_map *isl_map_compute_divs(
1336 __isl_take isl_map *map);
1337 __isl_give isl_union_set *isl_union_set_compute_divs(
1338 __isl_take isl_union_set *uset);
1339 __isl_give isl_union_map *isl_union_map_compute_divs(
1340 __isl_take isl_union_map *umap);
1342 This explicit representation defines the existentially quantified
1343 variables as integer divisions of the other variables, possibly
1344 including earlier existentially quantified variables.
1345 An explicitly represented existentially quantified variable therefore
1346 has a unique value when the values of the other variables are known.
1347 If, furthermore, the same existentials, i.e., existentials
1348 with the same explicit representations, should appear in the
1349 same order in each of the disjuncts of a set or map, then the user should call
1350 either of the following functions.
1352 __isl_give isl_set *isl_set_align_divs(
1353 __isl_take isl_set *set);
1354 __isl_give isl_map *isl_map_align_divs(
1355 __isl_take isl_map *map);
1357 Alternatively, the existentially quantified variables can be removed
1358 using the following functions, which compute an overapproximation.
1360 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1361 __isl_take isl_basic_set *bset);
1362 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1363 __isl_take isl_basic_map *bmap);
1364 __isl_give isl_set *isl_set_remove_divs(
1365 __isl_take isl_set *set);
1366 __isl_give isl_map *isl_map_remove_divs(
1367 __isl_take isl_map *map);
1369 To iterate over all the sets or maps in a union set or map, use
1371 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1372 int (*fn)(__isl_take isl_set *set, void *user),
1374 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1375 int (*fn)(__isl_take isl_map *map, void *user),
1378 The number of sets or maps in a union set or map can be obtained
1381 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1382 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1384 To extract the set or map in a given space from a union, use
1386 __isl_give isl_set *isl_union_set_extract_set(
1387 __isl_keep isl_union_set *uset,
1388 __isl_take isl_space *space);
1389 __isl_give isl_map *isl_union_map_extract_map(
1390 __isl_keep isl_union_map *umap,
1391 __isl_take isl_space *space);
1393 To iterate over all the basic sets or maps in a set or map, use
1395 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1396 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1398 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1399 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1402 The callback function C<fn> should return 0 if successful and
1403 -1 if an error occurs. In the latter case, or if any other error
1404 occurs, the above functions will return -1.
1406 It should be noted that C<isl> does not guarantee that
1407 the basic sets or maps passed to C<fn> are disjoint.
1408 If this is required, then the user should call one of
1409 the following functions first.
1411 __isl_give isl_set *isl_set_make_disjoint(
1412 __isl_take isl_set *set);
1413 __isl_give isl_map *isl_map_make_disjoint(
1414 __isl_take isl_map *map);
1416 The number of basic sets in a set can be obtained
1419 int isl_set_n_basic_set(__isl_keep isl_set *set);
1421 To iterate over the constraints of a basic set or map, use
1423 #include <isl/constraint.h>
1425 int isl_basic_set_foreach_constraint(
1426 __isl_keep isl_basic_set *bset,
1427 int (*fn)(__isl_take isl_constraint *c, void *user),
1429 int isl_basic_map_foreach_constraint(
1430 __isl_keep isl_basic_map *bmap,
1431 int (*fn)(__isl_take isl_constraint *c, void *user),
1433 void *isl_constraint_free(__isl_take isl_constraint *c);
1435 Again, the callback function C<fn> should return 0 if successful and
1436 -1 if an error occurs. In the latter case, or if any other error
1437 occurs, the above functions will return -1.
1438 The constraint C<c> represents either an equality or an inequality.
1439 Use the following function to find out whether a constraint
1440 represents an equality. If not, it represents an inequality.
1442 int isl_constraint_is_equality(
1443 __isl_keep isl_constraint *constraint);
1445 The coefficients of the constraints can be inspected using
1446 the following functions.
1448 void isl_constraint_get_constant(
1449 __isl_keep isl_constraint *constraint, isl_int *v);
1450 void isl_constraint_get_coefficient(
1451 __isl_keep isl_constraint *constraint,
1452 enum isl_dim_type type, int pos, isl_int *v);
1453 int isl_constraint_involves_dims(
1454 __isl_keep isl_constraint *constraint,
1455 enum isl_dim_type type, unsigned first, unsigned n);
1457 The explicit representations of the existentially quantified
1458 variables can be inspected using the following function.
1459 Note that the user is only allowed to use this function
1460 if the inspected set or map is the result of a call
1461 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1462 The existentially quantified variable is equal to the floor
1463 of the returned affine expression. The affine expression
1464 itself can be inspected using the functions in
1465 L<"Piecewise Quasi Affine Expressions">.
1467 __isl_give isl_aff *isl_constraint_get_div(
1468 __isl_keep isl_constraint *constraint, int pos);
1470 To obtain the constraints of a basic set or map in matrix
1471 form, use the following functions.
1473 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1474 __isl_keep isl_basic_set *bset,
1475 enum isl_dim_type c1, enum isl_dim_type c2,
1476 enum isl_dim_type c3, enum isl_dim_type c4);
1477 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1478 __isl_keep isl_basic_set *bset,
1479 enum isl_dim_type c1, enum isl_dim_type c2,
1480 enum isl_dim_type c3, enum isl_dim_type c4);
1481 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1482 __isl_keep isl_basic_map *bmap,
1483 enum isl_dim_type c1,
1484 enum isl_dim_type c2, enum isl_dim_type c3,
1485 enum isl_dim_type c4, enum isl_dim_type c5);
1486 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1487 __isl_keep isl_basic_map *bmap,
1488 enum isl_dim_type c1,
1489 enum isl_dim_type c2, enum isl_dim_type c3,
1490 enum isl_dim_type c4, enum isl_dim_type c5);
1492 The C<isl_dim_type> arguments dictate the order in which
1493 different kinds of variables appear in the resulting matrix
1494 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1495 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1497 The number of parameters, input, output or set dimensions can
1498 be obtained using the following functions.
1500 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1501 enum isl_dim_type type);
1502 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1503 enum isl_dim_type type);
1504 unsigned isl_set_dim(__isl_keep isl_set *set,
1505 enum isl_dim_type type);
1506 unsigned isl_map_dim(__isl_keep isl_map *map,
1507 enum isl_dim_type type);
1509 To check whether the description of a set or relation depends
1510 on one or more given dimensions, it is not necessary to iterate over all
1511 constraints. Instead the following functions can be used.
1513 int isl_basic_set_involves_dims(
1514 __isl_keep isl_basic_set *bset,
1515 enum isl_dim_type type, unsigned first, unsigned n);
1516 int isl_set_involves_dims(__isl_keep isl_set *set,
1517 enum isl_dim_type type, unsigned first, unsigned n);
1518 int isl_basic_map_involves_dims(
1519 __isl_keep isl_basic_map *bmap,
1520 enum isl_dim_type type, unsigned first, unsigned n);
1521 int isl_map_involves_dims(__isl_keep isl_map *map,
1522 enum isl_dim_type type, unsigned first, unsigned n);
1524 Similarly, the following functions can be used to check whether
1525 a given dimension is involved in any lower or upper bound.
1527 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1528 enum isl_dim_type type, unsigned pos);
1529 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1530 enum isl_dim_type type, unsigned pos);
1532 The identifiers or names of the domain and range spaces of a set
1533 or relation can be read off or set using the following functions.
1535 __isl_give isl_set *isl_set_set_tuple_id(
1536 __isl_take isl_set *set, __isl_take isl_id *id);
1537 __isl_give isl_set *isl_set_reset_tuple_id(
1538 __isl_take isl_set *set);
1539 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1540 __isl_give isl_id *isl_set_get_tuple_id(
1541 __isl_keep isl_set *set);
1542 __isl_give isl_map *isl_map_set_tuple_id(
1543 __isl_take isl_map *map, enum isl_dim_type type,
1544 __isl_take isl_id *id);
1545 __isl_give isl_map *isl_map_reset_tuple_id(
1546 __isl_take isl_map *map, enum isl_dim_type type);
1547 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1548 enum isl_dim_type type);
1549 __isl_give isl_id *isl_map_get_tuple_id(
1550 __isl_keep isl_map *map, enum isl_dim_type type);
1552 const char *isl_basic_set_get_tuple_name(
1553 __isl_keep isl_basic_set *bset);
1554 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1555 __isl_take isl_basic_set *set, const char *s);
1556 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1557 const char *isl_set_get_tuple_name(
1558 __isl_keep isl_set *set);
1559 const char *isl_basic_map_get_tuple_name(
1560 __isl_keep isl_basic_map *bmap,
1561 enum isl_dim_type type);
1562 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1563 __isl_take isl_basic_map *bmap,
1564 enum isl_dim_type type, const char *s);
1565 const char *isl_map_get_tuple_name(
1566 __isl_keep isl_map *map,
1567 enum isl_dim_type type);
1569 As with C<isl_space_get_tuple_name>, the value returned points to
1570 an internal data structure.
1571 The identifiers, positions or names of individual dimensions can be
1572 read off using the following functions.
1574 __isl_give isl_set *isl_set_set_dim_id(
1575 __isl_take isl_set *set, enum isl_dim_type type,
1576 unsigned pos, __isl_take isl_id *id);
1577 int isl_set_has_dim_id(__isl_keep isl_set *set,
1578 enum isl_dim_type type, unsigned pos);
1579 __isl_give isl_id *isl_set_get_dim_id(
1580 __isl_keep isl_set *set, enum isl_dim_type type,
1582 int isl_basic_map_has_dim_id(
1583 __isl_keep isl_basic_map *bmap,
1584 enum isl_dim_type type, unsigned pos);
1585 __isl_give isl_map *isl_map_set_dim_id(
1586 __isl_take isl_map *map, enum isl_dim_type type,
1587 unsigned pos, __isl_take isl_id *id);
1588 int isl_map_has_dim_id(__isl_keep isl_map *map,
1589 enum isl_dim_type type, unsigned pos);
1590 __isl_give isl_id *isl_map_get_dim_id(
1591 __isl_keep isl_map *map, enum isl_dim_type type,
1594 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1595 enum isl_dim_type type, __isl_keep isl_id *id);
1596 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1597 enum isl_dim_type type, __isl_keep isl_id *id);
1598 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1599 enum isl_dim_type type, const char *name);
1600 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1601 enum isl_dim_type type, const char *name);
1603 const char *isl_constraint_get_dim_name(
1604 __isl_keep isl_constraint *constraint,
1605 enum isl_dim_type type, unsigned pos);
1606 const char *isl_basic_set_get_dim_name(
1607 __isl_keep isl_basic_set *bset,
1608 enum isl_dim_type type, unsigned pos);
1609 int isl_set_has_dim_name(__isl_keep isl_set *set,
1610 enum isl_dim_type type, unsigned pos);
1611 const char *isl_set_get_dim_name(
1612 __isl_keep isl_set *set,
1613 enum isl_dim_type type, unsigned pos);
1614 const char *isl_basic_map_get_dim_name(
1615 __isl_keep isl_basic_map *bmap,
1616 enum isl_dim_type type, unsigned pos);
1617 const char *isl_map_get_dim_name(
1618 __isl_keep isl_map *map,
1619 enum isl_dim_type type, unsigned pos);
1621 These functions are mostly useful to obtain the identifiers, positions
1622 or names of the parameters. Identifiers of individual dimensions are
1623 essentially only useful for printing. They are ignored by all other
1624 operations and may not be preserved across those operations.
1628 =head3 Unary Properties
1634 The following functions test whether the given set or relation
1635 contains any integer points. The ``plain'' variants do not perform
1636 any computations, but simply check if the given set or relation
1637 is already known to be empty.
1639 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1640 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1641 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1642 int isl_set_is_empty(__isl_keep isl_set *set);
1643 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1644 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1645 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1646 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1647 int isl_map_is_empty(__isl_keep isl_map *map);
1648 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1650 =item * Universality
1652 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1653 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1654 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1656 =item * Single-valuedness
1658 int isl_map_plain_is_single_valued(
1659 __isl_keep isl_map *map);
1660 int isl_map_is_single_valued(__isl_keep isl_map *map);
1661 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1665 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1666 int isl_map_is_injective(__isl_keep isl_map *map);
1667 int isl_union_map_plain_is_injective(
1668 __isl_keep isl_union_map *umap);
1669 int isl_union_map_is_injective(
1670 __isl_keep isl_union_map *umap);
1674 int isl_map_is_bijective(__isl_keep isl_map *map);
1675 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1679 int isl_basic_map_plain_is_fixed(
1680 __isl_keep isl_basic_map *bmap,
1681 enum isl_dim_type type, unsigned pos,
1683 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1684 enum isl_dim_type type, unsigned pos,
1686 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1687 enum isl_dim_type type, unsigned pos,
1690 Check if the relation obviously lies on a hyperplane where the given dimension
1691 has a fixed value and if so, return that value in C<*val>.
1695 To check whether a set is a parameter domain, use this function:
1697 int isl_set_is_params(__isl_keep isl_set *set);
1698 int isl_union_set_is_params(
1699 __isl_keep isl_union_set *uset);
1703 The following functions check whether the domain of the given
1704 (basic) set is a wrapped relation.
1706 int isl_basic_set_is_wrapping(
1707 __isl_keep isl_basic_set *bset);
1708 int isl_set_is_wrapping(__isl_keep isl_set *set);
1710 =item * Internal Product
1712 int isl_basic_map_can_zip(
1713 __isl_keep isl_basic_map *bmap);
1714 int isl_map_can_zip(__isl_keep isl_map *map);
1716 Check whether the product of domain and range of the given relation
1718 i.e., whether both domain and range are nested relations.
1722 int isl_basic_map_can_curry(
1723 __isl_keep isl_basic_map *bmap);
1724 int isl_map_can_curry(__isl_keep isl_map *map);
1726 Check whether the domain of the (basic) relation is a wrapped relation.
1730 =head3 Binary Properties
1736 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1737 __isl_keep isl_set *set2);
1738 int isl_set_is_equal(__isl_keep isl_set *set1,
1739 __isl_keep isl_set *set2);
1740 int isl_union_set_is_equal(
1741 __isl_keep isl_union_set *uset1,
1742 __isl_keep isl_union_set *uset2);
1743 int isl_basic_map_is_equal(
1744 __isl_keep isl_basic_map *bmap1,
1745 __isl_keep isl_basic_map *bmap2);
1746 int isl_map_is_equal(__isl_keep isl_map *map1,
1747 __isl_keep isl_map *map2);
1748 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1749 __isl_keep isl_map *map2);
1750 int isl_union_map_is_equal(
1751 __isl_keep isl_union_map *umap1,
1752 __isl_keep isl_union_map *umap2);
1754 =item * Disjointness
1756 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1757 __isl_keep isl_set *set2);
1761 int isl_basic_set_is_subset(
1762 __isl_keep isl_basic_set *bset1,
1763 __isl_keep isl_basic_set *bset2);
1764 int isl_set_is_subset(__isl_keep isl_set *set1,
1765 __isl_keep isl_set *set2);
1766 int isl_set_is_strict_subset(
1767 __isl_keep isl_set *set1,
1768 __isl_keep isl_set *set2);
1769 int isl_union_set_is_subset(
1770 __isl_keep isl_union_set *uset1,
1771 __isl_keep isl_union_set *uset2);
1772 int isl_union_set_is_strict_subset(
1773 __isl_keep isl_union_set *uset1,
1774 __isl_keep isl_union_set *uset2);
1775 int isl_basic_map_is_subset(
1776 __isl_keep isl_basic_map *bmap1,
1777 __isl_keep isl_basic_map *bmap2);
1778 int isl_basic_map_is_strict_subset(
1779 __isl_keep isl_basic_map *bmap1,
1780 __isl_keep isl_basic_map *bmap2);
1781 int isl_map_is_subset(
1782 __isl_keep isl_map *map1,
1783 __isl_keep isl_map *map2);
1784 int isl_map_is_strict_subset(
1785 __isl_keep isl_map *map1,
1786 __isl_keep isl_map *map2);
1787 int isl_union_map_is_subset(
1788 __isl_keep isl_union_map *umap1,
1789 __isl_keep isl_union_map *umap2);
1790 int isl_union_map_is_strict_subset(
1791 __isl_keep isl_union_map *umap1,
1792 __isl_keep isl_union_map *umap2);
1796 =head2 Unary Operations
1802 __isl_give isl_set *isl_set_complement(
1803 __isl_take isl_set *set);
1804 __isl_give isl_map *isl_map_complement(
1805 __isl_take isl_map *map);
1809 __isl_give isl_basic_map *isl_basic_map_reverse(
1810 __isl_take isl_basic_map *bmap);
1811 __isl_give isl_map *isl_map_reverse(
1812 __isl_take isl_map *map);
1813 __isl_give isl_union_map *isl_union_map_reverse(
1814 __isl_take isl_union_map *umap);
1818 __isl_give isl_basic_set *isl_basic_set_project_out(
1819 __isl_take isl_basic_set *bset,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 __isl_give isl_basic_map *isl_basic_map_project_out(
1822 __isl_take isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned first, unsigned n);
1824 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1825 enum isl_dim_type type, unsigned first, unsigned n);
1826 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1827 enum isl_dim_type type, unsigned first, unsigned n);
1828 __isl_give isl_basic_set *isl_basic_set_params(
1829 __isl_take isl_basic_set *bset);
1830 __isl_give isl_basic_set *isl_basic_map_domain(
1831 __isl_take isl_basic_map *bmap);
1832 __isl_give isl_basic_set *isl_basic_map_range(
1833 __isl_take isl_basic_map *bmap);
1834 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1835 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1836 __isl_give isl_set *isl_map_domain(
1837 __isl_take isl_map *bmap);
1838 __isl_give isl_set *isl_map_range(
1839 __isl_take isl_map *map);
1840 __isl_give isl_set *isl_union_set_params(
1841 __isl_take isl_union_set *uset);
1842 __isl_give isl_set *isl_union_map_params(
1843 __isl_take isl_union_map *umap);
1844 __isl_give isl_union_set *isl_union_map_domain(
1845 __isl_take isl_union_map *umap);
1846 __isl_give isl_union_set *isl_union_map_range(
1847 __isl_take isl_union_map *umap);
1849 __isl_give isl_basic_map *isl_basic_map_domain_map(
1850 __isl_take isl_basic_map *bmap);
1851 __isl_give isl_basic_map *isl_basic_map_range_map(
1852 __isl_take isl_basic_map *bmap);
1853 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1854 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1855 __isl_give isl_union_map *isl_union_map_domain_map(
1856 __isl_take isl_union_map *umap);
1857 __isl_give isl_union_map *isl_union_map_range_map(
1858 __isl_take isl_union_map *umap);
1860 The functions above construct a (basic, regular or union) relation
1861 that maps (a wrapped version of) the input relation to its domain or range.
1865 __isl_give isl_set *isl_set_eliminate(
1866 __isl_take isl_set *set, enum isl_dim_type type,
1867 unsigned first, unsigned n);
1868 __isl_give isl_basic_map *isl_basic_map_eliminate(
1869 __isl_take isl_basic_map *bmap,
1870 enum isl_dim_type type,
1871 unsigned first, unsigned n);
1872 __isl_give isl_map *isl_map_eliminate(
1873 __isl_take isl_map *map, enum isl_dim_type type,
1874 unsigned first, unsigned n);
1876 Eliminate the coefficients for the given dimensions from the constraints,
1877 without removing the dimensions.
1881 __isl_give isl_basic_set *isl_basic_set_fix(
1882 __isl_take isl_basic_set *bset,
1883 enum isl_dim_type type, unsigned pos,
1885 __isl_give isl_basic_set *isl_basic_set_fix_si(
1886 __isl_take isl_basic_set *bset,
1887 enum isl_dim_type type, unsigned pos, int value);
1888 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1889 enum isl_dim_type type, unsigned pos,
1891 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1892 enum isl_dim_type type, unsigned pos, int value);
1893 __isl_give isl_basic_map *isl_basic_map_fix_si(
1894 __isl_take isl_basic_map *bmap,
1895 enum isl_dim_type type, unsigned pos, int value);
1896 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1897 enum isl_dim_type type, unsigned pos, int value);
1899 Intersect the set or relation with the hyperplane where the given
1900 dimension has the fixed given value.
1902 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1903 __isl_take isl_basic_map *bmap,
1904 enum isl_dim_type type, unsigned pos, int value);
1905 __isl_give isl_set *isl_set_lower_bound(
1906 __isl_take isl_set *set,
1907 enum isl_dim_type type, unsigned pos,
1909 __isl_give isl_set *isl_set_lower_bound_si(
1910 __isl_take isl_set *set,
1911 enum isl_dim_type type, unsigned pos, int value);
1912 __isl_give isl_map *isl_map_lower_bound_si(
1913 __isl_take isl_map *map,
1914 enum isl_dim_type type, unsigned pos, int value);
1915 __isl_give isl_set *isl_set_upper_bound(
1916 __isl_take isl_set *set,
1917 enum isl_dim_type type, unsigned pos,
1919 __isl_give isl_set *isl_set_upper_bound_si(
1920 __isl_take isl_set *set,
1921 enum isl_dim_type type, unsigned pos, int value);
1922 __isl_give isl_map *isl_map_upper_bound_si(
1923 __isl_take isl_map *map,
1924 enum isl_dim_type type, unsigned pos, int value);
1926 Intersect the set or relation with the half-space where the given
1927 dimension has a value bounded by the fixed given value.
1929 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1930 enum isl_dim_type type1, int pos1,
1931 enum isl_dim_type type2, int pos2);
1932 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1933 enum isl_dim_type type1, int pos1,
1934 enum isl_dim_type type2, int pos2);
1936 Intersect the set or relation with the hyperplane where the given
1937 dimensions are equal to each other.
1939 __isl_give isl_map *isl_map_oppose(__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 hyperplane where the given
1944 dimensions have opposite values.
1946 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1947 enum isl_dim_type type1, int pos1,
1948 enum isl_dim_type type2, int pos2);
1950 Intersect the relation with the half-space where the given
1951 dimensions satisfy the given ordering.
1955 __isl_give isl_map *isl_set_identity(
1956 __isl_take isl_set *set);
1957 __isl_give isl_union_map *isl_union_set_identity(
1958 __isl_take isl_union_set *uset);
1960 Construct an identity relation on the given (union) set.
1964 __isl_give isl_basic_set *isl_basic_map_deltas(
1965 __isl_take isl_basic_map *bmap);
1966 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1967 __isl_give isl_union_set *isl_union_map_deltas(
1968 __isl_take isl_union_map *umap);
1970 These functions return a (basic) set containing the differences
1971 between image elements and corresponding domain elements in the input.
1973 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_map *isl_map_deltas_map(
1976 __isl_take isl_map *map);
1977 __isl_give isl_union_map *isl_union_map_deltas_map(
1978 __isl_take isl_union_map *umap);
1980 The functions above construct a (basic, regular or union) relation
1981 that maps (a wrapped version of) the input relation to its delta set.
1985 Simplify the representation of a set or relation by trying
1986 to combine pairs of basic sets or relations into a single
1987 basic set or relation.
1989 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1990 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1991 __isl_give isl_union_set *isl_union_set_coalesce(
1992 __isl_take isl_union_set *uset);
1993 __isl_give isl_union_map *isl_union_map_coalesce(
1994 __isl_take isl_union_map *umap);
1996 One of the methods for combining pairs of basic sets or relations
1997 can result in coefficients that are much larger than those that appear
1998 in the constraints of the input. By default, the coefficients are
1999 not allowed to grow larger, but this can be changed by unsetting
2000 the following option.
2002 int isl_options_set_coalesce_bounded_wrapping(
2003 isl_ctx *ctx, int val);
2004 int isl_options_get_coalesce_bounded_wrapping(
2007 =item * Detecting equalities
2009 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2010 __isl_take isl_basic_set *bset);
2011 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2012 __isl_take isl_basic_map *bmap);
2013 __isl_give isl_set *isl_set_detect_equalities(
2014 __isl_take isl_set *set);
2015 __isl_give isl_map *isl_map_detect_equalities(
2016 __isl_take isl_map *map);
2017 __isl_give isl_union_set *isl_union_set_detect_equalities(
2018 __isl_take isl_union_set *uset);
2019 __isl_give isl_union_map *isl_union_map_detect_equalities(
2020 __isl_take isl_union_map *umap);
2022 Simplify the representation of a set or relation by detecting implicit
2025 =item * Removing redundant constraints
2027 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2028 __isl_take isl_basic_set *bset);
2029 __isl_give isl_set *isl_set_remove_redundancies(
2030 __isl_take isl_set *set);
2031 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2032 __isl_take isl_basic_map *bmap);
2033 __isl_give isl_map *isl_map_remove_redundancies(
2034 __isl_take isl_map *map);
2038 __isl_give isl_basic_set *isl_set_convex_hull(
2039 __isl_take isl_set *set);
2040 __isl_give isl_basic_map *isl_map_convex_hull(
2041 __isl_take isl_map *map);
2043 If the input set or relation has any existentially quantified
2044 variables, then the result of these operations is currently undefined.
2048 __isl_give isl_basic_set *isl_set_simple_hull(
2049 __isl_take isl_set *set);
2050 __isl_give isl_basic_map *isl_map_simple_hull(
2051 __isl_take isl_map *map);
2052 __isl_give isl_union_map *isl_union_map_simple_hull(
2053 __isl_take isl_union_map *umap);
2055 These functions compute a single basic set or relation
2056 that contains the whole input set or relation.
2057 In particular, the output is described by translates
2058 of the constraints describing the basic sets or relations in the input.
2062 (See \autoref{s:simple hull}.)
2068 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2069 __isl_take isl_basic_set *bset);
2070 __isl_give isl_basic_set *isl_set_affine_hull(
2071 __isl_take isl_set *set);
2072 __isl_give isl_union_set *isl_union_set_affine_hull(
2073 __isl_take isl_union_set *uset);
2074 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2075 __isl_take isl_basic_map *bmap);
2076 __isl_give isl_basic_map *isl_map_affine_hull(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_map *isl_union_map_affine_hull(
2079 __isl_take isl_union_map *umap);
2081 In case of union sets and relations, the affine hull is computed
2084 =item * Polyhedral hull
2086 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2087 __isl_take isl_set *set);
2088 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2089 __isl_take isl_map *map);
2090 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2091 __isl_take isl_union_set *uset);
2092 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2093 __isl_take isl_union_map *umap);
2095 These functions compute a single basic set or relation
2096 not involving any existentially quantified variables
2097 that contains the whole input set or relation.
2098 In case of union sets and relations, the polyhedral hull is computed
2103 __isl_give isl_basic_set *isl_basic_set_sample(
2104 __isl_take isl_basic_set *bset);
2105 __isl_give isl_basic_set *isl_set_sample(
2106 __isl_take isl_set *set);
2107 __isl_give isl_basic_map *isl_basic_map_sample(
2108 __isl_take isl_basic_map *bmap);
2109 __isl_give isl_basic_map *isl_map_sample(
2110 __isl_take isl_map *map);
2112 If the input (basic) set or relation is non-empty, then return
2113 a singleton subset of the input. Otherwise, return an empty set.
2115 =item * Optimization
2117 #include <isl/ilp.h>
2118 enum isl_lp_result isl_basic_set_max(
2119 __isl_keep isl_basic_set *bset,
2120 __isl_keep isl_aff *obj, isl_int *opt)
2121 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2122 __isl_keep isl_aff *obj, isl_int *opt);
2123 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2124 __isl_keep isl_aff *obj, isl_int *opt);
2126 Compute the minimum or maximum of the integer affine expression C<obj>
2127 over the points in C<set>, returning the result in C<opt>.
2128 The return value may be one of C<isl_lp_error>,
2129 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2131 =item * Parametric optimization
2133 __isl_give isl_pw_aff *isl_set_dim_min(
2134 __isl_take isl_set *set, int pos);
2135 __isl_give isl_pw_aff *isl_set_dim_max(
2136 __isl_take isl_set *set, int pos);
2137 __isl_give isl_pw_aff *isl_map_dim_max(
2138 __isl_take isl_map *map, int pos);
2140 Compute the minimum or maximum of the given set or output dimension
2141 as a function of the parameters (and input dimensions), but independently
2142 of the other set or output dimensions.
2143 For lexicographic optimization, see L<"Lexicographic Optimization">.
2147 The following functions compute either the set of (rational) coefficient
2148 values of valid constraints for the given set or the set of (rational)
2149 values satisfying the constraints with coefficients from the given set.
2150 Internally, these two sets of functions perform essentially the
2151 same operations, except that the set of coefficients is assumed to
2152 be a cone, while the set of values may be any polyhedron.
2153 The current implementation is based on the Farkas lemma and
2154 Fourier-Motzkin elimination, but this may change or be made optional
2155 in future. In particular, future implementations may use different
2156 dualization algorithms or skip the elimination step.
2158 __isl_give isl_basic_set *isl_basic_set_coefficients(
2159 __isl_take isl_basic_set *bset);
2160 __isl_give isl_basic_set *isl_set_coefficients(
2161 __isl_take isl_set *set);
2162 __isl_give isl_union_set *isl_union_set_coefficients(
2163 __isl_take isl_union_set *bset);
2164 __isl_give isl_basic_set *isl_basic_set_solutions(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_basic_set *isl_set_solutions(
2167 __isl_take isl_set *set);
2168 __isl_give isl_union_set *isl_union_set_solutions(
2169 __isl_take isl_union_set *bset);
2173 __isl_give isl_map *isl_map_fixed_power(
2174 __isl_take isl_map *map, isl_int exp);
2175 __isl_give isl_union_map *isl_union_map_fixed_power(
2176 __isl_take isl_union_map *umap, isl_int exp);
2178 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2179 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2180 of C<map> is computed.
2182 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2184 __isl_give isl_union_map *isl_union_map_power(
2185 __isl_take isl_union_map *umap, int *exact);
2187 Compute a parametric representation for all positive powers I<k> of C<map>.
2188 The result maps I<k> to a nested relation corresponding to the
2189 I<k>th power of C<map>.
2190 The result may be an overapproximation. If the result is known to be exact,
2191 then C<*exact> is set to C<1>.
2193 =item * Transitive closure
2195 __isl_give isl_map *isl_map_transitive_closure(
2196 __isl_take isl_map *map, int *exact);
2197 __isl_give isl_union_map *isl_union_map_transitive_closure(
2198 __isl_take isl_union_map *umap, int *exact);
2200 Compute the transitive closure of C<map>.
2201 The result may be an overapproximation. If the result is known to be exact,
2202 then C<*exact> is set to C<1>.
2204 =item * Reaching path lengths
2206 __isl_give isl_map *isl_map_reaching_path_lengths(
2207 __isl_take isl_map *map, int *exact);
2209 Compute a relation that maps each element in the range of C<map>
2210 to the lengths of all paths composed of edges in C<map> that
2211 end up in the given element.
2212 The result may be an overapproximation. If the result is known to be exact,
2213 then C<*exact> is set to C<1>.
2214 To compute the I<maximal> path length, the resulting relation
2215 should be postprocessed by C<isl_map_lexmax>.
2216 In particular, if the input relation is a dependence relation
2217 (mapping sources to sinks), then the maximal path length corresponds
2218 to the free schedule.
2219 Note, however, that C<isl_map_lexmax> expects the maximum to be
2220 finite, so if the path lengths are unbounded (possibly due to
2221 the overapproximation), then you will get an error message.
2225 __isl_give isl_basic_set *isl_basic_map_wrap(
2226 __isl_take isl_basic_map *bmap);
2227 __isl_give isl_set *isl_map_wrap(
2228 __isl_take isl_map *map);
2229 __isl_give isl_union_set *isl_union_map_wrap(
2230 __isl_take isl_union_map *umap);
2231 __isl_give isl_basic_map *isl_basic_set_unwrap(
2232 __isl_take isl_basic_set *bset);
2233 __isl_give isl_map *isl_set_unwrap(
2234 __isl_take isl_set *set);
2235 __isl_give isl_union_map *isl_union_set_unwrap(
2236 __isl_take isl_union_set *uset);
2240 Remove any internal structure of domain (and range) of the given
2241 set or relation. If there is any such internal structure in the input,
2242 then the name of the space is also removed.
2244 __isl_give isl_basic_set *isl_basic_set_flatten(
2245 __isl_take isl_basic_set *bset);
2246 __isl_give isl_set *isl_set_flatten(
2247 __isl_take isl_set *set);
2248 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2249 __isl_take isl_basic_map *bmap);
2250 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2251 __isl_take isl_basic_map *bmap);
2252 __isl_give isl_map *isl_map_flatten_range(
2253 __isl_take isl_map *map);
2254 __isl_give isl_map *isl_map_flatten_domain(
2255 __isl_take isl_map *map);
2256 __isl_give isl_basic_map *isl_basic_map_flatten(
2257 __isl_take isl_basic_map *bmap);
2258 __isl_give isl_map *isl_map_flatten(
2259 __isl_take isl_map *map);
2261 __isl_give isl_map *isl_set_flatten_map(
2262 __isl_take isl_set *set);
2264 The function above constructs a relation
2265 that maps the input set to a flattened version of the set.
2269 Lift the input set to a space with extra dimensions corresponding
2270 to the existentially quantified variables in the input.
2271 In particular, the result lives in a wrapped map where the domain
2272 is the original space and the range corresponds to the original
2273 existentially quantified variables.
2275 __isl_give isl_basic_set *isl_basic_set_lift(
2276 __isl_take isl_basic_set *bset);
2277 __isl_give isl_set *isl_set_lift(
2278 __isl_take isl_set *set);
2279 __isl_give isl_union_set *isl_union_set_lift(
2280 __isl_take isl_union_set *uset);
2282 Given a local space that contains the existentially quantified
2283 variables of a set, a basic relation that, when applied to
2284 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2285 can be constructed using the following function.
2287 #include <isl/local_space.h>
2288 __isl_give isl_basic_map *isl_local_space_lifting(
2289 __isl_take isl_local_space *ls);
2291 =item * Internal Product
2293 __isl_give isl_basic_map *isl_basic_map_zip(
2294 __isl_take isl_basic_map *bmap);
2295 __isl_give isl_map *isl_map_zip(
2296 __isl_take isl_map *map);
2297 __isl_give isl_union_map *isl_union_map_zip(
2298 __isl_take isl_union_map *umap);
2300 Given a relation with nested relations for domain and range,
2301 interchange the range of the domain with the domain of the range.
2305 __isl_give isl_basic_map *isl_basic_map_curry(
2306 __isl_take isl_basic_map *bmap);
2307 __isl_give isl_map *isl_map_curry(
2308 __isl_take isl_map *map);
2309 __isl_give isl_union_map *isl_union_map_curry(
2310 __isl_take isl_union_map *umap);
2312 Given a relation with a nested relation for domain,
2313 move the range of the nested relation out of the domain
2314 and use it as the domain of a nested relation in the range,
2315 with the original range as range of this nested relation.
2317 =item * Aligning parameters
2319 __isl_give isl_set *isl_set_align_params(
2320 __isl_take isl_set *set,
2321 __isl_take isl_space *model);
2322 __isl_give isl_map *isl_map_align_params(
2323 __isl_take isl_map *map,
2324 __isl_take isl_space *model);
2326 Change the order of the parameters of the given set or relation
2327 such that the first parameters match those of C<model>.
2328 This may involve the introduction of extra parameters.
2329 All parameters need to be named.
2331 =item * Dimension manipulation
2333 __isl_give isl_set *isl_set_add_dims(
2334 __isl_take isl_set *set,
2335 enum isl_dim_type type, unsigned n);
2336 __isl_give isl_map *isl_map_add_dims(
2337 __isl_take isl_map *map,
2338 enum isl_dim_type type, unsigned n);
2339 __isl_give isl_set *isl_set_insert_dims(
2340 __isl_take isl_set *set,
2341 enum isl_dim_type type, unsigned pos, unsigned n);
2342 __isl_give isl_map *isl_map_insert_dims(
2343 __isl_take isl_map *map,
2344 enum isl_dim_type type, unsigned pos, unsigned n);
2345 __isl_give isl_basic_set *isl_basic_set_move_dims(
2346 __isl_take isl_basic_set *bset,
2347 enum isl_dim_type dst_type, unsigned dst_pos,
2348 enum isl_dim_type src_type, unsigned src_pos,
2350 __isl_give isl_basic_map *isl_basic_map_move_dims(
2351 __isl_take isl_basic_map *bmap,
2352 enum isl_dim_type dst_type, unsigned dst_pos,
2353 enum isl_dim_type src_type, unsigned src_pos,
2355 __isl_give isl_set *isl_set_move_dims(
2356 __isl_take isl_set *set,
2357 enum isl_dim_type dst_type, unsigned dst_pos,
2358 enum isl_dim_type src_type, unsigned src_pos,
2360 __isl_give isl_map *isl_map_move_dims(
2361 __isl_take isl_map *map,
2362 enum isl_dim_type dst_type, unsigned dst_pos,
2363 enum isl_dim_type src_type, unsigned src_pos,
2366 It is usually not advisable to directly change the (input or output)
2367 space of a set or a relation as this removes the name and the internal
2368 structure of the space. However, the above functions can be useful
2369 to add new parameters, assuming
2370 C<isl_set_align_params> and C<isl_map_align_params>
2375 =head2 Binary Operations
2377 The two arguments of a binary operation not only need to live
2378 in the same C<isl_ctx>, they currently also need to have
2379 the same (number of) parameters.
2381 =head3 Basic Operations
2385 =item * Intersection
2387 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2388 __isl_take isl_basic_set *bset1,
2389 __isl_take isl_basic_set *bset2);
2390 __isl_give isl_basic_set *isl_basic_set_intersect(
2391 __isl_take isl_basic_set *bset1,
2392 __isl_take isl_basic_set *bset2);
2393 __isl_give isl_set *isl_set_intersect_params(
2394 __isl_take isl_set *set,
2395 __isl_take isl_set *params);
2396 __isl_give isl_set *isl_set_intersect(
2397 __isl_take isl_set *set1,
2398 __isl_take isl_set *set2);
2399 __isl_give isl_union_set *isl_union_set_intersect_params(
2400 __isl_take isl_union_set *uset,
2401 __isl_take isl_set *set);
2402 __isl_give isl_union_map *isl_union_map_intersect_params(
2403 __isl_take isl_union_map *umap,
2404 __isl_take isl_set *set);
2405 __isl_give isl_union_set *isl_union_set_intersect(
2406 __isl_take isl_union_set *uset1,
2407 __isl_take isl_union_set *uset2);
2408 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2409 __isl_take isl_basic_map *bmap,
2410 __isl_take isl_basic_set *bset);
2411 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2412 __isl_take isl_basic_map *bmap,
2413 __isl_take isl_basic_set *bset);
2414 __isl_give isl_basic_map *isl_basic_map_intersect(
2415 __isl_take isl_basic_map *bmap1,
2416 __isl_take isl_basic_map *bmap2);
2417 __isl_give isl_map *isl_map_intersect_params(
2418 __isl_take isl_map *map,
2419 __isl_take isl_set *params);
2420 __isl_give isl_map *isl_map_intersect_domain(
2421 __isl_take isl_map *map,
2422 __isl_take isl_set *set);
2423 __isl_give isl_map *isl_map_intersect_range(
2424 __isl_take isl_map *map,
2425 __isl_take isl_set *set);
2426 __isl_give isl_map *isl_map_intersect(
2427 __isl_take isl_map *map1,
2428 __isl_take isl_map *map2);
2429 __isl_give isl_union_map *isl_union_map_intersect_domain(
2430 __isl_take isl_union_map *umap,
2431 __isl_take isl_union_set *uset);
2432 __isl_give isl_union_map *isl_union_map_intersect_range(
2433 __isl_take isl_union_map *umap,
2434 __isl_take isl_union_set *uset);
2435 __isl_give isl_union_map *isl_union_map_intersect(
2436 __isl_take isl_union_map *umap1,
2437 __isl_take isl_union_map *umap2);
2441 __isl_give isl_set *isl_basic_set_union(
2442 __isl_take isl_basic_set *bset1,
2443 __isl_take isl_basic_set *bset2);
2444 __isl_give isl_map *isl_basic_map_union(
2445 __isl_take isl_basic_map *bmap1,
2446 __isl_take isl_basic_map *bmap2);
2447 __isl_give isl_set *isl_set_union(
2448 __isl_take isl_set *set1,
2449 __isl_take isl_set *set2);
2450 __isl_give isl_map *isl_map_union(
2451 __isl_take isl_map *map1,
2452 __isl_take isl_map *map2);
2453 __isl_give isl_union_set *isl_union_set_union(
2454 __isl_take isl_union_set *uset1,
2455 __isl_take isl_union_set *uset2);
2456 __isl_give isl_union_map *isl_union_map_union(
2457 __isl_take isl_union_map *umap1,
2458 __isl_take isl_union_map *umap2);
2460 =item * Set difference
2462 __isl_give isl_set *isl_set_subtract(
2463 __isl_take isl_set *set1,
2464 __isl_take isl_set *set2);
2465 __isl_give isl_map *isl_map_subtract(
2466 __isl_take isl_map *map1,
2467 __isl_take isl_map *map2);
2468 __isl_give isl_map *isl_map_subtract_domain(
2469 __isl_take isl_map *map,
2470 __isl_take isl_set *dom);
2471 __isl_give isl_map *isl_map_subtract_range(
2472 __isl_take isl_map *map,
2473 __isl_take isl_set *dom);
2474 __isl_give isl_union_set *isl_union_set_subtract(
2475 __isl_take isl_union_set *uset1,
2476 __isl_take isl_union_set *uset2);
2477 __isl_give isl_union_map *isl_union_map_subtract(
2478 __isl_take isl_union_map *umap1,
2479 __isl_take isl_union_map *umap2);
2483 __isl_give isl_basic_set *isl_basic_set_apply(
2484 __isl_take isl_basic_set *bset,
2485 __isl_take isl_basic_map *bmap);
2486 __isl_give isl_set *isl_set_apply(
2487 __isl_take isl_set *set,
2488 __isl_take isl_map *map);
2489 __isl_give isl_union_set *isl_union_set_apply(
2490 __isl_take isl_union_set *uset,
2491 __isl_take isl_union_map *umap);
2492 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2493 __isl_take isl_basic_map *bmap1,
2494 __isl_take isl_basic_map *bmap2);
2495 __isl_give isl_basic_map *isl_basic_map_apply_range(
2496 __isl_take isl_basic_map *bmap1,
2497 __isl_take isl_basic_map *bmap2);
2498 __isl_give isl_map *isl_map_apply_domain(
2499 __isl_take isl_map *map1,
2500 __isl_take isl_map *map2);
2501 __isl_give isl_union_map *isl_union_map_apply_domain(
2502 __isl_take isl_union_map *umap1,
2503 __isl_take isl_union_map *umap2);
2504 __isl_give isl_map *isl_map_apply_range(
2505 __isl_take isl_map *map1,
2506 __isl_take isl_map *map2);
2507 __isl_give isl_union_map *isl_union_map_apply_range(
2508 __isl_take isl_union_map *umap1,
2509 __isl_take isl_union_map *umap2);
2511 =item * Cartesian Product
2513 __isl_give isl_set *isl_set_product(
2514 __isl_take isl_set *set1,
2515 __isl_take isl_set *set2);
2516 __isl_give isl_union_set *isl_union_set_product(
2517 __isl_take isl_union_set *uset1,
2518 __isl_take isl_union_set *uset2);
2519 __isl_give isl_basic_map *isl_basic_map_domain_product(
2520 __isl_take isl_basic_map *bmap1,
2521 __isl_take isl_basic_map *bmap2);
2522 __isl_give isl_basic_map *isl_basic_map_range_product(
2523 __isl_take isl_basic_map *bmap1,
2524 __isl_take isl_basic_map *bmap2);
2525 __isl_give isl_map *isl_map_domain_product(
2526 __isl_take isl_map *map1,
2527 __isl_take isl_map *map2);
2528 __isl_give isl_map *isl_map_range_product(
2529 __isl_take isl_map *map1,
2530 __isl_take isl_map *map2);
2531 __isl_give isl_union_map *isl_union_map_range_product(
2532 __isl_take isl_union_map *umap1,
2533 __isl_take isl_union_map *umap2);
2534 __isl_give isl_map *isl_map_product(
2535 __isl_take isl_map *map1,
2536 __isl_take isl_map *map2);
2537 __isl_give isl_union_map *isl_union_map_product(
2538 __isl_take isl_union_map *umap1,
2539 __isl_take isl_union_map *umap2);
2541 The above functions compute the cross product of the given
2542 sets or relations. The domains and ranges of the results
2543 are wrapped maps between domains and ranges of the inputs.
2544 To obtain a ``flat'' product, use the following functions
2547 __isl_give isl_basic_set *isl_basic_set_flat_product(
2548 __isl_take isl_basic_set *bset1,
2549 __isl_take isl_basic_set *bset2);
2550 __isl_give isl_set *isl_set_flat_product(
2551 __isl_take isl_set *set1,
2552 __isl_take isl_set *set2);
2553 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2554 __isl_take isl_basic_map *bmap1,
2555 __isl_take isl_basic_map *bmap2);
2556 __isl_give isl_map *isl_map_flat_domain_product(
2557 __isl_take isl_map *map1,
2558 __isl_take isl_map *map2);
2559 __isl_give isl_map *isl_map_flat_range_product(
2560 __isl_take isl_map *map1,
2561 __isl_take isl_map *map2);
2562 __isl_give isl_union_map *isl_union_map_flat_range_product(
2563 __isl_take isl_union_map *umap1,
2564 __isl_take isl_union_map *umap2);
2565 __isl_give isl_basic_map *isl_basic_map_flat_product(
2566 __isl_take isl_basic_map *bmap1,
2567 __isl_take isl_basic_map *bmap2);
2568 __isl_give isl_map *isl_map_flat_product(
2569 __isl_take isl_map *map1,
2570 __isl_take isl_map *map2);
2572 =item * Simplification
2574 __isl_give isl_basic_set *isl_basic_set_gist(
2575 __isl_take isl_basic_set *bset,
2576 __isl_take isl_basic_set *context);
2577 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2578 __isl_take isl_set *context);
2579 __isl_give isl_set *isl_set_gist_params(
2580 __isl_take isl_set *set,
2581 __isl_take isl_set *context);
2582 __isl_give isl_union_set *isl_union_set_gist(
2583 __isl_take isl_union_set *uset,
2584 __isl_take isl_union_set *context);
2585 __isl_give isl_union_set *isl_union_set_gist_params(
2586 __isl_take isl_union_set *uset,
2587 __isl_take isl_set *set);
2588 __isl_give isl_basic_map *isl_basic_map_gist(
2589 __isl_take isl_basic_map *bmap,
2590 __isl_take isl_basic_map *context);
2591 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2592 __isl_take isl_map *context);
2593 __isl_give isl_map *isl_map_gist_params(
2594 __isl_take isl_map *map,
2595 __isl_take isl_set *context);
2596 __isl_give isl_map *isl_map_gist_domain(
2597 __isl_take isl_map *map,
2598 __isl_take isl_set *context);
2599 __isl_give isl_map *isl_map_gist_range(
2600 __isl_take isl_map *map,
2601 __isl_take isl_set *context);
2602 __isl_give isl_union_map *isl_union_map_gist(
2603 __isl_take isl_union_map *umap,
2604 __isl_take isl_union_map *context);
2605 __isl_give isl_union_map *isl_union_map_gist_params(
2606 __isl_take isl_union_map *umap,
2607 __isl_take isl_set *set);
2608 __isl_give isl_union_map *isl_union_map_gist_domain(
2609 __isl_take isl_union_map *umap,
2610 __isl_take isl_union_set *uset);
2611 __isl_give isl_union_map *isl_union_map_gist_range(
2612 __isl_take isl_union_map *umap,
2613 __isl_take isl_union_set *uset);
2615 The gist operation returns a set or relation that has the
2616 same intersection with the context as the input set or relation.
2617 Any implicit equality in the intersection is made explicit in the result,
2618 while all inequalities that are redundant with respect to the intersection
2620 In case of union sets and relations, the gist operation is performed
2625 =head3 Lexicographic Optimization
2627 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2628 the following functions
2629 compute a set that contains the lexicographic minimum or maximum
2630 of the elements in C<set> (or C<bset>) for those values of the parameters
2631 that satisfy C<dom>.
2632 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2633 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2635 In other words, the union of the parameter values
2636 for which the result is non-empty and of C<*empty>
2639 __isl_give isl_set *isl_basic_set_partial_lexmin(
2640 __isl_take isl_basic_set *bset,
2641 __isl_take isl_basic_set *dom,
2642 __isl_give isl_set **empty);
2643 __isl_give isl_set *isl_basic_set_partial_lexmax(
2644 __isl_take isl_basic_set *bset,
2645 __isl_take isl_basic_set *dom,
2646 __isl_give isl_set **empty);
2647 __isl_give isl_set *isl_set_partial_lexmin(
2648 __isl_take isl_set *set, __isl_take isl_set *dom,
2649 __isl_give isl_set **empty);
2650 __isl_give isl_set *isl_set_partial_lexmax(
2651 __isl_take isl_set *set, __isl_take isl_set *dom,
2652 __isl_give isl_set **empty);
2654 Given a (basic) set C<set> (or C<bset>), the following functions simply
2655 return a set containing the lexicographic minimum or maximum
2656 of the elements in C<set> (or C<bset>).
2657 In case of union sets, the optimum is computed per space.
2659 __isl_give isl_set *isl_basic_set_lexmin(
2660 __isl_take isl_basic_set *bset);
2661 __isl_give isl_set *isl_basic_set_lexmax(
2662 __isl_take isl_basic_set *bset);
2663 __isl_give isl_set *isl_set_lexmin(
2664 __isl_take isl_set *set);
2665 __isl_give isl_set *isl_set_lexmax(
2666 __isl_take isl_set *set);
2667 __isl_give isl_union_set *isl_union_set_lexmin(
2668 __isl_take isl_union_set *uset);
2669 __isl_give isl_union_set *isl_union_set_lexmax(
2670 __isl_take isl_union_set *uset);
2672 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2673 the following functions
2674 compute a relation that maps each element of C<dom>
2675 to the single lexicographic minimum or maximum
2676 of the elements that are associated to that same
2677 element in C<map> (or C<bmap>).
2678 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2679 that contains the elements in C<dom> that do not map
2680 to any elements in C<map> (or C<bmap>).
2681 In other words, the union of the domain of the result and of C<*empty>
2684 __isl_give isl_map *isl_basic_map_partial_lexmax(
2685 __isl_take isl_basic_map *bmap,
2686 __isl_take isl_basic_set *dom,
2687 __isl_give isl_set **empty);
2688 __isl_give isl_map *isl_basic_map_partial_lexmin(
2689 __isl_take isl_basic_map *bmap,
2690 __isl_take isl_basic_set *dom,
2691 __isl_give isl_set **empty);
2692 __isl_give isl_map *isl_map_partial_lexmax(
2693 __isl_take isl_map *map, __isl_take isl_set *dom,
2694 __isl_give isl_set **empty);
2695 __isl_give isl_map *isl_map_partial_lexmin(
2696 __isl_take isl_map *map, __isl_take isl_set *dom,
2697 __isl_give isl_set **empty);
2699 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2700 return a map mapping each element in the domain of
2701 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2702 of all elements associated to that element.
2703 In case of union relations, the optimum is computed per space.
2705 __isl_give isl_map *isl_basic_map_lexmin(
2706 __isl_take isl_basic_map *bmap);
2707 __isl_give isl_map *isl_basic_map_lexmax(
2708 __isl_take isl_basic_map *bmap);
2709 __isl_give isl_map *isl_map_lexmin(
2710 __isl_take isl_map *map);
2711 __isl_give isl_map *isl_map_lexmax(
2712 __isl_take isl_map *map);
2713 __isl_give isl_union_map *isl_union_map_lexmin(
2714 __isl_take isl_union_map *umap);
2715 __isl_give isl_union_map *isl_union_map_lexmax(
2716 __isl_take isl_union_map *umap);
2718 The following functions return their result in the form of
2719 a piecewise multi-affine expression
2720 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2721 but are otherwise equivalent to the corresponding functions
2722 returning a basic set or relation.
2724 __isl_give isl_pw_multi_aff *
2725 isl_basic_map_lexmin_pw_multi_aff(
2726 __isl_take isl_basic_map *bmap);
2727 __isl_give isl_pw_multi_aff *
2728 isl_basic_set_partial_lexmin_pw_multi_aff(
2729 __isl_take isl_basic_set *bset,
2730 __isl_take isl_basic_set *dom,
2731 __isl_give isl_set **empty);
2732 __isl_give isl_pw_multi_aff *
2733 isl_basic_set_partial_lexmax_pw_multi_aff(
2734 __isl_take isl_basic_set *bset,
2735 __isl_take isl_basic_set *dom,
2736 __isl_give isl_set **empty);
2737 __isl_give isl_pw_multi_aff *
2738 isl_basic_map_partial_lexmin_pw_multi_aff(
2739 __isl_take isl_basic_map *bmap,
2740 __isl_take isl_basic_set *dom,
2741 __isl_give isl_set **empty);
2742 __isl_give isl_pw_multi_aff *
2743 isl_basic_map_partial_lexmax_pw_multi_aff(
2744 __isl_take isl_basic_map *bmap,
2745 __isl_take isl_basic_set *dom,
2746 __isl_give isl_set **empty);
2750 Lists are defined over several element types, including
2751 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2752 Here we take lists of C<isl_set>s as an example.
2753 Lists can be created, copied and freed using the following functions.
2755 #include <isl/list.h>
2756 __isl_give isl_set_list *isl_set_list_from_set(
2757 __isl_take isl_set *el);
2758 __isl_give isl_set_list *isl_set_list_alloc(
2759 isl_ctx *ctx, int n);
2760 __isl_give isl_set_list *isl_set_list_copy(
2761 __isl_keep isl_set_list *list);
2762 __isl_give isl_set_list *isl_set_list_add(
2763 __isl_take isl_set_list *list,
2764 __isl_take isl_set *el);
2765 __isl_give isl_set_list *isl_set_list_concat(
2766 __isl_take isl_set_list *list1,
2767 __isl_take isl_set_list *list2);
2768 void *isl_set_list_free(__isl_take isl_set_list *list);
2770 C<isl_set_list_alloc> creates an empty list with a capacity for
2771 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2774 Lists can be inspected using the following functions.
2776 #include <isl/list.h>
2777 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2778 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2779 __isl_give isl_set *isl_set_list_get_set(
2780 __isl_keep isl_set_list *list, int index);
2781 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2782 int (*fn)(__isl_take isl_set *el, void *user),
2785 Lists can be printed using
2787 #include <isl/list.h>
2788 __isl_give isl_printer *isl_printer_print_set_list(
2789 __isl_take isl_printer *p,
2790 __isl_keep isl_set_list *list);
2794 Vectors can be created, copied and freed using the following functions.
2796 #include <isl/vec.h>
2797 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2799 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2800 void isl_vec_free(__isl_take isl_vec *vec);
2802 Note that the elements of a newly created vector may have arbitrary values.
2803 The elements can be changed and inspected using the following functions.
2805 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2806 int isl_vec_size(__isl_keep isl_vec *vec);
2807 int isl_vec_get_element(__isl_keep isl_vec *vec,
2808 int pos, isl_int *v);
2809 __isl_give isl_vec *isl_vec_set_element(
2810 __isl_take isl_vec *vec, int pos, isl_int v);
2811 __isl_give isl_vec *isl_vec_set_element_si(
2812 __isl_take isl_vec *vec, int pos, int v);
2813 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2815 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2818 C<isl_vec_get_element> will return a negative value if anything went wrong.
2819 In that case, the value of C<*v> is undefined.
2823 Matrices can be created, copied and freed using the following functions.
2825 #include <isl/mat.h>
2826 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2827 unsigned n_row, unsigned n_col);
2828 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2829 void isl_mat_free(__isl_take isl_mat *mat);
2831 Note that the elements of a newly created matrix may have arbitrary values.
2832 The elements can be changed and inspected using the following functions.
2834 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2835 int isl_mat_rows(__isl_keep isl_mat *mat);
2836 int isl_mat_cols(__isl_keep isl_mat *mat);
2837 int isl_mat_get_element(__isl_keep isl_mat *mat,
2838 int row, int col, isl_int *v);
2839 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2840 int row, int col, isl_int v);
2841 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2842 int row, int col, int v);
2844 C<isl_mat_get_element> will return a negative value if anything went wrong.
2845 In that case, the value of C<*v> is undefined.
2847 The following function can be used to compute the (right) inverse
2848 of a matrix, i.e., a matrix such that the product of the original
2849 and the inverse (in that order) is a multiple of the identity matrix.
2850 The input matrix is assumed to be of full row-rank.
2852 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2854 The following function can be used to compute the (right) kernel
2855 (or null space) of a matrix, i.e., a matrix such that the product of
2856 the original and the kernel (in that order) is the zero matrix.
2858 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2860 =head2 Piecewise Quasi Affine Expressions
2862 The zero quasi affine expression on a given domain can be created using
2864 __isl_give isl_aff *isl_aff_zero_on_domain(
2865 __isl_take isl_local_space *ls);
2867 Note that the space in which the resulting object lives is a map space
2868 with the given space as domain and a one-dimensional range.
2870 An empty piecewise quasi affine expression (one with no cells)
2871 or a piecewise quasi affine expression with a single cell can
2872 be created using the following functions.
2874 #include <isl/aff.h>
2875 __isl_give isl_pw_aff *isl_pw_aff_empty(
2876 __isl_take isl_space *space);
2877 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2878 __isl_take isl_set *set, __isl_take isl_aff *aff);
2879 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2880 __isl_take isl_aff *aff);
2882 A piecewise quasi affine expression that is equal to 1 on a set
2883 and 0 outside the set can be created using the following function.
2885 #include <isl/aff.h>
2886 __isl_give isl_pw_aff *isl_set_indicator_function(
2887 __isl_take isl_set *set);
2889 Quasi affine expressions can be copied and freed using
2891 #include <isl/aff.h>
2892 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2893 void *isl_aff_free(__isl_take isl_aff *aff);
2895 __isl_give isl_pw_aff *isl_pw_aff_copy(
2896 __isl_keep isl_pw_aff *pwaff);
2897 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2899 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2900 using the following function. The constraint is required to have
2901 a non-zero coefficient for the specified dimension.
2903 #include <isl/constraint.h>
2904 __isl_give isl_aff *isl_constraint_get_bound(
2905 __isl_keep isl_constraint *constraint,
2906 enum isl_dim_type type, int pos);
2908 The entire affine expression of the constraint can also be extracted
2909 using the following function.
2911 #include <isl/constraint.h>
2912 __isl_give isl_aff *isl_constraint_get_aff(
2913 __isl_keep isl_constraint *constraint);
2915 Conversely, an equality constraint equating
2916 the affine expression to zero or an inequality constraint enforcing
2917 the affine expression to be non-negative, can be constructed using
2919 __isl_give isl_constraint *isl_equality_from_aff(
2920 __isl_take isl_aff *aff);
2921 __isl_give isl_constraint *isl_inequality_from_aff(
2922 __isl_take isl_aff *aff);
2924 The expression can be inspected using
2926 #include <isl/aff.h>
2927 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2928 int isl_aff_dim(__isl_keep isl_aff *aff,
2929 enum isl_dim_type type);
2930 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2931 __isl_keep isl_aff *aff);
2932 __isl_give isl_local_space *isl_aff_get_local_space(
2933 __isl_keep isl_aff *aff);
2934 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2935 enum isl_dim_type type, unsigned pos);
2936 const char *isl_pw_aff_get_dim_name(
2937 __isl_keep isl_pw_aff *pa,
2938 enum isl_dim_type type, unsigned pos);
2939 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2940 enum isl_dim_type type, unsigned pos);
2941 __isl_give isl_id *isl_pw_aff_get_dim_id(
2942 __isl_keep isl_pw_aff *pa,
2943 enum isl_dim_type type, unsigned pos);
2944 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2946 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2947 enum isl_dim_type type, int pos, isl_int *v);
2948 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2950 __isl_give isl_aff *isl_aff_get_div(
2951 __isl_keep isl_aff *aff, int pos);
2953 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2954 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2955 int (*fn)(__isl_take isl_set *set,
2956 __isl_take isl_aff *aff,
2957 void *user), void *user);
2959 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2960 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2962 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2963 enum isl_dim_type type, unsigned first, unsigned n);
2964 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2965 enum isl_dim_type type, unsigned first, unsigned n);
2967 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2968 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2969 enum isl_dim_type type);
2970 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2972 It can be modified using
2974 #include <isl/aff.h>
2975 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2976 __isl_take isl_pw_aff *pwaff,
2977 enum isl_dim_type type, __isl_take isl_id *id);
2978 __isl_give isl_aff *isl_aff_set_dim_name(
2979 __isl_take isl_aff *aff, enum isl_dim_type type,
2980 unsigned pos, const char *s);
2981 __isl_give isl_aff *isl_aff_set_dim_id(
2982 __isl_take isl_aff *aff, enum isl_dim_type type,
2983 unsigned pos, __isl_take isl_id *id);
2984 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2985 __isl_take isl_pw_aff *pma,
2986 enum isl_dim_type type, unsigned pos,
2987 __isl_take isl_id *id);
2988 __isl_give isl_aff *isl_aff_set_constant(
2989 __isl_take isl_aff *aff, isl_int v);
2990 __isl_give isl_aff *isl_aff_set_constant_si(
2991 __isl_take isl_aff *aff, int v);
2992 __isl_give isl_aff *isl_aff_set_coefficient(
2993 __isl_take isl_aff *aff,
2994 enum isl_dim_type type, int pos, isl_int v);
2995 __isl_give isl_aff *isl_aff_set_coefficient_si(
2996 __isl_take isl_aff *aff,
2997 enum isl_dim_type type, int pos, int v);
2998 __isl_give isl_aff *isl_aff_set_denominator(
2999 __isl_take isl_aff *aff, isl_int v);
3001 __isl_give isl_aff *isl_aff_add_constant(
3002 __isl_take isl_aff *aff, isl_int v);
3003 __isl_give isl_aff *isl_aff_add_constant_si(
3004 __isl_take isl_aff *aff, int v);
3005 __isl_give isl_aff *isl_aff_add_coefficient(
3006 __isl_take isl_aff *aff,
3007 enum isl_dim_type type, int pos, isl_int v);
3008 __isl_give isl_aff *isl_aff_add_coefficient_si(
3009 __isl_take isl_aff *aff,
3010 enum isl_dim_type type, int pos, int v);
3012 __isl_give isl_aff *isl_aff_insert_dims(
3013 __isl_take isl_aff *aff,
3014 enum isl_dim_type type, unsigned first, unsigned n);
3015 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3016 __isl_take isl_pw_aff *pwaff,
3017 enum isl_dim_type type, unsigned first, unsigned n);
3018 __isl_give isl_aff *isl_aff_add_dims(
3019 __isl_take isl_aff *aff,
3020 enum isl_dim_type type, unsigned n);
3021 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3022 __isl_take isl_pw_aff *pwaff,
3023 enum isl_dim_type type, unsigned n);
3024 __isl_give isl_aff *isl_aff_drop_dims(
3025 __isl_take isl_aff *aff,
3026 enum isl_dim_type type, unsigned first, unsigned n);
3027 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3028 __isl_take isl_pw_aff *pwaff,
3029 enum isl_dim_type type, unsigned first, unsigned n);
3031 Note that the C<set_constant> and C<set_coefficient> functions
3032 set the I<numerator> of the constant or coefficient, while
3033 C<add_constant> and C<add_coefficient> add an integer value to
3034 the possibly rational constant or coefficient.
3036 To check whether an affine expressions is obviously zero
3037 or obviously equal to some other affine expression, use
3039 #include <isl/aff.h>
3040 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3041 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3042 __isl_keep isl_aff *aff2);
3043 int isl_pw_aff_plain_is_equal(
3044 __isl_keep isl_pw_aff *pwaff1,
3045 __isl_keep isl_pw_aff *pwaff2);
3049 #include <isl/aff.h>
3050 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3051 __isl_take isl_aff *aff2);
3052 __isl_give isl_pw_aff *isl_pw_aff_add(
3053 __isl_take isl_pw_aff *pwaff1,
3054 __isl_take isl_pw_aff *pwaff2);
3055 __isl_give isl_pw_aff *isl_pw_aff_min(
3056 __isl_take isl_pw_aff *pwaff1,
3057 __isl_take isl_pw_aff *pwaff2);
3058 __isl_give isl_pw_aff *isl_pw_aff_max(
3059 __isl_take isl_pw_aff *pwaff1,
3060 __isl_take isl_pw_aff *pwaff2);
3061 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3062 __isl_take isl_aff *aff2);
3063 __isl_give isl_pw_aff *isl_pw_aff_sub(
3064 __isl_take isl_pw_aff *pwaff1,
3065 __isl_take isl_pw_aff *pwaff2);
3066 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3067 __isl_give isl_pw_aff *isl_pw_aff_neg(
3068 __isl_take isl_pw_aff *pwaff);
3069 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3070 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3071 __isl_take isl_pw_aff *pwaff);
3072 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3073 __isl_give isl_pw_aff *isl_pw_aff_floor(
3074 __isl_take isl_pw_aff *pwaff);
3075 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3077 __isl_give isl_pw_aff *isl_pw_aff_mod(
3078 __isl_take isl_pw_aff *pwaff, isl_int mod);
3079 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3081 __isl_give isl_pw_aff *isl_pw_aff_scale(
3082 __isl_take isl_pw_aff *pwaff, isl_int f);
3083 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3085 __isl_give isl_aff *isl_aff_scale_down_ui(
3086 __isl_take isl_aff *aff, unsigned f);
3087 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3088 __isl_take isl_pw_aff *pwaff, isl_int f);
3090 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3091 __isl_take isl_pw_aff_list *list);
3092 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3093 __isl_take isl_pw_aff_list *list);
3095 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3096 __isl_take isl_pw_aff *pwqp);
3098 __isl_give isl_aff *isl_aff_align_params(
3099 __isl_take isl_aff *aff,
3100 __isl_take isl_space *model);
3101 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3102 __isl_take isl_pw_aff *pwaff,
3103 __isl_take isl_space *model);
3105 __isl_give isl_aff *isl_aff_project_domain_on_params(
3106 __isl_take isl_aff *aff);
3108 __isl_give isl_aff *isl_aff_gist_params(
3109 __isl_take isl_aff *aff,
3110 __isl_take isl_set *context);
3111 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3112 __isl_take isl_set *context);
3113 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3114 __isl_take isl_pw_aff *pwaff,
3115 __isl_take isl_set *context);
3116 __isl_give isl_pw_aff *isl_pw_aff_gist(
3117 __isl_take isl_pw_aff *pwaff,
3118 __isl_take isl_set *context);
3120 __isl_give isl_set *isl_pw_aff_domain(
3121 __isl_take isl_pw_aff *pwaff);
3122 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3123 __isl_take isl_pw_aff *pa,
3124 __isl_take isl_set *set);
3125 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3126 __isl_take isl_pw_aff *pa,
3127 __isl_take isl_set *set);
3129 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3130 __isl_take isl_aff *aff2);
3131 __isl_give isl_pw_aff *isl_pw_aff_mul(
3132 __isl_take isl_pw_aff *pwaff1,
3133 __isl_take isl_pw_aff *pwaff2);
3135 When multiplying two affine expressions, at least one of the two needs
3138 #include <isl/aff.h>
3139 __isl_give isl_basic_set *isl_aff_le_basic_set(
3140 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3141 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3142 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3143 __isl_give isl_set *isl_pw_aff_eq_set(
3144 __isl_take isl_pw_aff *pwaff1,
3145 __isl_take isl_pw_aff *pwaff2);
3146 __isl_give isl_set *isl_pw_aff_ne_set(
3147 __isl_take isl_pw_aff *pwaff1,
3148 __isl_take isl_pw_aff *pwaff2);
3149 __isl_give isl_set *isl_pw_aff_le_set(
3150 __isl_take isl_pw_aff *pwaff1,
3151 __isl_take isl_pw_aff *pwaff2);
3152 __isl_give isl_set *isl_pw_aff_lt_set(
3153 __isl_take isl_pw_aff *pwaff1,
3154 __isl_take isl_pw_aff *pwaff2);
3155 __isl_give isl_set *isl_pw_aff_ge_set(
3156 __isl_take isl_pw_aff *pwaff1,
3157 __isl_take isl_pw_aff *pwaff2);
3158 __isl_give isl_set *isl_pw_aff_gt_set(
3159 __isl_take isl_pw_aff *pwaff1,
3160 __isl_take isl_pw_aff *pwaff2);
3162 __isl_give isl_set *isl_pw_aff_list_eq_set(
3163 __isl_take isl_pw_aff_list *list1,
3164 __isl_take isl_pw_aff_list *list2);
3165 __isl_give isl_set *isl_pw_aff_list_ne_set(
3166 __isl_take isl_pw_aff_list *list1,
3167 __isl_take isl_pw_aff_list *list2);
3168 __isl_give isl_set *isl_pw_aff_list_le_set(
3169 __isl_take isl_pw_aff_list *list1,
3170 __isl_take isl_pw_aff_list *list2);
3171 __isl_give isl_set *isl_pw_aff_list_lt_set(
3172 __isl_take isl_pw_aff_list *list1,
3173 __isl_take isl_pw_aff_list *list2);
3174 __isl_give isl_set *isl_pw_aff_list_ge_set(
3175 __isl_take isl_pw_aff_list *list1,
3176 __isl_take isl_pw_aff_list *list2);
3177 __isl_give isl_set *isl_pw_aff_list_gt_set(
3178 __isl_take isl_pw_aff_list *list1,
3179 __isl_take isl_pw_aff_list *list2);
3181 The function C<isl_aff_ge_basic_set> returns a basic set
3182 containing those elements in the shared space
3183 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3184 The function C<isl_aff_ge_set> returns a set
3185 containing those elements in the shared domain
3186 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3187 The functions operating on C<isl_pw_aff_list> apply the corresponding
3188 C<isl_pw_aff> function to each pair of elements in the two lists.
3190 #include <isl/aff.h>
3191 __isl_give isl_set *isl_pw_aff_nonneg_set(
3192 __isl_take isl_pw_aff *pwaff);
3193 __isl_give isl_set *isl_pw_aff_zero_set(
3194 __isl_take isl_pw_aff *pwaff);
3195 __isl_give isl_set *isl_pw_aff_non_zero_set(
3196 __isl_take isl_pw_aff *pwaff);
3198 The function C<isl_pw_aff_nonneg_set> returns a set
3199 containing those elements in the domain
3200 of C<pwaff> where C<pwaff> is non-negative.
3202 #include <isl/aff.h>
3203 __isl_give isl_pw_aff *isl_pw_aff_cond(
3204 __isl_take isl_pw_aff *cond,
3205 __isl_take isl_pw_aff *pwaff_true,
3206 __isl_take isl_pw_aff *pwaff_false);
3208 The function C<isl_pw_aff_cond> performs a conditional operator
3209 and returns an expression that is equal to C<pwaff_true>
3210 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3211 where C<cond> is zero.
3213 #include <isl/aff.h>
3214 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3215 __isl_take isl_pw_aff *pwaff1,
3216 __isl_take isl_pw_aff *pwaff2);
3217 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3218 __isl_take isl_pw_aff *pwaff1,
3219 __isl_take isl_pw_aff *pwaff2);
3220 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3221 __isl_take isl_pw_aff *pwaff1,
3222 __isl_take isl_pw_aff *pwaff2);
3224 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3225 expression with a domain that is the union of those of C<pwaff1> and
3226 C<pwaff2> and such that on each cell, the quasi-affine expression is
3227 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3228 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3229 associated expression is the defined one.
3231 An expression can be read from input using
3233 #include <isl/aff.h>
3234 __isl_give isl_aff *isl_aff_read_from_str(
3235 isl_ctx *ctx, const char *str);
3236 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3237 isl_ctx *ctx, const char *str);
3239 An expression can be printed using
3241 #include <isl/aff.h>
3242 __isl_give isl_printer *isl_printer_print_aff(
3243 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3245 __isl_give isl_printer *isl_printer_print_pw_aff(
3246 __isl_take isl_printer *p,
3247 __isl_keep isl_pw_aff *pwaff);
3249 =head2 Piecewise Multiple Quasi Affine Expressions
3251 An C<isl_multi_aff> object represents a sequence of
3252 zero or more affine expressions, all defined on the same domain space.
3254 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3257 #include <isl/aff.h>
3258 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3259 __isl_take isl_space *space,
3260 __isl_take isl_aff_list *list);
3262 An empty piecewise multiple quasi affine expression (one with no cells),
3263 the zero piecewise multiple quasi affine expression (with value zero
3264 for each output dimension),
3265 a piecewise multiple quasi affine expression with a single cell (with
3266 either a universe or a specified domain) or
3267 a zero-dimensional piecewise multiple quasi affine expression
3269 can be created using the following functions.
3271 #include <isl/aff.h>
3272 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3273 __isl_take isl_space *space);
3274 __isl_give isl_multi_aff *isl_multi_aff_zero(
3275 __isl_take isl_space *space);
3276 __isl_give isl_pw_multi_aff *
3277 isl_pw_multi_aff_from_multi_aff(
3278 __isl_take isl_multi_aff *ma);
3279 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3280 __isl_take isl_set *set,
3281 __isl_take isl_multi_aff *maff);
3282 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3283 __isl_take isl_set *set);
3285 __isl_give isl_union_pw_multi_aff *
3286 isl_union_pw_multi_aff_empty(
3287 __isl_take isl_space *space);
3288 __isl_give isl_union_pw_multi_aff *
3289 isl_union_pw_multi_aff_add_pw_multi_aff(
3290 __isl_take isl_union_pw_multi_aff *upma,
3291 __isl_take isl_pw_multi_aff *pma);
3292 __isl_give isl_union_pw_multi_aff *
3293 isl_union_pw_multi_aff_from_domain(
3294 __isl_take isl_union_set *uset);
3296 A piecewise multiple quasi affine expression can also be initialized
3297 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3298 and the C<isl_map> is single-valued.
3300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3301 __isl_take isl_set *set);
3302 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3303 __isl_take isl_map *map);
3305 Multiple quasi affine expressions can be copied and freed using
3307 #include <isl/aff.h>
3308 __isl_give isl_multi_aff *isl_multi_aff_copy(
3309 __isl_keep isl_multi_aff *maff);
3310 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3313 __isl_keep isl_pw_multi_aff *pma);
3314 void *isl_pw_multi_aff_free(
3315 __isl_take isl_pw_multi_aff *pma);
3317 __isl_give isl_union_pw_multi_aff *
3318 isl_union_pw_multi_aff_copy(
3319 __isl_keep isl_union_pw_multi_aff *upma);
3320 void *isl_union_pw_multi_aff_free(
3321 __isl_take isl_union_pw_multi_aff *upma);
3323 The expression can be inspected using
3325 #include <isl/aff.h>
3326 isl_ctx *isl_multi_aff_get_ctx(
3327 __isl_keep isl_multi_aff *maff);
3328 isl_ctx *isl_pw_multi_aff_get_ctx(
3329 __isl_keep isl_pw_multi_aff *pma);
3330 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3331 __isl_keep isl_union_pw_multi_aff *upma);
3332 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3333 enum isl_dim_type type);
3334 unsigned isl_pw_multi_aff_dim(
3335 __isl_keep isl_pw_multi_aff *pma,
3336 enum isl_dim_type type);
3337 __isl_give isl_aff *isl_multi_aff_get_aff(
3338 __isl_keep isl_multi_aff *multi, int pos);
3339 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3340 __isl_keep isl_pw_multi_aff *pma, int pos);
3341 const char *isl_pw_multi_aff_get_dim_name(
3342 __isl_keep isl_pw_multi_aff *pma,
3343 enum isl_dim_type type, unsigned pos);
3344 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3345 __isl_keep isl_pw_multi_aff *pma,
3346 enum isl_dim_type type, unsigned pos);
3347 const char *isl_multi_aff_get_tuple_name(
3348 __isl_keep isl_multi_aff *multi,
3349 enum isl_dim_type type);
3350 const char *isl_pw_multi_aff_get_tuple_name(
3351 __isl_keep isl_pw_multi_aff *pma,
3352 enum isl_dim_type type);
3353 int isl_pw_multi_aff_has_tuple_id(
3354 __isl_keep isl_pw_multi_aff *pma,
3355 enum isl_dim_type type);
3356 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3357 __isl_keep isl_pw_multi_aff *pma,
3358 enum isl_dim_type type);
3360 int isl_pw_multi_aff_foreach_piece(
3361 __isl_keep isl_pw_multi_aff *pma,
3362 int (*fn)(__isl_take isl_set *set,
3363 __isl_take isl_multi_aff *maff,
3364 void *user), void *user);
3366 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3367 __isl_keep isl_union_pw_multi_aff *upma,
3368 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3369 void *user), void *user);
3371 It can be modified using
3373 #include <isl/aff.h>
3374 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3375 __isl_take isl_multi_aff *multi, int pos,
3376 __isl_take isl_aff *aff);
3377 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3378 __isl_take isl_multi_aff *maff,
3379 enum isl_dim_type type, unsigned pos, const char *s);
3380 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3381 __isl_take isl_multi_aff *maff,
3382 enum isl_dim_type type, __isl_take isl_id *id);
3383 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3384 __isl_take isl_pw_multi_aff *pma,
3385 enum isl_dim_type type, __isl_take isl_id *id);
3387 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3388 __isl_take isl_multi_aff *maff,
3389 enum isl_dim_type type, unsigned first, unsigned n);
3391 To check whether two multiple affine expressions are
3392 obviously equal to each other, use
3394 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3395 __isl_keep isl_multi_aff *maff2);
3396 int isl_pw_multi_aff_plain_is_equal(
3397 __isl_keep isl_pw_multi_aff *pma1,
3398 __isl_keep isl_pw_multi_aff *pma2);
3402 #include <isl/aff.h>
3403 __isl_give isl_multi_aff *isl_multi_aff_add(
3404 __isl_take isl_multi_aff *maff1,
3405 __isl_take isl_multi_aff *maff2);
3406 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3407 __isl_take isl_pw_multi_aff *pma1,
3408 __isl_take isl_pw_multi_aff *pma2);
3409 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3410 __isl_take isl_union_pw_multi_aff *upma1,
3411 __isl_take isl_union_pw_multi_aff *upma2);
3412 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3413 __isl_take isl_pw_multi_aff *pma1,
3414 __isl_take isl_pw_multi_aff *pma2);
3415 __isl_give isl_multi_aff *isl_multi_aff_scale(
3416 __isl_take isl_multi_aff *maff,
3418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3419 __isl_take isl_pw_multi_aff *pma,
3420 __isl_take isl_set *set);
3421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3422 __isl_take isl_pw_multi_aff *pma,
3423 __isl_take isl_set *set);
3424 __isl_give isl_multi_aff *isl_multi_aff_lift(
3425 __isl_take isl_multi_aff *maff,
3426 __isl_give isl_local_space **ls);
3427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3428 __isl_take isl_pw_multi_aff *pma);
3429 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3430 __isl_take isl_multi_aff *maff,
3431 __isl_take isl_set *context);
3432 __isl_give isl_multi_aff *isl_multi_aff_gist(
3433 __isl_take isl_multi_aff *maff,
3434 __isl_take isl_set *context);
3435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3436 __isl_take isl_pw_multi_aff *pma,
3437 __isl_take isl_set *set);
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3439 __isl_take isl_pw_multi_aff *pma,
3440 __isl_take isl_set *set);
3441 __isl_give isl_set *isl_pw_multi_aff_domain(
3442 __isl_take isl_pw_multi_aff *pma);
3443 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3444 __isl_take isl_union_pw_multi_aff *upma);
3445 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3446 __isl_take isl_multi_aff *ma1,
3447 __isl_take isl_multi_aff *ma2);
3448 __isl_give isl_pw_multi_aff *
3449 isl_pw_multi_aff_flat_range_product(
3450 __isl_take isl_pw_multi_aff *pma1,
3451 __isl_take isl_pw_multi_aff *pma2);
3452 __isl_give isl_union_pw_multi_aff *
3453 isl_union_pw_multi_aff_flat_range_product(
3454 __isl_take isl_union_pw_multi_aff *upma1,
3455 __isl_take isl_union_pw_multi_aff *upma2);
3457 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3458 then it is assigned the local space that lies at the basis of
3459 the lifting applied.
3461 An expression can be read from input using
3463 #include <isl/aff.h>
3464 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3465 isl_ctx *ctx, const char *str);
3466 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3467 isl_ctx *ctx, const char *str);
3469 An expression can be printed using
3471 #include <isl/aff.h>
3472 __isl_give isl_printer *isl_printer_print_multi_aff(
3473 __isl_take isl_printer *p,
3474 __isl_keep isl_multi_aff *maff);
3475 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3476 __isl_take isl_printer *p,
3477 __isl_keep isl_pw_multi_aff *pma);
3478 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3479 __isl_take isl_printer *p,
3480 __isl_keep isl_union_pw_multi_aff *upma);
3484 Points are elements of a set. They can be used to construct
3485 simple sets (boxes) or they can be used to represent the
3486 individual elements of a set.
3487 The zero point (the origin) can be created using
3489 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3491 The coordinates of a point can be inspected, set and changed
3494 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3495 enum isl_dim_type type, int pos, isl_int *v);
3496 __isl_give isl_point *isl_point_set_coordinate(
3497 __isl_take isl_point *pnt,
3498 enum isl_dim_type type, int pos, isl_int v);
3500 __isl_give isl_point *isl_point_add_ui(
3501 __isl_take isl_point *pnt,
3502 enum isl_dim_type type, int pos, unsigned val);
3503 __isl_give isl_point *isl_point_sub_ui(
3504 __isl_take isl_point *pnt,
3505 enum isl_dim_type type, int pos, unsigned val);
3507 Other properties can be obtained using
3509 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3511 Points can be copied or freed using
3513 __isl_give isl_point *isl_point_copy(
3514 __isl_keep isl_point *pnt);
3515 void isl_point_free(__isl_take isl_point *pnt);
3517 A singleton set can be created from a point using
3519 __isl_give isl_basic_set *isl_basic_set_from_point(
3520 __isl_take isl_point *pnt);
3521 __isl_give isl_set *isl_set_from_point(
3522 __isl_take isl_point *pnt);
3524 and a box can be created from two opposite extremal points using
3526 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3527 __isl_take isl_point *pnt1,
3528 __isl_take isl_point *pnt2);
3529 __isl_give isl_set *isl_set_box_from_points(
3530 __isl_take isl_point *pnt1,
3531 __isl_take isl_point *pnt2);
3533 All elements of a B<bounded> (union) set can be enumerated using
3534 the following functions.
3536 int isl_set_foreach_point(__isl_keep isl_set *set,
3537 int (*fn)(__isl_take isl_point *pnt, void *user),
3539 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3540 int (*fn)(__isl_take isl_point *pnt, void *user),
3543 The function C<fn> is called for each integer point in
3544 C<set> with as second argument the last argument of
3545 the C<isl_set_foreach_point> call. The function C<fn>
3546 should return C<0> on success and C<-1> on failure.
3547 In the latter case, C<isl_set_foreach_point> will stop
3548 enumerating and return C<-1> as well.
3549 If the enumeration is performed successfully and to completion,
3550 then C<isl_set_foreach_point> returns C<0>.
3552 To obtain a single point of a (basic) set, use
3554 __isl_give isl_point *isl_basic_set_sample_point(
3555 __isl_take isl_basic_set *bset);
3556 __isl_give isl_point *isl_set_sample_point(
3557 __isl_take isl_set *set);
3559 If C<set> does not contain any (integer) points, then the
3560 resulting point will be ``void'', a property that can be
3563 int isl_point_is_void(__isl_keep isl_point *pnt);
3565 =head2 Piecewise Quasipolynomials
3567 A piecewise quasipolynomial is a particular kind of function that maps
3568 a parametric point to a rational value.
3569 More specifically, a quasipolynomial is a polynomial expression in greatest
3570 integer parts of affine expressions of parameters and variables.
3571 A piecewise quasipolynomial is a subdivision of a given parametric
3572 domain into disjoint cells with a quasipolynomial associated to
3573 each cell. The value of the piecewise quasipolynomial at a given
3574 point is the value of the quasipolynomial associated to the cell
3575 that contains the point. Outside of the union of cells,
3576 the value is assumed to be zero.
3577 For example, the piecewise quasipolynomial
3579 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3581 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3582 A given piecewise quasipolynomial has a fixed domain dimension.
3583 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3584 defined over different domains.
3585 Piecewise quasipolynomials are mainly used by the C<barvinok>
3586 library for representing the number of elements in a parametric set or map.
3587 For example, the piecewise quasipolynomial above represents
3588 the number of points in the map
3590 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3592 =head3 Input and Output
3594 Piecewise quasipolynomials can be read from input using
3596 __isl_give isl_union_pw_qpolynomial *
3597 isl_union_pw_qpolynomial_read_from_str(
3598 isl_ctx *ctx, const char *str);
3600 Quasipolynomials and piecewise quasipolynomials can be printed
3601 using the following functions.
3603 __isl_give isl_printer *isl_printer_print_qpolynomial(
3604 __isl_take isl_printer *p,
3605 __isl_keep isl_qpolynomial *qp);
3607 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3608 __isl_take isl_printer *p,
3609 __isl_keep isl_pw_qpolynomial *pwqp);
3611 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3612 __isl_take isl_printer *p,
3613 __isl_keep isl_union_pw_qpolynomial *upwqp);
3615 The output format of the printer
3616 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3617 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3619 In case of printing in C<ISL_FORMAT_C>, the user may want
3620 to set the names of all dimensions
3622 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3623 __isl_take isl_qpolynomial *qp,
3624 enum isl_dim_type type, unsigned pos,
3626 __isl_give isl_pw_qpolynomial *
3627 isl_pw_qpolynomial_set_dim_name(
3628 __isl_take isl_pw_qpolynomial *pwqp,
3629 enum isl_dim_type type, unsigned pos,
3632 =head3 Creating New (Piecewise) Quasipolynomials
3634 Some simple quasipolynomials can be created using the following functions.
3635 More complicated quasipolynomials can be created by applying
3636 operations such as addition and multiplication
3637 on the resulting quasipolynomials
3639 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3640 __isl_take isl_space *domain);
3641 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3642 __isl_take isl_space *domain);
3643 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3644 __isl_take isl_space *domain);
3645 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3646 __isl_take isl_space *domain);
3647 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3648 __isl_take isl_space *domain);
3649 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3650 __isl_take isl_space *domain,
3651 const isl_int n, const isl_int d);
3652 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3653 __isl_take isl_space *domain,
3654 enum isl_dim_type type, unsigned pos);
3655 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3656 __isl_take isl_aff *aff);
3658 Note that the space in which a quasipolynomial lives is a map space
3659 with a one-dimensional range. The C<domain> argument in some of
3660 the functions above corresponds to the domain of this map space.
3662 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3663 with a single cell can be created using the following functions.
3664 Multiple of these single cell piecewise quasipolynomials can
3665 be combined to create more complicated piecewise quasipolynomials.
3667 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3668 __isl_take isl_space *space);
3669 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3670 __isl_take isl_set *set,
3671 __isl_take isl_qpolynomial *qp);
3672 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3673 __isl_take isl_qpolynomial *qp);
3674 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3675 __isl_take isl_pw_aff *pwaff);
3677 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3678 __isl_take isl_space *space);
3679 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3680 __isl_take isl_pw_qpolynomial *pwqp);
3681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3682 __isl_take isl_union_pw_qpolynomial *upwqp,
3683 __isl_take isl_pw_qpolynomial *pwqp);
3685 Quasipolynomials can be copied and freed again using the following
3688 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3689 __isl_keep isl_qpolynomial *qp);
3690 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3692 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3693 __isl_keep isl_pw_qpolynomial *pwqp);
3694 void *isl_pw_qpolynomial_free(
3695 __isl_take isl_pw_qpolynomial *pwqp);
3697 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3698 __isl_keep isl_union_pw_qpolynomial *upwqp);
3699 void *isl_union_pw_qpolynomial_free(
3700 __isl_take isl_union_pw_qpolynomial *upwqp);
3702 =head3 Inspecting (Piecewise) Quasipolynomials
3704 To iterate over all piecewise quasipolynomials in a union
3705 piecewise quasipolynomial, use the following function
3707 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3708 __isl_keep isl_union_pw_qpolynomial *upwqp,
3709 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3712 To extract the piecewise quasipolynomial in a given space from a union, use
3714 __isl_give isl_pw_qpolynomial *
3715 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3716 __isl_keep isl_union_pw_qpolynomial *upwqp,
3717 __isl_take isl_space *space);
3719 To iterate over the cells in a piecewise quasipolynomial,
3720 use either of the following two functions
3722 int isl_pw_qpolynomial_foreach_piece(
3723 __isl_keep isl_pw_qpolynomial *pwqp,
3724 int (*fn)(__isl_take isl_set *set,
3725 __isl_take isl_qpolynomial *qp,
3726 void *user), void *user);
3727 int isl_pw_qpolynomial_foreach_lifted_piece(
3728 __isl_keep isl_pw_qpolynomial *pwqp,
3729 int (*fn)(__isl_take isl_set *set,
3730 __isl_take isl_qpolynomial *qp,
3731 void *user), void *user);
3733 As usual, the function C<fn> should return C<0> on success
3734 and C<-1> on failure. The difference between
3735 C<isl_pw_qpolynomial_foreach_piece> and
3736 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3737 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3738 compute unique representations for all existentially quantified
3739 variables and then turn these existentially quantified variables
3740 into extra set variables, adapting the associated quasipolynomial
3741 accordingly. This means that the C<set> passed to C<fn>
3742 will not have any existentially quantified variables, but that
3743 the dimensions of the sets may be different for different
3744 invocations of C<fn>.
3746 To iterate over all terms in a quasipolynomial,
3749 int isl_qpolynomial_foreach_term(
3750 __isl_keep isl_qpolynomial *qp,
3751 int (*fn)(__isl_take isl_term *term,
3752 void *user), void *user);
3754 The terms themselves can be inspected and freed using
3757 unsigned isl_term_dim(__isl_keep isl_term *term,
3758 enum isl_dim_type type);
3759 void isl_term_get_num(__isl_keep isl_term *term,
3761 void isl_term_get_den(__isl_keep isl_term *term,
3763 int isl_term_get_exp(__isl_keep isl_term *term,
3764 enum isl_dim_type type, unsigned pos);
3765 __isl_give isl_aff *isl_term_get_div(
3766 __isl_keep isl_term *term, unsigned pos);
3767 void isl_term_free(__isl_take isl_term *term);
3769 Each term is a product of parameters, set variables and
3770 integer divisions. The function C<isl_term_get_exp>
3771 returns the exponent of a given dimensions in the given term.
3772 The C<isl_int>s in the arguments of C<isl_term_get_num>
3773 and C<isl_term_get_den> need to have been initialized
3774 using C<isl_int_init> before calling these functions.
3776 =head3 Properties of (Piecewise) Quasipolynomials
3778 To check whether a quasipolynomial is actually a constant,
3779 use the following function.
3781 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3782 isl_int *n, isl_int *d);
3784 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3785 then the numerator and denominator of the constant
3786 are returned in C<*n> and C<*d>, respectively.
3788 To check whether two union piecewise quasipolynomials are
3789 obviously equal, use
3791 int isl_union_pw_qpolynomial_plain_is_equal(
3792 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3793 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3795 =head3 Operations on (Piecewise) Quasipolynomials
3797 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3798 __isl_take isl_qpolynomial *qp, isl_int v);
3799 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3800 __isl_take isl_qpolynomial *qp);
3801 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3802 __isl_take isl_qpolynomial *qp1,
3803 __isl_take isl_qpolynomial *qp2);
3804 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3805 __isl_take isl_qpolynomial *qp1,
3806 __isl_take isl_qpolynomial *qp2);
3807 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3808 __isl_take isl_qpolynomial *qp1,
3809 __isl_take isl_qpolynomial *qp2);
3810 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3811 __isl_take isl_qpolynomial *qp, unsigned exponent);
3813 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3814 __isl_take isl_pw_qpolynomial *pwqp1,
3815 __isl_take isl_pw_qpolynomial *pwqp2);
3816 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3817 __isl_take isl_pw_qpolynomial *pwqp1,
3818 __isl_take isl_pw_qpolynomial *pwqp2);
3819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3820 __isl_take isl_pw_qpolynomial *pwqp1,
3821 __isl_take isl_pw_qpolynomial *pwqp2);
3822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3823 __isl_take isl_pw_qpolynomial *pwqp);
3824 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3825 __isl_take isl_pw_qpolynomial *pwqp1,
3826 __isl_take isl_pw_qpolynomial *pwqp2);
3827 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3828 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3831 __isl_take isl_union_pw_qpolynomial *upwqp1,
3832 __isl_take isl_union_pw_qpolynomial *upwqp2);
3833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3834 __isl_take isl_union_pw_qpolynomial *upwqp1,
3835 __isl_take isl_union_pw_qpolynomial *upwqp2);
3836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3837 __isl_take isl_union_pw_qpolynomial *upwqp1,
3838 __isl_take isl_union_pw_qpolynomial *upwqp2);
3840 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3841 __isl_take isl_pw_qpolynomial *pwqp,
3842 __isl_take isl_point *pnt);
3844 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3845 __isl_take isl_union_pw_qpolynomial *upwqp,
3846 __isl_take isl_point *pnt);
3848 __isl_give isl_set *isl_pw_qpolynomial_domain(
3849 __isl_take isl_pw_qpolynomial *pwqp);
3850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3851 __isl_take isl_pw_qpolynomial *pwpq,
3852 __isl_take isl_set *set);
3853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3854 __isl_take isl_pw_qpolynomial *pwpq,
3855 __isl_take isl_set *set);
3857 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3858 __isl_take isl_union_pw_qpolynomial *upwqp);
3859 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3860 __isl_take isl_union_pw_qpolynomial *upwpq,
3861 __isl_take isl_union_set *uset);
3862 __isl_give isl_union_pw_qpolynomial *
3863 isl_union_pw_qpolynomial_intersect_params(
3864 __isl_take isl_union_pw_qpolynomial *upwpq,
3865 __isl_take isl_set *set);
3867 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3868 __isl_take isl_qpolynomial *qp,
3869 __isl_take isl_space *model);
3871 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3872 __isl_take isl_qpolynomial *qp);
3873 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3874 __isl_take isl_pw_qpolynomial *pwqp);
3876 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3877 __isl_take isl_union_pw_qpolynomial *upwqp);
3879 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3880 __isl_take isl_qpolynomial *qp,
3881 __isl_take isl_set *context);
3882 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3883 __isl_take isl_qpolynomial *qp,
3884 __isl_take isl_set *context);
3886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3887 __isl_take isl_pw_qpolynomial *pwqp,
3888 __isl_take isl_set *context);
3889 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3890 __isl_take isl_pw_qpolynomial *pwqp,
3891 __isl_take isl_set *context);
3893 __isl_give isl_union_pw_qpolynomial *
3894 isl_union_pw_qpolynomial_gist_params(
3895 __isl_take isl_union_pw_qpolynomial *upwqp,
3896 __isl_take isl_set *context);
3897 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3898 __isl_take isl_union_pw_qpolynomial *upwqp,
3899 __isl_take isl_union_set *context);
3901 The gist operation applies the gist operation to each of
3902 the cells in the domain of the input piecewise quasipolynomial.
3903 The context is also exploited
3904 to simplify the quasipolynomials associated to each cell.
3906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3907 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3908 __isl_give isl_union_pw_qpolynomial *
3909 isl_union_pw_qpolynomial_to_polynomial(
3910 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3912 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3913 the polynomial will be an overapproximation. If C<sign> is negative,
3914 it will be an underapproximation. If C<sign> is zero, the approximation
3915 will lie somewhere in between.
3917 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3919 A piecewise quasipolynomial reduction is a piecewise
3920 reduction (or fold) of quasipolynomials.
3921 In particular, the reduction can be maximum or a minimum.
3922 The objects are mainly used to represent the result of
3923 an upper or lower bound on a quasipolynomial over its domain,
3924 i.e., as the result of the following function.
3926 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3927 __isl_take isl_pw_qpolynomial *pwqp,
3928 enum isl_fold type, int *tight);
3930 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3931 __isl_take isl_union_pw_qpolynomial *upwqp,
3932 enum isl_fold type, int *tight);
3934 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3935 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3936 is the returned bound is known be tight, i.e., for each value
3937 of the parameters there is at least
3938 one element in the domain that reaches the bound.
3939 If the domain of C<pwqp> is not wrapping, then the bound is computed
3940 over all elements in that domain and the result has a purely parametric
3941 domain. If the domain of C<pwqp> is wrapping, then the bound is
3942 computed over the range of the wrapped relation. The domain of the
3943 wrapped relation becomes the domain of the result.
3945 A (piecewise) quasipolynomial reduction can be copied or freed using the
3946 following functions.
3948 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3949 __isl_keep isl_qpolynomial_fold *fold);
3950 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3951 __isl_keep isl_pw_qpolynomial_fold *pwf);
3952 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3953 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3954 void isl_qpolynomial_fold_free(
3955 __isl_take isl_qpolynomial_fold *fold);
3956 void *isl_pw_qpolynomial_fold_free(
3957 __isl_take isl_pw_qpolynomial_fold *pwf);
3958 void *isl_union_pw_qpolynomial_fold_free(
3959 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3961 =head3 Printing Piecewise Quasipolynomial Reductions
3963 Piecewise quasipolynomial reductions can be printed
3964 using the following function.
3966 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3967 __isl_take isl_printer *p,
3968 __isl_keep isl_pw_qpolynomial_fold *pwf);
3969 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3970 __isl_take isl_printer *p,
3971 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3973 For C<isl_printer_print_pw_qpolynomial_fold>,
3974 output format of the printer
3975 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3976 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3977 output format of the printer
3978 needs to be set to C<ISL_FORMAT_ISL>.
3979 In case of printing in C<ISL_FORMAT_C>, the user may want
3980 to set the names of all dimensions
3982 __isl_give isl_pw_qpolynomial_fold *
3983 isl_pw_qpolynomial_fold_set_dim_name(
3984 __isl_take isl_pw_qpolynomial_fold *pwf,
3985 enum isl_dim_type type, unsigned pos,
3988 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3990 To iterate over all piecewise quasipolynomial reductions in a union
3991 piecewise quasipolynomial reduction, use the following function
3993 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3994 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3995 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3996 void *user), void *user);
3998 To iterate over the cells in a piecewise quasipolynomial reduction,
3999 use either of the following two functions
4001 int isl_pw_qpolynomial_fold_foreach_piece(
4002 __isl_keep isl_pw_qpolynomial_fold *pwf,
4003 int (*fn)(__isl_take isl_set *set,
4004 __isl_take isl_qpolynomial_fold *fold,
4005 void *user), void *user);
4006 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4007 __isl_keep isl_pw_qpolynomial_fold *pwf,
4008 int (*fn)(__isl_take isl_set *set,
4009 __isl_take isl_qpolynomial_fold *fold,
4010 void *user), void *user);
4012 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4013 of the difference between these two functions.
4015 To iterate over all quasipolynomials in a reduction, use
4017 int isl_qpolynomial_fold_foreach_qpolynomial(
4018 __isl_keep isl_qpolynomial_fold *fold,
4019 int (*fn)(__isl_take isl_qpolynomial *qp,
4020 void *user), void *user);
4022 =head3 Properties of Piecewise Quasipolynomial Reductions
4024 To check whether two union piecewise quasipolynomial reductions are
4025 obviously equal, use
4027 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4028 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4029 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4031 =head3 Operations on Piecewise Quasipolynomial Reductions
4033 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4034 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4036 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4037 __isl_take isl_pw_qpolynomial_fold *pwf1,
4038 __isl_take isl_pw_qpolynomial_fold *pwf2);
4040 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4041 __isl_take isl_pw_qpolynomial_fold *pwf1,
4042 __isl_take isl_pw_qpolynomial_fold *pwf2);
4044 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4045 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4046 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4048 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4049 __isl_take isl_pw_qpolynomial_fold *pwf,
4050 __isl_take isl_point *pnt);
4052 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4053 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4054 __isl_take isl_point *pnt);
4056 __isl_give isl_pw_qpolynomial_fold *
4057 sl_pw_qpolynomial_fold_intersect_params(
4058 __isl_take isl_pw_qpolynomial_fold *pwf,
4059 __isl_take isl_set *set);
4061 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4062 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4063 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4064 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4065 __isl_take isl_union_set *uset);
4066 __isl_give isl_union_pw_qpolynomial_fold *
4067 isl_union_pw_qpolynomial_fold_intersect_params(
4068 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4069 __isl_take isl_set *set);
4071 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4072 __isl_take isl_pw_qpolynomial_fold *pwf);
4074 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4075 __isl_take isl_pw_qpolynomial_fold *pwf);
4077 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4078 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4080 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4081 __isl_take isl_qpolynomial_fold *fold,
4082 __isl_take isl_set *context);
4083 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4084 __isl_take isl_qpolynomial_fold *fold,
4085 __isl_take isl_set *context);
4087 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4088 __isl_take isl_pw_qpolynomial_fold *pwf,
4089 __isl_take isl_set *context);
4090 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4091 __isl_take isl_pw_qpolynomial_fold *pwf,
4092 __isl_take isl_set *context);
4094 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4095 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4096 __isl_take isl_union_set *context);
4097 __isl_give isl_union_pw_qpolynomial_fold *
4098 isl_union_pw_qpolynomial_fold_gist_params(
4099 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4100 __isl_take isl_set *context);
4102 The gist operation applies the gist operation to each of
4103 the cells in the domain of the input piecewise quasipolynomial reduction.
4104 In future, the operation will also exploit the context
4105 to simplify the quasipolynomial reductions associated to each cell.
4107 __isl_give isl_pw_qpolynomial_fold *
4108 isl_set_apply_pw_qpolynomial_fold(
4109 __isl_take isl_set *set,
4110 __isl_take isl_pw_qpolynomial_fold *pwf,
4112 __isl_give isl_pw_qpolynomial_fold *
4113 isl_map_apply_pw_qpolynomial_fold(
4114 __isl_take isl_map *map,
4115 __isl_take isl_pw_qpolynomial_fold *pwf,
4117 __isl_give isl_union_pw_qpolynomial_fold *
4118 isl_union_set_apply_union_pw_qpolynomial_fold(
4119 __isl_take isl_union_set *uset,
4120 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4122 __isl_give isl_union_pw_qpolynomial_fold *
4123 isl_union_map_apply_union_pw_qpolynomial_fold(
4124 __isl_take isl_union_map *umap,
4125 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4128 The functions taking a map
4129 compose the given map with the given piecewise quasipolynomial reduction.
4130 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4131 over all elements in the intersection of the range of the map
4132 and the domain of the piecewise quasipolynomial reduction
4133 as a function of an element in the domain of the map.
4134 The functions taking a set compute a bound over all elements in the
4135 intersection of the set and the domain of the
4136 piecewise quasipolynomial reduction.
4138 =head2 Dependence Analysis
4140 C<isl> contains specialized functionality for performing
4141 array dataflow analysis. That is, given a I<sink> access relation
4142 and a collection of possible I<source> access relations,
4143 C<isl> can compute relations that describe
4144 for each iteration of the sink access, which iteration
4145 of which of the source access relations was the last
4146 to access the same data element before the given iteration
4148 The resulting dependence relations map source iterations
4149 to the corresponding sink iterations.
4150 To compute standard flow dependences, the sink should be
4151 a read, while the sources should be writes.
4152 If any of the source accesses are marked as being I<may>
4153 accesses, then there will be a dependence from the last
4154 I<must> access B<and> from any I<may> access that follows
4155 this last I<must> access.
4156 In particular, if I<all> sources are I<may> accesses,
4157 then memory based dependence analysis is performed.
4158 If, on the other hand, all sources are I<must> accesses,
4159 then value based dependence analysis is performed.
4161 #include <isl/flow.h>
4163 typedef int (*isl_access_level_before)(void *first, void *second);
4165 __isl_give isl_access_info *isl_access_info_alloc(
4166 __isl_take isl_map *sink,
4167 void *sink_user, isl_access_level_before fn,
4169 __isl_give isl_access_info *isl_access_info_add_source(
4170 __isl_take isl_access_info *acc,
4171 __isl_take isl_map *source, int must,
4173 void isl_access_info_free(__isl_take isl_access_info *acc);
4175 __isl_give isl_flow *isl_access_info_compute_flow(
4176 __isl_take isl_access_info *acc);
4178 int isl_flow_foreach(__isl_keep isl_flow *deps,
4179 int (*fn)(__isl_take isl_map *dep, int must,
4180 void *dep_user, void *user),
4182 __isl_give isl_map *isl_flow_get_no_source(
4183 __isl_keep isl_flow *deps, int must);
4184 void isl_flow_free(__isl_take isl_flow *deps);
4186 The function C<isl_access_info_compute_flow> performs the actual
4187 dependence analysis. The other functions are used to construct
4188 the input for this function or to read off the output.
4190 The input is collected in an C<isl_access_info>, which can
4191 be created through a call to C<isl_access_info_alloc>.
4192 The arguments to this functions are the sink access relation
4193 C<sink>, a token C<sink_user> used to identify the sink
4194 access to the user, a callback function for specifying the
4195 relative order of source and sink accesses, and the number
4196 of source access relations that will be added.
4197 The callback function has type C<int (*)(void *first, void *second)>.
4198 The function is called with two user supplied tokens identifying
4199 either a source or the sink and it should return the shared nesting
4200 level and the relative order of the two accesses.
4201 In particular, let I<n> be the number of loops shared by
4202 the two accesses. If C<first> precedes C<second> textually,
4203 then the function should return I<2 * n + 1>; otherwise,
4204 it should return I<2 * n>.
4205 The sources can be added to the C<isl_access_info> by performing
4206 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4207 C<must> indicates whether the source is a I<must> access
4208 or a I<may> access. Note that a multi-valued access relation
4209 should only be marked I<must> if every iteration in the domain
4210 of the relation accesses I<all> elements in its image.
4211 The C<source_user> token is again used to identify
4212 the source access. The range of the source access relation
4213 C<source> should have the same dimension as the range
4214 of the sink access relation.
4215 The C<isl_access_info_free> function should usually not be
4216 called explicitly, because it is called implicitly by
4217 C<isl_access_info_compute_flow>.
4219 The result of the dependence analysis is collected in an
4220 C<isl_flow>. There may be elements of
4221 the sink access for which no preceding source access could be
4222 found or for which all preceding sources are I<may> accesses.
4223 The relations containing these elements can be obtained through
4224 calls to C<isl_flow_get_no_source>, the first with C<must> set
4225 and the second with C<must> unset.
4226 In the case of standard flow dependence analysis,
4227 with the sink a read and the sources I<must> writes,
4228 the first relation corresponds to the reads from uninitialized
4229 array elements and the second relation is empty.
4230 The actual flow dependences can be extracted using
4231 C<isl_flow_foreach>. This function will call the user-specified
4232 callback function C<fn> for each B<non-empty> dependence between
4233 a source and the sink. The callback function is called
4234 with four arguments, the actual flow dependence relation
4235 mapping source iterations to sink iterations, a boolean that
4236 indicates whether it is a I<must> or I<may> dependence, a token
4237 identifying the source and an additional C<void *> with value
4238 equal to the third argument of the C<isl_flow_foreach> call.
4239 A dependence is marked I<must> if it originates from a I<must>
4240 source and if it is not followed by any I<may> sources.
4242 After finishing with an C<isl_flow>, the user should call
4243 C<isl_flow_free> to free all associated memory.
4245 A higher-level interface to dependence analysis is provided
4246 by the following function.
4248 #include <isl/flow.h>
4250 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4251 __isl_take isl_union_map *must_source,
4252 __isl_take isl_union_map *may_source,
4253 __isl_take isl_union_map *schedule,
4254 __isl_give isl_union_map **must_dep,
4255 __isl_give isl_union_map **may_dep,
4256 __isl_give isl_union_map **must_no_source,
4257 __isl_give isl_union_map **may_no_source);
4259 The arrays are identified by the tuple names of the ranges
4260 of the accesses. The iteration domains by the tuple names
4261 of the domains of the accesses and of the schedule.
4262 The relative order of the iteration domains is given by the
4263 schedule. The relations returned through C<must_no_source>
4264 and C<may_no_source> are subsets of C<sink>.
4265 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4266 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4267 any of the other arguments is treated as an error.
4269 =head3 Interaction with Dependence Analysis
4271 During the dependence analysis, we frequently need to perform
4272 the following operation. Given a relation between sink iterations
4273 and potential soure iterations from a particular source domain,
4274 what is the last potential source iteration corresponding to each
4275 sink iteration. It can sometimes be convenient to adjust
4276 the set of potential source iterations before or after each such operation.
4277 The prototypical example is fuzzy array dataflow analysis,
4278 where we need to analyze if, based on data-dependent constraints,
4279 the sink iteration can ever be executed without one or more of
4280 the corresponding potential source iterations being executed.
4281 If so, we can introduce extra parameters and select an unknown
4282 but fixed source iteration from the potential source iterations.
4283 To be able to perform such manipulations, C<isl> provides the following
4286 #include <isl/flow.h>
4288 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4289 __isl_keep isl_map *source_map,
4290 __isl_keep isl_set *sink, void *source_user,
4292 __isl_give isl_access_info *isl_access_info_set_restrict(
4293 __isl_take isl_access_info *acc,
4294 isl_access_restrict fn, void *user);
4296 The function C<isl_access_info_set_restrict> should be called
4297 before calling C<isl_access_info_compute_flow> and registers a callback function
4298 that will be called any time C<isl> is about to compute the last
4299 potential source. The first argument is the (reverse) proto-dependence,
4300 mapping sink iterations to potential source iterations.
4301 The second argument represents the sink iterations for which
4302 we want to compute the last source iteration.
4303 The third argument is the token corresponding to the source
4304 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4305 The callback is expected to return a restriction on either the input or
4306 the output of the operation computing the last potential source.
4307 If the input needs to be restricted then restrictions are needed
4308 for both the source and the sink iterations. The sink iterations
4309 and the potential source iterations will be intersected with these sets.
4310 If the output needs to be restricted then only a restriction on the source
4311 iterations is required.
4312 If any error occurs, the callback should return C<NULL>.
4313 An C<isl_restriction> object can be created and freed using the following
4316 #include <isl/flow.h>
4318 __isl_give isl_restriction *isl_restriction_input(
4319 __isl_take isl_set *source_restr,
4320 __isl_take isl_set *sink_restr);
4321 __isl_give isl_restriction *isl_restriction_output(
4322 __isl_take isl_set *source_restr);
4323 __isl_give isl_restriction *isl_restriction_none(
4324 __isl_keep isl_map *source_map);
4325 __isl_give isl_restriction *isl_restriction_empty(
4326 __isl_keep isl_map *source_map);
4327 void *isl_restriction_free(
4328 __isl_take isl_restriction *restr);
4330 C<isl_restriction_none> and C<isl_restriction_empty> are special
4331 cases of C<isl_restriction_input>. C<isl_restriction_none>
4332 is essentially equivalent to
4334 isl_restriction_input(isl_set_universe(
4335 isl_space_range(isl_map_get_space(source_map))),
4337 isl_space_domain(isl_map_get_space(source_map))));
4339 whereas C<isl_restriction_empty> is essentially equivalent to
4341 isl_restriction_input(isl_set_empty(
4342 isl_space_range(isl_map_get_space(source_map))),
4344 isl_space_domain(isl_map_get_space(source_map))));
4348 B<The functionality described in this section is fairly new
4349 and may be subject to change.>
4351 The following function can be used to compute a schedule
4352 for a union of domains.
4353 By default, the algorithm used to construct the schedule is similar
4354 to that of C<Pluto>.
4355 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4357 The generated schedule respects all C<validity> dependences.
4358 That is, all dependence distances over these dependences in the
4359 scheduled space are lexicographically positive.
4360 The default algorithm tries to minimize the dependence distances over
4361 C<proximity> dependences.
4362 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4363 for groups of domains where the dependence distances have only
4364 non-negative values.
4365 When using Feautrier's algorithm, the C<proximity> dependence
4366 distances are only minimized during the extension to a
4367 full-dimensional schedule.
4369 #include <isl/schedule.h>
4370 __isl_give isl_schedule *isl_union_set_compute_schedule(
4371 __isl_take isl_union_set *domain,
4372 __isl_take isl_union_map *validity,
4373 __isl_take isl_union_map *proximity);
4374 void *isl_schedule_free(__isl_take isl_schedule *sched);
4376 A mapping from the domains to the scheduled space can be obtained
4377 from an C<isl_schedule> using the following function.
4379 __isl_give isl_union_map *isl_schedule_get_map(
4380 __isl_keep isl_schedule *sched);
4382 A representation of the schedule can be printed using
4384 __isl_give isl_printer *isl_printer_print_schedule(
4385 __isl_take isl_printer *p,
4386 __isl_keep isl_schedule *schedule);
4388 A representation of the schedule as a forest of bands can be obtained
4389 using the following function.
4391 __isl_give isl_band_list *isl_schedule_get_band_forest(
4392 __isl_keep isl_schedule *schedule);
4394 The list can be manipulated as explained in L<"Lists">.
4395 The bands inside the list can be copied and freed using the following
4398 #include <isl/band.h>
4399 __isl_give isl_band *isl_band_copy(
4400 __isl_keep isl_band *band);
4401 void *isl_band_free(__isl_take isl_band *band);
4403 Each band contains zero or more scheduling dimensions.
4404 These are referred to as the members of the band.
4405 The section of the schedule that corresponds to the band is
4406 referred to as the partial schedule of the band.
4407 For those nodes that participate in a band, the outer scheduling
4408 dimensions form the prefix schedule, while the inner scheduling
4409 dimensions form the suffix schedule.
4410 That is, if we take a cut of the band forest, then the union of
4411 the concatenations of the prefix, partial and suffix schedules of
4412 each band in the cut is equal to the entire schedule (modulo
4413 some possible padding at the end with zero scheduling dimensions).
4414 The properties of a band can be inspected using the following functions.
4416 #include <isl/band.h>
4417 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4419 int isl_band_has_children(__isl_keep isl_band *band);
4420 __isl_give isl_band_list *isl_band_get_children(
4421 __isl_keep isl_band *band);
4423 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4424 __isl_keep isl_band *band);
4425 __isl_give isl_union_map *isl_band_get_partial_schedule(
4426 __isl_keep isl_band *band);
4427 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4428 __isl_keep isl_band *band);
4430 int isl_band_n_member(__isl_keep isl_band *band);
4431 int isl_band_member_is_zero_distance(
4432 __isl_keep isl_band *band, int pos);
4434 Note that a scheduling dimension is considered to be ``zero
4435 distance'' if it does not carry any proximity dependences
4437 That is, if the dependence distances of the proximity
4438 dependences are all zero in that direction (for fixed
4439 iterations of outer bands).
4441 A representation of the band can be printed using
4443 #include <isl/band.h>
4444 __isl_give isl_printer *isl_printer_print_band(
4445 __isl_take isl_printer *p,
4446 __isl_keep isl_band *band);
4450 #include <isl/schedule.h>
4451 int isl_options_set_schedule_max_coefficient(
4452 isl_ctx *ctx, int val);
4453 int isl_options_get_schedule_max_coefficient(
4455 int isl_options_set_schedule_max_constant_term(
4456 isl_ctx *ctx, int val);
4457 int isl_options_get_schedule_max_constant_term(
4459 int isl_options_set_schedule_maximize_band_depth(
4460 isl_ctx *ctx, int val);
4461 int isl_options_get_schedule_maximize_band_depth(
4463 int isl_options_set_schedule_outer_zero_distance(
4464 isl_ctx *ctx, int val);
4465 int isl_options_get_schedule_outer_zero_distance(
4467 int isl_options_set_schedule_split_scaled(
4468 isl_ctx *ctx, int val);
4469 int isl_options_get_schedule_split_scaled(
4471 int isl_options_set_schedule_algorithm(
4472 isl_ctx *ctx, int val);
4473 int isl_options_get_schedule_algorithm(
4479 =item * schedule_max_coefficient
4481 This option enforces that the coefficients for variable and parameter
4482 dimensions in the calculated schedule are not larger than the specified value.
4483 This option can significantly increase the speed of the scheduling calculation
4484 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4485 this option does not introduce bounds on the variable or parameter
4488 =item * schedule_max_constant_term
4490 This option enforces that the constant coefficients in the calculated schedule
4491 are not larger than the maximal constant term. This option can significantly
4492 increase the speed of the scheduling calculation and may also prevent fusing of
4493 unrelated dimensions. A value of -1 means that this option does not introduce
4494 bounds on the constant coefficients.
4496 =item * schedule_maximize_band_depth
4498 If this option is set, we do not split bands at the point
4499 where we detect splitting is necessary. Instead, we
4500 backtrack and split bands as early as possible. This
4501 reduces the number of splits and maximizes the width of
4502 the bands. Wider bands give more possibilities for tiling.
4504 =item * schedule_outer_zero_distance
4506 If this option is set, then we try to construct schedules
4507 where the outermost scheduling dimension in each band
4508 results in a zero dependence distance over the proximity
4511 =item * schedule_split_scaled
4513 If this option is set, then we try to construct schedules in which the
4514 constant term is split off from the linear part if the linear parts of
4515 the scheduling rows for all nodes in the graphs have a common non-trivial
4517 The constant term is then placed in a separate band and the linear
4520 =item * schedule_algorithm
4522 Selects the scheduling algorithm to be used.
4523 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4524 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4528 =head2 Parametric Vertex Enumeration
4530 The parametric vertex enumeration described in this section
4531 is mainly intended to be used internally and by the C<barvinok>
4534 #include <isl/vertices.h>
4535 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4536 __isl_keep isl_basic_set *bset);
4538 The function C<isl_basic_set_compute_vertices> performs the
4539 actual computation of the parametric vertices and the chamber
4540 decomposition and store the result in an C<isl_vertices> object.
4541 This information can be queried by either iterating over all
4542 the vertices or iterating over all the chambers or cells
4543 and then iterating over all vertices that are active on the chamber.
4545 int isl_vertices_foreach_vertex(
4546 __isl_keep isl_vertices *vertices,
4547 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4550 int isl_vertices_foreach_cell(
4551 __isl_keep isl_vertices *vertices,
4552 int (*fn)(__isl_take isl_cell *cell, void *user),
4554 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4555 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4558 Other operations that can be performed on an C<isl_vertices> object are
4561 isl_ctx *isl_vertices_get_ctx(
4562 __isl_keep isl_vertices *vertices);
4563 int isl_vertices_get_n_vertices(
4564 __isl_keep isl_vertices *vertices);
4565 void isl_vertices_free(__isl_take isl_vertices *vertices);
4567 Vertices can be inspected and destroyed using the following functions.
4569 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4570 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4571 __isl_give isl_basic_set *isl_vertex_get_domain(
4572 __isl_keep isl_vertex *vertex);
4573 __isl_give isl_basic_set *isl_vertex_get_expr(
4574 __isl_keep isl_vertex *vertex);
4575 void isl_vertex_free(__isl_take isl_vertex *vertex);
4577 C<isl_vertex_get_expr> returns a singleton parametric set describing
4578 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4580 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4581 B<rational> basic sets, so they should mainly be used for inspection
4582 and should not be mixed with integer sets.
4584 Chambers can be inspected and destroyed using the following functions.
4586 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4587 __isl_give isl_basic_set *isl_cell_get_domain(
4588 __isl_keep isl_cell *cell);
4589 void isl_cell_free(__isl_take isl_cell *cell);
4593 Although C<isl> is mainly meant to be used as a library,
4594 it also contains some basic applications that use some
4595 of the functionality of C<isl>.
4596 The input may be specified in either the L<isl format>
4597 or the L<PolyLib format>.
4599 =head2 C<isl_polyhedron_sample>
4601 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4602 an integer element of the polyhedron, if there is any.
4603 The first column in the output is the denominator and is always
4604 equal to 1. If the polyhedron contains no integer points,
4605 then a vector of length zero is printed.
4609 C<isl_pip> takes the same input as the C<example> program
4610 from the C<piplib> distribution, i.e., a set of constraints
4611 on the parameters, a line containing only -1 and finally a set
4612 of constraints on a parametric polyhedron.
4613 The coefficients of the parameters appear in the last columns
4614 (but before the final constant column).
4615 The output is the lexicographic minimum of the parametric polyhedron.
4616 As C<isl> currently does not have its own output format, the output
4617 is just a dump of the internal state.
4619 =head2 C<isl_polyhedron_minimize>
4621 C<isl_polyhedron_minimize> computes the minimum of some linear
4622 or affine objective function over the integer points in a polyhedron.
4623 If an affine objective function
4624 is given, then the constant should appear in the last column.
4626 =head2 C<isl_polytope_scan>
4628 Given a polytope, C<isl_polytope_scan> prints
4629 all integer points in the polytope.