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)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
184 C<isl> is released under the MIT license.
188 Permission is hereby granted, free of charge, to any person obtaining a copy of
189 this software and associated documentation files (the "Software"), to deal in
190 the Software without restriction, including without limitation the rights to
191 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
192 of the Software, and to permit persons to whom the Software is furnished to do
193 so, subject to the following conditions:
195 The above copyright notice and this permission notice shall be included in all
196 copies or substantial portions of the Software.
198 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
199 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
200 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
201 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
202 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
203 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
208 Note that C<isl> currently requires C<GMP>, which is released
209 under the GNU Lesser General Public License (LGPL). This means
210 that code linked against C<isl> is also linked against LGPL code.
214 The source of C<isl> can be obtained either as a tarball
215 or from the git repository. Both are available from
216 L<http://freshmeat.net/projects/isl/>.
217 The installation process depends on how you obtained
220 =head2 Installation from the git repository
224 =item 1 Clone or update the repository
226 The first time the source is obtained, you need to clone
229 git clone git://repo.or.cz/isl.git
231 To obtain updates, you need to pull in the latest changes
235 =item 2 Generate C<configure>
241 After performing the above steps, continue
242 with the L<Common installation instructions>.
244 =head2 Common installation instructions
248 =item 1 Obtain C<GMP>
250 Building C<isl> requires C<GMP>, including its headers files.
251 Your distribution may not provide these header files by default
252 and you may need to install a package called C<gmp-devel> or something
253 similar. Alternatively, C<GMP> can be built from
254 source, available from L<http://gmplib.org/>.
258 C<isl> uses the standard C<autoconf> C<configure> script.
263 optionally followed by some configure options.
264 A complete list of options can be obtained by running
268 Below we discuss some of the more common options.
270 C<isl> can optionally use C<piplib>, but no
271 C<piplib> functionality is currently used by default.
272 The C<--with-piplib> option can
273 be used to specify which C<piplib>
274 library to use, either an installed version (C<system>),
275 an externally built version (C<build>)
276 or no version (C<no>). The option C<build> is mostly useful
277 in C<configure> scripts of larger projects that bundle both C<isl>
284 Installation prefix for C<isl>
286 =item C<--with-gmp-prefix>
288 Installation prefix for C<GMP> (architecture-independent files).
290 =item C<--with-gmp-exec-prefix>
292 Installation prefix for C<GMP> (architecture-dependent files).
294 =item C<--with-piplib>
296 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
298 =item C<--with-piplib-prefix>
300 Installation prefix for C<system> C<piplib> (architecture-independent files).
302 =item C<--with-piplib-exec-prefix>
304 Installation prefix for C<system> C<piplib> (architecture-dependent files).
306 =item C<--with-piplib-builddir>
308 Location where C<build> C<piplib> was built.
316 =item 4 Install (optional)
324 =head2 Initialization
326 All manipulations of integer sets and relations occur within
327 the context of an C<isl_ctx>.
328 A given C<isl_ctx> can only be used within a single thread.
329 All arguments of a function are required to have been allocated
330 within the same context.
331 There are currently no functions available for moving an object
332 from one C<isl_ctx> to another C<isl_ctx>. This means that
333 there is currently no way of safely moving an object from one
334 thread to another, unless the whole C<isl_ctx> is moved.
336 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
337 freed using C<isl_ctx_free>.
338 All objects allocated within an C<isl_ctx> should be freed
339 before the C<isl_ctx> itself is freed.
341 isl_ctx *isl_ctx_alloc();
342 void isl_ctx_free(isl_ctx *ctx);
346 All operations on integers, mainly the coefficients
347 of the constraints describing the sets and relations,
348 are performed in exact integer arithmetic using C<GMP>.
349 However, to allow future versions of C<isl> to optionally
350 support fixed integer arithmetic, all calls to C<GMP>
351 are wrapped inside C<isl> specific macros.
352 The basic type is C<isl_int> and the operations below
353 are available on this type.
354 The meanings of these operations are essentially the same
355 as their C<GMP> C<mpz_> counterparts.
356 As always with C<GMP> types, C<isl_int>s need to be
357 initialized with C<isl_int_init> before they can be used
358 and they need to be released with C<isl_int_clear>
360 The user should not assume that an C<isl_int> is represented
361 as a C<mpz_t>, but should instead explicitly convert between
362 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
363 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
367 =item isl_int_init(i)
369 =item isl_int_clear(i)
371 =item isl_int_set(r,i)
373 =item isl_int_set_si(r,i)
375 =item isl_int_set_gmp(r,g)
377 =item isl_int_get_gmp(i,g)
379 =item isl_int_abs(r,i)
381 =item isl_int_neg(r,i)
383 =item isl_int_swap(i,j)
385 =item isl_int_swap_or_set(i,j)
387 =item isl_int_add_ui(r,i,j)
389 =item isl_int_sub_ui(r,i,j)
391 =item isl_int_add(r,i,j)
393 =item isl_int_sub(r,i,j)
395 =item isl_int_mul(r,i,j)
397 =item isl_int_mul_ui(r,i,j)
399 =item isl_int_addmul(r,i,j)
401 =item isl_int_submul(r,i,j)
403 =item isl_int_gcd(r,i,j)
405 =item isl_int_lcm(r,i,j)
407 =item isl_int_divexact(r,i,j)
409 =item isl_int_cdiv_q(r,i,j)
411 =item isl_int_fdiv_q(r,i,j)
413 =item isl_int_fdiv_r(r,i,j)
415 =item isl_int_fdiv_q_ui(r,i,j)
417 =item isl_int_read(r,s)
419 =item isl_int_print(out,i,width)
423 =item isl_int_cmp(i,j)
425 =item isl_int_cmp_si(i,si)
427 =item isl_int_eq(i,j)
429 =item isl_int_ne(i,j)
431 =item isl_int_lt(i,j)
433 =item isl_int_le(i,j)
435 =item isl_int_gt(i,j)
437 =item isl_int_ge(i,j)
439 =item isl_int_abs_eq(i,j)
441 =item isl_int_abs_ne(i,j)
443 =item isl_int_abs_lt(i,j)
445 =item isl_int_abs_gt(i,j)
447 =item isl_int_abs_ge(i,j)
449 =item isl_int_is_zero(i)
451 =item isl_int_is_one(i)
453 =item isl_int_is_negone(i)
455 =item isl_int_is_pos(i)
457 =item isl_int_is_neg(i)
459 =item isl_int_is_nonpos(i)
461 =item isl_int_is_nonneg(i)
463 =item isl_int_is_divisible_by(i,j)
467 =head2 Sets and Relations
469 C<isl> uses six types of objects for representing sets and relations,
470 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
471 C<isl_union_set> and C<isl_union_map>.
472 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
473 can be described as a conjunction of affine constraints, while
474 C<isl_set> and C<isl_map> represent unions of
475 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
476 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
477 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
478 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
479 where spaces are considered different if they have a different number
480 of dimensions and/or different names (see L<"Spaces">).
481 The difference between sets and relations (maps) is that sets have
482 one set of variables, while relations have two sets of variables,
483 input variables and output variables.
485 =head2 Memory Management
487 Since a high-level operation on sets and/or relations usually involves
488 several substeps and since the user is usually not interested in
489 the intermediate results, most functions that return a new object
490 will also release all the objects passed as arguments.
491 If the user still wants to use one or more of these arguments
492 after the function call, she should pass along a copy of the
493 object rather than the object itself.
494 The user is then responsible for making sure that the original
495 object gets used somewhere else or is explicitly freed.
497 The arguments and return values of all documented functions are
498 annotated to make clear which arguments are released and which
499 arguments are preserved. In particular, the following annotations
506 C<__isl_give> means that a new object is returned.
507 The user should make sure that the returned pointer is
508 used exactly once as a value for an C<__isl_take> argument.
509 In between, it can be used as a value for as many
510 C<__isl_keep> arguments as the user likes.
511 There is one exception, and that is the case where the
512 pointer returned is C<NULL>. Is this case, the user
513 is free to use it as an C<__isl_take> argument or not.
517 C<__isl_take> means that the object the argument points to
518 is taken over by the function and may no longer be used
519 by the user as an argument to any other function.
520 The pointer value must be one returned by a function
521 returning an C<__isl_give> pointer.
522 If the user passes in a C<NULL> value, then this will
523 be treated as an error in the sense that the function will
524 not perform its usual operation. However, it will still
525 make sure that all the other C<__isl_take> arguments
530 C<__isl_keep> means that the function will only use the object
531 temporarily. After the function has finished, the user
532 can still use it as an argument to other functions.
533 A C<NULL> value will be treated in the same way as
534 a C<NULL> value for an C<__isl_take> argument.
538 =head2 Error Handling
540 C<isl> supports different ways to react in case a runtime error is triggered.
541 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
542 with two maps that have incompatible spaces. There are three possible ways
543 to react on error: to warn, to continue or to abort.
545 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
546 the last error in the corresponding C<isl_ctx> and the function in which the
547 error was triggered returns C<NULL>. An error does not corrupt internal state,
548 such that isl can continue to be used. C<isl> also provides functions to
549 read the last error and to reset the memory that stores the last error. The
550 last error is only stored for information purposes. Its presence does not
551 change the behavior of C<isl>. Hence, resetting an error is not required to
552 continue to use isl, but only to observe new errors.
555 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
556 void isl_ctx_reset_error(isl_ctx *ctx);
558 Another option is to continue on error. This is similar to warn on error mode,
559 except that C<isl> does not print any warning. This allows a program to
560 implement its own error reporting.
562 The last option is to directly abort the execution of the program from within
563 the isl library. This makes it obviously impossible to recover from an error,
564 but it allows to directly spot the error location. By aborting on error,
565 debuggers break at the location the error occurred and can provide a stack
566 trace. Other tools that automatically provide stack traces on abort or that do
567 not want to continue execution after an error was triggered may also prefer to
570 The on error behavior of isl can be specified by calling
571 C<isl_options_set_on_error> or by setting the command line option
572 C<--isl-on-error>. Valid arguments for the function call are
573 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
574 choices for the command line option are C<warn>, C<continue> and C<abort>.
575 It is also possible to query the current error mode.
577 #include <isl/options.h>
578 int isl_options_set_on_error(isl_ctx *ctx, int val);
579 int isl_options_get_on_error(isl_ctx *ctx);
583 Identifiers are used to identify both individual dimensions
584 and tuples of dimensions. They consist of an optional name and an optional
585 user pointer. The name and the user pointer cannot both be C<NULL>, however.
586 Identifiers with the same name but different pointer values
587 are considered to be distinct.
588 Similarly, identifiers with different names but the same pointer value
589 are also considered to be distinct.
590 Equal identifiers are represented using the same object.
591 Pairs of identifiers can therefore be tested for equality using the
593 Identifiers can be constructed, copied, freed, inspected and printed
594 using the following functions.
597 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
598 __isl_keep const char *name, void *user);
599 __isl_give isl_id *isl_id_copy(isl_id *id);
600 void *isl_id_free(__isl_take isl_id *id);
602 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
603 void *isl_id_get_user(__isl_keep isl_id *id);
604 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
606 __isl_give isl_printer *isl_printer_print_id(
607 __isl_take isl_printer *p, __isl_keep isl_id *id);
609 Note that C<isl_id_get_name> returns a pointer to some internal
610 data structure, so the result can only be used while the
611 corresponding C<isl_id> is alive.
615 Whenever a new set, relation or similiar object is created from scratch,
616 the space in which it lives needs to be specified using an C<isl_space>.
617 Each space involves zero or more parameters and zero, one or two
618 tuples of set or input/output dimensions. The parameters and dimensions
619 are identified by an C<isl_dim_type> and a position.
620 The type C<isl_dim_param> refers to parameters,
621 the type C<isl_dim_set> refers to set dimensions (for spaces
622 with a single tuple of dimensions) and the types C<isl_dim_in>
623 and C<isl_dim_out> refer to input and output dimensions
624 (for spaces with two tuples of dimensions).
625 Local spaces (see L</"Local Spaces">) also contain dimensions
626 of type C<isl_dim_div>.
627 Note that parameters are only identified by their position within
628 a given object. Across different objects, parameters are (usually)
629 identified by their names or identifiers. Only unnamed parameters
630 are identified by their positions across objects. The use of unnamed
631 parameters is discouraged.
633 #include <isl/space.h>
634 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
635 unsigned nparam, unsigned n_in, unsigned n_out);
636 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
638 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
639 unsigned nparam, unsigned dim);
640 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
641 void *isl_space_free(__isl_take isl_space *space);
642 unsigned isl_space_dim(__isl_keep isl_space *space,
643 enum isl_dim_type type);
645 The space used for creating a parameter domain
646 needs to be created using C<isl_space_params_alloc>.
647 For other sets, the space
648 needs to be created using C<isl_space_set_alloc>, while
649 for a relation, the space
650 needs to be created using C<isl_space_alloc>.
651 C<isl_space_dim> can be used
652 to find out the number of dimensions of each type in
653 a space, where type may be
654 C<isl_dim_param>, C<isl_dim_in> (only for relations),
655 C<isl_dim_out> (only for relations), C<isl_dim_set>
656 (only for sets) or C<isl_dim_all>.
658 To check whether a given space is that of a set or a map
659 or whether it is a parameter space, use these functions:
661 #include <isl/space.h>
662 int isl_space_is_params(__isl_keep isl_space *space);
663 int isl_space_is_set(__isl_keep isl_space *space);
664 int isl_space_is_map(__isl_keep isl_space *space);
666 Spaces can be compared using the following functions:
668 #include <isl/space.h>
669 int isl_space_is_equal(__isl_keep isl_space *space1,
670 __isl_keep isl_space *space2);
671 int isl_space_is_domain(__isl_keep isl_space *space1,
672 __isl_keep isl_space *space2);
673 int isl_space_is_range(__isl_keep isl_space *space1,
674 __isl_keep isl_space *space2);
676 C<isl_space_is_domain> checks whether the first argument is equal
677 to the domain of the second argument. This requires in particular that
678 the first argument is a set space and that the second argument
681 It is often useful to create objects that live in the
682 same space as some other object. This can be accomplished
683 by creating the new objects
684 (see L<Creating New Sets and Relations> or
685 L<Creating New (Piecewise) Quasipolynomials>) based on the space
686 of the original object.
689 __isl_give isl_space *isl_basic_set_get_space(
690 __isl_keep isl_basic_set *bset);
691 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
693 #include <isl/union_set.h>
694 __isl_give isl_space *isl_union_set_get_space(
695 __isl_keep isl_union_set *uset);
698 __isl_give isl_space *isl_basic_map_get_space(
699 __isl_keep isl_basic_map *bmap);
700 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
702 #include <isl/union_map.h>
703 __isl_give isl_space *isl_union_map_get_space(
704 __isl_keep isl_union_map *umap);
706 #include <isl/constraint.h>
707 __isl_give isl_space *isl_constraint_get_space(
708 __isl_keep isl_constraint *constraint);
710 #include <isl/polynomial.h>
711 __isl_give isl_space *isl_qpolynomial_get_domain_space(
712 __isl_keep isl_qpolynomial *qp);
713 __isl_give isl_space *isl_qpolynomial_get_space(
714 __isl_keep isl_qpolynomial *qp);
715 __isl_give isl_space *isl_qpolynomial_fold_get_space(
716 __isl_keep isl_qpolynomial_fold *fold);
717 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
718 __isl_keep isl_pw_qpolynomial *pwqp);
719 __isl_give isl_space *isl_pw_qpolynomial_get_space(
720 __isl_keep isl_pw_qpolynomial *pwqp);
721 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
722 __isl_keep isl_pw_qpolynomial_fold *pwf);
723 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
724 __isl_keep isl_pw_qpolynomial_fold *pwf);
725 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
726 __isl_keep isl_union_pw_qpolynomial *upwqp);
727 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
728 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
731 __isl_give isl_space *isl_aff_get_domain_space(
732 __isl_keep isl_aff *aff);
733 __isl_give isl_space *isl_aff_get_space(
734 __isl_keep isl_aff *aff);
735 __isl_give isl_space *isl_pw_aff_get_domain_space(
736 __isl_keep isl_pw_aff *pwaff);
737 __isl_give isl_space *isl_pw_aff_get_space(
738 __isl_keep isl_pw_aff *pwaff);
739 __isl_give isl_space *isl_multi_aff_get_domain_space(
740 __isl_keep isl_multi_aff *maff);
741 __isl_give isl_space *isl_multi_aff_get_space(
742 __isl_keep isl_multi_aff *maff);
743 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
744 __isl_keep isl_pw_multi_aff *pma);
745 __isl_give isl_space *isl_pw_multi_aff_get_space(
746 __isl_keep isl_pw_multi_aff *pma);
747 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
748 __isl_keep isl_union_pw_multi_aff *upma);
749 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
750 __isl_keep isl_multi_pw_aff *mpa);
751 __isl_give isl_space *isl_multi_pw_aff_get_space(
752 __isl_keep isl_multi_pw_aff *mpa);
754 #include <isl/point.h>
755 __isl_give isl_space *isl_point_get_space(
756 __isl_keep isl_point *pnt);
758 The identifiers or names of the individual dimensions may be set or read off
759 using the following functions.
761 #include <isl/space.h>
762 __isl_give isl_space *isl_space_set_dim_id(
763 __isl_take isl_space *space,
764 enum isl_dim_type type, unsigned pos,
765 __isl_take isl_id *id);
766 int isl_space_has_dim_id(__isl_keep isl_space *space,
767 enum isl_dim_type type, unsigned pos);
768 __isl_give isl_id *isl_space_get_dim_id(
769 __isl_keep isl_space *space,
770 enum isl_dim_type type, unsigned pos);
771 __isl_give isl_space *isl_space_set_dim_name(
772 __isl_take isl_space *space,
773 enum isl_dim_type type, unsigned pos,
774 __isl_keep const char *name);
775 int isl_space_has_dim_name(__isl_keep isl_space *space,
776 enum isl_dim_type type, unsigned pos);
777 __isl_keep const char *isl_space_get_dim_name(
778 __isl_keep isl_space *space,
779 enum isl_dim_type type, unsigned pos);
781 Note that C<isl_space_get_name> returns a pointer to some internal
782 data structure, so the result can only be used while the
783 corresponding C<isl_space> is alive.
784 Also note that every function that operates on two sets or relations
785 requires that both arguments have the same parameters. This also
786 means that if one of the arguments has named parameters, then the
787 other needs to have named parameters too and the names need to match.
788 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
789 arguments may have different parameters (as long as they are named),
790 in which case the result will have as parameters the union of the parameters of
793 Given the identifier or name of a dimension (typically a parameter),
794 its position can be obtained from the following function.
796 #include <isl/space.h>
797 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
798 enum isl_dim_type type, __isl_keep isl_id *id);
799 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
800 enum isl_dim_type type, const char *name);
802 The identifiers or names of entire spaces may be set or read off
803 using the following functions.
805 #include <isl/space.h>
806 __isl_give isl_space *isl_space_set_tuple_id(
807 __isl_take isl_space *space,
808 enum isl_dim_type type, __isl_take isl_id *id);
809 __isl_give isl_space *isl_space_reset_tuple_id(
810 __isl_take isl_space *space, enum isl_dim_type type);
811 int isl_space_has_tuple_id(__isl_keep isl_space *space,
812 enum isl_dim_type type);
813 __isl_give isl_id *isl_space_get_tuple_id(
814 __isl_keep isl_space *space, enum isl_dim_type type);
815 __isl_give isl_space *isl_space_set_tuple_name(
816 __isl_take isl_space *space,
817 enum isl_dim_type type, const char *s);
818 int isl_space_has_tuple_name(__isl_keep isl_space *space,
819 enum isl_dim_type type);
820 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
821 enum isl_dim_type type);
823 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
824 or C<isl_dim_set>. As with C<isl_space_get_name>,
825 the C<isl_space_get_tuple_name> function returns a pointer to some internal
827 Binary operations require the corresponding spaces of their arguments
828 to have the same name.
830 Spaces can be nested. In particular, the domain of a set or
831 the domain or range of a relation can be a nested relation.
832 The following functions can be used to construct and deconstruct
835 #include <isl/space.h>
836 int isl_space_is_wrapping(__isl_keep isl_space *space);
837 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
838 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
840 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
841 be the space of a set, while that of
842 C<isl_space_wrap> should be the space of a relation.
843 Conversely, the output of C<isl_space_unwrap> is the space
844 of a relation, while that of C<isl_space_wrap> is the space of a set.
846 Spaces can be created from other spaces
847 using the following functions.
849 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
850 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
851 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
852 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
853 __isl_give isl_space *isl_space_params(
854 __isl_take isl_space *space);
855 __isl_give isl_space *isl_space_set_from_params(
856 __isl_take isl_space *space);
857 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
858 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
859 __isl_take isl_space *right);
860 __isl_give isl_space *isl_space_align_params(
861 __isl_take isl_space *space1, __isl_take isl_space *space2)
862 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
863 enum isl_dim_type type, unsigned pos, unsigned n);
864 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
865 enum isl_dim_type type, unsigned n);
866 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
867 enum isl_dim_type type, unsigned first, unsigned n);
868 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
869 enum isl_dim_type dst_type, unsigned dst_pos,
870 enum isl_dim_type src_type, unsigned src_pos,
872 __isl_give isl_space *isl_space_map_from_set(
873 __isl_take isl_space *space);
874 __isl_give isl_space *isl_space_map_from_domain_and_range(
875 __isl_take isl_space *domain,
876 __isl_take isl_space *range);
877 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
878 __isl_give isl_space *isl_space_curry(
879 __isl_take isl_space *space);
880 __isl_give isl_space *isl_space_uncurry(
881 __isl_take isl_space *space);
883 Note that if dimensions are added or removed from a space, then
884 the name and the internal structure are lost.
888 A local space is essentially a space with
889 zero or more existentially quantified variables.
890 The local space of a (constraint of a) basic set or relation can be obtained
891 using the following functions.
893 #include <isl/constraint.h>
894 __isl_give isl_local_space *isl_constraint_get_local_space(
895 __isl_keep isl_constraint *constraint);
898 __isl_give isl_local_space *isl_basic_set_get_local_space(
899 __isl_keep isl_basic_set *bset);
902 __isl_give isl_local_space *isl_basic_map_get_local_space(
903 __isl_keep isl_basic_map *bmap);
905 A new local space can be created from a space using
907 #include <isl/local_space.h>
908 __isl_give isl_local_space *isl_local_space_from_space(
909 __isl_take isl_space *space);
911 They can be inspected, modified, copied and freed using the following functions.
913 #include <isl/local_space.h>
914 isl_ctx *isl_local_space_get_ctx(
915 __isl_keep isl_local_space *ls);
916 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
917 int isl_local_space_dim(__isl_keep isl_local_space *ls,
918 enum isl_dim_type type);
919 int isl_local_space_has_dim_id(
920 __isl_keep isl_local_space *ls,
921 enum isl_dim_type type, unsigned pos);
922 __isl_give isl_id *isl_local_space_get_dim_id(
923 __isl_keep isl_local_space *ls,
924 enum isl_dim_type type, unsigned pos);
925 int isl_local_space_has_dim_name(
926 __isl_keep isl_local_space *ls,
927 enum isl_dim_type type, unsigned pos)
928 const char *isl_local_space_get_dim_name(
929 __isl_keep isl_local_space *ls,
930 enum isl_dim_type type, unsigned pos);
931 __isl_give isl_local_space *isl_local_space_set_dim_name(
932 __isl_take isl_local_space *ls,
933 enum isl_dim_type type, unsigned pos, const char *s);
934 __isl_give isl_local_space *isl_local_space_set_dim_id(
935 __isl_take isl_local_space *ls,
936 enum isl_dim_type type, unsigned pos,
937 __isl_take isl_id *id);
938 __isl_give isl_space *isl_local_space_get_space(
939 __isl_keep isl_local_space *ls);
940 __isl_give isl_aff *isl_local_space_get_div(
941 __isl_keep isl_local_space *ls, int pos);
942 __isl_give isl_local_space *isl_local_space_copy(
943 __isl_keep isl_local_space *ls);
944 void *isl_local_space_free(__isl_take isl_local_space *ls);
946 Two local spaces can be compared using
948 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
949 __isl_keep isl_local_space *ls2);
951 Local spaces can be created from other local spaces
952 using the following functions.
954 __isl_give isl_local_space *isl_local_space_domain(
955 __isl_take isl_local_space *ls);
956 __isl_give isl_local_space *isl_local_space_range(
957 __isl_take isl_local_space *ls);
958 __isl_give isl_local_space *isl_local_space_from_domain(
959 __isl_take isl_local_space *ls);
960 __isl_give isl_local_space *isl_local_space_intersect(
961 __isl_take isl_local_space *ls1,
962 __isl_take isl_local_space *ls2);
963 __isl_give isl_local_space *isl_local_space_add_dims(
964 __isl_take isl_local_space *ls,
965 enum isl_dim_type type, unsigned n);
966 __isl_give isl_local_space *isl_local_space_insert_dims(
967 __isl_take isl_local_space *ls,
968 enum isl_dim_type type, unsigned first, unsigned n);
969 __isl_give isl_local_space *isl_local_space_drop_dims(
970 __isl_take isl_local_space *ls,
971 enum isl_dim_type type, unsigned first, unsigned n);
973 =head2 Input and Output
975 C<isl> supports its own input/output format, which is similar
976 to the C<Omega> format, but also supports the C<PolyLib> format
981 The C<isl> format is similar to that of C<Omega>, but has a different
982 syntax for describing the parameters and allows for the definition
983 of an existentially quantified variable as the integer division
984 of an affine expression.
985 For example, the set of integers C<i> between C<0> and C<n>
986 such that C<i % 10 <= 6> can be described as
988 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
991 A set or relation can have several disjuncts, separated
992 by the keyword C<or>. Each disjunct is either a conjunction
993 of constraints or a projection (C<exists>) of a conjunction
994 of constraints. The constraints are separated by the keyword
997 =head3 C<PolyLib> format
999 If the represented set is a union, then the first line
1000 contains a single number representing the number of disjuncts.
1001 Otherwise, a line containing the number C<1> is optional.
1003 Each disjunct is represented by a matrix of constraints.
1004 The first line contains two numbers representing
1005 the number of rows and columns,
1006 where the number of rows is equal to the number of constraints
1007 and the number of columns is equal to two plus the number of variables.
1008 The following lines contain the actual rows of the constraint matrix.
1009 In each row, the first column indicates whether the constraint
1010 is an equality (C<0>) or inequality (C<1>). The final column
1011 corresponds to the constant term.
1013 If the set is parametric, then the coefficients of the parameters
1014 appear in the last columns before the constant column.
1015 The coefficients of any existentially quantified variables appear
1016 between those of the set variables and those of the parameters.
1018 =head3 Extended C<PolyLib> format
1020 The extended C<PolyLib> format is nearly identical to the
1021 C<PolyLib> format. The only difference is that the line
1022 containing the number of rows and columns of a constraint matrix
1023 also contains four additional numbers:
1024 the number of output dimensions, the number of input dimensions,
1025 the number of local dimensions (i.e., the number of existentially
1026 quantified variables) and the number of parameters.
1027 For sets, the number of ``output'' dimensions is equal
1028 to the number of set dimensions, while the number of ``input''
1033 #include <isl/set.h>
1034 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1035 isl_ctx *ctx, FILE *input);
1036 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1037 isl_ctx *ctx, const char *str);
1038 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1040 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1043 #include <isl/map.h>
1044 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1045 isl_ctx *ctx, FILE *input);
1046 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1047 isl_ctx *ctx, const char *str);
1048 __isl_give isl_map *isl_map_read_from_file(
1049 isl_ctx *ctx, FILE *input);
1050 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1053 #include <isl/union_set.h>
1054 __isl_give isl_union_set *isl_union_set_read_from_file(
1055 isl_ctx *ctx, FILE *input);
1056 __isl_give isl_union_set *isl_union_set_read_from_str(
1057 isl_ctx *ctx, const char *str);
1059 #include <isl/union_map.h>
1060 __isl_give isl_union_map *isl_union_map_read_from_file(
1061 isl_ctx *ctx, FILE *input);
1062 __isl_give isl_union_map *isl_union_map_read_from_str(
1063 isl_ctx *ctx, const char *str);
1065 The input format is autodetected and may be either the C<PolyLib> format
1066 or the C<isl> format.
1070 Before anything can be printed, an C<isl_printer> needs to
1073 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1075 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1076 void *isl_printer_free(__isl_take isl_printer *printer);
1077 __isl_give char *isl_printer_get_str(
1078 __isl_keep isl_printer *printer);
1080 The printer can be inspected using the following functions.
1082 FILE *isl_printer_get_file(
1083 __isl_keep isl_printer *printer);
1084 int isl_printer_get_output_format(
1085 __isl_keep isl_printer *p);
1087 The behavior of the printer can be modified in various ways
1089 __isl_give isl_printer *isl_printer_set_output_format(
1090 __isl_take isl_printer *p, int output_format);
1091 __isl_give isl_printer *isl_printer_set_indent(
1092 __isl_take isl_printer *p, int indent);
1093 __isl_give isl_printer *isl_printer_indent(
1094 __isl_take isl_printer *p, int indent);
1095 __isl_give isl_printer *isl_printer_set_prefix(
1096 __isl_take isl_printer *p, const char *prefix);
1097 __isl_give isl_printer *isl_printer_set_suffix(
1098 __isl_take isl_printer *p, const char *suffix);
1100 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1101 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1102 and defaults to C<ISL_FORMAT_ISL>.
1103 Each line in the output is indented by C<indent> (set by
1104 C<isl_printer_set_indent>) spaces
1105 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1106 In the C<PolyLib> format output,
1107 the coefficients of the existentially quantified variables
1108 appear between those of the set variables and those
1110 The function C<isl_printer_indent> increases the indentation
1111 by the specified amount (which may be negative).
1113 To actually print something, use
1115 #include <isl/printer.h>
1116 __isl_give isl_printer *isl_printer_print_double(
1117 __isl_take isl_printer *p, double d);
1119 #include <isl/set.h>
1120 __isl_give isl_printer *isl_printer_print_basic_set(
1121 __isl_take isl_printer *printer,
1122 __isl_keep isl_basic_set *bset);
1123 __isl_give isl_printer *isl_printer_print_set(
1124 __isl_take isl_printer *printer,
1125 __isl_keep isl_set *set);
1127 #include <isl/map.h>
1128 __isl_give isl_printer *isl_printer_print_basic_map(
1129 __isl_take isl_printer *printer,
1130 __isl_keep isl_basic_map *bmap);
1131 __isl_give isl_printer *isl_printer_print_map(
1132 __isl_take isl_printer *printer,
1133 __isl_keep isl_map *map);
1135 #include <isl/union_set.h>
1136 __isl_give isl_printer *isl_printer_print_union_set(
1137 __isl_take isl_printer *p,
1138 __isl_keep isl_union_set *uset);
1140 #include <isl/union_map.h>
1141 __isl_give isl_printer *isl_printer_print_union_map(
1142 __isl_take isl_printer *p,
1143 __isl_keep isl_union_map *umap);
1145 When called on a file printer, the following function flushes
1146 the file. When called on a string printer, the buffer is cleared.
1148 __isl_give isl_printer *isl_printer_flush(
1149 __isl_take isl_printer *p);
1151 =head2 Creating New Sets and Relations
1153 C<isl> has functions for creating some standard sets and relations.
1157 =item * Empty sets and relations
1159 __isl_give isl_basic_set *isl_basic_set_empty(
1160 __isl_take isl_space *space);
1161 __isl_give isl_basic_map *isl_basic_map_empty(
1162 __isl_take isl_space *space);
1163 __isl_give isl_set *isl_set_empty(
1164 __isl_take isl_space *space);
1165 __isl_give isl_map *isl_map_empty(
1166 __isl_take isl_space *space);
1167 __isl_give isl_union_set *isl_union_set_empty(
1168 __isl_take isl_space *space);
1169 __isl_give isl_union_map *isl_union_map_empty(
1170 __isl_take isl_space *space);
1172 For C<isl_union_set>s and C<isl_union_map>s, the space
1173 is only used to specify the parameters.
1175 =item * Universe sets and relations
1177 __isl_give isl_basic_set *isl_basic_set_universe(
1178 __isl_take isl_space *space);
1179 __isl_give isl_basic_map *isl_basic_map_universe(
1180 __isl_take isl_space *space);
1181 __isl_give isl_set *isl_set_universe(
1182 __isl_take isl_space *space);
1183 __isl_give isl_map *isl_map_universe(
1184 __isl_take isl_space *space);
1185 __isl_give isl_union_set *isl_union_set_universe(
1186 __isl_take isl_union_set *uset);
1187 __isl_give isl_union_map *isl_union_map_universe(
1188 __isl_take isl_union_map *umap);
1190 The sets and relations constructed by the functions above
1191 contain all integer values, while those constructed by the
1192 functions below only contain non-negative values.
1194 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1195 __isl_take isl_space *space);
1196 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1197 __isl_take isl_space *space);
1198 __isl_give isl_set *isl_set_nat_universe(
1199 __isl_take isl_space *space);
1200 __isl_give isl_map *isl_map_nat_universe(
1201 __isl_take isl_space *space);
1203 =item * Identity relations
1205 __isl_give isl_basic_map *isl_basic_map_identity(
1206 __isl_take isl_space *space);
1207 __isl_give isl_map *isl_map_identity(
1208 __isl_take isl_space *space);
1210 The number of input and output dimensions in C<space> needs
1213 =item * Lexicographic order
1215 __isl_give isl_map *isl_map_lex_lt(
1216 __isl_take isl_space *set_space);
1217 __isl_give isl_map *isl_map_lex_le(
1218 __isl_take isl_space *set_space);
1219 __isl_give isl_map *isl_map_lex_gt(
1220 __isl_take isl_space *set_space);
1221 __isl_give isl_map *isl_map_lex_ge(
1222 __isl_take isl_space *set_space);
1223 __isl_give isl_map *isl_map_lex_lt_first(
1224 __isl_take isl_space *space, unsigned n);
1225 __isl_give isl_map *isl_map_lex_le_first(
1226 __isl_take isl_space *space, unsigned n);
1227 __isl_give isl_map *isl_map_lex_gt_first(
1228 __isl_take isl_space *space, unsigned n);
1229 __isl_give isl_map *isl_map_lex_ge_first(
1230 __isl_take isl_space *space, unsigned n);
1232 The first four functions take a space for a B<set>
1233 and return relations that express that the elements in the domain
1234 are lexicographically less
1235 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1236 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1237 than the elements in the range.
1238 The last four functions take a space for a map
1239 and return relations that express that the first C<n> dimensions
1240 in the domain are lexicographically less
1241 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1242 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1243 than the first C<n> dimensions in the range.
1247 A basic set or relation can be converted to a set or relation
1248 using the following functions.
1250 __isl_give isl_set *isl_set_from_basic_set(
1251 __isl_take isl_basic_set *bset);
1252 __isl_give isl_map *isl_map_from_basic_map(
1253 __isl_take isl_basic_map *bmap);
1255 Sets and relations can be converted to union sets and relations
1256 using the following functions.
1258 __isl_give isl_union_set *isl_union_set_from_basic_set(
1259 __isl_take isl_basic_set *bset);
1260 __isl_give isl_union_map *isl_union_map_from_basic_map(
1261 __isl_take isl_basic_map *bmap);
1262 __isl_give isl_union_set *isl_union_set_from_set(
1263 __isl_take isl_set *set);
1264 __isl_give isl_union_map *isl_union_map_from_map(
1265 __isl_take isl_map *map);
1267 The inverse conversions below can only be used if the input
1268 union set or relation is known to contain elements in exactly one
1271 __isl_give isl_set *isl_set_from_union_set(
1272 __isl_take isl_union_set *uset);
1273 __isl_give isl_map *isl_map_from_union_map(
1274 __isl_take isl_union_map *umap);
1276 A zero-dimensional set can be constructed on a given parameter domain
1277 using the following function.
1279 __isl_give isl_set *isl_set_from_params(
1280 __isl_take isl_set *set);
1282 Sets and relations can be copied and freed again using the following
1285 __isl_give isl_basic_set *isl_basic_set_copy(
1286 __isl_keep isl_basic_set *bset);
1287 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1288 __isl_give isl_union_set *isl_union_set_copy(
1289 __isl_keep isl_union_set *uset);
1290 __isl_give isl_basic_map *isl_basic_map_copy(
1291 __isl_keep isl_basic_map *bmap);
1292 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1293 __isl_give isl_union_map *isl_union_map_copy(
1294 __isl_keep isl_union_map *umap);
1295 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1296 void *isl_set_free(__isl_take isl_set *set);
1297 void *isl_union_set_free(__isl_take isl_union_set *uset);
1298 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1299 void *isl_map_free(__isl_take isl_map *map);
1300 void *isl_union_map_free(__isl_take isl_union_map *umap);
1302 Other sets and relations can be constructed by starting
1303 from a universe set or relation, adding equality and/or
1304 inequality constraints and then projecting out the
1305 existentially quantified variables, if any.
1306 Constraints can be constructed, manipulated and
1307 added to (or removed from) (basic) sets and relations
1308 using the following functions.
1310 #include <isl/constraint.h>
1311 __isl_give isl_constraint *isl_equality_alloc(
1312 __isl_take isl_local_space *ls);
1313 __isl_give isl_constraint *isl_inequality_alloc(
1314 __isl_take isl_local_space *ls);
1315 __isl_give isl_constraint *isl_constraint_set_constant(
1316 __isl_take isl_constraint *constraint, isl_int v);
1317 __isl_give isl_constraint *isl_constraint_set_constant_si(
1318 __isl_take isl_constraint *constraint, int v);
1319 __isl_give isl_constraint *isl_constraint_set_coefficient(
1320 __isl_take isl_constraint *constraint,
1321 enum isl_dim_type type, int pos, isl_int v);
1322 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1323 __isl_take isl_constraint *constraint,
1324 enum isl_dim_type type, int pos, int v);
1325 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1326 __isl_take isl_basic_map *bmap,
1327 __isl_take isl_constraint *constraint);
1328 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1329 __isl_take isl_basic_set *bset,
1330 __isl_take isl_constraint *constraint);
1331 __isl_give isl_map *isl_map_add_constraint(
1332 __isl_take isl_map *map,
1333 __isl_take isl_constraint *constraint);
1334 __isl_give isl_set *isl_set_add_constraint(
1335 __isl_take isl_set *set,
1336 __isl_take isl_constraint *constraint);
1337 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1338 __isl_take isl_basic_set *bset,
1339 __isl_take isl_constraint *constraint);
1341 For example, to create a set containing the even integers
1342 between 10 and 42, you would use the following code.
1345 isl_local_space *ls;
1347 isl_basic_set *bset;
1349 space = isl_space_set_alloc(ctx, 0, 2);
1350 bset = isl_basic_set_universe(isl_space_copy(space));
1351 ls = isl_local_space_from_space(space);
1353 c = isl_equality_alloc(isl_local_space_copy(ls));
1354 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1355 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1356 bset = isl_basic_set_add_constraint(bset, c);
1358 c = isl_inequality_alloc(isl_local_space_copy(ls));
1359 c = isl_constraint_set_constant_si(c, -10);
1360 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1361 bset = isl_basic_set_add_constraint(bset, c);
1363 c = isl_inequality_alloc(ls);
1364 c = isl_constraint_set_constant_si(c, 42);
1365 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1366 bset = isl_basic_set_add_constraint(bset, c);
1368 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1372 isl_basic_set *bset;
1373 bset = isl_basic_set_read_from_str(ctx,
1374 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1376 A basic set or relation can also be constructed from two matrices
1377 describing the equalities and the inequalities.
1379 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1380 __isl_take isl_space *space,
1381 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1382 enum isl_dim_type c1,
1383 enum isl_dim_type c2, enum isl_dim_type c3,
1384 enum isl_dim_type c4);
1385 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1386 __isl_take isl_space *space,
1387 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1388 enum isl_dim_type c1,
1389 enum isl_dim_type c2, enum isl_dim_type c3,
1390 enum isl_dim_type c4, enum isl_dim_type c5);
1392 The C<isl_dim_type> arguments indicate the order in which
1393 different kinds of variables appear in the input matrices
1394 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1395 C<isl_dim_set> and C<isl_dim_div> for sets and
1396 of C<isl_dim_cst>, C<isl_dim_param>,
1397 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1399 A (basic or union) set or relation can also be constructed from a
1400 (union) (piecewise) (multiple) affine expression
1401 or a list of affine expressions
1402 (See L<"Piecewise Quasi Affine Expressions"> and
1403 L<"Piecewise Multiple Quasi Affine Expressions">).
1405 __isl_give isl_basic_map *isl_basic_map_from_aff(
1406 __isl_take isl_aff *aff);
1407 __isl_give isl_map *isl_map_from_aff(
1408 __isl_take isl_aff *aff);
1409 __isl_give isl_set *isl_set_from_pw_aff(
1410 __isl_take isl_pw_aff *pwaff);
1411 __isl_give isl_map *isl_map_from_pw_aff(
1412 __isl_take isl_pw_aff *pwaff);
1413 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1414 __isl_take isl_space *domain_space,
1415 __isl_take isl_aff_list *list);
1416 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1417 __isl_take isl_multi_aff *maff)
1418 __isl_give isl_map *isl_map_from_multi_aff(
1419 __isl_take isl_multi_aff *maff)
1420 __isl_give isl_set *isl_set_from_pw_multi_aff(
1421 __isl_take isl_pw_multi_aff *pma);
1422 __isl_give isl_map *isl_map_from_pw_multi_aff(
1423 __isl_take isl_pw_multi_aff *pma);
1424 __isl_give isl_union_map *
1425 isl_union_map_from_union_pw_multi_aff(
1426 __isl_take isl_union_pw_multi_aff *upma);
1428 The C<domain_dim> argument describes the domain of the resulting
1429 basic relation. It is required because the C<list> may consist
1430 of zero affine expressions.
1432 =head2 Inspecting Sets and Relations
1434 Usually, the user should not have to care about the actual constraints
1435 of the sets and maps, but should instead apply the abstract operations
1436 explained in the following sections.
1437 Occasionally, however, it may be required to inspect the individual
1438 coefficients of the constraints. This section explains how to do so.
1439 In these cases, it may also be useful to have C<isl> compute
1440 an explicit representation of the existentially quantified variables.
1442 __isl_give isl_set *isl_set_compute_divs(
1443 __isl_take isl_set *set);
1444 __isl_give isl_map *isl_map_compute_divs(
1445 __isl_take isl_map *map);
1446 __isl_give isl_union_set *isl_union_set_compute_divs(
1447 __isl_take isl_union_set *uset);
1448 __isl_give isl_union_map *isl_union_map_compute_divs(
1449 __isl_take isl_union_map *umap);
1451 This explicit representation defines the existentially quantified
1452 variables as integer divisions of the other variables, possibly
1453 including earlier existentially quantified variables.
1454 An explicitly represented existentially quantified variable therefore
1455 has a unique value when the values of the other variables are known.
1456 If, furthermore, the same existentials, i.e., existentials
1457 with the same explicit representations, should appear in the
1458 same order in each of the disjuncts of a set or map, then the user should call
1459 either of the following functions.
1461 __isl_give isl_set *isl_set_align_divs(
1462 __isl_take isl_set *set);
1463 __isl_give isl_map *isl_map_align_divs(
1464 __isl_take isl_map *map);
1466 Alternatively, the existentially quantified variables can be removed
1467 using the following functions, which compute an overapproximation.
1469 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1470 __isl_take isl_basic_set *bset);
1471 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1472 __isl_take isl_basic_map *bmap);
1473 __isl_give isl_set *isl_set_remove_divs(
1474 __isl_take isl_set *set);
1475 __isl_give isl_map *isl_map_remove_divs(
1476 __isl_take isl_map *map);
1478 It is also possible to only remove those divs that are defined
1479 in terms of a given range of dimensions or only those for which
1480 no explicit representation is known.
1482 __isl_give isl_basic_set *
1483 isl_basic_set_remove_divs_involving_dims(
1484 __isl_take isl_basic_set *bset,
1485 enum isl_dim_type type,
1486 unsigned first, unsigned n);
1487 __isl_give isl_basic_map *
1488 isl_basic_map_remove_divs_involving_dims(
1489 __isl_take isl_basic_map *bmap,
1490 enum isl_dim_type type,
1491 unsigned first, unsigned n);
1492 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1493 __isl_take isl_set *set, enum isl_dim_type type,
1494 unsigned first, unsigned n);
1495 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1496 __isl_take isl_map *map, enum isl_dim_type type,
1497 unsigned first, unsigned n);
1499 __isl_give isl_basic_set *
1500 isl_basic_set_remove_unknown_divs(
1501 __isl_take isl_basic_set *bset);
1502 __isl_give isl_set *isl_set_remove_unknown_divs(
1503 __isl_take isl_set *set);
1504 __isl_give isl_map *isl_map_remove_unknown_divs(
1505 __isl_take isl_map *map);
1507 To iterate over all the sets or maps in a union set or map, use
1509 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1510 int (*fn)(__isl_take isl_set *set, void *user),
1512 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1513 int (*fn)(__isl_take isl_map *map, void *user),
1516 The number of sets or maps in a union set or map can be obtained
1519 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1520 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1522 To extract the set or map in a given space from a union, use
1524 __isl_give isl_set *isl_union_set_extract_set(
1525 __isl_keep isl_union_set *uset,
1526 __isl_take isl_space *space);
1527 __isl_give isl_map *isl_union_map_extract_map(
1528 __isl_keep isl_union_map *umap,
1529 __isl_take isl_space *space);
1531 To iterate over all the basic sets or maps in a set or map, use
1533 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1534 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1536 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1537 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1540 The callback function C<fn> should return 0 if successful and
1541 -1 if an error occurs. In the latter case, or if any other error
1542 occurs, the above functions will return -1.
1544 It should be noted that C<isl> does not guarantee that
1545 the basic sets or maps passed to C<fn> are disjoint.
1546 If this is required, then the user should call one of
1547 the following functions first.
1549 __isl_give isl_set *isl_set_make_disjoint(
1550 __isl_take isl_set *set);
1551 __isl_give isl_map *isl_map_make_disjoint(
1552 __isl_take isl_map *map);
1554 The number of basic sets in a set can be obtained
1557 int isl_set_n_basic_set(__isl_keep isl_set *set);
1559 To iterate over the constraints of a basic set or map, use
1561 #include <isl/constraint.h>
1563 int isl_basic_set_n_constraint(
1564 __isl_keep isl_basic_set *bset);
1565 int isl_basic_set_foreach_constraint(
1566 __isl_keep isl_basic_set *bset,
1567 int (*fn)(__isl_take isl_constraint *c, void *user),
1569 int isl_basic_map_foreach_constraint(
1570 __isl_keep isl_basic_map *bmap,
1571 int (*fn)(__isl_take isl_constraint *c, void *user),
1573 void *isl_constraint_free(__isl_take isl_constraint *c);
1575 Again, the callback function C<fn> should return 0 if successful and
1576 -1 if an error occurs. In the latter case, or if any other error
1577 occurs, the above functions will return -1.
1578 The constraint C<c> represents either an equality or an inequality.
1579 Use the following function to find out whether a constraint
1580 represents an equality. If not, it represents an inequality.
1582 int isl_constraint_is_equality(
1583 __isl_keep isl_constraint *constraint);
1585 The coefficients of the constraints can be inspected using
1586 the following functions.
1588 int isl_constraint_is_lower_bound(
1589 __isl_keep isl_constraint *constraint,
1590 enum isl_dim_type type, unsigned pos);
1591 int isl_constraint_is_upper_bound(
1592 __isl_keep isl_constraint *constraint,
1593 enum isl_dim_type type, unsigned pos);
1594 void isl_constraint_get_constant(
1595 __isl_keep isl_constraint *constraint, isl_int *v);
1596 void isl_constraint_get_coefficient(
1597 __isl_keep isl_constraint *constraint,
1598 enum isl_dim_type type, int pos, isl_int *v);
1599 int isl_constraint_involves_dims(
1600 __isl_keep isl_constraint *constraint,
1601 enum isl_dim_type type, unsigned first, unsigned n);
1603 The explicit representations of the existentially quantified
1604 variables can be inspected using the following function.
1605 Note that the user is only allowed to use this function
1606 if the inspected set or map is the result of a call
1607 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1608 The existentially quantified variable is equal to the floor
1609 of the returned affine expression. The affine expression
1610 itself can be inspected using the functions in
1611 L<"Piecewise Quasi Affine Expressions">.
1613 __isl_give isl_aff *isl_constraint_get_div(
1614 __isl_keep isl_constraint *constraint, int pos);
1616 To obtain the constraints of a basic set or map in matrix
1617 form, use the following functions.
1619 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1620 __isl_keep isl_basic_set *bset,
1621 enum isl_dim_type c1, enum isl_dim_type c2,
1622 enum isl_dim_type c3, enum isl_dim_type c4);
1623 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1624 __isl_keep isl_basic_set *bset,
1625 enum isl_dim_type c1, enum isl_dim_type c2,
1626 enum isl_dim_type c3, enum isl_dim_type c4);
1627 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1628 __isl_keep isl_basic_map *bmap,
1629 enum isl_dim_type c1,
1630 enum isl_dim_type c2, enum isl_dim_type c3,
1631 enum isl_dim_type c4, enum isl_dim_type c5);
1632 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1633 __isl_keep isl_basic_map *bmap,
1634 enum isl_dim_type c1,
1635 enum isl_dim_type c2, enum isl_dim_type c3,
1636 enum isl_dim_type c4, enum isl_dim_type c5);
1638 The C<isl_dim_type> arguments dictate the order in which
1639 different kinds of variables appear in the resulting matrix
1640 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1641 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1643 The number of parameters, input, output or set dimensions can
1644 be obtained using the following functions.
1646 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1647 enum isl_dim_type type);
1648 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1649 enum isl_dim_type type);
1650 unsigned isl_set_dim(__isl_keep isl_set *set,
1651 enum isl_dim_type type);
1652 unsigned isl_map_dim(__isl_keep isl_map *map,
1653 enum isl_dim_type type);
1655 To check whether the description of a set or relation depends
1656 on one or more given dimensions, it is not necessary to iterate over all
1657 constraints. Instead the following functions can be used.
1659 int isl_basic_set_involves_dims(
1660 __isl_keep isl_basic_set *bset,
1661 enum isl_dim_type type, unsigned first, unsigned n);
1662 int isl_set_involves_dims(__isl_keep isl_set *set,
1663 enum isl_dim_type type, unsigned first, unsigned n);
1664 int isl_basic_map_involves_dims(
1665 __isl_keep isl_basic_map *bmap,
1666 enum isl_dim_type type, unsigned first, unsigned n);
1667 int isl_map_involves_dims(__isl_keep isl_map *map,
1668 enum isl_dim_type type, unsigned first, unsigned n);
1670 Similarly, the following functions can be used to check whether
1671 a given dimension is involved in any lower or upper bound.
1673 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1674 enum isl_dim_type type, unsigned pos);
1675 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1676 enum isl_dim_type type, unsigned pos);
1678 The identifiers or names of the domain and range spaces of a set
1679 or relation can be read off or set using the following functions.
1681 __isl_give isl_set *isl_set_set_tuple_id(
1682 __isl_take isl_set *set, __isl_take isl_id *id);
1683 __isl_give isl_set *isl_set_reset_tuple_id(
1684 __isl_take isl_set *set);
1685 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1686 __isl_give isl_id *isl_set_get_tuple_id(
1687 __isl_keep isl_set *set);
1688 __isl_give isl_map *isl_map_set_tuple_id(
1689 __isl_take isl_map *map, enum isl_dim_type type,
1690 __isl_take isl_id *id);
1691 __isl_give isl_map *isl_map_reset_tuple_id(
1692 __isl_take isl_map *map, enum isl_dim_type type);
1693 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1694 enum isl_dim_type type);
1695 __isl_give isl_id *isl_map_get_tuple_id(
1696 __isl_keep isl_map *map, enum isl_dim_type type);
1698 const char *isl_basic_set_get_tuple_name(
1699 __isl_keep isl_basic_set *bset);
1700 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1701 __isl_take isl_basic_set *set, const char *s);
1702 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1703 const char *isl_set_get_tuple_name(
1704 __isl_keep isl_set *set);
1705 const char *isl_basic_map_get_tuple_name(
1706 __isl_keep isl_basic_map *bmap,
1707 enum isl_dim_type type);
1708 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1709 __isl_take isl_basic_map *bmap,
1710 enum isl_dim_type type, const char *s);
1711 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1712 enum isl_dim_type type);
1713 const char *isl_map_get_tuple_name(
1714 __isl_keep isl_map *map,
1715 enum isl_dim_type type);
1717 As with C<isl_space_get_tuple_name>, the value returned points to
1718 an internal data structure.
1719 The identifiers, positions or names of individual dimensions can be
1720 read off using the following functions.
1722 __isl_give isl_id *isl_basic_set_get_dim_id(
1723 __isl_keep isl_basic_set *bset,
1724 enum isl_dim_type type, unsigned pos);
1725 __isl_give isl_set *isl_set_set_dim_id(
1726 __isl_take isl_set *set, enum isl_dim_type type,
1727 unsigned pos, __isl_take isl_id *id);
1728 int isl_set_has_dim_id(__isl_keep isl_set *set,
1729 enum isl_dim_type type, unsigned pos);
1730 __isl_give isl_id *isl_set_get_dim_id(
1731 __isl_keep isl_set *set, enum isl_dim_type type,
1733 int isl_basic_map_has_dim_id(
1734 __isl_keep isl_basic_map *bmap,
1735 enum isl_dim_type type, unsigned pos);
1736 __isl_give isl_map *isl_map_set_dim_id(
1737 __isl_take isl_map *map, enum isl_dim_type type,
1738 unsigned pos, __isl_take isl_id *id);
1739 int isl_map_has_dim_id(__isl_keep isl_map *map,
1740 enum isl_dim_type type, unsigned pos);
1741 __isl_give isl_id *isl_map_get_dim_id(
1742 __isl_keep isl_map *map, enum isl_dim_type type,
1745 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1746 enum isl_dim_type type, __isl_keep isl_id *id);
1747 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1748 enum isl_dim_type type, __isl_keep isl_id *id);
1749 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1750 enum isl_dim_type type, const char *name);
1751 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1752 enum isl_dim_type type, const char *name);
1754 const char *isl_constraint_get_dim_name(
1755 __isl_keep isl_constraint *constraint,
1756 enum isl_dim_type type, unsigned pos);
1757 const char *isl_basic_set_get_dim_name(
1758 __isl_keep isl_basic_set *bset,
1759 enum isl_dim_type type, unsigned pos);
1760 int isl_set_has_dim_name(__isl_keep isl_set *set,
1761 enum isl_dim_type type, unsigned pos);
1762 const char *isl_set_get_dim_name(
1763 __isl_keep isl_set *set,
1764 enum isl_dim_type type, unsigned pos);
1765 const char *isl_basic_map_get_dim_name(
1766 __isl_keep isl_basic_map *bmap,
1767 enum isl_dim_type type, unsigned pos);
1768 int isl_map_has_dim_name(__isl_keep isl_map *map,
1769 enum isl_dim_type type, unsigned pos);
1770 const char *isl_map_get_dim_name(
1771 __isl_keep isl_map *map,
1772 enum isl_dim_type type, unsigned pos);
1774 These functions are mostly useful to obtain the identifiers, positions
1775 or names of the parameters. Identifiers of individual dimensions are
1776 essentially only useful for printing. They are ignored by all other
1777 operations and may not be preserved across those operations.
1781 =head3 Unary Properties
1787 The following functions test whether the given set or relation
1788 contains any integer points. The ``plain'' variants do not perform
1789 any computations, but simply check if the given set or relation
1790 is already known to be empty.
1792 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1793 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1794 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1795 int isl_set_is_empty(__isl_keep isl_set *set);
1796 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1797 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1798 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1799 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1800 int isl_map_is_empty(__isl_keep isl_map *map);
1801 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1803 =item * Universality
1805 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1806 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1807 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1809 =item * Single-valuedness
1811 int isl_basic_map_is_single_valued(
1812 __isl_keep isl_basic_map *bmap);
1813 int isl_map_plain_is_single_valued(
1814 __isl_keep isl_map *map);
1815 int isl_map_is_single_valued(__isl_keep isl_map *map);
1816 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1820 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1821 int isl_map_is_injective(__isl_keep isl_map *map);
1822 int isl_union_map_plain_is_injective(
1823 __isl_keep isl_union_map *umap);
1824 int isl_union_map_is_injective(
1825 __isl_keep isl_union_map *umap);
1829 int isl_map_is_bijective(__isl_keep isl_map *map);
1830 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1834 int isl_basic_map_plain_is_fixed(
1835 __isl_keep isl_basic_map *bmap,
1836 enum isl_dim_type type, unsigned pos,
1838 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1839 enum isl_dim_type type, unsigned pos,
1841 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1842 enum isl_dim_type type, unsigned pos,
1845 Check if the relation obviously lies on a hyperplane where the given dimension
1846 has a fixed value and if so, return that value in C<*val>.
1850 To check whether a set is a parameter domain, use this function:
1852 int isl_set_is_params(__isl_keep isl_set *set);
1853 int isl_union_set_is_params(
1854 __isl_keep isl_union_set *uset);
1858 The following functions check whether the domain of the given
1859 (basic) set is a wrapped relation.
1861 int isl_basic_set_is_wrapping(
1862 __isl_keep isl_basic_set *bset);
1863 int isl_set_is_wrapping(__isl_keep isl_set *set);
1865 =item * Internal Product
1867 int isl_basic_map_can_zip(
1868 __isl_keep isl_basic_map *bmap);
1869 int isl_map_can_zip(__isl_keep isl_map *map);
1871 Check whether the product of domain and range of the given relation
1873 i.e., whether both domain and range are nested relations.
1877 int isl_basic_map_can_curry(
1878 __isl_keep isl_basic_map *bmap);
1879 int isl_map_can_curry(__isl_keep isl_map *map);
1881 Check whether the domain of the (basic) relation is a wrapped relation.
1883 int isl_basic_map_can_uncurry(
1884 __isl_keep isl_basic_map *bmap);
1885 int isl_map_can_uncurry(__isl_keep isl_map *map);
1887 Check whether the range of the (basic) relation is a wrapped relation.
1891 =head3 Binary Properties
1897 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1898 __isl_keep isl_set *set2);
1899 int isl_set_is_equal(__isl_keep isl_set *set1,
1900 __isl_keep isl_set *set2);
1901 int isl_union_set_is_equal(
1902 __isl_keep isl_union_set *uset1,
1903 __isl_keep isl_union_set *uset2);
1904 int isl_basic_map_is_equal(
1905 __isl_keep isl_basic_map *bmap1,
1906 __isl_keep isl_basic_map *bmap2);
1907 int isl_map_is_equal(__isl_keep isl_map *map1,
1908 __isl_keep isl_map *map2);
1909 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1910 __isl_keep isl_map *map2);
1911 int isl_union_map_is_equal(
1912 __isl_keep isl_union_map *umap1,
1913 __isl_keep isl_union_map *umap2);
1915 =item * Disjointness
1917 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1918 __isl_keep isl_set *set2);
1919 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1920 __isl_keep isl_set *set2);
1921 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1922 __isl_keep isl_map *map2);
1926 int isl_basic_set_is_subset(
1927 __isl_keep isl_basic_set *bset1,
1928 __isl_keep isl_basic_set *bset2);
1929 int isl_set_is_subset(__isl_keep isl_set *set1,
1930 __isl_keep isl_set *set2);
1931 int isl_set_is_strict_subset(
1932 __isl_keep isl_set *set1,
1933 __isl_keep isl_set *set2);
1934 int isl_union_set_is_subset(
1935 __isl_keep isl_union_set *uset1,
1936 __isl_keep isl_union_set *uset2);
1937 int isl_union_set_is_strict_subset(
1938 __isl_keep isl_union_set *uset1,
1939 __isl_keep isl_union_set *uset2);
1940 int isl_basic_map_is_subset(
1941 __isl_keep isl_basic_map *bmap1,
1942 __isl_keep isl_basic_map *bmap2);
1943 int isl_basic_map_is_strict_subset(
1944 __isl_keep isl_basic_map *bmap1,
1945 __isl_keep isl_basic_map *bmap2);
1946 int isl_map_is_subset(
1947 __isl_keep isl_map *map1,
1948 __isl_keep isl_map *map2);
1949 int isl_map_is_strict_subset(
1950 __isl_keep isl_map *map1,
1951 __isl_keep isl_map *map2);
1952 int isl_union_map_is_subset(
1953 __isl_keep isl_union_map *umap1,
1954 __isl_keep isl_union_map *umap2);
1955 int isl_union_map_is_strict_subset(
1956 __isl_keep isl_union_map *umap1,
1957 __isl_keep isl_union_map *umap2);
1959 Check whether the first argument is a (strict) subset of the
1964 int isl_set_plain_cmp(__isl_keep isl_set *set1,
1965 __isl_keep isl_set *set2);
1967 This function is useful for sorting C<isl_set>s.
1968 The order depends on the internal representation of the inputs.
1969 The order is fixed over different calls to the function (assuming
1970 the internal representation of the inputs has not changed), but may
1971 change over different versions of C<isl>.
1975 =head2 Unary Operations
1981 __isl_give isl_set *isl_set_complement(
1982 __isl_take isl_set *set);
1983 __isl_give isl_map *isl_map_complement(
1984 __isl_take isl_map *map);
1988 __isl_give isl_basic_map *isl_basic_map_reverse(
1989 __isl_take isl_basic_map *bmap);
1990 __isl_give isl_map *isl_map_reverse(
1991 __isl_take isl_map *map);
1992 __isl_give isl_union_map *isl_union_map_reverse(
1993 __isl_take isl_union_map *umap);
1997 __isl_give isl_basic_set *isl_basic_set_project_out(
1998 __isl_take isl_basic_set *bset,
1999 enum isl_dim_type type, unsigned first, unsigned n);
2000 __isl_give isl_basic_map *isl_basic_map_project_out(
2001 __isl_take isl_basic_map *bmap,
2002 enum isl_dim_type type, unsigned first, unsigned n);
2003 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2004 enum isl_dim_type type, unsigned first, unsigned n);
2005 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2006 enum isl_dim_type type, unsigned first, unsigned n);
2007 __isl_give isl_basic_set *isl_basic_set_params(
2008 __isl_take isl_basic_set *bset);
2009 __isl_give isl_basic_set *isl_basic_map_domain(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_basic_set *isl_basic_map_range(
2012 __isl_take isl_basic_map *bmap);
2013 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2014 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2015 __isl_give isl_set *isl_map_domain(
2016 __isl_take isl_map *bmap);
2017 __isl_give isl_set *isl_map_range(
2018 __isl_take isl_map *map);
2019 __isl_give isl_set *isl_union_set_params(
2020 __isl_take isl_union_set *uset);
2021 __isl_give isl_set *isl_union_map_params(
2022 __isl_take isl_union_map *umap);
2023 __isl_give isl_union_set *isl_union_map_domain(
2024 __isl_take isl_union_map *umap);
2025 __isl_give isl_union_set *isl_union_map_range(
2026 __isl_take isl_union_map *umap);
2028 __isl_give isl_basic_map *isl_basic_map_domain_map(
2029 __isl_take isl_basic_map *bmap);
2030 __isl_give isl_basic_map *isl_basic_map_range_map(
2031 __isl_take isl_basic_map *bmap);
2032 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2033 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2034 __isl_give isl_union_map *isl_union_map_domain_map(
2035 __isl_take isl_union_map *umap);
2036 __isl_give isl_union_map *isl_union_map_range_map(
2037 __isl_take isl_union_map *umap);
2039 The functions above construct a (basic, regular or union) relation
2040 that maps (a wrapped version of) the input relation to its domain or range.
2044 __isl_give isl_basic_set *isl_basic_set_eliminate(
2045 __isl_take isl_basic_set *bset,
2046 enum isl_dim_type type,
2047 unsigned first, unsigned n);
2048 __isl_give isl_set *isl_set_eliminate(
2049 __isl_take isl_set *set, enum isl_dim_type type,
2050 unsigned first, unsigned n);
2051 __isl_give isl_basic_map *isl_basic_map_eliminate(
2052 __isl_take isl_basic_map *bmap,
2053 enum isl_dim_type type,
2054 unsigned first, unsigned n);
2055 __isl_give isl_map *isl_map_eliminate(
2056 __isl_take isl_map *map, enum isl_dim_type type,
2057 unsigned first, unsigned n);
2059 Eliminate the coefficients for the given dimensions from the constraints,
2060 without removing the dimensions.
2064 __isl_give isl_basic_set *isl_basic_set_fix(
2065 __isl_take isl_basic_set *bset,
2066 enum isl_dim_type type, unsigned pos,
2068 __isl_give isl_basic_set *isl_basic_set_fix_si(
2069 __isl_take isl_basic_set *bset,
2070 enum isl_dim_type type, unsigned pos, int value);
2071 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2072 enum isl_dim_type type, unsigned pos,
2074 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2075 enum isl_dim_type type, unsigned pos, int value);
2076 __isl_give isl_basic_map *isl_basic_map_fix_si(
2077 __isl_take isl_basic_map *bmap,
2078 enum isl_dim_type type, unsigned pos, int value);
2079 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2080 enum isl_dim_type type, unsigned pos,
2082 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2083 enum isl_dim_type type, unsigned pos, int value);
2085 Intersect the set or relation with the hyperplane where the given
2086 dimension has the fixed given value.
2088 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2089 __isl_take isl_basic_map *bmap,
2090 enum isl_dim_type type, unsigned pos, int value);
2091 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2092 __isl_take isl_basic_map *bmap,
2093 enum isl_dim_type type, unsigned pos, int value);
2094 __isl_give isl_set *isl_set_lower_bound(
2095 __isl_take isl_set *set,
2096 enum isl_dim_type type, unsigned pos,
2098 __isl_give isl_set *isl_set_lower_bound_si(
2099 __isl_take isl_set *set,
2100 enum isl_dim_type type, unsigned pos, int value);
2101 __isl_give isl_map *isl_map_lower_bound_si(
2102 __isl_take isl_map *map,
2103 enum isl_dim_type type, unsigned pos, int value);
2104 __isl_give isl_set *isl_set_upper_bound(
2105 __isl_take isl_set *set,
2106 enum isl_dim_type type, unsigned pos,
2108 __isl_give isl_set *isl_set_upper_bound_si(
2109 __isl_take isl_set *set,
2110 enum isl_dim_type type, unsigned pos, int value);
2111 __isl_give isl_map *isl_map_upper_bound_si(
2112 __isl_take isl_map *map,
2113 enum isl_dim_type type, unsigned pos, int value);
2115 Intersect the set or relation with the half-space where the given
2116 dimension has a value bounded by the fixed given value.
2118 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2119 enum isl_dim_type type1, int pos1,
2120 enum isl_dim_type type2, int pos2);
2121 __isl_give isl_basic_map *isl_basic_map_equate(
2122 __isl_take isl_basic_map *bmap,
2123 enum isl_dim_type type1, int pos1,
2124 enum isl_dim_type type2, int pos2);
2125 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2126 enum isl_dim_type type1, int pos1,
2127 enum isl_dim_type type2, int pos2);
2129 Intersect the set or relation with the hyperplane where the given
2130 dimensions are equal to each other.
2132 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2133 enum isl_dim_type type1, int pos1,
2134 enum isl_dim_type type2, int pos2);
2136 Intersect the relation with the hyperplane where the given
2137 dimensions have opposite values.
2139 __isl_give isl_basic_map *isl_basic_map_order_ge(
2140 __isl_take isl_basic_map *bmap,
2141 enum isl_dim_type type1, int pos1,
2142 enum isl_dim_type type2, int pos2);
2143 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2144 enum isl_dim_type type1, int pos1,
2145 enum isl_dim_type type2, int pos2);
2146 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2147 enum isl_dim_type type1, int pos1,
2148 enum isl_dim_type type2, int pos2);
2150 Intersect the relation with the half-space where the given
2151 dimensions satisfy the given ordering.
2155 __isl_give isl_map *isl_set_identity(
2156 __isl_take isl_set *set);
2157 __isl_give isl_union_map *isl_union_set_identity(
2158 __isl_take isl_union_set *uset);
2160 Construct an identity relation on the given (union) set.
2164 __isl_give isl_basic_set *isl_basic_map_deltas(
2165 __isl_take isl_basic_map *bmap);
2166 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2167 __isl_give isl_union_set *isl_union_map_deltas(
2168 __isl_take isl_union_map *umap);
2170 These functions return a (basic) set containing the differences
2171 between image elements and corresponding domain elements in the input.
2173 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2174 __isl_take isl_basic_map *bmap);
2175 __isl_give isl_map *isl_map_deltas_map(
2176 __isl_take isl_map *map);
2177 __isl_give isl_union_map *isl_union_map_deltas_map(
2178 __isl_take isl_union_map *umap);
2180 The functions above construct a (basic, regular or union) relation
2181 that maps (a wrapped version of) the input relation to its delta set.
2185 Simplify the representation of a set or relation by trying
2186 to combine pairs of basic sets or relations into a single
2187 basic set or relation.
2189 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2190 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2191 __isl_give isl_union_set *isl_union_set_coalesce(
2192 __isl_take isl_union_set *uset);
2193 __isl_give isl_union_map *isl_union_map_coalesce(
2194 __isl_take isl_union_map *umap);
2196 One of the methods for combining pairs of basic sets or relations
2197 can result in coefficients that are much larger than those that appear
2198 in the constraints of the input. By default, the coefficients are
2199 not allowed to grow larger, but this can be changed by unsetting
2200 the following option.
2202 int isl_options_set_coalesce_bounded_wrapping(
2203 isl_ctx *ctx, int val);
2204 int isl_options_get_coalesce_bounded_wrapping(
2207 =item * Detecting equalities
2209 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2212 __isl_take isl_basic_map *bmap);
2213 __isl_give isl_set *isl_set_detect_equalities(
2214 __isl_take isl_set *set);
2215 __isl_give isl_map *isl_map_detect_equalities(
2216 __isl_take isl_map *map);
2217 __isl_give isl_union_set *isl_union_set_detect_equalities(
2218 __isl_take isl_union_set *uset);
2219 __isl_give isl_union_map *isl_union_map_detect_equalities(
2220 __isl_take isl_union_map *umap);
2222 Simplify the representation of a set or relation by detecting implicit
2225 =item * Removing redundant constraints
2227 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2228 __isl_take isl_basic_set *bset);
2229 __isl_give isl_set *isl_set_remove_redundancies(
2230 __isl_take isl_set *set);
2231 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2232 __isl_take isl_basic_map *bmap);
2233 __isl_give isl_map *isl_map_remove_redundancies(
2234 __isl_take isl_map *map);
2238 __isl_give isl_basic_set *isl_set_convex_hull(
2239 __isl_take isl_set *set);
2240 __isl_give isl_basic_map *isl_map_convex_hull(
2241 __isl_take isl_map *map);
2243 If the input set or relation has any existentially quantified
2244 variables, then the result of these operations is currently undefined.
2248 __isl_give isl_basic_set *
2249 isl_set_unshifted_simple_hull(
2250 __isl_take isl_set *set);
2251 __isl_give isl_basic_map *
2252 isl_map_unshifted_simple_hull(
2253 __isl_take isl_map *map);
2254 __isl_give isl_basic_set *isl_set_simple_hull(
2255 __isl_take isl_set *set);
2256 __isl_give isl_basic_map *isl_map_simple_hull(
2257 __isl_take isl_map *map);
2258 __isl_give isl_union_map *isl_union_map_simple_hull(
2259 __isl_take isl_union_map *umap);
2261 These functions compute a single basic set or relation
2262 that contains the whole input set or relation.
2263 In particular, the output is described by translates
2264 of the constraints describing the basic sets or relations in the input.
2265 In case of C<isl_set_unshifted_simple_hull>, only the original
2266 constraints are used, without any translation.
2270 (See \autoref{s:simple hull}.)
2276 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2277 __isl_take isl_basic_set *bset);
2278 __isl_give isl_basic_set *isl_set_affine_hull(
2279 __isl_take isl_set *set);
2280 __isl_give isl_union_set *isl_union_set_affine_hull(
2281 __isl_take isl_union_set *uset);
2282 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2283 __isl_take isl_basic_map *bmap);
2284 __isl_give isl_basic_map *isl_map_affine_hull(
2285 __isl_take isl_map *map);
2286 __isl_give isl_union_map *isl_union_map_affine_hull(
2287 __isl_take isl_union_map *umap);
2289 In case of union sets and relations, the affine hull is computed
2292 =item * Polyhedral hull
2294 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2295 __isl_take isl_set *set);
2296 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2297 __isl_take isl_map *map);
2298 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2299 __isl_take isl_union_set *uset);
2300 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2301 __isl_take isl_union_map *umap);
2303 These functions compute a single basic set or relation
2304 not involving any existentially quantified variables
2305 that contains the whole input set or relation.
2306 In case of union sets and relations, the polyhedral hull is computed
2309 =item * Other approximations
2311 __isl_give isl_basic_set *
2312 isl_basic_set_drop_constraints_involving_dims(
2313 __isl_take isl_basic_set *bset,
2314 enum isl_dim_type type,
2315 unsigned first, unsigned n);
2316 __isl_give isl_basic_set *
2317 isl_basic_set_drop_constraints_not_involving_dims(
2318 __isl_take isl_basic_set *bset,
2319 enum isl_dim_type type,
2320 unsigned first, unsigned n);
2321 __isl_give isl_set *
2322 isl_set_drop_constraints_involving_dims(
2323 __isl_take isl_set *set,
2324 enum isl_dim_type type,
2325 unsigned first, unsigned n);
2326 __isl_give isl_map *
2327 isl_map_drop_constraints_involving_dims(
2328 __isl_take isl_map *map,
2329 enum isl_dim_type type,
2330 unsigned first, unsigned n);
2332 These functions drop any constraints (not) involving the specified dimensions.
2333 Note that the result depends on the representation of the input.
2337 __isl_give isl_basic_set *isl_basic_set_sample(
2338 __isl_take isl_basic_set *bset);
2339 __isl_give isl_basic_set *isl_set_sample(
2340 __isl_take isl_set *set);
2341 __isl_give isl_basic_map *isl_basic_map_sample(
2342 __isl_take isl_basic_map *bmap);
2343 __isl_give isl_basic_map *isl_map_sample(
2344 __isl_take isl_map *map);
2346 If the input (basic) set or relation is non-empty, then return
2347 a singleton subset of the input. Otherwise, return an empty set.
2349 =item * Optimization
2351 #include <isl/ilp.h>
2352 enum isl_lp_result isl_basic_set_max(
2353 __isl_keep isl_basic_set *bset,
2354 __isl_keep isl_aff *obj, isl_int *opt)
2355 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2356 __isl_keep isl_aff *obj, isl_int *opt);
2357 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2358 __isl_keep isl_aff *obj, isl_int *opt);
2360 Compute the minimum or maximum of the integer affine expression C<obj>
2361 over the points in C<set>, returning the result in C<opt>.
2362 The return value may be one of C<isl_lp_error>,
2363 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2365 =item * Parametric optimization
2367 __isl_give isl_pw_aff *isl_set_dim_min(
2368 __isl_take isl_set *set, int pos);
2369 __isl_give isl_pw_aff *isl_set_dim_max(
2370 __isl_take isl_set *set, int pos);
2371 __isl_give isl_pw_aff *isl_map_dim_max(
2372 __isl_take isl_map *map, int pos);
2374 Compute the minimum or maximum of the given set or output dimension
2375 as a function of the parameters (and input dimensions), but independently
2376 of the other set or output dimensions.
2377 For lexicographic optimization, see L<"Lexicographic Optimization">.
2381 The following functions compute either the set of (rational) coefficient
2382 values of valid constraints for the given set or the set of (rational)
2383 values satisfying the constraints with coefficients from the given set.
2384 Internally, these two sets of functions perform essentially the
2385 same operations, except that the set of coefficients is assumed to
2386 be a cone, while the set of values may be any polyhedron.
2387 The current implementation is based on the Farkas lemma and
2388 Fourier-Motzkin elimination, but this may change or be made optional
2389 in future. In particular, future implementations may use different
2390 dualization algorithms or skip the elimination step.
2392 __isl_give isl_basic_set *isl_basic_set_coefficients(
2393 __isl_take isl_basic_set *bset);
2394 __isl_give isl_basic_set *isl_set_coefficients(
2395 __isl_take isl_set *set);
2396 __isl_give isl_union_set *isl_union_set_coefficients(
2397 __isl_take isl_union_set *bset);
2398 __isl_give isl_basic_set *isl_basic_set_solutions(
2399 __isl_take isl_basic_set *bset);
2400 __isl_give isl_basic_set *isl_set_solutions(
2401 __isl_take isl_set *set);
2402 __isl_give isl_union_set *isl_union_set_solutions(
2403 __isl_take isl_union_set *bset);
2407 __isl_give isl_map *isl_map_fixed_power(
2408 __isl_take isl_map *map, isl_int exp);
2409 __isl_give isl_union_map *isl_union_map_fixed_power(
2410 __isl_take isl_union_map *umap, isl_int exp);
2412 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2413 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2414 of C<map> is computed.
2416 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2418 __isl_give isl_union_map *isl_union_map_power(
2419 __isl_take isl_union_map *umap, int *exact);
2421 Compute a parametric representation for all positive powers I<k> of C<map>.
2422 The result maps I<k> to a nested relation corresponding to the
2423 I<k>th power of C<map>.
2424 The result may be an overapproximation. If the result is known to be exact,
2425 then C<*exact> is set to C<1>.
2427 =item * Transitive closure
2429 __isl_give isl_map *isl_map_transitive_closure(
2430 __isl_take isl_map *map, int *exact);
2431 __isl_give isl_union_map *isl_union_map_transitive_closure(
2432 __isl_take isl_union_map *umap, int *exact);
2434 Compute the transitive closure of C<map>.
2435 The result may be an overapproximation. If the result is known to be exact,
2436 then C<*exact> is set to C<1>.
2438 =item * Reaching path lengths
2440 __isl_give isl_map *isl_map_reaching_path_lengths(
2441 __isl_take isl_map *map, int *exact);
2443 Compute a relation that maps each element in the range of C<map>
2444 to the lengths of all paths composed of edges in C<map> that
2445 end up in the given element.
2446 The result may be an overapproximation. If the result is known to be exact,
2447 then C<*exact> is set to C<1>.
2448 To compute the I<maximal> path length, the resulting relation
2449 should be postprocessed by C<isl_map_lexmax>.
2450 In particular, if the input relation is a dependence relation
2451 (mapping sources to sinks), then the maximal path length corresponds
2452 to the free schedule.
2453 Note, however, that C<isl_map_lexmax> expects the maximum to be
2454 finite, so if the path lengths are unbounded (possibly due to
2455 the overapproximation), then you will get an error message.
2459 __isl_give isl_basic_set *isl_basic_map_wrap(
2460 __isl_take isl_basic_map *bmap);
2461 __isl_give isl_set *isl_map_wrap(
2462 __isl_take isl_map *map);
2463 __isl_give isl_union_set *isl_union_map_wrap(
2464 __isl_take isl_union_map *umap);
2465 __isl_give isl_basic_map *isl_basic_set_unwrap(
2466 __isl_take isl_basic_set *bset);
2467 __isl_give isl_map *isl_set_unwrap(
2468 __isl_take isl_set *set);
2469 __isl_give isl_union_map *isl_union_set_unwrap(
2470 __isl_take isl_union_set *uset);
2474 Remove any internal structure of domain (and range) of the given
2475 set or relation. If there is any such internal structure in the input,
2476 then the name of the space is also removed.
2478 __isl_give isl_basic_set *isl_basic_set_flatten(
2479 __isl_take isl_basic_set *bset);
2480 __isl_give isl_set *isl_set_flatten(
2481 __isl_take isl_set *set);
2482 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2483 __isl_take isl_basic_map *bmap);
2484 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2485 __isl_take isl_basic_map *bmap);
2486 __isl_give isl_map *isl_map_flatten_range(
2487 __isl_take isl_map *map);
2488 __isl_give isl_map *isl_map_flatten_domain(
2489 __isl_take isl_map *map);
2490 __isl_give isl_basic_map *isl_basic_map_flatten(
2491 __isl_take isl_basic_map *bmap);
2492 __isl_give isl_map *isl_map_flatten(
2493 __isl_take isl_map *map);
2495 __isl_give isl_map *isl_set_flatten_map(
2496 __isl_take isl_set *set);
2498 The function above constructs a relation
2499 that maps the input set to a flattened version of the set.
2503 Lift the input set to a space with extra dimensions corresponding
2504 to the existentially quantified variables in the input.
2505 In particular, the result lives in a wrapped map where the domain
2506 is the original space and the range corresponds to the original
2507 existentially quantified variables.
2509 __isl_give isl_basic_set *isl_basic_set_lift(
2510 __isl_take isl_basic_set *bset);
2511 __isl_give isl_set *isl_set_lift(
2512 __isl_take isl_set *set);
2513 __isl_give isl_union_set *isl_union_set_lift(
2514 __isl_take isl_union_set *uset);
2516 Given a local space that contains the existentially quantified
2517 variables of a set, a basic relation that, when applied to
2518 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2519 can be constructed using the following function.
2521 #include <isl/local_space.h>
2522 __isl_give isl_basic_map *isl_local_space_lifting(
2523 __isl_take isl_local_space *ls);
2525 =item * Internal Product
2527 __isl_give isl_basic_map *isl_basic_map_zip(
2528 __isl_take isl_basic_map *bmap);
2529 __isl_give isl_map *isl_map_zip(
2530 __isl_take isl_map *map);
2531 __isl_give isl_union_map *isl_union_map_zip(
2532 __isl_take isl_union_map *umap);
2534 Given a relation with nested relations for domain and range,
2535 interchange the range of the domain with the domain of the range.
2539 __isl_give isl_basic_map *isl_basic_map_curry(
2540 __isl_take isl_basic_map *bmap);
2541 __isl_give isl_basic_map *isl_basic_map_uncurry(
2542 __isl_take isl_basic_map *bmap);
2543 __isl_give isl_map *isl_map_curry(
2544 __isl_take isl_map *map);
2545 __isl_give isl_map *isl_map_uncurry(
2546 __isl_take isl_map *map);
2547 __isl_give isl_union_map *isl_union_map_curry(
2548 __isl_take isl_union_map *umap);
2550 Given a relation with a nested relation for domain,
2551 the C<curry> functions
2552 move the range of the nested relation out of the domain
2553 and use it as the domain of a nested relation in the range,
2554 with the original range as range of this nested relation.
2555 The C<uncurry> functions perform the inverse operation.
2557 =item * Aligning parameters
2559 __isl_give isl_basic_set *isl_basic_set_align_params(
2560 __isl_take isl_basic_set *bset,
2561 __isl_take isl_space *model);
2562 __isl_give isl_set *isl_set_align_params(
2563 __isl_take isl_set *set,
2564 __isl_take isl_space *model);
2565 __isl_give isl_basic_map *isl_basic_map_align_params(
2566 __isl_take isl_basic_map *bmap,
2567 __isl_take isl_space *model);
2568 __isl_give isl_map *isl_map_align_params(
2569 __isl_take isl_map *map,
2570 __isl_take isl_space *model);
2572 Change the order of the parameters of the given set or relation
2573 such that the first parameters match those of C<model>.
2574 This may involve the introduction of extra parameters.
2575 All parameters need to be named.
2577 =item * Dimension manipulation
2579 __isl_give isl_set *isl_set_add_dims(
2580 __isl_take isl_set *set,
2581 enum isl_dim_type type, unsigned n);
2582 __isl_give isl_map *isl_map_add_dims(
2583 __isl_take isl_map *map,
2584 enum isl_dim_type type, unsigned n);
2585 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2586 __isl_take isl_basic_set *bset,
2587 enum isl_dim_type type, unsigned pos,
2589 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2590 __isl_take isl_basic_map *bmap,
2591 enum isl_dim_type type, unsigned pos,
2593 __isl_give isl_set *isl_set_insert_dims(
2594 __isl_take isl_set *set,
2595 enum isl_dim_type type, unsigned pos, unsigned n);
2596 __isl_give isl_map *isl_map_insert_dims(
2597 __isl_take isl_map *map,
2598 enum isl_dim_type type, unsigned pos, unsigned n);
2599 __isl_give isl_basic_set *isl_basic_set_move_dims(
2600 __isl_take isl_basic_set *bset,
2601 enum isl_dim_type dst_type, unsigned dst_pos,
2602 enum isl_dim_type src_type, unsigned src_pos,
2604 __isl_give isl_basic_map *isl_basic_map_move_dims(
2605 __isl_take isl_basic_map *bmap,
2606 enum isl_dim_type dst_type, unsigned dst_pos,
2607 enum isl_dim_type src_type, unsigned src_pos,
2609 __isl_give isl_set *isl_set_move_dims(
2610 __isl_take isl_set *set,
2611 enum isl_dim_type dst_type, unsigned dst_pos,
2612 enum isl_dim_type src_type, unsigned src_pos,
2614 __isl_give isl_map *isl_map_move_dims(
2615 __isl_take isl_map *map,
2616 enum isl_dim_type dst_type, unsigned dst_pos,
2617 enum isl_dim_type src_type, unsigned src_pos,
2620 It is usually not advisable to directly change the (input or output)
2621 space of a set or a relation as this removes the name and the internal
2622 structure of the space. However, the above functions can be useful
2623 to add new parameters, assuming
2624 C<isl_set_align_params> and C<isl_map_align_params>
2629 =head2 Binary Operations
2631 The two arguments of a binary operation not only need to live
2632 in the same C<isl_ctx>, they currently also need to have
2633 the same (number of) parameters.
2635 =head3 Basic Operations
2639 =item * Intersection
2641 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2642 __isl_take isl_basic_set *bset1,
2643 __isl_take isl_basic_set *bset2);
2644 __isl_give isl_basic_set *isl_basic_set_intersect(
2645 __isl_take isl_basic_set *bset1,
2646 __isl_take isl_basic_set *bset2);
2647 __isl_give isl_set *isl_set_intersect_params(
2648 __isl_take isl_set *set,
2649 __isl_take isl_set *params);
2650 __isl_give isl_set *isl_set_intersect(
2651 __isl_take isl_set *set1,
2652 __isl_take isl_set *set2);
2653 __isl_give isl_union_set *isl_union_set_intersect_params(
2654 __isl_take isl_union_set *uset,
2655 __isl_take isl_set *set);
2656 __isl_give isl_union_map *isl_union_map_intersect_params(
2657 __isl_take isl_union_map *umap,
2658 __isl_take isl_set *set);
2659 __isl_give isl_union_set *isl_union_set_intersect(
2660 __isl_take isl_union_set *uset1,
2661 __isl_take isl_union_set *uset2);
2662 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2663 __isl_take isl_basic_map *bmap,
2664 __isl_take isl_basic_set *bset);
2665 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2666 __isl_take isl_basic_map *bmap,
2667 __isl_take isl_basic_set *bset);
2668 __isl_give isl_basic_map *isl_basic_map_intersect(
2669 __isl_take isl_basic_map *bmap1,
2670 __isl_take isl_basic_map *bmap2);
2671 __isl_give isl_map *isl_map_intersect_params(
2672 __isl_take isl_map *map,
2673 __isl_take isl_set *params);
2674 __isl_give isl_map *isl_map_intersect_domain(
2675 __isl_take isl_map *map,
2676 __isl_take isl_set *set);
2677 __isl_give isl_map *isl_map_intersect_range(
2678 __isl_take isl_map *map,
2679 __isl_take isl_set *set);
2680 __isl_give isl_map *isl_map_intersect(
2681 __isl_take isl_map *map1,
2682 __isl_take isl_map *map2);
2683 __isl_give isl_union_map *isl_union_map_intersect_domain(
2684 __isl_take isl_union_map *umap,
2685 __isl_take isl_union_set *uset);
2686 __isl_give isl_union_map *isl_union_map_intersect_range(
2687 __isl_take isl_union_map *umap,
2688 __isl_take isl_union_set *uset);
2689 __isl_give isl_union_map *isl_union_map_intersect(
2690 __isl_take isl_union_map *umap1,
2691 __isl_take isl_union_map *umap2);
2693 The second argument to the C<_params> functions needs to be
2694 a parametric (basic) set. For the other functions, a parametric set
2695 for either argument is only allowed if the other argument is
2696 a parametric set as well.
2700 __isl_give isl_set *isl_basic_set_union(
2701 __isl_take isl_basic_set *bset1,
2702 __isl_take isl_basic_set *bset2);
2703 __isl_give isl_map *isl_basic_map_union(
2704 __isl_take isl_basic_map *bmap1,
2705 __isl_take isl_basic_map *bmap2);
2706 __isl_give isl_set *isl_set_union(
2707 __isl_take isl_set *set1,
2708 __isl_take isl_set *set2);
2709 __isl_give isl_map *isl_map_union(
2710 __isl_take isl_map *map1,
2711 __isl_take isl_map *map2);
2712 __isl_give isl_union_set *isl_union_set_union(
2713 __isl_take isl_union_set *uset1,
2714 __isl_take isl_union_set *uset2);
2715 __isl_give isl_union_map *isl_union_map_union(
2716 __isl_take isl_union_map *umap1,
2717 __isl_take isl_union_map *umap2);
2719 =item * Set difference
2721 __isl_give isl_set *isl_set_subtract(
2722 __isl_take isl_set *set1,
2723 __isl_take isl_set *set2);
2724 __isl_give isl_map *isl_map_subtract(
2725 __isl_take isl_map *map1,
2726 __isl_take isl_map *map2);
2727 __isl_give isl_map *isl_map_subtract_domain(
2728 __isl_take isl_map *map,
2729 __isl_take isl_set *dom);
2730 __isl_give isl_map *isl_map_subtract_range(
2731 __isl_take isl_map *map,
2732 __isl_take isl_set *dom);
2733 __isl_give isl_union_set *isl_union_set_subtract(
2734 __isl_take isl_union_set *uset1,
2735 __isl_take isl_union_set *uset2);
2736 __isl_give isl_union_map *isl_union_map_subtract(
2737 __isl_take isl_union_map *umap1,
2738 __isl_take isl_union_map *umap2);
2739 __isl_give isl_union_map *isl_union_map_subtract_domain(
2740 __isl_take isl_union_map *umap,
2741 __isl_take isl_union_set *dom);
2742 __isl_give isl_union_map *isl_union_map_subtract_range(
2743 __isl_take isl_union_map *umap,
2744 __isl_take isl_union_set *dom);
2748 __isl_give isl_basic_set *isl_basic_set_apply(
2749 __isl_take isl_basic_set *bset,
2750 __isl_take isl_basic_map *bmap);
2751 __isl_give isl_set *isl_set_apply(
2752 __isl_take isl_set *set,
2753 __isl_take isl_map *map);
2754 __isl_give isl_union_set *isl_union_set_apply(
2755 __isl_take isl_union_set *uset,
2756 __isl_take isl_union_map *umap);
2757 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2758 __isl_take isl_basic_map *bmap1,
2759 __isl_take isl_basic_map *bmap2);
2760 __isl_give isl_basic_map *isl_basic_map_apply_range(
2761 __isl_take isl_basic_map *bmap1,
2762 __isl_take isl_basic_map *bmap2);
2763 __isl_give isl_map *isl_map_apply_domain(
2764 __isl_take isl_map *map1,
2765 __isl_take isl_map *map2);
2766 __isl_give isl_union_map *isl_union_map_apply_domain(
2767 __isl_take isl_union_map *umap1,
2768 __isl_take isl_union_map *umap2);
2769 __isl_give isl_map *isl_map_apply_range(
2770 __isl_take isl_map *map1,
2771 __isl_take isl_map *map2);
2772 __isl_give isl_union_map *isl_union_map_apply_range(
2773 __isl_take isl_union_map *umap1,
2774 __isl_take isl_union_map *umap2);
2776 =item * Cartesian Product
2778 __isl_give isl_set *isl_set_product(
2779 __isl_take isl_set *set1,
2780 __isl_take isl_set *set2);
2781 __isl_give isl_union_set *isl_union_set_product(
2782 __isl_take isl_union_set *uset1,
2783 __isl_take isl_union_set *uset2);
2784 __isl_give isl_basic_map *isl_basic_map_domain_product(
2785 __isl_take isl_basic_map *bmap1,
2786 __isl_take isl_basic_map *bmap2);
2787 __isl_give isl_basic_map *isl_basic_map_range_product(
2788 __isl_take isl_basic_map *bmap1,
2789 __isl_take isl_basic_map *bmap2);
2790 __isl_give isl_basic_map *isl_basic_map_product(
2791 __isl_take isl_basic_map *bmap1,
2792 __isl_take isl_basic_map *bmap2);
2793 __isl_give isl_map *isl_map_domain_product(
2794 __isl_take isl_map *map1,
2795 __isl_take isl_map *map2);
2796 __isl_give isl_map *isl_map_range_product(
2797 __isl_take isl_map *map1,
2798 __isl_take isl_map *map2);
2799 __isl_give isl_union_map *isl_union_map_domain_product(
2800 __isl_take isl_union_map *umap1,
2801 __isl_take isl_union_map *umap2);
2802 __isl_give isl_union_map *isl_union_map_range_product(
2803 __isl_take isl_union_map *umap1,
2804 __isl_take isl_union_map *umap2);
2805 __isl_give isl_map *isl_map_product(
2806 __isl_take isl_map *map1,
2807 __isl_take isl_map *map2);
2808 __isl_give isl_union_map *isl_union_map_product(
2809 __isl_take isl_union_map *umap1,
2810 __isl_take isl_union_map *umap2);
2812 The above functions compute the cross product of the given
2813 sets or relations. The domains and ranges of the results
2814 are wrapped maps between domains and ranges of the inputs.
2815 To obtain a ``flat'' product, use the following functions
2818 __isl_give isl_basic_set *isl_basic_set_flat_product(
2819 __isl_take isl_basic_set *bset1,
2820 __isl_take isl_basic_set *bset2);
2821 __isl_give isl_set *isl_set_flat_product(
2822 __isl_take isl_set *set1,
2823 __isl_take isl_set *set2);
2824 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2825 __isl_take isl_basic_map *bmap1,
2826 __isl_take isl_basic_map *bmap2);
2827 __isl_give isl_map *isl_map_flat_domain_product(
2828 __isl_take isl_map *map1,
2829 __isl_take isl_map *map2);
2830 __isl_give isl_map *isl_map_flat_range_product(
2831 __isl_take isl_map *map1,
2832 __isl_take isl_map *map2);
2833 __isl_give isl_union_map *isl_union_map_flat_range_product(
2834 __isl_take isl_union_map *umap1,
2835 __isl_take isl_union_map *umap2);
2836 __isl_give isl_basic_map *isl_basic_map_flat_product(
2837 __isl_take isl_basic_map *bmap1,
2838 __isl_take isl_basic_map *bmap2);
2839 __isl_give isl_map *isl_map_flat_product(
2840 __isl_take isl_map *map1,
2841 __isl_take isl_map *map2);
2843 =item * Simplification
2845 __isl_give isl_basic_set *isl_basic_set_gist(
2846 __isl_take isl_basic_set *bset,
2847 __isl_take isl_basic_set *context);
2848 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2849 __isl_take isl_set *context);
2850 __isl_give isl_set *isl_set_gist_params(
2851 __isl_take isl_set *set,
2852 __isl_take isl_set *context);
2853 __isl_give isl_union_set *isl_union_set_gist(
2854 __isl_take isl_union_set *uset,
2855 __isl_take isl_union_set *context);
2856 __isl_give isl_union_set *isl_union_set_gist_params(
2857 __isl_take isl_union_set *uset,
2858 __isl_take isl_set *set);
2859 __isl_give isl_basic_map *isl_basic_map_gist(
2860 __isl_take isl_basic_map *bmap,
2861 __isl_take isl_basic_map *context);
2862 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2863 __isl_take isl_map *context);
2864 __isl_give isl_map *isl_map_gist_params(
2865 __isl_take isl_map *map,
2866 __isl_take isl_set *context);
2867 __isl_give isl_map *isl_map_gist_domain(
2868 __isl_take isl_map *map,
2869 __isl_take isl_set *context);
2870 __isl_give isl_map *isl_map_gist_range(
2871 __isl_take isl_map *map,
2872 __isl_take isl_set *context);
2873 __isl_give isl_union_map *isl_union_map_gist(
2874 __isl_take isl_union_map *umap,
2875 __isl_take isl_union_map *context);
2876 __isl_give isl_union_map *isl_union_map_gist_params(
2877 __isl_take isl_union_map *umap,
2878 __isl_take isl_set *set);
2879 __isl_give isl_union_map *isl_union_map_gist_domain(
2880 __isl_take isl_union_map *umap,
2881 __isl_take isl_union_set *uset);
2882 __isl_give isl_union_map *isl_union_map_gist_range(
2883 __isl_take isl_union_map *umap,
2884 __isl_take isl_union_set *uset);
2886 The gist operation returns a set or relation that has the
2887 same intersection with the context as the input set or relation.
2888 Any implicit equality in the intersection is made explicit in the result,
2889 while all inequalities that are redundant with respect to the intersection
2891 In case of union sets and relations, the gist operation is performed
2896 =head3 Lexicographic Optimization
2898 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2899 the following functions
2900 compute a set that contains the lexicographic minimum or maximum
2901 of the elements in C<set> (or C<bset>) for those values of the parameters
2902 that satisfy C<dom>.
2903 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2904 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2906 In other words, the union of the parameter values
2907 for which the result is non-empty and of C<*empty>
2910 __isl_give isl_set *isl_basic_set_partial_lexmin(
2911 __isl_take isl_basic_set *bset,
2912 __isl_take isl_basic_set *dom,
2913 __isl_give isl_set **empty);
2914 __isl_give isl_set *isl_basic_set_partial_lexmax(
2915 __isl_take isl_basic_set *bset,
2916 __isl_take isl_basic_set *dom,
2917 __isl_give isl_set **empty);
2918 __isl_give isl_set *isl_set_partial_lexmin(
2919 __isl_take isl_set *set, __isl_take isl_set *dom,
2920 __isl_give isl_set **empty);
2921 __isl_give isl_set *isl_set_partial_lexmax(
2922 __isl_take isl_set *set, __isl_take isl_set *dom,
2923 __isl_give isl_set **empty);
2925 Given a (basic) set C<set> (or C<bset>), the following functions simply
2926 return a set containing the lexicographic minimum or maximum
2927 of the elements in C<set> (or C<bset>).
2928 In case of union sets, the optimum is computed per space.
2930 __isl_give isl_set *isl_basic_set_lexmin(
2931 __isl_take isl_basic_set *bset);
2932 __isl_give isl_set *isl_basic_set_lexmax(
2933 __isl_take isl_basic_set *bset);
2934 __isl_give isl_set *isl_set_lexmin(
2935 __isl_take isl_set *set);
2936 __isl_give isl_set *isl_set_lexmax(
2937 __isl_take isl_set *set);
2938 __isl_give isl_union_set *isl_union_set_lexmin(
2939 __isl_take isl_union_set *uset);
2940 __isl_give isl_union_set *isl_union_set_lexmax(
2941 __isl_take isl_union_set *uset);
2943 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2944 the following functions
2945 compute a relation that maps each element of C<dom>
2946 to the single lexicographic minimum or maximum
2947 of the elements that are associated to that same
2948 element in C<map> (or C<bmap>).
2949 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2950 that contains the elements in C<dom> that do not map
2951 to any elements in C<map> (or C<bmap>).
2952 In other words, the union of the domain of the result and of C<*empty>
2955 __isl_give isl_map *isl_basic_map_partial_lexmax(
2956 __isl_take isl_basic_map *bmap,
2957 __isl_take isl_basic_set *dom,
2958 __isl_give isl_set **empty);
2959 __isl_give isl_map *isl_basic_map_partial_lexmin(
2960 __isl_take isl_basic_map *bmap,
2961 __isl_take isl_basic_set *dom,
2962 __isl_give isl_set **empty);
2963 __isl_give isl_map *isl_map_partial_lexmax(
2964 __isl_take isl_map *map, __isl_take isl_set *dom,
2965 __isl_give isl_set **empty);
2966 __isl_give isl_map *isl_map_partial_lexmin(
2967 __isl_take isl_map *map, __isl_take isl_set *dom,
2968 __isl_give isl_set **empty);
2970 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2971 return a map mapping each element in the domain of
2972 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2973 of all elements associated to that element.
2974 In case of union relations, the optimum is computed per space.
2976 __isl_give isl_map *isl_basic_map_lexmin(
2977 __isl_take isl_basic_map *bmap);
2978 __isl_give isl_map *isl_basic_map_lexmax(
2979 __isl_take isl_basic_map *bmap);
2980 __isl_give isl_map *isl_map_lexmin(
2981 __isl_take isl_map *map);
2982 __isl_give isl_map *isl_map_lexmax(
2983 __isl_take isl_map *map);
2984 __isl_give isl_union_map *isl_union_map_lexmin(
2985 __isl_take isl_union_map *umap);
2986 __isl_give isl_union_map *isl_union_map_lexmax(
2987 __isl_take isl_union_map *umap);
2989 The following functions return their result in the form of
2990 a piecewise multi-affine expression
2991 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2992 but are otherwise equivalent to the corresponding functions
2993 returning a basic set or relation.
2995 __isl_give isl_pw_multi_aff *
2996 isl_basic_map_lexmin_pw_multi_aff(
2997 __isl_take isl_basic_map *bmap);
2998 __isl_give isl_pw_multi_aff *
2999 isl_basic_set_partial_lexmin_pw_multi_aff(
3000 __isl_take isl_basic_set *bset,
3001 __isl_take isl_basic_set *dom,
3002 __isl_give isl_set **empty);
3003 __isl_give isl_pw_multi_aff *
3004 isl_basic_set_partial_lexmax_pw_multi_aff(
3005 __isl_take isl_basic_set *bset,
3006 __isl_take isl_basic_set *dom,
3007 __isl_give isl_set **empty);
3008 __isl_give isl_pw_multi_aff *
3009 isl_basic_map_partial_lexmin_pw_multi_aff(
3010 __isl_take isl_basic_map *bmap,
3011 __isl_take isl_basic_set *dom,
3012 __isl_give isl_set **empty);
3013 __isl_give isl_pw_multi_aff *
3014 isl_basic_map_partial_lexmax_pw_multi_aff(
3015 __isl_take isl_basic_map *bmap,
3016 __isl_take isl_basic_set *dom,
3017 __isl_give isl_set **empty);
3018 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3019 __isl_take isl_map *map);
3020 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3021 __isl_take isl_map *map);
3025 Lists are defined over several element types, including
3026 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3027 C<isl_basic_set> and C<isl_set>.
3028 Here we take lists of C<isl_set>s as an example.
3029 Lists can be created, copied, modified and freed using the following functions.
3031 #include <isl/list.h>
3032 __isl_give isl_set_list *isl_set_list_from_set(
3033 __isl_take isl_set *el);
3034 __isl_give isl_set_list *isl_set_list_alloc(
3035 isl_ctx *ctx, int n);
3036 __isl_give isl_set_list *isl_set_list_copy(
3037 __isl_keep isl_set_list *list);
3038 __isl_give isl_set_list *isl_set_list_insert(
3039 __isl_take isl_set_list *list, unsigned pos,
3040 __isl_take isl_set *el);
3041 __isl_give isl_set_list *isl_set_list_add(
3042 __isl_take isl_set_list *list,
3043 __isl_take isl_set *el);
3044 __isl_give isl_set_list *isl_set_list_drop(
3045 __isl_take isl_set_list *list,
3046 unsigned first, unsigned n);
3047 __isl_give isl_set_list *isl_set_list_set_set(
3048 __isl_take isl_set_list *list, int index,
3049 __isl_take isl_set *set);
3050 __isl_give isl_set_list *isl_set_list_concat(
3051 __isl_take isl_set_list *list1,
3052 __isl_take isl_set_list *list2);
3053 void *isl_set_list_free(__isl_take isl_set_list *list);
3055 C<isl_set_list_alloc> creates an empty list with a capacity for
3056 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3059 Lists can be inspected using the following functions.
3061 #include <isl/list.h>
3062 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3063 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3064 __isl_give isl_set *isl_set_list_get_set(
3065 __isl_keep isl_set_list *list, int index);
3066 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3067 int (*fn)(__isl_take isl_set *el, void *user),
3070 Lists can be printed using
3072 #include <isl/list.h>
3073 __isl_give isl_printer *isl_printer_print_set_list(
3074 __isl_take isl_printer *p,
3075 __isl_keep isl_set_list *list);
3079 Vectors can be created, copied and freed using the following functions.
3081 #include <isl/vec.h>
3082 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3084 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3085 void *isl_vec_free(__isl_take isl_vec *vec);
3087 Note that the elements of a newly created vector may have arbitrary values.
3088 The elements can be changed and inspected using the following functions.
3090 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3091 int isl_vec_size(__isl_keep isl_vec *vec);
3092 int isl_vec_get_element(__isl_keep isl_vec *vec,
3093 int pos, isl_int *v);
3094 __isl_give isl_vec *isl_vec_set_element(
3095 __isl_take isl_vec *vec, int pos, isl_int v);
3096 __isl_give isl_vec *isl_vec_set_element_si(
3097 __isl_take isl_vec *vec, int pos, int v);
3098 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3100 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3102 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3105 C<isl_vec_get_element> will return a negative value if anything went wrong.
3106 In that case, the value of C<*v> is undefined.
3108 The following function can be used to concatenate two vectors.
3110 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3111 __isl_take isl_vec *vec2);
3115 Matrices can be created, copied and freed using the following functions.
3117 #include <isl/mat.h>
3118 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3119 unsigned n_row, unsigned n_col);
3120 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3121 void isl_mat_free(__isl_take isl_mat *mat);
3123 Note that the elements of a newly created matrix may have arbitrary values.
3124 The elements can be changed and inspected using the following functions.
3126 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3127 int isl_mat_rows(__isl_keep isl_mat *mat);
3128 int isl_mat_cols(__isl_keep isl_mat *mat);
3129 int isl_mat_get_element(__isl_keep isl_mat *mat,
3130 int row, int col, isl_int *v);
3131 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3132 int row, int col, isl_int v);
3133 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3134 int row, int col, int v);
3136 C<isl_mat_get_element> will return a negative value if anything went wrong.
3137 In that case, the value of C<*v> is undefined.
3139 The following function can be used to compute the (right) inverse
3140 of a matrix, i.e., a matrix such that the product of the original
3141 and the inverse (in that order) is a multiple of the identity matrix.
3142 The input matrix is assumed to be of full row-rank.
3144 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3146 The following function can be used to compute the (right) kernel
3147 (or null space) of a matrix, i.e., a matrix such that the product of
3148 the original and the kernel (in that order) is the zero matrix.
3150 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3152 =head2 Piecewise Quasi Affine Expressions
3154 The zero quasi affine expression or the quasi affine expression
3155 that is equal to a specified dimension on a given domain can be created using
3157 __isl_give isl_aff *isl_aff_zero_on_domain(
3158 __isl_take isl_local_space *ls);
3159 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3160 __isl_take isl_local_space *ls);
3161 __isl_give isl_aff *isl_aff_var_on_domain(
3162 __isl_take isl_local_space *ls,
3163 enum isl_dim_type type, unsigned pos);
3164 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3165 __isl_take isl_local_space *ls,
3166 enum isl_dim_type type, unsigned pos);
3168 Note that the space in which the resulting objects live is a map space
3169 with the given space as domain and a one-dimensional range.
3171 An empty piecewise quasi affine expression (one with no cells)
3172 or a piecewise quasi affine expression with a single cell can
3173 be created using the following functions.
3175 #include <isl/aff.h>
3176 __isl_give isl_pw_aff *isl_pw_aff_empty(
3177 __isl_take isl_space *space);
3178 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3179 __isl_take isl_set *set, __isl_take isl_aff *aff);
3180 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3181 __isl_take isl_aff *aff);
3183 A piecewise quasi affine expression that is equal to 1 on a set
3184 and 0 outside the set can be created using the following function.
3186 #include <isl/aff.h>
3187 __isl_give isl_pw_aff *isl_set_indicator_function(
3188 __isl_take isl_set *set);
3190 Quasi affine expressions can be copied and freed using
3192 #include <isl/aff.h>
3193 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3194 void *isl_aff_free(__isl_take isl_aff *aff);
3196 __isl_give isl_pw_aff *isl_pw_aff_copy(
3197 __isl_keep isl_pw_aff *pwaff);
3198 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3200 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3201 using the following function. The constraint is required to have
3202 a non-zero coefficient for the specified dimension.
3204 #include <isl/constraint.h>
3205 __isl_give isl_aff *isl_constraint_get_bound(
3206 __isl_keep isl_constraint *constraint,
3207 enum isl_dim_type type, int pos);
3209 The entire affine expression of the constraint can also be extracted
3210 using the following function.
3212 #include <isl/constraint.h>
3213 __isl_give isl_aff *isl_constraint_get_aff(
3214 __isl_keep isl_constraint *constraint);
3216 Conversely, an equality constraint equating
3217 the affine expression to zero or an inequality constraint enforcing
3218 the affine expression to be non-negative, can be constructed using
3220 __isl_give isl_constraint *isl_equality_from_aff(
3221 __isl_take isl_aff *aff);
3222 __isl_give isl_constraint *isl_inequality_from_aff(
3223 __isl_take isl_aff *aff);
3225 The expression can be inspected using
3227 #include <isl/aff.h>
3228 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3229 int isl_aff_dim(__isl_keep isl_aff *aff,
3230 enum isl_dim_type type);
3231 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3232 __isl_keep isl_aff *aff);
3233 __isl_give isl_local_space *isl_aff_get_local_space(
3234 __isl_keep isl_aff *aff);
3235 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3236 enum isl_dim_type type, unsigned pos);
3237 const char *isl_pw_aff_get_dim_name(
3238 __isl_keep isl_pw_aff *pa,
3239 enum isl_dim_type type, unsigned pos);
3240 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3241 enum isl_dim_type type, unsigned pos);
3242 __isl_give isl_id *isl_pw_aff_get_dim_id(
3243 __isl_keep isl_pw_aff *pa,
3244 enum isl_dim_type type, unsigned pos);
3245 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3246 __isl_keep isl_pw_aff *pa,
3247 enum isl_dim_type type);
3248 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3250 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3251 enum isl_dim_type type, int pos, isl_int *v);
3252 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3254 __isl_give isl_aff *isl_aff_get_div(
3255 __isl_keep isl_aff *aff, int pos);
3257 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3258 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3259 int (*fn)(__isl_take isl_set *set,
3260 __isl_take isl_aff *aff,
3261 void *user), void *user);
3263 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3264 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3266 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3267 enum isl_dim_type type, unsigned first, unsigned n);
3268 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3269 enum isl_dim_type type, unsigned first, unsigned n);
3271 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3272 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3273 enum isl_dim_type type);
3274 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3276 It can be modified using
3278 #include <isl/aff.h>
3279 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3280 __isl_take isl_pw_aff *pwaff,
3281 enum isl_dim_type type, __isl_take isl_id *id);
3282 __isl_give isl_aff *isl_aff_set_dim_name(
3283 __isl_take isl_aff *aff, enum isl_dim_type type,
3284 unsigned pos, const char *s);
3285 __isl_give isl_aff *isl_aff_set_dim_id(
3286 __isl_take isl_aff *aff, enum isl_dim_type type,
3287 unsigned pos, __isl_take isl_id *id);
3288 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3289 __isl_take isl_pw_aff *pma,
3290 enum isl_dim_type type, unsigned pos,
3291 __isl_take isl_id *id);
3292 __isl_give isl_aff *isl_aff_set_constant(
3293 __isl_take isl_aff *aff, isl_int v);
3294 __isl_give isl_aff *isl_aff_set_constant_si(
3295 __isl_take isl_aff *aff, int v);
3296 __isl_give isl_aff *isl_aff_set_coefficient(
3297 __isl_take isl_aff *aff,
3298 enum isl_dim_type type, int pos, isl_int v);
3299 __isl_give isl_aff *isl_aff_set_coefficient_si(
3300 __isl_take isl_aff *aff,
3301 enum isl_dim_type type, int pos, int v);
3302 __isl_give isl_aff *isl_aff_set_denominator(
3303 __isl_take isl_aff *aff, isl_int v);
3305 __isl_give isl_aff *isl_aff_add_constant(
3306 __isl_take isl_aff *aff, isl_int v);
3307 __isl_give isl_aff *isl_aff_add_constant_si(
3308 __isl_take isl_aff *aff, int v);
3309 __isl_give isl_aff *isl_aff_add_constant_num(
3310 __isl_take isl_aff *aff, isl_int v);
3311 __isl_give isl_aff *isl_aff_add_constant_num_si(
3312 __isl_take isl_aff *aff, int v);
3313 __isl_give isl_aff *isl_aff_add_coefficient(
3314 __isl_take isl_aff *aff,
3315 enum isl_dim_type type, int pos, isl_int v);
3316 __isl_give isl_aff *isl_aff_add_coefficient_si(
3317 __isl_take isl_aff *aff,
3318 enum isl_dim_type type, int pos, int v);
3320 __isl_give isl_aff *isl_aff_insert_dims(
3321 __isl_take isl_aff *aff,
3322 enum isl_dim_type type, unsigned first, unsigned n);
3323 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3324 __isl_take isl_pw_aff *pwaff,
3325 enum isl_dim_type type, unsigned first, unsigned n);
3326 __isl_give isl_aff *isl_aff_add_dims(
3327 __isl_take isl_aff *aff,
3328 enum isl_dim_type type, unsigned n);
3329 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3330 __isl_take isl_pw_aff *pwaff,
3331 enum isl_dim_type type, unsigned n);
3332 __isl_give isl_aff *isl_aff_drop_dims(
3333 __isl_take isl_aff *aff,
3334 enum isl_dim_type type, unsigned first, unsigned n);
3335 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3336 __isl_take isl_pw_aff *pwaff,
3337 enum isl_dim_type type, unsigned first, unsigned n);
3339 Note that the C<set_constant> and C<set_coefficient> functions
3340 set the I<numerator> of the constant or coefficient, while
3341 C<add_constant> and C<add_coefficient> add an integer value to
3342 the possibly rational constant or coefficient.
3343 The C<add_constant_num> functions add an integer value to
3346 To check whether an affine expressions is obviously zero
3347 or obviously equal to some other affine expression, use
3349 #include <isl/aff.h>
3350 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3351 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3352 __isl_keep isl_aff *aff2);
3353 int isl_pw_aff_plain_is_equal(
3354 __isl_keep isl_pw_aff *pwaff1,
3355 __isl_keep isl_pw_aff *pwaff2);
3359 #include <isl/aff.h>
3360 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3361 __isl_take isl_aff *aff2);
3362 __isl_give isl_pw_aff *isl_pw_aff_add(
3363 __isl_take isl_pw_aff *pwaff1,
3364 __isl_take isl_pw_aff *pwaff2);
3365 __isl_give isl_pw_aff *isl_pw_aff_min(
3366 __isl_take isl_pw_aff *pwaff1,
3367 __isl_take isl_pw_aff *pwaff2);
3368 __isl_give isl_pw_aff *isl_pw_aff_max(
3369 __isl_take isl_pw_aff *pwaff1,
3370 __isl_take isl_pw_aff *pwaff2);
3371 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3372 __isl_take isl_aff *aff2);
3373 __isl_give isl_pw_aff *isl_pw_aff_sub(
3374 __isl_take isl_pw_aff *pwaff1,
3375 __isl_take isl_pw_aff *pwaff2);
3376 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3377 __isl_give isl_pw_aff *isl_pw_aff_neg(
3378 __isl_take isl_pw_aff *pwaff);
3379 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3380 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3381 __isl_take isl_pw_aff *pwaff);
3382 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3383 __isl_give isl_pw_aff *isl_pw_aff_floor(
3384 __isl_take isl_pw_aff *pwaff);
3385 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3387 __isl_give isl_pw_aff *isl_pw_aff_mod(
3388 __isl_take isl_pw_aff *pwaff, isl_int mod);
3389 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3391 __isl_give isl_pw_aff *isl_pw_aff_scale(
3392 __isl_take isl_pw_aff *pwaff, isl_int f);
3393 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3395 __isl_give isl_aff *isl_aff_scale_down_ui(
3396 __isl_take isl_aff *aff, unsigned f);
3397 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3398 __isl_take isl_pw_aff *pwaff, isl_int f);
3400 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3401 __isl_take isl_pw_aff_list *list);
3402 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3403 __isl_take isl_pw_aff_list *list);
3405 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3406 __isl_take isl_pw_aff *pwqp);
3408 __isl_give isl_aff *isl_aff_align_params(
3409 __isl_take isl_aff *aff,
3410 __isl_take isl_space *model);
3411 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3412 __isl_take isl_pw_aff *pwaff,
3413 __isl_take isl_space *model);
3415 __isl_give isl_aff *isl_aff_project_domain_on_params(
3416 __isl_take isl_aff *aff);
3418 __isl_give isl_aff *isl_aff_gist_params(
3419 __isl_take isl_aff *aff,
3420 __isl_take isl_set *context);
3421 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3422 __isl_take isl_set *context);
3423 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3424 __isl_take isl_pw_aff *pwaff,
3425 __isl_take isl_set *context);
3426 __isl_give isl_pw_aff *isl_pw_aff_gist(
3427 __isl_take isl_pw_aff *pwaff,
3428 __isl_take isl_set *context);
3430 __isl_give isl_set *isl_pw_aff_domain(
3431 __isl_take isl_pw_aff *pwaff);
3432 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3433 __isl_take isl_pw_aff *pa,
3434 __isl_take isl_set *set);
3435 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3436 __isl_take isl_pw_aff *pa,
3437 __isl_take isl_set *set);
3439 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3440 __isl_take isl_aff *aff2);
3441 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3442 __isl_take isl_aff *aff2);
3443 __isl_give isl_pw_aff *isl_pw_aff_mul(
3444 __isl_take isl_pw_aff *pwaff1,
3445 __isl_take isl_pw_aff *pwaff2);
3446 __isl_give isl_pw_aff *isl_pw_aff_div(
3447 __isl_take isl_pw_aff *pa1,
3448 __isl_take isl_pw_aff *pa2);
3449 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3450 __isl_take isl_pw_aff *pa1,
3451 __isl_take isl_pw_aff *pa2);
3452 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3453 __isl_take isl_pw_aff *pa1,
3454 __isl_take isl_pw_aff *pa2);
3456 When multiplying two affine expressions, at least one of the two needs
3457 to be a constant. Similarly, when dividing an affine expression by another,
3458 the second expression needs to be a constant.
3459 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3460 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3463 #include <isl/aff.h>
3464 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3465 __isl_take isl_aff *aff);
3466 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3467 __isl_take isl_aff *aff);
3468 __isl_give isl_basic_set *isl_aff_le_basic_set(
3469 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3470 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3471 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3472 __isl_give isl_set *isl_pw_aff_eq_set(
3473 __isl_take isl_pw_aff *pwaff1,
3474 __isl_take isl_pw_aff *pwaff2);
3475 __isl_give isl_set *isl_pw_aff_ne_set(
3476 __isl_take isl_pw_aff *pwaff1,
3477 __isl_take isl_pw_aff *pwaff2);
3478 __isl_give isl_set *isl_pw_aff_le_set(
3479 __isl_take isl_pw_aff *pwaff1,
3480 __isl_take isl_pw_aff *pwaff2);
3481 __isl_give isl_set *isl_pw_aff_lt_set(
3482 __isl_take isl_pw_aff *pwaff1,
3483 __isl_take isl_pw_aff *pwaff2);
3484 __isl_give isl_set *isl_pw_aff_ge_set(
3485 __isl_take isl_pw_aff *pwaff1,
3486 __isl_take isl_pw_aff *pwaff2);
3487 __isl_give isl_set *isl_pw_aff_gt_set(
3488 __isl_take isl_pw_aff *pwaff1,
3489 __isl_take isl_pw_aff *pwaff2);
3491 __isl_give isl_set *isl_pw_aff_list_eq_set(
3492 __isl_take isl_pw_aff_list *list1,
3493 __isl_take isl_pw_aff_list *list2);
3494 __isl_give isl_set *isl_pw_aff_list_ne_set(
3495 __isl_take isl_pw_aff_list *list1,
3496 __isl_take isl_pw_aff_list *list2);
3497 __isl_give isl_set *isl_pw_aff_list_le_set(
3498 __isl_take isl_pw_aff_list *list1,
3499 __isl_take isl_pw_aff_list *list2);
3500 __isl_give isl_set *isl_pw_aff_list_lt_set(
3501 __isl_take isl_pw_aff_list *list1,
3502 __isl_take isl_pw_aff_list *list2);
3503 __isl_give isl_set *isl_pw_aff_list_ge_set(
3504 __isl_take isl_pw_aff_list *list1,
3505 __isl_take isl_pw_aff_list *list2);
3506 __isl_give isl_set *isl_pw_aff_list_gt_set(
3507 __isl_take isl_pw_aff_list *list1,
3508 __isl_take isl_pw_aff_list *list2);
3510 The function C<isl_aff_neg_basic_set> returns a basic set
3511 containing those elements in the domain space
3512 of C<aff> where C<aff> is negative.
3513 The function C<isl_aff_ge_basic_set> returns a basic set
3514 containing those elements in the shared space
3515 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3516 The function C<isl_pw_aff_ge_set> returns a set
3517 containing those elements in the shared domain
3518 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3519 The functions operating on C<isl_pw_aff_list> apply the corresponding
3520 C<isl_pw_aff> function to each pair of elements in the two lists.
3522 #include <isl/aff.h>
3523 __isl_give isl_set *isl_pw_aff_nonneg_set(
3524 __isl_take isl_pw_aff *pwaff);
3525 __isl_give isl_set *isl_pw_aff_zero_set(
3526 __isl_take isl_pw_aff *pwaff);
3527 __isl_give isl_set *isl_pw_aff_non_zero_set(
3528 __isl_take isl_pw_aff *pwaff);
3530 The function C<isl_pw_aff_nonneg_set> returns a set
3531 containing those elements in the domain
3532 of C<pwaff> where C<pwaff> is non-negative.
3534 #include <isl/aff.h>
3535 __isl_give isl_pw_aff *isl_pw_aff_cond(
3536 __isl_take isl_pw_aff *cond,
3537 __isl_take isl_pw_aff *pwaff_true,
3538 __isl_take isl_pw_aff *pwaff_false);
3540 The function C<isl_pw_aff_cond> performs a conditional operator
3541 and returns an expression that is equal to C<pwaff_true>
3542 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3543 where C<cond> is zero.
3545 #include <isl/aff.h>
3546 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3547 __isl_take isl_pw_aff *pwaff1,
3548 __isl_take isl_pw_aff *pwaff2);
3549 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3550 __isl_take isl_pw_aff *pwaff1,
3551 __isl_take isl_pw_aff *pwaff2);
3552 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3553 __isl_take isl_pw_aff *pwaff1,
3554 __isl_take isl_pw_aff *pwaff2);
3556 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3557 expression with a domain that is the union of those of C<pwaff1> and
3558 C<pwaff2> and such that on each cell, the quasi-affine expression is
3559 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3560 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3561 associated expression is the defined one.
3563 An expression can be read from input using
3565 #include <isl/aff.h>
3566 __isl_give isl_aff *isl_aff_read_from_str(
3567 isl_ctx *ctx, const char *str);
3568 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3569 isl_ctx *ctx, const char *str);
3571 An expression can be printed using
3573 #include <isl/aff.h>
3574 __isl_give isl_printer *isl_printer_print_aff(
3575 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3577 __isl_give isl_printer *isl_printer_print_pw_aff(
3578 __isl_take isl_printer *p,
3579 __isl_keep isl_pw_aff *pwaff);
3581 =head2 Piecewise Multiple Quasi Affine Expressions
3583 An C<isl_multi_aff> object represents a sequence of
3584 zero or more affine expressions, all defined on the same domain space.
3585 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3586 zero or more piecewise affine expressions.
3588 An C<isl_multi_aff> can be constructed from a single
3589 C<isl_aff> or an C<isl_aff_list> using the
3590 following functions. Similarly for C<isl_multi_pw_aff>.
3592 #include <isl/aff.h>
3593 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3594 __isl_take isl_aff *aff);
3595 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3596 __isl_take isl_pw_aff *pa);
3597 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3598 __isl_take isl_space *space,
3599 __isl_take isl_aff_list *list);
3601 An empty piecewise multiple quasi affine expression (one with no cells),
3602 the zero piecewise multiple quasi affine expression (with value zero
3603 for each output dimension),
3604 a piecewise multiple quasi affine expression with a single cell (with
3605 either a universe or a specified domain) or
3606 a zero-dimensional piecewise multiple quasi affine expression
3608 can be created using the following functions.
3610 #include <isl/aff.h>
3611 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3612 __isl_take isl_space *space);
3613 __isl_give isl_multi_aff *isl_multi_aff_zero(
3614 __isl_take isl_space *space);
3615 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3616 __isl_take isl_space *space);
3617 __isl_give isl_multi_aff *isl_multi_aff_identity(
3618 __isl_take isl_space *space);
3619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3620 __isl_take isl_space *space);
3621 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3622 __isl_take isl_space *space);
3623 __isl_give isl_pw_multi_aff *
3624 isl_pw_multi_aff_from_multi_aff(
3625 __isl_take isl_multi_aff *ma);
3626 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3627 __isl_take isl_set *set,
3628 __isl_take isl_multi_aff *maff);
3629 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3630 __isl_take isl_set *set);
3632 __isl_give isl_union_pw_multi_aff *
3633 isl_union_pw_multi_aff_empty(
3634 __isl_take isl_space *space);
3635 __isl_give isl_union_pw_multi_aff *
3636 isl_union_pw_multi_aff_add_pw_multi_aff(
3637 __isl_take isl_union_pw_multi_aff *upma,
3638 __isl_take isl_pw_multi_aff *pma);
3639 __isl_give isl_union_pw_multi_aff *
3640 isl_union_pw_multi_aff_from_domain(
3641 __isl_take isl_union_set *uset);
3643 A piecewise multiple quasi affine expression can also be initialized
3644 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3645 and the C<isl_map> is single-valued.
3647 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3648 __isl_take isl_set *set);
3649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3650 __isl_take isl_map *map);
3652 Multiple quasi affine expressions can be copied and freed using
3654 #include <isl/aff.h>
3655 __isl_give isl_multi_aff *isl_multi_aff_copy(
3656 __isl_keep isl_multi_aff *maff);
3657 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3659 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3660 __isl_keep isl_pw_multi_aff *pma);
3661 void *isl_pw_multi_aff_free(
3662 __isl_take isl_pw_multi_aff *pma);
3664 __isl_give isl_union_pw_multi_aff *
3665 isl_union_pw_multi_aff_copy(
3666 __isl_keep isl_union_pw_multi_aff *upma);
3667 void *isl_union_pw_multi_aff_free(
3668 __isl_take isl_union_pw_multi_aff *upma);
3670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3671 __isl_keep isl_multi_pw_aff *mpa);
3672 void *isl_multi_pw_aff_free(
3673 __isl_take isl_multi_pw_aff *mpa);
3675 The expression can be inspected using
3677 #include <isl/aff.h>
3678 isl_ctx *isl_multi_aff_get_ctx(
3679 __isl_keep isl_multi_aff *maff);
3680 isl_ctx *isl_pw_multi_aff_get_ctx(
3681 __isl_keep isl_pw_multi_aff *pma);
3682 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3683 __isl_keep isl_union_pw_multi_aff *upma);
3684 isl_ctx *isl_multi_pw_aff_get_ctx(
3685 __isl_keep isl_multi_pw_aff *mpa);
3686 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3687 enum isl_dim_type type);
3688 unsigned isl_pw_multi_aff_dim(
3689 __isl_keep isl_pw_multi_aff *pma,
3690 enum isl_dim_type type);
3691 unsigned isl_multi_pw_aff_dim(
3692 __isl_keep isl_multi_pw_aff *mpa,
3693 enum isl_dim_type type);
3694 __isl_give isl_aff *isl_multi_aff_get_aff(
3695 __isl_keep isl_multi_aff *multi, int pos);
3696 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3697 __isl_keep isl_pw_multi_aff *pma, int pos);
3698 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3699 __isl_keep isl_multi_pw_aff *mpa, int pos);
3700 const char *isl_pw_multi_aff_get_dim_name(
3701 __isl_keep isl_pw_multi_aff *pma,
3702 enum isl_dim_type type, unsigned pos);
3703 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3704 __isl_keep isl_pw_multi_aff *pma,
3705 enum isl_dim_type type, unsigned pos);
3706 const char *isl_multi_aff_get_tuple_name(
3707 __isl_keep isl_multi_aff *multi,
3708 enum isl_dim_type type);
3709 int isl_pw_multi_aff_has_tuple_name(
3710 __isl_keep isl_pw_multi_aff *pma,
3711 enum isl_dim_type type);
3712 const char *isl_pw_multi_aff_get_tuple_name(
3713 __isl_keep isl_pw_multi_aff *pma,
3714 enum isl_dim_type type);
3715 int isl_pw_multi_aff_has_tuple_id(
3716 __isl_keep isl_pw_multi_aff *pma,
3717 enum isl_dim_type type);
3718 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3719 __isl_keep isl_pw_multi_aff *pma,
3720 enum isl_dim_type type);
3722 int isl_pw_multi_aff_foreach_piece(
3723 __isl_keep isl_pw_multi_aff *pma,
3724 int (*fn)(__isl_take isl_set *set,
3725 __isl_take isl_multi_aff *maff,
3726 void *user), void *user);
3728 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3729 __isl_keep isl_union_pw_multi_aff *upma,
3730 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3731 void *user), void *user);
3733 It can be modified using
3735 #include <isl/aff.h>
3736 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3737 __isl_take isl_multi_aff *multi, int pos,
3738 __isl_take isl_aff *aff);
3739 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3740 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3741 __isl_take isl_pw_aff *pa);
3742 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3743 __isl_take isl_multi_aff *maff,
3744 enum isl_dim_type type, unsigned pos, const char *s);
3745 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3746 __isl_take isl_multi_aff *maff,
3747 enum isl_dim_type type, const char *s);
3748 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3749 __isl_take isl_multi_aff *maff,
3750 enum isl_dim_type type, __isl_take isl_id *id);
3751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3752 __isl_take isl_pw_multi_aff *pma,
3753 enum isl_dim_type type, __isl_take isl_id *id);
3755 __isl_give isl_multi_pw_aff *
3756 isl_multi_pw_aff_set_dim_name(
3757 __isl_take isl_multi_pw_aff *mpa,
3758 enum isl_dim_type type, unsigned pos, const char *s);
3759 __isl_give isl_multi_pw_aff *
3760 isl_multi_pw_aff_set_tuple_name(
3761 __isl_take isl_multi_pw_aff *mpa,
3762 enum isl_dim_type type, const char *s);
3764 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3765 __isl_take isl_multi_aff *ma,
3766 enum isl_dim_type type, unsigned first, unsigned n);
3767 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3768 __isl_take isl_multi_aff *ma,
3769 enum isl_dim_type type, unsigned n);
3770 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3771 __isl_take isl_multi_aff *maff,
3772 enum isl_dim_type type, unsigned first, unsigned n);
3773 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3774 __isl_take isl_pw_multi_aff *pma,
3775 enum isl_dim_type type, unsigned first, unsigned n);
3777 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3778 __isl_take isl_multi_pw_aff *mpa,
3779 enum isl_dim_type type, unsigned first, unsigned n);
3780 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3781 __isl_take isl_multi_pw_aff *mpa,
3782 enum isl_dim_type type, unsigned n);
3784 To check whether two multiple affine expressions are
3785 obviously equal to each other, use
3787 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3788 __isl_keep isl_multi_aff *maff2);
3789 int isl_pw_multi_aff_plain_is_equal(
3790 __isl_keep isl_pw_multi_aff *pma1,
3791 __isl_keep isl_pw_multi_aff *pma2);
3795 #include <isl/aff.h>
3796 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3797 __isl_take isl_pw_multi_aff *pma1,
3798 __isl_take isl_pw_multi_aff *pma2);
3799 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3800 __isl_take isl_pw_multi_aff *pma1,
3801 __isl_take isl_pw_multi_aff *pma2);
3802 __isl_give isl_multi_aff *isl_multi_aff_add(
3803 __isl_take isl_multi_aff *maff1,
3804 __isl_take isl_multi_aff *maff2);
3805 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3806 __isl_take isl_pw_multi_aff *pma1,
3807 __isl_take isl_pw_multi_aff *pma2);
3808 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3809 __isl_take isl_union_pw_multi_aff *upma1,
3810 __isl_take isl_union_pw_multi_aff *upma2);
3811 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3812 __isl_take isl_pw_multi_aff *pma1,
3813 __isl_take isl_pw_multi_aff *pma2);
3814 __isl_give isl_multi_aff *isl_multi_aff_scale(
3815 __isl_take isl_multi_aff *maff,
3817 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3818 __isl_take isl_pw_multi_aff *pma,
3819 __isl_take isl_set *set);
3820 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3821 __isl_take isl_pw_multi_aff *pma,
3822 __isl_take isl_set *set);
3823 __isl_give isl_multi_aff *isl_multi_aff_lift(
3824 __isl_take isl_multi_aff *maff,
3825 __isl_give isl_local_space **ls);
3826 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3827 __isl_take isl_pw_multi_aff *pma);
3828 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3829 __isl_take isl_multi_aff *multi,
3830 __isl_take isl_space *model);
3831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3832 __isl_take isl_pw_multi_aff *pma,
3833 __isl_take isl_space *model);
3834 __isl_give isl_pw_multi_aff *
3835 isl_pw_multi_aff_project_domain_on_params(
3836 __isl_take isl_pw_multi_aff *pma);
3837 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3838 __isl_take isl_multi_aff *maff,
3839 __isl_take isl_set *context);
3840 __isl_give isl_multi_aff *isl_multi_aff_gist(
3841 __isl_take isl_multi_aff *maff,
3842 __isl_take isl_set *context);
3843 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3844 __isl_take isl_pw_multi_aff *pma,
3845 __isl_take isl_set *set);
3846 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3847 __isl_take isl_pw_multi_aff *pma,
3848 __isl_take isl_set *set);
3849 __isl_give isl_set *isl_pw_multi_aff_domain(
3850 __isl_take isl_pw_multi_aff *pma);
3851 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3852 __isl_take isl_union_pw_multi_aff *upma);
3853 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3854 __isl_take isl_multi_aff *ma1, unsigned pos,
3855 __isl_take isl_multi_aff *ma2);
3856 __isl_give isl_multi_aff *isl_multi_aff_splice(
3857 __isl_take isl_multi_aff *ma1,
3858 unsigned in_pos, unsigned out_pos,
3859 __isl_take isl_multi_aff *ma2);
3860 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3861 __isl_take isl_multi_aff *ma1,
3862 __isl_take isl_multi_aff *ma2);
3863 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3864 __isl_take isl_multi_aff *ma1,
3865 __isl_take isl_multi_aff *ma2);
3866 __isl_give isl_multi_aff *isl_multi_aff_product(
3867 __isl_take isl_multi_aff *ma1,
3868 __isl_take isl_multi_aff *ma2);
3869 __isl_give isl_pw_multi_aff *
3870 isl_pw_multi_aff_range_product(
3871 __isl_take isl_pw_multi_aff *pma1,
3872 __isl_take isl_pw_multi_aff *pma2);
3873 __isl_give isl_pw_multi_aff *
3874 isl_pw_multi_aff_flat_range_product(
3875 __isl_take isl_pw_multi_aff *pma1,
3876 __isl_take isl_pw_multi_aff *pma2);
3877 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3878 __isl_take isl_pw_multi_aff *pma1,
3879 __isl_take isl_pw_multi_aff *pma2);
3880 __isl_give isl_union_pw_multi_aff *
3881 isl_union_pw_multi_aff_flat_range_product(
3882 __isl_take isl_union_pw_multi_aff *upma1,
3883 __isl_take isl_union_pw_multi_aff *upma2);
3884 __isl_give isl_multi_pw_aff *
3885 isl_multi_pw_aff_range_splice(
3886 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
3887 __isl_take isl_multi_pw_aff *mpa2);
3888 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
3889 __isl_take isl_multi_pw_aff *mpa1,
3890 unsigned in_pos, unsigned out_pos,
3891 __isl_take isl_multi_pw_aff *mpa2);
3892 __isl_give isl_multi_pw_aff *
3893 isl_multi_pw_aff_range_product(
3894 __isl_take isl_multi_pw_aff *mpa1,
3895 __isl_take isl_multi_pw_aff *mpa2);
3896 __isl_give isl_multi_pw_aff *
3897 isl_multi_pw_aff_flat_range_product(
3898 __isl_take isl_multi_pw_aff *mpa1,
3899 __isl_take isl_multi_pw_aff *mpa2);
3901 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3902 then it is assigned the local space that lies at the basis of
3903 the lifting applied.
3905 __isl_give isl_set *isl_multi_aff_lex_le_set(
3906 __isl_take isl_multi_aff *ma1,
3907 __isl_take isl_multi_aff *ma2);
3908 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3909 __isl_take isl_multi_aff *ma1,
3910 __isl_take isl_multi_aff *ma2);
3912 The function C<isl_multi_aff_lex_le_set> returns a set
3913 containing those elements in the shared domain space
3914 where C<ma1> is lexicographically smaller than or
3917 An expression can be read from input using
3919 #include <isl/aff.h>
3920 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3921 isl_ctx *ctx, const char *str);
3922 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3923 isl_ctx *ctx, const char *str);
3925 An expression can be printed using
3927 #include <isl/aff.h>
3928 __isl_give isl_printer *isl_printer_print_multi_aff(
3929 __isl_take isl_printer *p,
3930 __isl_keep isl_multi_aff *maff);
3931 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3932 __isl_take isl_printer *p,
3933 __isl_keep isl_pw_multi_aff *pma);
3934 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3935 __isl_take isl_printer *p,
3936 __isl_keep isl_union_pw_multi_aff *upma);
3937 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3938 __isl_take isl_printer *p,
3939 __isl_keep isl_multi_pw_aff *mpa);
3943 Points are elements of a set. They can be used to construct
3944 simple sets (boxes) or they can be used to represent the
3945 individual elements of a set.
3946 The zero point (the origin) can be created using
3948 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3950 The coordinates of a point can be inspected, set and changed
3953 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3954 enum isl_dim_type type, int pos, isl_int *v);
3955 __isl_give isl_point *isl_point_set_coordinate(
3956 __isl_take isl_point *pnt,
3957 enum isl_dim_type type, int pos, isl_int v);
3959 __isl_give isl_point *isl_point_add_ui(
3960 __isl_take isl_point *pnt,
3961 enum isl_dim_type type, int pos, unsigned val);
3962 __isl_give isl_point *isl_point_sub_ui(
3963 __isl_take isl_point *pnt,
3964 enum isl_dim_type type, int pos, unsigned val);
3966 Other properties can be obtained using
3968 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3970 Points can be copied or freed using
3972 __isl_give isl_point *isl_point_copy(
3973 __isl_keep isl_point *pnt);
3974 void isl_point_free(__isl_take isl_point *pnt);
3976 A singleton set can be created from a point using
3978 __isl_give isl_basic_set *isl_basic_set_from_point(
3979 __isl_take isl_point *pnt);
3980 __isl_give isl_set *isl_set_from_point(
3981 __isl_take isl_point *pnt);
3983 and a box can be created from two opposite extremal points using
3985 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3986 __isl_take isl_point *pnt1,
3987 __isl_take isl_point *pnt2);
3988 __isl_give isl_set *isl_set_box_from_points(
3989 __isl_take isl_point *pnt1,
3990 __isl_take isl_point *pnt2);
3992 All elements of a B<bounded> (union) set can be enumerated using
3993 the following functions.
3995 int isl_set_foreach_point(__isl_keep isl_set *set,
3996 int (*fn)(__isl_take isl_point *pnt, void *user),
3998 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3999 int (*fn)(__isl_take isl_point *pnt, void *user),
4002 The function C<fn> is called for each integer point in
4003 C<set> with as second argument the last argument of
4004 the C<isl_set_foreach_point> call. The function C<fn>
4005 should return C<0> on success and C<-1> on failure.
4006 In the latter case, C<isl_set_foreach_point> will stop
4007 enumerating and return C<-1> as well.
4008 If the enumeration is performed successfully and to completion,
4009 then C<isl_set_foreach_point> returns C<0>.
4011 To obtain a single point of a (basic) set, use
4013 __isl_give isl_point *isl_basic_set_sample_point(
4014 __isl_take isl_basic_set *bset);
4015 __isl_give isl_point *isl_set_sample_point(
4016 __isl_take isl_set *set);
4018 If C<set> does not contain any (integer) points, then the
4019 resulting point will be ``void'', a property that can be
4022 int isl_point_is_void(__isl_keep isl_point *pnt);
4024 =head2 Piecewise Quasipolynomials
4026 A piecewise quasipolynomial is a particular kind of function that maps
4027 a parametric point to a rational value.
4028 More specifically, a quasipolynomial is a polynomial expression in greatest
4029 integer parts of affine expressions of parameters and variables.
4030 A piecewise quasipolynomial is a subdivision of a given parametric
4031 domain into disjoint cells with a quasipolynomial associated to
4032 each cell. The value of the piecewise quasipolynomial at a given
4033 point is the value of the quasipolynomial associated to the cell
4034 that contains the point. Outside of the union of cells,
4035 the value is assumed to be zero.
4036 For example, the piecewise quasipolynomial
4038 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4040 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4041 A given piecewise quasipolynomial has a fixed domain dimension.
4042 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4043 defined over different domains.
4044 Piecewise quasipolynomials are mainly used by the C<barvinok>
4045 library for representing the number of elements in a parametric set or map.
4046 For example, the piecewise quasipolynomial above represents
4047 the number of points in the map
4049 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4051 =head3 Input and Output
4053 Piecewise quasipolynomials can be read from input using
4055 __isl_give isl_union_pw_qpolynomial *
4056 isl_union_pw_qpolynomial_read_from_str(
4057 isl_ctx *ctx, const char *str);
4059 Quasipolynomials and piecewise quasipolynomials can be printed
4060 using the following functions.
4062 __isl_give isl_printer *isl_printer_print_qpolynomial(
4063 __isl_take isl_printer *p,
4064 __isl_keep isl_qpolynomial *qp);
4066 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4067 __isl_take isl_printer *p,
4068 __isl_keep isl_pw_qpolynomial *pwqp);
4070 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4071 __isl_take isl_printer *p,
4072 __isl_keep isl_union_pw_qpolynomial *upwqp);
4074 The output format of the printer
4075 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4076 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4078 In case of printing in C<ISL_FORMAT_C>, the user may want
4079 to set the names of all dimensions
4081 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4082 __isl_take isl_qpolynomial *qp,
4083 enum isl_dim_type type, unsigned pos,
4085 __isl_give isl_pw_qpolynomial *
4086 isl_pw_qpolynomial_set_dim_name(
4087 __isl_take isl_pw_qpolynomial *pwqp,
4088 enum isl_dim_type type, unsigned pos,
4091 =head3 Creating New (Piecewise) Quasipolynomials
4093 Some simple quasipolynomials can be created using the following functions.
4094 More complicated quasipolynomials can be created by applying
4095 operations such as addition and multiplication
4096 on the resulting quasipolynomials
4098 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4099 __isl_take isl_space *domain);
4100 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4101 __isl_take isl_space *domain);
4102 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4103 __isl_take isl_space *domain);
4104 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4105 __isl_take isl_space *domain);
4106 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4107 __isl_take isl_space *domain);
4108 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4109 __isl_take isl_space *domain,
4110 const isl_int n, const isl_int d);
4111 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4112 __isl_take isl_space *domain,
4113 enum isl_dim_type type, unsigned pos);
4114 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4115 __isl_take isl_aff *aff);
4117 Note that the space in which a quasipolynomial lives is a map space
4118 with a one-dimensional range. The C<domain> argument in some of
4119 the functions above corresponds to the domain of this map space.
4121 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4122 with a single cell can be created using the following functions.
4123 Multiple of these single cell piecewise quasipolynomials can
4124 be combined to create more complicated piecewise quasipolynomials.
4126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4127 __isl_take isl_space *space);
4128 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4129 __isl_take isl_set *set,
4130 __isl_take isl_qpolynomial *qp);
4131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4132 __isl_take isl_qpolynomial *qp);
4133 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4134 __isl_take isl_pw_aff *pwaff);
4136 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4137 __isl_take isl_space *space);
4138 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4139 __isl_take isl_pw_qpolynomial *pwqp);
4140 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4141 __isl_take isl_union_pw_qpolynomial *upwqp,
4142 __isl_take isl_pw_qpolynomial *pwqp);
4144 Quasipolynomials can be copied and freed again using the following
4147 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4148 __isl_keep isl_qpolynomial *qp);
4149 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4151 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4152 __isl_keep isl_pw_qpolynomial *pwqp);
4153 void *isl_pw_qpolynomial_free(
4154 __isl_take isl_pw_qpolynomial *pwqp);
4156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4157 __isl_keep isl_union_pw_qpolynomial *upwqp);
4158 void *isl_union_pw_qpolynomial_free(
4159 __isl_take isl_union_pw_qpolynomial *upwqp);
4161 =head3 Inspecting (Piecewise) Quasipolynomials
4163 To iterate over all piecewise quasipolynomials in a union
4164 piecewise quasipolynomial, use the following function
4166 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4167 __isl_keep isl_union_pw_qpolynomial *upwqp,
4168 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4171 To extract the piecewise quasipolynomial in a given space from a union, use
4173 __isl_give isl_pw_qpolynomial *
4174 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4175 __isl_keep isl_union_pw_qpolynomial *upwqp,
4176 __isl_take isl_space *space);
4178 To iterate over the cells in a piecewise quasipolynomial,
4179 use either of the following two functions
4181 int isl_pw_qpolynomial_foreach_piece(
4182 __isl_keep isl_pw_qpolynomial *pwqp,
4183 int (*fn)(__isl_take isl_set *set,
4184 __isl_take isl_qpolynomial *qp,
4185 void *user), void *user);
4186 int isl_pw_qpolynomial_foreach_lifted_piece(
4187 __isl_keep isl_pw_qpolynomial *pwqp,
4188 int (*fn)(__isl_take isl_set *set,
4189 __isl_take isl_qpolynomial *qp,
4190 void *user), void *user);
4192 As usual, the function C<fn> should return C<0> on success
4193 and C<-1> on failure. The difference between
4194 C<isl_pw_qpolynomial_foreach_piece> and
4195 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4196 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4197 compute unique representations for all existentially quantified
4198 variables and then turn these existentially quantified variables
4199 into extra set variables, adapting the associated quasipolynomial
4200 accordingly. This means that the C<set> passed to C<fn>
4201 will not have any existentially quantified variables, but that
4202 the dimensions of the sets may be different for different
4203 invocations of C<fn>.
4205 To iterate over all terms in a quasipolynomial,
4208 int isl_qpolynomial_foreach_term(
4209 __isl_keep isl_qpolynomial *qp,
4210 int (*fn)(__isl_take isl_term *term,
4211 void *user), void *user);
4213 The terms themselves can be inspected and freed using
4216 unsigned isl_term_dim(__isl_keep isl_term *term,
4217 enum isl_dim_type type);
4218 void isl_term_get_num(__isl_keep isl_term *term,
4220 void isl_term_get_den(__isl_keep isl_term *term,
4222 int isl_term_get_exp(__isl_keep isl_term *term,
4223 enum isl_dim_type type, unsigned pos);
4224 __isl_give isl_aff *isl_term_get_div(
4225 __isl_keep isl_term *term, unsigned pos);
4226 void isl_term_free(__isl_take isl_term *term);
4228 Each term is a product of parameters, set variables and
4229 integer divisions. The function C<isl_term_get_exp>
4230 returns the exponent of a given dimensions in the given term.
4231 The C<isl_int>s in the arguments of C<isl_term_get_num>
4232 and C<isl_term_get_den> need to have been initialized
4233 using C<isl_int_init> before calling these functions.
4235 =head3 Properties of (Piecewise) Quasipolynomials
4237 To check whether a quasipolynomial is actually a constant,
4238 use the following function.
4240 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4241 isl_int *n, isl_int *d);
4243 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4244 then the numerator and denominator of the constant
4245 are returned in C<*n> and C<*d>, respectively.
4247 To check whether two union piecewise quasipolynomials are
4248 obviously equal, use
4250 int isl_union_pw_qpolynomial_plain_is_equal(
4251 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4252 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4254 =head3 Operations on (Piecewise) Quasipolynomials
4256 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4257 __isl_take isl_qpolynomial *qp, isl_int v);
4258 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4259 __isl_take isl_qpolynomial *qp);
4260 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4261 __isl_take isl_qpolynomial *qp1,
4262 __isl_take isl_qpolynomial *qp2);
4263 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4264 __isl_take isl_qpolynomial *qp1,
4265 __isl_take isl_qpolynomial *qp2);
4266 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4267 __isl_take isl_qpolynomial *qp1,
4268 __isl_take isl_qpolynomial *qp2);
4269 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4270 __isl_take isl_qpolynomial *qp, unsigned exponent);
4272 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4273 __isl_take isl_pw_qpolynomial *pwqp1,
4274 __isl_take isl_pw_qpolynomial *pwqp2);
4275 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4276 __isl_take isl_pw_qpolynomial *pwqp1,
4277 __isl_take isl_pw_qpolynomial *pwqp2);
4278 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4279 __isl_take isl_pw_qpolynomial *pwqp1,
4280 __isl_take isl_pw_qpolynomial *pwqp2);
4281 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4282 __isl_take isl_pw_qpolynomial *pwqp);
4283 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4284 __isl_take isl_pw_qpolynomial *pwqp1,
4285 __isl_take isl_pw_qpolynomial *pwqp2);
4286 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4287 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4289 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4290 __isl_take isl_union_pw_qpolynomial *upwqp1,
4291 __isl_take isl_union_pw_qpolynomial *upwqp2);
4292 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4293 __isl_take isl_union_pw_qpolynomial *upwqp1,
4294 __isl_take isl_union_pw_qpolynomial *upwqp2);
4295 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4296 __isl_take isl_union_pw_qpolynomial *upwqp1,
4297 __isl_take isl_union_pw_qpolynomial *upwqp2);
4299 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4300 __isl_take isl_pw_qpolynomial *pwqp,
4301 __isl_take isl_point *pnt);
4303 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4304 __isl_take isl_union_pw_qpolynomial *upwqp,
4305 __isl_take isl_point *pnt);
4307 __isl_give isl_set *isl_pw_qpolynomial_domain(
4308 __isl_take isl_pw_qpolynomial *pwqp);
4309 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4310 __isl_take isl_pw_qpolynomial *pwpq,
4311 __isl_take isl_set *set);
4312 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4313 __isl_take isl_pw_qpolynomial *pwpq,
4314 __isl_take isl_set *set);
4316 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4317 __isl_take isl_union_pw_qpolynomial *upwqp);
4318 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4319 __isl_take isl_union_pw_qpolynomial *upwpq,
4320 __isl_take isl_union_set *uset);
4321 __isl_give isl_union_pw_qpolynomial *
4322 isl_union_pw_qpolynomial_intersect_params(
4323 __isl_take isl_union_pw_qpolynomial *upwpq,
4324 __isl_take isl_set *set);
4326 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4327 __isl_take isl_qpolynomial *qp,
4328 __isl_take isl_space *model);
4330 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4331 __isl_take isl_qpolynomial *qp);
4332 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4333 __isl_take isl_pw_qpolynomial *pwqp);
4335 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4336 __isl_take isl_union_pw_qpolynomial *upwqp);
4338 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4339 __isl_take isl_qpolynomial *qp,
4340 __isl_take isl_set *context);
4341 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4342 __isl_take isl_qpolynomial *qp,
4343 __isl_take isl_set *context);
4345 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4346 __isl_take isl_pw_qpolynomial *pwqp,
4347 __isl_take isl_set *context);
4348 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4349 __isl_take isl_pw_qpolynomial *pwqp,
4350 __isl_take isl_set *context);
4352 __isl_give isl_union_pw_qpolynomial *
4353 isl_union_pw_qpolynomial_gist_params(
4354 __isl_take isl_union_pw_qpolynomial *upwqp,
4355 __isl_take isl_set *context);
4356 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4357 __isl_take isl_union_pw_qpolynomial *upwqp,
4358 __isl_take isl_union_set *context);
4360 The gist operation applies the gist operation to each of
4361 the cells in the domain of the input piecewise quasipolynomial.
4362 The context is also exploited
4363 to simplify the quasipolynomials associated to each cell.
4365 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4366 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4367 __isl_give isl_union_pw_qpolynomial *
4368 isl_union_pw_qpolynomial_to_polynomial(
4369 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4371 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4372 the polynomial will be an overapproximation. If C<sign> is negative,
4373 it will be an underapproximation. If C<sign> is zero, the approximation
4374 will lie somewhere in between.
4376 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4378 A piecewise quasipolynomial reduction is a piecewise
4379 reduction (or fold) of quasipolynomials.
4380 In particular, the reduction can be maximum or a minimum.
4381 The objects are mainly used to represent the result of
4382 an upper or lower bound on a quasipolynomial over its domain,
4383 i.e., as the result of the following function.
4385 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4386 __isl_take isl_pw_qpolynomial *pwqp,
4387 enum isl_fold type, int *tight);
4389 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4390 __isl_take isl_union_pw_qpolynomial *upwqp,
4391 enum isl_fold type, int *tight);
4393 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4394 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4395 is the returned bound is known be tight, i.e., for each value
4396 of the parameters there is at least
4397 one element in the domain that reaches the bound.
4398 If the domain of C<pwqp> is not wrapping, then the bound is computed
4399 over all elements in that domain and the result has a purely parametric
4400 domain. If the domain of C<pwqp> is wrapping, then the bound is
4401 computed over the range of the wrapped relation. The domain of the
4402 wrapped relation becomes the domain of the result.
4404 A (piecewise) quasipolynomial reduction can be copied or freed using the
4405 following functions.
4407 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4408 __isl_keep isl_qpolynomial_fold *fold);
4409 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4410 __isl_keep isl_pw_qpolynomial_fold *pwf);
4411 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4412 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4413 void isl_qpolynomial_fold_free(
4414 __isl_take isl_qpolynomial_fold *fold);
4415 void *isl_pw_qpolynomial_fold_free(
4416 __isl_take isl_pw_qpolynomial_fold *pwf);
4417 void *isl_union_pw_qpolynomial_fold_free(
4418 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4420 =head3 Printing Piecewise Quasipolynomial Reductions
4422 Piecewise quasipolynomial reductions can be printed
4423 using the following function.
4425 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4426 __isl_take isl_printer *p,
4427 __isl_keep isl_pw_qpolynomial_fold *pwf);
4428 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4429 __isl_take isl_printer *p,
4430 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4432 For C<isl_printer_print_pw_qpolynomial_fold>,
4433 output format of the printer
4434 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4435 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4436 output format of the printer
4437 needs to be set to C<ISL_FORMAT_ISL>.
4438 In case of printing in C<ISL_FORMAT_C>, the user may want
4439 to set the names of all dimensions
4441 __isl_give isl_pw_qpolynomial_fold *
4442 isl_pw_qpolynomial_fold_set_dim_name(
4443 __isl_take isl_pw_qpolynomial_fold *pwf,
4444 enum isl_dim_type type, unsigned pos,
4447 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4449 To iterate over all piecewise quasipolynomial reductions in a union
4450 piecewise quasipolynomial reduction, use the following function
4452 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4453 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4454 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4455 void *user), void *user);
4457 To iterate over the cells in a piecewise quasipolynomial reduction,
4458 use either of the following two functions
4460 int isl_pw_qpolynomial_fold_foreach_piece(
4461 __isl_keep isl_pw_qpolynomial_fold *pwf,
4462 int (*fn)(__isl_take isl_set *set,
4463 __isl_take isl_qpolynomial_fold *fold,
4464 void *user), void *user);
4465 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4466 __isl_keep isl_pw_qpolynomial_fold *pwf,
4467 int (*fn)(__isl_take isl_set *set,
4468 __isl_take isl_qpolynomial_fold *fold,
4469 void *user), void *user);
4471 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4472 of the difference between these two functions.
4474 To iterate over all quasipolynomials in a reduction, use
4476 int isl_qpolynomial_fold_foreach_qpolynomial(
4477 __isl_keep isl_qpolynomial_fold *fold,
4478 int (*fn)(__isl_take isl_qpolynomial *qp,
4479 void *user), void *user);
4481 =head3 Properties of Piecewise Quasipolynomial Reductions
4483 To check whether two union piecewise quasipolynomial reductions are
4484 obviously equal, use
4486 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4487 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4488 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4490 =head3 Operations on Piecewise Quasipolynomial Reductions
4492 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4493 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4495 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4496 __isl_take isl_pw_qpolynomial_fold *pwf1,
4497 __isl_take isl_pw_qpolynomial_fold *pwf2);
4499 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4500 __isl_take isl_pw_qpolynomial_fold *pwf1,
4501 __isl_take isl_pw_qpolynomial_fold *pwf2);
4503 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4504 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4505 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4507 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4508 __isl_take isl_pw_qpolynomial_fold *pwf,
4509 __isl_take isl_point *pnt);
4511 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4512 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4513 __isl_take isl_point *pnt);
4515 __isl_give isl_pw_qpolynomial_fold *
4516 isl_pw_qpolynomial_fold_intersect_params(
4517 __isl_take isl_pw_qpolynomial_fold *pwf,
4518 __isl_take isl_set *set);
4520 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4521 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4522 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4523 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4524 __isl_take isl_union_set *uset);
4525 __isl_give isl_union_pw_qpolynomial_fold *
4526 isl_union_pw_qpolynomial_fold_intersect_params(
4527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4528 __isl_take isl_set *set);
4530 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4531 __isl_take isl_pw_qpolynomial_fold *pwf);
4533 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4534 __isl_take isl_pw_qpolynomial_fold *pwf);
4536 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4537 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4539 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4540 __isl_take isl_qpolynomial_fold *fold,
4541 __isl_take isl_set *context);
4542 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4543 __isl_take isl_qpolynomial_fold *fold,
4544 __isl_take isl_set *context);
4546 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4547 __isl_take isl_pw_qpolynomial_fold *pwf,
4548 __isl_take isl_set *context);
4549 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4550 __isl_take isl_pw_qpolynomial_fold *pwf,
4551 __isl_take isl_set *context);
4553 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4554 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4555 __isl_take isl_union_set *context);
4556 __isl_give isl_union_pw_qpolynomial_fold *
4557 isl_union_pw_qpolynomial_fold_gist_params(
4558 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4559 __isl_take isl_set *context);
4561 The gist operation applies the gist operation to each of
4562 the cells in the domain of the input piecewise quasipolynomial reduction.
4563 In future, the operation will also exploit the context
4564 to simplify the quasipolynomial reductions associated to each cell.
4566 __isl_give isl_pw_qpolynomial_fold *
4567 isl_set_apply_pw_qpolynomial_fold(
4568 __isl_take isl_set *set,
4569 __isl_take isl_pw_qpolynomial_fold *pwf,
4571 __isl_give isl_pw_qpolynomial_fold *
4572 isl_map_apply_pw_qpolynomial_fold(
4573 __isl_take isl_map *map,
4574 __isl_take isl_pw_qpolynomial_fold *pwf,
4576 __isl_give isl_union_pw_qpolynomial_fold *
4577 isl_union_set_apply_union_pw_qpolynomial_fold(
4578 __isl_take isl_union_set *uset,
4579 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4581 __isl_give isl_union_pw_qpolynomial_fold *
4582 isl_union_map_apply_union_pw_qpolynomial_fold(
4583 __isl_take isl_union_map *umap,
4584 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4587 The functions taking a map
4588 compose the given map with the given piecewise quasipolynomial reduction.
4589 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4590 over all elements in the intersection of the range of the map
4591 and the domain of the piecewise quasipolynomial reduction
4592 as a function of an element in the domain of the map.
4593 The functions taking a set compute a bound over all elements in the
4594 intersection of the set and the domain of the
4595 piecewise quasipolynomial reduction.
4597 =head2 Dependence Analysis
4599 C<isl> contains specialized functionality for performing
4600 array dataflow analysis. That is, given a I<sink> access relation
4601 and a collection of possible I<source> access relations,
4602 C<isl> can compute relations that describe
4603 for each iteration of the sink access, which iteration
4604 of which of the source access relations was the last
4605 to access the same data element before the given iteration
4607 The resulting dependence relations map source iterations
4608 to the corresponding sink iterations.
4609 To compute standard flow dependences, the sink should be
4610 a read, while the sources should be writes.
4611 If any of the source accesses are marked as being I<may>
4612 accesses, then there will be a dependence from the last
4613 I<must> access B<and> from any I<may> access that follows
4614 this last I<must> access.
4615 In particular, if I<all> sources are I<may> accesses,
4616 then memory based dependence analysis is performed.
4617 If, on the other hand, all sources are I<must> accesses,
4618 then value based dependence analysis is performed.
4620 #include <isl/flow.h>
4622 typedef int (*isl_access_level_before)(void *first, void *second);
4624 __isl_give isl_access_info *isl_access_info_alloc(
4625 __isl_take isl_map *sink,
4626 void *sink_user, isl_access_level_before fn,
4628 __isl_give isl_access_info *isl_access_info_add_source(
4629 __isl_take isl_access_info *acc,
4630 __isl_take isl_map *source, int must,
4632 void *isl_access_info_free(__isl_take isl_access_info *acc);
4634 __isl_give isl_flow *isl_access_info_compute_flow(
4635 __isl_take isl_access_info *acc);
4637 int isl_flow_foreach(__isl_keep isl_flow *deps,
4638 int (*fn)(__isl_take isl_map *dep, int must,
4639 void *dep_user, void *user),
4641 __isl_give isl_map *isl_flow_get_no_source(
4642 __isl_keep isl_flow *deps, int must);
4643 void isl_flow_free(__isl_take isl_flow *deps);
4645 The function C<isl_access_info_compute_flow> performs the actual
4646 dependence analysis. The other functions are used to construct
4647 the input for this function or to read off the output.
4649 The input is collected in an C<isl_access_info>, which can
4650 be created through a call to C<isl_access_info_alloc>.
4651 The arguments to this functions are the sink access relation
4652 C<sink>, a token C<sink_user> used to identify the sink
4653 access to the user, a callback function for specifying the
4654 relative order of source and sink accesses, and the number
4655 of source access relations that will be added.
4656 The callback function has type C<int (*)(void *first, void *second)>.
4657 The function is called with two user supplied tokens identifying
4658 either a source or the sink and it should return the shared nesting
4659 level and the relative order of the two accesses.
4660 In particular, let I<n> be the number of loops shared by
4661 the two accesses. If C<first> precedes C<second> textually,
4662 then the function should return I<2 * n + 1>; otherwise,
4663 it should return I<2 * n>.
4664 The sources can be added to the C<isl_access_info> by performing
4665 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4666 C<must> indicates whether the source is a I<must> access
4667 or a I<may> access. Note that a multi-valued access relation
4668 should only be marked I<must> if every iteration in the domain
4669 of the relation accesses I<all> elements in its image.
4670 The C<source_user> token is again used to identify
4671 the source access. The range of the source access relation
4672 C<source> should have the same dimension as the range
4673 of the sink access relation.
4674 The C<isl_access_info_free> function should usually not be
4675 called explicitly, because it is called implicitly by
4676 C<isl_access_info_compute_flow>.
4678 The result of the dependence analysis is collected in an
4679 C<isl_flow>. There may be elements of
4680 the sink access for which no preceding source access could be
4681 found or for which all preceding sources are I<may> accesses.
4682 The relations containing these elements can be obtained through
4683 calls to C<isl_flow_get_no_source>, the first with C<must> set
4684 and the second with C<must> unset.
4685 In the case of standard flow dependence analysis,
4686 with the sink a read and the sources I<must> writes,
4687 the first relation corresponds to the reads from uninitialized
4688 array elements and the second relation is empty.
4689 The actual flow dependences can be extracted using
4690 C<isl_flow_foreach>. This function will call the user-specified
4691 callback function C<fn> for each B<non-empty> dependence between
4692 a source and the sink. The callback function is called
4693 with four arguments, the actual flow dependence relation
4694 mapping source iterations to sink iterations, a boolean that
4695 indicates whether it is a I<must> or I<may> dependence, a token
4696 identifying the source and an additional C<void *> with value
4697 equal to the third argument of the C<isl_flow_foreach> call.
4698 A dependence is marked I<must> if it originates from a I<must>
4699 source and if it is not followed by any I<may> sources.
4701 After finishing with an C<isl_flow>, the user should call
4702 C<isl_flow_free> to free all associated memory.
4704 A higher-level interface to dependence analysis is provided
4705 by the following function.
4707 #include <isl/flow.h>
4709 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4710 __isl_take isl_union_map *must_source,
4711 __isl_take isl_union_map *may_source,
4712 __isl_take isl_union_map *schedule,
4713 __isl_give isl_union_map **must_dep,
4714 __isl_give isl_union_map **may_dep,
4715 __isl_give isl_union_map **must_no_source,
4716 __isl_give isl_union_map **may_no_source);
4718 The arrays are identified by the tuple names of the ranges
4719 of the accesses. The iteration domains by the tuple names
4720 of the domains of the accesses and of the schedule.
4721 The relative order of the iteration domains is given by the
4722 schedule. The relations returned through C<must_no_source>
4723 and C<may_no_source> are subsets of C<sink>.
4724 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4725 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4726 any of the other arguments is treated as an error.
4728 =head3 Interaction with Dependence Analysis
4730 During the dependence analysis, we frequently need to perform
4731 the following operation. Given a relation between sink iterations
4732 and potential source iterations from a particular source domain,
4733 what is the last potential source iteration corresponding to each
4734 sink iteration. It can sometimes be convenient to adjust
4735 the set of potential source iterations before or after each such operation.
4736 The prototypical example is fuzzy array dataflow analysis,
4737 where we need to analyze if, based on data-dependent constraints,
4738 the sink iteration can ever be executed without one or more of
4739 the corresponding potential source iterations being executed.
4740 If so, we can introduce extra parameters and select an unknown
4741 but fixed source iteration from the potential source iterations.
4742 To be able to perform such manipulations, C<isl> provides the following
4745 #include <isl/flow.h>
4747 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4748 __isl_keep isl_map *source_map,
4749 __isl_keep isl_set *sink, void *source_user,
4751 __isl_give isl_access_info *isl_access_info_set_restrict(
4752 __isl_take isl_access_info *acc,
4753 isl_access_restrict fn, void *user);
4755 The function C<isl_access_info_set_restrict> should be called
4756 before calling C<isl_access_info_compute_flow> and registers a callback function
4757 that will be called any time C<isl> is about to compute the last
4758 potential source. The first argument is the (reverse) proto-dependence,
4759 mapping sink iterations to potential source iterations.
4760 The second argument represents the sink iterations for which
4761 we want to compute the last source iteration.
4762 The third argument is the token corresponding to the source
4763 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4764 The callback is expected to return a restriction on either the input or
4765 the output of the operation computing the last potential source.
4766 If the input needs to be restricted then restrictions are needed
4767 for both the source and the sink iterations. The sink iterations
4768 and the potential source iterations will be intersected with these sets.
4769 If the output needs to be restricted then only a restriction on the source
4770 iterations is required.
4771 If any error occurs, the callback should return C<NULL>.
4772 An C<isl_restriction> object can be created, freed and inspected
4773 using the following functions.
4775 #include <isl/flow.h>
4777 __isl_give isl_restriction *isl_restriction_input(
4778 __isl_take isl_set *source_restr,
4779 __isl_take isl_set *sink_restr);
4780 __isl_give isl_restriction *isl_restriction_output(
4781 __isl_take isl_set *source_restr);
4782 __isl_give isl_restriction *isl_restriction_none(
4783 __isl_take isl_map *source_map);
4784 __isl_give isl_restriction *isl_restriction_empty(
4785 __isl_take isl_map *source_map);
4786 void *isl_restriction_free(
4787 __isl_take isl_restriction *restr);
4788 isl_ctx *isl_restriction_get_ctx(
4789 __isl_keep isl_restriction *restr);
4791 C<isl_restriction_none> and C<isl_restriction_empty> are special
4792 cases of C<isl_restriction_input>. C<isl_restriction_none>
4793 is essentially equivalent to
4795 isl_restriction_input(isl_set_universe(
4796 isl_space_range(isl_map_get_space(source_map))),
4798 isl_space_domain(isl_map_get_space(source_map))));
4800 whereas C<isl_restriction_empty> is essentially equivalent to
4802 isl_restriction_input(isl_set_empty(
4803 isl_space_range(isl_map_get_space(source_map))),
4805 isl_space_domain(isl_map_get_space(source_map))));
4809 B<The functionality described in this section is fairly new
4810 and may be subject to change.>
4812 The following function can be used to compute a schedule
4813 for a union of domains.
4814 By default, the algorithm used to construct the schedule is similar
4815 to that of C<Pluto>.
4816 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4818 The generated schedule respects all C<validity> dependences.
4819 That is, all dependence distances over these dependences in the
4820 scheduled space are lexicographically positive.
4821 The default algorithm tries to minimize the dependence distances over
4822 C<proximity> dependences.
4823 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4824 for groups of domains where the dependence distances have only
4825 non-negative values.
4826 When using Feautrier's algorithm, the C<proximity> dependence
4827 distances are only minimized during the extension to a
4828 full-dimensional schedule.
4830 #include <isl/schedule.h>
4831 __isl_give isl_schedule *isl_union_set_compute_schedule(
4832 __isl_take isl_union_set *domain,
4833 __isl_take isl_union_map *validity,
4834 __isl_take isl_union_map *proximity);
4835 void *isl_schedule_free(__isl_take isl_schedule *sched);
4837 A mapping from the domains to the scheduled space can be obtained
4838 from an C<isl_schedule> using the following function.
4840 __isl_give isl_union_map *isl_schedule_get_map(
4841 __isl_keep isl_schedule *sched);
4843 A representation of the schedule can be printed using
4845 __isl_give isl_printer *isl_printer_print_schedule(
4846 __isl_take isl_printer *p,
4847 __isl_keep isl_schedule *schedule);
4849 A representation of the schedule as a forest of bands can be obtained
4850 using the following function.
4852 __isl_give isl_band_list *isl_schedule_get_band_forest(
4853 __isl_keep isl_schedule *schedule);
4855 The individual bands can be visited in depth-first post-order
4856 using the following function.
4858 #include <isl/schedule.h>
4859 int isl_schedule_foreach_band(
4860 __isl_keep isl_schedule *sched,
4861 int (*fn)(__isl_keep isl_band *band, void *user),
4864 The list can be manipulated as explained in L<"Lists">.
4865 The bands inside the list can be copied and freed using the following
4868 #include <isl/band.h>
4869 __isl_give isl_band *isl_band_copy(
4870 __isl_keep isl_band *band);
4871 void *isl_band_free(__isl_take isl_band *band);
4873 Each band contains zero or more scheduling dimensions.
4874 These are referred to as the members of the band.
4875 The section of the schedule that corresponds to the band is
4876 referred to as the partial schedule of the band.
4877 For those nodes that participate in a band, the outer scheduling
4878 dimensions form the prefix schedule, while the inner scheduling
4879 dimensions form the suffix schedule.
4880 That is, if we take a cut of the band forest, then the union of
4881 the concatenations of the prefix, partial and suffix schedules of
4882 each band in the cut is equal to the entire schedule (modulo
4883 some possible padding at the end with zero scheduling dimensions).
4884 The properties of a band can be inspected using the following functions.
4886 #include <isl/band.h>
4887 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4889 int isl_band_has_children(__isl_keep isl_band *band);
4890 __isl_give isl_band_list *isl_band_get_children(
4891 __isl_keep isl_band *band);
4893 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4894 __isl_keep isl_band *band);
4895 __isl_give isl_union_map *isl_band_get_partial_schedule(
4896 __isl_keep isl_band *band);
4897 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4898 __isl_keep isl_band *band);
4900 int isl_band_n_member(__isl_keep isl_band *band);
4901 int isl_band_member_is_zero_distance(
4902 __isl_keep isl_band *band, int pos);
4904 int isl_band_list_foreach_band(
4905 __isl_keep isl_band_list *list,
4906 int (*fn)(__isl_keep isl_band *band, void *user),
4909 Note that a scheduling dimension is considered to be ``zero
4910 distance'' if it does not carry any proximity dependences
4912 That is, if the dependence distances of the proximity
4913 dependences are all zero in that direction (for fixed
4914 iterations of outer bands).
4915 Like C<isl_schedule_foreach_band>,
4916 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4917 in depth-first post-order.
4919 A band can be tiled using the following function.
4921 #include <isl/band.h>
4922 int isl_band_tile(__isl_keep isl_band *band,
4923 __isl_take isl_vec *sizes);
4925 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4927 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4929 The C<isl_band_tile> function tiles the band using the given tile sizes
4930 inside its schedule.
4931 A new child band is created to represent the point loops and it is
4932 inserted between the modified band and its children.
4933 The C<tile_scale_tile_loops> option specifies whether the tile
4934 loops iterators should be scaled by the tile sizes.
4936 A representation of the band can be printed using
4938 #include <isl/band.h>
4939 __isl_give isl_printer *isl_printer_print_band(
4940 __isl_take isl_printer *p,
4941 __isl_keep isl_band *band);
4945 #include <isl/schedule.h>
4946 int isl_options_set_schedule_max_coefficient(
4947 isl_ctx *ctx, int val);
4948 int isl_options_get_schedule_max_coefficient(
4950 int isl_options_set_schedule_max_constant_term(
4951 isl_ctx *ctx, int val);
4952 int isl_options_get_schedule_max_constant_term(
4954 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4955 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4956 int isl_options_set_schedule_maximize_band_depth(
4957 isl_ctx *ctx, int val);
4958 int isl_options_get_schedule_maximize_band_depth(
4960 int isl_options_set_schedule_outer_zero_distance(
4961 isl_ctx *ctx, int val);
4962 int isl_options_get_schedule_outer_zero_distance(
4964 int isl_options_set_schedule_split_scaled(
4965 isl_ctx *ctx, int val);
4966 int isl_options_get_schedule_split_scaled(
4968 int isl_options_set_schedule_algorithm(
4969 isl_ctx *ctx, int val);
4970 int isl_options_get_schedule_algorithm(
4972 int isl_options_set_schedule_separate_components(
4973 isl_ctx *ctx, int val);
4974 int isl_options_get_schedule_separate_components(
4979 =item * schedule_max_coefficient
4981 This option enforces that the coefficients for variable and parameter
4982 dimensions in the calculated schedule are not larger than the specified value.
4983 This option can significantly increase the speed of the scheduling calculation
4984 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4985 this option does not introduce bounds on the variable or parameter
4988 =item * schedule_max_constant_term
4990 This option enforces that the constant coefficients in the calculated schedule
4991 are not larger than the maximal constant term. This option can significantly
4992 increase the speed of the scheduling calculation and may also prevent fusing of
4993 unrelated dimensions. A value of -1 means that this option does not introduce
4994 bounds on the constant coefficients.
4996 =item * schedule_fuse
4998 This option controls the level of fusion.
4999 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5000 resulting schedule will be distributed as much as possible.
5001 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5002 try to fuse loops in the resulting schedule.
5004 =item * schedule_maximize_band_depth
5006 If this option is set, we do not split bands at the point
5007 where we detect splitting is necessary. Instead, we
5008 backtrack and split bands as early as possible. This
5009 reduces the number of splits and maximizes the width of
5010 the bands. Wider bands give more possibilities for tiling.
5011 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5012 then bands will be split as early as possible, even if there is no need.
5013 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5015 =item * schedule_outer_zero_distance
5017 If this option is set, then we try to construct schedules
5018 where the outermost scheduling dimension in each band
5019 results in a zero dependence distance over the proximity
5022 =item * schedule_split_scaled
5024 If this option is set, then we try to construct schedules in which the
5025 constant term is split off from the linear part if the linear parts of
5026 the scheduling rows for all nodes in the graphs have a common non-trivial
5028 The constant term is then placed in a separate band and the linear
5031 =item * schedule_algorithm
5033 Selects the scheduling algorithm to be used.
5034 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5035 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5037 =item * schedule_separate_components
5039 If at any point the dependence graph contains any (weakly connected) components,
5040 then these components are scheduled separately.
5041 If this option is not set, then some iterations of the domains
5042 in these components may be scheduled together.
5043 If this option is set, then the components are given consecutive
5048 =head2 Parametric Vertex Enumeration
5050 The parametric vertex enumeration described in this section
5051 is mainly intended to be used internally and by the C<barvinok>
5054 #include <isl/vertices.h>
5055 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5056 __isl_keep isl_basic_set *bset);
5058 The function C<isl_basic_set_compute_vertices> performs the
5059 actual computation of the parametric vertices and the chamber
5060 decomposition and store the result in an C<isl_vertices> object.
5061 This information can be queried by either iterating over all
5062 the vertices or iterating over all the chambers or cells
5063 and then iterating over all vertices that are active on the chamber.
5065 int isl_vertices_foreach_vertex(
5066 __isl_keep isl_vertices *vertices,
5067 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5070 int isl_vertices_foreach_cell(
5071 __isl_keep isl_vertices *vertices,
5072 int (*fn)(__isl_take isl_cell *cell, void *user),
5074 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5075 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5078 Other operations that can be performed on an C<isl_vertices> object are
5081 isl_ctx *isl_vertices_get_ctx(
5082 __isl_keep isl_vertices *vertices);
5083 int isl_vertices_get_n_vertices(
5084 __isl_keep isl_vertices *vertices);
5085 void isl_vertices_free(__isl_take isl_vertices *vertices);
5087 Vertices can be inspected and destroyed using the following functions.
5089 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5090 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5091 __isl_give isl_basic_set *isl_vertex_get_domain(
5092 __isl_keep isl_vertex *vertex);
5093 __isl_give isl_basic_set *isl_vertex_get_expr(
5094 __isl_keep isl_vertex *vertex);
5095 void isl_vertex_free(__isl_take isl_vertex *vertex);
5097 C<isl_vertex_get_expr> returns a singleton parametric set describing
5098 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5100 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5101 B<rational> basic sets, so they should mainly be used for inspection
5102 and should not be mixed with integer sets.
5104 Chambers can be inspected and destroyed using the following functions.
5106 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5107 __isl_give isl_basic_set *isl_cell_get_domain(
5108 __isl_keep isl_cell *cell);
5109 void isl_cell_free(__isl_take isl_cell *cell);
5113 Although C<isl> is mainly meant to be used as a library,
5114 it also contains some basic applications that use some
5115 of the functionality of C<isl>.
5116 The input may be specified in either the L<isl format>
5117 or the L<PolyLib format>.
5119 =head2 C<isl_polyhedron_sample>
5121 C<isl_polyhedron_sample> takes a polyhedron as input and prints
5122 an integer element of the polyhedron, if there is any.
5123 The first column in the output is the denominator and is always
5124 equal to 1. If the polyhedron contains no integer points,
5125 then a vector of length zero is printed.
5129 C<isl_pip> takes the same input as the C<example> program
5130 from the C<piplib> distribution, i.e., a set of constraints
5131 on the parameters, a line containing only -1 and finally a set
5132 of constraints on a parametric polyhedron.
5133 The coefficients of the parameters appear in the last columns
5134 (but before the final constant column).
5135 The output is the lexicographic minimum of the parametric polyhedron.
5136 As C<isl> currently does not have its own output format, the output
5137 is just a dump of the internal state.
5139 =head2 C<isl_polyhedron_minimize>
5141 C<isl_polyhedron_minimize> computes the minimum of some linear
5142 or affine objective function over the integer points in a polyhedron.
5143 If an affine objective function
5144 is given, then the constant should appear in the last column.
5146 =head2 C<isl_polytope_scan>
5148 Given a polytope, C<isl_polytope_scan> prints
5149 all integer points in the polytope.