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 functions.
990 FILE *isl_printer_get_file(
991 __isl_keep isl_printer *printer);
992 int isl_printer_get_output_format(
993 __isl_keep isl_printer *p);
995 The behavior of the printer can be modified in various ways
997 __isl_give isl_printer *isl_printer_set_output_format(
998 __isl_take isl_printer *p, int output_format);
999 __isl_give isl_printer *isl_printer_set_indent(
1000 __isl_take isl_printer *p, int indent);
1001 __isl_give isl_printer *isl_printer_indent(
1002 __isl_take isl_printer *p, int indent);
1003 __isl_give isl_printer *isl_printer_set_prefix(
1004 __isl_take isl_printer *p, const char *prefix);
1005 __isl_give isl_printer *isl_printer_set_suffix(
1006 __isl_take isl_printer *p, const char *suffix);
1008 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1009 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1010 and defaults to C<ISL_FORMAT_ISL>.
1011 Each line in the output is indented by C<indent> (set by
1012 C<isl_printer_set_indent>) spaces
1013 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1014 In the C<PolyLib> format output,
1015 the coefficients of the existentially quantified variables
1016 appear between those of the set variables and those
1018 The function C<isl_printer_indent> increases the indentation
1019 by the specified amount (which may be negative).
1021 To actually print something, use
1023 #include <isl/set.h>
1024 __isl_give isl_printer *isl_printer_print_basic_set(
1025 __isl_take isl_printer *printer,
1026 __isl_keep isl_basic_set *bset);
1027 __isl_give isl_printer *isl_printer_print_set(
1028 __isl_take isl_printer *printer,
1029 __isl_keep isl_set *set);
1031 #include <isl/map.h>
1032 __isl_give isl_printer *isl_printer_print_basic_map(
1033 __isl_take isl_printer *printer,
1034 __isl_keep isl_basic_map *bmap);
1035 __isl_give isl_printer *isl_printer_print_map(
1036 __isl_take isl_printer *printer,
1037 __isl_keep isl_map *map);
1039 #include <isl/union_set.h>
1040 __isl_give isl_printer *isl_printer_print_union_set(
1041 __isl_take isl_printer *p,
1042 __isl_keep isl_union_set *uset);
1044 #include <isl/union_map.h>
1045 __isl_give isl_printer *isl_printer_print_union_map(
1046 __isl_take isl_printer *p,
1047 __isl_keep isl_union_map *umap);
1049 When called on a file printer, the following function flushes
1050 the file. When called on a string printer, the buffer is cleared.
1052 __isl_give isl_printer *isl_printer_flush(
1053 __isl_take isl_printer *p);
1055 =head2 Creating New Sets and Relations
1057 C<isl> has functions for creating some standard sets and relations.
1061 =item * Empty sets and relations
1063 __isl_give isl_basic_set *isl_basic_set_empty(
1064 __isl_take isl_space *space);
1065 __isl_give isl_basic_map *isl_basic_map_empty(
1066 __isl_take isl_space *space);
1067 __isl_give isl_set *isl_set_empty(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_empty(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_set *isl_union_set_empty(
1072 __isl_take isl_space *space);
1073 __isl_give isl_union_map *isl_union_map_empty(
1074 __isl_take isl_space *space);
1076 For C<isl_union_set>s and C<isl_union_map>s, the space
1077 is only used to specify the parameters.
1079 =item * Universe sets and relations
1081 __isl_give isl_basic_set *isl_basic_set_universe(
1082 __isl_take isl_space *space);
1083 __isl_give isl_basic_map *isl_basic_map_universe(
1084 __isl_take isl_space *space);
1085 __isl_give isl_set *isl_set_universe(
1086 __isl_take isl_space *space);
1087 __isl_give isl_map *isl_map_universe(
1088 __isl_take isl_space *space);
1089 __isl_give isl_union_set *isl_union_set_universe(
1090 __isl_take isl_union_set *uset);
1091 __isl_give isl_union_map *isl_union_map_universe(
1092 __isl_take isl_union_map *umap);
1094 The sets and relations constructed by the functions above
1095 contain all integer values, while those constructed by the
1096 functions below only contain non-negative values.
1098 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1099 __isl_take isl_space *space);
1100 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_set *isl_set_nat_universe(
1103 __isl_take isl_space *space);
1104 __isl_give isl_map *isl_map_nat_universe(
1105 __isl_take isl_space *space);
1107 =item * Identity relations
1109 __isl_give isl_basic_map *isl_basic_map_identity(
1110 __isl_take isl_space *space);
1111 __isl_give isl_map *isl_map_identity(
1112 __isl_take isl_space *space);
1114 The number of input and output dimensions in C<space> needs
1117 =item * Lexicographic order
1119 __isl_give isl_map *isl_map_lex_lt(
1120 __isl_take isl_space *set_space);
1121 __isl_give isl_map *isl_map_lex_le(
1122 __isl_take isl_space *set_space);
1123 __isl_give isl_map *isl_map_lex_gt(
1124 __isl_take isl_space *set_space);
1125 __isl_give isl_map *isl_map_lex_ge(
1126 __isl_take isl_space *set_space);
1127 __isl_give isl_map *isl_map_lex_lt_first(
1128 __isl_take isl_space *space, unsigned n);
1129 __isl_give isl_map *isl_map_lex_le_first(
1130 __isl_take isl_space *space, unsigned n);
1131 __isl_give isl_map *isl_map_lex_gt_first(
1132 __isl_take isl_space *space, unsigned n);
1133 __isl_give isl_map *isl_map_lex_ge_first(
1134 __isl_take isl_space *space, unsigned n);
1136 The first four functions take a space for a B<set>
1137 and return relations that express that the elements in the domain
1138 are lexicographically less
1139 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1140 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1141 than the elements in the range.
1142 The last four functions take a space for a map
1143 and return relations that express that the first C<n> dimensions
1144 in the domain are lexicographically less
1145 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1146 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1147 than the first C<n> dimensions in the range.
1151 A basic set or relation can be converted to a set or relation
1152 using the following functions.
1154 __isl_give isl_set *isl_set_from_basic_set(
1155 __isl_take isl_basic_set *bset);
1156 __isl_give isl_map *isl_map_from_basic_map(
1157 __isl_take isl_basic_map *bmap);
1159 Sets and relations can be converted to union sets and relations
1160 using the following functions.
1162 __isl_give isl_union_map *isl_union_map_from_map(
1163 __isl_take isl_map *map);
1164 __isl_give isl_union_set *isl_union_set_from_set(
1165 __isl_take isl_set *set);
1167 The inverse conversions below can only be used if the input
1168 union set or relation is known to contain elements in exactly one
1171 __isl_give isl_set *isl_set_from_union_set(
1172 __isl_take isl_union_set *uset);
1173 __isl_give isl_map *isl_map_from_union_map(
1174 __isl_take isl_union_map *umap);
1176 A zero-dimensional set can be constructed on a given parameter domain
1177 using the following function.
1179 __isl_give isl_set *isl_set_from_params(
1180 __isl_take isl_set *set);
1182 Sets and relations can be copied and freed again using the following
1185 __isl_give isl_basic_set *isl_basic_set_copy(
1186 __isl_keep isl_basic_set *bset);
1187 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1188 __isl_give isl_union_set *isl_union_set_copy(
1189 __isl_keep isl_union_set *uset);
1190 __isl_give isl_basic_map *isl_basic_map_copy(
1191 __isl_keep isl_basic_map *bmap);
1192 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1193 __isl_give isl_union_map *isl_union_map_copy(
1194 __isl_keep isl_union_map *umap);
1195 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1196 void isl_set_free(__isl_take isl_set *set);
1197 void *isl_union_set_free(__isl_take isl_union_set *uset);
1198 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1199 void isl_map_free(__isl_take isl_map *map);
1200 void *isl_union_map_free(__isl_take isl_union_map *umap);
1202 Other sets and relations can be constructed by starting
1203 from a universe set or relation, adding equality and/or
1204 inequality constraints and then projecting out the
1205 existentially quantified variables, if any.
1206 Constraints can be constructed, manipulated and
1207 added to (or removed from) (basic) sets and relations
1208 using the following functions.
1210 #include <isl/constraint.h>
1211 __isl_give isl_constraint *isl_equality_alloc(
1212 __isl_take isl_local_space *ls);
1213 __isl_give isl_constraint *isl_inequality_alloc(
1214 __isl_take isl_local_space *ls);
1215 __isl_give isl_constraint *isl_constraint_set_constant(
1216 __isl_take isl_constraint *constraint, isl_int v);
1217 __isl_give isl_constraint *isl_constraint_set_constant_si(
1218 __isl_take isl_constraint *constraint, int v);
1219 __isl_give isl_constraint *isl_constraint_set_coefficient(
1220 __isl_take isl_constraint *constraint,
1221 enum isl_dim_type type, int pos, isl_int v);
1222 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1223 __isl_take isl_constraint *constraint,
1224 enum isl_dim_type type, int pos, int v);
1225 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1226 __isl_take isl_basic_map *bmap,
1227 __isl_take isl_constraint *constraint);
1228 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1229 __isl_take isl_basic_set *bset,
1230 __isl_take isl_constraint *constraint);
1231 __isl_give isl_map *isl_map_add_constraint(
1232 __isl_take isl_map *map,
1233 __isl_take isl_constraint *constraint);
1234 __isl_give isl_set *isl_set_add_constraint(
1235 __isl_take isl_set *set,
1236 __isl_take isl_constraint *constraint);
1237 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1238 __isl_take isl_basic_set *bset,
1239 __isl_take isl_constraint *constraint);
1241 For example, to create a set containing the even integers
1242 between 10 and 42, you would use the following code.
1245 isl_local_space *ls;
1247 isl_basic_set *bset;
1249 space = isl_space_set_alloc(ctx, 0, 2);
1250 bset = isl_basic_set_universe(isl_space_copy(space));
1251 ls = isl_local_space_from_space(space);
1253 c = isl_equality_alloc(isl_local_space_copy(ls));
1254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1256 bset = isl_basic_set_add_constraint(bset, c);
1258 c = isl_inequality_alloc(isl_local_space_copy(ls));
1259 c = isl_constraint_set_constant_si(c, -10);
1260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1261 bset = isl_basic_set_add_constraint(bset, c);
1263 c = isl_inequality_alloc(ls);
1264 c = isl_constraint_set_constant_si(c, 42);
1265 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1266 bset = isl_basic_set_add_constraint(bset, c);
1268 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1272 isl_basic_set *bset;
1273 bset = isl_basic_set_read_from_str(ctx,
1274 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1276 A basic set or relation can also be constructed from two matrices
1277 describing the equalities and the inequalities.
1279 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1280 __isl_take isl_space *space,
1281 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1282 enum isl_dim_type c1,
1283 enum isl_dim_type c2, enum isl_dim_type c3,
1284 enum isl_dim_type c4);
1285 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1286 __isl_take isl_space *space,
1287 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1288 enum isl_dim_type c1,
1289 enum isl_dim_type c2, enum isl_dim_type c3,
1290 enum isl_dim_type c4, enum isl_dim_type c5);
1292 The C<isl_dim_type> arguments indicate the order in which
1293 different kinds of variables appear in the input matrices
1294 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1295 C<isl_dim_set> and C<isl_dim_div> for sets and
1296 of C<isl_dim_cst>, C<isl_dim_param>,
1297 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1299 A (basic or union) set or relation can also be constructed from a
1300 (union) (piecewise) (multiple) affine expression
1301 or a list of affine expressions
1302 (See L<"Piecewise Quasi Affine Expressions"> and
1303 L<"Piecewise Multiple Quasi Affine Expressions">).
1305 __isl_give isl_basic_map *isl_basic_map_from_aff(
1306 __isl_take isl_aff *aff);
1307 __isl_give isl_map *isl_map_from_aff(
1308 __isl_take isl_aff *aff);
1309 __isl_give isl_set *isl_set_from_pw_aff(
1310 __isl_take isl_pw_aff *pwaff);
1311 __isl_give isl_map *isl_map_from_pw_aff(
1312 __isl_take isl_pw_aff *pwaff);
1313 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1314 __isl_take isl_space *domain_space,
1315 __isl_take isl_aff_list *list);
1316 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1317 __isl_take isl_multi_aff *maff)
1318 __isl_give isl_map *isl_map_from_multi_aff(
1319 __isl_take isl_multi_aff *maff)
1320 __isl_give isl_set *isl_set_from_pw_multi_aff(
1321 __isl_take isl_pw_multi_aff *pma);
1322 __isl_give isl_map *isl_map_from_pw_multi_aff(
1323 __isl_take isl_pw_multi_aff *pma);
1324 __isl_give isl_union_map *
1325 isl_union_map_from_union_pw_multi_aff(
1326 __isl_take isl_union_pw_multi_aff *upma);
1328 The C<domain_dim> argument describes the domain of the resulting
1329 basic relation. It is required because the C<list> may consist
1330 of zero affine expressions.
1332 =head2 Inspecting Sets and Relations
1334 Usually, the user should not have to care about the actual constraints
1335 of the sets and maps, but should instead apply the abstract operations
1336 explained in the following sections.
1337 Occasionally, however, it may be required to inspect the individual
1338 coefficients of the constraints. This section explains how to do so.
1339 In these cases, it may also be useful to have C<isl> compute
1340 an explicit representation of the existentially quantified variables.
1342 __isl_give isl_set *isl_set_compute_divs(
1343 __isl_take isl_set *set);
1344 __isl_give isl_map *isl_map_compute_divs(
1345 __isl_take isl_map *map);
1346 __isl_give isl_union_set *isl_union_set_compute_divs(
1347 __isl_take isl_union_set *uset);
1348 __isl_give isl_union_map *isl_union_map_compute_divs(
1349 __isl_take isl_union_map *umap);
1351 This explicit representation defines the existentially quantified
1352 variables as integer divisions of the other variables, possibly
1353 including earlier existentially quantified variables.
1354 An explicitly represented existentially quantified variable therefore
1355 has a unique value when the values of the other variables are known.
1356 If, furthermore, the same existentials, i.e., existentials
1357 with the same explicit representations, should appear in the
1358 same order in each of the disjuncts of a set or map, then the user should call
1359 either of the following functions.
1361 __isl_give isl_set *isl_set_align_divs(
1362 __isl_take isl_set *set);
1363 __isl_give isl_map *isl_map_align_divs(
1364 __isl_take isl_map *map);
1366 Alternatively, the existentially quantified variables can be removed
1367 using the following functions, which compute an overapproximation.
1369 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1370 __isl_take isl_basic_set *bset);
1371 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1372 __isl_take isl_basic_map *bmap);
1373 __isl_give isl_set *isl_set_remove_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_remove_divs(
1376 __isl_take isl_map *map);
1378 To iterate over all the sets or maps in a union set or map, use
1380 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1381 int (*fn)(__isl_take isl_set *set, void *user),
1383 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1384 int (*fn)(__isl_take isl_map *map, void *user),
1387 The number of sets or maps in a union set or map can be obtained
1390 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1391 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1393 To extract the set or map in a given space from a union, use
1395 __isl_give isl_set *isl_union_set_extract_set(
1396 __isl_keep isl_union_set *uset,
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_union_map_extract_map(
1399 __isl_keep isl_union_map *umap,
1400 __isl_take isl_space *space);
1402 To iterate over all the basic sets or maps in a set or map, use
1404 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1405 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1407 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1408 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1411 The callback function C<fn> should return 0 if successful and
1412 -1 if an error occurs. In the latter case, or if any other error
1413 occurs, the above functions will return -1.
1415 It should be noted that C<isl> does not guarantee that
1416 the basic sets or maps passed to C<fn> are disjoint.
1417 If this is required, then the user should call one of
1418 the following functions first.
1420 __isl_give isl_set *isl_set_make_disjoint(
1421 __isl_take isl_set *set);
1422 __isl_give isl_map *isl_map_make_disjoint(
1423 __isl_take isl_map *map);
1425 The number of basic sets in a set can be obtained
1428 int isl_set_n_basic_set(__isl_keep isl_set *set);
1430 To iterate over the constraints of a basic set or map, use
1432 #include <isl/constraint.h>
1434 int isl_basic_set_n_constraint(
1435 __isl_keep isl_basic_set *bset);
1436 int isl_basic_set_foreach_constraint(
1437 __isl_keep isl_basic_set *bset,
1438 int (*fn)(__isl_take isl_constraint *c, void *user),
1440 int isl_basic_map_foreach_constraint(
1441 __isl_keep isl_basic_map *bmap,
1442 int (*fn)(__isl_take isl_constraint *c, void *user),
1444 void *isl_constraint_free(__isl_take isl_constraint *c);
1446 Again, the callback function C<fn> should return 0 if successful and
1447 -1 if an error occurs. In the latter case, or if any other error
1448 occurs, the above functions will return -1.
1449 The constraint C<c> represents either an equality or an inequality.
1450 Use the following function to find out whether a constraint
1451 represents an equality. If not, it represents an inequality.
1453 int isl_constraint_is_equality(
1454 __isl_keep isl_constraint *constraint);
1456 The coefficients of the constraints can be inspected using
1457 the following functions.
1459 int isl_constraint_is_lower_bound(
1460 __isl_keep isl_constraint *constraint,
1461 enum isl_dim_type type, unsigned pos);
1462 int isl_constraint_is_upper_bound(
1463 __isl_keep isl_constraint *constraint,
1464 enum isl_dim_type type, unsigned pos);
1465 void isl_constraint_get_constant(
1466 __isl_keep isl_constraint *constraint, isl_int *v);
1467 void isl_constraint_get_coefficient(
1468 __isl_keep isl_constraint *constraint,
1469 enum isl_dim_type type, int pos, isl_int *v);
1470 int isl_constraint_involves_dims(
1471 __isl_keep isl_constraint *constraint,
1472 enum isl_dim_type type, unsigned first, unsigned n);
1474 The explicit representations of the existentially quantified
1475 variables can be inspected using the following function.
1476 Note that the user is only allowed to use this function
1477 if the inspected set or map is the result of a call
1478 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1479 The existentially quantified variable is equal to the floor
1480 of the returned affine expression. The affine expression
1481 itself can be inspected using the functions in
1482 L<"Piecewise Quasi Affine Expressions">.
1484 __isl_give isl_aff *isl_constraint_get_div(
1485 __isl_keep isl_constraint *constraint, int pos);
1487 To obtain the constraints of a basic set or map in matrix
1488 form, use the following functions.
1490 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1491 __isl_keep isl_basic_set *bset,
1492 enum isl_dim_type c1, enum isl_dim_type c2,
1493 enum isl_dim_type c3, enum isl_dim_type c4);
1494 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1495 __isl_keep isl_basic_set *bset,
1496 enum isl_dim_type c1, enum isl_dim_type c2,
1497 enum isl_dim_type c3, enum isl_dim_type c4);
1498 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1499 __isl_keep isl_basic_map *bmap,
1500 enum isl_dim_type c1,
1501 enum isl_dim_type c2, enum isl_dim_type c3,
1502 enum isl_dim_type c4, enum isl_dim_type c5);
1503 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1504 __isl_keep isl_basic_map *bmap,
1505 enum isl_dim_type c1,
1506 enum isl_dim_type c2, enum isl_dim_type c3,
1507 enum isl_dim_type c4, enum isl_dim_type c5);
1509 The C<isl_dim_type> arguments dictate the order in which
1510 different kinds of variables appear in the resulting matrix
1511 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1512 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1514 The number of parameters, input, output or set dimensions can
1515 be obtained using the following functions.
1517 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1518 enum isl_dim_type type);
1519 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1520 enum isl_dim_type type);
1521 unsigned isl_set_dim(__isl_keep isl_set *set,
1522 enum isl_dim_type type);
1523 unsigned isl_map_dim(__isl_keep isl_map *map,
1524 enum isl_dim_type type);
1526 To check whether the description of a set or relation depends
1527 on one or more given dimensions, it is not necessary to iterate over all
1528 constraints. Instead the following functions can be used.
1530 int isl_basic_set_involves_dims(
1531 __isl_keep isl_basic_set *bset,
1532 enum isl_dim_type type, unsigned first, unsigned n);
1533 int isl_set_involves_dims(__isl_keep isl_set *set,
1534 enum isl_dim_type type, unsigned first, unsigned n);
1535 int isl_basic_map_involves_dims(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type, unsigned first, unsigned n);
1538 int isl_map_involves_dims(__isl_keep isl_map *map,
1539 enum isl_dim_type type, unsigned first, unsigned n);
1541 Similarly, the following functions can be used to check whether
1542 a given dimension is involved in any lower or upper bound.
1544 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1545 enum isl_dim_type type, unsigned pos);
1546 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1547 enum isl_dim_type type, unsigned pos);
1549 The identifiers or names of the domain and range spaces of a set
1550 or relation can be read off or set using the following functions.
1552 __isl_give isl_set *isl_set_set_tuple_id(
1553 __isl_take isl_set *set, __isl_take isl_id *id);
1554 __isl_give isl_set *isl_set_reset_tuple_id(
1555 __isl_take isl_set *set);
1556 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1557 __isl_give isl_id *isl_set_get_tuple_id(
1558 __isl_keep isl_set *set);
1559 __isl_give isl_map *isl_map_set_tuple_id(
1560 __isl_take isl_map *map, enum isl_dim_type type,
1561 __isl_take isl_id *id);
1562 __isl_give isl_map *isl_map_reset_tuple_id(
1563 __isl_take isl_map *map, enum isl_dim_type type);
1564 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1565 enum isl_dim_type type);
1566 __isl_give isl_id *isl_map_get_tuple_id(
1567 __isl_keep isl_map *map, enum isl_dim_type type);
1569 const char *isl_basic_set_get_tuple_name(
1570 __isl_keep isl_basic_set *bset);
1571 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1572 __isl_take isl_basic_set *set, const char *s);
1573 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1574 const char *isl_set_get_tuple_name(
1575 __isl_keep isl_set *set);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 const char *isl_map_get_tuple_name(
1583 __isl_keep isl_map *map,
1584 enum isl_dim_type type);
1586 As with C<isl_space_get_tuple_name>, the value returned points to
1587 an internal data structure.
1588 The identifiers, positions or names of individual dimensions can be
1589 read off using the following functions.
1591 __isl_give isl_id *isl_basic_set_get_dim_id(
1592 __isl_keep isl_basic_set *bset,
1593 enum isl_dim_type type, unsigned pos);
1594 __isl_give isl_set *isl_set_set_dim_id(
1595 __isl_take isl_set *set, enum isl_dim_type type,
1596 unsigned pos, __isl_take isl_id *id);
1597 int isl_set_has_dim_id(__isl_keep isl_set *set,
1598 enum isl_dim_type type, unsigned pos);
1599 __isl_give isl_id *isl_set_get_dim_id(
1600 __isl_keep isl_set *set, enum isl_dim_type type,
1602 int isl_basic_map_has_dim_id(
1603 __isl_keep isl_basic_map *bmap,
1604 enum isl_dim_type type, unsigned pos);
1605 __isl_give isl_map *isl_map_set_dim_id(
1606 __isl_take isl_map *map, enum isl_dim_type type,
1607 unsigned pos, __isl_take isl_id *id);
1608 int isl_map_has_dim_id(__isl_keep isl_map *map,
1609 enum isl_dim_type type, unsigned pos);
1610 __isl_give isl_id *isl_map_get_dim_id(
1611 __isl_keep isl_map *map, enum isl_dim_type type,
1614 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1615 enum isl_dim_type type, __isl_keep isl_id *id);
1616 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1617 enum isl_dim_type type, __isl_keep isl_id *id);
1618 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1619 enum isl_dim_type type, const char *name);
1620 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1621 enum isl_dim_type type, const char *name);
1623 const char *isl_constraint_get_dim_name(
1624 __isl_keep isl_constraint *constraint,
1625 enum isl_dim_type type, unsigned pos);
1626 const char *isl_basic_set_get_dim_name(
1627 __isl_keep isl_basic_set *bset,
1628 enum isl_dim_type type, unsigned pos);
1629 int isl_set_has_dim_name(__isl_keep isl_set *set,
1630 enum isl_dim_type type, unsigned pos);
1631 const char *isl_set_get_dim_name(
1632 __isl_keep isl_set *set,
1633 enum isl_dim_type type, unsigned pos);
1634 const char *isl_basic_map_get_dim_name(
1635 __isl_keep isl_basic_map *bmap,
1636 enum isl_dim_type type, unsigned pos);
1637 const char *isl_map_get_dim_name(
1638 __isl_keep isl_map *map,
1639 enum isl_dim_type type, unsigned pos);
1641 These functions are mostly useful to obtain the identifiers, positions
1642 or names of the parameters. Identifiers of individual dimensions are
1643 essentially only useful for printing. They are ignored by all other
1644 operations and may not be preserved across those operations.
1648 =head3 Unary Properties
1654 The following functions test whether the given set or relation
1655 contains any integer points. The ``plain'' variants do not perform
1656 any computations, but simply check if the given set or relation
1657 is already known to be empty.
1659 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1660 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1661 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1662 int isl_set_is_empty(__isl_keep isl_set *set);
1663 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1664 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1665 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1666 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1667 int isl_map_is_empty(__isl_keep isl_map *map);
1668 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1670 =item * Universality
1672 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1673 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1674 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1676 =item * Single-valuedness
1678 int isl_map_plain_is_single_valued(
1679 __isl_keep isl_map *map);
1680 int isl_map_is_single_valued(__isl_keep isl_map *map);
1681 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1685 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1686 int isl_map_is_injective(__isl_keep isl_map *map);
1687 int isl_union_map_plain_is_injective(
1688 __isl_keep isl_union_map *umap);
1689 int isl_union_map_is_injective(
1690 __isl_keep isl_union_map *umap);
1694 int isl_map_is_bijective(__isl_keep isl_map *map);
1695 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1699 int isl_basic_map_plain_is_fixed(
1700 __isl_keep isl_basic_map *bmap,
1701 enum isl_dim_type type, unsigned pos,
1703 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1704 enum isl_dim_type type, unsigned pos,
1706 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1707 enum isl_dim_type type, unsigned pos,
1710 Check if the relation obviously lies on a hyperplane where the given dimension
1711 has a fixed value and if so, return that value in C<*val>.
1715 To check whether a set is a parameter domain, use this function:
1717 int isl_set_is_params(__isl_keep isl_set *set);
1718 int isl_union_set_is_params(
1719 __isl_keep isl_union_set *uset);
1723 The following functions check whether the domain of the given
1724 (basic) set is a wrapped relation.
1726 int isl_basic_set_is_wrapping(
1727 __isl_keep isl_basic_set *bset);
1728 int isl_set_is_wrapping(__isl_keep isl_set *set);
1730 =item * Internal Product
1732 int isl_basic_map_can_zip(
1733 __isl_keep isl_basic_map *bmap);
1734 int isl_map_can_zip(__isl_keep isl_map *map);
1736 Check whether the product of domain and range of the given relation
1738 i.e., whether both domain and range are nested relations.
1742 int isl_basic_map_can_curry(
1743 __isl_keep isl_basic_map *bmap);
1744 int isl_map_can_curry(__isl_keep isl_map *map);
1746 Check whether the domain of the (basic) relation is a wrapped relation.
1750 =head3 Binary Properties
1756 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1757 __isl_keep isl_set *set2);
1758 int isl_set_is_equal(__isl_keep isl_set *set1,
1759 __isl_keep isl_set *set2);
1760 int isl_union_set_is_equal(
1761 __isl_keep isl_union_set *uset1,
1762 __isl_keep isl_union_set *uset2);
1763 int isl_basic_map_is_equal(
1764 __isl_keep isl_basic_map *bmap1,
1765 __isl_keep isl_basic_map *bmap2);
1766 int isl_map_is_equal(__isl_keep isl_map *map1,
1767 __isl_keep isl_map *map2);
1768 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1769 __isl_keep isl_map *map2);
1770 int isl_union_map_is_equal(
1771 __isl_keep isl_union_map *umap1,
1772 __isl_keep isl_union_map *umap2);
1774 =item * Disjointness
1776 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1777 __isl_keep isl_set *set2);
1781 int isl_basic_set_is_subset(
1782 __isl_keep isl_basic_set *bset1,
1783 __isl_keep isl_basic_set *bset2);
1784 int isl_set_is_subset(__isl_keep isl_set *set1,
1785 __isl_keep isl_set *set2);
1786 int isl_set_is_strict_subset(
1787 __isl_keep isl_set *set1,
1788 __isl_keep isl_set *set2);
1789 int isl_union_set_is_subset(
1790 __isl_keep isl_union_set *uset1,
1791 __isl_keep isl_union_set *uset2);
1792 int isl_union_set_is_strict_subset(
1793 __isl_keep isl_union_set *uset1,
1794 __isl_keep isl_union_set *uset2);
1795 int isl_basic_map_is_subset(
1796 __isl_keep isl_basic_map *bmap1,
1797 __isl_keep isl_basic_map *bmap2);
1798 int isl_basic_map_is_strict_subset(
1799 __isl_keep isl_basic_map *bmap1,
1800 __isl_keep isl_basic_map *bmap2);
1801 int isl_map_is_subset(
1802 __isl_keep isl_map *map1,
1803 __isl_keep isl_map *map2);
1804 int isl_map_is_strict_subset(
1805 __isl_keep isl_map *map1,
1806 __isl_keep isl_map *map2);
1807 int isl_union_map_is_subset(
1808 __isl_keep isl_union_map *umap1,
1809 __isl_keep isl_union_map *umap2);
1810 int isl_union_map_is_strict_subset(
1811 __isl_keep isl_union_map *umap1,
1812 __isl_keep isl_union_map *umap2);
1816 =head2 Unary Operations
1822 __isl_give isl_set *isl_set_complement(
1823 __isl_take isl_set *set);
1824 __isl_give isl_map *isl_map_complement(
1825 __isl_take isl_map *map);
1829 __isl_give isl_basic_map *isl_basic_map_reverse(
1830 __isl_take isl_basic_map *bmap);
1831 __isl_give isl_map *isl_map_reverse(
1832 __isl_take isl_map *map);
1833 __isl_give isl_union_map *isl_union_map_reverse(
1834 __isl_take isl_union_map *umap);
1838 __isl_give isl_basic_set *isl_basic_set_project_out(
1839 __isl_take isl_basic_set *bset,
1840 enum isl_dim_type type, unsigned first, unsigned n);
1841 __isl_give isl_basic_map *isl_basic_map_project_out(
1842 __isl_take isl_basic_map *bmap,
1843 enum isl_dim_type type, unsigned first, unsigned n);
1844 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1845 enum isl_dim_type type, unsigned first, unsigned n);
1846 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1847 enum isl_dim_type type, unsigned first, unsigned n);
1848 __isl_give isl_basic_set *isl_basic_set_params(
1849 __isl_take isl_basic_set *bset);
1850 __isl_give isl_basic_set *isl_basic_map_domain(
1851 __isl_take isl_basic_map *bmap);
1852 __isl_give isl_basic_set *isl_basic_map_range(
1853 __isl_take isl_basic_map *bmap);
1854 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1855 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1856 __isl_give isl_set *isl_map_domain(
1857 __isl_take isl_map *bmap);
1858 __isl_give isl_set *isl_map_range(
1859 __isl_take isl_map *map);
1860 __isl_give isl_set *isl_union_set_params(
1861 __isl_take isl_union_set *uset);
1862 __isl_give isl_set *isl_union_map_params(
1863 __isl_take isl_union_map *umap);
1864 __isl_give isl_union_set *isl_union_map_domain(
1865 __isl_take isl_union_map *umap);
1866 __isl_give isl_union_set *isl_union_map_range(
1867 __isl_take isl_union_map *umap);
1869 __isl_give isl_basic_map *isl_basic_map_domain_map(
1870 __isl_take isl_basic_map *bmap);
1871 __isl_give isl_basic_map *isl_basic_map_range_map(
1872 __isl_take isl_basic_map *bmap);
1873 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1874 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1875 __isl_give isl_union_map *isl_union_map_domain_map(
1876 __isl_take isl_union_map *umap);
1877 __isl_give isl_union_map *isl_union_map_range_map(
1878 __isl_take isl_union_map *umap);
1880 The functions above construct a (basic, regular or union) relation
1881 that maps (a wrapped version of) the input relation to its domain or range.
1885 __isl_give isl_set *isl_set_eliminate(
1886 __isl_take isl_set *set, enum isl_dim_type type,
1887 unsigned first, unsigned n);
1888 __isl_give isl_basic_map *isl_basic_map_eliminate(
1889 __isl_take isl_basic_map *bmap,
1890 enum isl_dim_type type,
1891 unsigned first, unsigned n);
1892 __isl_give isl_map *isl_map_eliminate(
1893 __isl_take isl_map *map, enum isl_dim_type type,
1894 unsigned first, unsigned n);
1896 Eliminate the coefficients for the given dimensions from the constraints,
1897 without removing the dimensions.
1901 __isl_give isl_basic_set *isl_basic_set_fix(
1902 __isl_take isl_basic_set *bset,
1903 enum isl_dim_type type, unsigned pos,
1905 __isl_give isl_basic_set *isl_basic_set_fix_si(
1906 __isl_take isl_basic_set *bset,
1907 enum isl_dim_type type, unsigned pos, int value);
1908 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1909 enum isl_dim_type type, unsigned pos,
1911 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1912 enum isl_dim_type type, unsigned pos, int value);
1913 __isl_give isl_basic_map *isl_basic_map_fix_si(
1914 __isl_take isl_basic_map *bmap,
1915 enum isl_dim_type type, unsigned pos, int value);
1916 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1917 enum isl_dim_type type, unsigned pos, int value);
1919 Intersect the set or relation with the hyperplane where the given
1920 dimension has the fixed given value.
1922 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1923 __isl_take isl_basic_map *bmap,
1924 enum isl_dim_type type, unsigned pos, int value);
1925 __isl_give isl_set *isl_set_lower_bound(
1926 __isl_take isl_set *set,
1927 enum isl_dim_type type, unsigned pos,
1929 __isl_give isl_set *isl_set_lower_bound_si(
1930 __isl_take isl_set *set,
1931 enum isl_dim_type type, unsigned pos, int value);
1932 __isl_give isl_map *isl_map_lower_bound_si(
1933 __isl_take isl_map *map,
1934 enum isl_dim_type type, unsigned pos, int value);
1935 __isl_give isl_set *isl_set_upper_bound(
1936 __isl_take isl_set *set,
1937 enum isl_dim_type type, unsigned pos,
1939 __isl_give isl_set *isl_set_upper_bound_si(
1940 __isl_take isl_set *set,
1941 enum isl_dim_type type, unsigned pos, int value);
1942 __isl_give isl_map *isl_map_upper_bound_si(
1943 __isl_take isl_map *map,
1944 enum isl_dim_type type, unsigned pos, int value);
1946 Intersect the set or relation with the half-space where the given
1947 dimension has a value bounded by the fixed given value.
1949 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1950 enum isl_dim_type type1, int pos1,
1951 enum isl_dim_type type2, int pos2);
1952 __isl_give isl_basic_map *isl_basic_map_equate(
1953 __isl_take isl_basic_map *bmap,
1954 enum isl_dim_type type1, int pos1,
1955 enum isl_dim_type type2, int pos2);
1956 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1957 enum isl_dim_type type1, int pos1,
1958 enum isl_dim_type type2, int pos2);
1960 Intersect the set or relation with the hyperplane where the given
1961 dimensions are equal to each other.
1963 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1964 enum isl_dim_type type1, int pos1,
1965 enum isl_dim_type type2, int pos2);
1967 Intersect the relation with the hyperplane where the given
1968 dimensions have opposite values.
1970 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1971 enum isl_dim_type type1, int pos1,
1972 enum isl_dim_type type2, int pos2);
1974 Intersect the relation with the half-space where the given
1975 dimensions satisfy the given ordering.
1979 __isl_give isl_map *isl_set_identity(
1980 __isl_take isl_set *set);
1981 __isl_give isl_union_map *isl_union_set_identity(
1982 __isl_take isl_union_set *uset);
1984 Construct an identity relation on the given (union) set.
1988 __isl_give isl_basic_set *isl_basic_map_deltas(
1989 __isl_take isl_basic_map *bmap);
1990 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1991 __isl_give isl_union_set *isl_union_map_deltas(
1992 __isl_take isl_union_map *umap);
1994 These functions return a (basic) set containing the differences
1995 between image elements and corresponding domain elements in the input.
1997 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1998 __isl_take isl_basic_map *bmap);
1999 __isl_give isl_map *isl_map_deltas_map(
2000 __isl_take isl_map *map);
2001 __isl_give isl_union_map *isl_union_map_deltas_map(
2002 __isl_take isl_union_map *umap);
2004 The functions above construct a (basic, regular or union) relation
2005 that maps (a wrapped version of) the input relation to its delta set.
2009 Simplify the representation of a set or relation by trying
2010 to combine pairs of basic sets or relations into a single
2011 basic set or relation.
2013 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2014 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2015 __isl_give isl_union_set *isl_union_set_coalesce(
2016 __isl_take isl_union_set *uset);
2017 __isl_give isl_union_map *isl_union_map_coalesce(
2018 __isl_take isl_union_map *umap);
2020 One of the methods for combining pairs of basic sets or relations
2021 can result in coefficients that are much larger than those that appear
2022 in the constraints of the input. By default, the coefficients are
2023 not allowed to grow larger, but this can be changed by unsetting
2024 the following option.
2026 int isl_options_set_coalesce_bounded_wrapping(
2027 isl_ctx *ctx, int val);
2028 int isl_options_get_coalesce_bounded_wrapping(
2031 =item * Detecting equalities
2033 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2034 __isl_take isl_basic_set *bset);
2035 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2036 __isl_take isl_basic_map *bmap);
2037 __isl_give isl_set *isl_set_detect_equalities(
2038 __isl_take isl_set *set);
2039 __isl_give isl_map *isl_map_detect_equalities(
2040 __isl_take isl_map *map);
2041 __isl_give isl_union_set *isl_union_set_detect_equalities(
2042 __isl_take isl_union_set *uset);
2043 __isl_give isl_union_map *isl_union_map_detect_equalities(
2044 __isl_take isl_union_map *umap);
2046 Simplify the representation of a set or relation by detecting implicit
2049 =item * Removing redundant constraints
2051 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2052 __isl_take isl_basic_set *bset);
2053 __isl_give isl_set *isl_set_remove_redundancies(
2054 __isl_take isl_set *set);
2055 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2056 __isl_take isl_basic_map *bmap);
2057 __isl_give isl_map *isl_map_remove_redundancies(
2058 __isl_take isl_map *map);
2062 __isl_give isl_basic_set *isl_set_convex_hull(
2063 __isl_take isl_set *set);
2064 __isl_give isl_basic_map *isl_map_convex_hull(
2065 __isl_take isl_map *map);
2067 If the input set or relation has any existentially quantified
2068 variables, then the result of these operations is currently undefined.
2072 __isl_give isl_basic_set *isl_set_simple_hull(
2073 __isl_take isl_set *set);
2074 __isl_give isl_basic_map *isl_map_simple_hull(
2075 __isl_take isl_map *map);
2076 __isl_give isl_union_map *isl_union_map_simple_hull(
2077 __isl_take isl_union_map *umap);
2079 These functions compute a single basic set or relation
2080 that contains the whole input set or relation.
2081 In particular, the output is described by translates
2082 of the constraints describing the basic sets or relations in the input.
2086 (See \autoref{s:simple hull}.)
2092 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2093 __isl_take isl_basic_set *bset);
2094 __isl_give isl_basic_set *isl_set_affine_hull(
2095 __isl_take isl_set *set);
2096 __isl_give isl_union_set *isl_union_set_affine_hull(
2097 __isl_take isl_union_set *uset);
2098 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2099 __isl_take isl_basic_map *bmap);
2100 __isl_give isl_basic_map *isl_map_affine_hull(
2101 __isl_take isl_map *map);
2102 __isl_give isl_union_map *isl_union_map_affine_hull(
2103 __isl_take isl_union_map *umap);
2105 In case of union sets and relations, the affine hull is computed
2108 =item * Polyhedral hull
2110 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2111 __isl_take isl_set *set);
2112 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2113 __isl_take isl_map *map);
2114 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2115 __isl_take isl_union_set *uset);
2116 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2117 __isl_take isl_union_map *umap);
2119 These functions compute a single basic set or relation
2120 not involving any existentially quantified variables
2121 that contains the whole input set or relation.
2122 In case of union sets and relations, the polyhedral hull is computed
2127 __isl_give isl_basic_set *isl_basic_set_sample(
2128 __isl_take isl_basic_set *bset);
2129 __isl_give isl_basic_set *isl_set_sample(
2130 __isl_take isl_set *set);
2131 __isl_give isl_basic_map *isl_basic_map_sample(
2132 __isl_take isl_basic_map *bmap);
2133 __isl_give isl_basic_map *isl_map_sample(
2134 __isl_take isl_map *map);
2136 If the input (basic) set or relation is non-empty, then return
2137 a singleton subset of the input. Otherwise, return an empty set.
2139 =item * Optimization
2141 #include <isl/ilp.h>
2142 enum isl_lp_result isl_basic_set_max(
2143 __isl_keep isl_basic_set *bset,
2144 __isl_keep isl_aff *obj, isl_int *opt)
2145 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2146 __isl_keep isl_aff *obj, isl_int *opt);
2147 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2148 __isl_keep isl_aff *obj, isl_int *opt);
2150 Compute the minimum or maximum of the integer affine expression C<obj>
2151 over the points in C<set>, returning the result in C<opt>.
2152 The return value may be one of C<isl_lp_error>,
2153 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2155 =item * Parametric optimization
2157 __isl_give isl_pw_aff *isl_set_dim_min(
2158 __isl_take isl_set *set, int pos);
2159 __isl_give isl_pw_aff *isl_set_dim_max(
2160 __isl_take isl_set *set, int pos);
2161 __isl_give isl_pw_aff *isl_map_dim_max(
2162 __isl_take isl_map *map, int pos);
2164 Compute the minimum or maximum of the given set or output dimension
2165 as a function of the parameters (and input dimensions), but independently
2166 of the other set or output dimensions.
2167 For lexicographic optimization, see L<"Lexicographic Optimization">.
2171 The following functions compute either the set of (rational) coefficient
2172 values of valid constraints for the given set or the set of (rational)
2173 values satisfying the constraints with coefficients from the given set.
2174 Internally, these two sets of functions perform essentially the
2175 same operations, except that the set of coefficients is assumed to
2176 be a cone, while the set of values may be any polyhedron.
2177 The current implementation is based on the Farkas lemma and
2178 Fourier-Motzkin elimination, but this may change or be made optional
2179 in future. In particular, future implementations may use different
2180 dualization algorithms or skip the elimination step.
2182 __isl_give isl_basic_set *isl_basic_set_coefficients(
2183 __isl_take isl_basic_set *bset);
2184 __isl_give isl_basic_set *isl_set_coefficients(
2185 __isl_take isl_set *set);
2186 __isl_give isl_union_set *isl_union_set_coefficients(
2187 __isl_take isl_union_set *bset);
2188 __isl_give isl_basic_set *isl_basic_set_solutions(
2189 __isl_take isl_basic_set *bset);
2190 __isl_give isl_basic_set *isl_set_solutions(
2191 __isl_take isl_set *set);
2192 __isl_give isl_union_set *isl_union_set_solutions(
2193 __isl_take isl_union_set *bset);
2197 __isl_give isl_map *isl_map_fixed_power(
2198 __isl_take isl_map *map, isl_int exp);
2199 __isl_give isl_union_map *isl_union_map_fixed_power(
2200 __isl_take isl_union_map *umap, isl_int exp);
2202 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2203 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2204 of C<map> is computed.
2206 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2208 __isl_give isl_union_map *isl_union_map_power(
2209 __isl_take isl_union_map *umap, int *exact);
2211 Compute a parametric representation for all positive powers I<k> of C<map>.
2212 The result maps I<k> to a nested relation corresponding to the
2213 I<k>th power of C<map>.
2214 The result may be an overapproximation. If the result is known to be exact,
2215 then C<*exact> is set to C<1>.
2217 =item * Transitive closure
2219 __isl_give isl_map *isl_map_transitive_closure(
2220 __isl_take isl_map *map, int *exact);
2221 __isl_give isl_union_map *isl_union_map_transitive_closure(
2222 __isl_take isl_union_map *umap, int *exact);
2224 Compute the transitive closure of C<map>.
2225 The result may be an overapproximation. If the result is known to be exact,
2226 then C<*exact> is set to C<1>.
2228 =item * Reaching path lengths
2230 __isl_give isl_map *isl_map_reaching_path_lengths(
2231 __isl_take isl_map *map, int *exact);
2233 Compute a relation that maps each element in the range of C<map>
2234 to the lengths of all paths composed of edges in C<map> that
2235 end up in the given element.
2236 The result may be an overapproximation. If the result is known to be exact,
2237 then C<*exact> is set to C<1>.
2238 To compute the I<maximal> path length, the resulting relation
2239 should be postprocessed by C<isl_map_lexmax>.
2240 In particular, if the input relation is a dependence relation
2241 (mapping sources to sinks), then the maximal path length corresponds
2242 to the free schedule.
2243 Note, however, that C<isl_map_lexmax> expects the maximum to be
2244 finite, so if the path lengths are unbounded (possibly due to
2245 the overapproximation), then you will get an error message.
2249 __isl_give isl_basic_set *isl_basic_map_wrap(
2250 __isl_take isl_basic_map *bmap);
2251 __isl_give isl_set *isl_map_wrap(
2252 __isl_take isl_map *map);
2253 __isl_give isl_union_set *isl_union_map_wrap(
2254 __isl_take isl_union_map *umap);
2255 __isl_give isl_basic_map *isl_basic_set_unwrap(
2256 __isl_take isl_basic_set *bset);
2257 __isl_give isl_map *isl_set_unwrap(
2258 __isl_take isl_set *set);
2259 __isl_give isl_union_map *isl_union_set_unwrap(
2260 __isl_take isl_union_set *uset);
2264 Remove any internal structure of domain (and range) of the given
2265 set or relation. If there is any such internal structure in the input,
2266 then the name of the space is also removed.
2268 __isl_give isl_basic_set *isl_basic_set_flatten(
2269 __isl_take isl_basic_set *bset);
2270 __isl_give isl_set *isl_set_flatten(
2271 __isl_take isl_set *set);
2272 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2273 __isl_take isl_basic_map *bmap);
2274 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2275 __isl_take isl_basic_map *bmap);
2276 __isl_give isl_map *isl_map_flatten_range(
2277 __isl_take isl_map *map);
2278 __isl_give isl_map *isl_map_flatten_domain(
2279 __isl_take isl_map *map);
2280 __isl_give isl_basic_map *isl_basic_map_flatten(
2281 __isl_take isl_basic_map *bmap);
2282 __isl_give isl_map *isl_map_flatten(
2283 __isl_take isl_map *map);
2285 __isl_give isl_map *isl_set_flatten_map(
2286 __isl_take isl_set *set);
2288 The function above constructs a relation
2289 that maps the input set to a flattened version of the set.
2293 Lift the input set to a space with extra dimensions corresponding
2294 to the existentially quantified variables in the input.
2295 In particular, the result lives in a wrapped map where the domain
2296 is the original space and the range corresponds to the original
2297 existentially quantified variables.
2299 __isl_give isl_basic_set *isl_basic_set_lift(
2300 __isl_take isl_basic_set *bset);
2301 __isl_give isl_set *isl_set_lift(
2302 __isl_take isl_set *set);
2303 __isl_give isl_union_set *isl_union_set_lift(
2304 __isl_take isl_union_set *uset);
2306 Given a local space that contains the existentially quantified
2307 variables of a set, a basic relation that, when applied to
2308 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2309 can be constructed using the following function.
2311 #include <isl/local_space.h>
2312 __isl_give isl_basic_map *isl_local_space_lifting(
2313 __isl_take isl_local_space *ls);
2315 =item * Internal Product
2317 __isl_give isl_basic_map *isl_basic_map_zip(
2318 __isl_take isl_basic_map *bmap);
2319 __isl_give isl_map *isl_map_zip(
2320 __isl_take isl_map *map);
2321 __isl_give isl_union_map *isl_union_map_zip(
2322 __isl_take isl_union_map *umap);
2324 Given a relation with nested relations for domain and range,
2325 interchange the range of the domain with the domain of the range.
2329 __isl_give isl_basic_map *isl_basic_map_curry(
2330 __isl_take isl_basic_map *bmap);
2331 __isl_give isl_map *isl_map_curry(
2332 __isl_take isl_map *map);
2333 __isl_give isl_union_map *isl_union_map_curry(
2334 __isl_take isl_union_map *umap);
2336 Given a relation with a nested relation for domain,
2337 move the range of the nested relation out of the domain
2338 and use it as the domain of a nested relation in the range,
2339 with the original range as range of this nested relation.
2341 =item * Aligning parameters
2343 __isl_give isl_set *isl_set_align_params(
2344 __isl_take isl_set *set,
2345 __isl_take isl_space *model);
2346 __isl_give isl_map *isl_map_align_params(
2347 __isl_take isl_map *map,
2348 __isl_take isl_space *model);
2350 Change the order of the parameters of the given set or relation
2351 such that the first parameters match those of C<model>.
2352 This may involve the introduction of extra parameters.
2353 All parameters need to be named.
2355 =item * Dimension manipulation
2357 __isl_give isl_set *isl_set_add_dims(
2358 __isl_take isl_set *set,
2359 enum isl_dim_type type, unsigned n);
2360 __isl_give isl_map *isl_map_add_dims(
2361 __isl_take isl_map *map,
2362 enum isl_dim_type type, unsigned n);
2363 __isl_give isl_set *isl_set_insert_dims(
2364 __isl_take isl_set *set,
2365 enum isl_dim_type type, unsigned pos, unsigned n);
2366 __isl_give isl_map *isl_map_insert_dims(
2367 __isl_take isl_map *map,
2368 enum isl_dim_type type, unsigned pos, unsigned n);
2369 __isl_give isl_basic_set *isl_basic_set_move_dims(
2370 __isl_take isl_basic_set *bset,
2371 enum isl_dim_type dst_type, unsigned dst_pos,
2372 enum isl_dim_type src_type, unsigned src_pos,
2374 __isl_give isl_basic_map *isl_basic_map_move_dims(
2375 __isl_take isl_basic_map *bmap,
2376 enum isl_dim_type dst_type, unsigned dst_pos,
2377 enum isl_dim_type src_type, unsigned src_pos,
2379 __isl_give isl_set *isl_set_move_dims(
2380 __isl_take isl_set *set,
2381 enum isl_dim_type dst_type, unsigned dst_pos,
2382 enum isl_dim_type src_type, unsigned src_pos,
2384 __isl_give isl_map *isl_map_move_dims(
2385 __isl_take isl_map *map,
2386 enum isl_dim_type dst_type, unsigned dst_pos,
2387 enum isl_dim_type src_type, unsigned src_pos,
2390 It is usually not advisable to directly change the (input or output)
2391 space of a set or a relation as this removes the name and the internal
2392 structure of the space. However, the above functions can be useful
2393 to add new parameters, assuming
2394 C<isl_set_align_params> and C<isl_map_align_params>
2399 =head2 Binary Operations
2401 The two arguments of a binary operation not only need to live
2402 in the same C<isl_ctx>, they currently also need to have
2403 the same (number of) parameters.
2405 =head3 Basic Operations
2409 =item * Intersection
2411 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2412 __isl_take isl_basic_set *bset1,
2413 __isl_take isl_basic_set *bset2);
2414 __isl_give isl_basic_set *isl_basic_set_intersect(
2415 __isl_take isl_basic_set *bset1,
2416 __isl_take isl_basic_set *bset2);
2417 __isl_give isl_set *isl_set_intersect_params(
2418 __isl_take isl_set *set,
2419 __isl_take isl_set *params);
2420 __isl_give isl_set *isl_set_intersect(
2421 __isl_take isl_set *set1,
2422 __isl_take isl_set *set2);
2423 __isl_give isl_union_set *isl_union_set_intersect_params(
2424 __isl_take isl_union_set *uset,
2425 __isl_take isl_set *set);
2426 __isl_give isl_union_map *isl_union_map_intersect_params(
2427 __isl_take isl_union_map *umap,
2428 __isl_take isl_set *set);
2429 __isl_give isl_union_set *isl_union_set_intersect(
2430 __isl_take isl_union_set *uset1,
2431 __isl_take isl_union_set *uset2);
2432 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2433 __isl_take isl_basic_map *bmap,
2434 __isl_take isl_basic_set *bset);
2435 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2436 __isl_take isl_basic_map *bmap,
2437 __isl_take isl_basic_set *bset);
2438 __isl_give isl_basic_map *isl_basic_map_intersect(
2439 __isl_take isl_basic_map *bmap1,
2440 __isl_take isl_basic_map *bmap2);
2441 __isl_give isl_map *isl_map_intersect_params(
2442 __isl_take isl_map *map,
2443 __isl_take isl_set *params);
2444 __isl_give isl_map *isl_map_intersect_domain(
2445 __isl_take isl_map *map,
2446 __isl_take isl_set *set);
2447 __isl_give isl_map *isl_map_intersect_range(
2448 __isl_take isl_map *map,
2449 __isl_take isl_set *set);
2450 __isl_give isl_map *isl_map_intersect(
2451 __isl_take isl_map *map1,
2452 __isl_take isl_map *map2);
2453 __isl_give isl_union_map *isl_union_map_intersect_domain(
2454 __isl_take isl_union_map *umap,
2455 __isl_take isl_union_set *uset);
2456 __isl_give isl_union_map *isl_union_map_intersect_range(
2457 __isl_take isl_union_map *umap,
2458 __isl_take isl_union_set *uset);
2459 __isl_give isl_union_map *isl_union_map_intersect(
2460 __isl_take isl_union_map *umap1,
2461 __isl_take isl_union_map *umap2);
2465 __isl_give isl_set *isl_basic_set_union(
2466 __isl_take isl_basic_set *bset1,
2467 __isl_take isl_basic_set *bset2);
2468 __isl_give isl_map *isl_basic_map_union(
2469 __isl_take isl_basic_map *bmap1,
2470 __isl_take isl_basic_map *bmap2);
2471 __isl_give isl_set *isl_set_union(
2472 __isl_take isl_set *set1,
2473 __isl_take isl_set *set2);
2474 __isl_give isl_map *isl_map_union(
2475 __isl_take isl_map *map1,
2476 __isl_take isl_map *map2);
2477 __isl_give isl_union_set *isl_union_set_union(
2478 __isl_take isl_union_set *uset1,
2479 __isl_take isl_union_set *uset2);
2480 __isl_give isl_union_map *isl_union_map_union(
2481 __isl_take isl_union_map *umap1,
2482 __isl_take isl_union_map *umap2);
2484 =item * Set difference
2486 __isl_give isl_set *isl_set_subtract(
2487 __isl_take isl_set *set1,
2488 __isl_take isl_set *set2);
2489 __isl_give isl_map *isl_map_subtract(
2490 __isl_take isl_map *map1,
2491 __isl_take isl_map *map2);
2492 __isl_give isl_map *isl_map_subtract_domain(
2493 __isl_take isl_map *map,
2494 __isl_take isl_set *dom);
2495 __isl_give isl_map *isl_map_subtract_range(
2496 __isl_take isl_map *map,
2497 __isl_take isl_set *dom);
2498 __isl_give isl_union_set *isl_union_set_subtract(
2499 __isl_take isl_union_set *uset1,
2500 __isl_take isl_union_set *uset2);
2501 __isl_give isl_union_map *isl_union_map_subtract(
2502 __isl_take isl_union_map *umap1,
2503 __isl_take isl_union_map *umap2);
2507 __isl_give isl_basic_set *isl_basic_set_apply(
2508 __isl_take isl_basic_set *bset,
2509 __isl_take isl_basic_map *bmap);
2510 __isl_give isl_set *isl_set_apply(
2511 __isl_take isl_set *set,
2512 __isl_take isl_map *map);
2513 __isl_give isl_union_set *isl_union_set_apply(
2514 __isl_take isl_union_set *uset,
2515 __isl_take isl_union_map *umap);
2516 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2517 __isl_take isl_basic_map *bmap1,
2518 __isl_take isl_basic_map *bmap2);
2519 __isl_give isl_basic_map *isl_basic_map_apply_range(
2520 __isl_take isl_basic_map *bmap1,
2521 __isl_take isl_basic_map *bmap2);
2522 __isl_give isl_map *isl_map_apply_domain(
2523 __isl_take isl_map *map1,
2524 __isl_take isl_map *map2);
2525 __isl_give isl_union_map *isl_union_map_apply_domain(
2526 __isl_take isl_union_map *umap1,
2527 __isl_take isl_union_map *umap2);
2528 __isl_give isl_map *isl_map_apply_range(
2529 __isl_take isl_map *map1,
2530 __isl_take isl_map *map2);
2531 __isl_give isl_union_map *isl_union_map_apply_range(
2532 __isl_take isl_union_map *umap1,
2533 __isl_take isl_union_map *umap2);
2535 =item * Cartesian Product
2537 __isl_give isl_set *isl_set_product(
2538 __isl_take isl_set *set1,
2539 __isl_take isl_set *set2);
2540 __isl_give isl_union_set *isl_union_set_product(
2541 __isl_take isl_union_set *uset1,
2542 __isl_take isl_union_set *uset2);
2543 __isl_give isl_basic_map *isl_basic_map_domain_product(
2544 __isl_take isl_basic_map *bmap1,
2545 __isl_take isl_basic_map *bmap2);
2546 __isl_give isl_basic_map *isl_basic_map_range_product(
2547 __isl_take isl_basic_map *bmap1,
2548 __isl_take isl_basic_map *bmap2);
2549 __isl_give isl_map *isl_map_domain_product(
2550 __isl_take isl_map *map1,
2551 __isl_take isl_map *map2);
2552 __isl_give isl_map *isl_map_range_product(
2553 __isl_take isl_map *map1,
2554 __isl_take isl_map *map2);
2555 __isl_give isl_union_map *isl_union_map_range_product(
2556 __isl_take isl_union_map *umap1,
2557 __isl_take isl_union_map *umap2);
2558 __isl_give isl_map *isl_map_product(
2559 __isl_take isl_map *map1,
2560 __isl_take isl_map *map2);
2561 __isl_give isl_union_map *isl_union_map_product(
2562 __isl_take isl_union_map *umap1,
2563 __isl_take isl_union_map *umap2);
2565 The above functions compute the cross product of the given
2566 sets or relations. The domains and ranges of the results
2567 are wrapped maps between domains and ranges of the inputs.
2568 To obtain a ``flat'' product, use the following functions
2571 __isl_give isl_basic_set *isl_basic_set_flat_product(
2572 __isl_take isl_basic_set *bset1,
2573 __isl_take isl_basic_set *bset2);
2574 __isl_give isl_set *isl_set_flat_product(
2575 __isl_take isl_set *set1,
2576 __isl_take isl_set *set2);
2577 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2578 __isl_take isl_basic_map *bmap1,
2579 __isl_take isl_basic_map *bmap2);
2580 __isl_give isl_map *isl_map_flat_domain_product(
2581 __isl_take isl_map *map1,
2582 __isl_take isl_map *map2);
2583 __isl_give isl_map *isl_map_flat_range_product(
2584 __isl_take isl_map *map1,
2585 __isl_take isl_map *map2);
2586 __isl_give isl_union_map *isl_union_map_flat_range_product(
2587 __isl_take isl_union_map *umap1,
2588 __isl_take isl_union_map *umap2);
2589 __isl_give isl_basic_map *isl_basic_map_flat_product(
2590 __isl_take isl_basic_map *bmap1,
2591 __isl_take isl_basic_map *bmap2);
2592 __isl_give isl_map *isl_map_flat_product(
2593 __isl_take isl_map *map1,
2594 __isl_take isl_map *map2);
2596 =item * Simplification
2598 __isl_give isl_basic_set *isl_basic_set_gist(
2599 __isl_take isl_basic_set *bset,
2600 __isl_take isl_basic_set *context);
2601 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2602 __isl_take isl_set *context);
2603 __isl_give isl_set *isl_set_gist_params(
2604 __isl_take isl_set *set,
2605 __isl_take isl_set *context);
2606 __isl_give isl_union_set *isl_union_set_gist(
2607 __isl_take isl_union_set *uset,
2608 __isl_take isl_union_set *context);
2609 __isl_give isl_union_set *isl_union_set_gist_params(
2610 __isl_take isl_union_set *uset,
2611 __isl_take isl_set *set);
2612 __isl_give isl_basic_map *isl_basic_map_gist(
2613 __isl_take isl_basic_map *bmap,
2614 __isl_take isl_basic_map *context);
2615 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2616 __isl_take isl_map *context);
2617 __isl_give isl_map *isl_map_gist_params(
2618 __isl_take isl_map *map,
2619 __isl_take isl_set *context);
2620 __isl_give isl_map *isl_map_gist_domain(
2621 __isl_take isl_map *map,
2622 __isl_take isl_set *context);
2623 __isl_give isl_map *isl_map_gist_range(
2624 __isl_take isl_map *map,
2625 __isl_take isl_set *context);
2626 __isl_give isl_union_map *isl_union_map_gist(
2627 __isl_take isl_union_map *umap,
2628 __isl_take isl_union_map *context);
2629 __isl_give isl_union_map *isl_union_map_gist_params(
2630 __isl_take isl_union_map *umap,
2631 __isl_take isl_set *set);
2632 __isl_give isl_union_map *isl_union_map_gist_domain(
2633 __isl_take isl_union_map *umap,
2634 __isl_take isl_union_set *uset);
2635 __isl_give isl_union_map *isl_union_map_gist_range(
2636 __isl_take isl_union_map *umap,
2637 __isl_take isl_union_set *uset);
2639 The gist operation returns a set or relation that has the
2640 same intersection with the context as the input set or relation.
2641 Any implicit equality in the intersection is made explicit in the result,
2642 while all inequalities that are redundant with respect to the intersection
2644 In case of union sets and relations, the gist operation is performed
2649 =head3 Lexicographic Optimization
2651 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2652 the following functions
2653 compute a set that contains the lexicographic minimum or maximum
2654 of the elements in C<set> (or C<bset>) for those values of the parameters
2655 that satisfy C<dom>.
2656 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2657 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2659 In other words, the union of the parameter values
2660 for which the result is non-empty and of C<*empty>
2663 __isl_give isl_set *isl_basic_set_partial_lexmin(
2664 __isl_take isl_basic_set *bset,
2665 __isl_take isl_basic_set *dom,
2666 __isl_give isl_set **empty);
2667 __isl_give isl_set *isl_basic_set_partial_lexmax(
2668 __isl_take isl_basic_set *bset,
2669 __isl_take isl_basic_set *dom,
2670 __isl_give isl_set **empty);
2671 __isl_give isl_set *isl_set_partial_lexmin(
2672 __isl_take isl_set *set, __isl_take isl_set *dom,
2673 __isl_give isl_set **empty);
2674 __isl_give isl_set *isl_set_partial_lexmax(
2675 __isl_take isl_set *set, __isl_take isl_set *dom,
2676 __isl_give isl_set **empty);
2678 Given a (basic) set C<set> (or C<bset>), the following functions simply
2679 return a set containing the lexicographic minimum or maximum
2680 of the elements in C<set> (or C<bset>).
2681 In case of union sets, the optimum is computed per space.
2683 __isl_give isl_set *isl_basic_set_lexmin(
2684 __isl_take isl_basic_set *bset);
2685 __isl_give isl_set *isl_basic_set_lexmax(
2686 __isl_take isl_basic_set *bset);
2687 __isl_give isl_set *isl_set_lexmin(
2688 __isl_take isl_set *set);
2689 __isl_give isl_set *isl_set_lexmax(
2690 __isl_take isl_set *set);
2691 __isl_give isl_union_set *isl_union_set_lexmin(
2692 __isl_take isl_union_set *uset);
2693 __isl_give isl_union_set *isl_union_set_lexmax(
2694 __isl_take isl_union_set *uset);
2696 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2697 the following functions
2698 compute a relation that maps each element of C<dom>
2699 to the single lexicographic minimum or maximum
2700 of the elements that are associated to that same
2701 element in C<map> (or C<bmap>).
2702 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2703 that contains the elements in C<dom> that do not map
2704 to any elements in C<map> (or C<bmap>).
2705 In other words, the union of the domain of the result and of C<*empty>
2708 __isl_give isl_map *isl_basic_map_partial_lexmax(
2709 __isl_take isl_basic_map *bmap,
2710 __isl_take isl_basic_set *dom,
2711 __isl_give isl_set **empty);
2712 __isl_give isl_map *isl_basic_map_partial_lexmin(
2713 __isl_take isl_basic_map *bmap,
2714 __isl_take isl_basic_set *dom,
2715 __isl_give isl_set **empty);
2716 __isl_give isl_map *isl_map_partial_lexmax(
2717 __isl_take isl_map *map, __isl_take isl_set *dom,
2718 __isl_give isl_set **empty);
2719 __isl_give isl_map *isl_map_partial_lexmin(
2720 __isl_take isl_map *map, __isl_take isl_set *dom,
2721 __isl_give isl_set **empty);
2723 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2724 return a map mapping each element in the domain of
2725 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2726 of all elements associated to that element.
2727 In case of union relations, the optimum is computed per space.
2729 __isl_give isl_map *isl_basic_map_lexmin(
2730 __isl_take isl_basic_map *bmap);
2731 __isl_give isl_map *isl_basic_map_lexmax(
2732 __isl_take isl_basic_map *bmap);
2733 __isl_give isl_map *isl_map_lexmin(
2734 __isl_take isl_map *map);
2735 __isl_give isl_map *isl_map_lexmax(
2736 __isl_take isl_map *map);
2737 __isl_give isl_union_map *isl_union_map_lexmin(
2738 __isl_take isl_union_map *umap);
2739 __isl_give isl_union_map *isl_union_map_lexmax(
2740 __isl_take isl_union_map *umap);
2742 The following functions return their result in the form of
2743 a piecewise multi-affine expression
2744 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2745 but are otherwise equivalent to the corresponding functions
2746 returning a basic set or relation.
2748 __isl_give isl_pw_multi_aff *
2749 isl_basic_map_lexmin_pw_multi_aff(
2750 __isl_take isl_basic_map *bmap);
2751 __isl_give isl_pw_multi_aff *
2752 isl_basic_set_partial_lexmin_pw_multi_aff(
2753 __isl_take isl_basic_set *bset,
2754 __isl_take isl_basic_set *dom,
2755 __isl_give isl_set **empty);
2756 __isl_give isl_pw_multi_aff *
2757 isl_basic_set_partial_lexmax_pw_multi_aff(
2758 __isl_take isl_basic_set *bset,
2759 __isl_take isl_basic_set *dom,
2760 __isl_give isl_set **empty);
2761 __isl_give isl_pw_multi_aff *
2762 isl_basic_map_partial_lexmin_pw_multi_aff(
2763 __isl_take isl_basic_map *bmap,
2764 __isl_take isl_basic_set *dom,
2765 __isl_give isl_set **empty);
2766 __isl_give isl_pw_multi_aff *
2767 isl_basic_map_partial_lexmax_pw_multi_aff(
2768 __isl_take isl_basic_map *bmap,
2769 __isl_take isl_basic_set *dom,
2770 __isl_give isl_set **empty);
2774 Lists are defined over several element types, including
2775 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2776 Here we take lists of C<isl_set>s as an example.
2777 Lists can be created, copied and freed using the following functions.
2779 #include <isl/list.h>
2780 __isl_give isl_set_list *isl_set_list_from_set(
2781 __isl_take isl_set *el);
2782 __isl_give isl_set_list *isl_set_list_alloc(
2783 isl_ctx *ctx, int n);
2784 __isl_give isl_set_list *isl_set_list_copy(
2785 __isl_keep isl_set_list *list);
2786 __isl_give isl_set_list *isl_set_list_add(
2787 __isl_take isl_set_list *list,
2788 __isl_take isl_set *el);
2789 __isl_give isl_set_list *isl_set_list_concat(
2790 __isl_take isl_set_list *list1,
2791 __isl_take isl_set_list *list2);
2792 void *isl_set_list_free(__isl_take isl_set_list *list);
2794 C<isl_set_list_alloc> creates an empty list with a capacity for
2795 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2798 Lists can be inspected using the following functions.
2800 #include <isl/list.h>
2801 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2802 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2803 __isl_give isl_set *isl_set_list_get_set(
2804 __isl_keep isl_set_list *list, int index);
2805 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2806 int (*fn)(__isl_take isl_set *el, void *user),
2809 Lists can be printed using
2811 #include <isl/list.h>
2812 __isl_give isl_printer *isl_printer_print_set_list(
2813 __isl_take isl_printer *p,
2814 __isl_keep isl_set_list *list);
2818 Vectors can be created, copied and freed using the following functions.
2820 #include <isl/vec.h>
2821 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2823 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2824 void isl_vec_free(__isl_take isl_vec *vec);
2826 Note that the elements of a newly created vector may have arbitrary values.
2827 The elements can be changed and inspected using the following functions.
2829 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2830 int isl_vec_size(__isl_keep isl_vec *vec);
2831 int isl_vec_get_element(__isl_keep isl_vec *vec,
2832 int pos, isl_int *v);
2833 __isl_give isl_vec *isl_vec_set_element(
2834 __isl_take isl_vec *vec, int pos, isl_int v);
2835 __isl_give isl_vec *isl_vec_set_element_si(
2836 __isl_take isl_vec *vec, int pos, int v);
2837 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2839 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2842 C<isl_vec_get_element> will return a negative value if anything went wrong.
2843 In that case, the value of C<*v> is undefined.
2847 Matrices can be created, copied and freed using the following functions.
2849 #include <isl/mat.h>
2850 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2851 unsigned n_row, unsigned n_col);
2852 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2853 void isl_mat_free(__isl_take isl_mat *mat);
2855 Note that the elements of a newly created matrix may have arbitrary values.
2856 The elements can be changed and inspected using the following functions.
2858 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2859 int isl_mat_rows(__isl_keep isl_mat *mat);
2860 int isl_mat_cols(__isl_keep isl_mat *mat);
2861 int isl_mat_get_element(__isl_keep isl_mat *mat,
2862 int row, int col, isl_int *v);
2863 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2864 int row, int col, isl_int v);
2865 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2866 int row, int col, int v);
2868 C<isl_mat_get_element> will return a negative value if anything went wrong.
2869 In that case, the value of C<*v> is undefined.
2871 The following function can be used to compute the (right) inverse
2872 of a matrix, i.e., a matrix such that the product of the original
2873 and the inverse (in that order) is a multiple of the identity matrix.
2874 The input matrix is assumed to be of full row-rank.
2876 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2878 The following function can be used to compute the (right) kernel
2879 (or null space) of a matrix, i.e., a matrix such that the product of
2880 the original and the kernel (in that order) is the zero matrix.
2882 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2884 =head2 Piecewise Quasi Affine Expressions
2886 The zero quasi affine expression on a given domain can be created using
2888 __isl_give isl_aff *isl_aff_zero_on_domain(
2889 __isl_take isl_local_space *ls);
2891 Note that the space in which the resulting object lives is a map space
2892 with the given space as domain and a one-dimensional range.
2894 An empty piecewise quasi affine expression (one with no cells)
2895 or a piecewise quasi affine expression with a single cell can
2896 be created using the following functions.
2898 #include <isl/aff.h>
2899 __isl_give isl_pw_aff *isl_pw_aff_empty(
2900 __isl_take isl_space *space);
2901 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2902 __isl_take isl_set *set, __isl_take isl_aff *aff);
2903 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2904 __isl_take isl_aff *aff);
2906 A piecewise quasi affine expression that is equal to 1 on a set
2907 and 0 outside the set can be created using the following function.
2909 #include <isl/aff.h>
2910 __isl_give isl_pw_aff *isl_set_indicator_function(
2911 __isl_take isl_set *set);
2913 Quasi affine expressions can be copied and freed using
2915 #include <isl/aff.h>
2916 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2917 void *isl_aff_free(__isl_take isl_aff *aff);
2919 __isl_give isl_pw_aff *isl_pw_aff_copy(
2920 __isl_keep isl_pw_aff *pwaff);
2921 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2923 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2924 using the following function. The constraint is required to have
2925 a non-zero coefficient for the specified dimension.
2927 #include <isl/constraint.h>
2928 __isl_give isl_aff *isl_constraint_get_bound(
2929 __isl_keep isl_constraint *constraint,
2930 enum isl_dim_type type, int pos);
2932 The entire affine expression of the constraint can also be extracted
2933 using the following function.
2935 #include <isl/constraint.h>
2936 __isl_give isl_aff *isl_constraint_get_aff(
2937 __isl_keep isl_constraint *constraint);
2939 Conversely, an equality constraint equating
2940 the affine expression to zero or an inequality constraint enforcing
2941 the affine expression to be non-negative, can be constructed using
2943 __isl_give isl_constraint *isl_equality_from_aff(
2944 __isl_take isl_aff *aff);
2945 __isl_give isl_constraint *isl_inequality_from_aff(
2946 __isl_take isl_aff *aff);
2948 The expression can be inspected using
2950 #include <isl/aff.h>
2951 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2952 int isl_aff_dim(__isl_keep isl_aff *aff,
2953 enum isl_dim_type type);
2954 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2955 __isl_keep isl_aff *aff);
2956 __isl_give isl_local_space *isl_aff_get_local_space(
2957 __isl_keep isl_aff *aff);
2958 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2959 enum isl_dim_type type, unsigned pos);
2960 const char *isl_pw_aff_get_dim_name(
2961 __isl_keep isl_pw_aff *pa,
2962 enum isl_dim_type type, unsigned pos);
2963 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2964 enum isl_dim_type type, unsigned pos);
2965 __isl_give isl_id *isl_pw_aff_get_dim_id(
2966 __isl_keep isl_pw_aff *pa,
2967 enum isl_dim_type type, unsigned pos);
2968 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2970 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2971 enum isl_dim_type type, int pos, isl_int *v);
2972 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2974 __isl_give isl_aff *isl_aff_get_div(
2975 __isl_keep isl_aff *aff, int pos);
2977 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2978 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2979 int (*fn)(__isl_take isl_set *set,
2980 __isl_take isl_aff *aff,
2981 void *user), void *user);
2983 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2984 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2986 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2987 enum isl_dim_type type, unsigned first, unsigned n);
2988 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2989 enum isl_dim_type type, unsigned first, unsigned n);
2991 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2992 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2993 enum isl_dim_type type);
2994 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2996 It can be modified using
2998 #include <isl/aff.h>
2999 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3000 __isl_take isl_pw_aff *pwaff,
3001 enum isl_dim_type type, __isl_take isl_id *id);
3002 __isl_give isl_aff *isl_aff_set_dim_name(
3003 __isl_take isl_aff *aff, enum isl_dim_type type,
3004 unsigned pos, const char *s);
3005 __isl_give isl_aff *isl_aff_set_dim_id(
3006 __isl_take isl_aff *aff, enum isl_dim_type type,
3007 unsigned pos, __isl_take isl_id *id);
3008 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3009 __isl_take isl_pw_aff *pma,
3010 enum isl_dim_type type, unsigned pos,
3011 __isl_take isl_id *id);
3012 __isl_give isl_aff *isl_aff_set_constant(
3013 __isl_take isl_aff *aff, isl_int v);
3014 __isl_give isl_aff *isl_aff_set_constant_si(
3015 __isl_take isl_aff *aff, int v);
3016 __isl_give isl_aff *isl_aff_set_coefficient(
3017 __isl_take isl_aff *aff,
3018 enum isl_dim_type type, int pos, isl_int v);
3019 __isl_give isl_aff *isl_aff_set_coefficient_si(
3020 __isl_take isl_aff *aff,
3021 enum isl_dim_type type, int pos, int v);
3022 __isl_give isl_aff *isl_aff_set_denominator(
3023 __isl_take isl_aff *aff, isl_int v);
3025 __isl_give isl_aff *isl_aff_add_constant(
3026 __isl_take isl_aff *aff, isl_int v);
3027 __isl_give isl_aff *isl_aff_add_constant_si(
3028 __isl_take isl_aff *aff, int v);
3029 __isl_give isl_aff *isl_aff_add_coefficient(
3030 __isl_take isl_aff *aff,
3031 enum isl_dim_type type, int pos, isl_int v);
3032 __isl_give isl_aff *isl_aff_add_coefficient_si(
3033 __isl_take isl_aff *aff,
3034 enum isl_dim_type type, int pos, int v);
3036 __isl_give isl_aff *isl_aff_insert_dims(
3037 __isl_take isl_aff *aff,
3038 enum isl_dim_type type, unsigned first, unsigned n);
3039 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3040 __isl_take isl_pw_aff *pwaff,
3041 enum isl_dim_type type, unsigned first, unsigned n);
3042 __isl_give isl_aff *isl_aff_add_dims(
3043 __isl_take isl_aff *aff,
3044 enum isl_dim_type type, unsigned n);
3045 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3046 __isl_take isl_pw_aff *pwaff,
3047 enum isl_dim_type type, unsigned n);
3048 __isl_give isl_aff *isl_aff_drop_dims(
3049 __isl_take isl_aff *aff,
3050 enum isl_dim_type type, unsigned first, unsigned n);
3051 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3052 __isl_take isl_pw_aff *pwaff,
3053 enum isl_dim_type type, unsigned first, unsigned n);
3055 Note that the C<set_constant> and C<set_coefficient> functions
3056 set the I<numerator> of the constant or coefficient, while
3057 C<add_constant> and C<add_coefficient> add an integer value to
3058 the possibly rational constant or coefficient.
3060 To check whether an affine expressions is obviously zero
3061 or obviously equal to some other affine expression, use
3063 #include <isl/aff.h>
3064 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3065 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3066 __isl_keep isl_aff *aff2);
3067 int isl_pw_aff_plain_is_equal(
3068 __isl_keep isl_pw_aff *pwaff1,
3069 __isl_keep isl_pw_aff *pwaff2);
3073 #include <isl/aff.h>
3074 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3075 __isl_take isl_aff *aff2);
3076 __isl_give isl_pw_aff *isl_pw_aff_add(
3077 __isl_take isl_pw_aff *pwaff1,
3078 __isl_take isl_pw_aff *pwaff2);
3079 __isl_give isl_pw_aff *isl_pw_aff_min(
3080 __isl_take isl_pw_aff *pwaff1,
3081 __isl_take isl_pw_aff *pwaff2);
3082 __isl_give isl_pw_aff *isl_pw_aff_max(
3083 __isl_take isl_pw_aff *pwaff1,
3084 __isl_take isl_pw_aff *pwaff2);
3085 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3086 __isl_take isl_aff *aff2);
3087 __isl_give isl_pw_aff *isl_pw_aff_sub(
3088 __isl_take isl_pw_aff *pwaff1,
3089 __isl_take isl_pw_aff *pwaff2);
3090 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3091 __isl_give isl_pw_aff *isl_pw_aff_neg(
3092 __isl_take isl_pw_aff *pwaff);
3093 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3094 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3095 __isl_take isl_pw_aff *pwaff);
3096 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3097 __isl_give isl_pw_aff *isl_pw_aff_floor(
3098 __isl_take isl_pw_aff *pwaff);
3099 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3101 __isl_give isl_pw_aff *isl_pw_aff_mod(
3102 __isl_take isl_pw_aff *pwaff, isl_int mod);
3103 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3105 __isl_give isl_pw_aff *isl_pw_aff_scale(
3106 __isl_take isl_pw_aff *pwaff, isl_int f);
3107 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3109 __isl_give isl_aff *isl_aff_scale_down_ui(
3110 __isl_take isl_aff *aff, unsigned f);
3111 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3112 __isl_take isl_pw_aff *pwaff, isl_int f);
3114 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3115 __isl_take isl_pw_aff_list *list);
3116 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3117 __isl_take isl_pw_aff_list *list);
3119 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3120 __isl_take isl_pw_aff *pwqp);
3122 __isl_give isl_aff *isl_aff_align_params(
3123 __isl_take isl_aff *aff,
3124 __isl_take isl_space *model);
3125 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3126 __isl_take isl_pw_aff *pwaff,
3127 __isl_take isl_space *model);
3129 __isl_give isl_aff *isl_aff_project_domain_on_params(
3130 __isl_take isl_aff *aff);
3132 __isl_give isl_aff *isl_aff_gist_params(
3133 __isl_take isl_aff *aff,
3134 __isl_take isl_set *context);
3135 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3136 __isl_take isl_set *context);
3137 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3138 __isl_take isl_pw_aff *pwaff,
3139 __isl_take isl_set *context);
3140 __isl_give isl_pw_aff *isl_pw_aff_gist(
3141 __isl_take isl_pw_aff *pwaff,
3142 __isl_take isl_set *context);
3144 __isl_give isl_set *isl_pw_aff_domain(
3145 __isl_take isl_pw_aff *pwaff);
3146 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3147 __isl_take isl_pw_aff *pa,
3148 __isl_take isl_set *set);
3149 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3150 __isl_take isl_pw_aff *pa,
3151 __isl_take isl_set *set);
3153 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3154 __isl_take isl_aff *aff2);
3155 __isl_give isl_pw_aff *isl_pw_aff_mul(
3156 __isl_take isl_pw_aff *pwaff1,
3157 __isl_take isl_pw_aff *pwaff2);
3159 When multiplying two affine expressions, at least one of the two needs
3162 #include <isl/aff.h>
3163 __isl_give isl_basic_set *isl_aff_le_basic_set(
3164 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3165 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3166 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3167 __isl_give isl_set *isl_pw_aff_eq_set(
3168 __isl_take isl_pw_aff *pwaff1,
3169 __isl_take isl_pw_aff *pwaff2);
3170 __isl_give isl_set *isl_pw_aff_ne_set(
3171 __isl_take isl_pw_aff *pwaff1,
3172 __isl_take isl_pw_aff *pwaff2);
3173 __isl_give isl_set *isl_pw_aff_le_set(
3174 __isl_take isl_pw_aff *pwaff1,
3175 __isl_take isl_pw_aff *pwaff2);
3176 __isl_give isl_set *isl_pw_aff_lt_set(
3177 __isl_take isl_pw_aff *pwaff1,
3178 __isl_take isl_pw_aff *pwaff2);
3179 __isl_give isl_set *isl_pw_aff_ge_set(
3180 __isl_take isl_pw_aff *pwaff1,
3181 __isl_take isl_pw_aff *pwaff2);
3182 __isl_give isl_set *isl_pw_aff_gt_set(
3183 __isl_take isl_pw_aff *pwaff1,
3184 __isl_take isl_pw_aff *pwaff2);
3186 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_set(
3193 __isl_take isl_pw_aff_list *list1,
3194 __isl_take isl_pw_aff_list *list2);
3195 __isl_give isl_set *isl_pw_aff_list_lt_set(
3196 __isl_take isl_pw_aff_list *list1,
3197 __isl_take isl_pw_aff_list *list2);
3198 __isl_give isl_set *isl_pw_aff_list_ge_set(
3199 __isl_take isl_pw_aff_list *list1,
3200 __isl_take isl_pw_aff_list *list2);
3201 __isl_give isl_set *isl_pw_aff_list_gt_set(
3202 __isl_take isl_pw_aff_list *list1,
3203 __isl_take isl_pw_aff_list *list2);
3205 The function C<isl_aff_ge_basic_set> returns a basic set
3206 containing those elements in the shared space
3207 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3208 The function C<isl_aff_ge_set> returns a set
3209 containing those elements in the shared domain
3210 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3211 The functions operating on C<isl_pw_aff_list> apply the corresponding
3212 C<isl_pw_aff> function to each pair of elements in the two lists.
3214 #include <isl/aff.h>
3215 __isl_give isl_set *isl_pw_aff_nonneg_set(
3216 __isl_take isl_pw_aff *pwaff);
3217 __isl_give isl_set *isl_pw_aff_zero_set(
3218 __isl_take isl_pw_aff *pwaff);
3219 __isl_give isl_set *isl_pw_aff_non_zero_set(
3220 __isl_take isl_pw_aff *pwaff);
3222 The function C<isl_pw_aff_nonneg_set> returns a set
3223 containing those elements in the domain
3224 of C<pwaff> where C<pwaff> is non-negative.
3226 #include <isl/aff.h>
3227 __isl_give isl_pw_aff *isl_pw_aff_cond(
3228 __isl_take isl_pw_aff *cond,
3229 __isl_take isl_pw_aff *pwaff_true,
3230 __isl_take isl_pw_aff *pwaff_false);
3232 The function C<isl_pw_aff_cond> performs a conditional operator
3233 and returns an expression that is equal to C<pwaff_true>
3234 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3235 where C<cond> is zero.
3237 #include <isl/aff.h>
3238 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3239 __isl_take isl_pw_aff *pwaff1,
3240 __isl_take isl_pw_aff *pwaff2);
3241 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3242 __isl_take isl_pw_aff *pwaff1,
3243 __isl_take isl_pw_aff *pwaff2);
3244 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3245 __isl_take isl_pw_aff *pwaff1,
3246 __isl_take isl_pw_aff *pwaff2);
3248 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3249 expression with a domain that is the union of those of C<pwaff1> and
3250 C<pwaff2> and such that on each cell, the quasi-affine expression is
3251 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3252 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3253 associated expression is the defined one.
3255 An expression can be read from input using
3257 #include <isl/aff.h>
3258 __isl_give isl_aff *isl_aff_read_from_str(
3259 isl_ctx *ctx, const char *str);
3260 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3261 isl_ctx *ctx, const char *str);
3263 An expression can be printed using
3265 #include <isl/aff.h>
3266 __isl_give isl_printer *isl_printer_print_aff(
3267 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3269 __isl_give isl_printer *isl_printer_print_pw_aff(
3270 __isl_take isl_printer *p,
3271 __isl_keep isl_pw_aff *pwaff);
3273 =head2 Piecewise Multiple Quasi Affine Expressions
3275 An C<isl_multi_aff> object represents a sequence of
3276 zero or more affine expressions, all defined on the same domain space.
3278 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3281 #include <isl/aff.h>
3282 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3283 __isl_take isl_space *space,
3284 __isl_take isl_aff_list *list);
3286 An empty piecewise multiple quasi affine expression (one with no cells),
3287 the zero piecewise multiple quasi affine expression (with value zero
3288 for each output dimension),
3289 a piecewise multiple quasi affine expression with a single cell (with
3290 either a universe or a specified domain) or
3291 a zero-dimensional piecewise multiple quasi affine expression
3293 can be created using the following functions.
3295 #include <isl/aff.h>
3296 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3297 __isl_take isl_space *space);
3298 __isl_give isl_multi_aff *isl_multi_aff_zero(
3299 __isl_take isl_space *space);
3300 __isl_give isl_pw_multi_aff *
3301 isl_pw_multi_aff_from_multi_aff(
3302 __isl_take isl_multi_aff *ma);
3303 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3304 __isl_take isl_set *set,
3305 __isl_take isl_multi_aff *maff);
3306 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3307 __isl_take isl_set *set);
3309 __isl_give isl_union_pw_multi_aff *
3310 isl_union_pw_multi_aff_empty(
3311 __isl_take isl_space *space);
3312 __isl_give isl_union_pw_multi_aff *
3313 isl_union_pw_multi_aff_add_pw_multi_aff(
3314 __isl_take isl_union_pw_multi_aff *upma,
3315 __isl_take isl_pw_multi_aff *pma);
3316 __isl_give isl_union_pw_multi_aff *
3317 isl_union_pw_multi_aff_from_domain(
3318 __isl_take isl_union_set *uset);
3320 A piecewise multiple quasi affine expression can also be initialized
3321 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3322 and the C<isl_map> is single-valued.
3324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3325 __isl_take isl_set *set);
3326 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3327 __isl_take isl_map *map);
3329 Multiple quasi affine expressions can be copied and freed using
3331 #include <isl/aff.h>
3332 __isl_give isl_multi_aff *isl_multi_aff_copy(
3333 __isl_keep isl_multi_aff *maff);
3334 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3337 __isl_keep isl_pw_multi_aff *pma);
3338 void *isl_pw_multi_aff_free(
3339 __isl_take isl_pw_multi_aff *pma);
3341 __isl_give isl_union_pw_multi_aff *
3342 isl_union_pw_multi_aff_copy(
3343 __isl_keep isl_union_pw_multi_aff *upma);
3344 void *isl_union_pw_multi_aff_free(
3345 __isl_take isl_union_pw_multi_aff *upma);
3347 The expression can be inspected using
3349 #include <isl/aff.h>
3350 isl_ctx *isl_multi_aff_get_ctx(
3351 __isl_keep isl_multi_aff *maff);
3352 isl_ctx *isl_pw_multi_aff_get_ctx(
3353 __isl_keep isl_pw_multi_aff *pma);
3354 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3355 __isl_keep isl_union_pw_multi_aff *upma);
3356 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3357 enum isl_dim_type type);
3358 unsigned isl_pw_multi_aff_dim(
3359 __isl_keep isl_pw_multi_aff *pma,
3360 enum isl_dim_type type);
3361 __isl_give isl_aff *isl_multi_aff_get_aff(
3362 __isl_keep isl_multi_aff *multi, int pos);
3363 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3364 __isl_keep isl_pw_multi_aff *pma, int pos);
3365 const char *isl_pw_multi_aff_get_dim_name(
3366 __isl_keep isl_pw_multi_aff *pma,
3367 enum isl_dim_type type, unsigned pos);
3368 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3369 __isl_keep isl_pw_multi_aff *pma,
3370 enum isl_dim_type type, unsigned pos);
3371 const char *isl_multi_aff_get_tuple_name(
3372 __isl_keep isl_multi_aff *multi,
3373 enum isl_dim_type type);
3374 const char *isl_pw_multi_aff_get_tuple_name(
3375 __isl_keep isl_pw_multi_aff *pma,
3376 enum isl_dim_type type);
3377 int isl_pw_multi_aff_has_tuple_id(
3378 __isl_keep isl_pw_multi_aff *pma,
3379 enum isl_dim_type type);
3380 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3381 __isl_keep isl_pw_multi_aff *pma,
3382 enum isl_dim_type type);
3384 int isl_pw_multi_aff_foreach_piece(
3385 __isl_keep isl_pw_multi_aff *pma,
3386 int (*fn)(__isl_take isl_set *set,
3387 __isl_take isl_multi_aff *maff,
3388 void *user), void *user);
3390 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3391 __isl_keep isl_union_pw_multi_aff *upma,
3392 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3393 void *user), void *user);
3395 It can be modified using
3397 #include <isl/aff.h>
3398 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3399 __isl_take isl_multi_aff *multi, int pos,
3400 __isl_take isl_aff *aff);
3401 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3402 __isl_take isl_multi_aff *maff,
3403 enum isl_dim_type type, unsigned pos, const char *s);
3404 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3405 __isl_take isl_multi_aff *maff,
3406 enum isl_dim_type type, __isl_take isl_id *id);
3407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3408 __isl_take isl_pw_multi_aff *pma,
3409 enum isl_dim_type type, __isl_take isl_id *id);
3411 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3412 __isl_take isl_multi_aff *maff,
3413 enum isl_dim_type type, unsigned first, unsigned n);
3415 To check whether two multiple affine expressions are
3416 obviously equal to each other, use
3418 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3419 __isl_keep isl_multi_aff *maff2);
3420 int isl_pw_multi_aff_plain_is_equal(
3421 __isl_keep isl_pw_multi_aff *pma1,
3422 __isl_keep isl_pw_multi_aff *pma2);
3426 #include <isl/aff.h>
3427 __isl_give isl_multi_aff *isl_multi_aff_add(
3428 __isl_take isl_multi_aff *maff1,
3429 __isl_take isl_multi_aff *maff2);
3430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3431 __isl_take isl_pw_multi_aff *pma1,
3432 __isl_take isl_pw_multi_aff *pma2);
3433 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3434 __isl_take isl_union_pw_multi_aff *upma1,
3435 __isl_take isl_union_pw_multi_aff *upma2);
3436 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3437 __isl_take isl_pw_multi_aff *pma1,
3438 __isl_take isl_pw_multi_aff *pma2);
3439 __isl_give isl_multi_aff *isl_multi_aff_scale(
3440 __isl_take isl_multi_aff *maff,
3442 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3443 __isl_take isl_pw_multi_aff *pma,
3444 __isl_take isl_set *set);
3445 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3446 __isl_take isl_pw_multi_aff *pma,
3447 __isl_take isl_set *set);
3448 __isl_give isl_multi_aff *isl_multi_aff_lift(
3449 __isl_take isl_multi_aff *maff,
3450 __isl_give isl_local_space **ls);
3451 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3452 __isl_take isl_pw_multi_aff *pma);
3453 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3454 __isl_take isl_multi_aff *maff,
3455 __isl_take isl_set *context);
3456 __isl_give isl_multi_aff *isl_multi_aff_gist(
3457 __isl_take isl_multi_aff *maff,
3458 __isl_take isl_set *context);
3459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3460 __isl_take isl_pw_multi_aff *pma,
3461 __isl_take isl_set *set);
3462 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3463 __isl_take isl_pw_multi_aff *pma,
3464 __isl_take isl_set *set);
3465 __isl_give isl_set *isl_pw_multi_aff_domain(
3466 __isl_take isl_pw_multi_aff *pma);
3467 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3468 __isl_take isl_union_pw_multi_aff *upma);
3469 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3470 __isl_take isl_multi_aff *ma1,
3471 __isl_take isl_multi_aff *ma2);
3472 __isl_give isl_pw_multi_aff *
3473 isl_pw_multi_aff_flat_range_product(
3474 __isl_take isl_pw_multi_aff *pma1,
3475 __isl_take isl_pw_multi_aff *pma2);
3476 __isl_give isl_union_pw_multi_aff *
3477 isl_union_pw_multi_aff_flat_range_product(
3478 __isl_take isl_union_pw_multi_aff *upma1,
3479 __isl_take isl_union_pw_multi_aff *upma2);
3481 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3482 then it is assigned the local space that lies at the basis of
3483 the lifting applied.
3485 An expression can be read from input using
3487 #include <isl/aff.h>
3488 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3489 isl_ctx *ctx, const char *str);
3490 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3491 isl_ctx *ctx, const char *str);
3493 An expression can be printed using
3495 #include <isl/aff.h>
3496 __isl_give isl_printer *isl_printer_print_multi_aff(
3497 __isl_take isl_printer *p,
3498 __isl_keep isl_multi_aff *maff);
3499 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3500 __isl_take isl_printer *p,
3501 __isl_keep isl_pw_multi_aff *pma);
3502 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3503 __isl_take isl_printer *p,
3504 __isl_keep isl_union_pw_multi_aff *upma);
3508 Points are elements of a set. They can be used to construct
3509 simple sets (boxes) or they can be used to represent the
3510 individual elements of a set.
3511 The zero point (the origin) can be created using
3513 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3515 The coordinates of a point can be inspected, set and changed
3518 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3519 enum isl_dim_type type, int pos, isl_int *v);
3520 __isl_give isl_point *isl_point_set_coordinate(
3521 __isl_take isl_point *pnt,
3522 enum isl_dim_type type, int pos, isl_int v);
3524 __isl_give isl_point *isl_point_add_ui(
3525 __isl_take isl_point *pnt,
3526 enum isl_dim_type type, int pos, unsigned val);
3527 __isl_give isl_point *isl_point_sub_ui(
3528 __isl_take isl_point *pnt,
3529 enum isl_dim_type type, int pos, unsigned val);
3531 Other properties can be obtained using
3533 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3535 Points can be copied or freed using
3537 __isl_give isl_point *isl_point_copy(
3538 __isl_keep isl_point *pnt);
3539 void isl_point_free(__isl_take isl_point *pnt);
3541 A singleton set can be created from a point using
3543 __isl_give isl_basic_set *isl_basic_set_from_point(
3544 __isl_take isl_point *pnt);
3545 __isl_give isl_set *isl_set_from_point(
3546 __isl_take isl_point *pnt);
3548 and a box can be created from two opposite extremal points using
3550 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3551 __isl_take isl_point *pnt1,
3552 __isl_take isl_point *pnt2);
3553 __isl_give isl_set *isl_set_box_from_points(
3554 __isl_take isl_point *pnt1,
3555 __isl_take isl_point *pnt2);
3557 All elements of a B<bounded> (union) set can be enumerated using
3558 the following functions.
3560 int isl_set_foreach_point(__isl_keep isl_set *set,
3561 int (*fn)(__isl_take isl_point *pnt, void *user),
3563 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3564 int (*fn)(__isl_take isl_point *pnt, void *user),
3567 The function C<fn> is called for each integer point in
3568 C<set> with as second argument the last argument of
3569 the C<isl_set_foreach_point> call. The function C<fn>
3570 should return C<0> on success and C<-1> on failure.
3571 In the latter case, C<isl_set_foreach_point> will stop
3572 enumerating and return C<-1> as well.
3573 If the enumeration is performed successfully and to completion,
3574 then C<isl_set_foreach_point> returns C<0>.
3576 To obtain a single point of a (basic) set, use
3578 __isl_give isl_point *isl_basic_set_sample_point(
3579 __isl_take isl_basic_set *bset);
3580 __isl_give isl_point *isl_set_sample_point(
3581 __isl_take isl_set *set);
3583 If C<set> does not contain any (integer) points, then the
3584 resulting point will be ``void'', a property that can be
3587 int isl_point_is_void(__isl_keep isl_point *pnt);
3589 =head2 Piecewise Quasipolynomials
3591 A piecewise quasipolynomial is a particular kind of function that maps
3592 a parametric point to a rational value.
3593 More specifically, a quasipolynomial is a polynomial expression in greatest
3594 integer parts of affine expressions of parameters and variables.
3595 A piecewise quasipolynomial is a subdivision of a given parametric
3596 domain into disjoint cells with a quasipolynomial associated to
3597 each cell. The value of the piecewise quasipolynomial at a given
3598 point is the value of the quasipolynomial associated to the cell
3599 that contains the point. Outside of the union of cells,
3600 the value is assumed to be zero.
3601 For example, the piecewise quasipolynomial
3603 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3605 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3606 A given piecewise quasipolynomial has a fixed domain dimension.
3607 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3608 defined over different domains.
3609 Piecewise quasipolynomials are mainly used by the C<barvinok>
3610 library for representing the number of elements in a parametric set or map.
3611 For example, the piecewise quasipolynomial above represents
3612 the number of points in the map
3614 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3616 =head3 Input and Output
3618 Piecewise quasipolynomials can be read from input using
3620 __isl_give isl_union_pw_qpolynomial *
3621 isl_union_pw_qpolynomial_read_from_str(
3622 isl_ctx *ctx, const char *str);
3624 Quasipolynomials and piecewise quasipolynomials can be printed
3625 using the following functions.
3627 __isl_give isl_printer *isl_printer_print_qpolynomial(
3628 __isl_take isl_printer *p,
3629 __isl_keep isl_qpolynomial *qp);
3631 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3632 __isl_take isl_printer *p,
3633 __isl_keep isl_pw_qpolynomial *pwqp);
3635 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3636 __isl_take isl_printer *p,
3637 __isl_keep isl_union_pw_qpolynomial *upwqp);
3639 The output format of the printer
3640 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3641 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3643 In case of printing in C<ISL_FORMAT_C>, the user may want
3644 to set the names of all dimensions
3646 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3647 __isl_take isl_qpolynomial *qp,
3648 enum isl_dim_type type, unsigned pos,
3650 __isl_give isl_pw_qpolynomial *
3651 isl_pw_qpolynomial_set_dim_name(
3652 __isl_take isl_pw_qpolynomial *pwqp,
3653 enum isl_dim_type type, unsigned pos,
3656 =head3 Creating New (Piecewise) Quasipolynomials
3658 Some simple quasipolynomials can be created using the following functions.
3659 More complicated quasipolynomials can be created by applying
3660 operations such as addition and multiplication
3661 on the resulting quasipolynomials
3663 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3664 __isl_take isl_space *domain);
3665 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3666 __isl_take isl_space *domain);
3667 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3668 __isl_take isl_space *domain);
3669 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3670 __isl_take isl_space *domain);
3671 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3672 __isl_take isl_space *domain);
3673 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3674 __isl_take isl_space *domain,
3675 const isl_int n, const isl_int d);
3676 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3677 __isl_take isl_space *domain,
3678 enum isl_dim_type type, unsigned pos);
3679 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3680 __isl_take isl_aff *aff);
3682 Note that the space in which a quasipolynomial lives is a map space
3683 with a one-dimensional range. The C<domain> argument in some of
3684 the functions above corresponds to the domain of this map space.
3686 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3687 with a single cell can be created using the following functions.
3688 Multiple of these single cell piecewise quasipolynomials can
3689 be combined to create more complicated piecewise quasipolynomials.
3691 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3692 __isl_take isl_space *space);
3693 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3694 __isl_take isl_set *set,
3695 __isl_take isl_qpolynomial *qp);
3696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3697 __isl_take isl_qpolynomial *qp);
3698 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3699 __isl_take isl_pw_aff *pwaff);
3701 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3702 __isl_take isl_space *space);
3703 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3704 __isl_take isl_pw_qpolynomial *pwqp);
3705 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3706 __isl_take isl_union_pw_qpolynomial *upwqp,
3707 __isl_take isl_pw_qpolynomial *pwqp);
3709 Quasipolynomials can be copied and freed again using the following
3712 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3713 __isl_keep isl_qpolynomial *qp);
3714 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3716 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3717 __isl_keep isl_pw_qpolynomial *pwqp);
3718 void *isl_pw_qpolynomial_free(
3719 __isl_take isl_pw_qpolynomial *pwqp);
3721 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3722 __isl_keep isl_union_pw_qpolynomial *upwqp);
3723 void *isl_union_pw_qpolynomial_free(
3724 __isl_take isl_union_pw_qpolynomial *upwqp);
3726 =head3 Inspecting (Piecewise) Quasipolynomials
3728 To iterate over all piecewise quasipolynomials in a union
3729 piecewise quasipolynomial, use the following function
3731 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3732 __isl_keep isl_union_pw_qpolynomial *upwqp,
3733 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3736 To extract the piecewise quasipolynomial in a given space from a union, use
3738 __isl_give isl_pw_qpolynomial *
3739 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3740 __isl_keep isl_union_pw_qpolynomial *upwqp,
3741 __isl_take isl_space *space);
3743 To iterate over the cells in a piecewise quasipolynomial,
3744 use either of the following two functions
3746 int isl_pw_qpolynomial_foreach_piece(
3747 __isl_keep isl_pw_qpolynomial *pwqp,
3748 int (*fn)(__isl_take isl_set *set,
3749 __isl_take isl_qpolynomial *qp,
3750 void *user), void *user);
3751 int isl_pw_qpolynomial_foreach_lifted_piece(
3752 __isl_keep isl_pw_qpolynomial *pwqp,
3753 int (*fn)(__isl_take isl_set *set,
3754 __isl_take isl_qpolynomial *qp,
3755 void *user), void *user);
3757 As usual, the function C<fn> should return C<0> on success
3758 and C<-1> on failure. The difference between
3759 C<isl_pw_qpolynomial_foreach_piece> and
3760 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3761 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3762 compute unique representations for all existentially quantified
3763 variables and then turn these existentially quantified variables
3764 into extra set variables, adapting the associated quasipolynomial
3765 accordingly. This means that the C<set> passed to C<fn>
3766 will not have any existentially quantified variables, but that
3767 the dimensions of the sets may be different for different
3768 invocations of C<fn>.
3770 To iterate over all terms in a quasipolynomial,
3773 int isl_qpolynomial_foreach_term(
3774 __isl_keep isl_qpolynomial *qp,
3775 int (*fn)(__isl_take isl_term *term,
3776 void *user), void *user);
3778 The terms themselves can be inspected and freed using
3781 unsigned isl_term_dim(__isl_keep isl_term *term,
3782 enum isl_dim_type type);
3783 void isl_term_get_num(__isl_keep isl_term *term,
3785 void isl_term_get_den(__isl_keep isl_term *term,
3787 int isl_term_get_exp(__isl_keep isl_term *term,
3788 enum isl_dim_type type, unsigned pos);
3789 __isl_give isl_aff *isl_term_get_div(
3790 __isl_keep isl_term *term, unsigned pos);
3791 void isl_term_free(__isl_take isl_term *term);
3793 Each term is a product of parameters, set variables and
3794 integer divisions. The function C<isl_term_get_exp>
3795 returns the exponent of a given dimensions in the given term.
3796 The C<isl_int>s in the arguments of C<isl_term_get_num>
3797 and C<isl_term_get_den> need to have been initialized
3798 using C<isl_int_init> before calling these functions.
3800 =head3 Properties of (Piecewise) Quasipolynomials
3802 To check whether a quasipolynomial is actually a constant,
3803 use the following function.
3805 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3806 isl_int *n, isl_int *d);
3808 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3809 then the numerator and denominator of the constant
3810 are returned in C<*n> and C<*d>, respectively.
3812 To check whether two union piecewise quasipolynomials are
3813 obviously equal, use
3815 int isl_union_pw_qpolynomial_plain_is_equal(
3816 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3817 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3819 =head3 Operations on (Piecewise) Quasipolynomials
3821 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3822 __isl_take isl_qpolynomial *qp, isl_int v);
3823 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3824 __isl_take isl_qpolynomial *qp);
3825 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3826 __isl_take isl_qpolynomial *qp1,
3827 __isl_take isl_qpolynomial *qp2);
3828 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3829 __isl_take isl_qpolynomial *qp1,
3830 __isl_take isl_qpolynomial *qp2);
3831 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3832 __isl_take isl_qpolynomial *qp1,
3833 __isl_take isl_qpolynomial *qp2);
3834 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3835 __isl_take isl_qpolynomial *qp, unsigned exponent);
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3838 __isl_take isl_pw_qpolynomial *pwqp1,
3839 __isl_take isl_pw_qpolynomial *pwqp2);
3840 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3841 __isl_take isl_pw_qpolynomial *pwqp1,
3842 __isl_take isl_pw_qpolynomial *pwqp2);
3843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3844 __isl_take isl_pw_qpolynomial *pwqp1,
3845 __isl_take isl_pw_qpolynomial *pwqp2);
3846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3847 __isl_take isl_pw_qpolynomial *pwqp);
3848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3849 __isl_take isl_pw_qpolynomial *pwqp1,
3850 __isl_take isl_pw_qpolynomial *pwqp2);
3851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3852 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3855 __isl_take isl_union_pw_qpolynomial *upwqp1,
3856 __isl_take isl_union_pw_qpolynomial *upwqp2);
3857 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3858 __isl_take isl_union_pw_qpolynomial *upwqp1,
3859 __isl_take isl_union_pw_qpolynomial *upwqp2);
3860 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3861 __isl_take isl_union_pw_qpolynomial *upwqp1,
3862 __isl_take isl_union_pw_qpolynomial *upwqp2);
3864 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3865 __isl_take isl_pw_qpolynomial *pwqp,
3866 __isl_take isl_point *pnt);
3868 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3869 __isl_take isl_union_pw_qpolynomial *upwqp,
3870 __isl_take isl_point *pnt);
3872 __isl_give isl_set *isl_pw_qpolynomial_domain(
3873 __isl_take isl_pw_qpolynomial *pwqp);
3874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3875 __isl_take isl_pw_qpolynomial *pwpq,
3876 __isl_take isl_set *set);
3877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3878 __isl_take isl_pw_qpolynomial *pwpq,
3879 __isl_take isl_set *set);
3881 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3882 __isl_take isl_union_pw_qpolynomial *upwqp);
3883 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3884 __isl_take isl_union_pw_qpolynomial *upwpq,
3885 __isl_take isl_union_set *uset);
3886 __isl_give isl_union_pw_qpolynomial *
3887 isl_union_pw_qpolynomial_intersect_params(
3888 __isl_take isl_union_pw_qpolynomial *upwpq,
3889 __isl_take isl_set *set);
3891 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3892 __isl_take isl_qpolynomial *qp,
3893 __isl_take isl_space *model);
3895 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3896 __isl_take isl_qpolynomial *qp);
3897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3898 __isl_take isl_pw_qpolynomial *pwqp);
3900 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3901 __isl_take isl_union_pw_qpolynomial *upwqp);
3903 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3904 __isl_take isl_qpolynomial *qp,
3905 __isl_take isl_set *context);
3906 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3907 __isl_take isl_qpolynomial *qp,
3908 __isl_take isl_set *context);
3910 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3911 __isl_take isl_pw_qpolynomial *pwqp,
3912 __isl_take isl_set *context);
3913 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3914 __isl_take isl_pw_qpolynomial *pwqp,
3915 __isl_take isl_set *context);
3917 __isl_give isl_union_pw_qpolynomial *
3918 isl_union_pw_qpolynomial_gist_params(
3919 __isl_take isl_union_pw_qpolynomial *upwqp,
3920 __isl_take isl_set *context);
3921 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3922 __isl_take isl_union_pw_qpolynomial *upwqp,
3923 __isl_take isl_union_set *context);
3925 The gist operation applies the gist operation to each of
3926 the cells in the domain of the input piecewise quasipolynomial.
3927 The context is also exploited
3928 to simplify the quasipolynomials associated to each cell.
3930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3931 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3932 __isl_give isl_union_pw_qpolynomial *
3933 isl_union_pw_qpolynomial_to_polynomial(
3934 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3936 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3937 the polynomial will be an overapproximation. If C<sign> is negative,
3938 it will be an underapproximation. If C<sign> is zero, the approximation
3939 will lie somewhere in between.
3941 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3943 A piecewise quasipolynomial reduction is a piecewise
3944 reduction (or fold) of quasipolynomials.
3945 In particular, the reduction can be maximum or a minimum.
3946 The objects are mainly used to represent the result of
3947 an upper or lower bound on a quasipolynomial over its domain,
3948 i.e., as the result of the following function.
3950 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3951 __isl_take isl_pw_qpolynomial *pwqp,
3952 enum isl_fold type, int *tight);
3954 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3955 __isl_take isl_union_pw_qpolynomial *upwqp,
3956 enum isl_fold type, int *tight);
3958 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3959 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3960 is the returned bound is known be tight, i.e., for each value
3961 of the parameters there is at least
3962 one element in the domain that reaches the bound.
3963 If the domain of C<pwqp> is not wrapping, then the bound is computed
3964 over all elements in that domain and the result has a purely parametric
3965 domain. If the domain of C<pwqp> is wrapping, then the bound is
3966 computed over the range of the wrapped relation. The domain of the
3967 wrapped relation becomes the domain of the result.
3969 A (piecewise) quasipolynomial reduction can be copied or freed using the
3970 following functions.
3972 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3973 __isl_keep isl_qpolynomial_fold *fold);
3974 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3975 __isl_keep isl_pw_qpolynomial_fold *pwf);
3976 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3977 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3978 void isl_qpolynomial_fold_free(
3979 __isl_take isl_qpolynomial_fold *fold);
3980 void *isl_pw_qpolynomial_fold_free(
3981 __isl_take isl_pw_qpolynomial_fold *pwf);
3982 void *isl_union_pw_qpolynomial_fold_free(
3983 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3985 =head3 Printing Piecewise Quasipolynomial Reductions
3987 Piecewise quasipolynomial reductions can be printed
3988 using the following function.
3990 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3991 __isl_take isl_printer *p,
3992 __isl_keep isl_pw_qpolynomial_fold *pwf);
3993 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3994 __isl_take isl_printer *p,
3995 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3997 For C<isl_printer_print_pw_qpolynomial_fold>,
3998 output format of the printer
3999 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4000 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4001 output format of the printer
4002 needs to be set to C<ISL_FORMAT_ISL>.
4003 In case of printing in C<ISL_FORMAT_C>, the user may want
4004 to set the names of all dimensions
4006 __isl_give isl_pw_qpolynomial_fold *
4007 isl_pw_qpolynomial_fold_set_dim_name(
4008 __isl_take isl_pw_qpolynomial_fold *pwf,
4009 enum isl_dim_type type, unsigned pos,
4012 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4014 To iterate over all piecewise quasipolynomial reductions in a union
4015 piecewise quasipolynomial reduction, use the following function
4017 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4018 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4019 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4020 void *user), void *user);
4022 To iterate over the cells in a piecewise quasipolynomial reduction,
4023 use either of the following two functions
4025 int isl_pw_qpolynomial_fold_foreach_piece(
4026 __isl_keep isl_pw_qpolynomial_fold *pwf,
4027 int (*fn)(__isl_take isl_set *set,
4028 __isl_take isl_qpolynomial_fold *fold,
4029 void *user), void *user);
4030 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4031 __isl_keep isl_pw_qpolynomial_fold *pwf,
4032 int (*fn)(__isl_take isl_set *set,
4033 __isl_take isl_qpolynomial_fold *fold,
4034 void *user), void *user);
4036 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4037 of the difference between these two functions.
4039 To iterate over all quasipolynomials in a reduction, use
4041 int isl_qpolynomial_fold_foreach_qpolynomial(
4042 __isl_keep isl_qpolynomial_fold *fold,
4043 int (*fn)(__isl_take isl_qpolynomial *qp,
4044 void *user), void *user);
4046 =head3 Properties of Piecewise Quasipolynomial Reductions
4048 To check whether two union piecewise quasipolynomial reductions are
4049 obviously equal, use
4051 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4052 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4053 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4055 =head3 Operations on Piecewise Quasipolynomial Reductions
4057 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4058 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4060 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4061 __isl_take isl_pw_qpolynomial_fold *pwf1,
4062 __isl_take isl_pw_qpolynomial_fold *pwf2);
4064 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4065 __isl_take isl_pw_qpolynomial_fold *pwf1,
4066 __isl_take isl_pw_qpolynomial_fold *pwf2);
4068 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4069 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4070 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4072 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4073 __isl_take isl_pw_qpolynomial_fold *pwf,
4074 __isl_take isl_point *pnt);
4076 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4077 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4078 __isl_take isl_point *pnt);
4080 __isl_give isl_pw_qpolynomial_fold *
4081 sl_pw_qpolynomial_fold_intersect_params(
4082 __isl_take isl_pw_qpolynomial_fold *pwf,
4083 __isl_take isl_set *set);
4085 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4086 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4087 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4088 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4089 __isl_take isl_union_set *uset);
4090 __isl_give isl_union_pw_qpolynomial_fold *
4091 isl_union_pw_qpolynomial_fold_intersect_params(
4092 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4093 __isl_take isl_set *set);
4095 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4096 __isl_take isl_pw_qpolynomial_fold *pwf);
4098 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4099 __isl_take isl_pw_qpolynomial_fold *pwf);
4101 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4102 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4104 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4105 __isl_take isl_qpolynomial_fold *fold,
4106 __isl_take isl_set *context);
4107 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4108 __isl_take isl_qpolynomial_fold *fold,
4109 __isl_take isl_set *context);
4111 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4112 __isl_take isl_pw_qpolynomial_fold *pwf,
4113 __isl_take isl_set *context);
4114 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4115 __isl_take isl_pw_qpolynomial_fold *pwf,
4116 __isl_take isl_set *context);
4118 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4119 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4120 __isl_take isl_union_set *context);
4121 __isl_give isl_union_pw_qpolynomial_fold *
4122 isl_union_pw_qpolynomial_fold_gist_params(
4123 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4124 __isl_take isl_set *context);
4126 The gist operation applies the gist operation to each of
4127 the cells in the domain of the input piecewise quasipolynomial reduction.
4128 In future, the operation will also exploit the context
4129 to simplify the quasipolynomial reductions associated to each cell.
4131 __isl_give isl_pw_qpolynomial_fold *
4132 isl_set_apply_pw_qpolynomial_fold(
4133 __isl_take isl_set *set,
4134 __isl_take isl_pw_qpolynomial_fold *pwf,
4136 __isl_give isl_pw_qpolynomial_fold *
4137 isl_map_apply_pw_qpolynomial_fold(
4138 __isl_take isl_map *map,
4139 __isl_take isl_pw_qpolynomial_fold *pwf,
4141 __isl_give isl_union_pw_qpolynomial_fold *
4142 isl_union_set_apply_union_pw_qpolynomial_fold(
4143 __isl_take isl_union_set *uset,
4144 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4146 __isl_give isl_union_pw_qpolynomial_fold *
4147 isl_union_map_apply_union_pw_qpolynomial_fold(
4148 __isl_take isl_union_map *umap,
4149 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4152 The functions taking a map
4153 compose the given map with the given piecewise quasipolynomial reduction.
4154 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4155 over all elements in the intersection of the range of the map
4156 and the domain of the piecewise quasipolynomial reduction
4157 as a function of an element in the domain of the map.
4158 The functions taking a set compute a bound over all elements in the
4159 intersection of the set and the domain of the
4160 piecewise quasipolynomial reduction.
4162 =head2 Dependence Analysis
4164 C<isl> contains specialized functionality for performing
4165 array dataflow analysis. That is, given a I<sink> access relation
4166 and a collection of possible I<source> access relations,
4167 C<isl> can compute relations that describe
4168 for each iteration of the sink access, which iteration
4169 of which of the source access relations was the last
4170 to access the same data element before the given iteration
4172 The resulting dependence relations map source iterations
4173 to the corresponding sink iterations.
4174 To compute standard flow dependences, the sink should be
4175 a read, while the sources should be writes.
4176 If any of the source accesses are marked as being I<may>
4177 accesses, then there will be a dependence from the last
4178 I<must> access B<and> from any I<may> access that follows
4179 this last I<must> access.
4180 In particular, if I<all> sources are I<may> accesses,
4181 then memory based dependence analysis is performed.
4182 If, on the other hand, all sources are I<must> accesses,
4183 then value based dependence analysis is performed.
4185 #include <isl/flow.h>
4187 typedef int (*isl_access_level_before)(void *first, void *second);
4189 __isl_give isl_access_info *isl_access_info_alloc(
4190 __isl_take isl_map *sink,
4191 void *sink_user, isl_access_level_before fn,
4193 __isl_give isl_access_info *isl_access_info_add_source(
4194 __isl_take isl_access_info *acc,
4195 __isl_take isl_map *source, int must,
4197 void isl_access_info_free(__isl_take isl_access_info *acc);
4199 __isl_give isl_flow *isl_access_info_compute_flow(
4200 __isl_take isl_access_info *acc);
4202 int isl_flow_foreach(__isl_keep isl_flow *deps,
4203 int (*fn)(__isl_take isl_map *dep, int must,
4204 void *dep_user, void *user),
4206 __isl_give isl_map *isl_flow_get_no_source(
4207 __isl_keep isl_flow *deps, int must);
4208 void isl_flow_free(__isl_take isl_flow *deps);
4210 The function C<isl_access_info_compute_flow> performs the actual
4211 dependence analysis. The other functions are used to construct
4212 the input for this function or to read off the output.
4214 The input is collected in an C<isl_access_info>, which can
4215 be created through a call to C<isl_access_info_alloc>.
4216 The arguments to this functions are the sink access relation
4217 C<sink>, a token C<sink_user> used to identify the sink
4218 access to the user, a callback function for specifying the
4219 relative order of source and sink accesses, and the number
4220 of source access relations that will be added.
4221 The callback function has type C<int (*)(void *first, void *second)>.
4222 The function is called with two user supplied tokens identifying
4223 either a source or the sink and it should return the shared nesting
4224 level and the relative order of the two accesses.
4225 In particular, let I<n> be the number of loops shared by
4226 the two accesses. If C<first> precedes C<second> textually,
4227 then the function should return I<2 * n + 1>; otherwise,
4228 it should return I<2 * n>.
4229 The sources can be added to the C<isl_access_info> by performing
4230 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4231 C<must> indicates whether the source is a I<must> access
4232 or a I<may> access. Note that a multi-valued access relation
4233 should only be marked I<must> if every iteration in the domain
4234 of the relation accesses I<all> elements in its image.
4235 The C<source_user> token is again used to identify
4236 the source access. The range of the source access relation
4237 C<source> should have the same dimension as the range
4238 of the sink access relation.
4239 The C<isl_access_info_free> function should usually not be
4240 called explicitly, because it is called implicitly by
4241 C<isl_access_info_compute_flow>.
4243 The result of the dependence analysis is collected in an
4244 C<isl_flow>. There may be elements of
4245 the sink access for which no preceding source access could be
4246 found or for which all preceding sources are I<may> accesses.
4247 The relations containing these elements can be obtained through
4248 calls to C<isl_flow_get_no_source>, the first with C<must> set
4249 and the second with C<must> unset.
4250 In the case of standard flow dependence analysis,
4251 with the sink a read and the sources I<must> writes,
4252 the first relation corresponds to the reads from uninitialized
4253 array elements and the second relation is empty.
4254 The actual flow dependences can be extracted using
4255 C<isl_flow_foreach>. This function will call the user-specified
4256 callback function C<fn> for each B<non-empty> dependence between
4257 a source and the sink. The callback function is called
4258 with four arguments, the actual flow dependence relation
4259 mapping source iterations to sink iterations, a boolean that
4260 indicates whether it is a I<must> or I<may> dependence, a token
4261 identifying the source and an additional C<void *> with value
4262 equal to the third argument of the C<isl_flow_foreach> call.
4263 A dependence is marked I<must> if it originates from a I<must>
4264 source and if it is not followed by any I<may> sources.
4266 After finishing with an C<isl_flow>, the user should call
4267 C<isl_flow_free> to free all associated memory.
4269 A higher-level interface to dependence analysis is provided
4270 by the following function.
4272 #include <isl/flow.h>
4274 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4275 __isl_take isl_union_map *must_source,
4276 __isl_take isl_union_map *may_source,
4277 __isl_take isl_union_map *schedule,
4278 __isl_give isl_union_map **must_dep,
4279 __isl_give isl_union_map **may_dep,
4280 __isl_give isl_union_map **must_no_source,
4281 __isl_give isl_union_map **may_no_source);
4283 The arrays are identified by the tuple names of the ranges
4284 of the accesses. The iteration domains by the tuple names
4285 of the domains of the accesses and of the schedule.
4286 The relative order of the iteration domains is given by the
4287 schedule. The relations returned through C<must_no_source>
4288 and C<may_no_source> are subsets of C<sink>.
4289 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4290 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4291 any of the other arguments is treated as an error.
4293 =head3 Interaction with Dependence Analysis
4295 During the dependence analysis, we frequently need to perform
4296 the following operation. Given a relation between sink iterations
4297 and potential soure iterations from a particular source domain,
4298 what is the last potential source iteration corresponding to each
4299 sink iteration. It can sometimes be convenient to adjust
4300 the set of potential source iterations before or after each such operation.
4301 The prototypical example is fuzzy array dataflow analysis,
4302 where we need to analyze if, based on data-dependent constraints,
4303 the sink iteration can ever be executed without one or more of
4304 the corresponding potential source iterations being executed.
4305 If so, we can introduce extra parameters and select an unknown
4306 but fixed source iteration from the potential source iterations.
4307 To be able to perform such manipulations, C<isl> provides the following
4310 #include <isl/flow.h>
4312 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4313 __isl_keep isl_map *source_map,
4314 __isl_keep isl_set *sink, void *source_user,
4316 __isl_give isl_access_info *isl_access_info_set_restrict(
4317 __isl_take isl_access_info *acc,
4318 isl_access_restrict fn, void *user);
4320 The function C<isl_access_info_set_restrict> should be called
4321 before calling C<isl_access_info_compute_flow> and registers a callback function
4322 that will be called any time C<isl> is about to compute the last
4323 potential source. The first argument is the (reverse) proto-dependence,
4324 mapping sink iterations to potential source iterations.
4325 The second argument represents the sink iterations for which
4326 we want to compute the last source iteration.
4327 The third argument is the token corresponding to the source
4328 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4329 The callback is expected to return a restriction on either the input or
4330 the output of the operation computing the last potential source.
4331 If the input needs to be restricted then restrictions are needed
4332 for both the source and the sink iterations. The sink iterations
4333 and the potential source iterations will be intersected with these sets.
4334 If the output needs to be restricted then only a restriction on the source
4335 iterations is required.
4336 If any error occurs, the callback should return C<NULL>.
4337 An C<isl_restriction> object can be created and freed using the following
4340 #include <isl/flow.h>
4342 __isl_give isl_restriction *isl_restriction_input(
4343 __isl_take isl_set *source_restr,
4344 __isl_take isl_set *sink_restr);
4345 __isl_give isl_restriction *isl_restriction_output(
4346 __isl_take isl_set *source_restr);
4347 __isl_give isl_restriction *isl_restriction_none(
4348 __isl_keep isl_map *source_map);
4349 __isl_give isl_restriction *isl_restriction_empty(
4350 __isl_keep isl_map *source_map);
4351 void *isl_restriction_free(
4352 __isl_take isl_restriction *restr);
4354 C<isl_restriction_none> and C<isl_restriction_empty> are special
4355 cases of C<isl_restriction_input>. C<isl_restriction_none>
4356 is essentially equivalent to
4358 isl_restriction_input(isl_set_universe(
4359 isl_space_range(isl_map_get_space(source_map))),
4361 isl_space_domain(isl_map_get_space(source_map))));
4363 whereas C<isl_restriction_empty> is essentially equivalent to
4365 isl_restriction_input(isl_set_empty(
4366 isl_space_range(isl_map_get_space(source_map))),
4368 isl_space_domain(isl_map_get_space(source_map))));
4372 B<The functionality described in this section is fairly new
4373 and may be subject to change.>
4375 The following function can be used to compute a schedule
4376 for a union of domains.
4377 By default, the algorithm used to construct the schedule is similar
4378 to that of C<Pluto>.
4379 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4381 The generated schedule respects all C<validity> dependences.
4382 That is, all dependence distances over these dependences in the
4383 scheduled space are lexicographically positive.
4384 The default algorithm tries to minimize the dependence distances over
4385 C<proximity> dependences.
4386 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4387 for groups of domains where the dependence distances have only
4388 non-negative values.
4389 When using Feautrier's algorithm, the C<proximity> dependence
4390 distances are only minimized during the extension to a
4391 full-dimensional schedule.
4393 #include <isl/schedule.h>
4394 __isl_give isl_schedule *isl_union_set_compute_schedule(
4395 __isl_take isl_union_set *domain,
4396 __isl_take isl_union_map *validity,
4397 __isl_take isl_union_map *proximity);
4398 void *isl_schedule_free(__isl_take isl_schedule *sched);
4400 A mapping from the domains to the scheduled space can be obtained
4401 from an C<isl_schedule> using the following function.
4403 __isl_give isl_union_map *isl_schedule_get_map(
4404 __isl_keep isl_schedule *sched);
4406 A representation of the schedule can be printed using
4408 __isl_give isl_printer *isl_printer_print_schedule(
4409 __isl_take isl_printer *p,
4410 __isl_keep isl_schedule *schedule);
4412 A representation of the schedule as a forest of bands can be obtained
4413 using the following function.
4415 __isl_give isl_band_list *isl_schedule_get_band_forest(
4416 __isl_keep isl_schedule *schedule);
4418 The list can be manipulated as explained in L<"Lists">.
4419 The bands inside the list can be copied and freed using the following
4422 #include <isl/band.h>
4423 __isl_give isl_band *isl_band_copy(
4424 __isl_keep isl_band *band);
4425 void *isl_band_free(__isl_take isl_band *band);
4427 Each band contains zero or more scheduling dimensions.
4428 These are referred to as the members of the band.
4429 The section of the schedule that corresponds to the band is
4430 referred to as the partial schedule of the band.
4431 For those nodes that participate in a band, the outer scheduling
4432 dimensions form the prefix schedule, while the inner scheduling
4433 dimensions form the suffix schedule.
4434 That is, if we take a cut of the band forest, then the union of
4435 the concatenations of the prefix, partial and suffix schedules of
4436 each band in the cut is equal to the entire schedule (modulo
4437 some possible padding at the end with zero scheduling dimensions).
4438 The properties of a band can be inspected using the following functions.
4440 #include <isl/band.h>
4441 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4443 int isl_band_has_children(__isl_keep isl_band *band);
4444 __isl_give isl_band_list *isl_band_get_children(
4445 __isl_keep isl_band *band);
4447 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4448 __isl_keep isl_band *band);
4449 __isl_give isl_union_map *isl_band_get_partial_schedule(
4450 __isl_keep isl_band *band);
4451 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4452 __isl_keep isl_band *band);
4454 int isl_band_n_member(__isl_keep isl_band *band);
4455 int isl_band_member_is_zero_distance(
4456 __isl_keep isl_band *band, int pos);
4458 Note that a scheduling dimension is considered to be ``zero
4459 distance'' if it does not carry any proximity dependences
4461 That is, if the dependence distances of the proximity
4462 dependences are all zero in that direction (for fixed
4463 iterations of outer bands).
4465 A representation of the band can be printed using
4467 #include <isl/band.h>
4468 __isl_give isl_printer *isl_printer_print_band(
4469 __isl_take isl_printer *p,
4470 __isl_keep isl_band *band);
4474 #include <isl/schedule.h>
4475 int isl_options_set_schedule_max_coefficient(
4476 isl_ctx *ctx, int val);
4477 int isl_options_get_schedule_max_coefficient(
4479 int isl_options_set_schedule_max_constant_term(
4480 isl_ctx *ctx, int val);
4481 int isl_options_get_schedule_max_constant_term(
4483 int isl_options_set_schedule_maximize_band_depth(
4484 isl_ctx *ctx, int val);
4485 int isl_options_get_schedule_maximize_band_depth(
4487 int isl_options_set_schedule_outer_zero_distance(
4488 isl_ctx *ctx, int val);
4489 int isl_options_get_schedule_outer_zero_distance(
4491 int isl_options_set_schedule_split_scaled(
4492 isl_ctx *ctx, int val);
4493 int isl_options_get_schedule_split_scaled(
4495 int isl_options_set_schedule_algorithm(
4496 isl_ctx *ctx, int val);
4497 int isl_options_get_schedule_algorithm(
4503 =item * schedule_max_coefficient
4505 This option enforces that the coefficients for variable and parameter
4506 dimensions in the calculated schedule are not larger than the specified value.
4507 This option can significantly increase the speed of the scheduling calculation
4508 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4509 this option does not introduce bounds on the variable or parameter
4512 =item * schedule_max_constant_term
4514 This option enforces that the constant coefficients in the calculated schedule
4515 are not larger than the maximal constant term. This option can significantly
4516 increase the speed of the scheduling calculation and may also prevent fusing of
4517 unrelated dimensions. A value of -1 means that this option does not introduce
4518 bounds on the constant coefficients.
4520 =item * schedule_maximize_band_depth
4522 If this option is set, we do not split bands at the point
4523 where we detect splitting is necessary. Instead, we
4524 backtrack and split bands as early as possible. This
4525 reduces the number of splits and maximizes the width of
4526 the bands. Wider bands give more possibilities for tiling.
4528 =item * schedule_outer_zero_distance
4530 If this option is set, then we try to construct schedules
4531 where the outermost scheduling dimension in each band
4532 results in a zero dependence distance over the proximity
4535 =item * schedule_split_scaled
4537 If this option is set, then we try to construct schedules in which the
4538 constant term is split off from the linear part if the linear parts of
4539 the scheduling rows for all nodes in the graphs have a common non-trivial
4541 The constant term is then placed in a separate band and the linear
4544 =item * schedule_algorithm
4546 Selects the scheduling algorithm to be used.
4547 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4548 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4552 =head2 Parametric Vertex Enumeration
4554 The parametric vertex enumeration described in this section
4555 is mainly intended to be used internally and by the C<barvinok>
4558 #include <isl/vertices.h>
4559 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4560 __isl_keep isl_basic_set *bset);
4562 The function C<isl_basic_set_compute_vertices> performs the
4563 actual computation of the parametric vertices and the chamber
4564 decomposition and store the result in an C<isl_vertices> object.
4565 This information can be queried by either iterating over all
4566 the vertices or iterating over all the chambers or cells
4567 and then iterating over all vertices that are active on the chamber.
4569 int isl_vertices_foreach_vertex(
4570 __isl_keep isl_vertices *vertices,
4571 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4574 int isl_vertices_foreach_cell(
4575 __isl_keep isl_vertices *vertices,
4576 int (*fn)(__isl_take isl_cell *cell, void *user),
4578 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4579 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4582 Other operations that can be performed on an C<isl_vertices> object are
4585 isl_ctx *isl_vertices_get_ctx(
4586 __isl_keep isl_vertices *vertices);
4587 int isl_vertices_get_n_vertices(
4588 __isl_keep isl_vertices *vertices);
4589 void isl_vertices_free(__isl_take isl_vertices *vertices);
4591 Vertices can be inspected and destroyed using the following functions.
4593 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4594 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4595 __isl_give isl_basic_set *isl_vertex_get_domain(
4596 __isl_keep isl_vertex *vertex);
4597 __isl_give isl_basic_set *isl_vertex_get_expr(
4598 __isl_keep isl_vertex *vertex);
4599 void isl_vertex_free(__isl_take isl_vertex *vertex);
4601 C<isl_vertex_get_expr> returns a singleton parametric set describing
4602 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4604 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4605 B<rational> basic sets, so they should mainly be used for inspection
4606 and should not be mixed with integer sets.
4608 Chambers can be inspected and destroyed using the following functions.
4610 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4611 __isl_give isl_basic_set *isl_cell_get_domain(
4612 __isl_keep isl_cell *cell);
4613 void isl_cell_free(__isl_take isl_cell *cell);
4617 Although C<isl> is mainly meant to be used as a library,
4618 it also contains some basic applications that use some
4619 of the functionality of C<isl>.
4620 The input may be specified in either the L<isl format>
4621 or the L<PolyLib format>.
4623 =head2 C<isl_polyhedron_sample>
4625 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4626 an integer element of the polyhedron, if there is any.
4627 The first column in the output is the denominator and is always
4628 equal to 1. If the polyhedron contains no integer points,
4629 then a vector of length zero is printed.
4633 C<isl_pip> takes the same input as the C<example> program
4634 from the C<piplib> distribution, i.e., a set of constraints
4635 on the parameters, a line containing only -1 and finally a set
4636 of constraints on a parametric polyhedron.
4637 The coefficients of the parameters appear in the last columns
4638 (but before the final constant column).
4639 The output is the lexicographic minimum of the parametric polyhedron.
4640 As C<isl> currently does not have its own output format, the output
4641 is just a dump of the internal state.
4643 =head2 C<isl_polyhedron_minimize>
4645 C<isl_polyhedron_minimize> computes the minimum of some linear
4646 or affine objective function over the integer points in a polyhedron.
4647 If an affine objective function
4648 is given, then the constant should appear in the last column.
4650 =head2 C<isl_polytope_scan>
4652 Given a polytope, C<isl_polytope_scan> prints
4653 all integer points in the polytope.