3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 int isl_space_has_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
736 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
737 enum isl_dim_type type);
739 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
740 or C<isl_dim_set>. As with C<isl_space_get_name>,
741 the C<isl_space_get_tuple_name> function returns a pointer to some internal
743 Binary operations require the corresponding spaces of their arguments
744 to have the same name.
746 Spaces can be nested. In particular, the domain of a set or
747 the domain or range of a relation can be a nested relation.
748 The following functions can be used to construct and deconstruct
751 #include <isl/space.h>
752 int isl_space_is_wrapping(__isl_keep isl_space *space);
753 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
754 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
756 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
757 be the space of a set, while that of
758 C<isl_space_wrap> should be the space of a relation.
759 Conversely, the output of C<isl_space_unwrap> is the space
760 of a relation, while that of C<isl_space_wrap> is the space of a set.
762 Spaces can be created from other spaces
763 using the following functions.
765 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
768 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_set_from_params(
772 __isl_take isl_space *space);
773 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
774 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
775 __isl_take isl_space *right);
776 __isl_give isl_space *isl_space_align_params(
777 __isl_take isl_space *space1, __isl_take isl_space *space2)
778 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned pos, unsigned n);
780 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned n);
782 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
783 enum isl_dim_type type, unsigned first, unsigned n);
784 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
785 enum isl_dim_type dst_type, unsigned dst_pos,
786 enum isl_dim_type src_type, unsigned src_pos,
788 __isl_give isl_space *isl_space_map_from_set(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_map_from_domain_and_range(
791 __isl_take isl_space *domain,
792 __isl_take isl_space *range);
793 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
794 __isl_give isl_space *isl_space_curry(
795 __isl_take isl_space *space);
797 Note that if dimensions are added or removed from a space, then
798 the name and the internal structure are lost.
802 A local space is essentially a space with
803 zero or more existentially quantified variables.
804 The local space of a (constraint of a) basic set or relation can be obtained
805 using the following functions.
807 #include <isl/constraint.h>
808 __isl_give isl_local_space *isl_constraint_get_local_space(
809 __isl_keep isl_constraint *constraint);
812 __isl_give isl_local_space *isl_basic_set_get_local_space(
813 __isl_keep isl_basic_set *bset);
816 __isl_give isl_local_space *isl_basic_map_get_local_space(
817 __isl_keep isl_basic_map *bmap);
819 A new local space can be created from a space using
821 #include <isl/local_space.h>
822 __isl_give isl_local_space *isl_local_space_from_space(
823 __isl_take isl_space *space);
825 They can be inspected, modified, copied and freed using the following functions.
827 #include <isl/local_space.h>
828 isl_ctx *isl_local_space_get_ctx(
829 __isl_keep isl_local_space *ls);
830 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
831 int isl_local_space_dim(__isl_keep isl_local_space *ls,
832 enum isl_dim_type type);
833 int isl_local_space_has_dim_name(
834 __isl_keep isl_local_space *ls,
835 enum isl_dim_type type, unsigned pos)
836 const char *isl_local_space_get_dim_name(
837 __isl_keep isl_local_space *ls,
838 enum isl_dim_type type, unsigned pos);
839 __isl_give isl_local_space *isl_local_space_set_dim_name(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned pos, const char *s);
842 __isl_give isl_local_space *isl_local_space_set_dim_id(
843 __isl_take isl_local_space *ls,
844 enum isl_dim_type type, unsigned pos,
845 __isl_take isl_id *id);
846 __isl_give isl_space *isl_local_space_get_space(
847 __isl_keep isl_local_space *ls);
848 __isl_give isl_aff *isl_local_space_get_div(
849 __isl_keep isl_local_space *ls, int pos);
850 __isl_give isl_local_space *isl_local_space_copy(
851 __isl_keep isl_local_space *ls);
852 void *isl_local_space_free(__isl_take isl_local_space *ls);
854 Two local spaces can be compared using
856 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
857 __isl_keep isl_local_space *ls2);
859 Local spaces can be created from other local spaces
860 using the following functions.
862 __isl_give isl_local_space *isl_local_space_domain(
863 __isl_take isl_local_space *ls);
864 __isl_give isl_local_space *isl_local_space_range(
865 __isl_take isl_local_space *ls);
866 __isl_give isl_local_space *isl_local_space_from_domain(
867 __isl_take isl_local_space *ls);
868 __isl_give isl_local_space *isl_local_space_intersect(
869 __isl_take isl_local_space *ls1,
870 __isl_take isl_local_space *ls2);
871 __isl_give isl_local_space *isl_local_space_add_dims(
872 __isl_take isl_local_space *ls,
873 enum isl_dim_type type, unsigned n);
874 __isl_give isl_local_space *isl_local_space_insert_dims(
875 __isl_take isl_local_space *ls,
876 enum isl_dim_type type, unsigned first, unsigned n);
877 __isl_give isl_local_space *isl_local_space_drop_dims(
878 __isl_take isl_local_space *ls,
879 enum isl_dim_type type, unsigned first, unsigned n);
881 =head2 Input and Output
883 C<isl> supports its own input/output format, which is similar
884 to the C<Omega> format, but also supports the C<PolyLib> format
889 The C<isl> format is similar to that of C<Omega>, but has a different
890 syntax for describing the parameters and allows for the definition
891 of an existentially quantified variable as the integer division
892 of an affine expression.
893 For example, the set of integers C<i> between C<0> and C<n>
894 such that C<i % 10 <= 6> can be described as
896 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
899 A set or relation can have several disjuncts, separated
900 by the keyword C<or>. Each disjunct is either a conjunction
901 of constraints or a projection (C<exists>) of a conjunction
902 of constraints. The constraints are separated by the keyword
905 =head3 C<PolyLib> format
907 If the represented set is a union, then the first line
908 contains a single number representing the number of disjuncts.
909 Otherwise, a line containing the number C<1> is optional.
911 Each disjunct is represented by a matrix of constraints.
912 The first line contains two numbers representing
913 the number of rows and columns,
914 where the number of rows is equal to the number of constraints
915 and the number of columns is equal to two plus the number of variables.
916 The following lines contain the actual rows of the constraint matrix.
917 In each row, the first column indicates whether the constraint
918 is an equality (C<0>) or inequality (C<1>). The final column
919 corresponds to the constant term.
921 If the set is parametric, then the coefficients of the parameters
922 appear in the last columns before the constant column.
923 The coefficients of any existentially quantified variables appear
924 between those of the set variables and those of the parameters.
926 =head3 Extended C<PolyLib> format
928 The extended C<PolyLib> format is nearly identical to the
929 C<PolyLib> format. The only difference is that the line
930 containing the number of rows and columns of a constraint matrix
931 also contains four additional numbers:
932 the number of output dimensions, the number of input dimensions,
933 the number of local dimensions (i.e., the number of existentially
934 quantified variables) and the number of parameters.
935 For sets, the number of ``output'' dimensions is equal
936 to the number of set dimensions, while the number of ``input''
942 __isl_give isl_basic_set *isl_basic_set_read_from_file(
943 isl_ctx *ctx, FILE *input);
944 __isl_give isl_basic_set *isl_basic_set_read_from_str(
945 isl_ctx *ctx, const char *str);
946 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
948 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
952 __isl_give isl_basic_map *isl_basic_map_read_from_file(
953 isl_ctx *ctx, FILE *input);
954 __isl_give isl_basic_map *isl_basic_map_read_from_str(
955 isl_ctx *ctx, const char *str);
956 __isl_give isl_map *isl_map_read_from_file(
957 isl_ctx *ctx, FILE *input);
958 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
961 #include <isl/union_set.h>
962 __isl_give isl_union_set *isl_union_set_read_from_file(
963 isl_ctx *ctx, FILE *input);
964 __isl_give isl_union_set *isl_union_set_read_from_str(
965 isl_ctx *ctx, const char *str);
967 #include <isl/union_map.h>
968 __isl_give isl_union_map *isl_union_map_read_from_file(
969 isl_ctx *ctx, FILE *input);
970 __isl_give isl_union_map *isl_union_map_read_from_str(
971 isl_ctx *ctx, const char *str);
973 The input format is autodetected and may be either the C<PolyLib> format
974 or the C<isl> format.
978 Before anything can be printed, an C<isl_printer> needs to
981 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
983 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
984 void isl_printer_free(__isl_take isl_printer *printer);
985 __isl_give char *isl_printer_get_str(
986 __isl_keep isl_printer *printer);
988 The printer can be inspected using the following function.
990 FILE *isl_printer_get_file(
991 __isl_keep isl_printer *printer);
993 The behavior of the printer can be modified in various ways
995 __isl_give isl_printer *isl_printer_set_output_format(
996 __isl_take isl_printer *p, int output_format);
997 __isl_give isl_printer *isl_printer_set_indent(
998 __isl_take isl_printer *p, int indent);
999 __isl_give isl_printer *isl_printer_indent(
1000 __isl_take isl_printer *p, int indent);
1001 __isl_give isl_printer *isl_printer_set_prefix(
1002 __isl_take isl_printer *p, const char *prefix);
1003 __isl_give isl_printer *isl_printer_set_suffix(
1004 __isl_take isl_printer *p, const char *suffix);
1006 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1007 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1008 and defaults to C<ISL_FORMAT_ISL>.
1009 Each line in the output is indented by C<indent> (set by
1010 C<isl_printer_set_indent>) spaces
1011 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1012 In the C<PolyLib> format output,
1013 the coefficients of the existentially quantified variables
1014 appear between those of the set variables and those
1016 The function C<isl_printer_indent> increases the indentation
1017 by the specified amount (which may be negative).
1019 To actually print something, use
1021 #include <isl/set.h>
1022 __isl_give isl_printer *isl_printer_print_basic_set(
1023 __isl_take isl_printer *printer,
1024 __isl_keep isl_basic_set *bset);
1025 __isl_give isl_printer *isl_printer_print_set(
1026 __isl_take isl_printer *printer,
1027 __isl_keep isl_set *set);
1029 #include <isl/map.h>
1030 __isl_give isl_printer *isl_printer_print_basic_map(
1031 __isl_take isl_printer *printer,
1032 __isl_keep isl_basic_map *bmap);
1033 __isl_give isl_printer *isl_printer_print_map(
1034 __isl_take isl_printer *printer,
1035 __isl_keep isl_map *map);
1037 #include <isl/union_set.h>
1038 __isl_give isl_printer *isl_printer_print_union_set(
1039 __isl_take isl_printer *p,
1040 __isl_keep isl_union_set *uset);
1042 #include <isl/union_map.h>
1043 __isl_give isl_printer *isl_printer_print_union_map(
1044 __isl_take isl_printer *p,
1045 __isl_keep isl_union_map *umap);
1047 When called on a file printer, the following function flushes
1048 the file. When called on a string printer, the buffer is cleared.
1050 __isl_give isl_printer *isl_printer_flush(
1051 __isl_take isl_printer *p);
1053 =head2 Creating New Sets and Relations
1055 C<isl> has functions for creating some standard sets and relations.
1059 =item * Empty sets and relations
1061 __isl_give isl_basic_set *isl_basic_set_empty(
1062 __isl_take isl_space *space);
1063 __isl_give isl_basic_map *isl_basic_map_empty(
1064 __isl_take isl_space *space);
1065 __isl_give isl_set *isl_set_empty(
1066 __isl_take isl_space *space);
1067 __isl_give isl_map *isl_map_empty(
1068 __isl_take isl_space *space);
1069 __isl_give isl_union_set *isl_union_set_empty(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_map *isl_union_map_empty(
1072 __isl_take isl_space *space);
1074 For C<isl_union_set>s and C<isl_union_map>s, the space
1075 is only used to specify the parameters.
1077 =item * Universe sets and relations
1079 __isl_give isl_basic_set *isl_basic_set_universe(
1080 __isl_take isl_space *space);
1081 __isl_give isl_basic_map *isl_basic_map_universe(
1082 __isl_take isl_space *space);
1083 __isl_give isl_set *isl_set_universe(
1084 __isl_take isl_space *space);
1085 __isl_give isl_map *isl_map_universe(
1086 __isl_take isl_space *space);
1087 __isl_give isl_union_set *isl_union_set_universe(
1088 __isl_take isl_union_set *uset);
1089 __isl_give isl_union_map *isl_union_map_universe(
1090 __isl_take isl_union_map *umap);
1092 The sets and relations constructed by the functions above
1093 contain all integer values, while those constructed by the
1094 functions below only contain non-negative values.
1096 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1097 __isl_take isl_space *space);
1098 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1099 __isl_take isl_space *space);
1100 __isl_give isl_set *isl_set_nat_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_map *isl_map_nat_universe(
1103 __isl_take isl_space *space);
1105 =item * Identity relations
1107 __isl_give isl_basic_map *isl_basic_map_identity(
1108 __isl_take isl_space *space);
1109 __isl_give isl_map *isl_map_identity(
1110 __isl_take isl_space *space);
1112 The number of input and output dimensions in C<space> needs
1115 =item * Lexicographic order
1117 __isl_give isl_map *isl_map_lex_lt(
1118 __isl_take isl_space *set_space);
1119 __isl_give isl_map *isl_map_lex_le(
1120 __isl_take isl_space *set_space);
1121 __isl_give isl_map *isl_map_lex_gt(
1122 __isl_take isl_space *set_space);
1123 __isl_give isl_map *isl_map_lex_ge(
1124 __isl_take isl_space *set_space);
1125 __isl_give isl_map *isl_map_lex_lt_first(
1126 __isl_take isl_space *space, unsigned n);
1127 __isl_give isl_map *isl_map_lex_le_first(
1128 __isl_take isl_space *space, unsigned n);
1129 __isl_give isl_map *isl_map_lex_gt_first(
1130 __isl_take isl_space *space, unsigned n);
1131 __isl_give isl_map *isl_map_lex_ge_first(
1132 __isl_take isl_space *space, unsigned n);
1134 The first four functions take a space for a B<set>
1135 and return relations that express that the elements in the domain
1136 are lexicographically less
1137 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1138 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1139 than the elements in the range.
1140 The last four functions take a space for a map
1141 and return relations that express that the first C<n> dimensions
1142 in the domain are lexicographically less
1143 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1144 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1145 than the first C<n> dimensions in the range.
1149 A basic set or relation can be converted to a set or relation
1150 using the following functions.
1152 __isl_give isl_set *isl_set_from_basic_set(
1153 __isl_take isl_basic_set *bset);
1154 __isl_give isl_map *isl_map_from_basic_map(
1155 __isl_take isl_basic_map *bmap);
1157 Sets and relations can be converted to union sets and relations
1158 using the following functions.
1160 __isl_give isl_union_map *isl_union_map_from_map(
1161 __isl_take isl_map *map);
1162 __isl_give isl_union_set *isl_union_set_from_set(
1163 __isl_take isl_set *set);
1165 The inverse conversions below can only be used if the input
1166 union set or relation is known to contain elements in exactly one
1169 __isl_give isl_set *isl_set_from_union_set(
1170 __isl_take isl_union_set *uset);
1171 __isl_give isl_map *isl_map_from_union_map(
1172 __isl_take isl_union_map *umap);
1174 A zero-dimensional set can be constructed on a given parameter domain
1175 using the following function.
1177 __isl_give isl_set *isl_set_from_params(
1178 __isl_take isl_set *set);
1180 Sets and relations can be copied and freed again using the following
1183 __isl_give isl_basic_set *isl_basic_set_copy(
1184 __isl_keep isl_basic_set *bset);
1185 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1186 __isl_give isl_union_set *isl_union_set_copy(
1187 __isl_keep isl_union_set *uset);
1188 __isl_give isl_basic_map *isl_basic_map_copy(
1189 __isl_keep isl_basic_map *bmap);
1190 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1191 __isl_give isl_union_map *isl_union_map_copy(
1192 __isl_keep isl_union_map *umap);
1193 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1194 void isl_set_free(__isl_take isl_set *set);
1195 void *isl_union_set_free(__isl_take isl_union_set *uset);
1196 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1197 void isl_map_free(__isl_take isl_map *map);
1198 void *isl_union_map_free(__isl_take isl_union_map *umap);
1200 Other sets and relations can be constructed by starting
1201 from a universe set or relation, adding equality and/or
1202 inequality constraints and then projecting out the
1203 existentially quantified variables, if any.
1204 Constraints can be constructed, manipulated and
1205 added to (or removed from) (basic) sets and relations
1206 using the following functions.
1208 #include <isl/constraint.h>
1209 __isl_give isl_constraint *isl_equality_alloc(
1210 __isl_take isl_local_space *ls);
1211 __isl_give isl_constraint *isl_inequality_alloc(
1212 __isl_take isl_local_space *ls);
1213 __isl_give isl_constraint *isl_constraint_set_constant(
1214 __isl_take isl_constraint *constraint, isl_int v);
1215 __isl_give isl_constraint *isl_constraint_set_constant_si(
1216 __isl_take isl_constraint *constraint, int v);
1217 __isl_give isl_constraint *isl_constraint_set_coefficient(
1218 __isl_take isl_constraint *constraint,
1219 enum isl_dim_type type, int pos, isl_int v);
1220 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1221 __isl_take isl_constraint *constraint,
1222 enum isl_dim_type type, int pos, int v);
1223 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1224 __isl_take isl_basic_map *bmap,
1225 __isl_take isl_constraint *constraint);
1226 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1227 __isl_take isl_basic_set *bset,
1228 __isl_take isl_constraint *constraint);
1229 __isl_give isl_map *isl_map_add_constraint(
1230 __isl_take isl_map *map,
1231 __isl_take isl_constraint *constraint);
1232 __isl_give isl_set *isl_set_add_constraint(
1233 __isl_take isl_set *set,
1234 __isl_take isl_constraint *constraint);
1235 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1236 __isl_take isl_basic_set *bset,
1237 __isl_take isl_constraint *constraint);
1239 For example, to create a set containing the even integers
1240 between 10 and 42, you would use the following code.
1243 isl_local_space *ls;
1245 isl_basic_set *bset;
1247 space = isl_space_set_alloc(ctx, 0, 2);
1248 bset = isl_basic_set_universe(isl_space_copy(space));
1249 ls = isl_local_space_from_space(space);
1251 c = isl_equality_alloc(isl_local_space_copy(ls));
1252 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1253 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1254 bset = isl_basic_set_add_constraint(bset, c);
1256 c = isl_inequality_alloc(isl_local_space_copy(ls));
1257 c = isl_constraint_set_constant_si(c, -10);
1258 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1259 bset = isl_basic_set_add_constraint(bset, c);
1261 c = isl_inequality_alloc(ls);
1262 c = isl_constraint_set_constant_si(c, 42);
1263 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1264 bset = isl_basic_set_add_constraint(bset, c);
1266 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1270 isl_basic_set *bset;
1271 bset = isl_basic_set_read_from_str(ctx,
1272 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1274 A basic set or relation can also be constructed from two matrices
1275 describing the equalities and the inequalities.
1277 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1278 __isl_take isl_space *space,
1279 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1280 enum isl_dim_type c1,
1281 enum isl_dim_type c2, enum isl_dim_type c3,
1282 enum isl_dim_type c4);
1283 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1284 __isl_take isl_space *space,
1285 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1286 enum isl_dim_type c1,
1287 enum isl_dim_type c2, enum isl_dim_type c3,
1288 enum isl_dim_type c4, enum isl_dim_type c5);
1290 The C<isl_dim_type> arguments indicate the order in which
1291 different kinds of variables appear in the input matrices
1292 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1293 C<isl_dim_set> and C<isl_dim_div> for sets and
1294 of C<isl_dim_cst>, C<isl_dim_param>,
1295 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1297 A (basic or union) set or relation can also be constructed from a
1298 (union) (piecewise) (multiple) affine expression
1299 or a list of affine expressions
1300 (See L<"Piecewise Quasi Affine Expressions"> and
1301 L<"Piecewise Multiple Quasi Affine Expressions">).
1303 __isl_give isl_basic_map *isl_basic_map_from_aff(
1304 __isl_take isl_aff *aff);
1305 __isl_give isl_map *isl_map_from_aff(
1306 __isl_take isl_aff *aff);
1307 __isl_give isl_set *isl_set_from_pw_aff(
1308 __isl_take isl_pw_aff *pwaff);
1309 __isl_give isl_map *isl_map_from_pw_aff(
1310 __isl_take isl_pw_aff *pwaff);
1311 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1312 __isl_take isl_space *domain_space,
1313 __isl_take isl_aff_list *list);
1314 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1315 __isl_take isl_multi_aff *maff)
1316 __isl_give isl_map *isl_map_from_multi_aff(
1317 __isl_take isl_multi_aff *maff)
1318 __isl_give isl_set *isl_set_from_pw_multi_aff(
1319 __isl_take isl_pw_multi_aff *pma);
1320 __isl_give isl_map *isl_map_from_pw_multi_aff(
1321 __isl_take isl_pw_multi_aff *pma);
1322 __isl_give isl_union_map *
1323 isl_union_map_from_union_pw_multi_aff(
1324 __isl_take isl_union_pw_multi_aff *upma);
1326 The C<domain_dim> argument describes the domain of the resulting
1327 basic relation. It is required because the C<list> may consist
1328 of zero affine expressions.
1330 =head2 Inspecting Sets and Relations
1332 Usually, the user should not have to care about the actual constraints
1333 of the sets and maps, but should instead apply the abstract operations
1334 explained in the following sections.
1335 Occasionally, however, it may be required to inspect the individual
1336 coefficients of the constraints. This section explains how to do so.
1337 In these cases, it may also be useful to have C<isl> compute
1338 an explicit representation of the existentially quantified variables.
1340 __isl_give isl_set *isl_set_compute_divs(
1341 __isl_take isl_set *set);
1342 __isl_give isl_map *isl_map_compute_divs(
1343 __isl_take isl_map *map);
1344 __isl_give isl_union_set *isl_union_set_compute_divs(
1345 __isl_take isl_union_set *uset);
1346 __isl_give isl_union_map *isl_union_map_compute_divs(
1347 __isl_take isl_union_map *umap);
1349 This explicit representation defines the existentially quantified
1350 variables as integer divisions of the other variables, possibly
1351 including earlier existentially quantified variables.
1352 An explicitly represented existentially quantified variable therefore
1353 has a unique value when the values of the other variables are known.
1354 If, furthermore, the same existentials, i.e., existentials
1355 with the same explicit representations, should appear in the
1356 same order in each of the disjuncts of a set or map, then the user should call
1357 either of the following functions.
1359 __isl_give isl_set *isl_set_align_divs(
1360 __isl_take isl_set *set);
1361 __isl_give isl_map *isl_map_align_divs(
1362 __isl_take isl_map *map);
1364 Alternatively, the existentially quantified variables can be removed
1365 using the following functions, which compute an overapproximation.
1367 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1368 __isl_take isl_basic_set *bset);
1369 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1370 __isl_take isl_basic_map *bmap);
1371 __isl_give isl_set *isl_set_remove_divs(
1372 __isl_take isl_set *set);
1373 __isl_give isl_map *isl_map_remove_divs(
1374 __isl_take isl_map *map);
1376 To iterate over all the sets or maps in a union set or map, use
1378 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1379 int (*fn)(__isl_take isl_set *set, void *user),
1381 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1382 int (*fn)(__isl_take isl_map *map, void *user),
1385 The number of sets or maps in a union set or map can be obtained
1388 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1389 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1391 To extract the set or map in a given space from a union, use
1393 __isl_give isl_set *isl_union_set_extract_set(
1394 __isl_keep isl_union_set *uset,
1395 __isl_take isl_space *space);
1396 __isl_give isl_map *isl_union_map_extract_map(
1397 __isl_keep isl_union_map *umap,
1398 __isl_take isl_space *space);
1400 To iterate over all the basic sets or maps in a set or map, use
1402 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1403 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1405 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1406 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1409 The callback function C<fn> should return 0 if successful and
1410 -1 if an error occurs. In the latter case, or if any other error
1411 occurs, the above functions will return -1.
1413 It should be noted that C<isl> does not guarantee that
1414 the basic sets or maps passed to C<fn> are disjoint.
1415 If this is required, then the user should call one of
1416 the following functions first.
1418 __isl_give isl_set *isl_set_make_disjoint(
1419 __isl_take isl_set *set);
1420 __isl_give isl_map *isl_map_make_disjoint(
1421 __isl_take isl_map *map);
1423 The number of basic sets in a set can be obtained
1426 int isl_set_n_basic_set(__isl_keep isl_set *set);
1428 To iterate over the constraints of a basic set or map, use
1430 #include <isl/constraint.h>
1432 int isl_basic_set_n_constraint(
1433 __isl_keep isl_basic_set *bset);
1434 int isl_basic_set_foreach_constraint(
1435 __isl_keep isl_basic_set *bset,
1436 int (*fn)(__isl_take isl_constraint *c, void *user),
1438 int isl_basic_map_foreach_constraint(
1439 __isl_keep isl_basic_map *bmap,
1440 int (*fn)(__isl_take isl_constraint *c, void *user),
1442 void *isl_constraint_free(__isl_take isl_constraint *c);
1444 Again, the callback function C<fn> should return 0 if successful and
1445 -1 if an error occurs. In the latter case, or if any other error
1446 occurs, the above functions will return -1.
1447 The constraint C<c> represents either an equality or an inequality.
1448 Use the following function to find out whether a constraint
1449 represents an equality. If not, it represents an inequality.
1451 int isl_constraint_is_equality(
1452 __isl_keep isl_constraint *constraint);
1454 The coefficients of the constraints can be inspected using
1455 the following functions.
1457 int isl_constraint_is_lower_bound(
1458 __isl_keep isl_constraint *constraint,
1459 enum isl_dim_type type, unsigned pos);
1460 int isl_constraint_is_upper_bound(
1461 __isl_keep isl_constraint *constraint,
1462 enum isl_dim_type type, unsigned pos);
1463 void isl_constraint_get_constant(
1464 __isl_keep isl_constraint *constraint, isl_int *v);
1465 void isl_constraint_get_coefficient(
1466 __isl_keep isl_constraint *constraint,
1467 enum isl_dim_type type, int pos, isl_int *v);
1468 int isl_constraint_involves_dims(
1469 __isl_keep isl_constraint *constraint,
1470 enum isl_dim_type type, unsigned first, unsigned n);
1472 The explicit representations of the existentially quantified
1473 variables can be inspected using the following function.
1474 Note that the user is only allowed to use this function
1475 if the inspected set or map is the result of a call
1476 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1477 The existentially quantified variable is equal to the floor
1478 of the returned affine expression. The affine expression
1479 itself can be inspected using the functions in
1480 L<"Piecewise Quasi Affine Expressions">.
1482 __isl_give isl_aff *isl_constraint_get_div(
1483 __isl_keep isl_constraint *constraint, int pos);
1485 To obtain the constraints of a basic set or map in matrix
1486 form, use the following functions.
1488 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1489 __isl_keep isl_basic_set *bset,
1490 enum isl_dim_type c1, enum isl_dim_type c2,
1491 enum isl_dim_type c3, enum isl_dim_type c4);
1492 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1493 __isl_keep isl_basic_set *bset,
1494 enum isl_dim_type c1, enum isl_dim_type c2,
1495 enum isl_dim_type c3, enum isl_dim_type c4);
1496 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1497 __isl_keep isl_basic_map *bmap,
1498 enum isl_dim_type c1,
1499 enum isl_dim_type c2, enum isl_dim_type c3,
1500 enum isl_dim_type c4, enum isl_dim_type c5);
1501 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1502 __isl_keep isl_basic_map *bmap,
1503 enum isl_dim_type c1,
1504 enum isl_dim_type c2, enum isl_dim_type c3,
1505 enum isl_dim_type c4, enum isl_dim_type c5);
1507 The C<isl_dim_type> arguments dictate the order in which
1508 different kinds of variables appear in the resulting matrix
1509 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1510 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1512 The number of parameters, input, output or set dimensions can
1513 be obtained using the following functions.
1515 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1516 enum isl_dim_type type);
1517 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1518 enum isl_dim_type type);
1519 unsigned isl_set_dim(__isl_keep isl_set *set,
1520 enum isl_dim_type type);
1521 unsigned isl_map_dim(__isl_keep isl_map *map,
1522 enum isl_dim_type type);
1524 To check whether the description of a set or relation depends
1525 on one or more given dimensions, it is not necessary to iterate over all
1526 constraints. Instead the following functions can be used.
1528 int isl_basic_set_involves_dims(
1529 __isl_keep isl_basic_set *bset,
1530 enum isl_dim_type type, unsigned first, unsigned n);
1531 int isl_set_involves_dims(__isl_keep isl_set *set,
1532 enum isl_dim_type type, unsigned first, unsigned n);
1533 int isl_basic_map_involves_dims(
1534 __isl_keep isl_basic_map *bmap,
1535 enum isl_dim_type type, unsigned first, unsigned n);
1536 int isl_map_involves_dims(__isl_keep isl_map *map,
1537 enum isl_dim_type type, unsigned first, unsigned n);
1539 Similarly, the following functions can be used to check whether
1540 a given dimension is involved in any lower or upper bound.
1542 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1543 enum isl_dim_type type, unsigned pos);
1544 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1545 enum isl_dim_type type, unsigned pos);
1547 The identifiers or names of the domain and range spaces of a set
1548 or relation can be read off or set using the following functions.
1550 __isl_give isl_set *isl_set_set_tuple_id(
1551 __isl_take isl_set *set, __isl_take isl_id *id);
1552 __isl_give isl_set *isl_set_reset_tuple_id(
1553 __isl_take isl_set *set);
1554 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1555 __isl_give isl_id *isl_set_get_tuple_id(
1556 __isl_keep isl_set *set);
1557 __isl_give isl_map *isl_map_set_tuple_id(
1558 __isl_take isl_map *map, enum isl_dim_type type,
1559 __isl_take isl_id *id);
1560 __isl_give isl_map *isl_map_reset_tuple_id(
1561 __isl_take isl_map *map, enum isl_dim_type type);
1562 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1563 enum isl_dim_type type);
1564 __isl_give isl_id *isl_map_get_tuple_id(
1565 __isl_keep isl_map *map, enum isl_dim_type type);
1567 const char *isl_basic_set_get_tuple_name(
1568 __isl_keep isl_basic_set *bset);
1569 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1570 __isl_take isl_basic_set *set, const char *s);
1571 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1572 const char *isl_set_get_tuple_name(
1573 __isl_keep isl_set *set);
1574 const char *isl_basic_map_get_tuple_name(
1575 __isl_keep isl_basic_map *bmap,
1576 enum isl_dim_type type);
1577 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1578 __isl_take isl_basic_map *bmap,
1579 enum isl_dim_type type, const char *s);
1580 const char *isl_map_get_tuple_name(
1581 __isl_keep isl_map *map,
1582 enum isl_dim_type type);
1584 As with C<isl_space_get_tuple_name>, the value returned points to
1585 an internal data structure.
1586 The identifiers, positions or names of individual dimensions can be
1587 read off using the following functions.
1589 __isl_give isl_set *isl_set_set_dim_id(
1590 __isl_take isl_set *set, enum isl_dim_type type,
1591 unsigned pos, __isl_take isl_id *id);
1592 int isl_set_has_dim_id(__isl_keep isl_set *set,
1593 enum isl_dim_type type, unsigned pos);
1594 __isl_give isl_id *isl_set_get_dim_id(
1595 __isl_keep isl_set *set, enum isl_dim_type type,
1597 int isl_basic_map_has_dim_id(
1598 __isl_keep isl_basic_map *bmap,
1599 enum isl_dim_type type, unsigned pos);
1600 __isl_give isl_map *isl_map_set_dim_id(
1601 __isl_take isl_map *map, enum isl_dim_type type,
1602 unsigned pos, __isl_take isl_id *id);
1603 int isl_map_has_dim_id(__isl_keep isl_map *map,
1604 enum isl_dim_type type, unsigned pos);
1605 __isl_give isl_id *isl_map_get_dim_id(
1606 __isl_keep isl_map *map, enum isl_dim_type type,
1609 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1610 enum isl_dim_type type, __isl_keep isl_id *id);
1611 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1612 enum isl_dim_type type, __isl_keep isl_id *id);
1613 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1614 enum isl_dim_type type, const char *name);
1615 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1616 enum isl_dim_type type, const char *name);
1618 const char *isl_constraint_get_dim_name(
1619 __isl_keep isl_constraint *constraint,
1620 enum isl_dim_type type, unsigned pos);
1621 const char *isl_basic_set_get_dim_name(
1622 __isl_keep isl_basic_set *bset,
1623 enum isl_dim_type type, unsigned pos);
1624 int isl_set_has_dim_name(__isl_keep isl_set *set,
1625 enum isl_dim_type type, unsigned pos);
1626 const char *isl_set_get_dim_name(
1627 __isl_keep isl_set *set,
1628 enum isl_dim_type type, unsigned pos);
1629 const char *isl_basic_map_get_dim_name(
1630 __isl_keep isl_basic_map *bmap,
1631 enum isl_dim_type type, unsigned pos);
1632 const char *isl_map_get_dim_name(
1633 __isl_keep isl_map *map,
1634 enum isl_dim_type type, unsigned pos);
1636 These functions are mostly useful to obtain the identifiers, positions
1637 or names of the parameters. Identifiers of individual dimensions are
1638 essentially only useful for printing. They are ignored by all other
1639 operations and may not be preserved across those operations.
1643 =head3 Unary Properties
1649 The following functions test whether the given set or relation
1650 contains any integer points. The ``plain'' variants do not perform
1651 any computations, but simply check if the given set or relation
1652 is already known to be empty.
1654 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1655 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1656 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1657 int isl_set_is_empty(__isl_keep isl_set *set);
1658 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1659 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1660 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1661 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1662 int isl_map_is_empty(__isl_keep isl_map *map);
1663 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1665 =item * Universality
1667 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1668 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1669 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1671 =item * Single-valuedness
1673 int isl_map_plain_is_single_valued(
1674 __isl_keep isl_map *map);
1675 int isl_map_is_single_valued(__isl_keep isl_map *map);
1676 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1680 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1681 int isl_map_is_injective(__isl_keep isl_map *map);
1682 int isl_union_map_plain_is_injective(
1683 __isl_keep isl_union_map *umap);
1684 int isl_union_map_is_injective(
1685 __isl_keep isl_union_map *umap);
1689 int isl_map_is_bijective(__isl_keep isl_map *map);
1690 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1694 int isl_basic_map_plain_is_fixed(
1695 __isl_keep isl_basic_map *bmap,
1696 enum isl_dim_type type, unsigned pos,
1698 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1699 enum isl_dim_type type, unsigned pos,
1701 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1702 enum isl_dim_type type, unsigned pos,
1705 Check if the relation obviously lies on a hyperplane where the given dimension
1706 has a fixed value and if so, return that value in C<*val>.
1710 To check whether a set is a parameter domain, use this function:
1712 int isl_set_is_params(__isl_keep isl_set *set);
1713 int isl_union_set_is_params(
1714 __isl_keep isl_union_set *uset);
1718 The following functions check whether the domain of the given
1719 (basic) set is a wrapped relation.
1721 int isl_basic_set_is_wrapping(
1722 __isl_keep isl_basic_set *bset);
1723 int isl_set_is_wrapping(__isl_keep isl_set *set);
1725 =item * Internal Product
1727 int isl_basic_map_can_zip(
1728 __isl_keep isl_basic_map *bmap);
1729 int isl_map_can_zip(__isl_keep isl_map *map);
1731 Check whether the product of domain and range of the given relation
1733 i.e., whether both domain and range are nested relations.
1737 int isl_basic_map_can_curry(
1738 __isl_keep isl_basic_map *bmap);
1739 int isl_map_can_curry(__isl_keep isl_map *map);
1741 Check whether the domain of the (basic) relation is a wrapped relation.
1745 =head3 Binary Properties
1751 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1752 __isl_keep isl_set *set2);
1753 int isl_set_is_equal(__isl_keep isl_set *set1,
1754 __isl_keep isl_set *set2);
1755 int isl_union_set_is_equal(
1756 __isl_keep isl_union_set *uset1,
1757 __isl_keep isl_union_set *uset2);
1758 int isl_basic_map_is_equal(
1759 __isl_keep isl_basic_map *bmap1,
1760 __isl_keep isl_basic_map *bmap2);
1761 int isl_map_is_equal(__isl_keep isl_map *map1,
1762 __isl_keep isl_map *map2);
1763 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1764 __isl_keep isl_map *map2);
1765 int isl_union_map_is_equal(
1766 __isl_keep isl_union_map *umap1,
1767 __isl_keep isl_union_map *umap2);
1769 =item * Disjointness
1771 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1772 __isl_keep isl_set *set2);
1776 int isl_basic_set_is_subset(
1777 __isl_keep isl_basic_set *bset1,
1778 __isl_keep isl_basic_set *bset2);
1779 int isl_set_is_subset(__isl_keep isl_set *set1,
1780 __isl_keep isl_set *set2);
1781 int isl_set_is_strict_subset(
1782 __isl_keep isl_set *set1,
1783 __isl_keep isl_set *set2);
1784 int isl_union_set_is_subset(
1785 __isl_keep isl_union_set *uset1,
1786 __isl_keep isl_union_set *uset2);
1787 int isl_union_set_is_strict_subset(
1788 __isl_keep isl_union_set *uset1,
1789 __isl_keep isl_union_set *uset2);
1790 int isl_basic_map_is_subset(
1791 __isl_keep isl_basic_map *bmap1,
1792 __isl_keep isl_basic_map *bmap2);
1793 int isl_basic_map_is_strict_subset(
1794 __isl_keep isl_basic_map *bmap1,
1795 __isl_keep isl_basic_map *bmap2);
1796 int isl_map_is_subset(
1797 __isl_keep isl_map *map1,
1798 __isl_keep isl_map *map2);
1799 int isl_map_is_strict_subset(
1800 __isl_keep isl_map *map1,
1801 __isl_keep isl_map *map2);
1802 int isl_union_map_is_subset(
1803 __isl_keep isl_union_map *umap1,
1804 __isl_keep isl_union_map *umap2);
1805 int isl_union_map_is_strict_subset(
1806 __isl_keep isl_union_map *umap1,
1807 __isl_keep isl_union_map *umap2);
1811 =head2 Unary Operations
1817 __isl_give isl_set *isl_set_complement(
1818 __isl_take isl_set *set);
1819 __isl_give isl_map *isl_map_complement(
1820 __isl_take isl_map *map);
1824 __isl_give isl_basic_map *isl_basic_map_reverse(
1825 __isl_take isl_basic_map *bmap);
1826 __isl_give isl_map *isl_map_reverse(
1827 __isl_take isl_map *map);
1828 __isl_give isl_union_map *isl_union_map_reverse(
1829 __isl_take isl_union_map *umap);
1833 __isl_give isl_basic_set *isl_basic_set_project_out(
1834 __isl_take isl_basic_set *bset,
1835 enum isl_dim_type type, unsigned first, unsigned n);
1836 __isl_give isl_basic_map *isl_basic_map_project_out(
1837 __isl_take isl_basic_map *bmap,
1838 enum isl_dim_type type, unsigned first, unsigned n);
1839 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1840 enum isl_dim_type type, unsigned first, unsigned n);
1841 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1842 enum isl_dim_type type, unsigned first, unsigned n);
1843 __isl_give isl_basic_set *isl_basic_set_params(
1844 __isl_take isl_basic_set *bset);
1845 __isl_give isl_basic_set *isl_basic_map_domain(
1846 __isl_take isl_basic_map *bmap);
1847 __isl_give isl_basic_set *isl_basic_map_range(
1848 __isl_take isl_basic_map *bmap);
1849 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1850 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1851 __isl_give isl_set *isl_map_domain(
1852 __isl_take isl_map *bmap);
1853 __isl_give isl_set *isl_map_range(
1854 __isl_take isl_map *map);
1855 __isl_give isl_set *isl_union_set_params(
1856 __isl_take isl_union_set *uset);
1857 __isl_give isl_set *isl_union_map_params(
1858 __isl_take isl_union_map *umap);
1859 __isl_give isl_union_set *isl_union_map_domain(
1860 __isl_take isl_union_map *umap);
1861 __isl_give isl_union_set *isl_union_map_range(
1862 __isl_take isl_union_map *umap);
1864 __isl_give isl_basic_map *isl_basic_map_domain_map(
1865 __isl_take isl_basic_map *bmap);
1866 __isl_give isl_basic_map *isl_basic_map_range_map(
1867 __isl_take isl_basic_map *bmap);
1868 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1869 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1870 __isl_give isl_union_map *isl_union_map_domain_map(
1871 __isl_take isl_union_map *umap);
1872 __isl_give isl_union_map *isl_union_map_range_map(
1873 __isl_take isl_union_map *umap);
1875 The functions above construct a (basic, regular or union) relation
1876 that maps (a wrapped version of) the input relation to its domain or range.
1880 __isl_give isl_set *isl_set_eliminate(
1881 __isl_take isl_set *set, enum isl_dim_type type,
1882 unsigned first, unsigned n);
1883 __isl_give isl_basic_map *isl_basic_map_eliminate(
1884 __isl_take isl_basic_map *bmap,
1885 enum isl_dim_type type,
1886 unsigned first, unsigned n);
1887 __isl_give isl_map *isl_map_eliminate(
1888 __isl_take isl_map *map, enum isl_dim_type type,
1889 unsigned first, unsigned n);
1891 Eliminate the coefficients for the given dimensions from the constraints,
1892 without removing the dimensions.
1896 __isl_give isl_basic_set *isl_basic_set_fix(
1897 __isl_take isl_basic_set *bset,
1898 enum isl_dim_type type, unsigned pos,
1900 __isl_give isl_basic_set *isl_basic_set_fix_si(
1901 __isl_take isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned pos, int value);
1903 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1904 enum isl_dim_type type, unsigned pos,
1906 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1907 enum isl_dim_type type, unsigned pos, int value);
1908 __isl_give isl_basic_map *isl_basic_map_fix_si(
1909 __isl_take isl_basic_map *bmap,
1910 enum isl_dim_type type, unsigned pos, int value);
1911 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1912 enum isl_dim_type type, unsigned pos, int value);
1914 Intersect the set or relation with the hyperplane where the given
1915 dimension has the fixed given value.
1917 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1918 __isl_take isl_basic_map *bmap,
1919 enum isl_dim_type type, unsigned pos, int value);
1920 __isl_give isl_set *isl_set_lower_bound(
1921 __isl_take isl_set *set,
1922 enum isl_dim_type type, unsigned pos,
1924 __isl_give isl_set *isl_set_lower_bound_si(
1925 __isl_take isl_set *set,
1926 enum isl_dim_type type, unsigned pos, int value);
1927 __isl_give isl_map *isl_map_lower_bound_si(
1928 __isl_take isl_map *map,
1929 enum isl_dim_type type, unsigned pos, int value);
1930 __isl_give isl_set *isl_set_upper_bound(
1931 __isl_take isl_set *set,
1932 enum isl_dim_type type, unsigned pos,
1934 __isl_give isl_set *isl_set_upper_bound_si(
1935 __isl_take isl_set *set,
1936 enum isl_dim_type type, unsigned pos, int value);
1937 __isl_give isl_map *isl_map_upper_bound_si(
1938 __isl_take isl_map *map,
1939 enum isl_dim_type type, unsigned pos, int value);
1941 Intersect the set or relation with the half-space where the given
1942 dimension has a value bounded by the fixed given value.
1944 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1945 enum isl_dim_type type1, int pos1,
1946 enum isl_dim_type type2, int pos2);
1947 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1948 enum isl_dim_type type1, int pos1,
1949 enum isl_dim_type type2, int pos2);
1951 Intersect the set or relation with the hyperplane where the given
1952 dimensions are equal to each other.
1954 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1955 enum isl_dim_type type1, int pos1,
1956 enum isl_dim_type type2, int pos2);
1958 Intersect the relation with the hyperplane where the given
1959 dimensions have opposite values.
1961 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1962 enum isl_dim_type type1, int pos1,
1963 enum isl_dim_type type2, int pos2);
1965 Intersect the relation with the half-space where the given
1966 dimensions satisfy the given ordering.
1970 __isl_give isl_map *isl_set_identity(
1971 __isl_take isl_set *set);
1972 __isl_give isl_union_map *isl_union_set_identity(
1973 __isl_take isl_union_set *uset);
1975 Construct an identity relation on the given (union) set.
1979 __isl_give isl_basic_set *isl_basic_map_deltas(
1980 __isl_take isl_basic_map *bmap);
1981 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1982 __isl_give isl_union_set *isl_union_map_deltas(
1983 __isl_take isl_union_map *umap);
1985 These functions return a (basic) set containing the differences
1986 between image elements and corresponding domain elements in the input.
1988 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1989 __isl_take isl_basic_map *bmap);
1990 __isl_give isl_map *isl_map_deltas_map(
1991 __isl_take isl_map *map);
1992 __isl_give isl_union_map *isl_union_map_deltas_map(
1993 __isl_take isl_union_map *umap);
1995 The functions above construct a (basic, regular or union) relation
1996 that maps (a wrapped version of) the input relation to its delta set.
2000 Simplify the representation of a set or relation by trying
2001 to combine pairs of basic sets or relations into a single
2002 basic set or relation.
2004 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2005 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2006 __isl_give isl_union_set *isl_union_set_coalesce(
2007 __isl_take isl_union_set *uset);
2008 __isl_give isl_union_map *isl_union_map_coalesce(
2009 __isl_take isl_union_map *umap);
2011 One of the methods for combining pairs of basic sets or relations
2012 can result in coefficients that are much larger than those that appear
2013 in the constraints of the input. By default, the coefficients are
2014 not allowed to grow larger, but this can be changed by unsetting
2015 the following option.
2017 int isl_options_set_coalesce_bounded_wrapping(
2018 isl_ctx *ctx, int val);
2019 int isl_options_get_coalesce_bounded_wrapping(
2022 =item * Detecting equalities
2024 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2025 __isl_take isl_basic_set *bset);
2026 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2027 __isl_take isl_basic_map *bmap);
2028 __isl_give isl_set *isl_set_detect_equalities(
2029 __isl_take isl_set *set);
2030 __isl_give isl_map *isl_map_detect_equalities(
2031 __isl_take isl_map *map);
2032 __isl_give isl_union_set *isl_union_set_detect_equalities(
2033 __isl_take isl_union_set *uset);
2034 __isl_give isl_union_map *isl_union_map_detect_equalities(
2035 __isl_take isl_union_map *umap);
2037 Simplify the representation of a set or relation by detecting implicit
2040 =item * Removing redundant constraints
2042 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2043 __isl_take isl_basic_set *bset);
2044 __isl_give isl_set *isl_set_remove_redundancies(
2045 __isl_take isl_set *set);
2046 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2047 __isl_take isl_basic_map *bmap);
2048 __isl_give isl_map *isl_map_remove_redundancies(
2049 __isl_take isl_map *map);
2053 __isl_give isl_basic_set *isl_set_convex_hull(
2054 __isl_take isl_set *set);
2055 __isl_give isl_basic_map *isl_map_convex_hull(
2056 __isl_take isl_map *map);
2058 If the input set or relation has any existentially quantified
2059 variables, then the result of these operations is currently undefined.
2063 __isl_give isl_basic_set *isl_set_simple_hull(
2064 __isl_take isl_set *set);
2065 __isl_give isl_basic_map *isl_map_simple_hull(
2066 __isl_take isl_map *map);
2067 __isl_give isl_union_map *isl_union_map_simple_hull(
2068 __isl_take isl_union_map *umap);
2070 These functions compute a single basic set or relation
2071 that contains the whole input set or relation.
2072 In particular, the output is described by translates
2073 of the constraints describing the basic sets or relations in the input.
2077 (See \autoref{s:simple hull}.)
2083 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2084 __isl_take isl_basic_set *bset);
2085 __isl_give isl_basic_set *isl_set_affine_hull(
2086 __isl_take isl_set *set);
2087 __isl_give isl_union_set *isl_union_set_affine_hull(
2088 __isl_take isl_union_set *uset);
2089 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2090 __isl_take isl_basic_map *bmap);
2091 __isl_give isl_basic_map *isl_map_affine_hull(
2092 __isl_take isl_map *map);
2093 __isl_give isl_union_map *isl_union_map_affine_hull(
2094 __isl_take isl_union_map *umap);
2096 In case of union sets and relations, the affine hull is computed
2099 =item * Polyhedral hull
2101 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2102 __isl_take isl_set *set);
2103 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2104 __isl_take isl_map *map);
2105 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2106 __isl_take isl_union_set *uset);
2107 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2108 __isl_take isl_union_map *umap);
2110 These functions compute a single basic set or relation
2111 not involving any existentially quantified variables
2112 that contains the whole input set or relation.
2113 In case of union sets and relations, the polyhedral hull is computed
2118 __isl_give isl_basic_set *isl_basic_set_sample(
2119 __isl_take isl_basic_set *bset);
2120 __isl_give isl_basic_set *isl_set_sample(
2121 __isl_take isl_set *set);
2122 __isl_give isl_basic_map *isl_basic_map_sample(
2123 __isl_take isl_basic_map *bmap);
2124 __isl_give isl_basic_map *isl_map_sample(
2125 __isl_take isl_map *map);
2127 If the input (basic) set or relation is non-empty, then return
2128 a singleton subset of the input. Otherwise, return an empty set.
2130 =item * Optimization
2132 #include <isl/ilp.h>
2133 enum isl_lp_result isl_basic_set_max(
2134 __isl_keep isl_basic_set *bset,
2135 __isl_keep isl_aff *obj, isl_int *opt)
2136 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2137 __isl_keep isl_aff *obj, isl_int *opt);
2138 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2139 __isl_keep isl_aff *obj, isl_int *opt);
2141 Compute the minimum or maximum of the integer affine expression C<obj>
2142 over the points in C<set>, returning the result in C<opt>.
2143 The return value may be one of C<isl_lp_error>,
2144 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2146 =item * Parametric optimization
2148 __isl_give isl_pw_aff *isl_set_dim_min(
2149 __isl_take isl_set *set, int pos);
2150 __isl_give isl_pw_aff *isl_set_dim_max(
2151 __isl_take isl_set *set, int pos);
2152 __isl_give isl_pw_aff *isl_map_dim_max(
2153 __isl_take isl_map *map, int pos);
2155 Compute the minimum or maximum of the given set or output dimension
2156 as a function of the parameters (and input dimensions), but independently
2157 of the other set or output dimensions.
2158 For lexicographic optimization, see L<"Lexicographic Optimization">.
2162 The following functions compute either the set of (rational) coefficient
2163 values of valid constraints for the given set or the set of (rational)
2164 values satisfying the constraints with coefficients from the given set.
2165 Internally, these two sets of functions perform essentially the
2166 same operations, except that the set of coefficients is assumed to
2167 be a cone, while the set of values may be any polyhedron.
2168 The current implementation is based on the Farkas lemma and
2169 Fourier-Motzkin elimination, but this may change or be made optional
2170 in future. In particular, future implementations may use different
2171 dualization algorithms or skip the elimination step.
2173 __isl_give isl_basic_set *isl_basic_set_coefficients(
2174 __isl_take isl_basic_set *bset);
2175 __isl_give isl_basic_set *isl_set_coefficients(
2176 __isl_take isl_set *set);
2177 __isl_give isl_union_set *isl_union_set_coefficients(
2178 __isl_take isl_union_set *bset);
2179 __isl_give isl_basic_set *isl_basic_set_solutions(
2180 __isl_take isl_basic_set *bset);
2181 __isl_give isl_basic_set *isl_set_solutions(
2182 __isl_take isl_set *set);
2183 __isl_give isl_union_set *isl_union_set_solutions(
2184 __isl_take isl_union_set *bset);
2188 __isl_give isl_map *isl_map_fixed_power(
2189 __isl_take isl_map *map, isl_int exp);
2190 __isl_give isl_union_map *isl_union_map_fixed_power(
2191 __isl_take isl_union_map *umap, isl_int exp);
2193 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2194 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2195 of C<map> is computed.
2197 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2199 __isl_give isl_union_map *isl_union_map_power(
2200 __isl_take isl_union_map *umap, int *exact);
2202 Compute a parametric representation for all positive powers I<k> of C<map>.
2203 The result maps I<k> to a nested relation corresponding to the
2204 I<k>th power of C<map>.
2205 The result may be an overapproximation. If the result is known to be exact,
2206 then C<*exact> is set to C<1>.
2208 =item * Transitive closure
2210 __isl_give isl_map *isl_map_transitive_closure(
2211 __isl_take isl_map *map, int *exact);
2212 __isl_give isl_union_map *isl_union_map_transitive_closure(
2213 __isl_take isl_union_map *umap, int *exact);
2215 Compute the transitive closure of C<map>.
2216 The result may be an overapproximation. If the result is known to be exact,
2217 then C<*exact> is set to C<1>.
2219 =item * Reaching path lengths
2221 __isl_give isl_map *isl_map_reaching_path_lengths(
2222 __isl_take isl_map *map, int *exact);
2224 Compute a relation that maps each element in the range of C<map>
2225 to the lengths of all paths composed of edges in C<map> that
2226 end up in the given element.
2227 The result may be an overapproximation. If the result is known to be exact,
2228 then C<*exact> is set to C<1>.
2229 To compute the I<maximal> path length, the resulting relation
2230 should be postprocessed by C<isl_map_lexmax>.
2231 In particular, if the input relation is a dependence relation
2232 (mapping sources to sinks), then the maximal path length corresponds
2233 to the free schedule.
2234 Note, however, that C<isl_map_lexmax> expects the maximum to be
2235 finite, so if the path lengths are unbounded (possibly due to
2236 the overapproximation), then you will get an error message.
2240 __isl_give isl_basic_set *isl_basic_map_wrap(
2241 __isl_take isl_basic_map *bmap);
2242 __isl_give isl_set *isl_map_wrap(
2243 __isl_take isl_map *map);
2244 __isl_give isl_union_set *isl_union_map_wrap(
2245 __isl_take isl_union_map *umap);
2246 __isl_give isl_basic_map *isl_basic_set_unwrap(
2247 __isl_take isl_basic_set *bset);
2248 __isl_give isl_map *isl_set_unwrap(
2249 __isl_take isl_set *set);
2250 __isl_give isl_union_map *isl_union_set_unwrap(
2251 __isl_take isl_union_set *uset);
2255 Remove any internal structure of domain (and range) of the given
2256 set or relation. If there is any such internal structure in the input,
2257 then the name of the space is also removed.
2259 __isl_give isl_basic_set *isl_basic_set_flatten(
2260 __isl_take isl_basic_set *bset);
2261 __isl_give isl_set *isl_set_flatten(
2262 __isl_take isl_set *set);
2263 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2264 __isl_take isl_basic_map *bmap);
2265 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2266 __isl_take isl_basic_map *bmap);
2267 __isl_give isl_map *isl_map_flatten_range(
2268 __isl_take isl_map *map);
2269 __isl_give isl_map *isl_map_flatten_domain(
2270 __isl_take isl_map *map);
2271 __isl_give isl_basic_map *isl_basic_map_flatten(
2272 __isl_take isl_basic_map *bmap);
2273 __isl_give isl_map *isl_map_flatten(
2274 __isl_take isl_map *map);
2276 __isl_give isl_map *isl_set_flatten_map(
2277 __isl_take isl_set *set);
2279 The function above constructs a relation
2280 that maps the input set to a flattened version of the set.
2284 Lift the input set to a space with extra dimensions corresponding
2285 to the existentially quantified variables in the input.
2286 In particular, the result lives in a wrapped map where the domain
2287 is the original space and the range corresponds to the original
2288 existentially quantified variables.
2290 __isl_give isl_basic_set *isl_basic_set_lift(
2291 __isl_take isl_basic_set *bset);
2292 __isl_give isl_set *isl_set_lift(
2293 __isl_take isl_set *set);
2294 __isl_give isl_union_set *isl_union_set_lift(
2295 __isl_take isl_union_set *uset);
2297 Given a local space that contains the existentially quantified
2298 variables of a set, a basic relation that, when applied to
2299 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2300 can be constructed using the following function.
2302 #include <isl/local_space.h>
2303 __isl_give isl_basic_map *isl_local_space_lifting(
2304 __isl_take isl_local_space *ls);
2306 =item * Internal Product
2308 __isl_give isl_basic_map *isl_basic_map_zip(
2309 __isl_take isl_basic_map *bmap);
2310 __isl_give isl_map *isl_map_zip(
2311 __isl_take isl_map *map);
2312 __isl_give isl_union_map *isl_union_map_zip(
2313 __isl_take isl_union_map *umap);
2315 Given a relation with nested relations for domain and range,
2316 interchange the range of the domain with the domain of the range.
2320 __isl_give isl_basic_map *isl_basic_map_curry(
2321 __isl_take isl_basic_map *bmap);
2322 __isl_give isl_map *isl_map_curry(
2323 __isl_take isl_map *map);
2324 __isl_give isl_union_map *isl_union_map_curry(
2325 __isl_take isl_union_map *umap);
2327 Given a relation with a nested relation for domain,
2328 move the range of the nested relation out of the domain
2329 and use it as the domain of a nested relation in the range,
2330 with the original range as range of this nested relation.
2332 =item * Aligning parameters
2334 __isl_give isl_set *isl_set_align_params(
2335 __isl_take isl_set *set,
2336 __isl_take isl_space *model);
2337 __isl_give isl_map *isl_map_align_params(
2338 __isl_take isl_map *map,
2339 __isl_take isl_space *model);
2341 Change the order of the parameters of the given set or relation
2342 such that the first parameters match those of C<model>.
2343 This may involve the introduction of extra parameters.
2344 All parameters need to be named.
2346 =item * Dimension manipulation
2348 __isl_give isl_set *isl_set_add_dims(
2349 __isl_take isl_set *set,
2350 enum isl_dim_type type, unsigned n);
2351 __isl_give isl_map *isl_map_add_dims(
2352 __isl_take isl_map *map,
2353 enum isl_dim_type type, unsigned n);
2354 __isl_give isl_set *isl_set_insert_dims(
2355 __isl_take isl_set *set,
2356 enum isl_dim_type type, unsigned pos, unsigned n);
2357 __isl_give isl_map *isl_map_insert_dims(
2358 __isl_take isl_map *map,
2359 enum isl_dim_type type, unsigned pos, unsigned n);
2360 __isl_give isl_basic_set *isl_basic_set_move_dims(
2361 __isl_take isl_basic_set *bset,
2362 enum isl_dim_type dst_type, unsigned dst_pos,
2363 enum isl_dim_type src_type, unsigned src_pos,
2365 __isl_give isl_basic_map *isl_basic_map_move_dims(
2366 __isl_take isl_basic_map *bmap,
2367 enum isl_dim_type dst_type, unsigned dst_pos,
2368 enum isl_dim_type src_type, unsigned src_pos,
2370 __isl_give isl_set *isl_set_move_dims(
2371 __isl_take isl_set *set,
2372 enum isl_dim_type dst_type, unsigned dst_pos,
2373 enum isl_dim_type src_type, unsigned src_pos,
2375 __isl_give isl_map *isl_map_move_dims(
2376 __isl_take isl_map *map,
2377 enum isl_dim_type dst_type, unsigned dst_pos,
2378 enum isl_dim_type src_type, unsigned src_pos,
2381 It is usually not advisable to directly change the (input or output)
2382 space of a set or a relation as this removes the name and the internal
2383 structure of the space. However, the above functions can be useful
2384 to add new parameters, assuming
2385 C<isl_set_align_params> and C<isl_map_align_params>
2390 =head2 Binary Operations
2392 The two arguments of a binary operation not only need to live
2393 in the same C<isl_ctx>, they currently also need to have
2394 the same (number of) parameters.
2396 =head3 Basic Operations
2400 =item * Intersection
2402 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2403 __isl_take isl_basic_set *bset1,
2404 __isl_take isl_basic_set *bset2);
2405 __isl_give isl_basic_set *isl_basic_set_intersect(
2406 __isl_take isl_basic_set *bset1,
2407 __isl_take isl_basic_set *bset2);
2408 __isl_give isl_set *isl_set_intersect_params(
2409 __isl_take isl_set *set,
2410 __isl_take isl_set *params);
2411 __isl_give isl_set *isl_set_intersect(
2412 __isl_take isl_set *set1,
2413 __isl_take isl_set *set2);
2414 __isl_give isl_union_set *isl_union_set_intersect_params(
2415 __isl_take isl_union_set *uset,
2416 __isl_take isl_set *set);
2417 __isl_give isl_union_map *isl_union_map_intersect_params(
2418 __isl_take isl_union_map *umap,
2419 __isl_take isl_set *set);
2420 __isl_give isl_union_set *isl_union_set_intersect(
2421 __isl_take isl_union_set *uset1,
2422 __isl_take isl_union_set *uset2);
2423 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2424 __isl_take isl_basic_map *bmap,
2425 __isl_take isl_basic_set *bset);
2426 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2427 __isl_take isl_basic_map *bmap,
2428 __isl_take isl_basic_set *bset);
2429 __isl_give isl_basic_map *isl_basic_map_intersect(
2430 __isl_take isl_basic_map *bmap1,
2431 __isl_take isl_basic_map *bmap2);
2432 __isl_give isl_map *isl_map_intersect_params(
2433 __isl_take isl_map *map,
2434 __isl_take isl_set *params);
2435 __isl_give isl_map *isl_map_intersect_domain(
2436 __isl_take isl_map *map,
2437 __isl_take isl_set *set);
2438 __isl_give isl_map *isl_map_intersect_range(
2439 __isl_take isl_map *map,
2440 __isl_take isl_set *set);
2441 __isl_give isl_map *isl_map_intersect(
2442 __isl_take isl_map *map1,
2443 __isl_take isl_map *map2);
2444 __isl_give isl_union_map *isl_union_map_intersect_domain(
2445 __isl_take isl_union_map *umap,
2446 __isl_take isl_union_set *uset);
2447 __isl_give isl_union_map *isl_union_map_intersect_range(
2448 __isl_take isl_union_map *umap,
2449 __isl_take isl_union_set *uset);
2450 __isl_give isl_union_map *isl_union_map_intersect(
2451 __isl_take isl_union_map *umap1,
2452 __isl_take isl_union_map *umap2);
2456 __isl_give isl_set *isl_basic_set_union(
2457 __isl_take isl_basic_set *bset1,
2458 __isl_take isl_basic_set *bset2);
2459 __isl_give isl_map *isl_basic_map_union(
2460 __isl_take isl_basic_map *bmap1,
2461 __isl_take isl_basic_map *bmap2);
2462 __isl_give isl_set *isl_set_union(
2463 __isl_take isl_set *set1,
2464 __isl_take isl_set *set2);
2465 __isl_give isl_map *isl_map_union(
2466 __isl_take isl_map *map1,
2467 __isl_take isl_map *map2);
2468 __isl_give isl_union_set *isl_union_set_union(
2469 __isl_take isl_union_set *uset1,
2470 __isl_take isl_union_set *uset2);
2471 __isl_give isl_union_map *isl_union_map_union(
2472 __isl_take isl_union_map *umap1,
2473 __isl_take isl_union_map *umap2);
2475 =item * Set difference
2477 __isl_give isl_set *isl_set_subtract(
2478 __isl_take isl_set *set1,
2479 __isl_take isl_set *set2);
2480 __isl_give isl_map *isl_map_subtract(
2481 __isl_take isl_map *map1,
2482 __isl_take isl_map *map2);
2483 __isl_give isl_map *isl_map_subtract_domain(
2484 __isl_take isl_map *map,
2485 __isl_take isl_set *dom);
2486 __isl_give isl_map *isl_map_subtract_range(
2487 __isl_take isl_map *map,
2488 __isl_take isl_set *dom);
2489 __isl_give isl_union_set *isl_union_set_subtract(
2490 __isl_take isl_union_set *uset1,
2491 __isl_take isl_union_set *uset2);
2492 __isl_give isl_union_map *isl_union_map_subtract(
2493 __isl_take isl_union_map *umap1,
2494 __isl_take isl_union_map *umap2);
2498 __isl_give isl_basic_set *isl_basic_set_apply(
2499 __isl_take isl_basic_set *bset,
2500 __isl_take isl_basic_map *bmap);
2501 __isl_give isl_set *isl_set_apply(
2502 __isl_take isl_set *set,
2503 __isl_take isl_map *map);
2504 __isl_give isl_union_set *isl_union_set_apply(
2505 __isl_take isl_union_set *uset,
2506 __isl_take isl_union_map *umap);
2507 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2508 __isl_take isl_basic_map *bmap1,
2509 __isl_take isl_basic_map *bmap2);
2510 __isl_give isl_basic_map *isl_basic_map_apply_range(
2511 __isl_take isl_basic_map *bmap1,
2512 __isl_take isl_basic_map *bmap2);
2513 __isl_give isl_map *isl_map_apply_domain(
2514 __isl_take isl_map *map1,
2515 __isl_take isl_map *map2);
2516 __isl_give isl_union_map *isl_union_map_apply_domain(
2517 __isl_take isl_union_map *umap1,
2518 __isl_take isl_union_map *umap2);
2519 __isl_give isl_map *isl_map_apply_range(
2520 __isl_take isl_map *map1,
2521 __isl_take isl_map *map2);
2522 __isl_give isl_union_map *isl_union_map_apply_range(
2523 __isl_take isl_union_map *umap1,
2524 __isl_take isl_union_map *umap2);
2526 =item * Cartesian Product
2528 __isl_give isl_set *isl_set_product(
2529 __isl_take isl_set *set1,
2530 __isl_take isl_set *set2);
2531 __isl_give isl_union_set *isl_union_set_product(
2532 __isl_take isl_union_set *uset1,
2533 __isl_take isl_union_set *uset2);
2534 __isl_give isl_basic_map *isl_basic_map_domain_product(
2535 __isl_take isl_basic_map *bmap1,
2536 __isl_take isl_basic_map *bmap2);
2537 __isl_give isl_basic_map *isl_basic_map_range_product(
2538 __isl_take isl_basic_map *bmap1,
2539 __isl_take isl_basic_map *bmap2);
2540 __isl_give isl_map *isl_map_domain_product(
2541 __isl_take isl_map *map1,
2542 __isl_take isl_map *map2);
2543 __isl_give isl_map *isl_map_range_product(
2544 __isl_take isl_map *map1,
2545 __isl_take isl_map *map2);
2546 __isl_give isl_union_map *isl_union_map_range_product(
2547 __isl_take isl_union_map *umap1,
2548 __isl_take isl_union_map *umap2);
2549 __isl_give isl_map *isl_map_product(
2550 __isl_take isl_map *map1,
2551 __isl_take isl_map *map2);
2552 __isl_give isl_union_map *isl_union_map_product(
2553 __isl_take isl_union_map *umap1,
2554 __isl_take isl_union_map *umap2);
2556 The above functions compute the cross product of the given
2557 sets or relations. The domains and ranges of the results
2558 are wrapped maps between domains and ranges of the inputs.
2559 To obtain a ``flat'' product, use the following functions
2562 __isl_give isl_basic_set *isl_basic_set_flat_product(
2563 __isl_take isl_basic_set *bset1,
2564 __isl_take isl_basic_set *bset2);
2565 __isl_give isl_set *isl_set_flat_product(
2566 __isl_take isl_set *set1,
2567 __isl_take isl_set *set2);
2568 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2569 __isl_take isl_basic_map *bmap1,
2570 __isl_take isl_basic_map *bmap2);
2571 __isl_give isl_map *isl_map_flat_domain_product(
2572 __isl_take isl_map *map1,
2573 __isl_take isl_map *map2);
2574 __isl_give isl_map *isl_map_flat_range_product(
2575 __isl_take isl_map *map1,
2576 __isl_take isl_map *map2);
2577 __isl_give isl_union_map *isl_union_map_flat_range_product(
2578 __isl_take isl_union_map *umap1,
2579 __isl_take isl_union_map *umap2);
2580 __isl_give isl_basic_map *isl_basic_map_flat_product(
2581 __isl_take isl_basic_map *bmap1,
2582 __isl_take isl_basic_map *bmap2);
2583 __isl_give isl_map *isl_map_flat_product(
2584 __isl_take isl_map *map1,
2585 __isl_take isl_map *map2);
2587 =item * Simplification
2589 __isl_give isl_basic_set *isl_basic_set_gist(
2590 __isl_take isl_basic_set *bset,
2591 __isl_take isl_basic_set *context);
2592 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2593 __isl_take isl_set *context);
2594 __isl_give isl_set *isl_set_gist_params(
2595 __isl_take isl_set *set,
2596 __isl_take isl_set *context);
2597 __isl_give isl_union_set *isl_union_set_gist(
2598 __isl_take isl_union_set *uset,
2599 __isl_take isl_union_set *context);
2600 __isl_give isl_union_set *isl_union_set_gist_params(
2601 __isl_take isl_union_set *uset,
2602 __isl_take isl_set *set);
2603 __isl_give isl_basic_map *isl_basic_map_gist(
2604 __isl_take isl_basic_map *bmap,
2605 __isl_take isl_basic_map *context);
2606 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2607 __isl_take isl_map *context);
2608 __isl_give isl_map *isl_map_gist_params(
2609 __isl_take isl_map *map,
2610 __isl_take isl_set *context);
2611 __isl_give isl_map *isl_map_gist_domain(
2612 __isl_take isl_map *map,
2613 __isl_take isl_set *context);
2614 __isl_give isl_map *isl_map_gist_range(
2615 __isl_take isl_map *map,
2616 __isl_take isl_set *context);
2617 __isl_give isl_union_map *isl_union_map_gist(
2618 __isl_take isl_union_map *umap,
2619 __isl_take isl_union_map *context);
2620 __isl_give isl_union_map *isl_union_map_gist_params(
2621 __isl_take isl_union_map *umap,
2622 __isl_take isl_set *set);
2623 __isl_give isl_union_map *isl_union_map_gist_domain(
2624 __isl_take isl_union_map *umap,
2625 __isl_take isl_union_set *uset);
2626 __isl_give isl_union_map *isl_union_map_gist_range(
2627 __isl_take isl_union_map *umap,
2628 __isl_take isl_union_set *uset);
2630 The gist operation returns a set or relation that has the
2631 same intersection with the context as the input set or relation.
2632 Any implicit equality in the intersection is made explicit in the result,
2633 while all inequalities that are redundant with respect to the intersection
2635 In case of union sets and relations, the gist operation is performed
2640 =head3 Lexicographic Optimization
2642 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2643 the following functions
2644 compute a set that contains the lexicographic minimum or maximum
2645 of the elements in C<set> (or C<bset>) for those values of the parameters
2646 that satisfy C<dom>.
2647 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2648 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2650 In other words, the union of the parameter values
2651 for which the result is non-empty and of C<*empty>
2654 __isl_give isl_set *isl_basic_set_partial_lexmin(
2655 __isl_take isl_basic_set *bset,
2656 __isl_take isl_basic_set *dom,
2657 __isl_give isl_set **empty);
2658 __isl_give isl_set *isl_basic_set_partial_lexmax(
2659 __isl_take isl_basic_set *bset,
2660 __isl_take isl_basic_set *dom,
2661 __isl_give isl_set **empty);
2662 __isl_give isl_set *isl_set_partial_lexmin(
2663 __isl_take isl_set *set, __isl_take isl_set *dom,
2664 __isl_give isl_set **empty);
2665 __isl_give isl_set *isl_set_partial_lexmax(
2666 __isl_take isl_set *set, __isl_take isl_set *dom,
2667 __isl_give isl_set **empty);
2669 Given a (basic) set C<set> (or C<bset>), the following functions simply
2670 return a set containing the lexicographic minimum or maximum
2671 of the elements in C<set> (or C<bset>).
2672 In case of union sets, the optimum is computed per space.
2674 __isl_give isl_set *isl_basic_set_lexmin(
2675 __isl_take isl_basic_set *bset);
2676 __isl_give isl_set *isl_basic_set_lexmax(
2677 __isl_take isl_basic_set *bset);
2678 __isl_give isl_set *isl_set_lexmin(
2679 __isl_take isl_set *set);
2680 __isl_give isl_set *isl_set_lexmax(
2681 __isl_take isl_set *set);
2682 __isl_give isl_union_set *isl_union_set_lexmin(
2683 __isl_take isl_union_set *uset);
2684 __isl_give isl_union_set *isl_union_set_lexmax(
2685 __isl_take isl_union_set *uset);
2687 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2688 the following functions
2689 compute a relation that maps each element of C<dom>
2690 to the single lexicographic minimum or maximum
2691 of the elements that are associated to that same
2692 element in C<map> (or C<bmap>).
2693 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2694 that contains the elements in C<dom> that do not map
2695 to any elements in C<map> (or C<bmap>).
2696 In other words, the union of the domain of the result and of C<*empty>
2699 __isl_give isl_map *isl_basic_map_partial_lexmax(
2700 __isl_take isl_basic_map *bmap,
2701 __isl_take isl_basic_set *dom,
2702 __isl_give isl_set **empty);
2703 __isl_give isl_map *isl_basic_map_partial_lexmin(
2704 __isl_take isl_basic_map *bmap,
2705 __isl_take isl_basic_set *dom,
2706 __isl_give isl_set **empty);
2707 __isl_give isl_map *isl_map_partial_lexmax(
2708 __isl_take isl_map *map, __isl_take isl_set *dom,
2709 __isl_give isl_set **empty);
2710 __isl_give isl_map *isl_map_partial_lexmin(
2711 __isl_take isl_map *map, __isl_take isl_set *dom,
2712 __isl_give isl_set **empty);
2714 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2715 return a map mapping each element in the domain of
2716 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2717 of all elements associated to that element.
2718 In case of union relations, the optimum is computed per space.
2720 __isl_give isl_map *isl_basic_map_lexmin(
2721 __isl_take isl_basic_map *bmap);
2722 __isl_give isl_map *isl_basic_map_lexmax(
2723 __isl_take isl_basic_map *bmap);
2724 __isl_give isl_map *isl_map_lexmin(
2725 __isl_take isl_map *map);
2726 __isl_give isl_map *isl_map_lexmax(
2727 __isl_take isl_map *map);
2728 __isl_give isl_union_map *isl_union_map_lexmin(
2729 __isl_take isl_union_map *umap);
2730 __isl_give isl_union_map *isl_union_map_lexmax(
2731 __isl_take isl_union_map *umap);
2733 The following functions return their result in the form of
2734 a piecewise multi-affine expression
2735 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2736 but are otherwise equivalent to the corresponding functions
2737 returning a basic set or relation.
2739 __isl_give isl_pw_multi_aff *
2740 isl_basic_map_lexmin_pw_multi_aff(
2741 __isl_take isl_basic_map *bmap);
2742 __isl_give isl_pw_multi_aff *
2743 isl_basic_set_partial_lexmin_pw_multi_aff(
2744 __isl_take isl_basic_set *bset,
2745 __isl_take isl_basic_set *dom,
2746 __isl_give isl_set **empty);
2747 __isl_give isl_pw_multi_aff *
2748 isl_basic_set_partial_lexmax_pw_multi_aff(
2749 __isl_take isl_basic_set *bset,
2750 __isl_take isl_basic_set *dom,
2751 __isl_give isl_set **empty);
2752 __isl_give isl_pw_multi_aff *
2753 isl_basic_map_partial_lexmin_pw_multi_aff(
2754 __isl_take isl_basic_map *bmap,
2755 __isl_take isl_basic_set *dom,
2756 __isl_give isl_set **empty);
2757 __isl_give isl_pw_multi_aff *
2758 isl_basic_map_partial_lexmax_pw_multi_aff(
2759 __isl_take isl_basic_map *bmap,
2760 __isl_take isl_basic_set *dom,
2761 __isl_give isl_set **empty);
2765 Lists are defined over several element types, including
2766 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2767 Here we take lists of C<isl_set>s as an example.
2768 Lists can be created, copied and freed using the following functions.
2770 #include <isl/list.h>
2771 __isl_give isl_set_list *isl_set_list_from_set(
2772 __isl_take isl_set *el);
2773 __isl_give isl_set_list *isl_set_list_alloc(
2774 isl_ctx *ctx, int n);
2775 __isl_give isl_set_list *isl_set_list_copy(
2776 __isl_keep isl_set_list *list);
2777 __isl_give isl_set_list *isl_set_list_add(
2778 __isl_take isl_set_list *list,
2779 __isl_take isl_set *el);
2780 __isl_give isl_set_list *isl_set_list_concat(
2781 __isl_take isl_set_list *list1,
2782 __isl_take isl_set_list *list2);
2783 void *isl_set_list_free(__isl_take isl_set_list *list);
2785 C<isl_set_list_alloc> creates an empty list with a capacity for
2786 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2789 Lists can be inspected using the following functions.
2791 #include <isl/list.h>
2792 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2793 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2794 __isl_give isl_set *isl_set_list_get_set(
2795 __isl_keep isl_set_list *list, int index);
2796 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2797 int (*fn)(__isl_take isl_set *el, void *user),
2800 Lists can be printed using
2802 #include <isl/list.h>
2803 __isl_give isl_printer *isl_printer_print_set_list(
2804 __isl_take isl_printer *p,
2805 __isl_keep isl_set_list *list);
2809 Vectors can be created, copied and freed using the following functions.
2811 #include <isl/vec.h>
2812 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2814 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2815 void isl_vec_free(__isl_take isl_vec *vec);
2817 Note that the elements of a newly created vector may have arbitrary values.
2818 The elements can be changed and inspected using the following functions.
2820 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2821 int isl_vec_size(__isl_keep isl_vec *vec);
2822 int isl_vec_get_element(__isl_keep isl_vec *vec,
2823 int pos, isl_int *v);
2824 __isl_give isl_vec *isl_vec_set_element(
2825 __isl_take isl_vec *vec, int pos, isl_int v);
2826 __isl_give isl_vec *isl_vec_set_element_si(
2827 __isl_take isl_vec *vec, int pos, int v);
2828 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2830 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2833 C<isl_vec_get_element> will return a negative value if anything went wrong.
2834 In that case, the value of C<*v> is undefined.
2838 Matrices can be created, copied and freed using the following functions.
2840 #include <isl/mat.h>
2841 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2842 unsigned n_row, unsigned n_col);
2843 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2844 void isl_mat_free(__isl_take isl_mat *mat);
2846 Note that the elements of a newly created matrix may have arbitrary values.
2847 The elements can be changed and inspected using the following functions.
2849 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2850 int isl_mat_rows(__isl_keep isl_mat *mat);
2851 int isl_mat_cols(__isl_keep isl_mat *mat);
2852 int isl_mat_get_element(__isl_keep isl_mat *mat,
2853 int row, int col, isl_int *v);
2854 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2855 int row, int col, isl_int v);
2856 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2857 int row, int col, int v);
2859 C<isl_mat_get_element> will return a negative value if anything went wrong.
2860 In that case, the value of C<*v> is undefined.
2862 The following function can be used to compute the (right) inverse
2863 of a matrix, i.e., a matrix such that the product of the original
2864 and the inverse (in that order) is a multiple of the identity matrix.
2865 The input matrix is assumed to be of full row-rank.
2867 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2869 The following function can be used to compute the (right) kernel
2870 (or null space) of a matrix, i.e., a matrix such that the product of
2871 the original and the kernel (in that order) is the zero matrix.
2873 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2875 =head2 Piecewise Quasi Affine Expressions
2877 The zero quasi affine expression on a given domain can be created using
2879 __isl_give isl_aff *isl_aff_zero_on_domain(
2880 __isl_take isl_local_space *ls);
2882 Note that the space in which the resulting object lives is a map space
2883 with the given space as domain and a one-dimensional range.
2885 An empty piecewise quasi affine expression (one with no cells)
2886 or a piecewise quasi affine expression with a single cell can
2887 be created using the following functions.
2889 #include <isl/aff.h>
2890 __isl_give isl_pw_aff *isl_pw_aff_empty(
2891 __isl_take isl_space *space);
2892 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2893 __isl_take isl_set *set, __isl_take isl_aff *aff);
2894 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2895 __isl_take isl_aff *aff);
2897 A piecewise quasi affine expression that is equal to 1 on a set
2898 and 0 outside the set can be created using the following function.
2900 #include <isl/aff.h>
2901 __isl_give isl_pw_aff *isl_set_indicator_function(
2902 __isl_take isl_set *set);
2904 Quasi affine expressions can be copied and freed using
2906 #include <isl/aff.h>
2907 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2908 void *isl_aff_free(__isl_take isl_aff *aff);
2910 __isl_give isl_pw_aff *isl_pw_aff_copy(
2911 __isl_keep isl_pw_aff *pwaff);
2912 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2914 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2915 using the following function. The constraint is required to have
2916 a non-zero coefficient for the specified dimension.
2918 #include <isl/constraint.h>
2919 __isl_give isl_aff *isl_constraint_get_bound(
2920 __isl_keep isl_constraint *constraint,
2921 enum isl_dim_type type, int pos);
2923 The entire affine expression of the constraint can also be extracted
2924 using the following function.
2926 #include <isl/constraint.h>
2927 __isl_give isl_aff *isl_constraint_get_aff(
2928 __isl_keep isl_constraint *constraint);
2930 Conversely, an equality constraint equating
2931 the affine expression to zero or an inequality constraint enforcing
2932 the affine expression to be non-negative, can be constructed using
2934 __isl_give isl_constraint *isl_equality_from_aff(
2935 __isl_take isl_aff *aff);
2936 __isl_give isl_constraint *isl_inequality_from_aff(
2937 __isl_take isl_aff *aff);
2939 The expression can be inspected using
2941 #include <isl/aff.h>
2942 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2943 int isl_aff_dim(__isl_keep isl_aff *aff,
2944 enum isl_dim_type type);
2945 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2946 __isl_keep isl_aff *aff);
2947 __isl_give isl_local_space *isl_aff_get_local_space(
2948 __isl_keep isl_aff *aff);
2949 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2950 enum isl_dim_type type, unsigned pos);
2951 const char *isl_pw_aff_get_dim_name(
2952 __isl_keep isl_pw_aff *pa,
2953 enum isl_dim_type type, unsigned pos);
2954 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2955 enum isl_dim_type type, unsigned pos);
2956 __isl_give isl_id *isl_pw_aff_get_dim_id(
2957 __isl_keep isl_pw_aff *pa,
2958 enum isl_dim_type type, unsigned pos);
2959 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2961 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2962 enum isl_dim_type type, int pos, isl_int *v);
2963 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2965 __isl_give isl_aff *isl_aff_get_div(
2966 __isl_keep isl_aff *aff, int pos);
2968 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2969 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2970 int (*fn)(__isl_take isl_set *set,
2971 __isl_take isl_aff *aff,
2972 void *user), void *user);
2974 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2975 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2977 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2978 enum isl_dim_type type, unsigned first, unsigned n);
2979 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2980 enum isl_dim_type type, unsigned first, unsigned n);
2982 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2983 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2984 enum isl_dim_type type);
2985 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2987 It can be modified using
2989 #include <isl/aff.h>
2990 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2991 __isl_take isl_pw_aff *pwaff,
2992 enum isl_dim_type type, __isl_take isl_id *id);
2993 __isl_give isl_aff *isl_aff_set_dim_name(
2994 __isl_take isl_aff *aff, enum isl_dim_type type,
2995 unsigned pos, const char *s);
2996 __isl_give isl_aff *isl_aff_set_dim_id(
2997 __isl_take isl_aff *aff, enum isl_dim_type type,
2998 unsigned pos, __isl_take isl_id *id);
2999 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3000 __isl_take isl_pw_aff *pma,
3001 enum isl_dim_type type, unsigned pos,
3002 __isl_take isl_id *id);
3003 __isl_give isl_aff *isl_aff_set_constant(
3004 __isl_take isl_aff *aff, isl_int v);
3005 __isl_give isl_aff *isl_aff_set_constant_si(
3006 __isl_take isl_aff *aff, int v);
3007 __isl_give isl_aff *isl_aff_set_coefficient(
3008 __isl_take isl_aff *aff,
3009 enum isl_dim_type type, int pos, isl_int v);
3010 __isl_give isl_aff *isl_aff_set_coefficient_si(
3011 __isl_take isl_aff *aff,
3012 enum isl_dim_type type, int pos, int v);
3013 __isl_give isl_aff *isl_aff_set_denominator(
3014 __isl_take isl_aff *aff, isl_int v);
3016 __isl_give isl_aff *isl_aff_add_constant(
3017 __isl_take isl_aff *aff, isl_int v);
3018 __isl_give isl_aff *isl_aff_add_constant_si(
3019 __isl_take isl_aff *aff, int v);
3020 __isl_give isl_aff *isl_aff_add_coefficient(
3021 __isl_take isl_aff *aff,
3022 enum isl_dim_type type, int pos, isl_int v);
3023 __isl_give isl_aff *isl_aff_add_coefficient_si(
3024 __isl_take isl_aff *aff,
3025 enum isl_dim_type type, int pos, int v);
3027 __isl_give isl_aff *isl_aff_insert_dims(
3028 __isl_take isl_aff *aff,
3029 enum isl_dim_type type, unsigned first, unsigned n);
3030 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3031 __isl_take isl_pw_aff *pwaff,
3032 enum isl_dim_type type, unsigned first, unsigned n);
3033 __isl_give isl_aff *isl_aff_add_dims(
3034 __isl_take isl_aff *aff,
3035 enum isl_dim_type type, unsigned n);
3036 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3037 __isl_take isl_pw_aff *pwaff,
3038 enum isl_dim_type type, unsigned n);
3039 __isl_give isl_aff *isl_aff_drop_dims(
3040 __isl_take isl_aff *aff,
3041 enum isl_dim_type type, unsigned first, unsigned n);
3042 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3043 __isl_take isl_pw_aff *pwaff,
3044 enum isl_dim_type type, unsigned first, unsigned n);
3046 Note that the C<set_constant> and C<set_coefficient> functions
3047 set the I<numerator> of the constant or coefficient, while
3048 C<add_constant> and C<add_coefficient> add an integer value to
3049 the possibly rational constant or coefficient.
3051 To check whether an affine expressions is obviously zero
3052 or obviously equal to some other affine expression, use
3054 #include <isl/aff.h>
3055 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3056 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3057 __isl_keep isl_aff *aff2);
3058 int isl_pw_aff_plain_is_equal(
3059 __isl_keep isl_pw_aff *pwaff1,
3060 __isl_keep isl_pw_aff *pwaff2);
3064 #include <isl/aff.h>
3065 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3066 __isl_take isl_aff *aff2);
3067 __isl_give isl_pw_aff *isl_pw_aff_add(
3068 __isl_take isl_pw_aff *pwaff1,
3069 __isl_take isl_pw_aff *pwaff2);
3070 __isl_give isl_pw_aff *isl_pw_aff_min(
3071 __isl_take isl_pw_aff *pwaff1,
3072 __isl_take isl_pw_aff *pwaff2);
3073 __isl_give isl_pw_aff *isl_pw_aff_max(
3074 __isl_take isl_pw_aff *pwaff1,
3075 __isl_take isl_pw_aff *pwaff2);
3076 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3077 __isl_take isl_aff *aff2);
3078 __isl_give isl_pw_aff *isl_pw_aff_sub(
3079 __isl_take isl_pw_aff *pwaff1,
3080 __isl_take isl_pw_aff *pwaff2);
3081 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3082 __isl_give isl_pw_aff *isl_pw_aff_neg(
3083 __isl_take isl_pw_aff *pwaff);
3084 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3085 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3086 __isl_take isl_pw_aff *pwaff);
3087 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3088 __isl_give isl_pw_aff *isl_pw_aff_floor(
3089 __isl_take isl_pw_aff *pwaff);
3090 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3092 __isl_give isl_pw_aff *isl_pw_aff_mod(
3093 __isl_take isl_pw_aff *pwaff, isl_int mod);
3094 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3096 __isl_give isl_pw_aff *isl_pw_aff_scale(
3097 __isl_take isl_pw_aff *pwaff, isl_int f);
3098 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3100 __isl_give isl_aff *isl_aff_scale_down_ui(
3101 __isl_take isl_aff *aff, unsigned f);
3102 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3103 __isl_take isl_pw_aff *pwaff, isl_int f);
3105 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3106 __isl_take isl_pw_aff_list *list);
3107 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3108 __isl_take isl_pw_aff_list *list);
3110 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3111 __isl_take isl_pw_aff *pwqp);
3113 __isl_give isl_aff *isl_aff_align_params(
3114 __isl_take isl_aff *aff,
3115 __isl_take isl_space *model);
3116 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3117 __isl_take isl_pw_aff *pwaff,
3118 __isl_take isl_space *model);
3120 __isl_give isl_aff *isl_aff_project_domain_on_params(
3121 __isl_take isl_aff *aff);
3123 __isl_give isl_aff *isl_aff_gist_params(
3124 __isl_take isl_aff *aff,
3125 __isl_take isl_set *context);
3126 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3127 __isl_take isl_set *context);
3128 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3129 __isl_take isl_pw_aff *pwaff,
3130 __isl_take isl_set *context);
3131 __isl_give isl_pw_aff *isl_pw_aff_gist(
3132 __isl_take isl_pw_aff *pwaff,
3133 __isl_take isl_set *context);
3135 __isl_give isl_set *isl_pw_aff_domain(
3136 __isl_take isl_pw_aff *pwaff);
3137 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3138 __isl_take isl_pw_aff *pa,
3139 __isl_take isl_set *set);
3140 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3141 __isl_take isl_pw_aff *pa,
3142 __isl_take isl_set *set);
3144 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3145 __isl_take isl_aff *aff2);
3146 __isl_give isl_pw_aff *isl_pw_aff_mul(
3147 __isl_take isl_pw_aff *pwaff1,
3148 __isl_take isl_pw_aff *pwaff2);
3150 When multiplying two affine expressions, at least one of the two needs
3153 #include <isl/aff.h>
3154 __isl_give isl_basic_set *isl_aff_le_basic_set(
3155 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3156 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3157 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3158 __isl_give isl_set *isl_pw_aff_eq_set(
3159 __isl_take isl_pw_aff *pwaff1,
3160 __isl_take isl_pw_aff *pwaff2);
3161 __isl_give isl_set *isl_pw_aff_ne_set(
3162 __isl_take isl_pw_aff *pwaff1,
3163 __isl_take isl_pw_aff *pwaff2);
3164 __isl_give isl_set *isl_pw_aff_le_set(
3165 __isl_take isl_pw_aff *pwaff1,
3166 __isl_take isl_pw_aff *pwaff2);
3167 __isl_give isl_set *isl_pw_aff_lt_set(
3168 __isl_take isl_pw_aff *pwaff1,
3169 __isl_take isl_pw_aff *pwaff2);
3170 __isl_give isl_set *isl_pw_aff_ge_set(
3171 __isl_take isl_pw_aff *pwaff1,
3172 __isl_take isl_pw_aff *pwaff2);
3173 __isl_give isl_set *isl_pw_aff_gt_set(
3174 __isl_take isl_pw_aff *pwaff1,
3175 __isl_take isl_pw_aff *pwaff2);
3177 __isl_give isl_set *isl_pw_aff_list_eq_set(
3178 __isl_take isl_pw_aff_list *list1,
3179 __isl_take isl_pw_aff_list *list2);
3180 __isl_give isl_set *isl_pw_aff_list_ne_set(
3181 __isl_take isl_pw_aff_list *list1,
3182 __isl_take isl_pw_aff_list *list2);
3183 __isl_give isl_set *isl_pw_aff_list_le_set(
3184 __isl_take isl_pw_aff_list *list1,
3185 __isl_take isl_pw_aff_list *list2);
3186 __isl_give isl_set *isl_pw_aff_list_lt_set(
3187 __isl_take isl_pw_aff_list *list1,
3188 __isl_take isl_pw_aff_list *list2);
3189 __isl_give isl_set *isl_pw_aff_list_ge_set(
3190 __isl_take isl_pw_aff_list *list1,
3191 __isl_take isl_pw_aff_list *list2);
3192 __isl_give isl_set *isl_pw_aff_list_gt_set(
3193 __isl_take isl_pw_aff_list *list1,
3194 __isl_take isl_pw_aff_list *list2);
3196 The function C<isl_aff_ge_basic_set> returns a basic set
3197 containing those elements in the shared space
3198 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3199 The function C<isl_aff_ge_set> returns a set
3200 containing those elements in the shared domain
3201 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3202 The functions operating on C<isl_pw_aff_list> apply the corresponding
3203 C<isl_pw_aff> function to each pair of elements in the two lists.
3205 #include <isl/aff.h>
3206 __isl_give isl_set *isl_pw_aff_nonneg_set(
3207 __isl_take isl_pw_aff *pwaff);
3208 __isl_give isl_set *isl_pw_aff_zero_set(
3209 __isl_take isl_pw_aff *pwaff);
3210 __isl_give isl_set *isl_pw_aff_non_zero_set(
3211 __isl_take isl_pw_aff *pwaff);
3213 The function C<isl_pw_aff_nonneg_set> returns a set
3214 containing those elements in the domain
3215 of C<pwaff> where C<pwaff> is non-negative.
3217 #include <isl/aff.h>
3218 __isl_give isl_pw_aff *isl_pw_aff_cond(
3219 __isl_take isl_pw_aff *cond,
3220 __isl_take isl_pw_aff *pwaff_true,
3221 __isl_take isl_pw_aff *pwaff_false);
3223 The function C<isl_pw_aff_cond> performs a conditional operator
3224 and returns an expression that is equal to C<pwaff_true>
3225 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3226 where C<cond> is zero.
3228 #include <isl/aff.h>
3229 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3230 __isl_take isl_pw_aff *pwaff1,
3231 __isl_take isl_pw_aff *pwaff2);
3232 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3233 __isl_take isl_pw_aff *pwaff1,
3234 __isl_take isl_pw_aff *pwaff2);
3235 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3236 __isl_take isl_pw_aff *pwaff1,
3237 __isl_take isl_pw_aff *pwaff2);
3239 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3240 expression with a domain that is the union of those of C<pwaff1> and
3241 C<pwaff2> and such that on each cell, the quasi-affine expression is
3242 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3243 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3244 associated expression is the defined one.
3246 An expression can be read from input using
3248 #include <isl/aff.h>
3249 __isl_give isl_aff *isl_aff_read_from_str(
3250 isl_ctx *ctx, const char *str);
3251 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3252 isl_ctx *ctx, const char *str);
3254 An expression can be printed using
3256 #include <isl/aff.h>
3257 __isl_give isl_printer *isl_printer_print_aff(
3258 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3260 __isl_give isl_printer *isl_printer_print_pw_aff(
3261 __isl_take isl_printer *p,
3262 __isl_keep isl_pw_aff *pwaff);
3264 =head2 Piecewise Multiple Quasi Affine Expressions
3266 An C<isl_multi_aff> object represents a sequence of
3267 zero or more affine expressions, all defined on the same domain space.
3269 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3272 #include <isl/aff.h>
3273 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3274 __isl_take isl_space *space,
3275 __isl_take isl_aff_list *list);
3277 An empty piecewise multiple quasi affine expression (one with no cells),
3278 the zero piecewise multiple quasi affine expression (with value zero
3279 for each output dimension),
3280 a piecewise multiple quasi affine expression with a single cell (with
3281 either a universe or a specified domain) or
3282 a zero-dimensional piecewise multiple quasi affine expression
3284 can be created using the following functions.
3286 #include <isl/aff.h>
3287 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3288 __isl_take isl_space *space);
3289 __isl_give isl_multi_aff *isl_multi_aff_zero(
3290 __isl_take isl_space *space);
3291 __isl_give isl_pw_multi_aff *
3292 isl_pw_multi_aff_from_multi_aff(
3293 __isl_take isl_multi_aff *ma);
3294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3295 __isl_take isl_set *set,
3296 __isl_take isl_multi_aff *maff);
3297 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3298 __isl_take isl_set *set);
3300 __isl_give isl_union_pw_multi_aff *
3301 isl_union_pw_multi_aff_empty(
3302 __isl_take isl_space *space);
3303 __isl_give isl_union_pw_multi_aff *
3304 isl_union_pw_multi_aff_add_pw_multi_aff(
3305 __isl_take isl_union_pw_multi_aff *upma,
3306 __isl_take isl_pw_multi_aff *pma);
3307 __isl_give isl_union_pw_multi_aff *
3308 isl_union_pw_multi_aff_from_domain(
3309 __isl_take isl_union_set *uset);
3311 A piecewise multiple quasi affine expression can also be initialized
3312 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3313 and the C<isl_map> is single-valued.
3315 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3316 __isl_take isl_set *set);
3317 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3318 __isl_take isl_map *map);
3320 Multiple quasi affine expressions can be copied and freed using
3322 #include <isl/aff.h>
3323 __isl_give isl_multi_aff *isl_multi_aff_copy(
3324 __isl_keep isl_multi_aff *maff);
3325 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3327 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3328 __isl_keep isl_pw_multi_aff *pma);
3329 void *isl_pw_multi_aff_free(
3330 __isl_take isl_pw_multi_aff *pma);
3332 __isl_give isl_union_pw_multi_aff *
3333 isl_union_pw_multi_aff_copy(
3334 __isl_keep isl_union_pw_multi_aff *upma);
3335 void *isl_union_pw_multi_aff_free(
3336 __isl_take isl_union_pw_multi_aff *upma);
3338 The expression can be inspected using
3340 #include <isl/aff.h>
3341 isl_ctx *isl_multi_aff_get_ctx(
3342 __isl_keep isl_multi_aff *maff);
3343 isl_ctx *isl_pw_multi_aff_get_ctx(
3344 __isl_keep isl_pw_multi_aff *pma);
3345 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3346 __isl_keep isl_union_pw_multi_aff *upma);
3347 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3348 enum isl_dim_type type);
3349 unsigned isl_pw_multi_aff_dim(
3350 __isl_keep isl_pw_multi_aff *pma,
3351 enum isl_dim_type type);
3352 __isl_give isl_aff *isl_multi_aff_get_aff(
3353 __isl_keep isl_multi_aff *multi, int pos);
3354 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3355 __isl_keep isl_pw_multi_aff *pma, int pos);
3356 const char *isl_pw_multi_aff_get_dim_name(
3357 __isl_keep isl_pw_multi_aff *pma,
3358 enum isl_dim_type type, unsigned pos);
3359 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3360 __isl_keep isl_pw_multi_aff *pma,
3361 enum isl_dim_type type, unsigned pos);
3362 const char *isl_multi_aff_get_tuple_name(
3363 __isl_keep isl_multi_aff *multi,
3364 enum isl_dim_type type);
3365 const char *isl_pw_multi_aff_get_tuple_name(
3366 __isl_keep isl_pw_multi_aff *pma,
3367 enum isl_dim_type type);
3368 int isl_pw_multi_aff_has_tuple_id(
3369 __isl_keep isl_pw_multi_aff *pma,
3370 enum isl_dim_type type);
3371 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3372 __isl_keep isl_pw_multi_aff *pma,
3373 enum isl_dim_type type);
3375 int isl_pw_multi_aff_foreach_piece(
3376 __isl_keep isl_pw_multi_aff *pma,
3377 int (*fn)(__isl_take isl_set *set,
3378 __isl_take isl_multi_aff *maff,
3379 void *user), void *user);
3381 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3382 __isl_keep isl_union_pw_multi_aff *upma,
3383 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3384 void *user), void *user);
3386 It can be modified using
3388 #include <isl/aff.h>
3389 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3390 __isl_take isl_multi_aff *multi, int pos,
3391 __isl_take isl_aff *aff);
3392 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3393 __isl_take isl_multi_aff *maff,
3394 enum isl_dim_type type, unsigned pos, const char *s);
3395 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3396 __isl_take isl_multi_aff *maff,
3397 enum isl_dim_type type, __isl_take isl_id *id);
3398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3399 __isl_take isl_pw_multi_aff *pma,
3400 enum isl_dim_type type, __isl_take isl_id *id);
3402 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3403 __isl_take isl_multi_aff *maff,
3404 enum isl_dim_type type, unsigned first, unsigned n);
3406 To check whether two multiple affine expressions are
3407 obviously equal to each other, use
3409 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3410 __isl_keep isl_multi_aff *maff2);
3411 int isl_pw_multi_aff_plain_is_equal(
3412 __isl_keep isl_pw_multi_aff *pma1,
3413 __isl_keep isl_pw_multi_aff *pma2);
3417 #include <isl/aff.h>
3418 __isl_give isl_multi_aff *isl_multi_aff_add(
3419 __isl_take isl_multi_aff *maff1,
3420 __isl_take isl_multi_aff *maff2);
3421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3422 __isl_take isl_pw_multi_aff *pma1,
3423 __isl_take isl_pw_multi_aff *pma2);
3424 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3425 __isl_take isl_union_pw_multi_aff *upma1,
3426 __isl_take isl_union_pw_multi_aff *upma2);
3427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3428 __isl_take isl_pw_multi_aff *pma1,
3429 __isl_take isl_pw_multi_aff *pma2);
3430 __isl_give isl_multi_aff *isl_multi_aff_scale(
3431 __isl_take isl_multi_aff *maff,
3433 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3434 __isl_take isl_pw_multi_aff *pma,
3435 __isl_take isl_set *set);
3436 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3437 __isl_take isl_pw_multi_aff *pma,
3438 __isl_take isl_set *set);
3439 __isl_give isl_multi_aff *isl_multi_aff_lift(
3440 __isl_take isl_multi_aff *maff,
3441 __isl_give isl_local_space **ls);
3442 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3443 __isl_take isl_pw_multi_aff *pma);
3444 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3445 __isl_take isl_multi_aff *maff,
3446 __isl_take isl_set *context);
3447 __isl_give isl_multi_aff *isl_multi_aff_gist(
3448 __isl_take isl_multi_aff *maff,
3449 __isl_take isl_set *context);
3450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3451 __isl_take isl_pw_multi_aff *pma,
3452 __isl_take isl_set *set);
3453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3454 __isl_take isl_pw_multi_aff *pma,
3455 __isl_take isl_set *set);
3456 __isl_give isl_set *isl_pw_multi_aff_domain(
3457 __isl_take isl_pw_multi_aff *pma);
3458 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3459 __isl_take isl_union_pw_multi_aff *upma);
3460 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3461 __isl_take isl_multi_aff *ma1,
3462 __isl_take isl_multi_aff *ma2);
3463 __isl_give isl_pw_multi_aff *
3464 isl_pw_multi_aff_flat_range_product(
3465 __isl_take isl_pw_multi_aff *pma1,
3466 __isl_take isl_pw_multi_aff *pma2);
3467 __isl_give isl_union_pw_multi_aff *
3468 isl_union_pw_multi_aff_flat_range_product(
3469 __isl_take isl_union_pw_multi_aff *upma1,
3470 __isl_take isl_union_pw_multi_aff *upma2);
3472 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3473 then it is assigned the local space that lies at the basis of
3474 the lifting applied.
3476 An expression can be read from input using
3478 #include <isl/aff.h>
3479 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3480 isl_ctx *ctx, const char *str);
3481 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3482 isl_ctx *ctx, const char *str);
3484 An expression can be printed using
3486 #include <isl/aff.h>
3487 __isl_give isl_printer *isl_printer_print_multi_aff(
3488 __isl_take isl_printer *p,
3489 __isl_keep isl_multi_aff *maff);
3490 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3491 __isl_take isl_printer *p,
3492 __isl_keep isl_pw_multi_aff *pma);
3493 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3494 __isl_take isl_printer *p,
3495 __isl_keep isl_union_pw_multi_aff *upma);
3499 Points are elements of a set. They can be used to construct
3500 simple sets (boxes) or they can be used to represent the
3501 individual elements of a set.
3502 The zero point (the origin) can be created using
3504 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3506 The coordinates of a point can be inspected, set and changed
3509 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3510 enum isl_dim_type type, int pos, isl_int *v);
3511 __isl_give isl_point *isl_point_set_coordinate(
3512 __isl_take isl_point *pnt,
3513 enum isl_dim_type type, int pos, isl_int v);
3515 __isl_give isl_point *isl_point_add_ui(
3516 __isl_take isl_point *pnt,
3517 enum isl_dim_type type, int pos, unsigned val);
3518 __isl_give isl_point *isl_point_sub_ui(
3519 __isl_take isl_point *pnt,
3520 enum isl_dim_type type, int pos, unsigned val);
3522 Other properties can be obtained using
3524 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3526 Points can be copied or freed using
3528 __isl_give isl_point *isl_point_copy(
3529 __isl_keep isl_point *pnt);
3530 void isl_point_free(__isl_take isl_point *pnt);
3532 A singleton set can be created from a point using
3534 __isl_give isl_basic_set *isl_basic_set_from_point(
3535 __isl_take isl_point *pnt);
3536 __isl_give isl_set *isl_set_from_point(
3537 __isl_take isl_point *pnt);
3539 and a box can be created from two opposite extremal points using
3541 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3542 __isl_take isl_point *pnt1,
3543 __isl_take isl_point *pnt2);
3544 __isl_give isl_set *isl_set_box_from_points(
3545 __isl_take isl_point *pnt1,
3546 __isl_take isl_point *pnt2);
3548 All elements of a B<bounded> (union) set can be enumerated using
3549 the following functions.
3551 int isl_set_foreach_point(__isl_keep isl_set *set,
3552 int (*fn)(__isl_take isl_point *pnt, void *user),
3554 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3555 int (*fn)(__isl_take isl_point *pnt, void *user),
3558 The function C<fn> is called for each integer point in
3559 C<set> with as second argument the last argument of
3560 the C<isl_set_foreach_point> call. The function C<fn>
3561 should return C<0> on success and C<-1> on failure.
3562 In the latter case, C<isl_set_foreach_point> will stop
3563 enumerating and return C<-1> as well.
3564 If the enumeration is performed successfully and to completion,
3565 then C<isl_set_foreach_point> returns C<0>.
3567 To obtain a single point of a (basic) set, use
3569 __isl_give isl_point *isl_basic_set_sample_point(
3570 __isl_take isl_basic_set *bset);
3571 __isl_give isl_point *isl_set_sample_point(
3572 __isl_take isl_set *set);
3574 If C<set> does not contain any (integer) points, then the
3575 resulting point will be ``void'', a property that can be
3578 int isl_point_is_void(__isl_keep isl_point *pnt);
3580 =head2 Piecewise Quasipolynomials
3582 A piecewise quasipolynomial is a particular kind of function that maps
3583 a parametric point to a rational value.
3584 More specifically, a quasipolynomial is a polynomial expression in greatest
3585 integer parts of affine expressions of parameters and variables.
3586 A piecewise quasipolynomial is a subdivision of a given parametric
3587 domain into disjoint cells with a quasipolynomial associated to
3588 each cell. The value of the piecewise quasipolynomial at a given
3589 point is the value of the quasipolynomial associated to the cell
3590 that contains the point. Outside of the union of cells,
3591 the value is assumed to be zero.
3592 For example, the piecewise quasipolynomial
3594 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3596 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3597 A given piecewise quasipolynomial has a fixed domain dimension.
3598 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3599 defined over different domains.
3600 Piecewise quasipolynomials are mainly used by the C<barvinok>
3601 library for representing the number of elements in a parametric set or map.
3602 For example, the piecewise quasipolynomial above represents
3603 the number of points in the map
3605 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3607 =head3 Input and Output
3609 Piecewise quasipolynomials can be read from input using
3611 __isl_give isl_union_pw_qpolynomial *
3612 isl_union_pw_qpolynomial_read_from_str(
3613 isl_ctx *ctx, const char *str);
3615 Quasipolynomials and piecewise quasipolynomials can be printed
3616 using the following functions.
3618 __isl_give isl_printer *isl_printer_print_qpolynomial(
3619 __isl_take isl_printer *p,
3620 __isl_keep isl_qpolynomial *qp);
3622 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3623 __isl_take isl_printer *p,
3624 __isl_keep isl_pw_qpolynomial *pwqp);
3626 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3627 __isl_take isl_printer *p,
3628 __isl_keep isl_union_pw_qpolynomial *upwqp);
3630 The output format of the printer
3631 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3632 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3634 In case of printing in C<ISL_FORMAT_C>, the user may want
3635 to set the names of all dimensions
3637 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3638 __isl_take isl_qpolynomial *qp,
3639 enum isl_dim_type type, unsigned pos,
3641 __isl_give isl_pw_qpolynomial *
3642 isl_pw_qpolynomial_set_dim_name(
3643 __isl_take isl_pw_qpolynomial *pwqp,
3644 enum isl_dim_type type, unsigned pos,
3647 =head3 Creating New (Piecewise) Quasipolynomials
3649 Some simple quasipolynomials can be created using the following functions.
3650 More complicated quasipolynomials can be created by applying
3651 operations such as addition and multiplication
3652 on the resulting quasipolynomials
3654 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3655 __isl_take isl_space *domain);
3656 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3657 __isl_take isl_space *domain);
3658 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3659 __isl_take isl_space *domain);
3660 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3661 __isl_take isl_space *domain);
3662 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3663 __isl_take isl_space *domain);
3664 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3665 __isl_take isl_space *domain,
3666 const isl_int n, const isl_int d);
3667 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3668 __isl_take isl_space *domain,
3669 enum isl_dim_type type, unsigned pos);
3670 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3671 __isl_take isl_aff *aff);
3673 Note that the space in which a quasipolynomial lives is a map space
3674 with a one-dimensional range. The C<domain> argument in some of
3675 the functions above corresponds to the domain of this map space.
3677 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3678 with a single cell can be created using the following functions.
3679 Multiple of these single cell piecewise quasipolynomials can
3680 be combined to create more complicated piecewise quasipolynomials.
3682 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3683 __isl_take isl_space *space);
3684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3685 __isl_take isl_set *set,
3686 __isl_take isl_qpolynomial *qp);
3687 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3688 __isl_take isl_qpolynomial *qp);
3689 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3690 __isl_take isl_pw_aff *pwaff);
3692 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3693 __isl_take isl_space *space);
3694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3695 __isl_take isl_pw_qpolynomial *pwqp);
3696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3697 __isl_take isl_union_pw_qpolynomial *upwqp,
3698 __isl_take isl_pw_qpolynomial *pwqp);
3700 Quasipolynomials can be copied and freed again using the following
3703 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3704 __isl_keep isl_qpolynomial *qp);
3705 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3707 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3708 __isl_keep isl_pw_qpolynomial *pwqp);
3709 void *isl_pw_qpolynomial_free(
3710 __isl_take isl_pw_qpolynomial *pwqp);
3712 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3713 __isl_keep isl_union_pw_qpolynomial *upwqp);
3714 void *isl_union_pw_qpolynomial_free(
3715 __isl_take isl_union_pw_qpolynomial *upwqp);
3717 =head3 Inspecting (Piecewise) Quasipolynomials
3719 To iterate over all piecewise quasipolynomials in a union
3720 piecewise quasipolynomial, use the following function
3722 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3723 __isl_keep isl_union_pw_qpolynomial *upwqp,
3724 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3727 To extract the piecewise quasipolynomial in a given space from a union, use
3729 __isl_give isl_pw_qpolynomial *
3730 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3731 __isl_keep isl_union_pw_qpolynomial *upwqp,
3732 __isl_take isl_space *space);
3734 To iterate over the cells in a piecewise quasipolynomial,
3735 use either of the following two functions
3737 int isl_pw_qpolynomial_foreach_piece(
3738 __isl_keep isl_pw_qpolynomial *pwqp,
3739 int (*fn)(__isl_take isl_set *set,
3740 __isl_take isl_qpolynomial *qp,
3741 void *user), void *user);
3742 int isl_pw_qpolynomial_foreach_lifted_piece(
3743 __isl_keep isl_pw_qpolynomial *pwqp,
3744 int (*fn)(__isl_take isl_set *set,
3745 __isl_take isl_qpolynomial *qp,
3746 void *user), void *user);
3748 As usual, the function C<fn> should return C<0> on success
3749 and C<-1> on failure. The difference between
3750 C<isl_pw_qpolynomial_foreach_piece> and
3751 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3752 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3753 compute unique representations for all existentially quantified
3754 variables and then turn these existentially quantified variables
3755 into extra set variables, adapting the associated quasipolynomial
3756 accordingly. This means that the C<set> passed to C<fn>
3757 will not have any existentially quantified variables, but that
3758 the dimensions of the sets may be different for different
3759 invocations of C<fn>.
3761 To iterate over all terms in a quasipolynomial,
3764 int isl_qpolynomial_foreach_term(
3765 __isl_keep isl_qpolynomial *qp,
3766 int (*fn)(__isl_take isl_term *term,
3767 void *user), void *user);
3769 The terms themselves can be inspected and freed using
3772 unsigned isl_term_dim(__isl_keep isl_term *term,
3773 enum isl_dim_type type);
3774 void isl_term_get_num(__isl_keep isl_term *term,
3776 void isl_term_get_den(__isl_keep isl_term *term,
3778 int isl_term_get_exp(__isl_keep isl_term *term,
3779 enum isl_dim_type type, unsigned pos);
3780 __isl_give isl_aff *isl_term_get_div(
3781 __isl_keep isl_term *term, unsigned pos);
3782 void isl_term_free(__isl_take isl_term *term);
3784 Each term is a product of parameters, set variables and
3785 integer divisions. The function C<isl_term_get_exp>
3786 returns the exponent of a given dimensions in the given term.
3787 The C<isl_int>s in the arguments of C<isl_term_get_num>
3788 and C<isl_term_get_den> need to have been initialized
3789 using C<isl_int_init> before calling these functions.
3791 =head3 Properties of (Piecewise) Quasipolynomials
3793 To check whether a quasipolynomial is actually a constant,
3794 use the following function.
3796 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3797 isl_int *n, isl_int *d);
3799 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3800 then the numerator and denominator of the constant
3801 are returned in C<*n> and C<*d>, respectively.
3803 To check whether two union piecewise quasipolynomials are
3804 obviously equal, use
3806 int isl_union_pw_qpolynomial_plain_is_equal(
3807 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3808 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3810 =head3 Operations on (Piecewise) Quasipolynomials
3812 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3813 __isl_take isl_qpolynomial *qp, isl_int v);
3814 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3815 __isl_take isl_qpolynomial *qp);
3816 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3817 __isl_take isl_qpolynomial *qp1,
3818 __isl_take isl_qpolynomial *qp2);
3819 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3820 __isl_take isl_qpolynomial *qp1,
3821 __isl_take isl_qpolynomial *qp2);
3822 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3823 __isl_take isl_qpolynomial *qp1,
3824 __isl_take isl_qpolynomial *qp2);
3825 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3826 __isl_take isl_qpolynomial *qp, unsigned exponent);
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3829 __isl_take isl_pw_qpolynomial *pwqp1,
3830 __isl_take isl_pw_qpolynomial *pwqp2);
3831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3832 __isl_take isl_pw_qpolynomial *pwqp1,
3833 __isl_take isl_pw_qpolynomial *pwqp2);
3834 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3835 __isl_take isl_pw_qpolynomial *pwqp1,
3836 __isl_take isl_pw_qpolynomial *pwqp2);
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3838 __isl_take isl_pw_qpolynomial *pwqp);
3839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3840 __isl_take isl_pw_qpolynomial *pwqp1,
3841 __isl_take isl_pw_qpolynomial *pwqp2);
3842 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3843 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3845 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3846 __isl_take isl_union_pw_qpolynomial *upwqp1,
3847 __isl_take isl_union_pw_qpolynomial *upwqp2);
3848 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3849 __isl_take isl_union_pw_qpolynomial *upwqp1,
3850 __isl_take isl_union_pw_qpolynomial *upwqp2);
3851 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3852 __isl_take isl_union_pw_qpolynomial *upwqp1,
3853 __isl_take isl_union_pw_qpolynomial *upwqp2);
3855 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3856 __isl_take isl_pw_qpolynomial *pwqp,
3857 __isl_take isl_point *pnt);
3859 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3860 __isl_take isl_union_pw_qpolynomial *upwqp,
3861 __isl_take isl_point *pnt);
3863 __isl_give isl_set *isl_pw_qpolynomial_domain(
3864 __isl_take isl_pw_qpolynomial *pwqp);
3865 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3866 __isl_take isl_pw_qpolynomial *pwpq,
3867 __isl_take isl_set *set);
3868 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3869 __isl_take isl_pw_qpolynomial *pwpq,
3870 __isl_take isl_set *set);
3872 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3873 __isl_take isl_union_pw_qpolynomial *upwqp);
3874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3875 __isl_take isl_union_pw_qpolynomial *upwpq,
3876 __isl_take isl_union_set *uset);
3877 __isl_give isl_union_pw_qpolynomial *
3878 isl_union_pw_qpolynomial_intersect_params(
3879 __isl_take isl_union_pw_qpolynomial *upwpq,
3880 __isl_take isl_set *set);
3882 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3883 __isl_take isl_qpolynomial *qp,
3884 __isl_take isl_space *model);
3886 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3887 __isl_take isl_qpolynomial *qp);
3888 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3889 __isl_take isl_pw_qpolynomial *pwqp);
3891 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3892 __isl_take isl_union_pw_qpolynomial *upwqp);
3894 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3895 __isl_take isl_qpolynomial *qp,
3896 __isl_take isl_set *context);
3897 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3898 __isl_take isl_qpolynomial *qp,
3899 __isl_take isl_set *context);
3901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3902 __isl_take isl_pw_qpolynomial *pwqp,
3903 __isl_take isl_set *context);
3904 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3905 __isl_take isl_pw_qpolynomial *pwqp,
3906 __isl_take isl_set *context);
3908 __isl_give isl_union_pw_qpolynomial *
3909 isl_union_pw_qpolynomial_gist_params(
3910 __isl_take isl_union_pw_qpolynomial *upwqp,
3911 __isl_take isl_set *context);
3912 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3913 __isl_take isl_union_pw_qpolynomial *upwqp,
3914 __isl_take isl_union_set *context);
3916 The gist operation applies the gist operation to each of
3917 the cells in the domain of the input piecewise quasipolynomial.
3918 The context is also exploited
3919 to simplify the quasipolynomials associated to each cell.
3921 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3922 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3923 __isl_give isl_union_pw_qpolynomial *
3924 isl_union_pw_qpolynomial_to_polynomial(
3925 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3927 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3928 the polynomial will be an overapproximation. If C<sign> is negative,
3929 it will be an underapproximation. If C<sign> is zero, the approximation
3930 will lie somewhere in between.
3932 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3934 A piecewise quasipolynomial reduction is a piecewise
3935 reduction (or fold) of quasipolynomials.
3936 In particular, the reduction can be maximum or a minimum.
3937 The objects are mainly used to represent the result of
3938 an upper or lower bound on a quasipolynomial over its domain,
3939 i.e., as the result of the following function.
3941 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3942 __isl_take isl_pw_qpolynomial *pwqp,
3943 enum isl_fold type, int *tight);
3945 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3946 __isl_take isl_union_pw_qpolynomial *upwqp,
3947 enum isl_fold type, int *tight);
3949 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3950 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3951 is the returned bound is known be tight, i.e., for each value
3952 of the parameters there is at least
3953 one element in the domain that reaches the bound.
3954 If the domain of C<pwqp> is not wrapping, then the bound is computed
3955 over all elements in that domain and the result has a purely parametric
3956 domain. If the domain of C<pwqp> is wrapping, then the bound is
3957 computed over the range of the wrapped relation. The domain of the
3958 wrapped relation becomes the domain of the result.
3960 A (piecewise) quasipolynomial reduction can be copied or freed using the
3961 following functions.
3963 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3964 __isl_keep isl_qpolynomial_fold *fold);
3965 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3966 __isl_keep isl_pw_qpolynomial_fold *pwf);
3967 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3968 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3969 void isl_qpolynomial_fold_free(
3970 __isl_take isl_qpolynomial_fold *fold);
3971 void *isl_pw_qpolynomial_fold_free(
3972 __isl_take isl_pw_qpolynomial_fold *pwf);
3973 void *isl_union_pw_qpolynomial_fold_free(
3974 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3976 =head3 Printing Piecewise Quasipolynomial Reductions
3978 Piecewise quasipolynomial reductions can be printed
3979 using the following function.
3981 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3982 __isl_take isl_printer *p,
3983 __isl_keep isl_pw_qpolynomial_fold *pwf);
3984 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3985 __isl_take isl_printer *p,
3986 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3988 For C<isl_printer_print_pw_qpolynomial_fold>,
3989 output format of the printer
3990 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3991 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3992 output format of the printer
3993 needs to be set to C<ISL_FORMAT_ISL>.
3994 In case of printing in C<ISL_FORMAT_C>, the user may want
3995 to set the names of all dimensions
3997 __isl_give isl_pw_qpolynomial_fold *
3998 isl_pw_qpolynomial_fold_set_dim_name(
3999 __isl_take isl_pw_qpolynomial_fold *pwf,
4000 enum isl_dim_type type, unsigned pos,
4003 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4005 To iterate over all piecewise quasipolynomial reductions in a union
4006 piecewise quasipolynomial reduction, use the following function
4008 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4009 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4010 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4011 void *user), void *user);
4013 To iterate over the cells in a piecewise quasipolynomial reduction,
4014 use either of the following two functions
4016 int isl_pw_qpolynomial_fold_foreach_piece(
4017 __isl_keep isl_pw_qpolynomial_fold *pwf,
4018 int (*fn)(__isl_take isl_set *set,
4019 __isl_take isl_qpolynomial_fold *fold,
4020 void *user), void *user);
4021 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4022 __isl_keep isl_pw_qpolynomial_fold *pwf,
4023 int (*fn)(__isl_take isl_set *set,
4024 __isl_take isl_qpolynomial_fold *fold,
4025 void *user), void *user);
4027 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4028 of the difference between these two functions.
4030 To iterate over all quasipolynomials in a reduction, use
4032 int isl_qpolynomial_fold_foreach_qpolynomial(
4033 __isl_keep isl_qpolynomial_fold *fold,
4034 int (*fn)(__isl_take isl_qpolynomial *qp,
4035 void *user), void *user);
4037 =head3 Properties of Piecewise Quasipolynomial Reductions
4039 To check whether two union piecewise quasipolynomial reductions are
4040 obviously equal, use
4042 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4043 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4044 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4046 =head3 Operations on Piecewise Quasipolynomial Reductions
4048 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4049 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4051 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4052 __isl_take isl_pw_qpolynomial_fold *pwf1,
4053 __isl_take isl_pw_qpolynomial_fold *pwf2);
4055 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4056 __isl_take isl_pw_qpolynomial_fold *pwf1,
4057 __isl_take isl_pw_qpolynomial_fold *pwf2);
4059 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4060 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4061 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4063 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4064 __isl_take isl_pw_qpolynomial_fold *pwf,
4065 __isl_take isl_point *pnt);
4067 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4068 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4069 __isl_take isl_point *pnt);
4071 __isl_give isl_pw_qpolynomial_fold *
4072 sl_pw_qpolynomial_fold_intersect_params(
4073 __isl_take isl_pw_qpolynomial_fold *pwf,
4074 __isl_take isl_set *set);
4076 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4077 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4078 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4079 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4080 __isl_take isl_union_set *uset);
4081 __isl_give isl_union_pw_qpolynomial_fold *
4082 isl_union_pw_qpolynomial_fold_intersect_params(
4083 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4084 __isl_take isl_set *set);
4086 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4087 __isl_take isl_pw_qpolynomial_fold *pwf);
4089 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4090 __isl_take isl_pw_qpolynomial_fold *pwf);
4092 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4093 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4095 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4096 __isl_take isl_qpolynomial_fold *fold,
4097 __isl_take isl_set *context);
4098 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4099 __isl_take isl_qpolynomial_fold *fold,
4100 __isl_take isl_set *context);
4102 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4103 __isl_take isl_pw_qpolynomial_fold *pwf,
4104 __isl_take isl_set *context);
4105 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4106 __isl_take isl_pw_qpolynomial_fold *pwf,
4107 __isl_take isl_set *context);
4109 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4110 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4111 __isl_take isl_union_set *context);
4112 __isl_give isl_union_pw_qpolynomial_fold *
4113 isl_union_pw_qpolynomial_fold_gist_params(
4114 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4115 __isl_take isl_set *context);
4117 The gist operation applies the gist operation to each of
4118 the cells in the domain of the input piecewise quasipolynomial reduction.
4119 In future, the operation will also exploit the context
4120 to simplify the quasipolynomial reductions associated to each cell.
4122 __isl_give isl_pw_qpolynomial_fold *
4123 isl_set_apply_pw_qpolynomial_fold(
4124 __isl_take isl_set *set,
4125 __isl_take isl_pw_qpolynomial_fold *pwf,
4127 __isl_give isl_pw_qpolynomial_fold *
4128 isl_map_apply_pw_qpolynomial_fold(
4129 __isl_take isl_map *map,
4130 __isl_take isl_pw_qpolynomial_fold *pwf,
4132 __isl_give isl_union_pw_qpolynomial_fold *
4133 isl_union_set_apply_union_pw_qpolynomial_fold(
4134 __isl_take isl_union_set *uset,
4135 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4137 __isl_give isl_union_pw_qpolynomial_fold *
4138 isl_union_map_apply_union_pw_qpolynomial_fold(
4139 __isl_take isl_union_map *umap,
4140 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4143 The functions taking a map
4144 compose the given map with the given piecewise quasipolynomial reduction.
4145 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4146 over all elements in the intersection of the range of the map
4147 and the domain of the piecewise quasipolynomial reduction
4148 as a function of an element in the domain of the map.
4149 The functions taking a set compute a bound over all elements in the
4150 intersection of the set and the domain of the
4151 piecewise quasipolynomial reduction.
4153 =head2 Dependence Analysis
4155 C<isl> contains specialized functionality for performing
4156 array dataflow analysis. That is, given a I<sink> access relation
4157 and a collection of possible I<source> access relations,
4158 C<isl> can compute relations that describe
4159 for each iteration of the sink access, which iteration
4160 of which of the source access relations was the last
4161 to access the same data element before the given iteration
4163 The resulting dependence relations map source iterations
4164 to the corresponding sink iterations.
4165 To compute standard flow dependences, the sink should be
4166 a read, while the sources should be writes.
4167 If any of the source accesses are marked as being I<may>
4168 accesses, then there will be a dependence from the last
4169 I<must> access B<and> from any I<may> access that follows
4170 this last I<must> access.
4171 In particular, if I<all> sources are I<may> accesses,
4172 then memory based dependence analysis is performed.
4173 If, on the other hand, all sources are I<must> accesses,
4174 then value based dependence analysis is performed.
4176 #include <isl/flow.h>
4178 typedef int (*isl_access_level_before)(void *first, void *second);
4180 __isl_give isl_access_info *isl_access_info_alloc(
4181 __isl_take isl_map *sink,
4182 void *sink_user, isl_access_level_before fn,
4184 __isl_give isl_access_info *isl_access_info_add_source(
4185 __isl_take isl_access_info *acc,
4186 __isl_take isl_map *source, int must,
4188 void isl_access_info_free(__isl_take isl_access_info *acc);
4190 __isl_give isl_flow *isl_access_info_compute_flow(
4191 __isl_take isl_access_info *acc);
4193 int isl_flow_foreach(__isl_keep isl_flow *deps,
4194 int (*fn)(__isl_take isl_map *dep, int must,
4195 void *dep_user, void *user),
4197 __isl_give isl_map *isl_flow_get_no_source(
4198 __isl_keep isl_flow *deps, int must);
4199 void isl_flow_free(__isl_take isl_flow *deps);
4201 The function C<isl_access_info_compute_flow> performs the actual
4202 dependence analysis. The other functions are used to construct
4203 the input for this function or to read off the output.
4205 The input is collected in an C<isl_access_info>, which can
4206 be created through a call to C<isl_access_info_alloc>.
4207 The arguments to this functions are the sink access relation
4208 C<sink>, a token C<sink_user> used to identify the sink
4209 access to the user, a callback function for specifying the
4210 relative order of source and sink accesses, and the number
4211 of source access relations that will be added.
4212 The callback function has type C<int (*)(void *first, void *second)>.
4213 The function is called with two user supplied tokens identifying
4214 either a source or the sink and it should return the shared nesting
4215 level and the relative order of the two accesses.
4216 In particular, let I<n> be the number of loops shared by
4217 the two accesses. If C<first> precedes C<second> textually,
4218 then the function should return I<2 * n + 1>; otherwise,
4219 it should return I<2 * n>.
4220 The sources can be added to the C<isl_access_info> by performing
4221 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4222 C<must> indicates whether the source is a I<must> access
4223 or a I<may> access. Note that a multi-valued access relation
4224 should only be marked I<must> if every iteration in the domain
4225 of the relation accesses I<all> elements in its image.
4226 The C<source_user> token is again used to identify
4227 the source access. The range of the source access relation
4228 C<source> should have the same dimension as the range
4229 of the sink access relation.
4230 The C<isl_access_info_free> function should usually not be
4231 called explicitly, because it is called implicitly by
4232 C<isl_access_info_compute_flow>.
4234 The result of the dependence analysis is collected in an
4235 C<isl_flow>. There may be elements of
4236 the sink access for which no preceding source access could be
4237 found or for which all preceding sources are I<may> accesses.
4238 The relations containing these elements can be obtained through
4239 calls to C<isl_flow_get_no_source>, the first with C<must> set
4240 and the second with C<must> unset.
4241 In the case of standard flow dependence analysis,
4242 with the sink a read and the sources I<must> writes,
4243 the first relation corresponds to the reads from uninitialized
4244 array elements and the second relation is empty.
4245 The actual flow dependences can be extracted using
4246 C<isl_flow_foreach>. This function will call the user-specified
4247 callback function C<fn> for each B<non-empty> dependence between
4248 a source and the sink. The callback function is called
4249 with four arguments, the actual flow dependence relation
4250 mapping source iterations to sink iterations, a boolean that
4251 indicates whether it is a I<must> or I<may> dependence, a token
4252 identifying the source and an additional C<void *> with value
4253 equal to the third argument of the C<isl_flow_foreach> call.
4254 A dependence is marked I<must> if it originates from a I<must>
4255 source and if it is not followed by any I<may> sources.
4257 After finishing with an C<isl_flow>, the user should call
4258 C<isl_flow_free> to free all associated memory.
4260 A higher-level interface to dependence analysis is provided
4261 by the following function.
4263 #include <isl/flow.h>
4265 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4266 __isl_take isl_union_map *must_source,
4267 __isl_take isl_union_map *may_source,
4268 __isl_take isl_union_map *schedule,
4269 __isl_give isl_union_map **must_dep,
4270 __isl_give isl_union_map **may_dep,
4271 __isl_give isl_union_map **must_no_source,
4272 __isl_give isl_union_map **may_no_source);
4274 The arrays are identified by the tuple names of the ranges
4275 of the accesses. The iteration domains by the tuple names
4276 of the domains of the accesses and of the schedule.
4277 The relative order of the iteration domains is given by the
4278 schedule. The relations returned through C<must_no_source>
4279 and C<may_no_source> are subsets of C<sink>.
4280 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4281 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4282 any of the other arguments is treated as an error.
4284 =head3 Interaction with Dependence Analysis
4286 During the dependence analysis, we frequently need to perform
4287 the following operation. Given a relation between sink iterations
4288 and potential soure iterations from a particular source domain,
4289 what is the last potential source iteration corresponding to each
4290 sink iteration. It can sometimes be convenient to adjust
4291 the set of potential source iterations before or after each such operation.
4292 The prototypical example is fuzzy array dataflow analysis,
4293 where we need to analyze if, based on data-dependent constraints,
4294 the sink iteration can ever be executed without one or more of
4295 the corresponding potential source iterations being executed.
4296 If so, we can introduce extra parameters and select an unknown
4297 but fixed source iteration from the potential source iterations.
4298 To be able to perform such manipulations, C<isl> provides the following
4301 #include <isl/flow.h>
4303 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4304 __isl_keep isl_map *source_map,
4305 __isl_keep isl_set *sink, void *source_user,
4307 __isl_give isl_access_info *isl_access_info_set_restrict(
4308 __isl_take isl_access_info *acc,
4309 isl_access_restrict fn, void *user);
4311 The function C<isl_access_info_set_restrict> should be called
4312 before calling C<isl_access_info_compute_flow> and registers a callback function
4313 that will be called any time C<isl> is about to compute the last
4314 potential source. The first argument is the (reverse) proto-dependence,
4315 mapping sink iterations to potential source iterations.
4316 The second argument represents the sink iterations for which
4317 we want to compute the last source iteration.
4318 The third argument is the token corresponding to the source
4319 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4320 The callback is expected to return a restriction on either the input or
4321 the output of the operation computing the last potential source.
4322 If the input needs to be restricted then restrictions are needed
4323 for both the source and the sink iterations. The sink iterations
4324 and the potential source iterations will be intersected with these sets.
4325 If the output needs to be restricted then only a restriction on the source
4326 iterations is required.
4327 If any error occurs, the callback should return C<NULL>.
4328 An C<isl_restriction> object can be created and freed using the following
4331 #include <isl/flow.h>
4333 __isl_give isl_restriction *isl_restriction_input(
4334 __isl_take isl_set *source_restr,
4335 __isl_take isl_set *sink_restr);
4336 __isl_give isl_restriction *isl_restriction_output(
4337 __isl_take isl_set *source_restr);
4338 __isl_give isl_restriction *isl_restriction_none(
4339 __isl_keep isl_map *source_map);
4340 __isl_give isl_restriction *isl_restriction_empty(
4341 __isl_keep isl_map *source_map);
4342 void *isl_restriction_free(
4343 __isl_take isl_restriction *restr);
4345 C<isl_restriction_none> and C<isl_restriction_empty> are special
4346 cases of C<isl_restriction_input>. C<isl_restriction_none>
4347 is essentially equivalent to
4349 isl_restriction_input(isl_set_universe(
4350 isl_space_range(isl_map_get_space(source_map))),
4352 isl_space_domain(isl_map_get_space(source_map))));
4354 whereas C<isl_restriction_empty> is essentially equivalent to
4356 isl_restriction_input(isl_set_empty(
4357 isl_space_range(isl_map_get_space(source_map))),
4359 isl_space_domain(isl_map_get_space(source_map))));
4363 B<The functionality described in this section is fairly new
4364 and may be subject to change.>
4366 The following function can be used to compute a schedule
4367 for a union of domains.
4368 By default, the algorithm used to construct the schedule is similar
4369 to that of C<Pluto>.
4370 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4372 The generated schedule respects all C<validity> dependences.
4373 That is, all dependence distances over these dependences in the
4374 scheduled space are lexicographically positive.
4375 The default algorithm tries to minimize the dependence distances over
4376 C<proximity> dependences.
4377 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4378 for groups of domains where the dependence distances have only
4379 non-negative values.
4380 When using Feautrier's algorithm, the C<proximity> dependence
4381 distances are only minimized during the extension to a
4382 full-dimensional schedule.
4384 #include <isl/schedule.h>
4385 __isl_give isl_schedule *isl_union_set_compute_schedule(
4386 __isl_take isl_union_set *domain,
4387 __isl_take isl_union_map *validity,
4388 __isl_take isl_union_map *proximity);
4389 void *isl_schedule_free(__isl_take isl_schedule *sched);
4391 A mapping from the domains to the scheduled space can be obtained
4392 from an C<isl_schedule> using the following function.
4394 __isl_give isl_union_map *isl_schedule_get_map(
4395 __isl_keep isl_schedule *sched);
4397 A representation of the schedule can be printed using
4399 __isl_give isl_printer *isl_printer_print_schedule(
4400 __isl_take isl_printer *p,
4401 __isl_keep isl_schedule *schedule);
4403 A representation of the schedule as a forest of bands can be obtained
4404 using the following function.
4406 __isl_give isl_band_list *isl_schedule_get_band_forest(
4407 __isl_keep isl_schedule *schedule);
4409 The list can be manipulated as explained in L<"Lists">.
4410 The bands inside the list can be copied and freed using the following
4413 #include <isl/band.h>
4414 __isl_give isl_band *isl_band_copy(
4415 __isl_keep isl_band *band);
4416 void *isl_band_free(__isl_take isl_band *band);
4418 Each band contains zero or more scheduling dimensions.
4419 These are referred to as the members of the band.
4420 The section of the schedule that corresponds to the band is
4421 referred to as the partial schedule of the band.
4422 For those nodes that participate in a band, the outer scheduling
4423 dimensions form the prefix schedule, while the inner scheduling
4424 dimensions form the suffix schedule.
4425 That is, if we take a cut of the band forest, then the union of
4426 the concatenations of the prefix, partial and suffix schedules of
4427 each band in the cut is equal to the entire schedule (modulo
4428 some possible padding at the end with zero scheduling dimensions).
4429 The properties of a band can be inspected using the following functions.
4431 #include <isl/band.h>
4432 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4434 int isl_band_has_children(__isl_keep isl_band *band);
4435 __isl_give isl_band_list *isl_band_get_children(
4436 __isl_keep isl_band *band);
4438 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4439 __isl_keep isl_band *band);
4440 __isl_give isl_union_map *isl_band_get_partial_schedule(
4441 __isl_keep isl_band *band);
4442 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4443 __isl_keep isl_band *band);
4445 int isl_band_n_member(__isl_keep isl_band *band);
4446 int isl_band_member_is_zero_distance(
4447 __isl_keep isl_band *band, int pos);
4449 Note that a scheduling dimension is considered to be ``zero
4450 distance'' if it does not carry any proximity dependences
4452 That is, if the dependence distances of the proximity
4453 dependences are all zero in that direction (for fixed
4454 iterations of outer bands).
4456 A representation of the band can be printed using
4458 #include <isl/band.h>
4459 __isl_give isl_printer *isl_printer_print_band(
4460 __isl_take isl_printer *p,
4461 __isl_keep isl_band *band);
4465 #include <isl/schedule.h>
4466 int isl_options_set_schedule_max_coefficient(
4467 isl_ctx *ctx, int val);
4468 int isl_options_get_schedule_max_coefficient(
4470 int isl_options_set_schedule_max_constant_term(
4471 isl_ctx *ctx, int val);
4472 int isl_options_get_schedule_max_constant_term(
4474 int isl_options_set_schedule_maximize_band_depth(
4475 isl_ctx *ctx, int val);
4476 int isl_options_get_schedule_maximize_band_depth(
4478 int isl_options_set_schedule_outer_zero_distance(
4479 isl_ctx *ctx, int val);
4480 int isl_options_get_schedule_outer_zero_distance(
4482 int isl_options_set_schedule_split_scaled(
4483 isl_ctx *ctx, int val);
4484 int isl_options_get_schedule_split_scaled(
4486 int isl_options_set_schedule_algorithm(
4487 isl_ctx *ctx, int val);
4488 int isl_options_get_schedule_algorithm(
4494 =item * schedule_max_coefficient
4496 This option enforces that the coefficients for variable and parameter
4497 dimensions in the calculated schedule are not larger than the specified value.
4498 This option can significantly increase the speed of the scheduling calculation
4499 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4500 this option does not introduce bounds on the variable or parameter
4503 =item * schedule_max_constant_term
4505 This option enforces that the constant coefficients in the calculated schedule
4506 are not larger than the maximal constant term. This option can significantly
4507 increase the speed of the scheduling calculation and may also prevent fusing of
4508 unrelated dimensions. A value of -1 means that this option does not introduce
4509 bounds on the constant coefficients.
4511 =item * schedule_maximize_band_depth
4513 If this option is set, we do not split bands at the point
4514 where we detect splitting is necessary. Instead, we
4515 backtrack and split bands as early as possible. This
4516 reduces the number of splits and maximizes the width of
4517 the bands. Wider bands give more possibilities for tiling.
4519 =item * schedule_outer_zero_distance
4521 If this option is set, then we try to construct schedules
4522 where the outermost scheduling dimension in each band
4523 results in a zero dependence distance over the proximity
4526 =item * schedule_split_scaled
4528 If this option is set, then we try to construct schedules in which the
4529 constant term is split off from the linear part if the linear parts of
4530 the scheduling rows for all nodes in the graphs have a common non-trivial
4532 The constant term is then placed in a separate band and the linear
4535 =item * schedule_algorithm
4537 Selects the scheduling algorithm to be used.
4538 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4539 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4543 =head2 Parametric Vertex Enumeration
4545 The parametric vertex enumeration described in this section
4546 is mainly intended to be used internally and by the C<barvinok>
4549 #include <isl/vertices.h>
4550 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4551 __isl_keep isl_basic_set *bset);
4553 The function C<isl_basic_set_compute_vertices> performs the
4554 actual computation of the parametric vertices and the chamber
4555 decomposition and store the result in an C<isl_vertices> object.
4556 This information can be queried by either iterating over all
4557 the vertices or iterating over all the chambers or cells
4558 and then iterating over all vertices that are active on the chamber.
4560 int isl_vertices_foreach_vertex(
4561 __isl_keep isl_vertices *vertices,
4562 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4565 int isl_vertices_foreach_cell(
4566 __isl_keep isl_vertices *vertices,
4567 int (*fn)(__isl_take isl_cell *cell, void *user),
4569 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4570 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4573 Other operations that can be performed on an C<isl_vertices> object are
4576 isl_ctx *isl_vertices_get_ctx(
4577 __isl_keep isl_vertices *vertices);
4578 int isl_vertices_get_n_vertices(
4579 __isl_keep isl_vertices *vertices);
4580 void isl_vertices_free(__isl_take isl_vertices *vertices);
4582 Vertices can be inspected and destroyed using the following functions.
4584 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4585 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4586 __isl_give isl_basic_set *isl_vertex_get_domain(
4587 __isl_keep isl_vertex *vertex);
4588 __isl_give isl_basic_set *isl_vertex_get_expr(
4589 __isl_keep isl_vertex *vertex);
4590 void isl_vertex_free(__isl_take isl_vertex *vertex);
4592 C<isl_vertex_get_expr> returns a singleton parametric set describing
4593 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4595 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4596 B<rational> basic sets, so they should mainly be used for inspection
4597 and should not be mixed with integer sets.
4599 Chambers can be inspected and destroyed using the following functions.
4601 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4602 __isl_give isl_basic_set *isl_cell_get_domain(
4603 __isl_keep isl_cell *cell);
4604 void isl_cell_free(__isl_take isl_cell *cell);
4608 Although C<isl> is mainly meant to be used as a library,
4609 it also contains some basic applications that use some
4610 of the functionality of C<isl>.
4611 The input may be specified in either the L<isl format>
4612 or the L<PolyLib format>.
4614 =head2 C<isl_polyhedron_sample>
4616 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4617 an integer element of the polyhedron, if there is any.
4618 The first column in the output is the denominator and is always
4619 equal to 1. If the polyhedron contains no integer points,
4620 then a vector of length zero is printed.
4624 C<isl_pip> takes the same input as the C<example> program
4625 from the C<piplib> distribution, i.e., a set of constraints
4626 on the parameters, a line containing only -1 and finally a set
4627 of constraints on a parametric polyhedron.
4628 The coefficients of the parameters appear in the last columns
4629 (but before the final constant column).
4630 The output is the lexicographic minimum of the parametric polyhedron.
4631 As C<isl> currently does not have its own output format, the output
4632 is just a dump of the internal state.
4634 =head2 C<isl_polyhedron_minimize>
4636 C<isl_polyhedron_minimize> computes the minimum of some linear
4637 or affine objective function over the integer points in a polyhedron.
4638 If an affine objective function
4639 is given, then the constant should appear in the last column.
4641 =head2 C<isl_polytope_scan>
4643 Given a polytope, C<isl_polytope_scan> prints
4644 all integer points in the polytope.