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);
2778 __isl_give isl_basic_set *
2779 isl_basic_set_preimage_multi_aff(
2780 __isl_take isl_basic_set *bset,
2781 __isl_take isl_multi_aff *ma);
2782 __isl_give isl_set *isl_set_preimage_multi_aff(
2783 __isl_take isl_set *set,
2784 __isl_take isl_multi_aff *ma);
2786 These functions compute the preimage of the given set under
2787 the given function. In other words, the expression is plugged
2788 into the set description.
2789 Objects of type C<isl_multi_aff> are described in
2790 L</"Piecewise Multiple Quasi Affine Expressions">.
2792 =item * Cartesian Product
2794 __isl_give isl_set *isl_set_product(
2795 __isl_take isl_set *set1,
2796 __isl_take isl_set *set2);
2797 __isl_give isl_union_set *isl_union_set_product(
2798 __isl_take isl_union_set *uset1,
2799 __isl_take isl_union_set *uset2);
2800 __isl_give isl_basic_map *isl_basic_map_domain_product(
2801 __isl_take isl_basic_map *bmap1,
2802 __isl_take isl_basic_map *bmap2);
2803 __isl_give isl_basic_map *isl_basic_map_range_product(
2804 __isl_take isl_basic_map *bmap1,
2805 __isl_take isl_basic_map *bmap2);
2806 __isl_give isl_basic_map *isl_basic_map_product(
2807 __isl_take isl_basic_map *bmap1,
2808 __isl_take isl_basic_map *bmap2);
2809 __isl_give isl_map *isl_map_domain_product(
2810 __isl_take isl_map *map1,
2811 __isl_take isl_map *map2);
2812 __isl_give isl_map *isl_map_range_product(
2813 __isl_take isl_map *map1,
2814 __isl_take isl_map *map2);
2815 __isl_give isl_union_map *isl_union_map_domain_product(
2816 __isl_take isl_union_map *umap1,
2817 __isl_take isl_union_map *umap2);
2818 __isl_give isl_union_map *isl_union_map_range_product(
2819 __isl_take isl_union_map *umap1,
2820 __isl_take isl_union_map *umap2);
2821 __isl_give isl_map *isl_map_product(
2822 __isl_take isl_map *map1,
2823 __isl_take isl_map *map2);
2824 __isl_give isl_union_map *isl_union_map_product(
2825 __isl_take isl_union_map *umap1,
2826 __isl_take isl_union_map *umap2);
2828 The above functions compute the cross product of the given
2829 sets or relations. The domains and ranges of the results
2830 are wrapped maps between domains and ranges of the inputs.
2831 To obtain a ``flat'' product, use the following functions
2834 __isl_give isl_basic_set *isl_basic_set_flat_product(
2835 __isl_take isl_basic_set *bset1,
2836 __isl_take isl_basic_set *bset2);
2837 __isl_give isl_set *isl_set_flat_product(
2838 __isl_take isl_set *set1,
2839 __isl_take isl_set *set2);
2840 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2841 __isl_take isl_basic_map *bmap1,
2842 __isl_take isl_basic_map *bmap2);
2843 __isl_give isl_map *isl_map_flat_domain_product(
2844 __isl_take isl_map *map1,
2845 __isl_take isl_map *map2);
2846 __isl_give isl_map *isl_map_flat_range_product(
2847 __isl_take isl_map *map1,
2848 __isl_take isl_map *map2);
2849 __isl_give isl_union_map *isl_union_map_flat_range_product(
2850 __isl_take isl_union_map *umap1,
2851 __isl_take isl_union_map *umap2);
2852 __isl_give isl_basic_map *isl_basic_map_flat_product(
2853 __isl_take isl_basic_map *bmap1,
2854 __isl_take isl_basic_map *bmap2);
2855 __isl_give isl_map *isl_map_flat_product(
2856 __isl_take isl_map *map1,
2857 __isl_take isl_map *map2);
2859 =item * Simplification
2861 __isl_give isl_basic_set *isl_basic_set_gist(
2862 __isl_take isl_basic_set *bset,
2863 __isl_take isl_basic_set *context);
2864 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2865 __isl_take isl_set *context);
2866 __isl_give isl_set *isl_set_gist_params(
2867 __isl_take isl_set *set,
2868 __isl_take isl_set *context);
2869 __isl_give isl_union_set *isl_union_set_gist(
2870 __isl_take isl_union_set *uset,
2871 __isl_take isl_union_set *context);
2872 __isl_give isl_union_set *isl_union_set_gist_params(
2873 __isl_take isl_union_set *uset,
2874 __isl_take isl_set *set);
2875 __isl_give isl_basic_map *isl_basic_map_gist(
2876 __isl_take isl_basic_map *bmap,
2877 __isl_take isl_basic_map *context);
2878 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2879 __isl_take isl_map *context);
2880 __isl_give isl_map *isl_map_gist_params(
2881 __isl_take isl_map *map,
2882 __isl_take isl_set *context);
2883 __isl_give isl_map *isl_map_gist_domain(
2884 __isl_take isl_map *map,
2885 __isl_take isl_set *context);
2886 __isl_give isl_map *isl_map_gist_range(
2887 __isl_take isl_map *map,
2888 __isl_take isl_set *context);
2889 __isl_give isl_union_map *isl_union_map_gist(
2890 __isl_take isl_union_map *umap,
2891 __isl_take isl_union_map *context);
2892 __isl_give isl_union_map *isl_union_map_gist_params(
2893 __isl_take isl_union_map *umap,
2894 __isl_take isl_set *set);
2895 __isl_give isl_union_map *isl_union_map_gist_domain(
2896 __isl_take isl_union_map *umap,
2897 __isl_take isl_union_set *uset);
2898 __isl_give isl_union_map *isl_union_map_gist_range(
2899 __isl_take isl_union_map *umap,
2900 __isl_take isl_union_set *uset);
2902 The gist operation returns a set or relation that has the
2903 same intersection with the context as the input set or relation.
2904 Any implicit equality in the intersection is made explicit in the result,
2905 while all inequalities that are redundant with respect to the intersection
2907 In case of union sets and relations, the gist operation is performed
2912 =head3 Lexicographic Optimization
2914 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2915 the following functions
2916 compute a set that contains the lexicographic minimum or maximum
2917 of the elements in C<set> (or C<bset>) for those values of the parameters
2918 that satisfy C<dom>.
2919 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2920 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2922 In other words, the union of the parameter values
2923 for which the result is non-empty and of C<*empty>
2926 __isl_give isl_set *isl_basic_set_partial_lexmin(
2927 __isl_take isl_basic_set *bset,
2928 __isl_take isl_basic_set *dom,
2929 __isl_give isl_set **empty);
2930 __isl_give isl_set *isl_basic_set_partial_lexmax(
2931 __isl_take isl_basic_set *bset,
2932 __isl_take isl_basic_set *dom,
2933 __isl_give isl_set **empty);
2934 __isl_give isl_set *isl_set_partial_lexmin(
2935 __isl_take isl_set *set, __isl_take isl_set *dom,
2936 __isl_give isl_set **empty);
2937 __isl_give isl_set *isl_set_partial_lexmax(
2938 __isl_take isl_set *set, __isl_take isl_set *dom,
2939 __isl_give isl_set **empty);
2941 Given a (basic) set C<set> (or C<bset>), the following functions simply
2942 return a set containing the lexicographic minimum or maximum
2943 of the elements in C<set> (or C<bset>).
2944 In case of union sets, the optimum is computed per space.
2946 __isl_give isl_set *isl_basic_set_lexmin(
2947 __isl_take isl_basic_set *bset);
2948 __isl_give isl_set *isl_basic_set_lexmax(
2949 __isl_take isl_basic_set *bset);
2950 __isl_give isl_set *isl_set_lexmin(
2951 __isl_take isl_set *set);
2952 __isl_give isl_set *isl_set_lexmax(
2953 __isl_take isl_set *set);
2954 __isl_give isl_union_set *isl_union_set_lexmin(
2955 __isl_take isl_union_set *uset);
2956 __isl_give isl_union_set *isl_union_set_lexmax(
2957 __isl_take isl_union_set *uset);
2959 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2960 the following functions
2961 compute a relation that maps each element of C<dom>
2962 to the single lexicographic minimum or maximum
2963 of the elements that are associated to that same
2964 element in C<map> (or C<bmap>).
2965 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2966 that contains the elements in C<dom> that do not map
2967 to any elements in C<map> (or C<bmap>).
2968 In other words, the union of the domain of the result and of C<*empty>
2971 __isl_give isl_map *isl_basic_map_partial_lexmax(
2972 __isl_take isl_basic_map *bmap,
2973 __isl_take isl_basic_set *dom,
2974 __isl_give isl_set **empty);
2975 __isl_give isl_map *isl_basic_map_partial_lexmin(
2976 __isl_take isl_basic_map *bmap,
2977 __isl_take isl_basic_set *dom,
2978 __isl_give isl_set **empty);
2979 __isl_give isl_map *isl_map_partial_lexmax(
2980 __isl_take isl_map *map, __isl_take isl_set *dom,
2981 __isl_give isl_set **empty);
2982 __isl_give isl_map *isl_map_partial_lexmin(
2983 __isl_take isl_map *map, __isl_take isl_set *dom,
2984 __isl_give isl_set **empty);
2986 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2987 return a map mapping each element in the domain of
2988 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2989 of all elements associated to that element.
2990 In case of union relations, the optimum is computed per space.
2992 __isl_give isl_map *isl_basic_map_lexmin(
2993 __isl_take isl_basic_map *bmap);
2994 __isl_give isl_map *isl_basic_map_lexmax(
2995 __isl_take isl_basic_map *bmap);
2996 __isl_give isl_map *isl_map_lexmin(
2997 __isl_take isl_map *map);
2998 __isl_give isl_map *isl_map_lexmax(
2999 __isl_take isl_map *map);
3000 __isl_give isl_union_map *isl_union_map_lexmin(
3001 __isl_take isl_union_map *umap);
3002 __isl_give isl_union_map *isl_union_map_lexmax(
3003 __isl_take isl_union_map *umap);
3005 The following functions return their result in the form of
3006 a piecewise multi-affine expression
3007 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3008 but are otherwise equivalent to the corresponding functions
3009 returning a basic set or relation.
3011 __isl_give isl_pw_multi_aff *
3012 isl_basic_map_lexmin_pw_multi_aff(
3013 __isl_take isl_basic_map *bmap);
3014 __isl_give isl_pw_multi_aff *
3015 isl_basic_set_partial_lexmin_pw_multi_aff(
3016 __isl_take isl_basic_set *bset,
3017 __isl_take isl_basic_set *dom,
3018 __isl_give isl_set **empty);
3019 __isl_give isl_pw_multi_aff *
3020 isl_basic_set_partial_lexmax_pw_multi_aff(
3021 __isl_take isl_basic_set *bset,
3022 __isl_take isl_basic_set *dom,
3023 __isl_give isl_set **empty);
3024 __isl_give isl_pw_multi_aff *
3025 isl_basic_map_partial_lexmin_pw_multi_aff(
3026 __isl_take isl_basic_map *bmap,
3027 __isl_take isl_basic_set *dom,
3028 __isl_give isl_set **empty);
3029 __isl_give isl_pw_multi_aff *
3030 isl_basic_map_partial_lexmax_pw_multi_aff(
3031 __isl_take isl_basic_map *bmap,
3032 __isl_take isl_basic_set *dom,
3033 __isl_give isl_set **empty);
3034 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3035 __isl_take isl_map *map);
3036 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3037 __isl_take isl_map *map);
3041 Lists are defined over several element types, including
3042 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3043 C<isl_basic_set> and C<isl_set>.
3044 Here we take lists of C<isl_set>s as an example.
3045 Lists can be created, copied, modified and freed using the following functions.
3047 #include <isl/list.h>
3048 __isl_give isl_set_list *isl_set_list_from_set(
3049 __isl_take isl_set *el);
3050 __isl_give isl_set_list *isl_set_list_alloc(
3051 isl_ctx *ctx, int n);
3052 __isl_give isl_set_list *isl_set_list_copy(
3053 __isl_keep isl_set_list *list);
3054 __isl_give isl_set_list *isl_set_list_insert(
3055 __isl_take isl_set_list *list, unsigned pos,
3056 __isl_take isl_set *el);
3057 __isl_give isl_set_list *isl_set_list_add(
3058 __isl_take isl_set_list *list,
3059 __isl_take isl_set *el);
3060 __isl_give isl_set_list *isl_set_list_drop(
3061 __isl_take isl_set_list *list,
3062 unsigned first, unsigned n);
3063 __isl_give isl_set_list *isl_set_list_set_set(
3064 __isl_take isl_set_list *list, int index,
3065 __isl_take isl_set *set);
3066 __isl_give isl_set_list *isl_set_list_concat(
3067 __isl_take isl_set_list *list1,
3068 __isl_take isl_set_list *list2);
3069 void *isl_set_list_free(__isl_take isl_set_list *list);
3071 C<isl_set_list_alloc> creates an empty list with a capacity for
3072 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3075 Lists can be inspected using the following functions.
3077 #include <isl/list.h>
3078 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3079 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3080 __isl_give isl_set *isl_set_list_get_set(
3081 __isl_keep isl_set_list *list, int index);
3082 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3083 int (*fn)(__isl_take isl_set *el, void *user),
3086 Lists can be printed using
3088 #include <isl/list.h>
3089 __isl_give isl_printer *isl_printer_print_set_list(
3090 __isl_take isl_printer *p,
3091 __isl_keep isl_set_list *list);
3095 Vectors can be created, copied and freed using the following functions.
3097 #include <isl/vec.h>
3098 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3100 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3101 void *isl_vec_free(__isl_take isl_vec *vec);
3103 Note that the elements of a newly created vector may have arbitrary values.
3104 The elements can be changed and inspected using the following functions.
3106 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3107 int isl_vec_size(__isl_keep isl_vec *vec);
3108 int isl_vec_get_element(__isl_keep isl_vec *vec,
3109 int pos, isl_int *v);
3110 __isl_give isl_vec *isl_vec_set_element(
3111 __isl_take isl_vec *vec, int pos, isl_int v);
3112 __isl_give isl_vec *isl_vec_set_element_si(
3113 __isl_take isl_vec *vec, int pos, int v);
3114 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3116 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3118 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3121 C<isl_vec_get_element> will return a negative value if anything went wrong.
3122 In that case, the value of C<*v> is undefined.
3124 The following function can be used to concatenate two vectors.
3126 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3127 __isl_take isl_vec *vec2);
3131 Matrices can be created, copied and freed using the following functions.
3133 #include <isl/mat.h>
3134 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3135 unsigned n_row, unsigned n_col);
3136 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3137 void isl_mat_free(__isl_take isl_mat *mat);
3139 Note that the elements of a newly created matrix may have arbitrary values.
3140 The elements can be changed and inspected using the following functions.
3142 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3143 int isl_mat_rows(__isl_keep isl_mat *mat);
3144 int isl_mat_cols(__isl_keep isl_mat *mat);
3145 int isl_mat_get_element(__isl_keep isl_mat *mat,
3146 int row, int col, isl_int *v);
3147 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3148 int row, int col, isl_int v);
3149 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3150 int row, int col, int v);
3152 C<isl_mat_get_element> will return a negative value if anything went wrong.
3153 In that case, the value of C<*v> is undefined.
3155 The following function can be used to compute the (right) inverse
3156 of a matrix, i.e., a matrix such that the product of the original
3157 and the inverse (in that order) is a multiple of the identity matrix.
3158 The input matrix is assumed to be of full row-rank.
3160 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3162 The following function can be used to compute the (right) kernel
3163 (or null space) of a matrix, i.e., a matrix such that the product of
3164 the original and the kernel (in that order) is the zero matrix.
3166 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3168 =head2 Piecewise Quasi Affine Expressions
3170 The zero quasi affine expression or the quasi affine expression
3171 that is equal to a specified dimension on a given domain can be created using
3173 __isl_give isl_aff *isl_aff_zero_on_domain(
3174 __isl_take isl_local_space *ls);
3175 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3176 __isl_take isl_local_space *ls);
3177 __isl_give isl_aff *isl_aff_var_on_domain(
3178 __isl_take isl_local_space *ls,
3179 enum isl_dim_type type, unsigned pos);
3180 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3181 __isl_take isl_local_space *ls,
3182 enum isl_dim_type type, unsigned pos);
3184 Note that the space in which the resulting objects live is a map space
3185 with the given space as domain and a one-dimensional range.
3187 An empty piecewise quasi affine expression (one with no cells)
3188 or a piecewise quasi affine expression with a single cell can
3189 be created using the following functions.
3191 #include <isl/aff.h>
3192 __isl_give isl_pw_aff *isl_pw_aff_empty(
3193 __isl_take isl_space *space);
3194 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3195 __isl_take isl_set *set, __isl_take isl_aff *aff);
3196 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3197 __isl_take isl_aff *aff);
3199 A piecewise quasi affine expression that is equal to 1 on a set
3200 and 0 outside the set can be created using the following function.
3202 #include <isl/aff.h>
3203 __isl_give isl_pw_aff *isl_set_indicator_function(
3204 __isl_take isl_set *set);
3206 Quasi affine expressions can be copied and freed using
3208 #include <isl/aff.h>
3209 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3210 void *isl_aff_free(__isl_take isl_aff *aff);
3212 __isl_give isl_pw_aff *isl_pw_aff_copy(
3213 __isl_keep isl_pw_aff *pwaff);
3214 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3216 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3217 using the following function. The constraint is required to have
3218 a non-zero coefficient for the specified dimension.
3220 #include <isl/constraint.h>
3221 __isl_give isl_aff *isl_constraint_get_bound(
3222 __isl_keep isl_constraint *constraint,
3223 enum isl_dim_type type, int pos);
3225 The entire affine expression of the constraint can also be extracted
3226 using the following function.
3228 #include <isl/constraint.h>
3229 __isl_give isl_aff *isl_constraint_get_aff(
3230 __isl_keep isl_constraint *constraint);
3232 Conversely, an equality constraint equating
3233 the affine expression to zero or an inequality constraint enforcing
3234 the affine expression to be non-negative, can be constructed using
3236 __isl_give isl_constraint *isl_equality_from_aff(
3237 __isl_take isl_aff *aff);
3238 __isl_give isl_constraint *isl_inequality_from_aff(
3239 __isl_take isl_aff *aff);
3241 The expression can be inspected using
3243 #include <isl/aff.h>
3244 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3245 int isl_aff_dim(__isl_keep isl_aff *aff,
3246 enum isl_dim_type type);
3247 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3248 __isl_keep isl_aff *aff);
3249 __isl_give isl_local_space *isl_aff_get_local_space(
3250 __isl_keep isl_aff *aff);
3251 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3252 enum isl_dim_type type, unsigned pos);
3253 const char *isl_pw_aff_get_dim_name(
3254 __isl_keep isl_pw_aff *pa,
3255 enum isl_dim_type type, unsigned pos);
3256 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3257 enum isl_dim_type type, unsigned pos);
3258 __isl_give isl_id *isl_pw_aff_get_dim_id(
3259 __isl_keep isl_pw_aff *pa,
3260 enum isl_dim_type type, unsigned pos);
3261 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3262 __isl_keep isl_pw_aff *pa,
3263 enum isl_dim_type type);
3264 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3266 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3267 enum isl_dim_type type, int pos, isl_int *v);
3268 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3270 __isl_give isl_aff *isl_aff_get_div(
3271 __isl_keep isl_aff *aff, int pos);
3273 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3274 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3275 int (*fn)(__isl_take isl_set *set,
3276 __isl_take isl_aff *aff,
3277 void *user), void *user);
3279 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3280 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3282 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3283 enum isl_dim_type type, unsigned first, unsigned n);
3284 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3285 enum isl_dim_type type, unsigned first, unsigned n);
3287 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3288 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3289 enum isl_dim_type type);
3290 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3292 It can be modified using
3294 #include <isl/aff.h>
3295 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3296 __isl_take isl_pw_aff *pwaff,
3297 enum isl_dim_type type, __isl_take isl_id *id);
3298 __isl_give isl_aff *isl_aff_set_dim_name(
3299 __isl_take isl_aff *aff, enum isl_dim_type type,
3300 unsigned pos, const char *s);
3301 __isl_give isl_aff *isl_aff_set_dim_id(
3302 __isl_take isl_aff *aff, enum isl_dim_type type,
3303 unsigned pos, __isl_take isl_id *id);
3304 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3305 __isl_take isl_pw_aff *pma,
3306 enum isl_dim_type type, unsigned pos,
3307 __isl_take isl_id *id);
3308 __isl_give isl_aff *isl_aff_set_constant(
3309 __isl_take isl_aff *aff, isl_int v);
3310 __isl_give isl_aff *isl_aff_set_constant_si(
3311 __isl_take isl_aff *aff, int v);
3312 __isl_give isl_aff *isl_aff_set_coefficient(
3313 __isl_take isl_aff *aff,
3314 enum isl_dim_type type, int pos, isl_int v);
3315 __isl_give isl_aff *isl_aff_set_coefficient_si(
3316 __isl_take isl_aff *aff,
3317 enum isl_dim_type type, int pos, int v);
3318 __isl_give isl_aff *isl_aff_set_denominator(
3319 __isl_take isl_aff *aff, isl_int v);
3321 __isl_give isl_aff *isl_aff_add_constant(
3322 __isl_take isl_aff *aff, isl_int v);
3323 __isl_give isl_aff *isl_aff_add_constant_si(
3324 __isl_take isl_aff *aff, int v);
3325 __isl_give isl_aff *isl_aff_add_constant_num(
3326 __isl_take isl_aff *aff, isl_int v);
3327 __isl_give isl_aff *isl_aff_add_constant_num_si(
3328 __isl_take isl_aff *aff, int v);
3329 __isl_give isl_aff *isl_aff_add_coefficient(
3330 __isl_take isl_aff *aff,
3331 enum isl_dim_type type, int pos, isl_int v);
3332 __isl_give isl_aff *isl_aff_add_coefficient_si(
3333 __isl_take isl_aff *aff,
3334 enum isl_dim_type type, int pos, int v);
3336 __isl_give isl_aff *isl_aff_insert_dims(
3337 __isl_take isl_aff *aff,
3338 enum isl_dim_type type, unsigned first, unsigned n);
3339 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3340 __isl_take isl_pw_aff *pwaff,
3341 enum isl_dim_type type, unsigned first, unsigned n);
3342 __isl_give isl_aff *isl_aff_add_dims(
3343 __isl_take isl_aff *aff,
3344 enum isl_dim_type type, unsigned n);
3345 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3346 __isl_take isl_pw_aff *pwaff,
3347 enum isl_dim_type type, unsigned n);
3348 __isl_give isl_aff *isl_aff_drop_dims(
3349 __isl_take isl_aff *aff,
3350 enum isl_dim_type type, unsigned first, unsigned n);
3351 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3352 __isl_take isl_pw_aff *pwaff,
3353 enum isl_dim_type type, unsigned first, unsigned n);
3355 Note that the C<set_constant> and C<set_coefficient> functions
3356 set the I<numerator> of the constant or coefficient, while
3357 C<add_constant> and C<add_coefficient> add an integer value to
3358 the possibly rational constant or coefficient.
3359 The C<add_constant_num> functions add an integer value to
3362 To check whether an affine expressions is obviously zero
3363 or obviously equal to some other affine expression, use
3365 #include <isl/aff.h>
3366 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3367 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3368 __isl_keep isl_aff *aff2);
3369 int isl_pw_aff_plain_is_equal(
3370 __isl_keep isl_pw_aff *pwaff1,
3371 __isl_keep isl_pw_aff *pwaff2);
3375 #include <isl/aff.h>
3376 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3377 __isl_take isl_aff *aff2);
3378 __isl_give isl_pw_aff *isl_pw_aff_add(
3379 __isl_take isl_pw_aff *pwaff1,
3380 __isl_take isl_pw_aff *pwaff2);
3381 __isl_give isl_pw_aff *isl_pw_aff_min(
3382 __isl_take isl_pw_aff *pwaff1,
3383 __isl_take isl_pw_aff *pwaff2);
3384 __isl_give isl_pw_aff *isl_pw_aff_max(
3385 __isl_take isl_pw_aff *pwaff1,
3386 __isl_take isl_pw_aff *pwaff2);
3387 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3388 __isl_take isl_aff *aff2);
3389 __isl_give isl_pw_aff *isl_pw_aff_sub(
3390 __isl_take isl_pw_aff *pwaff1,
3391 __isl_take isl_pw_aff *pwaff2);
3392 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3393 __isl_give isl_pw_aff *isl_pw_aff_neg(
3394 __isl_take isl_pw_aff *pwaff);
3395 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3396 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3397 __isl_take isl_pw_aff *pwaff);
3398 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3399 __isl_give isl_pw_aff *isl_pw_aff_floor(
3400 __isl_take isl_pw_aff *pwaff);
3401 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3403 __isl_give isl_pw_aff *isl_pw_aff_mod(
3404 __isl_take isl_pw_aff *pwaff, isl_int mod);
3405 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3407 __isl_give isl_pw_aff *isl_pw_aff_scale(
3408 __isl_take isl_pw_aff *pwaff, isl_int f);
3409 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3411 __isl_give isl_aff *isl_aff_scale_down_ui(
3412 __isl_take isl_aff *aff, unsigned f);
3413 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3414 __isl_take isl_pw_aff *pwaff, isl_int f);
3416 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3417 __isl_take isl_pw_aff_list *list);
3418 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3419 __isl_take isl_pw_aff_list *list);
3421 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3422 __isl_take isl_pw_aff *pwqp);
3424 __isl_give isl_aff *isl_aff_align_params(
3425 __isl_take isl_aff *aff,
3426 __isl_take isl_space *model);
3427 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3428 __isl_take isl_pw_aff *pwaff,
3429 __isl_take isl_space *model);
3431 __isl_give isl_aff *isl_aff_project_domain_on_params(
3432 __isl_take isl_aff *aff);
3434 __isl_give isl_aff *isl_aff_gist_params(
3435 __isl_take isl_aff *aff,
3436 __isl_take isl_set *context);
3437 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3438 __isl_take isl_set *context);
3439 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3440 __isl_take isl_pw_aff *pwaff,
3441 __isl_take isl_set *context);
3442 __isl_give isl_pw_aff *isl_pw_aff_gist(
3443 __isl_take isl_pw_aff *pwaff,
3444 __isl_take isl_set *context);
3446 __isl_give isl_set *isl_pw_aff_domain(
3447 __isl_take isl_pw_aff *pwaff);
3448 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3449 __isl_take isl_pw_aff *pa,
3450 __isl_take isl_set *set);
3451 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3452 __isl_take isl_pw_aff *pa,
3453 __isl_take isl_set *set);
3455 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3456 __isl_take isl_aff *aff2);
3457 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3458 __isl_take isl_aff *aff2);
3459 __isl_give isl_pw_aff *isl_pw_aff_mul(
3460 __isl_take isl_pw_aff *pwaff1,
3461 __isl_take isl_pw_aff *pwaff2);
3462 __isl_give isl_pw_aff *isl_pw_aff_div(
3463 __isl_take isl_pw_aff *pa1,
3464 __isl_take isl_pw_aff *pa2);
3465 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3466 __isl_take isl_pw_aff *pa1,
3467 __isl_take isl_pw_aff *pa2);
3468 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3469 __isl_take isl_pw_aff *pa1,
3470 __isl_take isl_pw_aff *pa2);
3472 When multiplying two affine expressions, at least one of the two needs
3473 to be a constant. Similarly, when dividing an affine expression by another,
3474 the second expression needs to be a constant.
3475 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3476 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3479 #include <isl/aff.h>
3480 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3481 __isl_take isl_aff *aff);
3482 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3483 __isl_take isl_aff *aff);
3484 __isl_give isl_basic_set *isl_aff_le_basic_set(
3485 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3486 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3487 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3488 __isl_give isl_set *isl_pw_aff_eq_set(
3489 __isl_take isl_pw_aff *pwaff1,
3490 __isl_take isl_pw_aff *pwaff2);
3491 __isl_give isl_set *isl_pw_aff_ne_set(
3492 __isl_take isl_pw_aff *pwaff1,
3493 __isl_take isl_pw_aff *pwaff2);
3494 __isl_give isl_set *isl_pw_aff_le_set(
3495 __isl_take isl_pw_aff *pwaff1,
3496 __isl_take isl_pw_aff *pwaff2);
3497 __isl_give isl_set *isl_pw_aff_lt_set(
3498 __isl_take isl_pw_aff *pwaff1,
3499 __isl_take isl_pw_aff *pwaff2);
3500 __isl_give isl_set *isl_pw_aff_ge_set(
3501 __isl_take isl_pw_aff *pwaff1,
3502 __isl_take isl_pw_aff *pwaff2);
3503 __isl_give isl_set *isl_pw_aff_gt_set(
3504 __isl_take isl_pw_aff *pwaff1,
3505 __isl_take isl_pw_aff *pwaff2);
3507 __isl_give isl_set *isl_pw_aff_list_eq_set(
3508 __isl_take isl_pw_aff_list *list1,
3509 __isl_take isl_pw_aff_list *list2);
3510 __isl_give isl_set *isl_pw_aff_list_ne_set(
3511 __isl_take isl_pw_aff_list *list1,
3512 __isl_take isl_pw_aff_list *list2);
3513 __isl_give isl_set *isl_pw_aff_list_le_set(
3514 __isl_take isl_pw_aff_list *list1,
3515 __isl_take isl_pw_aff_list *list2);
3516 __isl_give isl_set *isl_pw_aff_list_lt_set(
3517 __isl_take isl_pw_aff_list *list1,
3518 __isl_take isl_pw_aff_list *list2);
3519 __isl_give isl_set *isl_pw_aff_list_ge_set(
3520 __isl_take isl_pw_aff_list *list1,
3521 __isl_take isl_pw_aff_list *list2);
3522 __isl_give isl_set *isl_pw_aff_list_gt_set(
3523 __isl_take isl_pw_aff_list *list1,
3524 __isl_take isl_pw_aff_list *list2);
3526 The function C<isl_aff_neg_basic_set> returns a basic set
3527 containing those elements in the domain space
3528 of C<aff> where C<aff> is negative.
3529 The function C<isl_aff_ge_basic_set> returns a basic set
3530 containing those elements in the shared space
3531 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3532 The function C<isl_pw_aff_ge_set> returns a set
3533 containing those elements in the shared domain
3534 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3535 The functions operating on C<isl_pw_aff_list> apply the corresponding
3536 C<isl_pw_aff> function to each pair of elements in the two lists.
3538 #include <isl/aff.h>
3539 __isl_give isl_set *isl_pw_aff_nonneg_set(
3540 __isl_take isl_pw_aff *pwaff);
3541 __isl_give isl_set *isl_pw_aff_zero_set(
3542 __isl_take isl_pw_aff *pwaff);
3543 __isl_give isl_set *isl_pw_aff_non_zero_set(
3544 __isl_take isl_pw_aff *pwaff);
3546 The function C<isl_pw_aff_nonneg_set> returns a set
3547 containing those elements in the domain
3548 of C<pwaff> where C<pwaff> is non-negative.
3550 #include <isl/aff.h>
3551 __isl_give isl_pw_aff *isl_pw_aff_cond(
3552 __isl_take isl_pw_aff *cond,
3553 __isl_take isl_pw_aff *pwaff_true,
3554 __isl_take isl_pw_aff *pwaff_false);
3556 The function C<isl_pw_aff_cond> performs a conditional operator
3557 and returns an expression that is equal to C<pwaff_true>
3558 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3559 where C<cond> is zero.
3561 #include <isl/aff.h>
3562 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3563 __isl_take isl_pw_aff *pwaff1,
3564 __isl_take isl_pw_aff *pwaff2);
3565 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3566 __isl_take isl_pw_aff *pwaff1,
3567 __isl_take isl_pw_aff *pwaff2);
3568 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3569 __isl_take isl_pw_aff *pwaff1,
3570 __isl_take isl_pw_aff *pwaff2);
3572 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3573 expression with a domain that is the union of those of C<pwaff1> and
3574 C<pwaff2> and such that on each cell, the quasi-affine expression is
3575 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3576 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3577 associated expression is the defined one.
3579 An expression can be read from input using
3581 #include <isl/aff.h>
3582 __isl_give isl_aff *isl_aff_read_from_str(
3583 isl_ctx *ctx, const char *str);
3584 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3585 isl_ctx *ctx, const char *str);
3587 An expression can be printed using
3589 #include <isl/aff.h>
3590 __isl_give isl_printer *isl_printer_print_aff(
3591 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3593 __isl_give isl_printer *isl_printer_print_pw_aff(
3594 __isl_take isl_printer *p,
3595 __isl_keep isl_pw_aff *pwaff);
3597 =head2 Piecewise Multiple Quasi Affine Expressions
3599 An C<isl_multi_aff> object represents a sequence of
3600 zero or more affine expressions, all defined on the same domain space.
3601 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3602 zero or more piecewise affine expressions.
3604 An C<isl_multi_aff> can be constructed from a single
3605 C<isl_aff> or an C<isl_aff_list> using the
3606 following functions. Similarly for C<isl_multi_pw_aff>.
3608 #include <isl/aff.h>
3609 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3610 __isl_take isl_aff *aff);
3611 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3612 __isl_take isl_pw_aff *pa);
3613 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3614 __isl_take isl_space *space,
3615 __isl_take isl_aff_list *list);
3617 An empty piecewise multiple quasi affine expression (one with no cells),
3618 the zero piecewise multiple quasi affine expression (with value zero
3619 for each output dimension),
3620 a piecewise multiple quasi affine expression with a single cell (with
3621 either a universe or a specified domain) or
3622 a zero-dimensional piecewise multiple quasi affine expression
3624 can be created using the following functions.
3626 #include <isl/aff.h>
3627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3628 __isl_take isl_space *space);
3629 __isl_give isl_multi_aff *isl_multi_aff_zero(
3630 __isl_take isl_space *space);
3631 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3632 __isl_take isl_space *space);
3633 __isl_give isl_multi_aff *isl_multi_aff_identity(
3634 __isl_take isl_space *space);
3635 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3636 __isl_take isl_space *space);
3637 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3638 __isl_take isl_space *space);
3639 __isl_give isl_pw_multi_aff *
3640 isl_pw_multi_aff_from_multi_aff(
3641 __isl_take isl_multi_aff *ma);
3642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3643 __isl_take isl_set *set,
3644 __isl_take isl_multi_aff *maff);
3645 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3646 __isl_take isl_set *set);
3648 __isl_give isl_union_pw_multi_aff *
3649 isl_union_pw_multi_aff_empty(
3650 __isl_take isl_space *space);
3651 __isl_give isl_union_pw_multi_aff *
3652 isl_union_pw_multi_aff_add_pw_multi_aff(
3653 __isl_take isl_union_pw_multi_aff *upma,
3654 __isl_take isl_pw_multi_aff *pma);
3655 __isl_give isl_union_pw_multi_aff *
3656 isl_union_pw_multi_aff_from_domain(
3657 __isl_take isl_union_set *uset);
3659 A piecewise multiple quasi affine expression can also be initialized
3660 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3661 and the C<isl_map> is single-valued.
3663 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3664 __isl_take isl_set *set);
3665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3666 __isl_take isl_map *map);
3668 Multiple quasi affine expressions can be copied and freed using
3670 #include <isl/aff.h>
3671 __isl_give isl_multi_aff *isl_multi_aff_copy(
3672 __isl_keep isl_multi_aff *maff);
3673 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3676 __isl_keep isl_pw_multi_aff *pma);
3677 void *isl_pw_multi_aff_free(
3678 __isl_take isl_pw_multi_aff *pma);
3680 __isl_give isl_union_pw_multi_aff *
3681 isl_union_pw_multi_aff_copy(
3682 __isl_keep isl_union_pw_multi_aff *upma);
3683 void *isl_union_pw_multi_aff_free(
3684 __isl_take isl_union_pw_multi_aff *upma);
3686 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3687 __isl_keep isl_multi_pw_aff *mpa);
3688 void *isl_multi_pw_aff_free(
3689 __isl_take isl_multi_pw_aff *mpa);
3691 The expression can be inspected using
3693 #include <isl/aff.h>
3694 isl_ctx *isl_multi_aff_get_ctx(
3695 __isl_keep isl_multi_aff *maff);
3696 isl_ctx *isl_pw_multi_aff_get_ctx(
3697 __isl_keep isl_pw_multi_aff *pma);
3698 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3699 __isl_keep isl_union_pw_multi_aff *upma);
3700 isl_ctx *isl_multi_pw_aff_get_ctx(
3701 __isl_keep isl_multi_pw_aff *mpa);
3702 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3703 enum isl_dim_type type);
3704 unsigned isl_pw_multi_aff_dim(
3705 __isl_keep isl_pw_multi_aff *pma,
3706 enum isl_dim_type type);
3707 unsigned isl_multi_pw_aff_dim(
3708 __isl_keep isl_multi_pw_aff *mpa,
3709 enum isl_dim_type type);
3710 __isl_give isl_aff *isl_multi_aff_get_aff(
3711 __isl_keep isl_multi_aff *multi, int pos);
3712 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3713 __isl_keep isl_pw_multi_aff *pma, int pos);
3714 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3715 __isl_keep isl_multi_pw_aff *mpa, int pos);
3716 const char *isl_pw_multi_aff_get_dim_name(
3717 __isl_keep isl_pw_multi_aff *pma,
3718 enum isl_dim_type type, unsigned pos);
3719 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3720 __isl_keep isl_pw_multi_aff *pma,
3721 enum isl_dim_type type, unsigned pos);
3722 const char *isl_multi_aff_get_tuple_name(
3723 __isl_keep isl_multi_aff *multi,
3724 enum isl_dim_type type);
3725 int isl_pw_multi_aff_has_tuple_name(
3726 __isl_keep isl_pw_multi_aff *pma,
3727 enum isl_dim_type type);
3728 const char *isl_pw_multi_aff_get_tuple_name(
3729 __isl_keep isl_pw_multi_aff *pma,
3730 enum isl_dim_type type);
3731 int isl_pw_multi_aff_has_tuple_id(
3732 __isl_keep isl_pw_multi_aff *pma,
3733 enum isl_dim_type type);
3734 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3735 __isl_keep isl_pw_multi_aff *pma,
3736 enum isl_dim_type type);
3738 int isl_pw_multi_aff_foreach_piece(
3739 __isl_keep isl_pw_multi_aff *pma,
3740 int (*fn)(__isl_take isl_set *set,
3741 __isl_take isl_multi_aff *maff,
3742 void *user), void *user);
3744 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3745 __isl_keep isl_union_pw_multi_aff *upma,
3746 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3747 void *user), void *user);
3749 It can be modified using
3751 #include <isl/aff.h>
3752 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3753 __isl_take isl_multi_aff *multi, int pos,
3754 __isl_take isl_aff *aff);
3755 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3756 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3757 __isl_take isl_pw_aff *pa);
3758 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3759 __isl_take isl_multi_aff *maff,
3760 enum isl_dim_type type, unsigned pos, const char *s);
3761 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3762 __isl_take isl_multi_aff *maff,
3763 enum isl_dim_type type, const char *s);
3764 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3765 __isl_take isl_multi_aff *maff,
3766 enum isl_dim_type type, __isl_take isl_id *id);
3767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3768 __isl_take isl_pw_multi_aff *pma,
3769 enum isl_dim_type type, __isl_take isl_id *id);
3771 __isl_give isl_multi_pw_aff *
3772 isl_multi_pw_aff_set_dim_name(
3773 __isl_take isl_multi_pw_aff *mpa,
3774 enum isl_dim_type type, unsigned pos, const char *s);
3775 __isl_give isl_multi_pw_aff *
3776 isl_multi_pw_aff_set_tuple_name(
3777 __isl_take isl_multi_pw_aff *mpa,
3778 enum isl_dim_type type, const char *s);
3780 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3781 __isl_take isl_multi_aff *ma,
3782 enum isl_dim_type type, unsigned first, unsigned n);
3783 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3784 __isl_take isl_multi_aff *ma,
3785 enum isl_dim_type type, unsigned n);
3786 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3787 __isl_take isl_multi_aff *maff,
3788 enum isl_dim_type type, unsigned first, unsigned n);
3789 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3790 __isl_take isl_pw_multi_aff *pma,
3791 enum isl_dim_type type, unsigned first, unsigned n);
3793 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3794 __isl_take isl_multi_pw_aff *mpa,
3795 enum isl_dim_type type, unsigned first, unsigned n);
3796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3797 __isl_take isl_multi_pw_aff *mpa,
3798 enum isl_dim_type type, unsigned n);
3800 To check whether two multiple affine expressions are
3801 obviously equal to each other, use
3803 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3804 __isl_keep isl_multi_aff *maff2);
3805 int isl_pw_multi_aff_plain_is_equal(
3806 __isl_keep isl_pw_multi_aff *pma1,
3807 __isl_keep isl_pw_multi_aff *pma2);
3811 #include <isl/aff.h>
3812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3813 __isl_take isl_pw_multi_aff *pma1,
3814 __isl_take isl_pw_multi_aff *pma2);
3815 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3816 __isl_take isl_pw_multi_aff *pma1,
3817 __isl_take isl_pw_multi_aff *pma2);
3818 __isl_give isl_multi_aff *isl_multi_aff_add(
3819 __isl_take isl_multi_aff *maff1,
3820 __isl_take isl_multi_aff *maff2);
3821 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3822 __isl_take isl_pw_multi_aff *pma1,
3823 __isl_take isl_pw_multi_aff *pma2);
3824 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3825 __isl_take isl_union_pw_multi_aff *upma1,
3826 __isl_take isl_union_pw_multi_aff *upma2);
3827 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3828 __isl_take isl_pw_multi_aff *pma1,
3829 __isl_take isl_pw_multi_aff *pma2);
3830 __isl_give isl_multi_aff *isl_multi_aff_scale(
3831 __isl_take isl_multi_aff *maff,
3833 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3834 __isl_take isl_pw_multi_aff *pma,
3835 __isl_take isl_set *set);
3836 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3837 __isl_take isl_pw_multi_aff *pma,
3838 __isl_take isl_set *set);
3839 __isl_give isl_multi_aff *isl_multi_aff_lift(
3840 __isl_take isl_multi_aff *maff,
3841 __isl_give isl_local_space **ls);
3842 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3843 __isl_take isl_pw_multi_aff *pma);
3844 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3845 __isl_take isl_multi_aff *multi,
3846 __isl_take isl_space *model);
3847 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3848 __isl_take isl_pw_multi_aff *pma,
3849 __isl_take isl_space *model);
3850 __isl_give isl_pw_multi_aff *
3851 isl_pw_multi_aff_project_domain_on_params(
3852 __isl_take isl_pw_multi_aff *pma);
3853 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3854 __isl_take isl_multi_aff *maff,
3855 __isl_take isl_set *context);
3856 __isl_give isl_multi_aff *isl_multi_aff_gist(
3857 __isl_take isl_multi_aff *maff,
3858 __isl_take isl_set *context);
3859 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3860 __isl_take isl_pw_multi_aff *pma,
3861 __isl_take isl_set *set);
3862 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3863 __isl_take isl_pw_multi_aff *pma,
3864 __isl_take isl_set *set);
3865 __isl_give isl_set *isl_pw_multi_aff_domain(
3866 __isl_take isl_pw_multi_aff *pma);
3867 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3868 __isl_take isl_union_pw_multi_aff *upma);
3869 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3870 __isl_take isl_multi_aff *ma1, unsigned pos,
3871 __isl_take isl_multi_aff *ma2);
3872 __isl_give isl_multi_aff *isl_multi_aff_splice(
3873 __isl_take isl_multi_aff *ma1,
3874 unsigned in_pos, unsigned out_pos,
3875 __isl_take isl_multi_aff *ma2);
3876 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3877 __isl_take isl_multi_aff *ma1,
3878 __isl_take isl_multi_aff *ma2);
3879 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3880 __isl_take isl_multi_aff *ma1,
3881 __isl_take isl_multi_aff *ma2);
3882 __isl_give isl_multi_aff *isl_multi_aff_product(
3883 __isl_take isl_multi_aff *ma1,
3884 __isl_take isl_multi_aff *ma2);
3885 __isl_give isl_pw_multi_aff *
3886 isl_pw_multi_aff_range_product(
3887 __isl_take isl_pw_multi_aff *pma1,
3888 __isl_take isl_pw_multi_aff *pma2);
3889 __isl_give isl_pw_multi_aff *
3890 isl_pw_multi_aff_flat_range_product(
3891 __isl_take isl_pw_multi_aff *pma1,
3892 __isl_take isl_pw_multi_aff *pma2);
3893 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3894 __isl_take isl_pw_multi_aff *pma1,
3895 __isl_take isl_pw_multi_aff *pma2);
3896 __isl_give isl_union_pw_multi_aff *
3897 isl_union_pw_multi_aff_flat_range_product(
3898 __isl_take isl_union_pw_multi_aff *upma1,
3899 __isl_take isl_union_pw_multi_aff *upma2);
3900 __isl_give isl_multi_pw_aff *
3901 isl_multi_pw_aff_range_splice(
3902 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
3903 __isl_take isl_multi_pw_aff *mpa2);
3904 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
3905 __isl_take isl_multi_pw_aff *mpa1,
3906 unsigned in_pos, unsigned out_pos,
3907 __isl_take isl_multi_pw_aff *mpa2);
3908 __isl_give isl_multi_pw_aff *
3909 isl_multi_pw_aff_range_product(
3910 __isl_take isl_multi_pw_aff *mpa1,
3911 __isl_take isl_multi_pw_aff *mpa2);
3912 __isl_give isl_multi_pw_aff *
3913 isl_multi_pw_aff_flat_range_product(
3914 __isl_take isl_multi_pw_aff *mpa1,
3915 __isl_take isl_multi_pw_aff *mpa2);
3917 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3918 then it is assigned the local space that lies at the basis of
3919 the lifting applied.
3921 __isl_give isl_set *isl_multi_aff_lex_le_set(
3922 __isl_take isl_multi_aff *ma1,
3923 __isl_take isl_multi_aff *ma2);
3924 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3925 __isl_take isl_multi_aff *ma1,
3926 __isl_take isl_multi_aff *ma2);
3928 The function C<isl_multi_aff_lex_le_set> returns a set
3929 containing those elements in the shared domain space
3930 where C<ma1> is lexicographically smaller than or
3933 An expression can be read from input using
3935 #include <isl/aff.h>
3936 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3937 isl_ctx *ctx, const char *str);
3938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3939 isl_ctx *ctx, const char *str);
3941 An expression can be printed using
3943 #include <isl/aff.h>
3944 __isl_give isl_printer *isl_printer_print_multi_aff(
3945 __isl_take isl_printer *p,
3946 __isl_keep isl_multi_aff *maff);
3947 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3948 __isl_take isl_printer *p,
3949 __isl_keep isl_pw_multi_aff *pma);
3950 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3951 __isl_take isl_printer *p,
3952 __isl_keep isl_union_pw_multi_aff *upma);
3953 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3954 __isl_take isl_printer *p,
3955 __isl_keep isl_multi_pw_aff *mpa);
3959 Points are elements of a set. They can be used to construct
3960 simple sets (boxes) or they can be used to represent the
3961 individual elements of a set.
3962 The zero point (the origin) can be created using
3964 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3966 The coordinates of a point can be inspected, set and changed
3969 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3970 enum isl_dim_type type, int pos, isl_int *v);
3971 __isl_give isl_point *isl_point_set_coordinate(
3972 __isl_take isl_point *pnt,
3973 enum isl_dim_type type, int pos, isl_int v);
3975 __isl_give isl_point *isl_point_add_ui(
3976 __isl_take isl_point *pnt,
3977 enum isl_dim_type type, int pos, unsigned val);
3978 __isl_give isl_point *isl_point_sub_ui(
3979 __isl_take isl_point *pnt,
3980 enum isl_dim_type type, int pos, unsigned val);
3982 Other properties can be obtained using
3984 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3986 Points can be copied or freed using
3988 __isl_give isl_point *isl_point_copy(
3989 __isl_keep isl_point *pnt);
3990 void isl_point_free(__isl_take isl_point *pnt);
3992 A singleton set can be created from a point using
3994 __isl_give isl_basic_set *isl_basic_set_from_point(
3995 __isl_take isl_point *pnt);
3996 __isl_give isl_set *isl_set_from_point(
3997 __isl_take isl_point *pnt);
3999 and a box can be created from two opposite extremal points using
4001 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4002 __isl_take isl_point *pnt1,
4003 __isl_take isl_point *pnt2);
4004 __isl_give isl_set *isl_set_box_from_points(
4005 __isl_take isl_point *pnt1,
4006 __isl_take isl_point *pnt2);
4008 All elements of a B<bounded> (union) set can be enumerated using
4009 the following functions.
4011 int isl_set_foreach_point(__isl_keep isl_set *set,
4012 int (*fn)(__isl_take isl_point *pnt, void *user),
4014 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4015 int (*fn)(__isl_take isl_point *pnt, void *user),
4018 The function C<fn> is called for each integer point in
4019 C<set> with as second argument the last argument of
4020 the C<isl_set_foreach_point> call. The function C<fn>
4021 should return C<0> on success and C<-1> on failure.
4022 In the latter case, C<isl_set_foreach_point> will stop
4023 enumerating and return C<-1> as well.
4024 If the enumeration is performed successfully and to completion,
4025 then C<isl_set_foreach_point> returns C<0>.
4027 To obtain a single point of a (basic) set, use
4029 __isl_give isl_point *isl_basic_set_sample_point(
4030 __isl_take isl_basic_set *bset);
4031 __isl_give isl_point *isl_set_sample_point(
4032 __isl_take isl_set *set);
4034 If C<set> does not contain any (integer) points, then the
4035 resulting point will be ``void'', a property that can be
4038 int isl_point_is_void(__isl_keep isl_point *pnt);
4040 =head2 Piecewise Quasipolynomials
4042 A piecewise quasipolynomial is a particular kind of function that maps
4043 a parametric point to a rational value.
4044 More specifically, a quasipolynomial is a polynomial expression in greatest
4045 integer parts of affine expressions of parameters and variables.
4046 A piecewise quasipolynomial is a subdivision of a given parametric
4047 domain into disjoint cells with a quasipolynomial associated to
4048 each cell. The value of the piecewise quasipolynomial at a given
4049 point is the value of the quasipolynomial associated to the cell
4050 that contains the point. Outside of the union of cells,
4051 the value is assumed to be zero.
4052 For example, the piecewise quasipolynomial
4054 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4056 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4057 A given piecewise quasipolynomial has a fixed domain dimension.
4058 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4059 defined over different domains.
4060 Piecewise quasipolynomials are mainly used by the C<barvinok>
4061 library for representing the number of elements in a parametric set or map.
4062 For example, the piecewise quasipolynomial above represents
4063 the number of points in the map
4065 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4067 =head3 Input and Output
4069 Piecewise quasipolynomials can be read from input using
4071 __isl_give isl_union_pw_qpolynomial *
4072 isl_union_pw_qpolynomial_read_from_str(
4073 isl_ctx *ctx, const char *str);
4075 Quasipolynomials and piecewise quasipolynomials can be printed
4076 using the following functions.
4078 __isl_give isl_printer *isl_printer_print_qpolynomial(
4079 __isl_take isl_printer *p,
4080 __isl_keep isl_qpolynomial *qp);
4082 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4083 __isl_take isl_printer *p,
4084 __isl_keep isl_pw_qpolynomial *pwqp);
4086 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4087 __isl_take isl_printer *p,
4088 __isl_keep isl_union_pw_qpolynomial *upwqp);
4090 The output format of the printer
4091 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4092 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4094 In case of printing in C<ISL_FORMAT_C>, the user may want
4095 to set the names of all dimensions
4097 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4098 __isl_take isl_qpolynomial *qp,
4099 enum isl_dim_type type, unsigned pos,
4101 __isl_give isl_pw_qpolynomial *
4102 isl_pw_qpolynomial_set_dim_name(
4103 __isl_take isl_pw_qpolynomial *pwqp,
4104 enum isl_dim_type type, unsigned pos,
4107 =head3 Creating New (Piecewise) Quasipolynomials
4109 Some simple quasipolynomials can be created using the following functions.
4110 More complicated quasipolynomials can be created by applying
4111 operations such as addition and multiplication
4112 on the resulting quasipolynomials
4114 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4115 __isl_take isl_space *domain);
4116 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4117 __isl_take isl_space *domain);
4118 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4119 __isl_take isl_space *domain);
4120 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4121 __isl_take isl_space *domain);
4122 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4123 __isl_take isl_space *domain);
4124 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4125 __isl_take isl_space *domain,
4126 const isl_int n, const isl_int d);
4127 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4128 __isl_take isl_space *domain,
4129 enum isl_dim_type type, unsigned pos);
4130 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4131 __isl_take isl_aff *aff);
4133 Note that the space in which a quasipolynomial lives is a map space
4134 with a one-dimensional range. The C<domain> argument in some of
4135 the functions above corresponds to the domain of this map space.
4137 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4138 with a single cell can be created using the following functions.
4139 Multiple of these single cell piecewise quasipolynomials can
4140 be combined to create more complicated piecewise quasipolynomials.
4142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4143 __isl_take isl_space *space);
4144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4145 __isl_take isl_set *set,
4146 __isl_take isl_qpolynomial *qp);
4147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4148 __isl_take isl_qpolynomial *qp);
4149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4150 __isl_take isl_pw_aff *pwaff);
4152 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4153 __isl_take isl_space *space);
4154 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4155 __isl_take isl_pw_qpolynomial *pwqp);
4156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4157 __isl_take isl_union_pw_qpolynomial *upwqp,
4158 __isl_take isl_pw_qpolynomial *pwqp);
4160 Quasipolynomials can be copied and freed again using the following
4163 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4164 __isl_keep isl_qpolynomial *qp);
4165 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4167 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4168 __isl_keep isl_pw_qpolynomial *pwqp);
4169 void *isl_pw_qpolynomial_free(
4170 __isl_take isl_pw_qpolynomial *pwqp);
4172 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4173 __isl_keep isl_union_pw_qpolynomial *upwqp);
4174 void *isl_union_pw_qpolynomial_free(
4175 __isl_take isl_union_pw_qpolynomial *upwqp);
4177 =head3 Inspecting (Piecewise) Quasipolynomials
4179 To iterate over all piecewise quasipolynomials in a union
4180 piecewise quasipolynomial, use the following function
4182 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4183 __isl_keep isl_union_pw_qpolynomial *upwqp,
4184 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4187 To extract the piecewise quasipolynomial in a given space from a union, use
4189 __isl_give isl_pw_qpolynomial *
4190 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4191 __isl_keep isl_union_pw_qpolynomial *upwqp,
4192 __isl_take isl_space *space);
4194 To iterate over the cells in a piecewise quasipolynomial,
4195 use either of the following two functions
4197 int isl_pw_qpolynomial_foreach_piece(
4198 __isl_keep isl_pw_qpolynomial *pwqp,
4199 int (*fn)(__isl_take isl_set *set,
4200 __isl_take isl_qpolynomial *qp,
4201 void *user), void *user);
4202 int isl_pw_qpolynomial_foreach_lifted_piece(
4203 __isl_keep isl_pw_qpolynomial *pwqp,
4204 int (*fn)(__isl_take isl_set *set,
4205 __isl_take isl_qpolynomial *qp,
4206 void *user), void *user);
4208 As usual, the function C<fn> should return C<0> on success
4209 and C<-1> on failure. The difference between
4210 C<isl_pw_qpolynomial_foreach_piece> and
4211 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4212 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4213 compute unique representations for all existentially quantified
4214 variables and then turn these existentially quantified variables
4215 into extra set variables, adapting the associated quasipolynomial
4216 accordingly. This means that the C<set> passed to C<fn>
4217 will not have any existentially quantified variables, but that
4218 the dimensions of the sets may be different for different
4219 invocations of C<fn>.
4221 To iterate over all terms in a quasipolynomial,
4224 int isl_qpolynomial_foreach_term(
4225 __isl_keep isl_qpolynomial *qp,
4226 int (*fn)(__isl_take isl_term *term,
4227 void *user), void *user);
4229 The terms themselves can be inspected and freed using
4232 unsigned isl_term_dim(__isl_keep isl_term *term,
4233 enum isl_dim_type type);
4234 void isl_term_get_num(__isl_keep isl_term *term,
4236 void isl_term_get_den(__isl_keep isl_term *term,
4238 int isl_term_get_exp(__isl_keep isl_term *term,
4239 enum isl_dim_type type, unsigned pos);
4240 __isl_give isl_aff *isl_term_get_div(
4241 __isl_keep isl_term *term, unsigned pos);
4242 void isl_term_free(__isl_take isl_term *term);
4244 Each term is a product of parameters, set variables and
4245 integer divisions. The function C<isl_term_get_exp>
4246 returns the exponent of a given dimensions in the given term.
4247 The C<isl_int>s in the arguments of C<isl_term_get_num>
4248 and C<isl_term_get_den> need to have been initialized
4249 using C<isl_int_init> before calling these functions.
4251 =head3 Properties of (Piecewise) Quasipolynomials
4253 To check whether a quasipolynomial is actually a constant,
4254 use the following function.
4256 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4257 isl_int *n, isl_int *d);
4259 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4260 then the numerator and denominator of the constant
4261 are returned in C<*n> and C<*d>, respectively.
4263 To check whether two union piecewise quasipolynomials are
4264 obviously equal, use
4266 int isl_union_pw_qpolynomial_plain_is_equal(
4267 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4268 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4270 =head3 Operations on (Piecewise) Quasipolynomials
4272 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4273 __isl_take isl_qpolynomial *qp, isl_int v);
4274 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4275 __isl_take isl_qpolynomial *qp);
4276 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4277 __isl_take isl_qpolynomial *qp1,
4278 __isl_take isl_qpolynomial *qp2);
4279 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4280 __isl_take isl_qpolynomial *qp1,
4281 __isl_take isl_qpolynomial *qp2);
4282 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4283 __isl_take isl_qpolynomial *qp1,
4284 __isl_take isl_qpolynomial *qp2);
4285 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4286 __isl_take isl_qpolynomial *qp, unsigned exponent);
4288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4289 __isl_take isl_pw_qpolynomial *pwqp1,
4290 __isl_take isl_pw_qpolynomial *pwqp2);
4291 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4292 __isl_take isl_pw_qpolynomial *pwqp1,
4293 __isl_take isl_pw_qpolynomial *pwqp2);
4294 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4295 __isl_take isl_pw_qpolynomial *pwqp1,
4296 __isl_take isl_pw_qpolynomial *pwqp2);
4297 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4298 __isl_take isl_pw_qpolynomial *pwqp);
4299 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4300 __isl_take isl_pw_qpolynomial *pwqp1,
4301 __isl_take isl_pw_qpolynomial *pwqp2);
4302 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4303 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4305 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4306 __isl_take isl_union_pw_qpolynomial *upwqp1,
4307 __isl_take isl_union_pw_qpolynomial *upwqp2);
4308 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4309 __isl_take isl_union_pw_qpolynomial *upwqp1,
4310 __isl_take isl_union_pw_qpolynomial *upwqp2);
4311 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4312 __isl_take isl_union_pw_qpolynomial *upwqp1,
4313 __isl_take isl_union_pw_qpolynomial *upwqp2);
4315 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4316 __isl_take isl_pw_qpolynomial *pwqp,
4317 __isl_take isl_point *pnt);
4319 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4320 __isl_take isl_union_pw_qpolynomial *upwqp,
4321 __isl_take isl_point *pnt);
4323 __isl_give isl_set *isl_pw_qpolynomial_domain(
4324 __isl_take isl_pw_qpolynomial *pwqp);
4325 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4326 __isl_take isl_pw_qpolynomial *pwpq,
4327 __isl_take isl_set *set);
4328 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4329 __isl_take isl_pw_qpolynomial *pwpq,
4330 __isl_take isl_set *set);
4332 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4333 __isl_take isl_union_pw_qpolynomial *upwqp);
4334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4335 __isl_take isl_union_pw_qpolynomial *upwpq,
4336 __isl_take isl_union_set *uset);
4337 __isl_give isl_union_pw_qpolynomial *
4338 isl_union_pw_qpolynomial_intersect_params(
4339 __isl_take isl_union_pw_qpolynomial *upwpq,
4340 __isl_take isl_set *set);
4342 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4343 __isl_take isl_qpolynomial *qp,
4344 __isl_take isl_space *model);
4346 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4347 __isl_take isl_qpolynomial *qp);
4348 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4349 __isl_take isl_pw_qpolynomial *pwqp);
4351 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4352 __isl_take isl_union_pw_qpolynomial *upwqp);
4354 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4355 __isl_take isl_qpolynomial *qp,
4356 __isl_take isl_set *context);
4357 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4358 __isl_take isl_qpolynomial *qp,
4359 __isl_take isl_set *context);
4361 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4362 __isl_take isl_pw_qpolynomial *pwqp,
4363 __isl_take isl_set *context);
4364 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4365 __isl_take isl_pw_qpolynomial *pwqp,
4366 __isl_take isl_set *context);
4368 __isl_give isl_union_pw_qpolynomial *
4369 isl_union_pw_qpolynomial_gist_params(
4370 __isl_take isl_union_pw_qpolynomial *upwqp,
4371 __isl_take isl_set *context);
4372 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4373 __isl_take isl_union_pw_qpolynomial *upwqp,
4374 __isl_take isl_union_set *context);
4376 The gist operation applies the gist operation to each of
4377 the cells in the domain of the input piecewise quasipolynomial.
4378 The context is also exploited
4379 to simplify the quasipolynomials associated to each cell.
4381 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4382 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4383 __isl_give isl_union_pw_qpolynomial *
4384 isl_union_pw_qpolynomial_to_polynomial(
4385 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4387 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4388 the polynomial will be an overapproximation. If C<sign> is negative,
4389 it will be an underapproximation. If C<sign> is zero, the approximation
4390 will lie somewhere in between.
4392 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4394 A piecewise quasipolynomial reduction is a piecewise
4395 reduction (or fold) of quasipolynomials.
4396 In particular, the reduction can be maximum or a minimum.
4397 The objects are mainly used to represent the result of
4398 an upper or lower bound on a quasipolynomial over its domain,
4399 i.e., as the result of the following function.
4401 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4402 __isl_take isl_pw_qpolynomial *pwqp,
4403 enum isl_fold type, int *tight);
4405 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4406 __isl_take isl_union_pw_qpolynomial *upwqp,
4407 enum isl_fold type, int *tight);
4409 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4410 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4411 is the returned bound is known be tight, i.e., for each value
4412 of the parameters there is at least
4413 one element in the domain that reaches the bound.
4414 If the domain of C<pwqp> is not wrapping, then the bound is computed
4415 over all elements in that domain and the result has a purely parametric
4416 domain. If the domain of C<pwqp> is wrapping, then the bound is
4417 computed over the range of the wrapped relation. The domain of the
4418 wrapped relation becomes the domain of the result.
4420 A (piecewise) quasipolynomial reduction can be copied or freed using the
4421 following functions.
4423 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4424 __isl_keep isl_qpolynomial_fold *fold);
4425 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4426 __isl_keep isl_pw_qpolynomial_fold *pwf);
4427 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4428 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4429 void isl_qpolynomial_fold_free(
4430 __isl_take isl_qpolynomial_fold *fold);
4431 void *isl_pw_qpolynomial_fold_free(
4432 __isl_take isl_pw_qpolynomial_fold *pwf);
4433 void *isl_union_pw_qpolynomial_fold_free(
4434 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4436 =head3 Printing Piecewise Quasipolynomial Reductions
4438 Piecewise quasipolynomial reductions can be printed
4439 using the following function.
4441 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4442 __isl_take isl_printer *p,
4443 __isl_keep isl_pw_qpolynomial_fold *pwf);
4444 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4445 __isl_take isl_printer *p,
4446 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4448 For C<isl_printer_print_pw_qpolynomial_fold>,
4449 output format of the printer
4450 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4451 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4452 output format of the printer
4453 needs to be set to C<ISL_FORMAT_ISL>.
4454 In case of printing in C<ISL_FORMAT_C>, the user may want
4455 to set the names of all dimensions
4457 __isl_give isl_pw_qpolynomial_fold *
4458 isl_pw_qpolynomial_fold_set_dim_name(
4459 __isl_take isl_pw_qpolynomial_fold *pwf,
4460 enum isl_dim_type type, unsigned pos,
4463 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4465 To iterate over all piecewise quasipolynomial reductions in a union
4466 piecewise quasipolynomial reduction, use the following function
4468 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4469 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4470 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4471 void *user), void *user);
4473 To iterate over the cells in a piecewise quasipolynomial reduction,
4474 use either of the following two functions
4476 int isl_pw_qpolynomial_fold_foreach_piece(
4477 __isl_keep isl_pw_qpolynomial_fold *pwf,
4478 int (*fn)(__isl_take isl_set *set,
4479 __isl_take isl_qpolynomial_fold *fold,
4480 void *user), void *user);
4481 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4482 __isl_keep isl_pw_qpolynomial_fold *pwf,
4483 int (*fn)(__isl_take isl_set *set,
4484 __isl_take isl_qpolynomial_fold *fold,
4485 void *user), void *user);
4487 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4488 of the difference between these two functions.
4490 To iterate over all quasipolynomials in a reduction, use
4492 int isl_qpolynomial_fold_foreach_qpolynomial(
4493 __isl_keep isl_qpolynomial_fold *fold,
4494 int (*fn)(__isl_take isl_qpolynomial *qp,
4495 void *user), void *user);
4497 =head3 Properties of Piecewise Quasipolynomial Reductions
4499 To check whether two union piecewise quasipolynomial reductions are
4500 obviously equal, use
4502 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4503 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4504 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4506 =head3 Operations on Piecewise Quasipolynomial Reductions
4508 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4509 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4511 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4512 __isl_take isl_pw_qpolynomial_fold *pwf1,
4513 __isl_take isl_pw_qpolynomial_fold *pwf2);
4515 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4516 __isl_take isl_pw_qpolynomial_fold *pwf1,
4517 __isl_take isl_pw_qpolynomial_fold *pwf2);
4519 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4520 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4521 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4523 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4524 __isl_take isl_pw_qpolynomial_fold *pwf,
4525 __isl_take isl_point *pnt);
4527 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4528 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4529 __isl_take isl_point *pnt);
4531 __isl_give isl_pw_qpolynomial_fold *
4532 isl_pw_qpolynomial_fold_intersect_params(
4533 __isl_take isl_pw_qpolynomial_fold *pwf,
4534 __isl_take isl_set *set);
4536 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4537 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4538 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4539 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4540 __isl_take isl_union_set *uset);
4541 __isl_give isl_union_pw_qpolynomial_fold *
4542 isl_union_pw_qpolynomial_fold_intersect_params(
4543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4544 __isl_take isl_set *set);
4546 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4547 __isl_take isl_pw_qpolynomial_fold *pwf);
4549 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4550 __isl_take isl_pw_qpolynomial_fold *pwf);
4552 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4553 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4555 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4556 __isl_take isl_qpolynomial_fold *fold,
4557 __isl_take isl_set *context);
4558 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4559 __isl_take isl_qpolynomial_fold *fold,
4560 __isl_take isl_set *context);
4562 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4563 __isl_take isl_pw_qpolynomial_fold *pwf,
4564 __isl_take isl_set *context);
4565 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4566 __isl_take isl_pw_qpolynomial_fold *pwf,
4567 __isl_take isl_set *context);
4569 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4570 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4571 __isl_take isl_union_set *context);
4572 __isl_give isl_union_pw_qpolynomial_fold *
4573 isl_union_pw_qpolynomial_fold_gist_params(
4574 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4575 __isl_take isl_set *context);
4577 The gist operation applies the gist operation to each of
4578 the cells in the domain of the input piecewise quasipolynomial reduction.
4579 In future, the operation will also exploit the context
4580 to simplify the quasipolynomial reductions associated to each cell.
4582 __isl_give isl_pw_qpolynomial_fold *
4583 isl_set_apply_pw_qpolynomial_fold(
4584 __isl_take isl_set *set,
4585 __isl_take isl_pw_qpolynomial_fold *pwf,
4587 __isl_give isl_pw_qpolynomial_fold *
4588 isl_map_apply_pw_qpolynomial_fold(
4589 __isl_take isl_map *map,
4590 __isl_take isl_pw_qpolynomial_fold *pwf,
4592 __isl_give isl_union_pw_qpolynomial_fold *
4593 isl_union_set_apply_union_pw_qpolynomial_fold(
4594 __isl_take isl_union_set *uset,
4595 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4597 __isl_give isl_union_pw_qpolynomial_fold *
4598 isl_union_map_apply_union_pw_qpolynomial_fold(
4599 __isl_take isl_union_map *umap,
4600 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4603 The functions taking a map
4604 compose the given map with the given piecewise quasipolynomial reduction.
4605 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4606 over all elements in the intersection of the range of the map
4607 and the domain of the piecewise quasipolynomial reduction
4608 as a function of an element in the domain of the map.
4609 The functions taking a set compute a bound over all elements in the
4610 intersection of the set and the domain of the
4611 piecewise quasipolynomial reduction.
4613 =head2 Dependence Analysis
4615 C<isl> contains specialized functionality for performing
4616 array dataflow analysis. That is, given a I<sink> access relation
4617 and a collection of possible I<source> access relations,
4618 C<isl> can compute relations that describe
4619 for each iteration of the sink access, which iteration
4620 of which of the source access relations was the last
4621 to access the same data element before the given iteration
4623 The resulting dependence relations map source iterations
4624 to the corresponding sink iterations.
4625 To compute standard flow dependences, the sink should be
4626 a read, while the sources should be writes.
4627 If any of the source accesses are marked as being I<may>
4628 accesses, then there will be a dependence from the last
4629 I<must> access B<and> from any I<may> access that follows
4630 this last I<must> access.
4631 In particular, if I<all> sources are I<may> accesses,
4632 then memory based dependence analysis is performed.
4633 If, on the other hand, all sources are I<must> accesses,
4634 then value based dependence analysis is performed.
4636 #include <isl/flow.h>
4638 typedef int (*isl_access_level_before)(void *first, void *second);
4640 __isl_give isl_access_info *isl_access_info_alloc(
4641 __isl_take isl_map *sink,
4642 void *sink_user, isl_access_level_before fn,
4644 __isl_give isl_access_info *isl_access_info_add_source(
4645 __isl_take isl_access_info *acc,
4646 __isl_take isl_map *source, int must,
4648 void *isl_access_info_free(__isl_take isl_access_info *acc);
4650 __isl_give isl_flow *isl_access_info_compute_flow(
4651 __isl_take isl_access_info *acc);
4653 int isl_flow_foreach(__isl_keep isl_flow *deps,
4654 int (*fn)(__isl_take isl_map *dep, int must,
4655 void *dep_user, void *user),
4657 __isl_give isl_map *isl_flow_get_no_source(
4658 __isl_keep isl_flow *deps, int must);
4659 void isl_flow_free(__isl_take isl_flow *deps);
4661 The function C<isl_access_info_compute_flow> performs the actual
4662 dependence analysis. The other functions are used to construct
4663 the input for this function or to read off the output.
4665 The input is collected in an C<isl_access_info>, which can
4666 be created through a call to C<isl_access_info_alloc>.
4667 The arguments to this functions are the sink access relation
4668 C<sink>, a token C<sink_user> used to identify the sink
4669 access to the user, a callback function for specifying the
4670 relative order of source and sink accesses, and the number
4671 of source access relations that will be added.
4672 The callback function has type C<int (*)(void *first, void *second)>.
4673 The function is called with two user supplied tokens identifying
4674 either a source or the sink and it should return the shared nesting
4675 level and the relative order of the two accesses.
4676 In particular, let I<n> be the number of loops shared by
4677 the two accesses. If C<first> precedes C<second> textually,
4678 then the function should return I<2 * n + 1>; otherwise,
4679 it should return I<2 * n>.
4680 The sources can be added to the C<isl_access_info> by performing
4681 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4682 C<must> indicates whether the source is a I<must> access
4683 or a I<may> access. Note that a multi-valued access relation
4684 should only be marked I<must> if every iteration in the domain
4685 of the relation accesses I<all> elements in its image.
4686 The C<source_user> token is again used to identify
4687 the source access. The range of the source access relation
4688 C<source> should have the same dimension as the range
4689 of the sink access relation.
4690 The C<isl_access_info_free> function should usually not be
4691 called explicitly, because it is called implicitly by
4692 C<isl_access_info_compute_flow>.
4694 The result of the dependence analysis is collected in an
4695 C<isl_flow>. There may be elements of
4696 the sink access for which no preceding source access could be
4697 found or for which all preceding sources are I<may> accesses.
4698 The relations containing these elements can be obtained through
4699 calls to C<isl_flow_get_no_source>, the first with C<must> set
4700 and the second with C<must> unset.
4701 In the case of standard flow dependence analysis,
4702 with the sink a read and the sources I<must> writes,
4703 the first relation corresponds to the reads from uninitialized
4704 array elements and the second relation is empty.
4705 The actual flow dependences can be extracted using
4706 C<isl_flow_foreach>. This function will call the user-specified
4707 callback function C<fn> for each B<non-empty> dependence between
4708 a source and the sink. The callback function is called
4709 with four arguments, the actual flow dependence relation
4710 mapping source iterations to sink iterations, a boolean that
4711 indicates whether it is a I<must> or I<may> dependence, a token
4712 identifying the source and an additional C<void *> with value
4713 equal to the third argument of the C<isl_flow_foreach> call.
4714 A dependence is marked I<must> if it originates from a I<must>
4715 source and if it is not followed by any I<may> sources.
4717 After finishing with an C<isl_flow>, the user should call
4718 C<isl_flow_free> to free all associated memory.
4720 A higher-level interface to dependence analysis is provided
4721 by the following function.
4723 #include <isl/flow.h>
4725 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4726 __isl_take isl_union_map *must_source,
4727 __isl_take isl_union_map *may_source,
4728 __isl_take isl_union_map *schedule,
4729 __isl_give isl_union_map **must_dep,
4730 __isl_give isl_union_map **may_dep,
4731 __isl_give isl_union_map **must_no_source,
4732 __isl_give isl_union_map **may_no_source);
4734 The arrays are identified by the tuple names of the ranges
4735 of the accesses. The iteration domains by the tuple names
4736 of the domains of the accesses and of the schedule.
4737 The relative order of the iteration domains is given by the
4738 schedule. The relations returned through C<must_no_source>
4739 and C<may_no_source> are subsets of C<sink>.
4740 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4741 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4742 any of the other arguments is treated as an error.
4744 =head3 Interaction with Dependence Analysis
4746 During the dependence analysis, we frequently need to perform
4747 the following operation. Given a relation between sink iterations
4748 and potential source iterations from a particular source domain,
4749 what is the last potential source iteration corresponding to each
4750 sink iteration. It can sometimes be convenient to adjust
4751 the set of potential source iterations before or after each such operation.
4752 The prototypical example is fuzzy array dataflow analysis,
4753 where we need to analyze if, based on data-dependent constraints,
4754 the sink iteration can ever be executed without one or more of
4755 the corresponding potential source iterations being executed.
4756 If so, we can introduce extra parameters and select an unknown
4757 but fixed source iteration from the potential source iterations.
4758 To be able to perform such manipulations, C<isl> provides the following
4761 #include <isl/flow.h>
4763 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4764 __isl_keep isl_map *source_map,
4765 __isl_keep isl_set *sink, void *source_user,
4767 __isl_give isl_access_info *isl_access_info_set_restrict(
4768 __isl_take isl_access_info *acc,
4769 isl_access_restrict fn, void *user);
4771 The function C<isl_access_info_set_restrict> should be called
4772 before calling C<isl_access_info_compute_flow> and registers a callback function
4773 that will be called any time C<isl> is about to compute the last
4774 potential source. The first argument is the (reverse) proto-dependence,
4775 mapping sink iterations to potential source iterations.
4776 The second argument represents the sink iterations for which
4777 we want to compute the last source iteration.
4778 The third argument is the token corresponding to the source
4779 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4780 The callback is expected to return a restriction on either the input or
4781 the output of the operation computing the last potential source.
4782 If the input needs to be restricted then restrictions are needed
4783 for both the source and the sink iterations. The sink iterations
4784 and the potential source iterations will be intersected with these sets.
4785 If the output needs to be restricted then only a restriction on the source
4786 iterations is required.
4787 If any error occurs, the callback should return C<NULL>.
4788 An C<isl_restriction> object can be created, freed and inspected
4789 using the following functions.
4791 #include <isl/flow.h>
4793 __isl_give isl_restriction *isl_restriction_input(
4794 __isl_take isl_set *source_restr,
4795 __isl_take isl_set *sink_restr);
4796 __isl_give isl_restriction *isl_restriction_output(
4797 __isl_take isl_set *source_restr);
4798 __isl_give isl_restriction *isl_restriction_none(
4799 __isl_take isl_map *source_map);
4800 __isl_give isl_restriction *isl_restriction_empty(
4801 __isl_take isl_map *source_map);
4802 void *isl_restriction_free(
4803 __isl_take isl_restriction *restr);
4804 isl_ctx *isl_restriction_get_ctx(
4805 __isl_keep isl_restriction *restr);
4807 C<isl_restriction_none> and C<isl_restriction_empty> are special
4808 cases of C<isl_restriction_input>. C<isl_restriction_none>
4809 is essentially equivalent to
4811 isl_restriction_input(isl_set_universe(
4812 isl_space_range(isl_map_get_space(source_map))),
4814 isl_space_domain(isl_map_get_space(source_map))));
4816 whereas C<isl_restriction_empty> is essentially equivalent to
4818 isl_restriction_input(isl_set_empty(
4819 isl_space_range(isl_map_get_space(source_map))),
4821 isl_space_domain(isl_map_get_space(source_map))));
4825 B<The functionality described in this section is fairly new
4826 and may be subject to change.>
4828 The following function can be used to compute a schedule
4829 for a union of domains.
4830 By default, the algorithm used to construct the schedule is similar
4831 to that of C<Pluto>.
4832 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4834 The generated schedule respects all C<validity> dependences.
4835 That is, all dependence distances over these dependences in the
4836 scheduled space are lexicographically positive.
4837 The default algorithm tries to minimize the dependence distances over
4838 C<proximity> dependences.
4839 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4840 for groups of domains where the dependence distances have only
4841 non-negative values.
4842 When using Feautrier's algorithm, the C<proximity> dependence
4843 distances are only minimized during the extension to a
4844 full-dimensional schedule.
4846 #include <isl/schedule.h>
4847 __isl_give isl_schedule *isl_union_set_compute_schedule(
4848 __isl_take isl_union_set *domain,
4849 __isl_take isl_union_map *validity,
4850 __isl_take isl_union_map *proximity);
4851 void *isl_schedule_free(__isl_take isl_schedule *sched);
4853 A mapping from the domains to the scheduled space can be obtained
4854 from an C<isl_schedule> using the following function.
4856 __isl_give isl_union_map *isl_schedule_get_map(
4857 __isl_keep isl_schedule *sched);
4859 A representation of the schedule can be printed using
4861 __isl_give isl_printer *isl_printer_print_schedule(
4862 __isl_take isl_printer *p,
4863 __isl_keep isl_schedule *schedule);
4865 A representation of the schedule as a forest of bands can be obtained
4866 using the following function.
4868 __isl_give isl_band_list *isl_schedule_get_band_forest(
4869 __isl_keep isl_schedule *schedule);
4871 The individual bands can be visited in depth-first post-order
4872 using the following function.
4874 #include <isl/schedule.h>
4875 int isl_schedule_foreach_band(
4876 __isl_keep isl_schedule *sched,
4877 int (*fn)(__isl_keep isl_band *band, void *user),
4880 The list can be manipulated as explained in L<"Lists">.
4881 The bands inside the list can be copied and freed using the following
4884 #include <isl/band.h>
4885 __isl_give isl_band *isl_band_copy(
4886 __isl_keep isl_band *band);
4887 void *isl_band_free(__isl_take isl_band *band);
4889 Each band contains zero or more scheduling dimensions.
4890 These are referred to as the members of the band.
4891 The section of the schedule that corresponds to the band is
4892 referred to as the partial schedule of the band.
4893 For those nodes that participate in a band, the outer scheduling
4894 dimensions form the prefix schedule, while the inner scheduling
4895 dimensions form the suffix schedule.
4896 That is, if we take a cut of the band forest, then the union of
4897 the concatenations of the prefix, partial and suffix schedules of
4898 each band in the cut is equal to the entire schedule (modulo
4899 some possible padding at the end with zero scheduling dimensions).
4900 The properties of a band can be inspected using the following functions.
4902 #include <isl/band.h>
4903 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4905 int isl_band_has_children(__isl_keep isl_band *band);
4906 __isl_give isl_band_list *isl_band_get_children(
4907 __isl_keep isl_band *band);
4909 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4910 __isl_keep isl_band *band);
4911 __isl_give isl_union_map *isl_band_get_partial_schedule(
4912 __isl_keep isl_band *band);
4913 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4914 __isl_keep isl_band *band);
4916 int isl_band_n_member(__isl_keep isl_band *band);
4917 int isl_band_member_is_zero_distance(
4918 __isl_keep isl_band *band, int pos);
4920 int isl_band_list_foreach_band(
4921 __isl_keep isl_band_list *list,
4922 int (*fn)(__isl_keep isl_band *band, void *user),
4925 Note that a scheduling dimension is considered to be ``zero
4926 distance'' if it does not carry any proximity dependences
4928 That is, if the dependence distances of the proximity
4929 dependences are all zero in that direction (for fixed
4930 iterations of outer bands).
4931 Like C<isl_schedule_foreach_band>,
4932 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4933 in depth-first post-order.
4935 A band can be tiled using the following function.
4937 #include <isl/band.h>
4938 int isl_band_tile(__isl_keep isl_band *band,
4939 __isl_take isl_vec *sizes);
4941 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4943 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4945 The C<isl_band_tile> function tiles the band using the given tile sizes
4946 inside its schedule.
4947 A new child band is created to represent the point loops and it is
4948 inserted between the modified band and its children.
4949 The C<tile_scale_tile_loops> option specifies whether the tile
4950 loops iterators should be scaled by the tile sizes.
4952 A representation of the band can be printed using
4954 #include <isl/band.h>
4955 __isl_give isl_printer *isl_printer_print_band(
4956 __isl_take isl_printer *p,
4957 __isl_keep isl_band *band);
4961 #include <isl/schedule.h>
4962 int isl_options_set_schedule_max_coefficient(
4963 isl_ctx *ctx, int val);
4964 int isl_options_get_schedule_max_coefficient(
4966 int isl_options_set_schedule_max_constant_term(
4967 isl_ctx *ctx, int val);
4968 int isl_options_get_schedule_max_constant_term(
4970 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4971 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4972 int isl_options_set_schedule_maximize_band_depth(
4973 isl_ctx *ctx, int val);
4974 int isl_options_get_schedule_maximize_band_depth(
4976 int isl_options_set_schedule_outer_zero_distance(
4977 isl_ctx *ctx, int val);
4978 int isl_options_get_schedule_outer_zero_distance(
4980 int isl_options_set_schedule_split_scaled(
4981 isl_ctx *ctx, int val);
4982 int isl_options_get_schedule_split_scaled(
4984 int isl_options_set_schedule_algorithm(
4985 isl_ctx *ctx, int val);
4986 int isl_options_get_schedule_algorithm(
4988 int isl_options_set_schedule_separate_components(
4989 isl_ctx *ctx, int val);
4990 int isl_options_get_schedule_separate_components(
4995 =item * schedule_max_coefficient
4997 This option enforces that the coefficients for variable and parameter
4998 dimensions in the calculated schedule are not larger than the specified value.
4999 This option can significantly increase the speed of the scheduling calculation
5000 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5001 this option does not introduce bounds on the variable or parameter
5004 =item * schedule_max_constant_term
5006 This option enforces that the constant coefficients in the calculated schedule
5007 are not larger than the maximal constant term. This option can significantly
5008 increase the speed of the scheduling calculation and may also prevent fusing of
5009 unrelated dimensions. A value of -1 means that this option does not introduce
5010 bounds on the constant coefficients.
5012 =item * schedule_fuse
5014 This option controls the level of fusion.
5015 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5016 resulting schedule will be distributed as much as possible.
5017 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5018 try to fuse loops in the resulting schedule.
5020 =item * schedule_maximize_band_depth
5022 If this option is set, we do not split bands at the point
5023 where we detect splitting is necessary. Instead, we
5024 backtrack and split bands as early as possible. This
5025 reduces the number of splits and maximizes the width of
5026 the bands. Wider bands give more possibilities for tiling.
5027 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5028 then bands will be split as early as possible, even if there is no need.
5029 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5031 =item * schedule_outer_zero_distance
5033 If this option is set, then we try to construct schedules
5034 where the outermost scheduling dimension in each band
5035 results in a zero dependence distance over the proximity
5038 =item * schedule_split_scaled
5040 If this option is set, then we try to construct schedules in which the
5041 constant term is split off from the linear part if the linear parts of
5042 the scheduling rows for all nodes in the graphs have a common non-trivial
5044 The constant term is then placed in a separate band and the linear
5047 =item * schedule_algorithm
5049 Selects the scheduling algorithm to be used.
5050 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5051 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5053 =item * schedule_separate_components
5055 If at any point the dependence graph contains any (weakly connected) components,
5056 then these components are scheduled separately.
5057 If this option is not set, then some iterations of the domains
5058 in these components may be scheduled together.
5059 If this option is set, then the components are given consecutive
5064 =head2 Parametric Vertex Enumeration
5066 The parametric vertex enumeration described in this section
5067 is mainly intended to be used internally and by the C<barvinok>
5070 #include <isl/vertices.h>
5071 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5072 __isl_keep isl_basic_set *bset);
5074 The function C<isl_basic_set_compute_vertices> performs the
5075 actual computation of the parametric vertices and the chamber
5076 decomposition and store the result in an C<isl_vertices> object.
5077 This information can be queried by either iterating over all
5078 the vertices or iterating over all the chambers or cells
5079 and then iterating over all vertices that are active on the chamber.
5081 int isl_vertices_foreach_vertex(
5082 __isl_keep isl_vertices *vertices,
5083 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5086 int isl_vertices_foreach_cell(
5087 __isl_keep isl_vertices *vertices,
5088 int (*fn)(__isl_take isl_cell *cell, void *user),
5090 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5091 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5094 Other operations that can be performed on an C<isl_vertices> object are
5097 isl_ctx *isl_vertices_get_ctx(
5098 __isl_keep isl_vertices *vertices);
5099 int isl_vertices_get_n_vertices(
5100 __isl_keep isl_vertices *vertices);
5101 void isl_vertices_free(__isl_take isl_vertices *vertices);
5103 Vertices can be inspected and destroyed using the following functions.
5105 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5106 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5107 __isl_give isl_basic_set *isl_vertex_get_domain(
5108 __isl_keep isl_vertex *vertex);
5109 __isl_give isl_basic_set *isl_vertex_get_expr(
5110 __isl_keep isl_vertex *vertex);
5111 void isl_vertex_free(__isl_take isl_vertex *vertex);
5113 C<isl_vertex_get_expr> returns a singleton parametric set describing
5114 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5116 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5117 B<rational> basic sets, so they should mainly be used for inspection
5118 and should not be mixed with integer sets.
5120 Chambers can be inspected and destroyed using the following functions.
5122 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5123 __isl_give isl_basic_set *isl_cell_get_domain(
5124 __isl_keep isl_cell *cell);
5125 void isl_cell_free(__isl_take isl_cell *cell);
5129 Although C<isl> is mainly meant to be used as a library,
5130 it also contains some basic applications that use some
5131 of the functionality of C<isl>.
5132 The input may be specified in either the L<isl format>
5133 or the L<PolyLib format>.
5135 =head2 C<isl_polyhedron_sample>
5137 C<isl_polyhedron_sample> takes a polyhedron as input and prints
5138 an integer element of the polyhedron, if there is any.
5139 The first column in the output is the denominator and is always
5140 equal to 1. If the polyhedron contains no integer points,
5141 then a vector of length zero is printed.
5145 C<isl_pip> takes the same input as the C<example> program
5146 from the C<piplib> distribution, i.e., a set of constraints
5147 on the parameters, a line containing only -1 and finally a set
5148 of constraints on a parametric polyhedron.
5149 The coefficients of the parameters appear in the last columns
5150 (but before the final constant column).
5151 The output is the lexicographic minimum of the parametric polyhedron.
5152 As C<isl> currently does not have its own output format, the output
5153 is just a dump of the internal state.
5155 =head2 C<isl_polyhedron_minimize>
5157 C<isl_polyhedron_minimize> computes the minimum of some linear
5158 or affine objective function over the integer points in a polyhedron.
5159 If an affine objective function
5160 is given, then the constant should appear in the last column.
5162 =head2 C<isl_polytope_scan>
5164 Given a polytope, C<isl_polytope_scan> prints
5165 all integer points in the polytope.