3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
737 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
738 or C<isl_dim_set>. As with C<isl_space_get_name>,
739 the C<isl_space_get_tuple_name> function returns a pointer to some internal
741 Binary operations require the corresponding spaces of their arguments
742 to have the same name.
744 Spaces can be nested. In particular, the domain of a set or
745 the domain or range of a relation can be a nested relation.
746 The following functions can be used to construct and deconstruct
749 #include <isl/space.h>
750 int isl_space_is_wrapping(__isl_keep isl_space *space);
751 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
752 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
754 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
755 be the space of a set, while that of
756 C<isl_space_wrap> should be the space of a relation.
757 Conversely, the output of C<isl_space_unwrap> is the space
758 of a relation, while that of C<isl_space_wrap> is the space of a set.
760 Spaces can be created from other spaces
761 using the following functions.
763 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
764 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
765 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_params(
768 __isl_take isl_space *space);
769 __isl_give isl_space *isl_space_set_from_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
772 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
773 __isl_take isl_space *right);
774 __isl_give isl_space *isl_space_align_params(
775 __isl_take isl_space *space1, __isl_take isl_space *space2)
776 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
777 enum isl_dim_type type, unsigned pos, unsigned n);
778 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned n);
780 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned first, unsigned n);
782 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
783 enum isl_dim_type dst_type, unsigned dst_pos,
784 enum isl_dim_type src_type, unsigned src_pos,
786 __isl_give isl_space *isl_space_map_from_set(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_map_from_domain_and_range(
789 __isl_take isl_space *domain,
790 __isl_take isl_space *range);
791 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
793 Note that if dimensions are added or removed from a space, then
794 the name and the internal structure are lost.
798 A local space is essentially a space with
799 zero or more existentially quantified variables.
800 The local space of a basic set or relation can be obtained
801 using the following functions.
804 __isl_give isl_local_space *isl_basic_set_get_local_space(
805 __isl_keep isl_basic_set *bset);
808 __isl_give isl_local_space *isl_basic_map_get_local_space(
809 __isl_keep isl_basic_map *bmap);
811 A new local space can be created from a space using
813 #include <isl/local_space.h>
814 __isl_give isl_local_space *isl_local_space_from_space(
815 __isl_take isl_space *space);
817 They can be inspected, modified, copied and freed using the following functions.
819 #include <isl/local_space.h>
820 isl_ctx *isl_local_space_get_ctx(
821 __isl_keep isl_local_space *ls);
822 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
823 int isl_local_space_dim(__isl_keep isl_local_space *ls,
824 enum isl_dim_type type);
825 const char *isl_local_space_get_dim_name(
826 __isl_keep isl_local_space *ls,
827 enum isl_dim_type type, unsigned pos);
828 __isl_give isl_local_space *isl_local_space_set_dim_name(
829 __isl_take isl_local_space *ls,
830 enum isl_dim_type type, unsigned pos, const char *s);
831 __isl_give isl_local_space *isl_local_space_set_dim_id(
832 __isl_take isl_local_space *ls,
833 enum isl_dim_type type, unsigned pos,
834 __isl_take isl_id *id);
835 __isl_give isl_space *isl_local_space_get_space(
836 __isl_keep isl_local_space *ls);
837 __isl_give isl_aff *isl_local_space_get_div(
838 __isl_keep isl_local_space *ls, int pos);
839 __isl_give isl_local_space *isl_local_space_copy(
840 __isl_keep isl_local_space *ls);
841 void *isl_local_space_free(__isl_take isl_local_space *ls);
843 Two local spaces can be compared using
845 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
846 __isl_keep isl_local_space *ls2);
848 Local spaces can be created from other local spaces
849 using the following functions.
851 __isl_give isl_local_space *isl_local_space_domain(
852 __isl_take isl_local_space *ls);
853 __isl_give isl_local_space *isl_local_space_range(
854 __isl_take isl_local_space *ls);
855 __isl_give isl_local_space *isl_local_space_from_domain(
856 __isl_take isl_local_space *ls);
857 __isl_give isl_local_space *isl_local_space_intersect(
858 __isl_take isl_local_space *ls1,
859 __isl_take isl_local_space *ls2);
860 __isl_give isl_local_space *isl_local_space_add_dims(
861 __isl_take isl_local_space *ls,
862 enum isl_dim_type type, unsigned n);
863 __isl_give isl_local_space *isl_local_space_insert_dims(
864 __isl_take isl_local_space *ls,
865 enum isl_dim_type type, unsigned first, unsigned n);
866 __isl_give isl_local_space *isl_local_space_drop_dims(
867 __isl_take isl_local_space *ls,
868 enum isl_dim_type type, unsigned first, unsigned n);
870 =head2 Input and Output
872 C<isl> supports its own input/output format, which is similar
873 to the C<Omega> format, but also supports the C<PolyLib> format
878 The C<isl> format is similar to that of C<Omega>, but has a different
879 syntax for describing the parameters and allows for the definition
880 of an existentially quantified variable as the integer division
881 of an affine expression.
882 For example, the set of integers C<i> between C<0> and C<n>
883 such that C<i % 10 <= 6> can be described as
885 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
888 A set or relation can have several disjuncts, separated
889 by the keyword C<or>. Each disjunct is either a conjunction
890 of constraints or a projection (C<exists>) of a conjunction
891 of constraints. The constraints are separated by the keyword
894 =head3 C<PolyLib> format
896 If the represented set is a union, then the first line
897 contains a single number representing the number of disjuncts.
898 Otherwise, a line containing the number C<1> is optional.
900 Each disjunct is represented by a matrix of constraints.
901 The first line contains two numbers representing
902 the number of rows and columns,
903 where the number of rows is equal to the number of constraints
904 and the number of columns is equal to two plus the number of variables.
905 The following lines contain the actual rows of the constraint matrix.
906 In each row, the first column indicates whether the constraint
907 is an equality (C<0>) or inequality (C<1>). The final column
908 corresponds to the constant term.
910 If the set is parametric, then the coefficients of the parameters
911 appear in the last columns before the constant column.
912 The coefficients of any existentially quantified variables appear
913 between those of the set variables and those of the parameters.
915 =head3 Extended C<PolyLib> format
917 The extended C<PolyLib> format is nearly identical to the
918 C<PolyLib> format. The only difference is that the line
919 containing the number of rows and columns of a constraint matrix
920 also contains four additional numbers:
921 the number of output dimensions, the number of input dimensions,
922 the number of local dimensions (i.e., the number of existentially
923 quantified variables) and the number of parameters.
924 For sets, the number of ``output'' dimensions is equal
925 to the number of set dimensions, while the number of ``input''
931 __isl_give isl_basic_set *isl_basic_set_read_from_file(
932 isl_ctx *ctx, FILE *input);
933 __isl_give isl_basic_set *isl_basic_set_read_from_str(
934 isl_ctx *ctx, const char *str);
935 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
937 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
941 __isl_give isl_basic_map *isl_basic_map_read_from_file(
942 isl_ctx *ctx, FILE *input);
943 __isl_give isl_basic_map *isl_basic_map_read_from_str(
944 isl_ctx *ctx, const char *str);
945 __isl_give isl_map *isl_map_read_from_file(
946 isl_ctx *ctx, FILE *input);
947 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
950 #include <isl/union_set.h>
951 __isl_give isl_union_set *isl_union_set_read_from_file(
952 isl_ctx *ctx, FILE *input);
953 __isl_give isl_union_set *isl_union_set_read_from_str(
954 isl_ctx *ctx, const char *str);
956 #include <isl/union_map.h>
957 __isl_give isl_union_map *isl_union_map_read_from_file(
958 isl_ctx *ctx, FILE *input);
959 __isl_give isl_union_map *isl_union_map_read_from_str(
960 isl_ctx *ctx, const char *str);
962 The input format is autodetected and may be either the C<PolyLib> format
963 or the C<isl> format.
967 Before anything can be printed, an C<isl_printer> needs to
970 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
972 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
973 void isl_printer_free(__isl_take isl_printer *printer);
974 __isl_give char *isl_printer_get_str(
975 __isl_keep isl_printer *printer);
977 The behavior of the printer can be modified in various ways
979 __isl_give isl_printer *isl_printer_set_output_format(
980 __isl_take isl_printer *p, int output_format);
981 __isl_give isl_printer *isl_printer_set_indent(
982 __isl_take isl_printer *p, int indent);
983 __isl_give isl_printer *isl_printer_indent(
984 __isl_take isl_printer *p, int indent);
985 __isl_give isl_printer *isl_printer_set_prefix(
986 __isl_take isl_printer *p, const char *prefix);
987 __isl_give isl_printer *isl_printer_set_suffix(
988 __isl_take isl_printer *p, const char *suffix);
990 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
991 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
992 and defaults to C<ISL_FORMAT_ISL>.
993 Each line in the output is indented by C<indent> (set by
994 C<isl_printer_set_indent>) spaces
995 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
996 In the C<PolyLib> format output,
997 the coefficients of the existentially quantified variables
998 appear between those of the set variables and those
1000 The function C<isl_printer_indent> increases the indentation
1001 by the specified amount (which may be negative).
1003 To actually print something, use
1005 #include <isl/set.h>
1006 __isl_give isl_printer *isl_printer_print_basic_set(
1007 __isl_take isl_printer *printer,
1008 __isl_keep isl_basic_set *bset);
1009 __isl_give isl_printer *isl_printer_print_set(
1010 __isl_take isl_printer *printer,
1011 __isl_keep isl_set *set);
1013 #include <isl/map.h>
1014 __isl_give isl_printer *isl_printer_print_basic_map(
1015 __isl_take isl_printer *printer,
1016 __isl_keep isl_basic_map *bmap);
1017 __isl_give isl_printer *isl_printer_print_map(
1018 __isl_take isl_printer *printer,
1019 __isl_keep isl_map *map);
1021 #include <isl/union_set.h>
1022 __isl_give isl_printer *isl_printer_print_union_set(
1023 __isl_take isl_printer *p,
1024 __isl_keep isl_union_set *uset);
1026 #include <isl/union_map.h>
1027 __isl_give isl_printer *isl_printer_print_union_map(
1028 __isl_take isl_printer *p,
1029 __isl_keep isl_union_map *umap);
1031 When called on a file printer, the following function flushes
1032 the file. When called on a string printer, the buffer is cleared.
1034 __isl_give isl_printer *isl_printer_flush(
1035 __isl_take isl_printer *p);
1037 =head2 Creating New Sets and Relations
1039 C<isl> has functions for creating some standard sets and relations.
1043 =item * Empty sets and relations
1045 __isl_give isl_basic_set *isl_basic_set_empty(
1046 __isl_take isl_space *space);
1047 __isl_give isl_basic_map *isl_basic_map_empty(
1048 __isl_take isl_space *space);
1049 __isl_give isl_set *isl_set_empty(
1050 __isl_take isl_space *space);
1051 __isl_give isl_map *isl_map_empty(
1052 __isl_take isl_space *space);
1053 __isl_give isl_union_set *isl_union_set_empty(
1054 __isl_take isl_space *space);
1055 __isl_give isl_union_map *isl_union_map_empty(
1056 __isl_take isl_space *space);
1058 For C<isl_union_set>s and C<isl_union_map>s, the space
1059 is only used to specify the parameters.
1061 =item * Universe sets and relations
1063 __isl_give isl_basic_set *isl_basic_set_universe(
1064 __isl_take isl_space *space);
1065 __isl_give isl_basic_map *isl_basic_map_universe(
1066 __isl_take isl_space *space);
1067 __isl_give isl_set *isl_set_universe(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_universe(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_set *isl_union_set_universe(
1072 __isl_take isl_union_set *uset);
1073 __isl_give isl_union_map *isl_union_map_universe(
1074 __isl_take isl_union_map *umap);
1076 The sets and relations constructed by the functions above
1077 contain all integer values, while those constructed by the
1078 functions below only contain non-negative values.
1080 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1081 __isl_take isl_space *space);
1082 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1083 __isl_take isl_space *space);
1084 __isl_give isl_set *isl_set_nat_universe(
1085 __isl_take isl_space *space);
1086 __isl_give isl_map *isl_map_nat_universe(
1087 __isl_take isl_space *space);
1089 =item * Identity relations
1091 __isl_give isl_basic_map *isl_basic_map_identity(
1092 __isl_take isl_space *space);
1093 __isl_give isl_map *isl_map_identity(
1094 __isl_take isl_space *space);
1096 The number of input and output dimensions in C<space> needs
1099 =item * Lexicographic order
1101 __isl_give isl_map *isl_map_lex_lt(
1102 __isl_take isl_space *set_space);
1103 __isl_give isl_map *isl_map_lex_le(
1104 __isl_take isl_space *set_space);
1105 __isl_give isl_map *isl_map_lex_gt(
1106 __isl_take isl_space *set_space);
1107 __isl_give isl_map *isl_map_lex_ge(
1108 __isl_take isl_space *set_space);
1109 __isl_give isl_map *isl_map_lex_lt_first(
1110 __isl_take isl_space *space, unsigned n);
1111 __isl_give isl_map *isl_map_lex_le_first(
1112 __isl_take isl_space *space, unsigned n);
1113 __isl_give isl_map *isl_map_lex_gt_first(
1114 __isl_take isl_space *space, unsigned n);
1115 __isl_give isl_map *isl_map_lex_ge_first(
1116 __isl_take isl_space *space, unsigned n);
1118 The first four functions take a space for a B<set>
1119 and return relations that express that the elements in the domain
1120 are lexicographically less
1121 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1122 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1123 than the elements in the range.
1124 The last four functions take a space for a map
1125 and return relations that express that the first C<n> dimensions
1126 in the domain are lexicographically less
1127 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1128 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1129 than the first C<n> dimensions in the range.
1133 A basic set or relation can be converted to a set or relation
1134 using the following functions.
1136 __isl_give isl_set *isl_set_from_basic_set(
1137 __isl_take isl_basic_set *bset);
1138 __isl_give isl_map *isl_map_from_basic_map(
1139 __isl_take isl_basic_map *bmap);
1141 Sets and relations can be converted to union sets and relations
1142 using the following functions.
1144 __isl_give isl_union_map *isl_union_map_from_map(
1145 __isl_take isl_map *map);
1146 __isl_give isl_union_set *isl_union_set_from_set(
1147 __isl_take isl_set *set);
1149 The inverse conversions below can only be used if the input
1150 union set or relation is known to contain elements in exactly one
1153 __isl_give isl_set *isl_set_from_union_set(
1154 __isl_take isl_union_set *uset);
1155 __isl_give isl_map *isl_map_from_union_map(
1156 __isl_take isl_union_map *umap);
1158 A zero-dimensional set can be constructed on a given parameter domain
1159 using the following function.
1161 __isl_give isl_set *isl_set_from_params(
1162 __isl_take isl_set *set);
1164 Sets and relations can be copied and freed again using the following
1167 __isl_give isl_basic_set *isl_basic_set_copy(
1168 __isl_keep isl_basic_set *bset);
1169 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1170 __isl_give isl_union_set *isl_union_set_copy(
1171 __isl_keep isl_union_set *uset);
1172 __isl_give isl_basic_map *isl_basic_map_copy(
1173 __isl_keep isl_basic_map *bmap);
1174 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1175 __isl_give isl_union_map *isl_union_map_copy(
1176 __isl_keep isl_union_map *umap);
1177 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1178 void isl_set_free(__isl_take isl_set *set);
1179 void *isl_union_set_free(__isl_take isl_union_set *uset);
1180 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1181 void isl_map_free(__isl_take isl_map *map);
1182 void *isl_union_map_free(__isl_take isl_union_map *umap);
1184 Other sets and relations can be constructed by starting
1185 from a universe set or relation, adding equality and/or
1186 inequality constraints and then projecting out the
1187 existentially quantified variables, if any.
1188 Constraints can be constructed, manipulated and
1189 added to (or removed from) (basic) sets and relations
1190 using the following functions.
1192 #include <isl/constraint.h>
1193 __isl_give isl_constraint *isl_equality_alloc(
1194 __isl_take isl_local_space *ls);
1195 __isl_give isl_constraint *isl_inequality_alloc(
1196 __isl_take isl_local_space *ls);
1197 __isl_give isl_constraint *isl_constraint_set_constant(
1198 __isl_take isl_constraint *constraint, isl_int v);
1199 __isl_give isl_constraint *isl_constraint_set_constant_si(
1200 __isl_take isl_constraint *constraint, int v);
1201 __isl_give isl_constraint *isl_constraint_set_coefficient(
1202 __isl_take isl_constraint *constraint,
1203 enum isl_dim_type type, int pos, isl_int v);
1204 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1205 __isl_take isl_constraint *constraint,
1206 enum isl_dim_type type, int pos, int v);
1207 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1208 __isl_take isl_basic_map *bmap,
1209 __isl_take isl_constraint *constraint);
1210 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1211 __isl_take isl_basic_set *bset,
1212 __isl_take isl_constraint *constraint);
1213 __isl_give isl_map *isl_map_add_constraint(
1214 __isl_take isl_map *map,
1215 __isl_take isl_constraint *constraint);
1216 __isl_give isl_set *isl_set_add_constraint(
1217 __isl_take isl_set *set,
1218 __isl_take isl_constraint *constraint);
1219 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1220 __isl_take isl_basic_set *bset,
1221 __isl_take isl_constraint *constraint);
1223 For example, to create a set containing the even integers
1224 between 10 and 42, you would use the following code.
1227 isl_local_space *ls;
1229 isl_basic_set *bset;
1231 space = isl_space_set_alloc(ctx, 0, 2);
1232 bset = isl_basic_set_universe(isl_space_copy(space));
1233 ls = isl_local_space_from_space(space);
1235 c = isl_equality_alloc(isl_local_space_copy(ls));
1236 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1237 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1238 bset = isl_basic_set_add_constraint(bset, c);
1240 c = isl_inequality_alloc(isl_local_space_copy(ls));
1241 c = isl_constraint_set_constant_si(c, -10);
1242 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1243 bset = isl_basic_set_add_constraint(bset, c);
1245 c = isl_inequality_alloc(ls);
1246 c = isl_constraint_set_constant_si(c, 42);
1247 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1248 bset = isl_basic_set_add_constraint(bset, c);
1250 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1254 isl_basic_set *bset;
1255 bset = isl_basic_set_read_from_str(ctx,
1256 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1258 A basic set or relation can also be constructed from two matrices
1259 describing the equalities and the inequalities.
1261 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1262 __isl_take isl_space *space,
1263 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1264 enum isl_dim_type c1,
1265 enum isl_dim_type c2, enum isl_dim_type c3,
1266 enum isl_dim_type c4);
1267 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1268 __isl_take isl_space *space,
1269 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1270 enum isl_dim_type c1,
1271 enum isl_dim_type c2, enum isl_dim_type c3,
1272 enum isl_dim_type c4, enum isl_dim_type c5);
1274 The C<isl_dim_type> arguments indicate the order in which
1275 different kinds of variables appear in the input matrices
1276 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1277 C<isl_dim_set> and C<isl_dim_div> for sets and
1278 of C<isl_dim_cst>, C<isl_dim_param>,
1279 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1281 A (basic or union) set or relation can also be constructed from a
1282 (union) (piecewise) (multiple) affine expression
1283 or a list of affine expressions
1284 (See L<"Piecewise Quasi Affine Expressions"> and
1285 L<"Piecewise Multiple Quasi Affine Expressions">).
1287 __isl_give isl_basic_map *isl_basic_map_from_aff(
1288 __isl_take isl_aff *aff);
1289 __isl_give isl_map *isl_map_from_aff(
1290 __isl_take isl_aff *aff);
1291 __isl_give isl_set *isl_set_from_pw_aff(
1292 __isl_take isl_pw_aff *pwaff);
1293 __isl_give isl_map *isl_map_from_pw_aff(
1294 __isl_take isl_pw_aff *pwaff);
1295 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1296 __isl_take isl_space *domain_space,
1297 __isl_take isl_aff_list *list);
1298 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1299 __isl_take isl_multi_aff *maff)
1300 __isl_give isl_map *isl_map_from_multi_aff(
1301 __isl_take isl_multi_aff *maff)
1302 __isl_give isl_set *isl_set_from_pw_multi_aff(
1303 __isl_take isl_pw_multi_aff *pma);
1304 __isl_give isl_map *isl_map_from_pw_multi_aff(
1305 __isl_take isl_pw_multi_aff *pma);
1306 __isl_give isl_union_map *
1307 isl_union_map_from_union_pw_multi_aff(
1308 __isl_take isl_union_pw_multi_aff *upma);
1310 The C<domain_dim> argument describes the domain of the resulting
1311 basic relation. It is required because the C<list> may consist
1312 of zero affine expressions.
1314 =head2 Inspecting Sets and Relations
1316 Usually, the user should not have to care about the actual constraints
1317 of the sets and maps, but should instead apply the abstract operations
1318 explained in the following sections.
1319 Occasionally, however, it may be required to inspect the individual
1320 coefficients of the constraints. This section explains how to do so.
1321 In these cases, it may also be useful to have C<isl> compute
1322 an explicit representation of the existentially quantified variables.
1324 __isl_give isl_set *isl_set_compute_divs(
1325 __isl_take isl_set *set);
1326 __isl_give isl_map *isl_map_compute_divs(
1327 __isl_take isl_map *map);
1328 __isl_give isl_union_set *isl_union_set_compute_divs(
1329 __isl_take isl_union_set *uset);
1330 __isl_give isl_union_map *isl_union_map_compute_divs(
1331 __isl_take isl_union_map *umap);
1333 This explicit representation defines the existentially quantified
1334 variables as integer divisions of the other variables, possibly
1335 including earlier existentially quantified variables.
1336 An explicitly represented existentially quantified variable therefore
1337 has a unique value when the values of the other variables are known.
1338 If, furthermore, the same existentials, i.e., existentials
1339 with the same explicit representations, should appear in the
1340 same order in each of the disjuncts of a set or map, then the user should call
1341 either of the following functions.
1343 __isl_give isl_set *isl_set_align_divs(
1344 __isl_take isl_set *set);
1345 __isl_give isl_map *isl_map_align_divs(
1346 __isl_take isl_map *map);
1348 Alternatively, the existentially quantified variables can be removed
1349 using the following functions, which compute an overapproximation.
1351 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1352 __isl_take isl_basic_set *bset);
1353 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1354 __isl_take isl_basic_map *bmap);
1355 __isl_give isl_set *isl_set_remove_divs(
1356 __isl_take isl_set *set);
1357 __isl_give isl_map *isl_map_remove_divs(
1358 __isl_take isl_map *map);
1360 To iterate over all the sets or maps in a union set or map, use
1362 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1363 int (*fn)(__isl_take isl_set *set, void *user),
1365 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1366 int (*fn)(__isl_take isl_map *map, void *user),
1369 The number of sets or maps in a union set or map can be obtained
1372 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1373 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1375 To extract the set or map in a given space from a union, use
1377 __isl_give isl_set *isl_union_set_extract_set(
1378 __isl_keep isl_union_set *uset,
1379 __isl_take isl_space *space);
1380 __isl_give isl_map *isl_union_map_extract_map(
1381 __isl_keep isl_union_map *umap,
1382 __isl_take isl_space *space);
1384 To iterate over all the basic sets or maps in a set or map, use
1386 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1387 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1389 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1390 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1393 The callback function C<fn> should return 0 if successful and
1394 -1 if an error occurs. In the latter case, or if any other error
1395 occurs, the above functions will return -1.
1397 It should be noted that C<isl> does not guarantee that
1398 the basic sets or maps passed to C<fn> are disjoint.
1399 If this is required, then the user should call one of
1400 the following functions first.
1402 __isl_give isl_set *isl_set_make_disjoint(
1403 __isl_take isl_set *set);
1404 __isl_give isl_map *isl_map_make_disjoint(
1405 __isl_take isl_map *map);
1407 The number of basic sets in a set can be obtained
1410 int isl_set_n_basic_set(__isl_keep isl_set *set);
1412 To iterate over the constraints of a basic set or map, use
1414 #include <isl/constraint.h>
1416 int isl_basic_map_foreach_constraint(
1417 __isl_keep isl_basic_map *bmap,
1418 int (*fn)(__isl_take isl_constraint *c, void *user),
1420 void *isl_constraint_free(__isl_take isl_constraint *c);
1422 Again, the callback function C<fn> should return 0 if successful and
1423 -1 if an error occurs. In the latter case, or if any other error
1424 occurs, the above functions will return -1.
1425 The constraint C<c> represents either an equality or an inequality.
1426 Use the following function to find out whether a constraint
1427 represents an equality. If not, it represents an inequality.
1429 int isl_constraint_is_equality(
1430 __isl_keep isl_constraint *constraint);
1432 The coefficients of the constraints can be inspected using
1433 the following functions.
1435 void isl_constraint_get_constant(
1436 __isl_keep isl_constraint *constraint, isl_int *v);
1437 void isl_constraint_get_coefficient(
1438 __isl_keep isl_constraint *constraint,
1439 enum isl_dim_type type, int pos, isl_int *v);
1440 int isl_constraint_involves_dims(
1441 __isl_keep isl_constraint *constraint,
1442 enum isl_dim_type type, unsigned first, unsigned n);
1444 The explicit representations of the existentially quantified
1445 variables can be inspected using the following function.
1446 Note that the user is only allowed to use this function
1447 if the inspected set or map is the result of a call
1448 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1449 The existentially quantified variable is equal to the floor
1450 of the returned affine expression. The affine expression
1451 itself can be inspected using the functions in
1452 L<"Piecewise Quasi Affine Expressions">.
1454 __isl_give isl_aff *isl_constraint_get_div(
1455 __isl_keep isl_constraint *constraint, int pos);
1457 To obtain the constraints of a basic set or map in matrix
1458 form, use the following functions.
1460 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1461 __isl_keep isl_basic_set *bset,
1462 enum isl_dim_type c1, enum isl_dim_type c2,
1463 enum isl_dim_type c3, enum isl_dim_type c4);
1464 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1465 __isl_keep isl_basic_set *bset,
1466 enum isl_dim_type c1, enum isl_dim_type c2,
1467 enum isl_dim_type c3, enum isl_dim_type c4);
1468 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1469 __isl_keep isl_basic_map *bmap,
1470 enum isl_dim_type c1,
1471 enum isl_dim_type c2, enum isl_dim_type c3,
1472 enum isl_dim_type c4, enum isl_dim_type c5);
1473 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1474 __isl_keep isl_basic_map *bmap,
1475 enum isl_dim_type c1,
1476 enum isl_dim_type c2, enum isl_dim_type c3,
1477 enum isl_dim_type c4, enum isl_dim_type c5);
1479 The C<isl_dim_type> arguments dictate the order in which
1480 different kinds of variables appear in the resulting matrix
1481 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1482 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1484 The number of parameters, input, output or set dimensions can
1485 be obtained using the following functions.
1487 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1488 enum isl_dim_type type);
1489 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1490 enum isl_dim_type type);
1491 unsigned isl_set_dim(__isl_keep isl_set *set,
1492 enum isl_dim_type type);
1493 unsigned isl_map_dim(__isl_keep isl_map *map,
1494 enum isl_dim_type type);
1496 To check whether the description of a set or relation depends
1497 on one or more given dimensions, it is not necessary to iterate over all
1498 constraints. Instead the following functions can be used.
1500 int isl_basic_set_involves_dims(
1501 __isl_keep isl_basic_set *bset,
1502 enum isl_dim_type type, unsigned first, unsigned n);
1503 int isl_set_involves_dims(__isl_keep isl_set *set,
1504 enum isl_dim_type type, unsigned first, unsigned n);
1505 int isl_basic_map_involves_dims(
1506 __isl_keep isl_basic_map *bmap,
1507 enum isl_dim_type type, unsigned first, unsigned n);
1508 int isl_map_involves_dims(__isl_keep isl_map *map,
1509 enum isl_dim_type type, unsigned first, unsigned n);
1511 Similarly, the following functions can be used to check whether
1512 a given dimension is involved in any lower or upper bound.
1514 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1515 enum isl_dim_type type, unsigned pos);
1516 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1517 enum isl_dim_type type, unsigned pos);
1519 The identifiers or names of the domain and range spaces of a set
1520 or relation can be read off or set using the following functions.
1522 __isl_give isl_set *isl_set_set_tuple_id(
1523 __isl_take isl_set *set, __isl_take isl_id *id);
1524 __isl_give isl_set *isl_set_reset_tuple_id(
1525 __isl_take isl_set *set);
1526 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1527 __isl_give isl_id *isl_set_get_tuple_id(
1528 __isl_keep isl_set *set);
1529 __isl_give isl_map *isl_map_set_tuple_id(
1530 __isl_take isl_map *map, enum isl_dim_type type,
1531 __isl_take isl_id *id);
1532 __isl_give isl_map *isl_map_reset_tuple_id(
1533 __isl_take isl_map *map, enum isl_dim_type type);
1534 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1535 enum isl_dim_type type);
1536 __isl_give isl_id *isl_map_get_tuple_id(
1537 __isl_keep isl_map *map, enum isl_dim_type type);
1539 const char *isl_basic_set_get_tuple_name(
1540 __isl_keep isl_basic_set *bset);
1541 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1542 __isl_take isl_basic_set *set, const char *s);
1543 const char *isl_set_get_tuple_name(
1544 __isl_keep isl_set *set);
1545 const char *isl_basic_map_get_tuple_name(
1546 __isl_keep isl_basic_map *bmap,
1547 enum isl_dim_type type);
1548 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1549 __isl_take isl_basic_map *bmap,
1550 enum isl_dim_type type, const char *s);
1551 const char *isl_map_get_tuple_name(
1552 __isl_keep isl_map *map,
1553 enum isl_dim_type type);
1555 As with C<isl_space_get_tuple_name>, the value returned points to
1556 an internal data structure.
1557 The identifiers, positions or names of individual dimensions can be
1558 read off using the following functions.
1560 __isl_give isl_set *isl_set_set_dim_id(
1561 __isl_take isl_set *set, enum isl_dim_type type,
1562 unsigned pos, __isl_take isl_id *id);
1563 int isl_set_has_dim_id(__isl_keep isl_set *set,
1564 enum isl_dim_type type, unsigned pos);
1565 __isl_give isl_id *isl_set_get_dim_id(
1566 __isl_keep isl_set *set, enum isl_dim_type type,
1568 int isl_basic_map_has_dim_id(
1569 __isl_keep isl_basic_map *bmap,
1570 enum isl_dim_type type, unsigned pos);
1571 __isl_give isl_map *isl_map_set_dim_id(
1572 __isl_take isl_map *map, enum isl_dim_type type,
1573 unsigned pos, __isl_take isl_id *id);
1574 int isl_map_has_dim_id(__isl_keep isl_map *map,
1575 enum isl_dim_type type, unsigned pos);
1576 __isl_give isl_id *isl_map_get_dim_id(
1577 __isl_keep isl_map *map, enum isl_dim_type type,
1580 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1581 enum isl_dim_type type, __isl_keep isl_id *id);
1582 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1583 enum isl_dim_type type, __isl_keep isl_id *id);
1584 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1585 enum isl_dim_type type, const char *name);
1586 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1587 enum isl_dim_type type, const char *name);
1589 const char *isl_constraint_get_dim_name(
1590 __isl_keep isl_constraint *constraint,
1591 enum isl_dim_type type, unsigned pos);
1592 const char *isl_basic_set_get_dim_name(
1593 __isl_keep isl_basic_set *bset,
1594 enum isl_dim_type type, unsigned pos);
1595 int isl_set_has_dim_name(__isl_keep isl_set *set,
1596 enum isl_dim_type type, unsigned pos);
1597 const char *isl_set_get_dim_name(
1598 __isl_keep isl_set *set,
1599 enum isl_dim_type type, unsigned pos);
1600 const char *isl_basic_map_get_dim_name(
1601 __isl_keep isl_basic_map *bmap,
1602 enum isl_dim_type type, unsigned pos);
1603 const char *isl_map_get_dim_name(
1604 __isl_keep isl_map *map,
1605 enum isl_dim_type type, unsigned pos);
1607 These functions are mostly useful to obtain the identifiers, positions
1608 or names of the parameters. Identifiers of individual dimensions are
1609 essentially only useful for printing. They are ignored by all other
1610 operations and may not be preserved across those operations.
1614 =head3 Unary Properties
1620 The following functions test whether the given set or relation
1621 contains any integer points. The ``plain'' variants do not perform
1622 any computations, but simply check if the given set or relation
1623 is already known to be empty.
1625 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1626 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1627 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1628 int isl_set_is_empty(__isl_keep isl_set *set);
1629 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1630 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1631 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1632 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1633 int isl_map_is_empty(__isl_keep isl_map *map);
1634 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1636 =item * Universality
1638 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1639 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1640 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1642 =item * Single-valuedness
1644 int isl_map_plain_is_single_valued(
1645 __isl_keep isl_map *map);
1646 int isl_map_is_single_valued(__isl_keep isl_map *map);
1647 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1651 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1652 int isl_map_is_injective(__isl_keep isl_map *map);
1653 int isl_union_map_plain_is_injective(
1654 __isl_keep isl_union_map *umap);
1655 int isl_union_map_is_injective(
1656 __isl_keep isl_union_map *umap);
1660 int isl_map_is_bijective(__isl_keep isl_map *map);
1661 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1665 int isl_basic_map_plain_is_fixed(
1666 __isl_keep isl_basic_map *bmap,
1667 enum isl_dim_type type, unsigned pos,
1669 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1670 enum isl_dim_type type, unsigned pos,
1672 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1673 enum isl_dim_type type, unsigned pos,
1676 Check if the relation obviously lies on a hyperplane where the given dimension
1677 has a fixed value and if so, return that value in C<*val>.
1681 To check whether a set is a parameter domain, use this function:
1683 int isl_set_is_params(__isl_keep isl_set *set);
1684 int isl_union_set_is_params(
1685 __isl_keep isl_union_set *uset);
1689 The following functions check whether the domain of the given
1690 (basic) set is a wrapped relation.
1692 int isl_basic_set_is_wrapping(
1693 __isl_keep isl_basic_set *bset);
1694 int isl_set_is_wrapping(__isl_keep isl_set *set);
1696 =item * Internal Product
1698 int isl_basic_map_can_zip(
1699 __isl_keep isl_basic_map *bmap);
1700 int isl_map_can_zip(__isl_keep isl_map *map);
1702 Check whether the product of domain and range of the given relation
1704 i.e., whether both domain and range are nested relations.
1708 =head3 Binary Properties
1714 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1715 __isl_keep isl_set *set2);
1716 int isl_set_is_equal(__isl_keep isl_set *set1,
1717 __isl_keep isl_set *set2);
1718 int isl_union_set_is_equal(
1719 __isl_keep isl_union_set *uset1,
1720 __isl_keep isl_union_set *uset2);
1721 int isl_basic_map_is_equal(
1722 __isl_keep isl_basic_map *bmap1,
1723 __isl_keep isl_basic_map *bmap2);
1724 int isl_map_is_equal(__isl_keep isl_map *map1,
1725 __isl_keep isl_map *map2);
1726 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1727 __isl_keep isl_map *map2);
1728 int isl_union_map_is_equal(
1729 __isl_keep isl_union_map *umap1,
1730 __isl_keep isl_union_map *umap2);
1732 =item * Disjointness
1734 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1735 __isl_keep isl_set *set2);
1739 int isl_basic_set_is_subset(
1740 __isl_keep isl_basic_set *bset1,
1741 __isl_keep isl_basic_set *bset2);
1742 int isl_set_is_subset(__isl_keep isl_set *set1,
1743 __isl_keep isl_set *set2);
1744 int isl_set_is_strict_subset(
1745 __isl_keep isl_set *set1,
1746 __isl_keep isl_set *set2);
1747 int isl_union_set_is_subset(
1748 __isl_keep isl_union_set *uset1,
1749 __isl_keep isl_union_set *uset2);
1750 int isl_union_set_is_strict_subset(
1751 __isl_keep isl_union_set *uset1,
1752 __isl_keep isl_union_set *uset2);
1753 int isl_basic_map_is_subset(
1754 __isl_keep isl_basic_map *bmap1,
1755 __isl_keep isl_basic_map *bmap2);
1756 int isl_basic_map_is_strict_subset(
1757 __isl_keep isl_basic_map *bmap1,
1758 __isl_keep isl_basic_map *bmap2);
1759 int isl_map_is_subset(
1760 __isl_keep isl_map *map1,
1761 __isl_keep isl_map *map2);
1762 int isl_map_is_strict_subset(
1763 __isl_keep isl_map *map1,
1764 __isl_keep isl_map *map2);
1765 int isl_union_map_is_subset(
1766 __isl_keep isl_union_map *umap1,
1767 __isl_keep isl_union_map *umap2);
1768 int isl_union_map_is_strict_subset(
1769 __isl_keep isl_union_map *umap1,
1770 __isl_keep isl_union_map *umap2);
1774 =head2 Unary Operations
1780 __isl_give isl_set *isl_set_complement(
1781 __isl_take isl_set *set);
1782 __isl_give isl_map *isl_map_complement(
1783 __isl_take isl_map *map);
1787 __isl_give isl_basic_map *isl_basic_map_reverse(
1788 __isl_take isl_basic_map *bmap);
1789 __isl_give isl_map *isl_map_reverse(
1790 __isl_take isl_map *map);
1791 __isl_give isl_union_map *isl_union_map_reverse(
1792 __isl_take isl_union_map *umap);
1796 __isl_give isl_basic_set *isl_basic_set_project_out(
1797 __isl_take isl_basic_set *bset,
1798 enum isl_dim_type type, unsigned first, unsigned n);
1799 __isl_give isl_basic_map *isl_basic_map_project_out(
1800 __isl_take isl_basic_map *bmap,
1801 enum isl_dim_type type, unsigned first, unsigned n);
1802 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1804 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1805 enum isl_dim_type type, unsigned first, unsigned n);
1806 __isl_give isl_basic_set *isl_basic_set_params(
1807 __isl_take isl_basic_set *bset);
1808 __isl_give isl_basic_set *isl_basic_map_domain(
1809 __isl_take isl_basic_map *bmap);
1810 __isl_give isl_basic_set *isl_basic_map_range(
1811 __isl_take isl_basic_map *bmap);
1812 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1813 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1814 __isl_give isl_set *isl_map_domain(
1815 __isl_take isl_map *bmap);
1816 __isl_give isl_set *isl_map_range(
1817 __isl_take isl_map *map);
1818 __isl_give isl_set *isl_union_set_params(
1819 __isl_take isl_union_set *uset);
1820 __isl_give isl_set *isl_union_map_params(
1821 __isl_take isl_union_map *umap);
1822 __isl_give isl_union_set *isl_union_map_domain(
1823 __isl_take isl_union_map *umap);
1824 __isl_give isl_union_set *isl_union_map_range(
1825 __isl_take isl_union_map *umap);
1827 __isl_give isl_basic_map *isl_basic_map_domain_map(
1828 __isl_take isl_basic_map *bmap);
1829 __isl_give isl_basic_map *isl_basic_map_range_map(
1830 __isl_take isl_basic_map *bmap);
1831 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1832 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1833 __isl_give isl_union_map *isl_union_map_domain_map(
1834 __isl_take isl_union_map *umap);
1835 __isl_give isl_union_map *isl_union_map_range_map(
1836 __isl_take isl_union_map *umap);
1838 The functions above construct a (basic, regular or union) relation
1839 that maps (a wrapped version of) the input relation to its domain or range.
1843 __isl_give isl_set *isl_set_eliminate(
1844 __isl_take isl_set *set, enum isl_dim_type type,
1845 unsigned first, unsigned n);
1846 __isl_give isl_basic_map *isl_basic_map_eliminate(
1847 __isl_take isl_basic_map *bmap,
1848 enum isl_dim_type type,
1849 unsigned first, unsigned n);
1850 __isl_give isl_map *isl_map_eliminate(
1851 __isl_take isl_map *map, enum isl_dim_type type,
1852 unsigned first, unsigned n);
1854 Eliminate the coefficients for the given dimensions from the constraints,
1855 without removing the dimensions.
1859 __isl_give isl_basic_set *isl_basic_set_fix(
1860 __isl_take isl_basic_set *bset,
1861 enum isl_dim_type type, unsigned pos,
1863 __isl_give isl_basic_set *isl_basic_set_fix_si(
1864 __isl_take isl_basic_set *bset,
1865 enum isl_dim_type type, unsigned pos, int value);
1866 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1867 enum isl_dim_type type, unsigned pos,
1869 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1870 enum isl_dim_type type, unsigned pos, int value);
1871 __isl_give isl_basic_map *isl_basic_map_fix_si(
1872 __isl_take isl_basic_map *bmap,
1873 enum isl_dim_type type, unsigned pos, int value);
1874 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1875 enum isl_dim_type type, unsigned pos, int value);
1877 Intersect the set or relation with the hyperplane where the given
1878 dimension has the fixed given value.
1880 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1881 __isl_take isl_basic_map *bmap,
1882 enum isl_dim_type type, unsigned pos, int value);
1883 __isl_give isl_set *isl_set_lower_bound(
1884 __isl_take isl_set *set,
1885 enum isl_dim_type type, unsigned pos,
1887 __isl_give isl_set *isl_set_lower_bound_si(
1888 __isl_take isl_set *set,
1889 enum isl_dim_type type, unsigned pos, int value);
1890 __isl_give isl_map *isl_map_lower_bound_si(
1891 __isl_take isl_map *map,
1892 enum isl_dim_type type, unsigned pos, int value);
1893 __isl_give isl_set *isl_set_upper_bound(
1894 __isl_take isl_set *set,
1895 enum isl_dim_type type, unsigned pos,
1897 __isl_give isl_set *isl_set_upper_bound_si(
1898 __isl_take isl_set *set,
1899 enum isl_dim_type type, unsigned pos, int value);
1900 __isl_give isl_map *isl_map_upper_bound_si(
1901 __isl_take isl_map *map,
1902 enum isl_dim_type type, unsigned pos, int value);
1904 Intersect the set or relation with the half-space where the given
1905 dimension has a value bounded by the fixed given value.
1907 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1908 enum isl_dim_type type1, int pos1,
1909 enum isl_dim_type type2, int pos2);
1910 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1911 enum isl_dim_type type1, int pos1,
1912 enum isl_dim_type type2, int pos2);
1914 Intersect the set or relation with the hyperplane where the given
1915 dimensions are equal to each other.
1917 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1918 enum isl_dim_type type1, int pos1,
1919 enum isl_dim_type type2, int pos2);
1921 Intersect the relation with the hyperplane where the given
1922 dimensions have opposite values.
1924 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1925 enum isl_dim_type type1, int pos1,
1926 enum isl_dim_type type2, int pos2);
1928 Intersect the relation with the half-space where the given
1929 dimensions satisfy the given ordering.
1933 __isl_give isl_map *isl_set_identity(
1934 __isl_take isl_set *set);
1935 __isl_give isl_union_map *isl_union_set_identity(
1936 __isl_take isl_union_set *uset);
1938 Construct an identity relation on the given (union) set.
1942 __isl_give isl_basic_set *isl_basic_map_deltas(
1943 __isl_take isl_basic_map *bmap);
1944 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1945 __isl_give isl_union_set *isl_union_map_deltas(
1946 __isl_take isl_union_map *umap);
1948 These functions return a (basic) set containing the differences
1949 between image elements and corresponding domain elements in the input.
1951 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1952 __isl_take isl_basic_map *bmap);
1953 __isl_give isl_map *isl_map_deltas_map(
1954 __isl_take isl_map *map);
1955 __isl_give isl_union_map *isl_union_map_deltas_map(
1956 __isl_take isl_union_map *umap);
1958 The functions above construct a (basic, regular or union) relation
1959 that maps (a wrapped version of) the input relation to its delta set.
1963 Simplify the representation of a set or relation by trying
1964 to combine pairs of basic sets or relations into a single
1965 basic set or relation.
1967 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1968 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1969 __isl_give isl_union_set *isl_union_set_coalesce(
1970 __isl_take isl_union_set *uset);
1971 __isl_give isl_union_map *isl_union_map_coalesce(
1972 __isl_take isl_union_map *umap);
1974 One of the methods for combining pairs of basic sets or relations
1975 can result in coefficients that are much larger than those that appear
1976 in the constraints of the input. By default, the coefficients are
1977 not allowed to grow larger, but this can be changed by unsetting
1978 the following option.
1980 int isl_options_set_coalesce_bounded_wrapping(
1981 isl_ctx *ctx, int val);
1982 int isl_options_get_coalesce_bounded_wrapping(
1985 =item * Detecting equalities
1987 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1988 __isl_take isl_basic_set *bset);
1989 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1990 __isl_take isl_basic_map *bmap);
1991 __isl_give isl_set *isl_set_detect_equalities(
1992 __isl_take isl_set *set);
1993 __isl_give isl_map *isl_map_detect_equalities(
1994 __isl_take isl_map *map);
1995 __isl_give isl_union_set *isl_union_set_detect_equalities(
1996 __isl_take isl_union_set *uset);
1997 __isl_give isl_union_map *isl_union_map_detect_equalities(
1998 __isl_take isl_union_map *umap);
2000 Simplify the representation of a set or relation by detecting implicit
2003 =item * Removing redundant constraints
2005 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2006 __isl_take isl_basic_set *bset);
2007 __isl_give isl_set *isl_set_remove_redundancies(
2008 __isl_take isl_set *set);
2009 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_map *isl_map_remove_redundancies(
2012 __isl_take isl_map *map);
2016 __isl_give isl_basic_set *isl_set_convex_hull(
2017 __isl_take isl_set *set);
2018 __isl_give isl_basic_map *isl_map_convex_hull(
2019 __isl_take isl_map *map);
2021 If the input set or relation has any existentially quantified
2022 variables, then the result of these operations is currently undefined.
2026 __isl_give isl_basic_set *isl_set_simple_hull(
2027 __isl_take isl_set *set);
2028 __isl_give isl_basic_map *isl_map_simple_hull(
2029 __isl_take isl_map *map);
2030 __isl_give isl_union_map *isl_union_map_simple_hull(
2031 __isl_take isl_union_map *umap);
2033 These functions compute a single basic set or relation
2034 that contains the whole input set or relation.
2035 In particular, the output is described by translates
2036 of the constraints describing the basic sets or relations in the input.
2040 (See \autoref{s:simple hull}.)
2046 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2047 __isl_take isl_basic_set *bset);
2048 __isl_give isl_basic_set *isl_set_affine_hull(
2049 __isl_take isl_set *set);
2050 __isl_give isl_union_set *isl_union_set_affine_hull(
2051 __isl_take isl_union_set *uset);
2052 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2053 __isl_take isl_basic_map *bmap);
2054 __isl_give isl_basic_map *isl_map_affine_hull(
2055 __isl_take isl_map *map);
2056 __isl_give isl_union_map *isl_union_map_affine_hull(
2057 __isl_take isl_union_map *umap);
2059 In case of union sets and relations, the affine hull is computed
2062 =item * Polyhedral hull
2064 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2065 __isl_take isl_set *set);
2066 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2067 __isl_take isl_map *map);
2068 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2069 __isl_take isl_union_set *uset);
2070 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2071 __isl_take isl_union_map *umap);
2073 These functions compute a single basic set or relation
2074 not involving any existentially quantified variables
2075 that contains the whole input set or relation.
2076 In case of union sets and relations, the polyhedral hull is computed
2081 __isl_give isl_basic_set *isl_basic_set_sample(
2082 __isl_take isl_basic_set *bset);
2083 __isl_give isl_basic_set *isl_set_sample(
2084 __isl_take isl_set *set);
2085 __isl_give isl_basic_map *isl_basic_map_sample(
2086 __isl_take isl_basic_map *bmap);
2087 __isl_give isl_basic_map *isl_map_sample(
2088 __isl_take isl_map *map);
2090 If the input (basic) set or relation is non-empty, then return
2091 a singleton subset of the input. Otherwise, return an empty set.
2093 =item * Optimization
2095 #include <isl/ilp.h>
2096 enum isl_lp_result isl_basic_set_max(
2097 __isl_keep isl_basic_set *bset,
2098 __isl_keep isl_aff *obj, isl_int *opt)
2099 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2100 __isl_keep isl_aff *obj, isl_int *opt);
2101 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2102 __isl_keep isl_aff *obj, isl_int *opt);
2104 Compute the minimum or maximum of the integer affine expression C<obj>
2105 over the points in C<set>, returning the result in C<opt>.
2106 The return value may be one of C<isl_lp_error>,
2107 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2109 =item * Parametric optimization
2111 __isl_give isl_pw_aff *isl_set_dim_min(
2112 __isl_take isl_set *set, int pos);
2113 __isl_give isl_pw_aff *isl_set_dim_max(
2114 __isl_take isl_set *set, int pos);
2115 __isl_give isl_pw_aff *isl_map_dim_max(
2116 __isl_take isl_map *map, int pos);
2118 Compute the minimum or maximum of the given set or output dimension
2119 as a function of the parameters (and input dimensions), but independently
2120 of the other set or output dimensions.
2121 For lexicographic optimization, see L<"Lexicographic Optimization">.
2125 The following functions compute either the set of (rational) coefficient
2126 values of valid constraints for the given set or the set of (rational)
2127 values satisfying the constraints with coefficients from the given set.
2128 Internally, these two sets of functions perform essentially the
2129 same operations, except that the set of coefficients is assumed to
2130 be a cone, while the set of values may be any polyhedron.
2131 The current implementation is based on the Farkas lemma and
2132 Fourier-Motzkin elimination, but this may change or be made optional
2133 in future. In particular, future implementations may use different
2134 dualization algorithms or skip the elimination step.
2136 __isl_give isl_basic_set *isl_basic_set_coefficients(
2137 __isl_take isl_basic_set *bset);
2138 __isl_give isl_basic_set *isl_set_coefficients(
2139 __isl_take isl_set *set);
2140 __isl_give isl_union_set *isl_union_set_coefficients(
2141 __isl_take isl_union_set *bset);
2142 __isl_give isl_basic_set *isl_basic_set_solutions(
2143 __isl_take isl_basic_set *bset);
2144 __isl_give isl_basic_set *isl_set_solutions(
2145 __isl_take isl_set *set);
2146 __isl_give isl_union_set *isl_union_set_solutions(
2147 __isl_take isl_union_set *bset);
2151 __isl_give isl_map *isl_map_fixed_power(
2152 __isl_take isl_map *map, isl_int exp);
2153 __isl_give isl_union_map *isl_union_map_fixed_power(
2154 __isl_take isl_union_map *umap, isl_int exp);
2156 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2157 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2158 of C<map> is computed.
2160 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2162 __isl_give isl_union_map *isl_union_map_power(
2163 __isl_take isl_union_map *umap, int *exact);
2165 Compute a parametric representation for all positive powers I<k> of C<map>.
2166 The result maps I<k> to a nested relation corresponding to the
2167 I<k>th power of C<map>.
2168 The result may be an overapproximation. If the result is known to be exact,
2169 then C<*exact> is set to C<1>.
2171 =item * Transitive closure
2173 __isl_give isl_map *isl_map_transitive_closure(
2174 __isl_take isl_map *map, int *exact);
2175 __isl_give isl_union_map *isl_union_map_transitive_closure(
2176 __isl_take isl_union_map *umap, int *exact);
2178 Compute the transitive closure of C<map>.
2179 The result may be an overapproximation. If the result is known to be exact,
2180 then C<*exact> is set to C<1>.
2182 =item * Reaching path lengths
2184 __isl_give isl_map *isl_map_reaching_path_lengths(
2185 __isl_take isl_map *map, int *exact);
2187 Compute a relation that maps each element in the range of C<map>
2188 to the lengths of all paths composed of edges in C<map> that
2189 end up in the given element.
2190 The result may be an overapproximation. If the result is known to be exact,
2191 then C<*exact> is set to C<1>.
2192 To compute the I<maximal> path length, the resulting relation
2193 should be postprocessed by C<isl_map_lexmax>.
2194 In particular, if the input relation is a dependence relation
2195 (mapping sources to sinks), then the maximal path length corresponds
2196 to the free schedule.
2197 Note, however, that C<isl_map_lexmax> expects the maximum to be
2198 finite, so if the path lengths are unbounded (possibly due to
2199 the overapproximation), then you will get an error message.
2203 __isl_give isl_basic_set *isl_basic_map_wrap(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_set *isl_map_wrap(
2206 __isl_take isl_map *map);
2207 __isl_give isl_union_set *isl_union_map_wrap(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_basic_map *isl_basic_set_unwrap(
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_map *isl_set_unwrap(
2212 __isl_take isl_set *set);
2213 __isl_give isl_union_map *isl_union_set_unwrap(
2214 __isl_take isl_union_set *uset);
2218 Remove any internal structure of domain (and range) of the given
2219 set or relation. If there is any such internal structure in the input,
2220 then the name of the space is also removed.
2222 __isl_give isl_basic_set *isl_basic_set_flatten(
2223 __isl_take isl_basic_set *bset);
2224 __isl_give isl_set *isl_set_flatten(
2225 __isl_take isl_set *set);
2226 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2229 __isl_take isl_basic_map *bmap);
2230 __isl_give isl_map *isl_map_flatten_range(
2231 __isl_take isl_map *map);
2232 __isl_give isl_map *isl_map_flatten_domain(
2233 __isl_take isl_map *map);
2234 __isl_give isl_basic_map *isl_basic_map_flatten(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_give isl_map *isl_map_flatten(
2237 __isl_take isl_map *map);
2239 __isl_give isl_map *isl_set_flatten_map(
2240 __isl_take isl_set *set);
2242 The function above constructs a relation
2243 that maps the input set to a flattened version of the set.
2247 Lift the input set to a space with extra dimensions corresponding
2248 to the existentially quantified variables in the input.
2249 In particular, the result lives in a wrapped map where the domain
2250 is the original space and the range corresponds to the original
2251 existentially quantified variables.
2253 __isl_give isl_basic_set *isl_basic_set_lift(
2254 __isl_take isl_basic_set *bset);
2255 __isl_give isl_set *isl_set_lift(
2256 __isl_take isl_set *set);
2257 __isl_give isl_union_set *isl_union_set_lift(
2258 __isl_take isl_union_set *uset);
2260 Given a local space that contains the existentially quantified
2261 variables of a set, a basic relation that, when applied to
2262 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2263 can be constructed using the following function.
2265 #include <isl/local_space.h>
2266 __isl_give isl_basic_map *isl_local_space_lifting(
2267 __isl_take isl_local_space *ls);
2269 =item * Internal Product
2271 __isl_give isl_basic_map *isl_basic_map_zip(
2272 __isl_take isl_basic_map *bmap);
2273 __isl_give isl_map *isl_map_zip(
2274 __isl_take isl_map *map);
2275 __isl_give isl_union_map *isl_union_map_zip(
2276 __isl_take isl_union_map *umap);
2278 Given a relation with nested relations for domain and range,
2279 interchange the range of the domain with the domain of the range.
2281 =item * Aligning parameters
2283 __isl_give isl_set *isl_set_align_params(
2284 __isl_take isl_set *set,
2285 __isl_take isl_space *model);
2286 __isl_give isl_map *isl_map_align_params(
2287 __isl_take isl_map *map,
2288 __isl_take isl_space *model);
2290 Change the order of the parameters of the given set or relation
2291 such that the first parameters match those of C<model>.
2292 This may involve the introduction of extra parameters.
2293 All parameters need to be named.
2295 =item * Dimension manipulation
2297 __isl_give isl_set *isl_set_add_dims(
2298 __isl_take isl_set *set,
2299 enum isl_dim_type type, unsigned n);
2300 __isl_give isl_map *isl_map_add_dims(
2301 __isl_take isl_map *map,
2302 enum isl_dim_type type, unsigned n);
2303 __isl_give isl_set *isl_set_insert_dims(
2304 __isl_take isl_set *set,
2305 enum isl_dim_type type, unsigned pos, unsigned n);
2306 __isl_give isl_map *isl_map_insert_dims(
2307 __isl_take isl_map *map,
2308 enum isl_dim_type type, unsigned pos, unsigned n);
2309 __isl_give isl_basic_set *isl_basic_set_move_dims(
2310 __isl_take isl_basic_set *bset,
2311 enum isl_dim_type dst_type, unsigned dst_pos,
2312 enum isl_dim_type src_type, unsigned src_pos,
2314 __isl_give isl_basic_map *isl_basic_map_move_dims(
2315 __isl_take isl_basic_map *bmap,
2316 enum isl_dim_type dst_type, unsigned dst_pos,
2317 enum isl_dim_type src_type, unsigned src_pos,
2319 __isl_give isl_set *isl_set_move_dims(
2320 __isl_take isl_set *set,
2321 enum isl_dim_type dst_type, unsigned dst_pos,
2322 enum isl_dim_type src_type, unsigned src_pos,
2324 __isl_give isl_map *isl_map_move_dims(
2325 __isl_take isl_map *map,
2326 enum isl_dim_type dst_type, unsigned dst_pos,
2327 enum isl_dim_type src_type, unsigned src_pos,
2330 It is usually not advisable to directly change the (input or output)
2331 space of a set or a relation as this removes the name and the internal
2332 structure of the space. However, the above functions can be useful
2333 to add new parameters, assuming
2334 C<isl_set_align_params> and C<isl_map_align_params>
2339 =head2 Binary Operations
2341 The two arguments of a binary operation not only need to live
2342 in the same C<isl_ctx>, they currently also need to have
2343 the same (number of) parameters.
2345 =head3 Basic Operations
2349 =item * Intersection
2351 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2352 __isl_take isl_basic_set *bset1,
2353 __isl_take isl_basic_set *bset2);
2354 __isl_give isl_basic_set *isl_basic_set_intersect(
2355 __isl_take isl_basic_set *bset1,
2356 __isl_take isl_basic_set *bset2);
2357 __isl_give isl_set *isl_set_intersect_params(
2358 __isl_take isl_set *set,
2359 __isl_take isl_set *params);
2360 __isl_give isl_set *isl_set_intersect(
2361 __isl_take isl_set *set1,
2362 __isl_take isl_set *set2);
2363 __isl_give isl_union_set *isl_union_set_intersect_params(
2364 __isl_take isl_union_set *uset,
2365 __isl_take isl_set *set);
2366 __isl_give isl_union_map *isl_union_map_intersect_params(
2367 __isl_take isl_union_map *umap,
2368 __isl_take isl_set *set);
2369 __isl_give isl_union_set *isl_union_set_intersect(
2370 __isl_take isl_union_set *uset1,
2371 __isl_take isl_union_set *uset2);
2372 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2373 __isl_take isl_basic_map *bmap,
2374 __isl_take isl_basic_set *bset);
2375 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2376 __isl_take isl_basic_map *bmap,
2377 __isl_take isl_basic_set *bset);
2378 __isl_give isl_basic_map *isl_basic_map_intersect(
2379 __isl_take isl_basic_map *bmap1,
2380 __isl_take isl_basic_map *bmap2);
2381 __isl_give isl_map *isl_map_intersect_params(
2382 __isl_take isl_map *map,
2383 __isl_take isl_set *params);
2384 __isl_give isl_map *isl_map_intersect_domain(
2385 __isl_take isl_map *map,
2386 __isl_take isl_set *set);
2387 __isl_give isl_map *isl_map_intersect_range(
2388 __isl_take isl_map *map,
2389 __isl_take isl_set *set);
2390 __isl_give isl_map *isl_map_intersect(
2391 __isl_take isl_map *map1,
2392 __isl_take isl_map *map2);
2393 __isl_give isl_union_map *isl_union_map_intersect_domain(
2394 __isl_take isl_union_map *umap,
2395 __isl_take isl_union_set *uset);
2396 __isl_give isl_union_map *isl_union_map_intersect_range(
2397 __isl_take isl_union_map *umap,
2398 __isl_take isl_union_set *uset);
2399 __isl_give isl_union_map *isl_union_map_intersect(
2400 __isl_take isl_union_map *umap1,
2401 __isl_take isl_union_map *umap2);
2405 __isl_give isl_set *isl_basic_set_union(
2406 __isl_take isl_basic_set *bset1,
2407 __isl_take isl_basic_set *bset2);
2408 __isl_give isl_map *isl_basic_map_union(
2409 __isl_take isl_basic_map *bmap1,
2410 __isl_take isl_basic_map *bmap2);
2411 __isl_give isl_set *isl_set_union(
2412 __isl_take isl_set *set1,
2413 __isl_take isl_set *set2);
2414 __isl_give isl_map *isl_map_union(
2415 __isl_take isl_map *map1,
2416 __isl_take isl_map *map2);
2417 __isl_give isl_union_set *isl_union_set_union(
2418 __isl_take isl_union_set *uset1,
2419 __isl_take isl_union_set *uset2);
2420 __isl_give isl_union_map *isl_union_map_union(
2421 __isl_take isl_union_map *umap1,
2422 __isl_take isl_union_map *umap2);
2424 =item * Set difference
2426 __isl_give isl_set *isl_set_subtract(
2427 __isl_take isl_set *set1,
2428 __isl_take isl_set *set2);
2429 __isl_give isl_map *isl_map_subtract(
2430 __isl_take isl_map *map1,
2431 __isl_take isl_map *map2);
2432 __isl_give isl_map *isl_map_subtract_domain(
2433 __isl_take isl_map *map,
2434 __isl_take isl_set *dom);
2435 __isl_give isl_map *isl_map_subtract_range(
2436 __isl_take isl_map *map,
2437 __isl_take isl_set *dom);
2438 __isl_give isl_union_set *isl_union_set_subtract(
2439 __isl_take isl_union_set *uset1,
2440 __isl_take isl_union_set *uset2);
2441 __isl_give isl_union_map *isl_union_map_subtract(
2442 __isl_take isl_union_map *umap1,
2443 __isl_take isl_union_map *umap2);
2447 __isl_give isl_basic_set *isl_basic_set_apply(
2448 __isl_take isl_basic_set *bset,
2449 __isl_take isl_basic_map *bmap);
2450 __isl_give isl_set *isl_set_apply(
2451 __isl_take isl_set *set,
2452 __isl_take isl_map *map);
2453 __isl_give isl_union_set *isl_union_set_apply(
2454 __isl_take isl_union_set *uset,
2455 __isl_take isl_union_map *umap);
2456 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2457 __isl_take isl_basic_map *bmap1,
2458 __isl_take isl_basic_map *bmap2);
2459 __isl_give isl_basic_map *isl_basic_map_apply_range(
2460 __isl_take isl_basic_map *bmap1,
2461 __isl_take isl_basic_map *bmap2);
2462 __isl_give isl_map *isl_map_apply_domain(
2463 __isl_take isl_map *map1,
2464 __isl_take isl_map *map2);
2465 __isl_give isl_union_map *isl_union_map_apply_domain(
2466 __isl_take isl_union_map *umap1,
2467 __isl_take isl_union_map *umap2);
2468 __isl_give isl_map *isl_map_apply_range(
2469 __isl_take isl_map *map1,
2470 __isl_take isl_map *map2);
2471 __isl_give isl_union_map *isl_union_map_apply_range(
2472 __isl_take isl_union_map *umap1,
2473 __isl_take isl_union_map *umap2);
2475 =item * Cartesian Product
2477 __isl_give isl_set *isl_set_product(
2478 __isl_take isl_set *set1,
2479 __isl_take isl_set *set2);
2480 __isl_give isl_union_set *isl_union_set_product(
2481 __isl_take isl_union_set *uset1,
2482 __isl_take isl_union_set *uset2);
2483 __isl_give isl_basic_map *isl_basic_map_domain_product(
2484 __isl_take isl_basic_map *bmap1,
2485 __isl_take isl_basic_map *bmap2);
2486 __isl_give isl_basic_map *isl_basic_map_range_product(
2487 __isl_take isl_basic_map *bmap1,
2488 __isl_take isl_basic_map *bmap2);
2489 __isl_give isl_map *isl_map_domain_product(
2490 __isl_take isl_map *map1,
2491 __isl_take isl_map *map2);
2492 __isl_give isl_map *isl_map_range_product(
2493 __isl_take isl_map *map1,
2494 __isl_take isl_map *map2);
2495 __isl_give isl_union_map *isl_union_map_range_product(
2496 __isl_take isl_union_map *umap1,
2497 __isl_take isl_union_map *umap2);
2498 __isl_give isl_map *isl_map_product(
2499 __isl_take isl_map *map1,
2500 __isl_take isl_map *map2);
2501 __isl_give isl_union_map *isl_union_map_product(
2502 __isl_take isl_union_map *umap1,
2503 __isl_take isl_union_map *umap2);
2505 The above functions compute the cross product of the given
2506 sets or relations. The domains and ranges of the results
2507 are wrapped maps between domains and ranges of the inputs.
2508 To obtain a ``flat'' product, use the following functions
2511 __isl_give isl_basic_set *isl_basic_set_flat_product(
2512 __isl_take isl_basic_set *bset1,
2513 __isl_take isl_basic_set *bset2);
2514 __isl_give isl_set *isl_set_flat_product(
2515 __isl_take isl_set *set1,
2516 __isl_take isl_set *set2);
2517 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2518 __isl_take isl_basic_map *bmap1,
2519 __isl_take isl_basic_map *bmap2);
2520 __isl_give isl_map *isl_map_flat_domain_product(
2521 __isl_take isl_map *map1,
2522 __isl_take isl_map *map2);
2523 __isl_give isl_map *isl_map_flat_range_product(
2524 __isl_take isl_map *map1,
2525 __isl_take isl_map *map2);
2526 __isl_give isl_union_map *isl_union_map_flat_range_product(
2527 __isl_take isl_union_map *umap1,
2528 __isl_take isl_union_map *umap2);
2529 __isl_give isl_basic_map *isl_basic_map_flat_product(
2530 __isl_take isl_basic_map *bmap1,
2531 __isl_take isl_basic_map *bmap2);
2532 __isl_give isl_map *isl_map_flat_product(
2533 __isl_take isl_map *map1,
2534 __isl_take isl_map *map2);
2536 =item * Simplification
2538 __isl_give isl_basic_set *isl_basic_set_gist(
2539 __isl_take isl_basic_set *bset,
2540 __isl_take isl_basic_set *context);
2541 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2542 __isl_take isl_set *context);
2543 __isl_give isl_set *isl_set_gist_params(
2544 __isl_take isl_set *set,
2545 __isl_take isl_set *context);
2546 __isl_give isl_union_set *isl_union_set_gist(
2547 __isl_take isl_union_set *uset,
2548 __isl_take isl_union_set *context);
2549 __isl_give isl_union_set *isl_union_set_gist_params(
2550 __isl_take isl_union_set *uset,
2551 __isl_take isl_set *set);
2552 __isl_give isl_basic_map *isl_basic_map_gist(
2553 __isl_take isl_basic_map *bmap,
2554 __isl_take isl_basic_map *context);
2555 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2556 __isl_take isl_map *context);
2557 __isl_give isl_map *isl_map_gist_params(
2558 __isl_take isl_map *map,
2559 __isl_take isl_set *context);
2560 __isl_give isl_map *isl_map_gist_domain(
2561 __isl_take isl_map *map,
2562 __isl_take isl_set *context);
2563 __isl_give isl_map *isl_map_gist_range(
2564 __isl_take isl_map *map,
2565 __isl_take isl_set *context);
2566 __isl_give isl_union_map *isl_union_map_gist(
2567 __isl_take isl_union_map *umap,
2568 __isl_take isl_union_map *context);
2569 __isl_give isl_union_map *isl_union_map_gist_params(
2570 __isl_take isl_union_map *umap,
2571 __isl_take isl_set *set);
2572 __isl_give isl_union_map *isl_union_map_gist_domain(
2573 __isl_take isl_union_map *umap,
2574 __isl_take isl_union_set *uset);
2575 __isl_give isl_union_map *isl_union_map_gist_range(
2576 __isl_take isl_union_map *umap,
2577 __isl_take isl_union_set *uset);
2579 The gist operation returns a set or relation that has the
2580 same intersection with the context as the input set or relation.
2581 Any implicit equality in the intersection is made explicit in the result,
2582 while all inequalities that are redundant with respect to the intersection
2584 In case of union sets and relations, the gist operation is performed
2589 =head3 Lexicographic Optimization
2591 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2592 the following functions
2593 compute a set that contains the lexicographic minimum or maximum
2594 of the elements in C<set> (or C<bset>) for those values of the parameters
2595 that satisfy C<dom>.
2596 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2597 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2599 In other words, the union of the parameter values
2600 for which the result is non-empty and of C<*empty>
2603 __isl_give isl_set *isl_basic_set_partial_lexmin(
2604 __isl_take isl_basic_set *bset,
2605 __isl_take isl_basic_set *dom,
2606 __isl_give isl_set **empty);
2607 __isl_give isl_set *isl_basic_set_partial_lexmax(
2608 __isl_take isl_basic_set *bset,
2609 __isl_take isl_basic_set *dom,
2610 __isl_give isl_set **empty);
2611 __isl_give isl_set *isl_set_partial_lexmin(
2612 __isl_take isl_set *set, __isl_take isl_set *dom,
2613 __isl_give isl_set **empty);
2614 __isl_give isl_set *isl_set_partial_lexmax(
2615 __isl_take isl_set *set, __isl_take isl_set *dom,
2616 __isl_give isl_set **empty);
2618 Given a (basic) set C<set> (or C<bset>), the following functions simply
2619 return a set containing the lexicographic minimum or maximum
2620 of the elements in C<set> (or C<bset>).
2621 In case of union sets, the optimum is computed per space.
2623 __isl_give isl_set *isl_basic_set_lexmin(
2624 __isl_take isl_basic_set *bset);
2625 __isl_give isl_set *isl_basic_set_lexmax(
2626 __isl_take isl_basic_set *bset);
2627 __isl_give isl_set *isl_set_lexmin(
2628 __isl_take isl_set *set);
2629 __isl_give isl_set *isl_set_lexmax(
2630 __isl_take isl_set *set);
2631 __isl_give isl_union_set *isl_union_set_lexmin(
2632 __isl_take isl_union_set *uset);
2633 __isl_give isl_union_set *isl_union_set_lexmax(
2634 __isl_take isl_union_set *uset);
2636 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2637 the following functions
2638 compute a relation that maps each element of C<dom>
2639 to the single lexicographic minimum or maximum
2640 of the elements that are associated to that same
2641 element in C<map> (or C<bmap>).
2642 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2643 that contains the elements in C<dom> that do not map
2644 to any elements in C<map> (or C<bmap>).
2645 In other words, the union of the domain of the result and of C<*empty>
2648 __isl_give isl_map *isl_basic_map_partial_lexmax(
2649 __isl_take isl_basic_map *bmap,
2650 __isl_take isl_basic_set *dom,
2651 __isl_give isl_set **empty);
2652 __isl_give isl_map *isl_basic_map_partial_lexmin(
2653 __isl_take isl_basic_map *bmap,
2654 __isl_take isl_basic_set *dom,
2655 __isl_give isl_set **empty);
2656 __isl_give isl_map *isl_map_partial_lexmax(
2657 __isl_take isl_map *map, __isl_take isl_set *dom,
2658 __isl_give isl_set **empty);
2659 __isl_give isl_map *isl_map_partial_lexmin(
2660 __isl_take isl_map *map, __isl_take isl_set *dom,
2661 __isl_give isl_set **empty);
2663 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2664 return a map mapping each element in the domain of
2665 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2666 of all elements associated to that element.
2667 In case of union relations, the optimum is computed per space.
2669 __isl_give isl_map *isl_basic_map_lexmin(
2670 __isl_take isl_basic_map *bmap);
2671 __isl_give isl_map *isl_basic_map_lexmax(
2672 __isl_take isl_basic_map *bmap);
2673 __isl_give isl_map *isl_map_lexmin(
2674 __isl_take isl_map *map);
2675 __isl_give isl_map *isl_map_lexmax(
2676 __isl_take isl_map *map);
2677 __isl_give isl_union_map *isl_union_map_lexmin(
2678 __isl_take isl_union_map *umap);
2679 __isl_give isl_union_map *isl_union_map_lexmax(
2680 __isl_take isl_union_map *umap);
2682 The following functions return their result in the form of
2683 a piecewise multi-affine expression
2684 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2685 but are otherwise equivalent to the corresponding functions
2686 returning a basic set or relation.
2688 __isl_give isl_pw_multi_aff *
2689 isl_basic_map_lexmin_pw_multi_aff(
2690 __isl_take isl_basic_map *bmap);
2691 __isl_give isl_pw_multi_aff *
2692 isl_basic_set_partial_lexmin_pw_multi_aff(
2693 __isl_take isl_basic_set *bset,
2694 __isl_take isl_basic_set *dom,
2695 __isl_give isl_set **empty);
2696 __isl_give isl_pw_multi_aff *
2697 isl_basic_set_partial_lexmax_pw_multi_aff(
2698 __isl_take isl_basic_set *bset,
2699 __isl_take isl_basic_set *dom,
2700 __isl_give isl_set **empty);
2701 __isl_give isl_pw_multi_aff *
2702 isl_basic_map_partial_lexmin_pw_multi_aff(
2703 __isl_take isl_basic_map *bmap,
2704 __isl_take isl_basic_set *dom,
2705 __isl_give isl_set **empty);
2706 __isl_give isl_pw_multi_aff *
2707 isl_basic_map_partial_lexmax_pw_multi_aff(
2708 __isl_take isl_basic_map *bmap,
2709 __isl_take isl_basic_set *dom,
2710 __isl_give isl_set **empty);
2714 Lists are defined over several element types, including
2715 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2716 Here we take lists of C<isl_set>s as an example.
2717 Lists can be created, copied and freed using the following functions.
2719 #include <isl/list.h>
2720 __isl_give isl_set_list *isl_set_list_from_set(
2721 __isl_take isl_set *el);
2722 __isl_give isl_set_list *isl_set_list_alloc(
2723 isl_ctx *ctx, int n);
2724 __isl_give isl_set_list *isl_set_list_copy(
2725 __isl_keep isl_set_list *list);
2726 __isl_give isl_set_list *isl_set_list_add(
2727 __isl_take isl_set_list *list,
2728 __isl_take isl_set *el);
2729 __isl_give isl_set_list *isl_set_list_concat(
2730 __isl_take isl_set_list *list1,
2731 __isl_take isl_set_list *list2);
2732 void *isl_set_list_free(__isl_take isl_set_list *list);
2734 C<isl_set_list_alloc> creates an empty list with a capacity for
2735 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2738 Lists can be inspected using the following functions.
2740 #include <isl/list.h>
2741 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2742 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2743 __isl_give isl_set *isl_set_list_get_set(
2744 __isl_keep isl_set_list *list, int index);
2745 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2746 int (*fn)(__isl_take isl_set *el, void *user),
2749 Lists can be printed using
2751 #include <isl/list.h>
2752 __isl_give isl_printer *isl_printer_print_set_list(
2753 __isl_take isl_printer *p,
2754 __isl_keep isl_set_list *list);
2758 Vectors can be created, copied and freed using the following functions.
2760 #include <isl/vec.h>
2761 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2763 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2764 void isl_vec_free(__isl_take isl_vec *vec);
2766 Note that the elements of a newly created vector may have arbitrary values.
2767 The elements can be changed and inspected using the following functions.
2769 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2770 int isl_vec_size(__isl_keep isl_vec *vec);
2771 int isl_vec_get_element(__isl_keep isl_vec *vec,
2772 int pos, isl_int *v);
2773 __isl_give isl_vec *isl_vec_set_element(
2774 __isl_take isl_vec *vec, int pos, isl_int v);
2775 __isl_give isl_vec *isl_vec_set_element_si(
2776 __isl_take isl_vec *vec, int pos, int v);
2777 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2779 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2782 C<isl_vec_get_element> will return a negative value if anything went wrong.
2783 In that case, the value of C<*v> is undefined.
2787 Matrices can be created, copied and freed using the following functions.
2789 #include <isl/mat.h>
2790 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2791 unsigned n_row, unsigned n_col);
2792 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2793 void isl_mat_free(__isl_take isl_mat *mat);
2795 Note that the elements of a newly created matrix may have arbitrary values.
2796 The elements can be changed and inspected using the following functions.
2798 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2799 int isl_mat_rows(__isl_keep isl_mat *mat);
2800 int isl_mat_cols(__isl_keep isl_mat *mat);
2801 int isl_mat_get_element(__isl_keep isl_mat *mat,
2802 int row, int col, isl_int *v);
2803 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2804 int row, int col, isl_int v);
2805 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2806 int row, int col, int v);
2808 C<isl_mat_get_element> will return a negative value if anything went wrong.
2809 In that case, the value of C<*v> is undefined.
2811 The following function can be used to compute the (right) inverse
2812 of a matrix, i.e., a matrix such that the product of the original
2813 and the inverse (in that order) is a multiple of the identity matrix.
2814 The input matrix is assumed to be of full row-rank.
2816 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2818 The following function can be used to compute the (right) kernel
2819 (or null space) of a matrix, i.e., a matrix such that the product of
2820 the original and the kernel (in that order) is the zero matrix.
2822 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2824 =head2 Piecewise Quasi Affine Expressions
2826 The zero quasi affine expression on a given domain can be created using
2828 __isl_give isl_aff *isl_aff_zero_on_domain(
2829 __isl_take isl_local_space *ls);
2831 Note that the space in which the resulting object lives is a map space
2832 with the given space as domain and a one-dimensional range.
2834 An empty piecewise quasi affine expression (one with no cells)
2835 or a piecewise quasi affine expression with a single cell can
2836 be created using the following functions.
2838 #include <isl/aff.h>
2839 __isl_give isl_pw_aff *isl_pw_aff_empty(
2840 __isl_take isl_space *space);
2841 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2842 __isl_take isl_set *set, __isl_take isl_aff *aff);
2843 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2844 __isl_take isl_aff *aff);
2846 A piecewise quasi affine expression that is equal to 1 on a set
2847 and 0 outside the set can be created using the following function.
2849 #include <isl/aff.h>
2850 __isl_give isl_pw_aff *isl_set_indicator_function(
2851 __isl_take isl_set *set);
2853 Quasi affine expressions can be copied and freed using
2855 #include <isl/aff.h>
2856 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2857 void *isl_aff_free(__isl_take isl_aff *aff);
2859 __isl_give isl_pw_aff *isl_pw_aff_copy(
2860 __isl_keep isl_pw_aff *pwaff);
2861 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2863 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2864 using the following function. The constraint is required to have
2865 a non-zero coefficient for the specified dimension.
2867 #include <isl/constraint.h>
2868 __isl_give isl_aff *isl_constraint_get_bound(
2869 __isl_keep isl_constraint *constraint,
2870 enum isl_dim_type type, int pos);
2872 The entire affine expression of the constraint can also be extracted
2873 using the following function.
2875 #include <isl/constraint.h>
2876 __isl_give isl_aff *isl_constraint_get_aff(
2877 __isl_keep isl_constraint *constraint);
2879 Conversely, an equality constraint equating
2880 the affine expression to zero or an inequality constraint enforcing
2881 the affine expression to be non-negative, can be constructed using
2883 __isl_give isl_constraint *isl_equality_from_aff(
2884 __isl_take isl_aff *aff);
2885 __isl_give isl_constraint *isl_inequality_from_aff(
2886 __isl_take isl_aff *aff);
2888 The expression can be inspected using
2890 #include <isl/aff.h>
2891 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2892 int isl_aff_dim(__isl_keep isl_aff *aff,
2893 enum isl_dim_type type);
2894 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2895 __isl_keep isl_aff *aff);
2896 __isl_give isl_local_space *isl_aff_get_local_space(
2897 __isl_keep isl_aff *aff);
2898 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2899 enum isl_dim_type type, unsigned pos);
2900 const char *isl_pw_aff_get_dim_name(
2901 __isl_keep isl_pw_aff *pa,
2902 enum isl_dim_type type, unsigned pos);
2903 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2904 enum isl_dim_type type, unsigned pos);
2905 __isl_give isl_id *isl_pw_aff_get_dim_id(
2906 __isl_keep isl_pw_aff *pa,
2907 enum isl_dim_type type, unsigned pos);
2908 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2910 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2911 enum isl_dim_type type, int pos, isl_int *v);
2912 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2914 __isl_give isl_aff *isl_aff_get_div(
2915 __isl_keep isl_aff *aff, int pos);
2917 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2918 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2919 int (*fn)(__isl_take isl_set *set,
2920 __isl_take isl_aff *aff,
2921 void *user), void *user);
2923 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2924 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2926 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2927 enum isl_dim_type type, unsigned first, unsigned n);
2928 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2929 enum isl_dim_type type, unsigned first, unsigned n);
2931 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2932 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2933 enum isl_dim_type type);
2934 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2936 It can be modified using
2938 #include <isl/aff.h>
2939 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2940 __isl_take isl_pw_aff *pwaff,
2941 enum isl_dim_type type, __isl_take isl_id *id);
2942 __isl_give isl_aff *isl_aff_set_dim_name(
2943 __isl_take isl_aff *aff, enum isl_dim_type type,
2944 unsigned pos, const char *s);
2945 __isl_give isl_aff *isl_aff_set_dim_id(
2946 __isl_take isl_aff *aff, enum isl_dim_type type,
2947 unsigned pos, __isl_take isl_id *id);
2948 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2949 __isl_take isl_pw_aff *pma,
2950 enum isl_dim_type type, unsigned pos,
2951 __isl_take isl_id *id);
2952 __isl_give isl_aff *isl_aff_set_constant(
2953 __isl_take isl_aff *aff, isl_int v);
2954 __isl_give isl_aff *isl_aff_set_constant_si(
2955 __isl_take isl_aff *aff, int v);
2956 __isl_give isl_aff *isl_aff_set_coefficient(
2957 __isl_take isl_aff *aff,
2958 enum isl_dim_type type, int pos, isl_int v);
2959 __isl_give isl_aff *isl_aff_set_coefficient_si(
2960 __isl_take isl_aff *aff,
2961 enum isl_dim_type type, int pos, int v);
2962 __isl_give isl_aff *isl_aff_set_denominator(
2963 __isl_take isl_aff *aff, isl_int v);
2965 __isl_give isl_aff *isl_aff_add_constant(
2966 __isl_take isl_aff *aff, isl_int v);
2967 __isl_give isl_aff *isl_aff_add_constant_si(
2968 __isl_take isl_aff *aff, int v);
2969 __isl_give isl_aff *isl_aff_add_coefficient(
2970 __isl_take isl_aff *aff,
2971 enum isl_dim_type type, int pos, isl_int v);
2972 __isl_give isl_aff *isl_aff_add_coefficient_si(
2973 __isl_take isl_aff *aff,
2974 enum isl_dim_type type, int pos, int v);
2976 __isl_give isl_aff *isl_aff_insert_dims(
2977 __isl_take isl_aff *aff,
2978 enum isl_dim_type type, unsigned first, unsigned n);
2979 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2980 __isl_take isl_pw_aff *pwaff,
2981 enum isl_dim_type type, unsigned first, unsigned n);
2982 __isl_give isl_aff *isl_aff_add_dims(
2983 __isl_take isl_aff *aff,
2984 enum isl_dim_type type, unsigned n);
2985 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2986 __isl_take isl_pw_aff *pwaff,
2987 enum isl_dim_type type, unsigned n);
2988 __isl_give isl_aff *isl_aff_drop_dims(
2989 __isl_take isl_aff *aff,
2990 enum isl_dim_type type, unsigned first, unsigned n);
2991 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2992 __isl_take isl_pw_aff *pwaff,
2993 enum isl_dim_type type, unsigned first, unsigned n);
2995 Note that the C<set_constant> and C<set_coefficient> functions
2996 set the I<numerator> of the constant or coefficient, while
2997 C<add_constant> and C<add_coefficient> add an integer value to
2998 the possibly rational constant or coefficient.
3000 To check whether an affine expressions is obviously zero
3001 or obviously equal to some other affine expression, use
3003 #include <isl/aff.h>
3004 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3005 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3006 __isl_keep isl_aff *aff2);
3007 int isl_pw_aff_plain_is_equal(
3008 __isl_keep isl_pw_aff *pwaff1,
3009 __isl_keep isl_pw_aff *pwaff2);
3013 #include <isl/aff.h>
3014 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3015 __isl_take isl_aff *aff2);
3016 __isl_give isl_pw_aff *isl_pw_aff_add(
3017 __isl_take isl_pw_aff *pwaff1,
3018 __isl_take isl_pw_aff *pwaff2);
3019 __isl_give isl_pw_aff *isl_pw_aff_min(
3020 __isl_take isl_pw_aff *pwaff1,
3021 __isl_take isl_pw_aff *pwaff2);
3022 __isl_give isl_pw_aff *isl_pw_aff_max(
3023 __isl_take isl_pw_aff *pwaff1,
3024 __isl_take isl_pw_aff *pwaff2);
3025 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3026 __isl_take isl_aff *aff2);
3027 __isl_give isl_pw_aff *isl_pw_aff_sub(
3028 __isl_take isl_pw_aff *pwaff1,
3029 __isl_take isl_pw_aff *pwaff2);
3030 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3031 __isl_give isl_pw_aff *isl_pw_aff_neg(
3032 __isl_take isl_pw_aff *pwaff);
3033 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3034 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3035 __isl_take isl_pw_aff *pwaff);
3036 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3037 __isl_give isl_pw_aff *isl_pw_aff_floor(
3038 __isl_take isl_pw_aff *pwaff);
3039 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3041 __isl_give isl_pw_aff *isl_pw_aff_mod(
3042 __isl_take isl_pw_aff *pwaff, isl_int mod);
3043 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3045 __isl_give isl_pw_aff *isl_pw_aff_scale(
3046 __isl_take isl_pw_aff *pwaff, isl_int f);
3047 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3049 __isl_give isl_aff *isl_aff_scale_down_ui(
3050 __isl_take isl_aff *aff, unsigned f);
3051 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3052 __isl_take isl_pw_aff *pwaff, isl_int f);
3054 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3055 __isl_take isl_pw_aff_list *list);
3056 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3057 __isl_take isl_pw_aff_list *list);
3059 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3060 __isl_take isl_pw_aff *pwqp);
3062 __isl_give isl_aff *isl_aff_align_params(
3063 __isl_take isl_aff *aff,
3064 __isl_take isl_space *model);
3065 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3066 __isl_take isl_pw_aff *pwaff,
3067 __isl_take isl_space *model);
3069 __isl_give isl_aff *isl_aff_project_domain_on_params(
3070 __isl_take isl_aff *aff);
3072 __isl_give isl_aff *isl_aff_gist_params(
3073 __isl_take isl_aff *aff,
3074 __isl_take isl_set *context);
3075 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3076 __isl_take isl_set *context);
3077 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3078 __isl_take isl_pw_aff *pwaff,
3079 __isl_take isl_set *context);
3080 __isl_give isl_pw_aff *isl_pw_aff_gist(
3081 __isl_take isl_pw_aff *pwaff,
3082 __isl_take isl_set *context);
3084 __isl_give isl_set *isl_pw_aff_domain(
3085 __isl_take isl_pw_aff *pwaff);
3086 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3087 __isl_take isl_pw_aff *pa,
3088 __isl_take isl_set *set);
3089 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3090 __isl_take isl_pw_aff *pa,
3091 __isl_take isl_set *set);
3093 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3094 __isl_take isl_aff *aff2);
3095 __isl_give isl_pw_aff *isl_pw_aff_mul(
3096 __isl_take isl_pw_aff *pwaff1,
3097 __isl_take isl_pw_aff *pwaff2);
3099 When multiplying two affine expressions, at least one of the two needs
3102 #include <isl/aff.h>
3103 __isl_give isl_basic_set *isl_aff_le_basic_set(
3104 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3105 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3106 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3107 __isl_give isl_set *isl_pw_aff_eq_set(
3108 __isl_take isl_pw_aff *pwaff1,
3109 __isl_take isl_pw_aff *pwaff2);
3110 __isl_give isl_set *isl_pw_aff_ne_set(
3111 __isl_take isl_pw_aff *pwaff1,
3112 __isl_take isl_pw_aff *pwaff2);
3113 __isl_give isl_set *isl_pw_aff_le_set(
3114 __isl_take isl_pw_aff *pwaff1,
3115 __isl_take isl_pw_aff *pwaff2);
3116 __isl_give isl_set *isl_pw_aff_lt_set(
3117 __isl_take isl_pw_aff *pwaff1,
3118 __isl_take isl_pw_aff *pwaff2);
3119 __isl_give isl_set *isl_pw_aff_ge_set(
3120 __isl_take isl_pw_aff *pwaff1,
3121 __isl_take isl_pw_aff *pwaff2);
3122 __isl_give isl_set *isl_pw_aff_gt_set(
3123 __isl_take isl_pw_aff *pwaff1,
3124 __isl_take isl_pw_aff *pwaff2);
3126 __isl_give isl_set *isl_pw_aff_list_eq_set(
3127 __isl_take isl_pw_aff_list *list1,
3128 __isl_take isl_pw_aff_list *list2);
3129 __isl_give isl_set *isl_pw_aff_list_ne_set(
3130 __isl_take isl_pw_aff_list *list1,
3131 __isl_take isl_pw_aff_list *list2);
3132 __isl_give isl_set *isl_pw_aff_list_le_set(
3133 __isl_take isl_pw_aff_list *list1,
3134 __isl_take isl_pw_aff_list *list2);
3135 __isl_give isl_set *isl_pw_aff_list_lt_set(
3136 __isl_take isl_pw_aff_list *list1,
3137 __isl_take isl_pw_aff_list *list2);
3138 __isl_give isl_set *isl_pw_aff_list_ge_set(
3139 __isl_take isl_pw_aff_list *list1,
3140 __isl_take isl_pw_aff_list *list2);
3141 __isl_give isl_set *isl_pw_aff_list_gt_set(
3142 __isl_take isl_pw_aff_list *list1,
3143 __isl_take isl_pw_aff_list *list2);
3145 The function C<isl_aff_ge_basic_set> returns a basic set
3146 containing those elements in the shared space
3147 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3148 The function C<isl_aff_ge_set> returns a set
3149 containing those elements in the shared domain
3150 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3151 The functions operating on C<isl_pw_aff_list> apply the corresponding
3152 C<isl_pw_aff> function to each pair of elements in the two lists.
3154 #include <isl/aff.h>
3155 __isl_give isl_set *isl_pw_aff_nonneg_set(
3156 __isl_take isl_pw_aff *pwaff);
3157 __isl_give isl_set *isl_pw_aff_zero_set(
3158 __isl_take isl_pw_aff *pwaff);
3159 __isl_give isl_set *isl_pw_aff_non_zero_set(
3160 __isl_take isl_pw_aff *pwaff);
3162 The function C<isl_pw_aff_nonneg_set> returns a set
3163 containing those elements in the domain
3164 of C<pwaff> where C<pwaff> is non-negative.
3166 #include <isl/aff.h>
3167 __isl_give isl_pw_aff *isl_pw_aff_cond(
3168 __isl_take isl_pw_aff *cond,
3169 __isl_take isl_pw_aff *pwaff_true,
3170 __isl_take isl_pw_aff *pwaff_false);
3172 The function C<isl_pw_aff_cond> performs a conditional operator
3173 and returns an expression that is equal to C<pwaff_true>
3174 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3175 where C<cond> is zero.
3177 #include <isl/aff.h>
3178 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3179 __isl_take isl_pw_aff *pwaff1,
3180 __isl_take isl_pw_aff *pwaff2);
3181 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3182 __isl_take isl_pw_aff *pwaff1,
3183 __isl_take isl_pw_aff *pwaff2);
3184 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3185 __isl_take isl_pw_aff *pwaff1,
3186 __isl_take isl_pw_aff *pwaff2);
3188 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3189 expression with a domain that is the union of those of C<pwaff1> and
3190 C<pwaff2> and such that on each cell, the quasi-affine expression is
3191 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3192 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3193 associated expression is the defined one.
3195 An expression can be read from input using
3197 #include <isl/aff.h>
3198 __isl_give isl_aff *isl_aff_read_from_str(
3199 isl_ctx *ctx, const char *str);
3200 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3201 isl_ctx *ctx, const char *str);
3203 An expression can be printed using
3205 #include <isl/aff.h>
3206 __isl_give isl_printer *isl_printer_print_aff(
3207 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3209 __isl_give isl_printer *isl_printer_print_pw_aff(
3210 __isl_take isl_printer *p,
3211 __isl_keep isl_pw_aff *pwaff);
3213 =head2 Piecewise Multiple Quasi Affine Expressions
3215 An C<isl_multi_aff> object represents a sequence of
3216 zero or more affine expressions, all defined on the same domain space.
3218 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3221 #include <isl/aff.h>
3222 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3223 __isl_take isl_space *space,
3224 __isl_take isl_aff_list *list);
3226 An empty piecewise multiple quasi affine expression (one with no cells),
3227 the zero piecewise multiple quasi affine expression (with value zero
3228 for each output dimension),
3229 a piecewise multiple quasi affine expression with a single cell (with
3230 either a universe or a specified domain) or
3231 a zero-dimensional piecewise multiple quasi affine expression
3233 can be created using the following functions.
3235 #include <isl/aff.h>
3236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3237 __isl_take isl_space *space);
3238 __isl_give isl_multi_aff *isl_multi_aff_zero(
3239 __isl_take isl_space *space);
3240 __isl_give isl_pw_multi_aff *
3241 isl_pw_multi_aff_from_multi_aff(
3242 __isl_take isl_multi_aff *ma);
3243 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3244 __isl_take isl_set *set,
3245 __isl_take isl_multi_aff *maff);
3246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3247 __isl_take isl_set *set);
3249 __isl_give isl_union_pw_multi_aff *
3250 isl_union_pw_multi_aff_empty(
3251 __isl_take isl_space *space);
3252 __isl_give isl_union_pw_multi_aff *
3253 isl_union_pw_multi_aff_add_pw_multi_aff(
3254 __isl_take isl_union_pw_multi_aff *upma,
3255 __isl_take isl_pw_multi_aff *pma);
3256 __isl_give isl_union_pw_multi_aff *
3257 isl_union_pw_multi_aff_from_domain(
3258 __isl_take isl_union_set *uset);
3260 A piecewise multiple quasi affine expression can also be initialized
3261 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3262 and the C<isl_map> is single-valued.
3264 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3265 __isl_take isl_set *set);
3266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3267 __isl_take isl_map *map);
3269 Multiple quasi affine expressions can be copied and freed using
3271 #include <isl/aff.h>
3272 __isl_give isl_multi_aff *isl_multi_aff_copy(
3273 __isl_keep isl_multi_aff *maff);
3274 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3276 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3277 __isl_keep isl_pw_multi_aff *pma);
3278 void *isl_pw_multi_aff_free(
3279 __isl_take isl_pw_multi_aff *pma);
3281 __isl_give isl_union_pw_multi_aff *
3282 isl_union_pw_multi_aff_copy(
3283 __isl_keep isl_union_pw_multi_aff *upma);
3284 void *isl_union_pw_multi_aff_free(
3285 __isl_take isl_union_pw_multi_aff *upma);
3287 The expression can be inspected using
3289 #include <isl/aff.h>
3290 isl_ctx *isl_multi_aff_get_ctx(
3291 __isl_keep isl_multi_aff *maff);
3292 isl_ctx *isl_pw_multi_aff_get_ctx(
3293 __isl_keep isl_pw_multi_aff *pma);
3294 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3295 __isl_keep isl_union_pw_multi_aff *upma);
3296 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3297 enum isl_dim_type type);
3298 unsigned isl_pw_multi_aff_dim(
3299 __isl_keep isl_pw_multi_aff *pma,
3300 enum isl_dim_type type);
3301 __isl_give isl_aff *isl_multi_aff_get_aff(
3302 __isl_keep isl_multi_aff *multi, int pos);
3303 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3304 __isl_keep isl_pw_multi_aff *pma, int pos);
3305 const char *isl_pw_multi_aff_get_dim_name(
3306 __isl_keep isl_pw_multi_aff *pma,
3307 enum isl_dim_type type, unsigned pos);
3308 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3309 __isl_keep isl_pw_multi_aff *pma,
3310 enum isl_dim_type type, unsigned pos);
3311 const char *isl_multi_aff_get_tuple_name(
3312 __isl_keep isl_multi_aff *multi,
3313 enum isl_dim_type type);
3314 const char *isl_pw_multi_aff_get_tuple_name(
3315 __isl_keep isl_pw_multi_aff *pma,
3316 enum isl_dim_type type);
3317 int isl_pw_multi_aff_has_tuple_id(
3318 __isl_keep isl_pw_multi_aff *pma,
3319 enum isl_dim_type type);
3320 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3321 __isl_keep isl_pw_multi_aff *pma,
3322 enum isl_dim_type type);
3324 int isl_pw_multi_aff_foreach_piece(
3325 __isl_keep isl_pw_multi_aff *pma,
3326 int (*fn)(__isl_take isl_set *set,
3327 __isl_take isl_multi_aff *maff,
3328 void *user), void *user);
3330 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3331 __isl_keep isl_union_pw_multi_aff *upma,
3332 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3333 void *user), void *user);
3335 It can be modified using
3337 #include <isl/aff.h>
3338 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3339 __isl_take isl_multi_aff *multi, int pos,
3340 __isl_take isl_aff *aff);
3341 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3342 __isl_take isl_multi_aff *maff,
3343 enum isl_dim_type type, unsigned pos, const char *s);
3344 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3345 __isl_take isl_multi_aff *maff,
3346 enum isl_dim_type type, __isl_take isl_id *id);
3347 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3348 __isl_take isl_pw_multi_aff *pma,
3349 enum isl_dim_type type, __isl_take isl_id *id);
3351 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3352 __isl_take isl_multi_aff *maff,
3353 enum isl_dim_type type, unsigned first, unsigned n);
3355 To check whether two multiple affine expressions are
3356 obviously equal to each other, use
3358 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3359 __isl_keep isl_multi_aff *maff2);
3360 int isl_pw_multi_aff_plain_is_equal(
3361 __isl_keep isl_pw_multi_aff *pma1,
3362 __isl_keep isl_pw_multi_aff *pma2);
3366 #include <isl/aff.h>
3367 __isl_give isl_multi_aff *isl_multi_aff_add(
3368 __isl_take isl_multi_aff *maff1,
3369 __isl_take isl_multi_aff *maff2);
3370 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3371 __isl_take isl_pw_multi_aff *pma1,
3372 __isl_take isl_pw_multi_aff *pma2);
3373 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3374 __isl_take isl_union_pw_multi_aff *upma1,
3375 __isl_take isl_union_pw_multi_aff *upma2);
3376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3377 __isl_take isl_pw_multi_aff *pma1,
3378 __isl_take isl_pw_multi_aff *pma2);
3379 __isl_give isl_multi_aff *isl_multi_aff_scale(
3380 __isl_take isl_multi_aff *maff,
3382 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3383 __isl_take isl_pw_multi_aff *pma,
3384 __isl_take isl_set *set);
3385 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3386 __isl_take isl_pw_multi_aff *pma,
3387 __isl_take isl_set *set);
3388 __isl_give isl_multi_aff *isl_multi_aff_lift(
3389 __isl_take isl_multi_aff *maff,
3390 __isl_give isl_local_space **ls);
3391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3392 __isl_take isl_pw_multi_aff *pma);
3393 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3394 __isl_take isl_multi_aff *maff,
3395 __isl_take isl_set *context);
3396 __isl_give isl_multi_aff *isl_multi_aff_gist(
3397 __isl_take isl_multi_aff *maff,
3398 __isl_take isl_set *context);
3399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3400 __isl_take isl_pw_multi_aff *pma,
3401 __isl_take isl_set *set);
3402 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3403 __isl_take isl_pw_multi_aff *pma,
3404 __isl_take isl_set *set);
3405 __isl_give isl_set *isl_pw_multi_aff_domain(
3406 __isl_take isl_pw_multi_aff *pma);
3407 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3408 __isl_take isl_union_pw_multi_aff *upma);
3409 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3410 __isl_take isl_multi_aff *ma1,
3411 __isl_take isl_multi_aff *ma2);
3412 __isl_give isl_pw_multi_aff *
3413 isl_pw_multi_aff_flat_range_product(
3414 __isl_take isl_pw_multi_aff *pma1,
3415 __isl_take isl_pw_multi_aff *pma2);
3416 __isl_give isl_union_pw_multi_aff *
3417 isl_union_pw_multi_aff_flat_range_product(
3418 __isl_take isl_union_pw_multi_aff *upma1,
3419 __isl_take isl_union_pw_multi_aff *upma2);
3421 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3422 then it is assigned the local space that lies at the basis of
3423 the lifting applied.
3425 An expression can be read from input using
3427 #include <isl/aff.h>
3428 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3429 isl_ctx *ctx, const char *str);
3430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3431 isl_ctx *ctx, const char *str);
3433 An expression can be printed using
3435 #include <isl/aff.h>
3436 __isl_give isl_printer *isl_printer_print_multi_aff(
3437 __isl_take isl_printer *p,
3438 __isl_keep isl_multi_aff *maff);
3439 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3440 __isl_take isl_printer *p,
3441 __isl_keep isl_pw_multi_aff *pma);
3442 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3443 __isl_take isl_printer *p,
3444 __isl_keep isl_union_pw_multi_aff *upma);
3448 Points are elements of a set. They can be used to construct
3449 simple sets (boxes) or they can be used to represent the
3450 individual elements of a set.
3451 The zero point (the origin) can be created using
3453 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3455 The coordinates of a point can be inspected, set and changed
3458 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3459 enum isl_dim_type type, int pos, isl_int *v);
3460 __isl_give isl_point *isl_point_set_coordinate(
3461 __isl_take isl_point *pnt,
3462 enum isl_dim_type type, int pos, isl_int v);
3464 __isl_give isl_point *isl_point_add_ui(
3465 __isl_take isl_point *pnt,
3466 enum isl_dim_type type, int pos, unsigned val);
3467 __isl_give isl_point *isl_point_sub_ui(
3468 __isl_take isl_point *pnt,
3469 enum isl_dim_type type, int pos, unsigned val);
3471 Other properties can be obtained using
3473 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3475 Points can be copied or freed using
3477 __isl_give isl_point *isl_point_copy(
3478 __isl_keep isl_point *pnt);
3479 void isl_point_free(__isl_take isl_point *pnt);
3481 A singleton set can be created from a point using
3483 __isl_give isl_basic_set *isl_basic_set_from_point(
3484 __isl_take isl_point *pnt);
3485 __isl_give isl_set *isl_set_from_point(
3486 __isl_take isl_point *pnt);
3488 and a box can be created from two opposite extremal points using
3490 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3491 __isl_take isl_point *pnt1,
3492 __isl_take isl_point *pnt2);
3493 __isl_give isl_set *isl_set_box_from_points(
3494 __isl_take isl_point *pnt1,
3495 __isl_take isl_point *pnt2);
3497 All elements of a B<bounded> (union) set can be enumerated using
3498 the following functions.
3500 int isl_set_foreach_point(__isl_keep isl_set *set,
3501 int (*fn)(__isl_take isl_point *pnt, void *user),
3503 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3504 int (*fn)(__isl_take isl_point *pnt, void *user),
3507 The function C<fn> is called for each integer point in
3508 C<set> with as second argument the last argument of
3509 the C<isl_set_foreach_point> call. The function C<fn>
3510 should return C<0> on success and C<-1> on failure.
3511 In the latter case, C<isl_set_foreach_point> will stop
3512 enumerating and return C<-1> as well.
3513 If the enumeration is performed successfully and to completion,
3514 then C<isl_set_foreach_point> returns C<0>.
3516 To obtain a single point of a (basic) set, use
3518 __isl_give isl_point *isl_basic_set_sample_point(
3519 __isl_take isl_basic_set *bset);
3520 __isl_give isl_point *isl_set_sample_point(
3521 __isl_take isl_set *set);
3523 If C<set> does not contain any (integer) points, then the
3524 resulting point will be ``void'', a property that can be
3527 int isl_point_is_void(__isl_keep isl_point *pnt);
3529 =head2 Piecewise Quasipolynomials
3531 A piecewise quasipolynomial is a particular kind of function that maps
3532 a parametric point to a rational value.
3533 More specifically, a quasipolynomial is a polynomial expression in greatest
3534 integer parts of affine expressions of parameters and variables.
3535 A piecewise quasipolynomial is a subdivision of a given parametric
3536 domain into disjoint cells with a quasipolynomial associated to
3537 each cell. The value of the piecewise quasipolynomial at a given
3538 point is the value of the quasipolynomial associated to the cell
3539 that contains the point. Outside of the union of cells,
3540 the value is assumed to be zero.
3541 For example, the piecewise quasipolynomial
3543 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3545 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3546 A given piecewise quasipolynomial has a fixed domain dimension.
3547 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3548 defined over different domains.
3549 Piecewise quasipolynomials are mainly used by the C<barvinok>
3550 library for representing the number of elements in a parametric set or map.
3551 For example, the piecewise quasipolynomial above represents
3552 the number of points in the map
3554 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3556 =head3 Input and Output
3558 Piecewise quasipolynomials can be read from input using
3560 __isl_give isl_union_pw_qpolynomial *
3561 isl_union_pw_qpolynomial_read_from_str(
3562 isl_ctx *ctx, const char *str);
3564 Quasipolynomials and piecewise quasipolynomials can be printed
3565 using the following functions.
3567 __isl_give isl_printer *isl_printer_print_qpolynomial(
3568 __isl_take isl_printer *p,
3569 __isl_keep isl_qpolynomial *qp);
3571 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3572 __isl_take isl_printer *p,
3573 __isl_keep isl_pw_qpolynomial *pwqp);
3575 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3576 __isl_take isl_printer *p,
3577 __isl_keep isl_union_pw_qpolynomial *upwqp);
3579 The output format of the printer
3580 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3581 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3583 In case of printing in C<ISL_FORMAT_C>, the user may want
3584 to set the names of all dimensions
3586 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3587 __isl_take isl_qpolynomial *qp,
3588 enum isl_dim_type type, unsigned pos,
3590 __isl_give isl_pw_qpolynomial *
3591 isl_pw_qpolynomial_set_dim_name(
3592 __isl_take isl_pw_qpolynomial *pwqp,
3593 enum isl_dim_type type, unsigned pos,
3596 =head3 Creating New (Piecewise) Quasipolynomials
3598 Some simple quasipolynomials can be created using the following functions.
3599 More complicated quasipolynomials can be created by applying
3600 operations such as addition and multiplication
3601 on the resulting quasipolynomials
3603 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3604 __isl_take isl_space *domain);
3605 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3606 __isl_take isl_space *domain);
3607 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3608 __isl_take isl_space *domain);
3609 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3610 __isl_take isl_space *domain);
3611 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3612 __isl_take isl_space *domain);
3613 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3614 __isl_take isl_space *domain,
3615 const isl_int n, const isl_int d);
3616 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3617 __isl_take isl_space *domain,
3618 enum isl_dim_type type, unsigned pos);
3619 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3620 __isl_take isl_aff *aff);
3622 Note that the space in which a quasipolynomial lives is a map space
3623 with a one-dimensional range. The C<domain> argument in some of
3624 the functions above corresponds to the domain of this map space.
3626 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3627 with a single cell can be created using the following functions.
3628 Multiple of these single cell piecewise quasipolynomials can
3629 be combined to create more complicated piecewise quasipolynomials.
3631 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3632 __isl_take isl_space *space);
3633 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3634 __isl_take isl_set *set,
3635 __isl_take isl_qpolynomial *qp);
3636 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3637 __isl_take isl_qpolynomial *qp);
3638 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3639 __isl_take isl_pw_aff *pwaff);
3641 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3642 __isl_take isl_space *space);
3643 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3644 __isl_take isl_pw_qpolynomial *pwqp);
3645 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3646 __isl_take isl_union_pw_qpolynomial *upwqp,
3647 __isl_take isl_pw_qpolynomial *pwqp);
3649 Quasipolynomials can be copied and freed again using the following
3652 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3653 __isl_keep isl_qpolynomial *qp);
3654 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3656 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3657 __isl_keep isl_pw_qpolynomial *pwqp);
3658 void *isl_pw_qpolynomial_free(
3659 __isl_take isl_pw_qpolynomial *pwqp);
3661 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3662 __isl_keep isl_union_pw_qpolynomial *upwqp);
3663 void *isl_union_pw_qpolynomial_free(
3664 __isl_take isl_union_pw_qpolynomial *upwqp);
3666 =head3 Inspecting (Piecewise) Quasipolynomials
3668 To iterate over all piecewise quasipolynomials in a union
3669 piecewise quasipolynomial, use the following function
3671 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3672 __isl_keep isl_union_pw_qpolynomial *upwqp,
3673 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3676 To extract the piecewise quasipolynomial in a given space from a union, use
3678 __isl_give isl_pw_qpolynomial *
3679 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3680 __isl_keep isl_union_pw_qpolynomial *upwqp,
3681 __isl_take isl_space *space);
3683 To iterate over the cells in a piecewise quasipolynomial,
3684 use either of the following two functions
3686 int isl_pw_qpolynomial_foreach_piece(
3687 __isl_keep isl_pw_qpolynomial *pwqp,
3688 int (*fn)(__isl_take isl_set *set,
3689 __isl_take isl_qpolynomial *qp,
3690 void *user), void *user);
3691 int isl_pw_qpolynomial_foreach_lifted_piece(
3692 __isl_keep isl_pw_qpolynomial *pwqp,
3693 int (*fn)(__isl_take isl_set *set,
3694 __isl_take isl_qpolynomial *qp,
3695 void *user), void *user);
3697 As usual, the function C<fn> should return C<0> on success
3698 and C<-1> on failure. The difference between
3699 C<isl_pw_qpolynomial_foreach_piece> and
3700 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3701 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3702 compute unique representations for all existentially quantified
3703 variables and then turn these existentially quantified variables
3704 into extra set variables, adapting the associated quasipolynomial
3705 accordingly. This means that the C<set> passed to C<fn>
3706 will not have any existentially quantified variables, but that
3707 the dimensions of the sets may be different for different
3708 invocations of C<fn>.
3710 To iterate over all terms in a quasipolynomial,
3713 int isl_qpolynomial_foreach_term(
3714 __isl_keep isl_qpolynomial *qp,
3715 int (*fn)(__isl_take isl_term *term,
3716 void *user), void *user);
3718 The terms themselves can be inspected and freed using
3721 unsigned isl_term_dim(__isl_keep isl_term *term,
3722 enum isl_dim_type type);
3723 void isl_term_get_num(__isl_keep isl_term *term,
3725 void isl_term_get_den(__isl_keep isl_term *term,
3727 int isl_term_get_exp(__isl_keep isl_term *term,
3728 enum isl_dim_type type, unsigned pos);
3729 __isl_give isl_aff *isl_term_get_div(
3730 __isl_keep isl_term *term, unsigned pos);
3731 void isl_term_free(__isl_take isl_term *term);
3733 Each term is a product of parameters, set variables and
3734 integer divisions. The function C<isl_term_get_exp>
3735 returns the exponent of a given dimensions in the given term.
3736 The C<isl_int>s in the arguments of C<isl_term_get_num>
3737 and C<isl_term_get_den> need to have been initialized
3738 using C<isl_int_init> before calling these functions.
3740 =head3 Properties of (Piecewise) Quasipolynomials
3742 To check whether a quasipolynomial is actually a constant,
3743 use the following function.
3745 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3746 isl_int *n, isl_int *d);
3748 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3749 then the numerator and denominator of the constant
3750 are returned in C<*n> and C<*d>, respectively.
3752 To check whether two union piecewise quasipolynomials are
3753 obviously equal, use
3755 int isl_union_pw_qpolynomial_plain_is_equal(
3756 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3757 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3759 =head3 Operations on (Piecewise) Quasipolynomials
3761 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3762 __isl_take isl_qpolynomial *qp, isl_int v);
3763 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3764 __isl_take isl_qpolynomial *qp);
3765 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3766 __isl_take isl_qpolynomial *qp1,
3767 __isl_take isl_qpolynomial *qp2);
3768 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3769 __isl_take isl_qpolynomial *qp1,
3770 __isl_take isl_qpolynomial *qp2);
3771 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3772 __isl_take isl_qpolynomial *qp1,
3773 __isl_take isl_qpolynomial *qp2);
3774 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3775 __isl_take isl_qpolynomial *qp, unsigned exponent);
3777 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3778 __isl_take isl_pw_qpolynomial *pwqp1,
3779 __isl_take isl_pw_qpolynomial *pwqp2);
3780 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3781 __isl_take isl_pw_qpolynomial *pwqp1,
3782 __isl_take isl_pw_qpolynomial *pwqp2);
3783 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3784 __isl_take isl_pw_qpolynomial *pwqp1,
3785 __isl_take isl_pw_qpolynomial *pwqp2);
3786 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3787 __isl_take isl_pw_qpolynomial *pwqp);
3788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3789 __isl_take isl_pw_qpolynomial *pwqp1,
3790 __isl_take isl_pw_qpolynomial *pwqp2);
3791 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3792 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3794 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3795 __isl_take isl_union_pw_qpolynomial *upwqp1,
3796 __isl_take isl_union_pw_qpolynomial *upwqp2);
3797 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3798 __isl_take isl_union_pw_qpolynomial *upwqp1,
3799 __isl_take isl_union_pw_qpolynomial *upwqp2);
3800 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3801 __isl_take isl_union_pw_qpolynomial *upwqp1,
3802 __isl_take isl_union_pw_qpolynomial *upwqp2);
3804 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3805 __isl_take isl_pw_qpolynomial *pwqp,
3806 __isl_take isl_point *pnt);
3808 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3809 __isl_take isl_union_pw_qpolynomial *upwqp,
3810 __isl_take isl_point *pnt);
3812 __isl_give isl_set *isl_pw_qpolynomial_domain(
3813 __isl_take isl_pw_qpolynomial *pwqp);
3814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3815 __isl_take isl_pw_qpolynomial *pwpq,
3816 __isl_take isl_set *set);
3817 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3818 __isl_take isl_pw_qpolynomial *pwpq,
3819 __isl_take isl_set *set);
3821 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3822 __isl_take isl_union_pw_qpolynomial *upwqp);
3823 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3824 __isl_take isl_union_pw_qpolynomial *upwpq,
3825 __isl_take isl_union_set *uset);
3826 __isl_give isl_union_pw_qpolynomial *
3827 isl_union_pw_qpolynomial_intersect_params(
3828 __isl_take isl_union_pw_qpolynomial *upwpq,
3829 __isl_take isl_set *set);
3831 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3832 __isl_take isl_qpolynomial *qp,
3833 __isl_take isl_space *model);
3835 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3836 __isl_take isl_qpolynomial *qp);
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3838 __isl_take isl_pw_qpolynomial *pwqp);
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3841 __isl_take isl_union_pw_qpolynomial *upwqp);
3843 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3844 __isl_take isl_qpolynomial *qp,
3845 __isl_take isl_set *context);
3846 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3847 __isl_take isl_qpolynomial *qp,
3848 __isl_take isl_set *context);
3850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3851 __isl_take isl_pw_qpolynomial *pwqp,
3852 __isl_take isl_set *context);
3853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3854 __isl_take isl_pw_qpolynomial *pwqp,
3855 __isl_take isl_set *context);
3857 __isl_give isl_union_pw_qpolynomial *
3858 isl_union_pw_qpolynomial_gist_params(
3859 __isl_take isl_union_pw_qpolynomial *upwqp,
3860 __isl_take isl_set *context);
3861 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3862 __isl_take isl_union_pw_qpolynomial *upwqp,
3863 __isl_take isl_union_set *context);
3865 The gist operation applies the gist operation to each of
3866 the cells in the domain of the input piecewise quasipolynomial.
3867 The context is also exploited
3868 to simplify the quasipolynomials associated to each cell.
3870 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3871 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3872 __isl_give isl_union_pw_qpolynomial *
3873 isl_union_pw_qpolynomial_to_polynomial(
3874 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3876 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3877 the polynomial will be an overapproximation. If C<sign> is negative,
3878 it will be an underapproximation. If C<sign> is zero, the approximation
3879 will lie somewhere in between.
3881 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3883 A piecewise quasipolynomial reduction is a piecewise
3884 reduction (or fold) of quasipolynomials.
3885 In particular, the reduction can be maximum or a minimum.
3886 The objects are mainly used to represent the result of
3887 an upper or lower bound on a quasipolynomial over its domain,
3888 i.e., as the result of the following function.
3890 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3891 __isl_take isl_pw_qpolynomial *pwqp,
3892 enum isl_fold type, int *tight);
3894 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3895 __isl_take isl_union_pw_qpolynomial *upwqp,
3896 enum isl_fold type, int *tight);
3898 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3899 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3900 is the returned bound is known be tight, i.e., for each value
3901 of the parameters there is at least
3902 one element in the domain that reaches the bound.
3903 If the domain of C<pwqp> is not wrapping, then the bound is computed
3904 over all elements in that domain and the result has a purely parametric
3905 domain. If the domain of C<pwqp> is wrapping, then the bound is
3906 computed over the range of the wrapped relation. The domain of the
3907 wrapped relation becomes the domain of the result.
3909 A (piecewise) quasipolynomial reduction can be copied or freed using the
3910 following functions.
3912 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3913 __isl_keep isl_qpolynomial_fold *fold);
3914 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3915 __isl_keep isl_pw_qpolynomial_fold *pwf);
3916 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3917 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3918 void isl_qpolynomial_fold_free(
3919 __isl_take isl_qpolynomial_fold *fold);
3920 void *isl_pw_qpolynomial_fold_free(
3921 __isl_take isl_pw_qpolynomial_fold *pwf);
3922 void *isl_union_pw_qpolynomial_fold_free(
3923 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3925 =head3 Printing Piecewise Quasipolynomial Reductions
3927 Piecewise quasipolynomial reductions can be printed
3928 using the following function.
3930 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3931 __isl_take isl_printer *p,
3932 __isl_keep isl_pw_qpolynomial_fold *pwf);
3933 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3934 __isl_take isl_printer *p,
3935 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3937 For C<isl_printer_print_pw_qpolynomial_fold>,
3938 output format of the printer
3939 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3940 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3941 output format of the printer
3942 needs to be set to C<ISL_FORMAT_ISL>.
3943 In case of printing in C<ISL_FORMAT_C>, the user may want
3944 to set the names of all dimensions
3946 __isl_give isl_pw_qpolynomial_fold *
3947 isl_pw_qpolynomial_fold_set_dim_name(
3948 __isl_take isl_pw_qpolynomial_fold *pwf,
3949 enum isl_dim_type type, unsigned pos,
3952 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3954 To iterate over all piecewise quasipolynomial reductions in a union
3955 piecewise quasipolynomial reduction, use the following function
3957 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3958 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3959 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3960 void *user), void *user);
3962 To iterate over the cells in a piecewise quasipolynomial reduction,
3963 use either of the following two functions
3965 int isl_pw_qpolynomial_fold_foreach_piece(
3966 __isl_keep isl_pw_qpolynomial_fold *pwf,
3967 int (*fn)(__isl_take isl_set *set,
3968 __isl_take isl_qpolynomial_fold *fold,
3969 void *user), void *user);
3970 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3971 __isl_keep isl_pw_qpolynomial_fold *pwf,
3972 int (*fn)(__isl_take isl_set *set,
3973 __isl_take isl_qpolynomial_fold *fold,
3974 void *user), void *user);
3976 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3977 of the difference between these two functions.
3979 To iterate over all quasipolynomials in a reduction, use
3981 int isl_qpolynomial_fold_foreach_qpolynomial(
3982 __isl_keep isl_qpolynomial_fold *fold,
3983 int (*fn)(__isl_take isl_qpolynomial *qp,
3984 void *user), void *user);
3986 =head3 Properties of Piecewise Quasipolynomial Reductions
3988 To check whether two union piecewise quasipolynomial reductions are
3989 obviously equal, use
3991 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3992 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3993 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3995 =head3 Operations on Piecewise Quasipolynomial Reductions
3997 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3998 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4000 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4001 __isl_take isl_pw_qpolynomial_fold *pwf1,
4002 __isl_take isl_pw_qpolynomial_fold *pwf2);
4004 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4005 __isl_take isl_pw_qpolynomial_fold *pwf1,
4006 __isl_take isl_pw_qpolynomial_fold *pwf2);
4008 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4009 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4010 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4012 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4013 __isl_take isl_pw_qpolynomial_fold *pwf,
4014 __isl_take isl_point *pnt);
4016 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4017 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4018 __isl_take isl_point *pnt);
4020 __isl_give isl_pw_qpolynomial_fold *
4021 sl_pw_qpolynomial_fold_intersect_params(
4022 __isl_take isl_pw_qpolynomial_fold *pwf,
4023 __isl_take isl_set *set);
4025 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4026 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4027 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4028 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4029 __isl_take isl_union_set *uset);
4030 __isl_give isl_union_pw_qpolynomial_fold *
4031 isl_union_pw_qpolynomial_fold_intersect_params(
4032 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4033 __isl_take isl_set *set);
4035 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4036 __isl_take isl_pw_qpolynomial_fold *pwf);
4038 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4039 __isl_take isl_pw_qpolynomial_fold *pwf);
4041 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4042 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4044 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4045 __isl_take isl_qpolynomial_fold *fold,
4046 __isl_take isl_set *context);
4047 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4048 __isl_take isl_qpolynomial_fold *fold,
4049 __isl_take isl_set *context);
4051 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4052 __isl_take isl_pw_qpolynomial_fold *pwf,
4053 __isl_take isl_set *context);
4054 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4055 __isl_take isl_pw_qpolynomial_fold *pwf,
4056 __isl_take isl_set *context);
4058 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4059 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4060 __isl_take isl_union_set *context);
4061 __isl_give isl_union_pw_qpolynomial_fold *
4062 isl_union_pw_qpolynomial_fold_gist_params(
4063 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4064 __isl_take isl_set *context);
4066 The gist operation applies the gist operation to each of
4067 the cells in the domain of the input piecewise quasipolynomial reduction.
4068 In future, the operation will also exploit the context
4069 to simplify the quasipolynomial reductions associated to each cell.
4071 __isl_give isl_pw_qpolynomial_fold *
4072 isl_set_apply_pw_qpolynomial_fold(
4073 __isl_take isl_set *set,
4074 __isl_take isl_pw_qpolynomial_fold *pwf,
4076 __isl_give isl_pw_qpolynomial_fold *
4077 isl_map_apply_pw_qpolynomial_fold(
4078 __isl_take isl_map *map,
4079 __isl_take isl_pw_qpolynomial_fold *pwf,
4081 __isl_give isl_union_pw_qpolynomial_fold *
4082 isl_union_set_apply_union_pw_qpolynomial_fold(
4083 __isl_take isl_union_set *uset,
4084 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4086 __isl_give isl_union_pw_qpolynomial_fold *
4087 isl_union_map_apply_union_pw_qpolynomial_fold(
4088 __isl_take isl_union_map *umap,
4089 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4092 The functions taking a map
4093 compose the given map with the given piecewise quasipolynomial reduction.
4094 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4095 over all elements in the intersection of the range of the map
4096 and the domain of the piecewise quasipolynomial reduction
4097 as a function of an element in the domain of the map.
4098 The functions taking a set compute a bound over all elements in the
4099 intersection of the set and the domain of the
4100 piecewise quasipolynomial reduction.
4102 =head2 Dependence Analysis
4104 C<isl> contains specialized functionality for performing
4105 array dataflow analysis. That is, given a I<sink> access relation
4106 and a collection of possible I<source> access relations,
4107 C<isl> can compute relations that describe
4108 for each iteration of the sink access, which iteration
4109 of which of the source access relations was the last
4110 to access the same data element before the given iteration
4112 The resulting dependence relations map source iterations
4113 to the corresponding sink iterations.
4114 To compute standard flow dependences, the sink should be
4115 a read, while the sources should be writes.
4116 If any of the source accesses are marked as being I<may>
4117 accesses, then there will be a dependence from the last
4118 I<must> access B<and> from any I<may> access that follows
4119 this last I<must> access.
4120 In particular, if I<all> sources are I<may> accesses,
4121 then memory based dependence analysis is performed.
4122 If, on the other hand, all sources are I<must> accesses,
4123 then value based dependence analysis is performed.
4125 #include <isl/flow.h>
4127 typedef int (*isl_access_level_before)(void *first, void *second);
4129 __isl_give isl_access_info *isl_access_info_alloc(
4130 __isl_take isl_map *sink,
4131 void *sink_user, isl_access_level_before fn,
4133 __isl_give isl_access_info *isl_access_info_add_source(
4134 __isl_take isl_access_info *acc,
4135 __isl_take isl_map *source, int must,
4137 void isl_access_info_free(__isl_take isl_access_info *acc);
4139 __isl_give isl_flow *isl_access_info_compute_flow(
4140 __isl_take isl_access_info *acc);
4142 int isl_flow_foreach(__isl_keep isl_flow *deps,
4143 int (*fn)(__isl_take isl_map *dep, int must,
4144 void *dep_user, void *user),
4146 __isl_give isl_map *isl_flow_get_no_source(
4147 __isl_keep isl_flow *deps, int must);
4148 void isl_flow_free(__isl_take isl_flow *deps);
4150 The function C<isl_access_info_compute_flow> performs the actual
4151 dependence analysis. The other functions are used to construct
4152 the input for this function or to read off the output.
4154 The input is collected in an C<isl_access_info>, which can
4155 be created through a call to C<isl_access_info_alloc>.
4156 The arguments to this functions are the sink access relation
4157 C<sink>, a token C<sink_user> used to identify the sink
4158 access to the user, a callback function for specifying the
4159 relative order of source and sink accesses, and the number
4160 of source access relations that will be added.
4161 The callback function has type C<int (*)(void *first, void *second)>.
4162 The function is called with two user supplied tokens identifying
4163 either a source or the sink and it should return the shared nesting
4164 level and the relative order of the two accesses.
4165 In particular, let I<n> be the number of loops shared by
4166 the two accesses. If C<first> precedes C<second> textually,
4167 then the function should return I<2 * n + 1>; otherwise,
4168 it should return I<2 * n>.
4169 The sources can be added to the C<isl_access_info> by performing
4170 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4171 C<must> indicates whether the source is a I<must> access
4172 or a I<may> access. Note that a multi-valued access relation
4173 should only be marked I<must> if every iteration in the domain
4174 of the relation accesses I<all> elements in its image.
4175 The C<source_user> token is again used to identify
4176 the source access. The range of the source access relation
4177 C<source> should have the same dimension as the range
4178 of the sink access relation.
4179 The C<isl_access_info_free> function should usually not be
4180 called explicitly, because it is called implicitly by
4181 C<isl_access_info_compute_flow>.
4183 The result of the dependence analysis is collected in an
4184 C<isl_flow>. There may be elements of
4185 the sink access for which no preceding source access could be
4186 found or for which all preceding sources are I<may> accesses.
4187 The relations containing these elements can be obtained through
4188 calls to C<isl_flow_get_no_source>, the first with C<must> set
4189 and the second with C<must> unset.
4190 In the case of standard flow dependence analysis,
4191 with the sink a read and the sources I<must> writes,
4192 the first relation corresponds to the reads from uninitialized
4193 array elements and the second relation is empty.
4194 The actual flow dependences can be extracted using
4195 C<isl_flow_foreach>. This function will call the user-specified
4196 callback function C<fn> for each B<non-empty> dependence between
4197 a source and the sink. The callback function is called
4198 with four arguments, the actual flow dependence relation
4199 mapping source iterations to sink iterations, a boolean that
4200 indicates whether it is a I<must> or I<may> dependence, a token
4201 identifying the source and an additional C<void *> with value
4202 equal to the third argument of the C<isl_flow_foreach> call.
4203 A dependence is marked I<must> if it originates from a I<must>
4204 source and if it is not followed by any I<may> sources.
4206 After finishing with an C<isl_flow>, the user should call
4207 C<isl_flow_free> to free all associated memory.
4209 A higher-level interface to dependence analysis is provided
4210 by the following function.
4212 #include <isl/flow.h>
4214 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4215 __isl_take isl_union_map *must_source,
4216 __isl_take isl_union_map *may_source,
4217 __isl_take isl_union_map *schedule,
4218 __isl_give isl_union_map **must_dep,
4219 __isl_give isl_union_map **may_dep,
4220 __isl_give isl_union_map **must_no_source,
4221 __isl_give isl_union_map **may_no_source);
4223 The arrays are identified by the tuple names of the ranges
4224 of the accesses. The iteration domains by the tuple names
4225 of the domains of the accesses and of the schedule.
4226 The relative order of the iteration domains is given by the
4227 schedule. The relations returned through C<must_no_source>
4228 and C<may_no_source> are subsets of C<sink>.
4229 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4230 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4231 any of the other arguments is treated as an error.
4233 =head3 Interaction with Dependence Analysis
4235 During the dependence analysis, we frequently need to perform
4236 the following operation. Given a relation between sink iterations
4237 and potential soure iterations from a particular source domain,
4238 what is the last potential source iteration corresponding to each
4239 sink iteration. It can sometimes be convenient to adjust
4240 the set of potential source iterations before or after each such operation.
4241 The prototypical example is fuzzy array dataflow analysis,
4242 where we need to analyze if, based on data-dependent constraints,
4243 the sink iteration can ever be executed without one or more of
4244 the corresponding potential source iterations being executed.
4245 If so, we can introduce extra parameters and select an unknown
4246 but fixed source iteration from the potential source iterations.
4247 To be able to perform such manipulations, C<isl> provides the following
4250 #include <isl/flow.h>
4252 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4253 __isl_keep isl_map *source_map,
4254 __isl_keep isl_set *sink, void *source_user,
4256 __isl_give isl_access_info *isl_access_info_set_restrict(
4257 __isl_take isl_access_info *acc,
4258 isl_access_restrict fn, void *user);
4260 The function C<isl_access_info_set_restrict> should be called
4261 before calling C<isl_access_info_compute_flow> and registers a callback function
4262 that will be called any time C<isl> is about to compute the last
4263 potential source. The first argument is the (reverse) proto-dependence,
4264 mapping sink iterations to potential source iterations.
4265 The second argument represents the sink iterations for which
4266 we want to compute the last source iteration.
4267 The third argument is the token corresponding to the source
4268 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4269 The callback is expected to return a restriction on either the input or
4270 the output of the operation computing the last potential source.
4271 If the input needs to be restricted then restrictions are needed
4272 for both the source and the sink iterations. The sink iterations
4273 and the potential source iterations will be intersected with these sets.
4274 If the output needs to be restricted then only a restriction on the source
4275 iterations is required.
4276 If any error occurs, the callback should return C<NULL>.
4277 An C<isl_restriction> object can be created and freed using the following
4280 #include <isl/flow.h>
4282 __isl_give isl_restriction *isl_restriction_input(
4283 __isl_take isl_set *source_restr,
4284 __isl_take isl_set *sink_restr);
4285 __isl_give isl_restriction *isl_restriction_output(
4286 __isl_take isl_set *source_restr);
4287 __isl_give isl_restriction *isl_restriction_none(
4288 __isl_keep isl_map *source_map);
4289 __isl_give isl_restriction *isl_restriction_empty(
4290 __isl_keep isl_map *source_map);
4291 void *isl_restriction_free(
4292 __isl_take isl_restriction *restr);
4294 C<isl_restriction_none> and C<isl_restriction_empty> are special
4295 cases of C<isl_restriction_input>. C<isl_restriction_none>
4296 is essentially equivalent to
4298 isl_restriction_input(isl_set_universe(
4299 isl_space_range(isl_map_get_space(source_map))),
4301 isl_space_domain(isl_map_get_space(source_map))));
4303 whereas C<isl_restriction_empty> is essentially equivalent to
4305 isl_restriction_input(isl_set_empty(
4306 isl_space_range(isl_map_get_space(source_map))),
4308 isl_space_domain(isl_map_get_space(source_map))));
4312 B<The functionality described in this section is fairly new
4313 and may be subject to change.>
4315 The following function can be used to compute a schedule
4316 for a union of domains.
4317 By default, the algorithm used to construct the schedule is similar
4318 to that of C<Pluto>.
4319 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4321 The generated schedule respects all C<validity> dependences.
4322 That is, all dependence distances over these dependences in the
4323 scheduled space are lexicographically positive.
4324 The default algorithm tries to minimize the dependence distances over
4325 C<proximity> dependences.
4326 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4327 for groups of domains where the dependence distances have only
4328 non-negative values.
4329 When using Feautrier's algorithm, the C<proximity> dependence
4330 distances are only minimized during the extension to a
4331 full-dimensional schedule.
4333 #include <isl/schedule.h>
4334 __isl_give isl_schedule *isl_union_set_compute_schedule(
4335 __isl_take isl_union_set *domain,
4336 __isl_take isl_union_map *validity,
4337 __isl_take isl_union_map *proximity);
4338 void *isl_schedule_free(__isl_take isl_schedule *sched);
4340 A mapping from the domains to the scheduled space can be obtained
4341 from an C<isl_schedule> using the following function.
4343 __isl_give isl_union_map *isl_schedule_get_map(
4344 __isl_keep isl_schedule *sched);
4346 A representation of the schedule can be printed using
4348 __isl_give isl_printer *isl_printer_print_schedule(
4349 __isl_take isl_printer *p,
4350 __isl_keep isl_schedule *schedule);
4352 A representation of the schedule as a forest of bands can be obtained
4353 using the following function.
4355 __isl_give isl_band_list *isl_schedule_get_band_forest(
4356 __isl_keep isl_schedule *schedule);
4358 The list can be manipulated as explained in L<"Lists">.
4359 The bands inside the list can be copied and freed using the following
4362 #include <isl/band.h>
4363 __isl_give isl_band *isl_band_copy(
4364 __isl_keep isl_band *band);
4365 void *isl_band_free(__isl_take isl_band *band);
4367 Each band contains zero or more scheduling dimensions.
4368 These are referred to as the members of the band.
4369 The section of the schedule that corresponds to the band is
4370 referred to as the partial schedule of the band.
4371 For those nodes that participate in a band, the outer scheduling
4372 dimensions form the prefix schedule, while the inner scheduling
4373 dimensions form the suffix schedule.
4374 That is, if we take a cut of the band forest, then the union of
4375 the concatenations of the prefix, partial and suffix schedules of
4376 each band in the cut is equal to the entire schedule (modulo
4377 some possible padding at the end with zero scheduling dimensions).
4378 The properties of a band can be inspected using the following functions.
4380 #include <isl/band.h>
4381 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4383 int isl_band_has_children(__isl_keep isl_band *band);
4384 __isl_give isl_band_list *isl_band_get_children(
4385 __isl_keep isl_band *band);
4387 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4388 __isl_keep isl_band *band);
4389 __isl_give isl_union_map *isl_band_get_partial_schedule(
4390 __isl_keep isl_band *band);
4391 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4392 __isl_keep isl_band *band);
4394 int isl_band_n_member(__isl_keep isl_band *band);
4395 int isl_band_member_is_zero_distance(
4396 __isl_keep isl_band *band, int pos);
4398 Note that a scheduling dimension is considered to be ``zero
4399 distance'' if it does not carry any proximity dependences
4401 That is, if the dependence distances of the proximity
4402 dependences are all zero in that direction (for fixed
4403 iterations of outer bands).
4405 A representation of the band can be printed using
4407 #include <isl/band.h>
4408 __isl_give isl_printer *isl_printer_print_band(
4409 __isl_take isl_printer *p,
4410 __isl_keep isl_band *band);
4414 #include <isl/schedule.h>
4415 int isl_options_set_schedule_max_coefficient(
4416 isl_ctx *ctx, int val);
4417 int isl_options_get_schedule_max_coefficient(
4419 int isl_options_set_schedule_max_constant_term(
4420 isl_ctx *ctx, int val);
4421 int isl_options_get_schedule_max_constant_term(
4423 int isl_options_set_schedule_maximize_band_depth(
4424 isl_ctx *ctx, int val);
4425 int isl_options_get_schedule_maximize_band_depth(
4427 int isl_options_set_schedule_outer_zero_distance(
4428 isl_ctx *ctx, int val);
4429 int isl_options_get_schedule_outer_zero_distance(
4431 int isl_options_set_schedule_split_scaled(
4432 isl_ctx *ctx, int val);
4433 int isl_options_get_schedule_split_scaled(
4435 int isl_options_set_schedule_algorithm(
4436 isl_ctx *ctx, int val);
4437 int isl_options_get_schedule_algorithm(
4443 =item * schedule_max_coefficient
4445 This option enforces that the coefficients for variable and parameter
4446 dimensions in the calculated schedule are not larger than the specified value.
4447 This option can significantly increase the speed of the scheduling calculation
4448 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4449 this option does not introduce bounds on the variable or parameter
4452 =item * schedule_max_constant_term
4454 This option enforces that the constant coefficients in the calculated schedule
4455 are not larger than the maximal constant term. This option can significantly
4456 increase the speed of the scheduling calculation and may also prevent fusing of
4457 unrelated dimensions. A value of -1 means that this option does not introduce
4458 bounds on the constant coefficients.
4460 =item * schedule_maximize_band_depth
4462 If this option is set, we do not split bands at the point
4463 where we detect splitting is necessary. Instead, we
4464 backtrack and split bands as early as possible. This
4465 reduces the number of splits and maximizes the width of
4466 the bands. Wider bands give more possibilities for tiling.
4468 =item * schedule_outer_zero_distance
4470 If this option is set, then we try to construct schedules
4471 where the outermost scheduling dimension in each band
4472 results in a zero dependence distance over the proximity
4475 =item * schedule_split_scaled
4477 If this option is set, then we try to construct schedules in which the
4478 constant term is split off from the linear part if the linear parts of
4479 the scheduling rows for all nodes in the graphs have a common non-trivial
4481 The constant term is then placed in a separate band and the linear
4484 =item * schedule_algorithm
4486 Selects the scheduling algorithm to be used.
4487 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4488 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4492 =head2 Parametric Vertex Enumeration
4494 The parametric vertex enumeration described in this section
4495 is mainly intended to be used internally and by the C<barvinok>
4498 #include <isl/vertices.h>
4499 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4500 __isl_keep isl_basic_set *bset);
4502 The function C<isl_basic_set_compute_vertices> performs the
4503 actual computation of the parametric vertices and the chamber
4504 decomposition and store the result in an C<isl_vertices> object.
4505 This information can be queried by either iterating over all
4506 the vertices or iterating over all the chambers or cells
4507 and then iterating over all vertices that are active on the chamber.
4509 int isl_vertices_foreach_vertex(
4510 __isl_keep isl_vertices *vertices,
4511 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4514 int isl_vertices_foreach_cell(
4515 __isl_keep isl_vertices *vertices,
4516 int (*fn)(__isl_take isl_cell *cell, void *user),
4518 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4519 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4522 Other operations that can be performed on an C<isl_vertices> object are
4525 isl_ctx *isl_vertices_get_ctx(
4526 __isl_keep isl_vertices *vertices);
4527 int isl_vertices_get_n_vertices(
4528 __isl_keep isl_vertices *vertices);
4529 void isl_vertices_free(__isl_take isl_vertices *vertices);
4531 Vertices can be inspected and destroyed using the following functions.
4533 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4534 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4535 __isl_give isl_basic_set *isl_vertex_get_domain(
4536 __isl_keep isl_vertex *vertex);
4537 __isl_give isl_basic_set *isl_vertex_get_expr(
4538 __isl_keep isl_vertex *vertex);
4539 void isl_vertex_free(__isl_take isl_vertex *vertex);
4541 C<isl_vertex_get_expr> returns a singleton parametric set describing
4542 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4544 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4545 B<rational> basic sets, so they should mainly be used for inspection
4546 and should not be mixed with integer sets.
4548 Chambers can be inspected and destroyed using the following functions.
4550 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4551 __isl_give isl_basic_set *isl_cell_get_domain(
4552 __isl_keep isl_cell *cell);
4553 void isl_cell_free(__isl_take isl_cell *cell);
4557 Although C<isl> is mainly meant to be used as a library,
4558 it also contains some basic applications that use some
4559 of the functionality of C<isl>.
4560 The input may be specified in either the L<isl format>
4561 or the L<PolyLib format>.
4563 =head2 C<isl_polyhedron_sample>
4565 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4566 an integer element of the polyhedron, if there is any.
4567 The first column in the output is the denominator and is always
4568 equal to 1. If the polyhedron contains no integer points,
4569 then a vector of length zero is printed.
4573 C<isl_pip> takes the same input as the C<example> program
4574 from the C<piplib> distribution, i.e., a set of constraints
4575 on the parameters, a line containing only -1 and finally a set
4576 of constraints on a parametric polyhedron.
4577 The coefficients of the parameters appear in the last columns
4578 (but before the final constant column).
4579 The output is the lexicographic minimum of the parametric polyhedron.
4580 As C<isl> currently does not have its own output format, the output
4581 is just a dump of the internal state.
4583 =head2 C<isl_polyhedron_minimize>
4585 C<isl_polyhedron_minimize> computes the minimum of some linear
4586 or affine objective function over the integer points in a polyhedron.
4587 If an affine objective function
4588 is given, then the constant should appear in the last column.
4590 =head2 C<isl_polytope_scan>
4592 Given a polytope, C<isl_polytope_scan> prints
4593 all integer points in the polytope.