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_map_foreach_constraint(
1426 __isl_keep isl_basic_map *bmap,
1427 int (*fn)(__isl_take isl_constraint *c, void *user),
1429 void *isl_constraint_free(__isl_take isl_constraint *c);
1431 Again, the callback function C<fn> should return 0 if successful and
1432 -1 if an error occurs. In the latter case, or if any other error
1433 occurs, the above functions will return -1.
1434 The constraint C<c> represents either an equality or an inequality.
1435 Use the following function to find out whether a constraint
1436 represents an equality. If not, it represents an inequality.
1438 int isl_constraint_is_equality(
1439 __isl_keep isl_constraint *constraint);
1441 The coefficients of the constraints can be inspected using
1442 the following functions.
1444 void isl_constraint_get_constant(
1445 __isl_keep isl_constraint *constraint, isl_int *v);
1446 void isl_constraint_get_coefficient(
1447 __isl_keep isl_constraint *constraint,
1448 enum isl_dim_type type, int pos, isl_int *v);
1449 int isl_constraint_involves_dims(
1450 __isl_keep isl_constraint *constraint,
1451 enum isl_dim_type type, unsigned first, unsigned n);
1453 The explicit representations of the existentially quantified
1454 variables can be inspected using the following function.
1455 Note that the user is only allowed to use this function
1456 if the inspected set or map is the result of a call
1457 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1458 The existentially quantified variable is equal to the floor
1459 of the returned affine expression. The affine expression
1460 itself can be inspected using the functions in
1461 L<"Piecewise Quasi Affine Expressions">.
1463 __isl_give isl_aff *isl_constraint_get_div(
1464 __isl_keep isl_constraint *constraint, int pos);
1466 To obtain the constraints of a basic set or map in matrix
1467 form, use the following functions.
1469 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1470 __isl_keep isl_basic_set *bset,
1471 enum isl_dim_type c1, enum isl_dim_type c2,
1472 enum isl_dim_type c3, enum isl_dim_type c4);
1473 __isl_give isl_mat *isl_basic_set_inequalities_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_map_equalities_matrix(
1478 __isl_keep isl_basic_map *bmap,
1479 enum isl_dim_type c1,
1480 enum isl_dim_type c2, enum isl_dim_type c3,
1481 enum isl_dim_type c4, enum isl_dim_type c5);
1482 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1483 __isl_keep isl_basic_map *bmap,
1484 enum isl_dim_type c1,
1485 enum isl_dim_type c2, enum isl_dim_type c3,
1486 enum isl_dim_type c4, enum isl_dim_type c5);
1488 The C<isl_dim_type> arguments dictate the order in which
1489 different kinds of variables appear in the resulting matrix
1490 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1491 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1493 The number of parameters, input, output or set dimensions can
1494 be obtained using the following functions.
1496 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1497 enum isl_dim_type type);
1498 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1499 enum isl_dim_type type);
1500 unsigned isl_set_dim(__isl_keep isl_set *set,
1501 enum isl_dim_type type);
1502 unsigned isl_map_dim(__isl_keep isl_map *map,
1503 enum isl_dim_type type);
1505 To check whether the description of a set or relation depends
1506 on one or more given dimensions, it is not necessary to iterate over all
1507 constraints. Instead the following functions can be used.
1509 int isl_basic_set_involves_dims(
1510 __isl_keep isl_basic_set *bset,
1511 enum isl_dim_type type, unsigned first, unsigned n);
1512 int isl_set_involves_dims(__isl_keep isl_set *set,
1513 enum isl_dim_type type, unsigned first, unsigned n);
1514 int isl_basic_map_involves_dims(
1515 __isl_keep isl_basic_map *bmap,
1516 enum isl_dim_type type, unsigned first, unsigned n);
1517 int isl_map_involves_dims(__isl_keep isl_map *map,
1518 enum isl_dim_type type, unsigned first, unsigned n);
1520 Similarly, the following functions can be used to check whether
1521 a given dimension is involved in any lower or upper bound.
1523 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1524 enum isl_dim_type type, unsigned pos);
1525 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1526 enum isl_dim_type type, unsigned pos);
1528 The identifiers or names of the domain and range spaces of a set
1529 or relation can be read off or set using the following functions.
1531 __isl_give isl_set *isl_set_set_tuple_id(
1532 __isl_take isl_set *set, __isl_take isl_id *id);
1533 __isl_give isl_set *isl_set_reset_tuple_id(
1534 __isl_take isl_set *set);
1535 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1536 __isl_give isl_id *isl_set_get_tuple_id(
1537 __isl_keep isl_set *set);
1538 __isl_give isl_map *isl_map_set_tuple_id(
1539 __isl_take isl_map *map, enum isl_dim_type type,
1540 __isl_take isl_id *id);
1541 __isl_give isl_map *isl_map_reset_tuple_id(
1542 __isl_take isl_map *map, enum isl_dim_type type);
1543 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1544 enum isl_dim_type type);
1545 __isl_give isl_id *isl_map_get_tuple_id(
1546 __isl_keep isl_map *map, enum isl_dim_type type);
1548 const char *isl_basic_set_get_tuple_name(
1549 __isl_keep isl_basic_set *bset);
1550 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1551 __isl_take isl_basic_set *set, const char *s);
1552 const char *isl_set_get_tuple_name(
1553 __isl_keep isl_set *set);
1554 const char *isl_basic_map_get_tuple_name(
1555 __isl_keep isl_basic_map *bmap,
1556 enum isl_dim_type type);
1557 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1558 __isl_take isl_basic_map *bmap,
1559 enum isl_dim_type type, const char *s);
1560 const char *isl_map_get_tuple_name(
1561 __isl_keep isl_map *map,
1562 enum isl_dim_type type);
1564 As with C<isl_space_get_tuple_name>, the value returned points to
1565 an internal data structure.
1566 The identifiers, positions or names of individual dimensions can be
1567 read off using the following functions.
1569 __isl_give isl_set *isl_set_set_dim_id(
1570 __isl_take isl_set *set, enum isl_dim_type type,
1571 unsigned pos, __isl_take isl_id *id);
1572 int isl_set_has_dim_id(__isl_keep isl_set *set,
1573 enum isl_dim_type type, unsigned pos);
1574 __isl_give isl_id *isl_set_get_dim_id(
1575 __isl_keep isl_set *set, enum isl_dim_type type,
1577 int isl_basic_map_has_dim_id(
1578 __isl_keep isl_basic_map *bmap,
1579 enum isl_dim_type type, unsigned pos);
1580 __isl_give isl_map *isl_map_set_dim_id(
1581 __isl_take isl_map *map, enum isl_dim_type type,
1582 unsigned pos, __isl_take isl_id *id);
1583 int isl_map_has_dim_id(__isl_keep isl_map *map,
1584 enum isl_dim_type type, unsigned pos);
1585 __isl_give isl_id *isl_map_get_dim_id(
1586 __isl_keep isl_map *map, enum isl_dim_type type,
1589 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1590 enum isl_dim_type type, __isl_keep isl_id *id);
1591 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1592 enum isl_dim_type type, __isl_keep isl_id *id);
1593 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1594 enum isl_dim_type type, const char *name);
1595 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1596 enum isl_dim_type type, const char *name);
1598 const char *isl_constraint_get_dim_name(
1599 __isl_keep isl_constraint *constraint,
1600 enum isl_dim_type type, unsigned pos);
1601 const char *isl_basic_set_get_dim_name(
1602 __isl_keep isl_basic_set *bset,
1603 enum isl_dim_type type, unsigned pos);
1604 int isl_set_has_dim_name(__isl_keep isl_set *set,
1605 enum isl_dim_type type, unsigned pos);
1606 const char *isl_set_get_dim_name(
1607 __isl_keep isl_set *set,
1608 enum isl_dim_type type, unsigned pos);
1609 const char *isl_basic_map_get_dim_name(
1610 __isl_keep isl_basic_map *bmap,
1611 enum isl_dim_type type, unsigned pos);
1612 const char *isl_map_get_dim_name(
1613 __isl_keep isl_map *map,
1614 enum isl_dim_type type, unsigned pos);
1616 These functions are mostly useful to obtain the identifiers, positions
1617 or names of the parameters. Identifiers of individual dimensions are
1618 essentially only useful for printing. They are ignored by all other
1619 operations and may not be preserved across those operations.
1623 =head3 Unary Properties
1629 The following functions test whether the given set or relation
1630 contains any integer points. The ``plain'' variants do not perform
1631 any computations, but simply check if the given set or relation
1632 is already known to be empty.
1634 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1635 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1636 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1637 int isl_set_is_empty(__isl_keep isl_set *set);
1638 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1639 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1640 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1641 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1642 int isl_map_is_empty(__isl_keep isl_map *map);
1643 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1645 =item * Universality
1647 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1648 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1649 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1651 =item * Single-valuedness
1653 int isl_map_plain_is_single_valued(
1654 __isl_keep isl_map *map);
1655 int isl_map_is_single_valued(__isl_keep isl_map *map);
1656 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1660 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1661 int isl_map_is_injective(__isl_keep isl_map *map);
1662 int isl_union_map_plain_is_injective(
1663 __isl_keep isl_union_map *umap);
1664 int isl_union_map_is_injective(
1665 __isl_keep isl_union_map *umap);
1669 int isl_map_is_bijective(__isl_keep isl_map *map);
1670 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1674 int isl_basic_map_plain_is_fixed(
1675 __isl_keep isl_basic_map *bmap,
1676 enum isl_dim_type type, unsigned pos,
1678 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1679 enum isl_dim_type type, unsigned pos,
1681 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1682 enum isl_dim_type type, unsigned pos,
1685 Check if the relation obviously lies on a hyperplane where the given dimension
1686 has a fixed value and if so, return that value in C<*val>.
1690 To check whether a set is a parameter domain, use this function:
1692 int isl_set_is_params(__isl_keep isl_set *set);
1693 int isl_union_set_is_params(
1694 __isl_keep isl_union_set *uset);
1698 The following functions check whether the domain of the given
1699 (basic) set is a wrapped relation.
1701 int isl_basic_set_is_wrapping(
1702 __isl_keep isl_basic_set *bset);
1703 int isl_set_is_wrapping(__isl_keep isl_set *set);
1705 =item * Internal Product
1707 int isl_basic_map_can_zip(
1708 __isl_keep isl_basic_map *bmap);
1709 int isl_map_can_zip(__isl_keep isl_map *map);
1711 Check whether the product of domain and range of the given relation
1713 i.e., whether both domain and range are nested relations.
1717 int isl_basic_map_can_curry(
1718 __isl_keep isl_basic_map *bmap);
1719 int isl_map_can_curry(__isl_keep isl_map *map);
1721 Check whether the domain of the (basic) relation is a wrapped relation.
1725 =head3 Binary Properties
1731 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1732 __isl_keep isl_set *set2);
1733 int isl_set_is_equal(__isl_keep isl_set *set1,
1734 __isl_keep isl_set *set2);
1735 int isl_union_set_is_equal(
1736 __isl_keep isl_union_set *uset1,
1737 __isl_keep isl_union_set *uset2);
1738 int isl_basic_map_is_equal(
1739 __isl_keep isl_basic_map *bmap1,
1740 __isl_keep isl_basic_map *bmap2);
1741 int isl_map_is_equal(__isl_keep isl_map *map1,
1742 __isl_keep isl_map *map2);
1743 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1744 __isl_keep isl_map *map2);
1745 int isl_union_map_is_equal(
1746 __isl_keep isl_union_map *umap1,
1747 __isl_keep isl_union_map *umap2);
1749 =item * Disjointness
1751 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1752 __isl_keep isl_set *set2);
1756 int isl_basic_set_is_subset(
1757 __isl_keep isl_basic_set *bset1,
1758 __isl_keep isl_basic_set *bset2);
1759 int isl_set_is_subset(__isl_keep isl_set *set1,
1760 __isl_keep isl_set *set2);
1761 int isl_set_is_strict_subset(
1762 __isl_keep isl_set *set1,
1763 __isl_keep isl_set *set2);
1764 int isl_union_set_is_subset(
1765 __isl_keep isl_union_set *uset1,
1766 __isl_keep isl_union_set *uset2);
1767 int isl_union_set_is_strict_subset(
1768 __isl_keep isl_union_set *uset1,
1769 __isl_keep isl_union_set *uset2);
1770 int isl_basic_map_is_subset(
1771 __isl_keep isl_basic_map *bmap1,
1772 __isl_keep isl_basic_map *bmap2);
1773 int isl_basic_map_is_strict_subset(
1774 __isl_keep isl_basic_map *bmap1,
1775 __isl_keep isl_basic_map *bmap2);
1776 int isl_map_is_subset(
1777 __isl_keep isl_map *map1,
1778 __isl_keep isl_map *map2);
1779 int isl_map_is_strict_subset(
1780 __isl_keep isl_map *map1,
1781 __isl_keep isl_map *map2);
1782 int isl_union_map_is_subset(
1783 __isl_keep isl_union_map *umap1,
1784 __isl_keep isl_union_map *umap2);
1785 int isl_union_map_is_strict_subset(
1786 __isl_keep isl_union_map *umap1,
1787 __isl_keep isl_union_map *umap2);
1791 =head2 Unary Operations
1797 __isl_give isl_set *isl_set_complement(
1798 __isl_take isl_set *set);
1799 __isl_give isl_map *isl_map_complement(
1800 __isl_take isl_map *map);
1804 __isl_give isl_basic_map *isl_basic_map_reverse(
1805 __isl_take isl_basic_map *bmap);
1806 __isl_give isl_map *isl_map_reverse(
1807 __isl_take isl_map *map);
1808 __isl_give isl_union_map *isl_union_map_reverse(
1809 __isl_take isl_union_map *umap);
1813 __isl_give isl_basic_set *isl_basic_set_project_out(
1814 __isl_take isl_basic_set *bset,
1815 enum isl_dim_type type, unsigned first, unsigned n);
1816 __isl_give isl_basic_map *isl_basic_map_project_out(
1817 __isl_take isl_basic_map *bmap,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1819 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1822 enum isl_dim_type type, unsigned first, unsigned n);
1823 __isl_give isl_basic_set *isl_basic_set_params(
1824 __isl_take isl_basic_set *bset);
1825 __isl_give isl_basic_set *isl_basic_map_domain(
1826 __isl_take isl_basic_map *bmap);
1827 __isl_give isl_basic_set *isl_basic_map_range(
1828 __isl_take isl_basic_map *bmap);
1829 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1830 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1831 __isl_give isl_set *isl_map_domain(
1832 __isl_take isl_map *bmap);
1833 __isl_give isl_set *isl_map_range(
1834 __isl_take isl_map *map);
1835 __isl_give isl_set *isl_union_set_params(
1836 __isl_take isl_union_set *uset);
1837 __isl_give isl_set *isl_union_map_params(
1838 __isl_take isl_union_map *umap);
1839 __isl_give isl_union_set *isl_union_map_domain(
1840 __isl_take isl_union_map *umap);
1841 __isl_give isl_union_set *isl_union_map_range(
1842 __isl_take isl_union_map *umap);
1844 __isl_give isl_basic_map *isl_basic_map_domain_map(
1845 __isl_take isl_basic_map *bmap);
1846 __isl_give isl_basic_map *isl_basic_map_range_map(
1847 __isl_take isl_basic_map *bmap);
1848 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1849 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1850 __isl_give isl_union_map *isl_union_map_domain_map(
1851 __isl_take isl_union_map *umap);
1852 __isl_give isl_union_map *isl_union_map_range_map(
1853 __isl_take isl_union_map *umap);
1855 The functions above construct a (basic, regular or union) relation
1856 that maps (a wrapped version of) the input relation to its domain or range.
1860 __isl_give isl_set *isl_set_eliminate(
1861 __isl_take isl_set *set, enum isl_dim_type type,
1862 unsigned first, unsigned n);
1863 __isl_give isl_basic_map *isl_basic_map_eliminate(
1864 __isl_take isl_basic_map *bmap,
1865 enum isl_dim_type type,
1866 unsigned first, unsigned n);
1867 __isl_give isl_map *isl_map_eliminate(
1868 __isl_take isl_map *map, enum isl_dim_type type,
1869 unsigned first, unsigned n);
1871 Eliminate the coefficients for the given dimensions from the constraints,
1872 without removing the dimensions.
1876 __isl_give isl_basic_set *isl_basic_set_fix(
1877 __isl_take isl_basic_set *bset,
1878 enum isl_dim_type type, unsigned pos,
1880 __isl_give isl_basic_set *isl_basic_set_fix_si(
1881 __isl_take isl_basic_set *bset,
1882 enum isl_dim_type type, unsigned pos, int value);
1883 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1884 enum isl_dim_type type, unsigned pos,
1886 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1887 enum isl_dim_type type, unsigned pos, int value);
1888 __isl_give isl_basic_map *isl_basic_map_fix_si(
1889 __isl_take isl_basic_map *bmap,
1890 enum isl_dim_type type, unsigned pos, int value);
1891 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1892 enum isl_dim_type type, unsigned pos, int value);
1894 Intersect the set or relation with the hyperplane where the given
1895 dimension has the fixed given value.
1897 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1898 __isl_take isl_basic_map *bmap,
1899 enum isl_dim_type type, unsigned pos, int value);
1900 __isl_give isl_set *isl_set_lower_bound(
1901 __isl_take isl_set *set,
1902 enum isl_dim_type type, unsigned pos,
1904 __isl_give isl_set *isl_set_lower_bound_si(
1905 __isl_take isl_set *set,
1906 enum isl_dim_type type, unsigned pos, int value);
1907 __isl_give isl_map *isl_map_lower_bound_si(
1908 __isl_take isl_map *map,
1909 enum isl_dim_type type, unsigned pos, int value);
1910 __isl_give isl_set *isl_set_upper_bound(
1911 __isl_take isl_set *set,
1912 enum isl_dim_type type, unsigned pos,
1914 __isl_give isl_set *isl_set_upper_bound_si(
1915 __isl_take isl_set *set,
1916 enum isl_dim_type type, unsigned pos, int value);
1917 __isl_give isl_map *isl_map_upper_bound_si(
1918 __isl_take isl_map *map,
1919 enum isl_dim_type type, unsigned pos, int value);
1921 Intersect the set or relation with the half-space where the given
1922 dimension has a value bounded by the fixed given value.
1924 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1925 enum isl_dim_type type1, int pos1,
1926 enum isl_dim_type type2, int pos2);
1927 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1928 enum isl_dim_type type1, int pos1,
1929 enum isl_dim_type type2, int pos2);
1931 Intersect the set or relation with the hyperplane where the given
1932 dimensions are equal to each other.
1934 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1935 enum isl_dim_type type1, int pos1,
1936 enum isl_dim_type type2, int pos2);
1938 Intersect the relation with the hyperplane where the given
1939 dimensions have opposite values.
1941 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1942 enum isl_dim_type type1, int pos1,
1943 enum isl_dim_type type2, int pos2);
1945 Intersect the relation with the half-space where the given
1946 dimensions satisfy the given ordering.
1950 __isl_give isl_map *isl_set_identity(
1951 __isl_take isl_set *set);
1952 __isl_give isl_union_map *isl_union_set_identity(
1953 __isl_take isl_union_set *uset);
1955 Construct an identity relation on the given (union) set.
1959 __isl_give isl_basic_set *isl_basic_map_deltas(
1960 __isl_take isl_basic_map *bmap);
1961 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1962 __isl_give isl_union_set *isl_union_map_deltas(
1963 __isl_take isl_union_map *umap);
1965 These functions return a (basic) set containing the differences
1966 between image elements and corresponding domain elements in the input.
1968 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1969 __isl_take isl_basic_map *bmap);
1970 __isl_give isl_map *isl_map_deltas_map(
1971 __isl_take isl_map *map);
1972 __isl_give isl_union_map *isl_union_map_deltas_map(
1973 __isl_take isl_union_map *umap);
1975 The functions above construct a (basic, regular or union) relation
1976 that maps (a wrapped version of) the input relation to its delta set.
1980 Simplify the representation of a set or relation by trying
1981 to combine pairs of basic sets or relations into a single
1982 basic set or relation.
1984 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1985 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1986 __isl_give isl_union_set *isl_union_set_coalesce(
1987 __isl_take isl_union_set *uset);
1988 __isl_give isl_union_map *isl_union_map_coalesce(
1989 __isl_take isl_union_map *umap);
1991 One of the methods for combining pairs of basic sets or relations
1992 can result in coefficients that are much larger than those that appear
1993 in the constraints of the input. By default, the coefficients are
1994 not allowed to grow larger, but this can be changed by unsetting
1995 the following option.
1997 int isl_options_set_coalesce_bounded_wrapping(
1998 isl_ctx *ctx, int val);
1999 int isl_options_get_coalesce_bounded_wrapping(
2002 =item * Detecting equalities
2004 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2005 __isl_take isl_basic_set *bset);
2006 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2007 __isl_take isl_basic_map *bmap);
2008 __isl_give isl_set *isl_set_detect_equalities(
2009 __isl_take isl_set *set);
2010 __isl_give isl_map *isl_map_detect_equalities(
2011 __isl_take isl_map *map);
2012 __isl_give isl_union_set *isl_union_set_detect_equalities(
2013 __isl_take isl_union_set *uset);
2014 __isl_give isl_union_map *isl_union_map_detect_equalities(
2015 __isl_take isl_union_map *umap);
2017 Simplify the representation of a set or relation by detecting implicit
2020 =item * Removing redundant constraints
2022 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2023 __isl_take isl_basic_set *bset);
2024 __isl_give isl_set *isl_set_remove_redundancies(
2025 __isl_take isl_set *set);
2026 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2027 __isl_take isl_basic_map *bmap);
2028 __isl_give isl_map *isl_map_remove_redundancies(
2029 __isl_take isl_map *map);
2033 __isl_give isl_basic_set *isl_set_convex_hull(
2034 __isl_take isl_set *set);
2035 __isl_give isl_basic_map *isl_map_convex_hull(
2036 __isl_take isl_map *map);
2038 If the input set or relation has any existentially quantified
2039 variables, then the result of these operations is currently undefined.
2043 __isl_give isl_basic_set *isl_set_simple_hull(
2044 __isl_take isl_set *set);
2045 __isl_give isl_basic_map *isl_map_simple_hull(
2046 __isl_take isl_map *map);
2047 __isl_give isl_union_map *isl_union_map_simple_hull(
2048 __isl_take isl_union_map *umap);
2050 These functions compute a single basic set or relation
2051 that contains the whole input set or relation.
2052 In particular, the output is described by translates
2053 of the constraints describing the basic sets or relations in the input.
2057 (See \autoref{s:simple hull}.)
2063 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2064 __isl_take isl_basic_set *bset);
2065 __isl_give isl_basic_set *isl_set_affine_hull(
2066 __isl_take isl_set *set);
2067 __isl_give isl_union_set *isl_union_set_affine_hull(
2068 __isl_take isl_union_set *uset);
2069 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2070 __isl_take isl_basic_map *bmap);
2071 __isl_give isl_basic_map *isl_map_affine_hull(
2072 __isl_take isl_map *map);
2073 __isl_give isl_union_map *isl_union_map_affine_hull(
2074 __isl_take isl_union_map *umap);
2076 In case of union sets and relations, the affine hull is computed
2079 =item * Polyhedral hull
2081 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2082 __isl_take isl_set *set);
2083 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2084 __isl_take isl_map *map);
2085 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2086 __isl_take isl_union_set *uset);
2087 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2088 __isl_take isl_union_map *umap);
2090 These functions compute a single basic set or relation
2091 not involving any existentially quantified variables
2092 that contains the whole input set or relation.
2093 In case of union sets and relations, the polyhedral hull is computed
2098 __isl_give isl_basic_set *isl_basic_set_sample(
2099 __isl_take isl_basic_set *bset);
2100 __isl_give isl_basic_set *isl_set_sample(
2101 __isl_take isl_set *set);
2102 __isl_give isl_basic_map *isl_basic_map_sample(
2103 __isl_take isl_basic_map *bmap);
2104 __isl_give isl_basic_map *isl_map_sample(
2105 __isl_take isl_map *map);
2107 If the input (basic) set or relation is non-empty, then return
2108 a singleton subset of the input. Otherwise, return an empty set.
2110 =item * Optimization
2112 #include <isl/ilp.h>
2113 enum isl_lp_result isl_basic_set_max(
2114 __isl_keep isl_basic_set *bset,
2115 __isl_keep isl_aff *obj, isl_int *opt)
2116 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2117 __isl_keep isl_aff *obj, isl_int *opt);
2118 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2119 __isl_keep isl_aff *obj, isl_int *opt);
2121 Compute the minimum or maximum of the integer affine expression C<obj>
2122 over the points in C<set>, returning the result in C<opt>.
2123 The return value may be one of C<isl_lp_error>,
2124 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2126 =item * Parametric optimization
2128 __isl_give isl_pw_aff *isl_set_dim_min(
2129 __isl_take isl_set *set, int pos);
2130 __isl_give isl_pw_aff *isl_set_dim_max(
2131 __isl_take isl_set *set, int pos);
2132 __isl_give isl_pw_aff *isl_map_dim_max(
2133 __isl_take isl_map *map, int pos);
2135 Compute the minimum or maximum of the given set or output dimension
2136 as a function of the parameters (and input dimensions), but independently
2137 of the other set or output dimensions.
2138 For lexicographic optimization, see L<"Lexicographic Optimization">.
2142 The following functions compute either the set of (rational) coefficient
2143 values of valid constraints for the given set or the set of (rational)
2144 values satisfying the constraints with coefficients from the given set.
2145 Internally, these two sets of functions perform essentially the
2146 same operations, except that the set of coefficients is assumed to
2147 be a cone, while the set of values may be any polyhedron.
2148 The current implementation is based on the Farkas lemma and
2149 Fourier-Motzkin elimination, but this may change or be made optional
2150 in future. In particular, future implementations may use different
2151 dualization algorithms or skip the elimination step.
2153 __isl_give isl_basic_set *isl_basic_set_coefficients(
2154 __isl_take isl_basic_set *bset);
2155 __isl_give isl_basic_set *isl_set_coefficients(
2156 __isl_take isl_set *set);
2157 __isl_give isl_union_set *isl_union_set_coefficients(
2158 __isl_take isl_union_set *bset);
2159 __isl_give isl_basic_set *isl_basic_set_solutions(
2160 __isl_take isl_basic_set *bset);
2161 __isl_give isl_basic_set *isl_set_solutions(
2162 __isl_take isl_set *set);
2163 __isl_give isl_union_set *isl_union_set_solutions(
2164 __isl_take isl_union_set *bset);
2168 __isl_give isl_map *isl_map_fixed_power(
2169 __isl_take isl_map *map, isl_int exp);
2170 __isl_give isl_union_map *isl_union_map_fixed_power(
2171 __isl_take isl_union_map *umap, isl_int exp);
2173 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2174 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2175 of C<map> is computed.
2177 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2179 __isl_give isl_union_map *isl_union_map_power(
2180 __isl_take isl_union_map *umap, int *exact);
2182 Compute a parametric representation for all positive powers I<k> of C<map>.
2183 The result maps I<k> to a nested relation corresponding to the
2184 I<k>th power of C<map>.
2185 The result may be an overapproximation. If the result is known to be exact,
2186 then C<*exact> is set to C<1>.
2188 =item * Transitive closure
2190 __isl_give isl_map *isl_map_transitive_closure(
2191 __isl_take isl_map *map, int *exact);
2192 __isl_give isl_union_map *isl_union_map_transitive_closure(
2193 __isl_take isl_union_map *umap, int *exact);
2195 Compute the transitive closure of C<map>.
2196 The result may be an overapproximation. If the result is known to be exact,
2197 then C<*exact> is set to C<1>.
2199 =item * Reaching path lengths
2201 __isl_give isl_map *isl_map_reaching_path_lengths(
2202 __isl_take isl_map *map, int *exact);
2204 Compute a relation that maps each element in the range of C<map>
2205 to the lengths of all paths composed of edges in C<map> that
2206 end up in the given element.
2207 The result may be an overapproximation. If the result is known to be exact,
2208 then C<*exact> is set to C<1>.
2209 To compute the I<maximal> path length, the resulting relation
2210 should be postprocessed by C<isl_map_lexmax>.
2211 In particular, if the input relation is a dependence relation
2212 (mapping sources to sinks), then the maximal path length corresponds
2213 to the free schedule.
2214 Note, however, that C<isl_map_lexmax> expects the maximum to be
2215 finite, so if the path lengths are unbounded (possibly due to
2216 the overapproximation), then you will get an error message.
2220 __isl_give isl_basic_set *isl_basic_map_wrap(
2221 __isl_take isl_basic_map *bmap);
2222 __isl_give isl_set *isl_map_wrap(
2223 __isl_take isl_map *map);
2224 __isl_give isl_union_set *isl_union_map_wrap(
2225 __isl_take isl_union_map *umap);
2226 __isl_give isl_basic_map *isl_basic_set_unwrap(
2227 __isl_take isl_basic_set *bset);
2228 __isl_give isl_map *isl_set_unwrap(
2229 __isl_take isl_set *set);
2230 __isl_give isl_union_map *isl_union_set_unwrap(
2231 __isl_take isl_union_set *uset);
2235 Remove any internal structure of domain (and range) of the given
2236 set or relation. If there is any such internal structure in the input,
2237 then the name of the space is also removed.
2239 __isl_give isl_basic_set *isl_basic_set_flatten(
2240 __isl_take isl_basic_set *bset);
2241 __isl_give isl_set *isl_set_flatten(
2242 __isl_take isl_set *set);
2243 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_flatten_range(
2248 __isl_take isl_map *map);
2249 __isl_give isl_map *isl_map_flatten_domain(
2250 __isl_take isl_map *map);
2251 __isl_give isl_basic_map *isl_basic_map_flatten(
2252 __isl_take isl_basic_map *bmap);
2253 __isl_give isl_map *isl_map_flatten(
2254 __isl_take isl_map *map);
2256 __isl_give isl_map *isl_set_flatten_map(
2257 __isl_take isl_set *set);
2259 The function above constructs a relation
2260 that maps the input set to a flattened version of the set.
2264 Lift the input set to a space with extra dimensions corresponding
2265 to the existentially quantified variables in the input.
2266 In particular, the result lives in a wrapped map where the domain
2267 is the original space and the range corresponds to the original
2268 existentially quantified variables.
2270 __isl_give isl_basic_set *isl_basic_set_lift(
2271 __isl_take isl_basic_set *bset);
2272 __isl_give isl_set *isl_set_lift(
2273 __isl_take isl_set *set);
2274 __isl_give isl_union_set *isl_union_set_lift(
2275 __isl_take isl_union_set *uset);
2277 Given a local space that contains the existentially quantified
2278 variables of a set, a basic relation that, when applied to
2279 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2280 can be constructed using the following function.
2282 #include <isl/local_space.h>
2283 __isl_give isl_basic_map *isl_local_space_lifting(
2284 __isl_take isl_local_space *ls);
2286 =item * Internal Product
2288 __isl_give isl_basic_map *isl_basic_map_zip(
2289 __isl_take isl_basic_map *bmap);
2290 __isl_give isl_map *isl_map_zip(
2291 __isl_take isl_map *map);
2292 __isl_give isl_union_map *isl_union_map_zip(
2293 __isl_take isl_union_map *umap);
2295 Given a relation with nested relations for domain and range,
2296 interchange the range of the domain with the domain of the range.
2300 __isl_give isl_basic_map *isl_basic_map_curry(
2301 __isl_take isl_basic_map *bmap);
2302 __isl_give isl_map *isl_map_curry(
2303 __isl_take isl_map *map);
2304 __isl_give isl_union_map *isl_union_map_curry(
2305 __isl_take isl_union_map *umap);
2307 Given a relation with a nested relation for domain,
2308 move the range of the nested relation out of the domain
2309 and use it as the domain of a nested relation in the range,
2310 with the original range as range of this nested relation.
2312 =item * Aligning parameters
2314 __isl_give isl_set *isl_set_align_params(
2315 __isl_take isl_set *set,
2316 __isl_take isl_space *model);
2317 __isl_give isl_map *isl_map_align_params(
2318 __isl_take isl_map *map,
2319 __isl_take isl_space *model);
2321 Change the order of the parameters of the given set or relation
2322 such that the first parameters match those of C<model>.
2323 This may involve the introduction of extra parameters.
2324 All parameters need to be named.
2326 =item * Dimension manipulation
2328 __isl_give isl_set *isl_set_add_dims(
2329 __isl_take isl_set *set,
2330 enum isl_dim_type type, unsigned n);
2331 __isl_give isl_map *isl_map_add_dims(
2332 __isl_take isl_map *map,
2333 enum isl_dim_type type, unsigned n);
2334 __isl_give isl_set *isl_set_insert_dims(
2335 __isl_take isl_set *set,
2336 enum isl_dim_type type, unsigned pos, unsigned n);
2337 __isl_give isl_map *isl_map_insert_dims(
2338 __isl_take isl_map *map,
2339 enum isl_dim_type type, unsigned pos, unsigned n);
2340 __isl_give isl_basic_set *isl_basic_set_move_dims(
2341 __isl_take isl_basic_set *bset,
2342 enum isl_dim_type dst_type, unsigned dst_pos,
2343 enum isl_dim_type src_type, unsigned src_pos,
2345 __isl_give isl_basic_map *isl_basic_map_move_dims(
2346 __isl_take isl_basic_map *bmap,
2347 enum isl_dim_type dst_type, unsigned dst_pos,
2348 enum isl_dim_type src_type, unsigned src_pos,
2350 __isl_give isl_set *isl_set_move_dims(
2351 __isl_take isl_set *set,
2352 enum isl_dim_type dst_type, unsigned dst_pos,
2353 enum isl_dim_type src_type, unsigned src_pos,
2355 __isl_give isl_map *isl_map_move_dims(
2356 __isl_take isl_map *map,
2357 enum isl_dim_type dst_type, unsigned dst_pos,
2358 enum isl_dim_type src_type, unsigned src_pos,
2361 It is usually not advisable to directly change the (input or output)
2362 space of a set or a relation as this removes the name and the internal
2363 structure of the space. However, the above functions can be useful
2364 to add new parameters, assuming
2365 C<isl_set_align_params> and C<isl_map_align_params>
2370 =head2 Binary Operations
2372 The two arguments of a binary operation not only need to live
2373 in the same C<isl_ctx>, they currently also need to have
2374 the same (number of) parameters.
2376 =head3 Basic Operations
2380 =item * Intersection
2382 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2383 __isl_take isl_basic_set *bset1,
2384 __isl_take isl_basic_set *bset2);
2385 __isl_give isl_basic_set *isl_basic_set_intersect(
2386 __isl_take isl_basic_set *bset1,
2387 __isl_take isl_basic_set *bset2);
2388 __isl_give isl_set *isl_set_intersect_params(
2389 __isl_take isl_set *set,
2390 __isl_take isl_set *params);
2391 __isl_give isl_set *isl_set_intersect(
2392 __isl_take isl_set *set1,
2393 __isl_take isl_set *set2);
2394 __isl_give isl_union_set *isl_union_set_intersect_params(
2395 __isl_take isl_union_set *uset,
2396 __isl_take isl_set *set);
2397 __isl_give isl_union_map *isl_union_map_intersect_params(
2398 __isl_take isl_union_map *umap,
2399 __isl_take isl_set *set);
2400 __isl_give isl_union_set *isl_union_set_intersect(
2401 __isl_take isl_union_set *uset1,
2402 __isl_take isl_union_set *uset2);
2403 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2404 __isl_take isl_basic_map *bmap,
2405 __isl_take isl_basic_set *bset);
2406 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2407 __isl_take isl_basic_map *bmap,
2408 __isl_take isl_basic_set *bset);
2409 __isl_give isl_basic_map *isl_basic_map_intersect(
2410 __isl_take isl_basic_map *bmap1,
2411 __isl_take isl_basic_map *bmap2);
2412 __isl_give isl_map *isl_map_intersect_params(
2413 __isl_take isl_map *map,
2414 __isl_take isl_set *params);
2415 __isl_give isl_map *isl_map_intersect_domain(
2416 __isl_take isl_map *map,
2417 __isl_take isl_set *set);
2418 __isl_give isl_map *isl_map_intersect_range(
2419 __isl_take isl_map *map,
2420 __isl_take isl_set *set);
2421 __isl_give isl_map *isl_map_intersect(
2422 __isl_take isl_map *map1,
2423 __isl_take isl_map *map2);
2424 __isl_give isl_union_map *isl_union_map_intersect_domain(
2425 __isl_take isl_union_map *umap,
2426 __isl_take isl_union_set *uset);
2427 __isl_give isl_union_map *isl_union_map_intersect_range(
2428 __isl_take isl_union_map *umap,
2429 __isl_take isl_union_set *uset);
2430 __isl_give isl_union_map *isl_union_map_intersect(
2431 __isl_take isl_union_map *umap1,
2432 __isl_take isl_union_map *umap2);
2436 __isl_give isl_set *isl_basic_set_union(
2437 __isl_take isl_basic_set *bset1,
2438 __isl_take isl_basic_set *bset2);
2439 __isl_give isl_map *isl_basic_map_union(
2440 __isl_take isl_basic_map *bmap1,
2441 __isl_take isl_basic_map *bmap2);
2442 __isl_give isl_set *isl_set_union(
2443 __isl_take isl_set *set1,
2444 __isl_take isl_set *set2);
2445 __isl_give isl_map *isl_map_union(
2446 __isl_take isl_map *map1,
2447 __isl_take isl_map *map2);
2448 __isl_give isl_union_set *isl_union_set_union(
2449 __isl_take isl_union_set *uset1,
2450 __isl_take isl_union_set *uset2);
2451 __isl_give isl_union_map *isl_union_map_union(
2452 __isl_take isl_union_map *umap1,
2453 __isl_take isl_union_map *umap2);
2455 =item * Set difference
2457 __isl_give isl_set *isl_set_subtract(
2458 __isl_take isl_set *set1,
2459 __isl_take isl_set *set2);
2460 __isl_give isl_map *isl_map_subtract(
2461 __isl_take isl_map *map1,
2462 __isl_take isl_map *map2);
2463 __isl_give isl_map *isl_map_subtract_domain(
2464 __isl_take isl_map *map,
2465 __isl_take isl_set *dom);
2466 __isl_give isl_map *isl_map_subtract_range(
2467 __isl_take isl_map *map,
2468 __isl_take isl_set *dom);
2469 __isl_give isl_union_set *isl_union_set_subtract(
2470 __isl_take isl_union_set *uset1,
2471 __isl_take isl_union_set *uset2);
2472 __isl_give isl_union_map *isl_union_map_subtract(
2473 __isl_take isl_union_map *umap1,
2474 __isl_take isl_union_map *umap2);
2478 __isl_give isl_basic_set *isl_basic_set_apply(
2479 __isl_take isl_basic_set *bset,
2480 __isl_take isl_basic_map *bmap);
2481 __isl_give isl_set *isl_set_apply(
2482 __isl_take isl_set *set,
2483 __isl_take isl_map *map);
2484 __isl_give isl_union_set *isl_union_set_apply(
2485 __isl_take isl_union_set *uset,
2486 __isl_take isl_union_map *umap);
2487 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2488 __isl_take isl_basic_map *bmap1,
2489 __isl_take isl_basic_map *bmap2);
2490 __isl_give isl_basic_map *isl_basic_map_apply_range(
2491 __isl_take isl_basic_map *bmap1,
2492 __isl_take isl_basic_map *bmap2);
2493 __isl_give isl_map *isl_map_apply_domain(
2494 __isl_take isl_map *map1,
2495 __isl_take isl_map *map2);
2496 __isl_give isl_union_map *isl_union_map_apply_domain(
2497 __isl_take isl_union_map *umap1,
2498 __isl_take isl_union_map *umap2);
2499 __isl_give isl_map *isl_map_apply_range(
2500 __isl_take isl_map *map1,
2501 __isl_take isl_map *map2);
2502 __isl_give isl_union_map *isl_union_map_apply_range(
2503 __isl_take isl_union_map *umap1,
2504 __isl_take isl_union_map *umap2);
2506 =item * Cartesian Product
2508 __isl_give isl_set *isl_set_product(
2509 __isl_take isl_set *set1,
2510 __isl_take isl_set *set2);
2511 __isl_give isl_union_set *isl_union_set_product(
2512 __isl_take isl_union_set *uset1,
2513 __isl_take isl_union_set *uset2);
2514 __isl_give isl_basic_map *isl_basic_map_domain_product(
2515 __isl_take isl_basic_map *bmap1,
2516 __isl_take isl_basic_map *bmap2);
2517 __isl_give isl_basic_map *isl_basic_map_range_product(
2518 __isl_take isl_basic_map *bmap1,
2519 __isl_take isl_basic_map *bmap2);
2520 __isl_give isl_map *isl_map_domain_product(
2521 __isl_take isl_map *map1,
2522 __isl_take isl_map *map2);
2523 __isl_give isl_map *isl_map_range_product(
2524 __isl_take isl_map *map1,
2525 __isl_take isl_map *map2);
2526 __isl_give isl_union_map *isl_union_map_range_product(
2527 __isl_take isl_union_map *umap1,
2528 __isl_take isl_union_map *umap2);
2529 __isl_give isl_map *isl_map_product(
2530 __isl_take isl_map *map1,
2531 __isl_take isl_map *map2);
2532 __isl_give isl_union_map *isl_union_map_product(
2533 __isl_take isl_union_map *umap1,
2534 __isl_take isl_union_map *umap2);
2536 The above functions compute the cross product of the given
2537 sets or relations. The domains and ranges of the results
2538 are wrapped maps between domains and ranges of the inputs.
2539 To obtain a ``flat'' product, use the following functions
2542 __isl_give isl_basic_set *isl_basic_set_flat_product(
2543 __isl_take isl_basic_set *bset1,
2544 __isl_take isl_basic_set *bset2);
2545 __isl_give isl_set *isl_set_flat_product(
2546 __isl_take isl_set *set1,
2547 __isl_take isl_set *set2);
2548 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2549 __isl_take isl_basic_map *bmap1,
2550 __isl_take isl_basic_map *bmap2);
2551 __isl_give isl_map *isl_map_flat_domain_product(
2552 __isl_take isl_map *map1,
2553 __isl_take isl_map *map2);
2554 __isl_give isl_map *isl_map_flat_range_product(
2555 __isl_take isl_map *map1,
2556 __isl_take isl_map *map2);
2557 __isl_give isl_union_map *isl_union_map_flat_range_product(
2558 __isl_take isl_union_map *umap1,
2559 __isl_take isl_union_map *umap2);
2560 __isl_give isl_basic_map *isl_basic_map_flat_product(
2561 __isl_take isl_basic_map *bmap1,
2562 __isl_take isl_basic_map *bmap2);
2563 __isl_give isl_map *isl_map_flat_product(
2564 __isl_take isl_map *map1,
2565 __isl_take isl_map *map2);
2567 =item * Simplification
2569 __isl_give isl_basic_set *isl_basic_set_gist(
2570 __isl_take isl_basic_set *bset,
2571 __isl_take isl_basic_set *context);
2572 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2573 __isl_take isl_set *context);
2574 __isl_give isl_set *isl_set_gist_params(
2575 __isl_take isl_set *set,
2576 __isl_take isl_set *context);
2577 __isl_give isl_union_set *isl_union_set_gist(
2578 __isl_take isl_union_set *uset,
2579 __isl_take isl_union_set *context);
2580 __isl_give isl_union_set *isl_union_set_gist_params(
2581 __isl_take isl_union_set *uset,
2582 __isl_take isl_set *set);
2583 __isl_give isl_basic_map *isl_basic_map_gist(
2584 __isl_take isl_basic_map *bmap,
2585 __isl_take isl_basic_map *context);
2586 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2587 __isl_take isl_map *context);
2588 __isl_give isl_map *isl_map_gist_params(
2589 __isl_take isl_map *map,
2590 __isl_take isl_set *context);
2591 __isl_give isl_map *isl_map_gist_domain(
2592 __isl_take isl_map *map,
2593 __isl_take isl_set *context);
2594 __isl_give isl_map *isl_map_gist_range(
2595 __isl_take isl_map *map,
2596 __isl_take isl_set *context);
2597 __isl_give isl_union_map *isl_union_map_gist(
2598 __isl_take isl_union_map *umap,
2599 __isl_take isl_union_map *context);
2600 __isl_give isl_union_map *isl_union_map_gist_params(
2601 __isl_take isl_union_map *umap,
2602 __isl_take isl_set *set);
2603 __isl_give isl_union_map *isl_union_map_gist_domain(
2604 __isl_take isl_union_map *umap,
2605 __isl_take isl_union_set *uset);
2606 __isl_give isl_union_map *isl_union_map_gist_range(
2607 __isl_take isl_union_map *umap,
2608 __isl_take isl_union_set *uset);
2610 The gist operation returns a set or relation that has the
2611 same intersection with the context as the input set or relation.
2612 Any implicit equality in the intersection is made explicit in the result,
2613 while all inequalities that are redundant with respect to the intersection
2615 In case of union sets and relations, the gist operation is performed
2620 =head3 Lexicographic Optimization
2622 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2623 the following functions
2624 compute a set that contains the lexicographic minimum or maximum
2625 of the elements in C<set> (or C<bset>) for those values of the parameters
2626 that satisfy C<dom>.
2627 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2628 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2630 In other words, the union of the parameter values
2631 for which the result is non-empty and of C<*empty>
2634 __isl_give isl_set *isl_basic_set_partial_lexmin(
2635 __isl_take isl_basic_set *bset,
2636 __isl_take isl_basic_set *dom,
2637 __isl_give isl_set **empty);
2638 __isl_give isl_set *isl_basic_set_partial_lexmax(
2639 __isl_take isl_basic_set *bset,
2640 __isl_take isl_basic_set *dom,
2641 __isl_give isl_set **empty);
2642 __isl_give isl_set *isl_set_partial_lexmin(
2643 __isl_take isl_set *set, __isl_take isl_set *dom,
2644 __isl_give isl_set **empty);
2645 __isl_give isl_set *isl_set_partial_lexmax(
2646 __isl_take isl_set *set, __isl_take isl_set *dom,
2647 __isl_give isl_set **empty);
2649 Given a (basic) set C<set> (or C<bset>), the following functions simply
2650 return a set containing the lexicographic minimum or maximum
2651 of the elements in C<set> (or C<bset>).
2652 In case of union sets, the optimum is computed per space.
2654 __isl_give isl_set *isl_basic_set_lexmin(
2655 __isl_take isl_basic_set *bset);
2656 __isl_give isl_set *isl_basic_set_lexmax(
2657 __isl_take isl_basic_set *bset);
2658 __isl_give isl_set *isl_set_lexmin(
2659 __isl_take isl_set *set);
2660 __isl_give isl_set *isl_set_lexmax(
2661 __isl_take isl_set *set);
2662 __isl_give isl_union_set *isl_union_set_lexmin(
2663 __isl_take isl_union_set *uset);
2664 __isl_give isl_union_set *isl_union_set_lexmax(
2665 __isl_take isl_union_set *uset);
2667 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2668 the following functions
2669 compute a relation that maps each element of C<dom>
2670 to the single lexicographic minimum or maximum
2671 of the elements that are associated to that same
2672 element in C<map> (or C<bmap>).
2673 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2674 that contains the elements in C<dom> that do not map
2675 to any elements in C<map> (or C<bmap>).
2676 In other words, the union of the domain of the result and of C<*empty>
2679 __isl_give isl_map *isl_basic_map_partial_lexmax(
2680 __isl_take isl_basic_map *bmap,
2681 __isl_take isl_basic_set *dom,
2682 __isl_give isl_set **empty);
2683 __isl_give isl_map *isl_basic_map_partial_lexmin(
2684 __isl_take isl_basic_map *bmap,
2685 __isl_take isl_basic_set *dom,
2686 __isl_give isl_set **empty);
2687 __isl_give isl_map *isl_map_partial_lexmax(
2688 __isl_take isl_map *map, __isl_take isl_set *dom,
2689 __isl_give isl_set **empty);
2690 __isl_give isl_map *isl_map_partial_lexmin(
2691 __isl_take isl_map *map, __isl_take isl_set *dom,
2692 __isl_give isl_set **empty);
2694 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2695 return a map mapping each element in the domain of
2696 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2697 of all elements associated to that element.
2698 In case of union relations, the optimum is computed per space.
2700 __isl_give isl_map *isl_basic_map_lexmin(
2701 __isl_take isl_basic_map *bmap);
2702 __isl_give isl_map *isl_basic_map_lexmax(
2703 __isl_take isl_basic_map *bmap);
2704 __isl_give isl_map *isl_map_lexmin(
2705 __isl_take isl_map *map);
2706 __isl_give isl_map *isl_map_lexmax(
2707 __isl_take isl_map *map);
2708 __isl_give isl_union_map *isl_union_map_lexmin(
2709 __isl_take isl_union_map *umap);
2710 __isl_give isl_union_map *isl_union_map_lexmax(
2711 __isl_take isl_union_map *umap);
2713 The following functions return their result in the form of
2714 a piecewise multi-affine expression
2715 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2716 but are otherwise equivalent to the corresponding functions
2717 returning a basic set or relation.
2719 __isl_give isl_pw_multi_aff *
2720 isl_basic_map_lexmin_pw_multi_aff(
2721 __isl_take isl_basic_map *bmap);
2722 __isl_give isl_pw_multi_aff *
2723 isl_basic_set_partial_lexmin_pw_multi_aff(
2724 __isl_take isl_basic_set *bset,
2725 __isl_take isl_basic_set *dom,
2726 __isl_give isl_set **empty);
2727 __isl_give isl_pw_multi_aff *
2728 isl_basic_set_partial_lexmax_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_map_partial_lexmin_pw_multi_aff(
2734 __isl_take isl_basic_map *bmap,
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_lexmax_pw_multi_aff(
2739 __isl_take isl_basic_map *bmap,
2740 __isl_take isl_basic_set *dom,
2741 __isl_give isl_set **empty);
2745 Lists are defined over several element types, including
2746 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2747 Here we take lists of C<isl_set>s as an example.
2748 Lists can be created, copied and freed using the following functions.
2750 #include <isl/list.h>
2751 __isl_give isl_set_list *isl_set_list_from_set(
2752 __isl_take isl_set *el);
2753 __isl_give isl_set_list *isl_set_list_alloc(
2754 isl_ctx *ctx, int n);
2755 __isl_give isl_set_list *isl_set_list_copy(
2756 __isl_keep isl_set_list *list);
2757 __isl_give isl_set_list *isl_set_list_add(
2758 __isl_take isl_set_list *list,
2759 __isl_take isl_set *el);
2760 __isl_give isl_set_list *isl_set_list_concat(
2761 __isl_take isl_set_list *list1,
2762 __isl_take isl_set_list *list2);
2763 void *isl_set_list_free(__isl_take isl_set_list *list);
2765 C<isl_set_list_alloc> creates an empty list with a capacity for
2766 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2769 Lists can be inspected using the following functions.
2771 #include <isl/list.h>
2772 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2773 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2774 __isl_give isl_set *isl_set_list_get_set(
2775 __isl_keep isl_set_list *list, int index);
2776 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2777 int (*fn)(__isl_take isl_set *el, void *user),
2780 Lists can be printed using
2782 #include <isl/list.h>
2783 __isl_give isl_printer *isl_printer_print_set_list(
2784 __isl_take isl_printer *p,
2785 __isl_keep isl_set_list *list);
2789 Vectors can be created, copied and freed using the following functions.
2791 #include <isl/vec.h>
2792 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2794 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2795 void isl_vec_free(__isl_take isl_vec *vec);
2797 Note that the elements of a newly created vector may have arbitrary values.
2798 The elements can be changed and inspected using the following functions.
2800 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2801 int isl_vec_size(__isl_keep isl_vec *vec);
2802 int isl_vec_get_element(__isl_keep isl_vec *vec,
2803 int pos, isl_int *v);
2804 __isl_give isl_vec *isl_vec_set_element(
2805 __isl_take isl_vec *vec, int pos, isl_int v);
2806 __isl_give isl_vec *isl_vec_set_element_si(
2807 __isl_take isl_vec *vec, int pos, int v);
2808 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2810 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2813 C<isl_vec_get_element> will return a negative value if anything went wrong.
2814 In that case, the value of C<*v> is undefined.
2818 Matrices can be created, copied and freed using the following functions.
2820 #include <isl/mat.h>
2821 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2822 unsigned n_row, unsigned n_col);
2823 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2824 void isl_mat_free(__isl_take isl_mat *mat);
2826 Note that the elements of a newly created matrix may have arbitrary values.
2827 The elements can be changed and inspected using the following functions.
2829 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2830 int isl_mat_rows(__isl_keep isl_mat *mat);
2831 int isl_mat_cols(__isl_keep isl_mat *mat);
2832 int isl_mat_get_element(__isl_keep isl_mat *mat,
2833 int row, int col, isl_int *v);
2834 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2835 int row, int col, isl_int v);
2836 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2837 int row, int col, int v);
2839 C<isl_mat_get_element> will return a negative value if anything went wrong.
2840 In that case, the value of C<*v> is undefined.
2842 The following function can be used to compute the (right) inverse
2843 of a matrix, i.e., a matrix such that the product of the original
2844 and the inverse (in that order) is a multiple of the identity matrix.
2845 The input matrix is assumed to be of full row-rank.
2847 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2849 The following function can be used to compute the (right) kernel
2850 (or null space) of a matrix, i.e., a matrix such that the product of
2851 the original and the kernel (in that order) is the zero matrix.
2853 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2855 =head2 Piecewise Quasi Affine Expressions
2857 The zero quasi affine expression on a given domain can be created using
2859 __isl_give isl_aff *isl_aff_zero_on_domain(
2860 __isl_take isl_local_space *ls);
2862 Note that the space in which the resulting object lives is a map space
2863 with the given space as domain and a one-dimensional range.
2865 An empty piecewise quasi affine expression (one with no cells)
2866 or a piecewise quasi affine expression with a single cell can
2867 be created using the following functions.
2869 #include <isl/aff.h>
2870 __isl_give isl_pw_aff *isl_pw_aff_empty(
2871 __isl_take isl_space *space);
2872 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2873 __isl_take isl_set *set, __isl_take isl_aff *aff);
2874 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2875 __isl_take isl_aff *aff);
2877 A piecewise quasi affine expression that is equal to 1 on a set
2878 and 0 outside the set can be created using the following function.
2880 #include <isl/aff.h>
2881 __isl_give isl_pw_aff *isl_set_indicator_function(
2882 __isl_take isl_set *set);
2884 Quasi affine expressions can be copied and freed using
2886 #include <isl/aff.h>
2887 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2888 void *isl_aff_free(__isl_take isl_aff *aff);
2890 __isl_give isl_pw_aff *isl_pw_aff_copy(
2891 __isl_keep isl_pw_aff *pwaff);
2892 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2894 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2895 using the following function. The constraint is required to have
2896 a non-zero coefficient for the specified dimension.
2898 #include <isl/constraint.h>
2899 __isl_give isl_aff *isl_constraint_get_bound(
2900 __isl_keep isl_constraint *constraint,
2901 enum isl_dim_type type, int pos);
2903 The entire affine expression of the constraint can also be extracted
2904 using the following function.
2906 #include <isl/constraint.h>
2907 __isl_give isl_aff *isl_constraint_get_aff(
2908 __isl_keep isl_constraint *constraint);
2910 Conversely, an equality constraint equating
2911 the affine expression to zero or an inequality constraint enforcing
2912 the affine expression to be non-negative, can be constructed using
2914 __isl_give isl_constraint *isl_equality_from_aff(
2915 __isl_take isl_aff *aff);
2916 __isl_give isl_constraint *isl_inequality_from_aff(
2917 __isl_take isl_aff *aff);
2919 The expression can be inspected using
2921 #include <isl/aff.h>
2922 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2923 int isl_aff_dim(__isl_keep isl_aff *aff,
2924 enum isl_dim_type type);
2925 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2926 __isl_keep isl_aff *aff);
2927 __isl_give isl_local_space *isl_aff_get_local_space(
2928 __isl_keep isl_aff *aff);
2929 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2930 enum isl_dim_type type, unsigned pos);
2931 const char *isl_pw_aff_get_dim_name(
2932 __isl_keep isl_pw_aff *pa,
2933 enum isl_dim_type type, unsigned pos);
2934 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2935 enum isl_dim_type type, unsigned pos);
2936 __isl_give isl_id *isl_pw_aff_get_dim_id(
2937 __isl_keep isl_pw_aff *pa,
2938 enum isl_dim_type type, unsigned pos);
2939 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2941 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2942 enum isl_dim_type type, int pos, isl_int *v);
2943 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2945 __isl_give isl_aff *isl_aff_get_div(
2946 __isl_keep isl_aff *aff, int pos);
2948 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2949 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2950 int (*fn)(__isl_take isl_set *set,
2951 __isl_take isl_aff *aff,
2952 void *user), void *user);
2954 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2955 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2957 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2958 enum isl_dim_type type, unsigned first, unsigned n);
2959 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2960 enum isl_dim_type type, unsigned first, unsigned n);
2962 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2963 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2964 enum isl_dim_type type);
2965 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2967 It can be modified using
2969 #include <isl/aff.h>
2970 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2971 __isl_take isl_pw_aff *pwaff,
2972 enum isl_dim_type type, __isl_take isl_id *id);
2973 __isl_give isl_aff *isl_aff_set_dim_name(
2974 __isl_take isl_aff *aff, enum isl_dim_type type,
2975 unsigned pos, const char *s);
2976 __isl_give isl_aff *isl_aff_set_dim_id(
2977 __isl_take isl_aff *aff, enum isl_dim_type type,
2978 unsigned pos, __isl_take isl_id *id);
2979 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2980 __isl_take isl_pw_aff *pma,
2981 enum isl_dim_type type, unsigned pos,
2982 __isl_take isl_id *id);
2983 __isl_give isl_aff *isl_aff_set_constant(
2984 __isl_take isl_aff *aff, isl_int v);
2985 __isl_give isl_aff *isl_aff_set_constant_si(
2986 __isl_take isl_aff *aff, int v);
2987 __isl_give isl_aff *isl_aff_set_coefficient(
2988 __isl_take isl_aff *aff,
2989 enum isl_dim_type type, int pos, isl_int v);
2990 __isl_give isl_aff *isl_aff_set_coefficient_si(
2991 __isl_take isl_aff *aff,
2992 enum isl_dim_type type, int pos, int v);
2993 __isl_give isl_aff *isl_aff_set_denominator(
2994 __isl_take isl_aff *aff, isl_int v);
2996 __isl_give isl_aff *isl_aff_add_constant(
2997 __isl_take isl_aff *aff, isl_int v);
2998 __isl_give isl_aff *isl_aff_add_constant_si(
2999 __isl_take isl_aff *aff, int v);
3000 __isl_give isl_aff *isl_aff_add_coefficient(
3001 __isl_take isl_aff *aff,
3002 enum isl_dim_type type, int pos, isl_int v);
3003 __isl_give isl_aff *isl_aff_add_coefficient_si(
3004 __isl_take isl_aff *aff,
3005 enum isl_dim_type type, int pos, int v);
3007 __isl_give isl_aff *isl_aff_insert_dims(
3008 __isl_take isl_aff *aff,
3009 enum isl_dim_type type, unsigned first, unsigned n);
3010 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3011 __isl_take isl_pw_aff *pwaff,
3012 enum isl_dim_type type, unsigned first, unsigned n);
3013 __isl_give isl_aff *isl_aff_add_dims(
3014 __isl_take isl_aff *aff,
3015 enum isl_dim_type type, unsigned n);
3016 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3017 __isl_take isl_pw_aff *pwaff,
3018 enum isl_dim_type type, unsigned n);
3019 __isl_give isl_aff *isl_aff_drop_dims(
3020 __isl_take isl_aff *aff,
3021 enum isl_dim_type type, unsigned first, unsigned n);
3022 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3023 __isl_take isl_pw_aff *pwaff,
3024 enum isl_dim_type type, unsigned first, unsigned n);
3026 Note that the C<set_constant> and C<set_coefficient> functions
3027 set the I<numerator> of the constant or coefficient, while
3028 C<add_constant> and C<add_coefficient> add an integer value to
3029 the possibly rational constant or coefficient.
3031 To check whether an affine expressions is obviously zero
3032 or obviously equal to some other affine expression, use
3034 #include <isl/aff.h>
3035 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3036 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3037 __isl_keep isl_aff *aff2);
3038 int isl_pw_aff_plain_is_equal(
3039 __isl_keep isl_pw_aff *pwaff1,
3040 __isl_keep isl_pw_aff *pwaff2);
3044 #include <isl/aff.h>
3045 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3046 __isl_take isl_aff *aff2);
3047 __isl_give isl_pw_aff *isl_pw_aff_add(
3048 __isl_take isl_pw_aff *pwaff1,
3049 __isl_take isl_pw_aff *pwaff2);
3050 __isl_give isl_pw_aff *isl_pw_aff_min(
3051 __isl_take isl_pw_aff *pwaff1,
3052 __isl_take isl_pw_aff *pwaff2);
3053 __isl_give isl_pw_aff *isl_pw_aff_max(
3054 __isl_take isl_pw_aff *pwaff1,
3055 __isl_take isl_pw_aff *pwaff2);
3056 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3057 __isl_take isl_aff *aff2);
3058 __isl_give isl_pw_aff *isl_pw_aff_sub(
3059 __isl_take isl_pw_aff *pwaff1,
3060 __isl_take isl_pw_aff *pwaff2);
3061 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3062 __isl_give isl_pw_aff *isl_pw_aff_neg(
3063 __isl_take isl_pw_aff *pwaff);
3064 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3065 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3066 __isl_take isl_pw_aff *pwaff);
3067 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3068 __isl_give isl_pw_aff *isl_pw_aff_floor(
3069 __isl_take isl_pw_aff *pwaff);
3070 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3072 __isl_give isl_pw_aff *isl_pw_aff_mod(
3073 __isl_take isl_pw_aff *pwaff, isl_int mod);
3074 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3076 __isl_give isl_pw_aff *isl_pw_aff_scale(
3077 __isl_take isl_pw_aff *pwaff, isl_int f);
3078 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3080 __isl_give isl_aff *isl_aff_scale_down_ui(
3081 __isl_take isl_aff *aff, unsigned f);
3082 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3083 __isl_take isl_pw_aff *pwaff, isl_int f);
3085 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3086 __isl_take isl_pw_aff_list *list);
3087 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3088 __isl_take isl_pw_aff_list *list);
3090 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3091 __isl_take isl_pw_aff *pwqp);
3093 __isl_give isl_aff *isl_aff_align_params(
3094 __isl_take isl_aff *aff,
3095 __isl_take isl_space *model);
3096 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3097 __isl_take isl_pw_aff *pwaff,
3098 __isl_take isl_space *model);
3100 __isl_give isl_aff *isl_aff_project_domain_on_params(
3101 __isl_take isl_aff *aff);
3103 __isl_give isl_aff *isl_aff_gist_params(
3104 __isl_take isl_aff *aff,
3105 __isl_take isl_set *context);
3106 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3107 __isl_take isl_set *context);
3108 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3109 __isl_take isl_pw_aff *pwaff,
3110 __isl_take isl_set *context);
3111 __isl_give isl_pw_aff *isl_pw_aff_gist(
3112 __isl_take isl_pw_aff *pwaff,
3113 __isl_take isl_set *context);
3115 __isl_give isl_set *isl_pw_aff_domain(
3116 __isl_take isl_pw_aff *pwaff);
3117 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3118 __isl_take isl_pw_aff *pa,
3119 __isl_take isl_set *set);
3120 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3121 __isl_take isl_pw_aff *pa,
3122 __isl_take isl_set *set);
3124 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3125 __isl_take isl_aff *aff2);
3126 __isl_give isl_pw_aff *isl_pw_aff_mul(
3127 __isl_take isl_pw_aff *pwaff1,
3128 __isl_take isl_pw_aff *pwaff2);
3130 When multiplying two affine expressions, at least one of the two needs
3133 #include <isl/aff.h>
3134 __isl_give isl_basic_set *isl_aff_le_basic_set(
3135 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3136 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3137 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3138 __isl_give isl_set *isl_pw_aff_eq_set(
3139 __isl_take isl_pw_aff *pwaff1,
3140 __isl_take isl_pw_aff *pwaff2);
3141 __isl_give isl_set *isl_pw_aff_ne_set(
3142 __isl_take isl_pw_aff *pwaff1,
3143 __isl_take isl_pw_aff *pwaff2);
3144 __isl_give isl_set *isl_pw_aff_le_set(
3145 __isl_take isl_pw_aff *pwaff1,
3146 __isl_take isl_pw_aff *pwaff2);
3147 __isl_give isl_set *isl_pw_aff_lt_set(
3148 __isl_take isl_pw_aff *pwaff1,
3149 __isl_take isl_pw_aff *pwaff2);
3150 __isl_give isl_set *isl_pw_aff_ge_set(
3151 __isl_take isl_pw_aff *pwaff1,
3152 __isl_take isl_pw_aff *pwaff2);
3153 __isl_give isl_set *isl_pw_aff_gt_set(
3154 __isl_take isl_pw_aff *pwaff1,
3155 __isl_take isl_pw_aff *pwaff2);
3157 __isl_give isl_set *isl_pw_aff_list_eq_set(
3158 __isl_take isl_pw_aff_list *list1,
3159 __isl_take isl_pw_aff_list *list2);
3160 __isl_give isl_set *isl_pw_aff_list_ne_set(
3161 __isl_take isl_pw_aff_list *list1,
3162 __isl_take isl_pw_aff_list *list2);
3163 __isl_give isl_set *isl_pw_aff_list_le_set(
3164 __isl_take isl_pw_aff_list *list1,
3165 __isl_take isl_pw_aff_list *list2);
3166 __isl_give isl_set *isl_pw_aff_list_lt_set(
3167 __isl_take isl_pw_aff_list *list1,
3168 __isl_take isl_pw_aff_list *list2);
3169 __isl_give isl_set *isl_pw_aff_list_ge_set(
3170 __isl_take isl_pw_aff_list *list1,
3171 __isl_take isl_pw_aff_list *list2);
3172 __isl_give isl_set *isl_pw_aff_list_gt_set(
3173 __isl_take isl_pw_aff_list *list1,
3174 __isl_take isl_pw_aff_list *list2);
3176 The function C<isl_aff_ge_basic_set> returns a basic set
3177 containing those elements in the shared space
3178 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3179 The function C<isl_aff_ge_set> returns a set
3180 containing those elements in the shared domain
3181 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3182 The functions operating on C<isl_pw_aff_list> apply the corresponding
3183 C<isl_pw_aff> function to each pair of elements in the two lists.
3185 #include <isl/aff.h>
3186 __isl_give isl_set *isl_pw_aff_nonneg_set(
3187 __isl_take isl_pw_aff *pwaff);
3188 __isl_give isl_set *isl_pw_aff_zero_set(
3189 __isl_take isl_pw_aff *pwaff);
3190 __isl_give isl_set *isl_pw_aff_non_zero_set(
3191 __isl_take isl_pw_aff *pwaff);
3193 The function C<isl_pw_aff_nonneg_set> returns a set
3194 containing those elements in the domain
3195 of C<pwaff> where C<pwaff> is non-negative.
3197 #include <isl/aff.h>
3198 __isl_give isl_pw_aff *isl_pw_aff_cond(
3199 __isl_take isl_pw_aff *cond,
3200 __isl_take isl_pw_aff *pwaff_true,
3201 __isl_take isl_pw_aff *pwaff_false);
3203 The function C<isl_pw_aff_cond> performs a conditional operator
3204 and returns an expression that is equal to C<pwaff_true>
3205 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3206 where C<cond> is zero.
3208 #include <isl/aff.h>
3209 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3210 __isl_take isl_pw_aff *pwaff1,
3211 __isl_take isl_pw_aff *pwaff2);
3212 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3213 __isl_take isl_pw_aff *pwaff1,
3214 __isl_take isl_pw_aff *pwaff2);
3215 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3216 __isl_take isl_pw_aff *pwaff1,
3217 __isl_take isl_pw_aff *pwaff2);
3219 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3220 expression with a domain that is the union of those of C<pwaff1> and
3221 C<pwaff2> and such that on each cell, the quasi-affine expression is
3222 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3223 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3224 associated expression is the defined one.
3226 An expression can be read from input using
3228 #include <isl/aff.h>
3229 __isl_give isl_aff *isl_aff_read_from_str(
3230 isl_ctx *ctx, const char *str);
3231 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3232 isl_ctx *ctx, const char *str);
3234 An expression can be printed using
3236 #include <isl/aff.h>
3237 __isl_give isl_printer *isl_printer_print_aff(
3238 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3240 __isl_give isl_printer *isl_printer_print_pw_aff(
3241 __isl_take isl_printer *p,
3242 __isl_keep isl_pw_aff *pwaff);
3244 =head2 Piecewise Multiple Quasi Affine Expressions
3246 An C<isl_multi_aff> object represents a sequence of
3247 zero or more affine expressions, all defined on the same domain space.
3249 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3252 #include <isl/aff.h>
3253 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3254 __isl_take isl_space *space,
3255 __isl_take isl_aff_list *list);
3257 An empty piecewise multiple quasi affine expression (one with no cells),
3258 the zero piecewise multiple quasi affine expression (with value zero
3259 for each output dimension),
3260 a piecewise multiple quasi affine expression with a single cell (with
3261 either a universe or a specified domain) or
3262 a zero-dimensional piecewise multiple quasi affine expression
3264 can be created using the following functions.
3266 #include <isl/aff.h>
3267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3268 __isl_take isl_space *space);
3269 __isl_give isl_multi_aff *isl_multi_aff_zero(
3270 __isl_take isl_space *space);
3271 __isl_give isl_pw_multi_aff *
3272 isl_pw_multi_aff_from_multi_aff(
3273 __isl_take isl_multi_aff *ma);
3274 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3275 __isl_take isl_set *set,
3276 __isl_take isl_multi_aff *maff);
3277 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3278 __isl_take isl_set *set);
3280 __isl_give isl_union_pw_multi_aff *
3281 isl_union_pw_multi_aff_empty(
3282 __isl_take isl_space *space);
3283 __isl_give isl_union_pw_multi_aff *
3284 isl_union_pw_multi_aff_add_pw_multi_aff(
3285 __isl_take isl_union_pw_multi_aff *upma,
3286 __isl_take isl_pw_multi_aff *pma);
3287 __isl_give isl_union_pw_multi_aff *
3288 isl_union_pw_multi_aff_from_domain(
3289 __isl_take isl_union_set *uset);
3291 A piecewise multiple quasi affine expression can also be initialized
3292 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3293 and the C<isl_map> is single-valued.
3295 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3296 __isl_take isl_set *set);
3297 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3298 __isl_take isl_map *map);
3300 Multiple quasi affine expressions can be copied and freed using
3302 #include <isl/aff.h>
3303 __isl_give isl_multi_aff *isl_multi_aff_copy(
3304 __isl_keep isl_multi_aff *maff);
3305 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3307 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3308 __isl_keep isl_pw_multi_aff *pma);
3309 void *isl_pw_multi_aff_free(
3310 __isl_take isl_pw_multi_aff *pma);
3312 __isl_give isl_union_pw_multi_aff *
3313 isl_union_pw_multi_aff_copy(
3314 __isl_keep isl_union_pw_multi_aff *upma);
3315 void *isl_union_pw_multi_aff_free(
3316 __isl_take isl_union_pw_multi_aff *upma);
3318 The expression can be inspected using
3320 #include <isl/aff.h>
3321 isl_ctx *isl_multi_aff_get_ctx(
3322 __isl_keep isl_multi_aff *maff);
3323 isl_ctx *isl_pw_multi_aff_get_ctx(
3324 __isl_keep isl_pw_multi_aff *pma);
3325 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3326 __isl_keep isl_union_pw_multi_aff *upma);
3327 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3328 enum isl_dim_type type);
3329 unsigned isl_pw_multi_aff_dim(
3330 __isl_keep isl_pw_multi_aff *pma,
3331 enum isl_dim_type type);
3332 __isl_give isl_aff *isl_multi_aff_get_aff(
3333 __isl_keep isl_multi_aff *multi, int pos);
3334 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3335 __isl_keep isl_pw_multi_aff *pma, int pos);
3336 const char *isl_pw_multi_aff_get_dim_name(
3337 __isl_keep isl_pw_multi_aff *pma,
3338 enum isl_dim_type type, unsigned pos);
3339 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3340 __isl_keep isl_pw_multi_aff *pma,
3341 enum isl_dim_type type, unsigned pos);
3342 const char *isl_multi_aff_get_tuple_name(
3343 __isl_keep isl_multi_aff *multi,
3344 enum isl_dim_type type);
3345 const char *isl_pw_multi_aff_get_tuple_name(
3346 __isl_keep isl_pw_multi_aff *pma,
3347 enum isl_dim_type type);
3348 int isl_pw_multi_aff_has_tuple_id(
3349 __isl_keep isl_pw_multi_aff *pma,
3350 enum isl_dim_type type);
3351 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3352 __isl_keep isl_pw_multi_aff *pma,
3353 enum isl_dim_type type);
3355 int isl_pw_multi_aff_foreach_piece(
3356 __isl_keep isl_pw_multi_aff *pma,
3357 int (*fn)(__isl_take isl_set *set,
3358 __isl_take isl_multi_aff *maff,
3359 void *user), void *user);
3361 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3362 __isl_keep isl_union_pw_multi_aff *upma,
3363 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3364 void *user), void *user);
3366 It can be modified using
3368 #include <isl/aff.h>
3369 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3370 __isl_take isl_multi_aff *multi, int pos,
3371 __isl_take isl_aff *aff);
3372 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3373 __isl_take isl_multi_aff *maff,
3374 enum isl_dim_type type, unsigned pos, const char *s);
3375 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3376 __isl_take isl_multi_aff *maff,
3377 enum isl_dim_type type, __isl_take isl_id *id);
3378 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3379 __isl_take isl_pw_multi_aff *pma,
3380 enum isl_dim_type type, __isl_take isl_id *id);
3382 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3383 __isl_take isl_multi_aff *maff,
3384 enum isl_dim_type type, unsigned first, unsigned n);
3386 To check whether two multiple affine expressions are
3387 obviously equal to each other, use
3389 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3390 __isl_keep isl_multi_aff *maff2);
3391 int isl_pw_multi_aff_plain_is_equal(
3392 __isl_keep isl_pw_multi_aff *pma1,
3393 __isl_keep isl_pw_multi_aff *pma2);
3397 #include <isl/aff.h>
3398 __isl_give isl_multi_aff *isl_multi_aff_add(
3399 __isl_take isl_multi_aff *maff1,
3400 __isl_take isl_multi_aff *maff2);
3401 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3402 __isl_take isl_pw_multi_aff *pma1,
3403 __isl_take isl_pw_multi_aff *pma2);
3404 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3405 __isl_take isl_union_pw_multi_aff *upma1,
3406 __isl_take isl_union_pw_multi_aff *upma2);
3407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3408 __isl_take isl_pw_multi_aff *pma1,
3409 __isl_take isl_pw_multi_aff *pma2);
3410 __isl_give isl_multi_aff *isl_multi_aff_scale(
3411 __isl_take isl_multi_aff *maff,
3413 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3414 __isl_take isl_pw_multi_aff *pma,
3415 __isl_take isl_set *set);
3416 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3417 __isl_take isl_pw_multi_aff *pma,
3418 __isl_take isl_set *set);
3419 __isl_give isl_multi_aff *isl_multi_aff_lift(
3420 __isl_take isl_multi_aff *maff,
3421 __isl_give isl_local_space **ls);
3422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3423 __isl_take isl_pw_multi_aff *pma);
3424 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3425 __isl_take isl_multi_aff *maff,
3426 __isl_take isl_set *context);
3427 __isl_give isl_multi_aff *isl_multi_aff_gist(
3428 __isl_take isl_multi_aff *maff,
3429 __isl_take isl_set *context);
3430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3431 __isl_take isl_pw_multi_aff *pma,
3432 __isl_take isl_set *set);
3433 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3434 __isl_take isl_pw_multi_aff *pma,
3435 __isl_take isl_set *set);
3436 __isl_give isl_set *isl_pw_multi_aff_domain(
3437 __isl_take isl_pw_multi_aff *pma);
3438 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3439 __isl_take isl_union_pw_multi_aff *upma);
3440 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3441 __isl_take isl_multi_aff *ma1,
3442 __isl_take isl_multi_aff *ma2);
3443 __isl_give isl_pw_multi_aff *
3444 isl_pw_multi_aff_flat_range_product(
3445 __isl_take isl_pw_multi_aff *pma1,
3446 __isl_take isl_pw_multi_aff *pma2);
3447 __isl_give isl_union_pw_multi_aff *
3448 isl_union_pw_multi_aff_flat_range_product(
3449 __isl_take isl_union_pw_multi_aff *upma1,
3450 __isl_take isl_union_pw_multi_aff *upma2);
3452 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3453 then it is assigned the local space that lies at the basis of
3454 the lifting applied.
3456 An expression can be read from input using
3458 #include <isl/aff.h>
3459 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3460 isl_ctx *ctx, const char *str);
3461 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3462 isl_ctx *ctx, const char *str);
3464 An expression can be printed using
3466 #include <isl/aff.h>
3467 __isl_give isl_printer *isl_printer_print_multi_aff(
3468 __isl_take isl_printer *p,
3469 __isl_keep isl_multi_aff *maff);
3470 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3471 __isl_take isl_printer *p,
3472 __isl_keep isl_pw_multi_aff *pma);
3473 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3474 __isl_take isl_printer *p,
3475 __isl_keep isl_union_pw_multi_aff *upma);
3479 Points are elements of a set. They can be used to construct
3480 simple sets (boxes) or they can be used to represent the
3481 individual elements of a set.
3482 The zero point (the origin) can be created using
3484 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3486 The coordinates of a point can be inspected, set and changed
3489 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3490 enum isl_dim_type type, int pos, isl_int *v);
3491 __isl_give isl_point *isl_point_set_coordinate(
3492 __isl_take isl_point *pnt,
3493 enum isl_dim_type type, int pos, isl_int v);
3495 __isl_give isl_point *isl_point_add_ui(
3496 __isl_take isl_point *pnt,
3497 enum isl_dim_type type, int pos, unsigned val);
3498 __isl_give isl_point *isl_point_sub_ui(
3499 __isl_take isl_point *pnt,
3500 enum isl_dim_type type, int pos, unsigned val);
3502 Other properties can be obtained using
3504 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3506 Points can be copied or freed using
3508 __isl_give isl_point *isl_point_copy(
3509 __isl_keep isl_point *pnt);
3510 void isl_point_free(__isl_take isl_point *pnt);
3512 A singleton set can be created from a point using
3514 __isl_give isl_basic_set *isl_basic_set_from_point(
3515 __isl_take isl_point *pnt);
3516 __isl_give isl_set *isl_set_from_point(
3517 __isl_take isl_point *pnt);
3519 and a box can be created from two opposite extremal points using
3521 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3522 __isl_take isl_point *pnt1,
3523 __isl_take isl_point *pnt2);
3524 __isl_give isl_set *isl_set_box_from_points(
3525 __isl_take isl_point *pnt1,
3526 __isl_take isl_point *pnt2);
3528 All elements of a B<bounded> (union) set can be enumerated using
3529 the following functions.
3531 int isl_set_foreach_point(__isl_keep isl_set *set,
3532 int (*fn)(__isl_take isl_point *pnt, void *user),
3534 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3535 int (*fn)(__isl_take isl_point *pnt, void *user),
3538 The function C<fn> is called for each integer point in
3539 C<set> with as second argument the last argument of
3540 the C<isl_set_foreach_point> call. The function C<fn>
3541 should return C<0> on success and C<-1> on failure.
3542 In the latter case, C<isl_set_foreach_point> will stop
3543 enumerating and return C<-1> as well.
3544 If the enumeration is performed successfully and to completion,
3545 then C<isl_set_foreach_point> returns C<0>.
3547 To obtain a single point of a (basic) set, use
3549 __isl_give isl_point *isl_basic_set_sample_point(
3550 __isl_take isl_basic_set *bset);
3551 __isl_give isl_point *isl_set_sample_point(
3552 __isl_take isl_set *set);
3554 If C<set> does not contain any (integer) points, then the
3555 resulting point will be ``void'', a property that can be
3558 int isl_point_is_void(__isl_keep isl_point *pnt);
3560 =head2 Piecewise Quasipolynomials
3562 A piecewise quasipolynomial is a particular kind of function that maps
3563 a parametric point to a rational value.
3564 More specifically, a quasipolynomial is a polynomial expression in greatest
3565 integer parts of affine expressions of parameters and variables.
3566 A piecewise quasipolynomial is a subdivision of a given parametric
3567 domain into disjoint cells with a quasipolynomial associated to
3568 each cell. The value of the piecewise quasipolynomial at a given
3569 point is the value of the quasipolynomial associated to the cell
3570 that contains the point. Outside of the union of cells,
3571 the value is assumed to be zero.
3572 For example, the piecewise quasipolynomial
3574 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3576 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3577 A given piecewise quasipolynomial has a fixed domain dimension.
3578 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3579 defined over different domains.
3580 Piecewise quasipolynomials are mainly used by the C<barvinok>
3581 library for representing the number of elements in a parametric set or map.
3582 For example, the piecewise quasipolynomial above represents
3583 the number of points in the map
3585 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3587 =head3 Input and Output
3589 Piecewise quasipolynomials can be read from input using
3591 __isl_give isl_union_pw_qpolynomial *
3592 isl_union_pw_qpolynomial_read_from_str(
3593 isl_ctx *ctx, const char *str);
3595 Quasipolynomials and piecewise quasipolynomials can be printed
3596 using the following functions.
3598 __isl_give isl_printer *isl_printer_print_qpolynomial(
3599 __isl_take isl_printer *p,
3600 __isl_keep isl_qpolynomial *qp);
3602 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3603 __isl_take isl_printer *p,
3604 __isl_keep isl_pw_qpolynomial *pwqp);
3606 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3607 __isl_take isl_printer *p,
3608 __isl_keep isl_union_pw_qpolynomial *upwqp);
3610 The output format of the printer
3611 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3612 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3614 In case of printing in C<ISL_FORMAT_C>, the user may want
3615 to set the names of all dimensions
3617 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3618 __isl_take isl_qpolynomial *qp,
3619 enum isl_dim_type type, unsigned pos,
3621 __isl_give isl_pw_qpolynomial *
3622 isl_pw_qpolynomial_set_dim_name(
3623 __isl_take isl_pw_qpolynomial *pwqp,
3624 enum isl_dim_type type, unsigned pos,
3627 =head3 Creating New (Piecewise) Quasipolynomials
3629 Some simple quasipolynomials can be created using the following functions.
3630 More complicated quasipolynomials can be created by applying
3631 operations such as addition and multiplication
3632 on the resulting quasipolynomials
3634 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3635 __isl_take isl_space *domain);
3636 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3637 __isl_take isl_space *domain);
3638 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3639 __isl_take isl_space *domain);
3640 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3641 __isl_take isl_space *domain);
3642 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3643 __isl_take isl_space *domain);
3644 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3645 __isl_take isl_space *domain,
3646 const isl_int n, const isl_int d);
3647 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3648 __isl_take isl_space *domain,
3649 enum isl_dim_type type, unsigned pos);
3650 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3651 __isl_take isl_aff *aff);
3653 Note that the space in which a quasipolynomial lives is a map space
3654 with a one-dimensional range. The C<domain> argument in some of
3655 the functions above corresponds to the domain of this map space.
3657 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3658 with a single cell can be created using the following functions.
3659 Multiple of these single cell piecewise quasipolynomials can
3660 be combined to create more complicated piecewise quasipolynomials.
3662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3663 __isl_take isl_space *space);
3664 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3665 __isl_take isl_set *set,
3666 __isl_take isl_qpolynomial *qp);
3667 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3668 __isl_take isl_qpolynomial *qp);
3669 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3670 __isl_take isl_pw_aff *pwaff);
3672 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3673 __isl_take isl_space *space);
3674 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3675 __isl_take isl_pw_qpolynomial *pwqp);
3676 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3677 __isl_take isl_union_pw_qpolynomial *upwqp,
3678 __isl_take isl_pw_qpolynomial *pwqp);
3680 Quasipolynomials can be copied and freed again using the following
3683 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3684 __isl_keep isl_qpolynomial *qp);
3685 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3687 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3688 __isl_keep isl_pw_qpolynomial *pwqp);
3689 void *isl_pw_qpolynomial_free(
3690 __isl_take isl_pw_qpolynomial *pwqp);
3692 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3693 __isl_keep isl_union_pw_qpolynomial *upwqp);
3694 void *isl_union_pw_qpolynomial_free(
3695 __isl_take isl_union_pw_qpolynomial *upwqp);
3697 =head3 Inspecting (Piecewise) Quasipolynomials
3699 To iterate over all piecewise quasipolynomials in a union
3700 piecewise quasipolynomial, use the following function
3702 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3703 __isl_keep isl_union_pw_qpolynomial *upwqp,
3704 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3707 To extract the piecewise quasipolynomial in a given space from a union, use
3709 __isl_give isl_pw_qpolynomial *
3710 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3711 __isl_keep isl_union_pw_qpolynomial *upwqp,
3712 __isl_take isl_space *space);
3714 To iterate over the cells in a piecewise quasipolynomial,
3715 use either of the following two functions
3717 int isl_pw_qpolynomial_foreach_piece(
3718 __isl_keep isl_pw_qpolynomial *pwqp,
3719 int (*fn)(__isl_take isl_set *set,
3720 __isl_take isl_qpolynomial *qp,
3721 void *user), void *user);
3722 int isl_pw_qpolynomial_foreach_lifted_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);
3728 As usual, the function C<fn> should return C<0> on success
3729 and C<-1> on failure. The difference between
3730 C<isl_pw_qpolynomial_foreach_piece> and
3731 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3732 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3733 compute unique representations for all existentially quantified
3734 variables and then turn these existentially quantified variables
3735 into extra set variables, adapting the associated quasipolynomial
3736 accordingly. This means that the C<set> passed to C<fn>
3737 will not have any existentially quantified variables, but that
3738 the dimensions of the sets may be different for different
3739 invocations of C<fn>.
3741 To iterate over all terms in a quasipolynomial,
3744 int isl_qpolynomial_foreach_term(
3745 __isl_keep isl_qpolynomial *qp,
3746 int (*fn)(__isl_take isl_term *term,
3747 void *user), void *user);
3749 The terms themselves can be inspected and freed using
3752 unsigned isl_term_dim(__isl_keep isl_term *term,
3753 enum isl_dim_type type);
3754 void isl_term_get_num(__isl_keep isl_term *term,
3756 void isl_term_get_den(__isl_keep isl_term *term,
3758 int isl_term_get_exp(__isl_keep isl_term *term,
3759 enum isl_dim_type type, unsigned pos);
3760 __isl_give isl_aff *isl_term_get_div(
3761 __isl_keep isl_term *term, unsigned pos);
3762 void isl_term_free(__isl_take isl_term *term);
3764 Each term is a product of parameters, set variables and
3765 integer divisions. The function C<isl_term_get_exp>
3766 returns the exponent of a given dimensions in the given term.
3767 The C<isl_int>s in the arguments of C<isl_term_get_num>
3768 and C<isl_term_get_den> need to have been initialized
3769 using C<isl_int_init> before calling these functions.
3771 =head3 Properties of (Piecewise) Quasipolynomials
3773 To check whether a quasipolynomial is actually a constant,
3774 use the following function.
3776 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3777 isl_int *n, isl_int *d);
3779 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3780 then the numerator and denominator of the constant
3781 are returned in C<*n> and C<*d>, respectively.
3783 To check whether two union piecewise quasipolynomials are
3784 obviously equal, use
3786 int isl_union_pw_qpolynomial_plain_is_equal(
3787 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3788 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3790 =head3 Operations on (Piecewise) Quasipolynomials
3792 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3793 __isl_take isl_qpolynomial *qp, isl_int v);
3794 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3795 __isl_take isl_qpolynomial *qp);
3796 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3797 __isl_take isl_qpolynomial *qp1,
3798 __isl_take isl_qpolynomial *qp2);
3799 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3800 __isl_take isl_qpolynomial *qp1,
3801 __isl_take isl_qpolynomial *qp2);
3802 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3803 __isl_take isl_qpolynomial *qp1,
3804 __isl_take isl_qpolynomial *qp2);
3805 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3806 __isl_take isl_qpolynomial *qp, unsigned exponent);
3808 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3809 __isl_take isl_pw_qpolynomial *pwqp1,
3810 __isl_take isl_pw_qpolynomial *pwqp2);
3811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3812 __isl_take isl_pw_qpolynomial *pwqp1,
3813 __isl_take isl_pw_qpolynomial *pwqp2);
3814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3815 __isl_take isl_pw_qpolynomial *pwqp1,
3816 __isl_take isl_pw_qpolynomial *pwqp2);
3817 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3818 __isl_take isl_pw_qpolynomial *pwqp);
3819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3820 __isl_take isl_pw_qpolynomial *pwqp1,
3821 __isl_take isl_pw_qpolynomial *pwqp2);
3822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3823 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3825 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3826 __isl_take isl_union_pw_qpolynomial *upwqp1,
3827 __isl_take isl_union_pw_qpolynomial *upwqp2);
3828 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3829 __isl_take isl_union_pw_qpolynomial *upwqp1,
3830 __isl_take isl_union_pw_qpolynomial *upwqp2);
3831 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3832 __isl_take isl_union_pw_qpolynomial *upwqp1,
3833 __isl_take isl_union_pw_qpolynomial *upwqp2);
3835 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3836 __isl_take isl_pw_qpolynomial *pwqp,
3837 __isl_take isl_point *pnt);
3839 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3840 __isl_take isl_union_pw_qpolynomial *upwqp,
3841 __isl_take isl_point *pnt);
3843 __isl_give isl_set *isl_pw_qpolynomial_domain(
3844 __isl_take isl_pw_qpolynomial *pwqp);
3845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3846 __isl_take isl_pw_qpolynomial *pwpq,
3847 __isl_take isl_set *set);
3848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3849 __isl_take isl_pw_qpolynomial *pwpq,
3850 __isl_take isl_set *set);
3852 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3853 __isl_take isl_union_pw_qpolynomial *upwqp);
3854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3855 __isl_take isl_union_pw_qpolynomial *upwpq,
3856 __isl_take isl_union_set *uset);
3857 __isl_give isl_union_pw_qpolynomial *
3858 isl_union_pw_qpolynomial_intersect_params(
3859 __isl_take isl_union_pw_qpolynomial *upwpq,
3860 __isl_take isl_set *set);
3862 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3863 __isl_take isl_qpolynomial *qp,
3864 __isl_take isl_space *model);
3866 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3867 __isl_take isl_qpolynomial *qp);
3868 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3869 __isl_take isl_pw_qpolynomial *pwqp);
3871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3872 __isl_take isl_union_pw_qpolynomial *upwqp);
3874 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3875 __isl_take isl_qpolynomial *qp,
3876 __isl_take isl_set *context);
3877 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3878 __isl_take isl_qpolynomial *qp,
3879 __isl_take isl_set *context);
3881 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3882 __isl_take isl_pw_qpolynomial *pwqp,
3883 __isl_take isl_set *context);
3884 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3885 __isl_take isl_pw_qpolynomial *pwqp,
3886 __isl_take isl_set *context);
3888 __isl_give isl_union_pw_qpolynomial *
3889 isl_union_pw_qpolynomial_gist_params(
3890 __isl_take isl_union_pw_qpolynomial *upwqp,
3891 __isl_take isl_set *context);
3892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3893 __isl_take isl_union_pw_qpolynomial *upwqp,
3894 __isl_take isl_union_set *context);
3896 The gist operation applies the gist operation to each of
3897 the cells in the domain of the input piecewise quasipolynomial.
3898 The context is also exploited
3899 to simplify the quasipolynomials associated to each cell.
3901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3902 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3903 __isl_give isl_union_pw_qpolynomial *
3904 isl_union_pw_qpolynomial_to_polynomial(
3905 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3907 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3908 the polynomial will be an overapproximation. If C<sign> is negative,
3909 it will be an underapproximation. If C<sign> is zero, the approximation
3910 will lie somewhere in between.
3912 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3914 A piecewise quasipolynomial reduction is a piecewise
3915 reduction (or fold) of quasipolynomials.
3916 In particular, the reduction can be maximum or a minimum.
3917 The objects are mainly used to represent the result of
3918 an upper or lower bound on a quasipolynomial over its domain,
3919 i.e., as the result of the following function.
3921 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3922 __isl_take isl_pw_qpolynomial *pwqp,
3923 enum isl_fold type, int *tight);
3925 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3926 __isl_take isl_union_pw_qpolynomial *upwqp,
3927 enum isl_fold type, int *tight);
3929 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3930 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3931 is the returned bound is known be tight, i.e., for each value
3932 of the parameters there is at least
3933 one element in the domain that reaches the bound.
3934 If the domain of C<pwqp> is not wrapping, then the bound is computed
3935 over all elements in that domain and the result has a purely parametric
3936 domain. If the domain of C<pwqp> is wrapping, then the bound is
3937 computed over the range of the wrapped relation. The domain of the
3938 wrapped relation becomes the domain of the result.
3940 A (piecewise) quasipolynomial reduction can be copied or freed using the
3941 following functions.
3943 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3944 __isl_keep isl_qpolynomial_fold *fold);
3945 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3946 __isl_keep isl_pw_qpolynomial_fold *pwf);
3947 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3948 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3949 void isl_qpolynomial_fold_free(
3950 __isl_take isl_qpolynomial_fold *fold);
3951 void *isl_pw_qpolynomial_fold_free(
3952 __isl_take isl_pw_qpolynomial_fold *pwf);
3953 void *isl_union_pw_qpolynomial_fold_free(
3954 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3956 =head3 Printing Piecewise Quasipolynomial Reductions
3958 Piecewise quasipolynomial reductions can be printed
3959 using the following function.
3961 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3962 __isl_take isl_printer *p,
3963 __isl_keep isl_pw_qpolynomial_fold *pwf);
3964 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3965 __isl_take isl_printer *p,
3966 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3968 For C<isl_printer_print_pw_qpolynomial_fold>,
3969 output format of the printer
3970 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3971 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3972 output format of the printer
3973 needs to be set to C<ISL_FORMAT_ISL>.
3974 In case of printing in C<ISL_FORMAT_C>, the user may want
3975 to set the names of all dimensions
3977 __isl_give isl_pw_qpolynomial_fold *
3978 isl_pw_qpolynomial_fold_set_dim_name(
3979 __isl_take isl_pw_qpolynomial_fold *pwf,
3980 enum isl_dim_type type, unsigned pos,
3983 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3985 To iterate over all piecewise quasipolynomial reductions in a union
3986 piecewise quasipolynomial reduction, use the following function
3988 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3989 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3990 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3991 void *user), void *user);
3993 To iterate over the cells in a piecewise quasipolynomial reduction,
3994 use either of the following two functions
3996 int isl_pw_qpolynomial_fold_foreach_piece(
3997 __isl_keep isl_pw_qpolynomial_fold *pwf,
3998 int (*fn)(__isl_take isl_set *set,
3999 __isl_take isl_qpolynomial_fold *fold,
4000 void *user), void *user);
4001 int isl_pw_qpolynomial_fold_foreach_lifted_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);
4007 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4008 of the difference between these two functions.
4010 To iterate over all quasipolynomials in a reduction, use
4012 int isl_qpolynomial_fold_foreach_qpolynomial(
4013 __isl_keep isl_qpolynomial_fold *fold,
4014 int (*fn)(__isl_take isl_qpolynomial *qp,
4015 void *user), void *user);
4017 =head3 Properties of Piecewise Quasipolynomial Reductions
4019 To check whether two union piecewise quasipolynomial reductions are
4020 obviously equal, use
4022 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4023 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4024 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4026 =head3 Operations on Piecewise Quasipolynomial Reductions
4028 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4029 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4031 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4032 __isl_take isl_pw_qpolynomial_fold *pwf1,
4033 __isl_take isl_pw_qpolynomial_fold *pwf2);
4035 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4036 __isl_take isl_pw_qpolynomial_fold *pwf1,
4037 __isl_take isl_pw_qpolynomial_fold *pwf2);
4039 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4040 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4041 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4043 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4044 __isl_take isl_pw_qpolynomial_fold *pwf,
4045 __isl_take isl_point *pnt);
4047 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4048 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4049 __isl_take isl_point *pnt);
4051 __isl_give isl_pw_qpolynomial_fold *
4052 sl_pw_qpolynomial_fold_intersect_params(
4053 __isl_take isl_pw_qpolynomial_fold *pwf,
4054 __isl_take isl_set *set);
4056 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4057 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4058 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4059 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4060 __isl_take isl_union_set *uset);
4061 __isl_give isl_union_pw_qpolynomial_fold *
4062 isl_union_pw_qpolynomial_fold_intersect_params(
4063 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4064 __isl_take isl_set *set);
4066 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4067 __isl_take isl_pw_qpolynomial_fold *pwf);
4069 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4070 __isl_take isl_pw_qpolynomial_fold *pwf);
4072 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4073 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4075 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4076 __isl_take isl_qpolynomial_fold *fold,
4077 __isl_take isl_set *context);
4078 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4079 __isl_take isl_qpolynomial_fold *fold,
4080 __isl_take isl_set *context);
4082 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4083 __isl_take isl_pw_qpolynomial_fold *pwf,
4084 __isl_take isl_set *context);
4085 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4086 __isl_take isl_pw_qpolynomial_fold *pwf,
4087 __isl_take isl_set *context);
4089 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4090 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4091 __isl_take isl_union_set *context);
4092 __isl_give isl_union_pw_qpolynomial_fold *
4093 isl_union_pw_qpolynomial_fold_gist_params(
4094 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4095 __isl_take isl_set *context);
4097 The gist operation applies the gist operation to each of
4098 the cells in the domain of the input piecewise quasipolynomial reduction.
4099 In future, the operation will also exploit the context
4100 to simplify the quasipolynomial reductions associated to each cell.
4102 __isl_give isl_pw_qpolynomial_fold *
4103 isl_set_apply_pw_qpolynomial_fold(
4104 __isl_take isl_set *set,
4105 __isl_take isl_pw_qpolynomial_fold *pwf,
4107 __isl_give isl_pw_qpolynomial_fold *
4108 isl_map_apply_pw_qpolynomial_fold(
4109 __isl_take isl_map *map,
4110 __isl_take isl_pw_qpolynomial_fold *pwf,
4112 __isl_give isl_union_pw_qpolynomial_fold *
4113 isl_union_set_apply_union_pw_qpolynomial_fold(
4114 __isl_take isl_union_set *uset,
4115 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4117 __isl_give isl_union_pw_qpolynomial_fold *
4118 isl_union_map_apply_union_pw_qpolynomial_fold(
4119 __isl_take isl_union_map *umap,
4120 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4123 The functions taking a map
4124 compose the given map with the given piecewise quasipolynomial reduction.
4125 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4126 over all elements in the intersection of the range of the map
4127 and the domain of the piecewise quasipolynomial reduction
4128 as a function of an element in the domain of the map.
4129 The functions taking a set compute a bound over all elements in the
4130 intersection of the set and the domain of the
4131 piecewise quasipolynomial reduction.
4133 =head2 Dependence Analysis
4135 C<isl> contains specialized functionality for performing
4136 array dataflow analysis. That is, given a I<sink> access relation
4137 and a collection of possible I<source> access relations,
4138 C<isl> can compute relations that describe
4139 for each iteration of the sink access, which iteration
4140 of which of the source access relations was the last
4141 to access the same data element before the given iteration
4143 The resulting dependence relations map source iterations
4144 to the corresponding sink iterations.
4145 To compute standard flow dependences, the sink should be
4146 a read, while the sources should be writes.
4147 If any of the source accesses are marked as being I<may>
4148 accesses, then there will be a dependence from the last
4149 I<must> access B<and> from any I<may> access that follows
4150 this last I<must> access.
4151 In particular, if I<all> sources are I<may> accesses,
4152 then memory based dependence analysis is performed.
4153 If, on the other hand, all sources are I<must> accesses,
4154 then value based dependence analysis is performed.
4156 #include <isl/flow.h>
4158 typedef int (*isl_access_level_before)(void *first, void *second);
4160 __isl_give isl_access_info *isl_access_info_alloc(
4161 __isl_take isl_map *sink,
4162 void *sink_user, isl_access_level_before fn,
4164 __isl_give isl_access_info *isl_access_info_add_source(
4165 __isl_take isl_access_info *acc,
4166 __isl_take isl_map *source, int must,
4168 void isl_access_info_free(__isl_take isl_access_info *acc);
4170 __isl_give isl_flow *isl_access_info_compute_flow(
4171 __isl_take isl_access_info *acc);
4173 int isl_flow_foreach(__isl_keep isl_flow *deps,
4174 int (*fn)(__isl_take isl_map *dep, int must,
4175 void *dep_user, void *user),
4177 __isl_give isl_map *isl_flow_get_no_source(
4178 __isl_keep isl_flow *deps, int must);
4179 void isl_flow_free(__isl_take isl_flow *deps);
4181 The function C<isl_access_info_compute_flow> performs the actual
4182 dependence analysis. The other functions are used to construct
4183 the input for this function or to read off the output.
4185 The input is collected in an C<isl_access_info>, which can
4186 be created through a call to C<isl_access_info_alloc>.
4187 The arguments to this functions are the sink access relation
4188 C<sink>, a token C<sink_user> used to identify the sink
4189 access to the user, a callback function for specifying the
4190 relative order of source and sink accesses, and the number
4191 of source access relations that will be added.
4192 The callback function has type C<int (*)(void *first, void *second)>.
4193 The function is called with two user supplied tokens identifying
4194 either a source or the sink and it should return the shared nesting
4195 level and the relative order of the two accesses.
4196 In particular, let I<n> be the number of loops shared by
4197 the two accesses. If C<first> precedes C<second> textually,
4198 then the function should return I<2 * n + 1>; otherwise,
4199 it should return I<2 * n>.
4200 The sources can be added to the C<isl_access_info> by performing
4201 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4202 C<must> indicates whether the source is a I<must> access
4203 or a I<may> access. Note that a multi-valued access relation
4204 should only be marked I<must> if every iteration in the domain
4205 of the relation accesses I<all> elements in its image.
4206 The C<source_user> token is again used to identify
4207 the source access. The range of the source access relation
4208 C<source> should have the same dimension as the range
4209 of the sink access relation.
4210 The C<isl_access_info_free> function should usually not be
4211 called explicitly, because it is called implicitly by
4212 C<isl_access_info_compute_flow>.
4214 The result of the dependence analysis is collected in an
4215 C<isl_flow>. There may be elements of
4216 the sink access for which no preceding source access could be
4217 found or for which all preceding sources are I<may> accesses.
4218 The relations containing these elements can be obtained through
4219 calls to C<isl_flow_get_no_source>, the first with C<must> set
4220 and the second with C<must> unset.
4221 In the case of standard flow dependence analysis,
4222 with the sink a read and the sources I<must> writes,
4223 the first relation corresponds to the reads from uninitialized
4224 array elements and the second relation is empty.
4225 The actual flow dependences can be extracted using
4226 C<isl_flow_foreach>. This function will call the user-specified
4227 callback function C<fn> for each B<non-empty> dependence between
4228 a source and the sink. The callback function is called
4229 with four arguments, the actual flow dependence relation
4230 mapping source iterations to sink iterations, a boolean that
4231 indicates whether it is a I<must> or I<may> dependence, a token
4232 identifying the source and an additional C<void *> with value
4233 equal to the third argument of the C<isl_flow_foreach> call.
4234 A dependence is marked I<must> if it originates from a I<must>
4235 source and if it is not followed by any I<may> sources.
4237 After finishing with an C<isl_flow>, the user should call
4238 C<isl_flow_free> to free all associated memory.
4240 A higher-level interface to dependence analysis is provided
4241 by the following function.
4243 #include <isl/flow.h>
4245 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4246 __isl_take isl_union_map *must_source,
4247 __isl_take isl_union_map *may_source,
4248 __isl_take isl_union_map *schedule,
4249 __isl_give isl_union_map **must_dep,
4250 __isl_give isl_union_map **may_dep,
4251 __isl_give isl_union_map **must_no_source,
4252 __isl_give isl_union_map **may_no_source);
4254 The arrays are identified by the tuple names of the ranges
4255 of the accesses. The iteration domains by the tuple names
4256 of the domains of the accesses and of the schedule.
4257 The relative order of the iteration domains is given by the
4258 schedule. The relations returned through C<must_no_source>
4259 and C<may_no_source> are subsets of C<sink>.
4260 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4261 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4262 any of the other arguments is treated as an error.
4264 =head3 Interaction with Dependence Analysis
4266 During the dependence analysis, we frequently need to perform
4267 the following operation. Given a relation between sink iterations
4268 and potential soure iterations from a particular source domain,
4269 what is the last potential source iteration corresponding to each
4270 sink iteration. It can sometimes be convenient to adjust
4271 the set of potential source iterations before or after each such operation.
4272 The prototypical example is fuzzy array dataflow analysis,
4273 where we need to analyze if, based on data-dependent constraints,
4274 the sink iteration can ever be executed without one or more of
4275 the corresponding potential source iterations being executed.
4276 If so, we can introduce extra parameters and select an unknown
4277 but fixed source iteration from the potential source iterations.
4278 To be able to perform such manipulations, C<isl> provides the following
4281 #include <isl/flow.h>
4283 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4284 __isl_keep isl_map *source_map,
4285 __isl_keep isl_set *sink, void *source_user,
4287 __isl_give isl_access_info *isl_access_info_set_restrict(
4288 __isl_take isl_access_info *acc,
4289 isl_access_restrict fn, void *user);
4291 The function C<isl_access_info_set_restrict> should be called
4292 before calling C<isl_access_info_compute_flow> and registers a callback function
4293 that will be called any time C<isl> is about to compute the last
4294 potential source. The first argument is the (reverse) proto-dependence,
4295 mapping sink iterations to potential source iterations.
4296 The second argument represents the sink iterations for which
4297 we want to compute the last source iteration.
4298 The third argument is the token corresponding to the source
4299 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4300 The callback is expected to return a restriction on either the input or
4301 the output of the operation computing the last potential source.
4302 If the input needs to be restricted then restrictions are needed
4303 for both the source and the sink iterations. The sink iterations
4304 and the potential source iterations will be intersected with these sets.
4305 If the output needs to be restricted then only a restriction on the source
4306 iterations is required.
4307 If any error occurs, the callback should return C<NULL>.
4308 An C<isl_restriction> object can be created and freed using the following
4311 #include <isl/flow.h>
4313 __isl_give isl_restriction *isl_restriction_input(
4314 __isl_take isl_set *source_restr,
4315 __isl_take isl_set *sink_restr);
4316 __isl_give isl_restriction *isl_restriction_output(
4317 __isl_take isl_set *source_restr);
4318 __isl_give isl_restriction *isl_restriction_none(
4319 __isl_keep isl_map *source_map);
4320 __isl_give isl_restriction *isl_restriction_empty(
4321 __isl_keep isl_map *source_map);
4322 void *isl_restriction_free(
4323 __isl_take isl_restriction *restr);
4325 C<isl_restriction_none> and C<isl_restriction_empty> are special
4326 cases of C<isl_restriction_input>. C<isl_restriction_none>
4327 is essentially equivalent to
4329 isl_restriction_input(isl_set_universe(
4330 isl_space_range(isl_map_get_space(source_map))),
4332 isl_space_domain(isl_map_get_space(source_map))));
4334 whereas C<isl_restriction_empty> is essentially equivalent to
4336 isl_restriction_input(isl_set_empty(
4337 isl_space_range(isl_map_get_space(source_map))),
4339 isl_space_domain(isl_map_get_space(source_map))));
4343 B<The functionality described in this section is fairly new
4344 and may be subject to change.>
4346 The following function can be used to compute a schedule
4347 for a union of domains.
4348 By default, the algorithm used to construct the schedule is similar
4349 to that of C<Pluto>.
4350 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4352 The generated schedule respects all C<validity> dependences.
4353 That is, all dependence distances over these dependences in the
4354 scheduled space are lexicographically positive.
4355 The default algorithm tries to minimize the dependence distances over
4356 C<proximity> dependences.
4357 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4358 for groups of domains where the dependence distances have only
4359 non-negative values.
4360 When using Feautrier's algorithm, the C<proximity> dependence
4361 distances are only minimized during the extension to a
4362 full-dimensional schedule.
4364 #include <isl/schedule.h>
4365 __isl_give isl_schedule *isl_union_set_compute_schedule(
4366 __isl_take isl_union_set *domain,
4367 __isl_take isl_union_map *validity,
4368 __isl_take isl_union_map *proximity);
4369 void *isl_schedule_free(__isl_take isl_schedule *sched);
4371 A mapping from the domains to the scheduled space can be obtained
4372 from an C<isl_schedule> using the following function.
4374 __isl_give isl_union_map *isl_schedule_get_map(
4375 __isl_keep isl_schedule *sched);
4377 A representation of the schedule can be printed using
4379 __isl_give isl_printer *isl_printer_print_schedule(
4380 __isl_take isl_printer *p,
4381 __isl_keep isl_schedule *schedule);
4383 A representation of the schedule as a forest of bands can be obtained
4384 using the following function.
4386 __isl_give isl_band_list *isl_schedule_get_band_forest(
4387 __isl_keep isl_schedule *schedule);
4389 The list can be manipulated as explained in L<"Lists">.
4390 The bands inside the list can be copied and freed using the following
4393 #include <isl/band.h>
4394 __isl_give isl_band *isl_band_copy(
4395 __isl_keep isl_band *band);
4396 void *isl_band_free(__isl_take isl_band *band);
4398 Each band contains zero or more scheduling dimensions.
4399 These are referred to as the members of the band.
4400 The section of the schedule that corresponds to the band is
4401 referred to as the partial schedule of the band.
4402 For those nodes that participate in a band, the outer scheduling
4403 dimensions form the prefix schedule, while the inner scheduling
4404 dimensions form the suffix schedule.
4405 That is, if we take a cut of the band forest, then the union of
4406 the concatenations of the prefix, partial and suffix schedules of
4407 each band in the cut is equal to the entire schedule (modulo
4408 some possible padding at the end with zero scheduling dimensions).
4409 The properties of a band can be inspected using the following functions.
4411 #include <isl/band.h>
4412 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4414 int isl_band_has_children(__isl_keep isl_band *band);
4415 __isl_give isl_band_list *isl_band_get_children(
4416 __isl_keep isl_band *band);
4418 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4419 __isl_keep isl_band *band);
4420 __isl_give isl_union_map *isl_band_get_partial_schedule(
4421 __isl_keep isl_band *band);
4422 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4423 __isl_keep isl_band *band);
4425 int isl_band_n_member(__isl_keep isl_band *band);
4426 int isl_band_member_is_zero_distance(
4427 __isl_keep isl_band *band, int pos);
4429 Note that a scheduling dimension is considered to be ``zero
4430 distance'' if it does not carry any proximity dependences
4432 That is, if the dependence distances of the proximity
4433 dependences are all zero in that direction (for fixed
4434 iterations of outer bands).
4436 A representation of the band can be printed using
4438 #include <isl/band.h>
4439 __isl_give isl_printer *isl_printer_print_band(
4440 __isl_take isl_printer *p,
4441 __isl_keep isl_band *band);
4445 #include <isl/schedule.h>
4446 int isl_options_set_schedule_max_coefficient(
4447 isl_ctx *ctx, int val);
4448 int isl_options_get_schedule_max_coefficient(
4450 int isl_options_set_schedule_max_constant_term(
4451 isl_ctx *ctx, int val);
4452 int isl_options_get_schedule_max_constant_term(
4454 int isl_options_set_schedule_maximize_band_depth(
4455 isl_ctx *ctx, int val);
4456 int isl_options_get_schedule_maximize_band_depth(
4458 int isl_options_set_schedule_outer_zero_distance(
4459 isl_ctx *ctx, int val);
4460 int isl_options_get_schedule_outer_zero_distance(
4462 int isl_options_set_schedule_split_scaled(
4463 isl_ctx *ctx, int val);
4464 int isl_options_get_schedule_split_scaled(
4466 int isl_options_set_schedule_algorithm(
4467 isl_ctx *ctx, int val);
4468 int isl_options_get_schedule_algorithm(
4474 =item * schedule_max_coefficient
4476 This option enforces that the coefficients for variable and parameter
4477 dimensions in the calculated schedule are not larger than the specified value.
4478 This option can significantly increase the speed of the scheduling calculation
4479 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4480 this option does not introduce bounds on the variable or parameter
4483 =item * schedule_max_constant_term
4485 This option enforces that the constant coefficients in the calculated schedule
4486 are not larger than the maximal constant term. This option can significantly
4487 increase the speed of the scheduling calculation and may also prevent fusing of
4488 unrelated dimensions. A value of -1 means that this option does not introduce
4489 bounds on the constant coefficients.
4491 =item * schedule_maximize_band_depth
4493 If this option is set, we do not split bands at the point
4494 where we detect splitting is necessary. Instead, we
4495 backtrack and split bands as early as possible. This
4496 reduces the number of splits and maximizes the width of
4497 the bands. Wider bands give more possibilities for tiling.
4499 =item * schedule_outer_zero_distance
4501 If this option is set, then we try to construct schedules
4502 where the outermost scheduling dimension in each band
4503 results in a zero dependence distance over the proximity
4506 =item * schedule_split_scaled
4508 If this option is set, then we try to construct schedules in which the
4509 constant term is split off from the linear part if the linear parts of
4510 the scheduling rows for all nodes in the graphs have a common non-trivial
4512 The constant term is then placed in a separate band and the linear
4515 =item * schedule_algorithm
4517 Selects the scheduling algorithm to be used.
4518 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4519 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4523 =head2 Parametric Vertex Enumeration
4525 The parametric vertex enumeration described in this section
4526 is mainly intended to be used internally and by the C<barvinok>
4529 #include <isl/vertices.h>
4530 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4531 __isl_keep isl_basic_set *bset);
4533 The function C<isl_basic_set_compute_vertices> performs the
4534 actual computation of the parametric vertices and the chamber
4535 decomposition and store the result in an C<isl_vertices> object.
4536 This information can be queried by either iterating over all
4537 the vertices or iterating over all the chambers or cells
4538 and then iterating over all vertices that are active on the chamber.
4540 int isl_vertices_foreach_vertex(
4541 __isl_keep isl_vertices *vertices,
4542 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4545 int isl_vertices_foreach_cell(
4546 __isl_keep isl_vertices *vertices,
4547 int (*fn)(__isl_take isl_cell *cell, void *user),
4549 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4550 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4553 Other operations that can be performed on an C<isl_vertices> object are
4556 isl_ctx *isl_vertices_get_ctx(
4557 __isl_keep isl_vertices *vertices);
4558 int isl_vertices_get_n_vertices(
4559 __isl_keep isl_vertices *vertices);
4560 void isl_vertices_free(__isl_take isl_vertices *vertices);
4562 Vertices can be inspected and destroyed using the following functions.
4564 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4565 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4566 __isl_give isl_basic_set *isl_vertex_get_domain(
4567 __isl_keep isl_vertex *vertex);
4568 __isl_give isl_basic_set *isl_vertex_get_expr(
4569 __isl_keep isl_vertex *vertex);
4570 void isl_vertex_free(__isl_take isl_vertex *vertex);
4572 C<isl_vertex_get_expr> returns a singleton parametric set describing
4573 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4575 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4576 B<rational> basic sets, so they should mainly be used for inspection
4577 and should not be mixed with integer sets.
4579 Chambers can be inspected and destroyed using the following functions.
4581 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4582 __isl_give isl_basic_set *isl_cell_get_domain(
4583 __isl_keep isl_cell *cell);
4584 void isl_cell_free(__isl_take isl_cell *cell);
4588 Although C<isl> is mainly meant to be used as a library,
4589 it also contains some basic applications that use some
4590 of the functionality of C<isl>.
4591 The input may be specified in either the L<isl format>
4592 or the L<PolyLib format>.
4594 =head2 C<isl_polyhedron_sample>
4596 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4597 an integer element of the polyhedron, if there is any.
4598 The first column in the output is the denominator and is always
4599 equal to 1. If the polyhedron contains no integer points,
4600 then a vector of length zero is printed.
4604 C<isl_pip> takes the same input as the C<example> program
4605 from the C<piplib> distribution, i.e., a set of constraints
4606 on the parameters, a line containing only -1 and finally a set
4607 of constraints on a parametric polyhedron.
4608 The coefficients of the parameters appear in the last columns
4609 (but before the final constant column).
4610 The output is the lexicographic minimum of the parametric polyhedron.
4611 As C<isl> currently does not have its own output format, the output
4612 is just a dump of the internal state.
4614 =head2 C<isl_polyhedron_minimize>
4616 C<isl_polyhedron_minimize> computes the minimum of some linear
4617 or affine objective function over the integer points in a polyhedron.
4618 If an affine objective function
4619 is given, then the constant should appear in the last column.
4621 =head2 C<isl_polytope_scan>
4623 Given a polytope, C<isl_polytope_scan> prints
4624 all integer points in the polytope.