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);
750 #include <isl/point.h>
751 __isl_give isl_space *isl_point_get_space(
752 __isl_keep isl_point *pnt);
754 The identifiers or names of the individual dimensions may be set or read off
755 using the following functions.
757 #include <isl/space.h>
758 __isl_give isl_space *isl_space_set_dim_id(
759 __isl_take isl_space *space,
760 enum isl_dim_type type, unsigned pos,
761 __isl_take isl_id *id);
762 int isl_space_has_dim_id(__isl_keep isl_space *space,
763 enum isl_dim_type type, unsigned pos);
764 __isl_give isl_id *isl_space_get_dim_id(
765 __isl_keep isl_space *space,
766 enum isl_dim_type type, unsigned pos);
767 __isl_give isl_space *isl_space_set_dim_name(
768 __isl_take isl_space *space,
769 enum isl_dim_type type, unsigned pos,
770 __isl_keep const char *name);
771 int isl_space_has_dim_name(__isl_keep isl_space *space,
772 enum isl_dim_type type, unsigned pos);
773 __isl_keep const char *isl_space_get_dim_name(
774 __isl_keep isl_space *space,
775 enum isl_dim_type type, unsigned pos);
777 Note that C<isl_space_get_name> returns a pointer to some internal
778 data structure, so the result can only be used while the
779 corresponding C<isl_space> is alive.
780 Also note that every function that operates on two sets or relations
781 requires that both arguments have the same parameters. This also
782 means that if one of the arguments has named parameters, then the
783 other needs to have named parameters too and the names need to match.
784 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
785 arguments may have different parameters (as long as they are named),
786 in which case the result will have as parameters the union of the parameters of
789 Given the identifier or name of a dimension (typically a parameter),
790 its position can be obtained from the following function.
792 #include <isl/space.h>
793 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
794 enum isl_dim_type type, __isl_keep isl_id *id);
795 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
796 enum isl_dim_type type, const char *name);
798 The identifiers or names of entire spaces may be set or read off
799 using the following functions.
801 #include <isl/space.h>
802 __isl_give isl_space *isl_space_set_tuple_id(
803 __isl_take isl_space *space,
804 enum isl_dim_type type, __isl_take isl_id *id);
805 __isl_give isl_space *isl_space_reset_tuple_id(
806 __isl_take isl_space *space, enum isl_dim_type type);
807 int isl_space_has_tuple_id(__isl_keep isl_space *space,
808 enum isl_dim_type type);
809 __isl_give isl_id *isl_space_get_tuple_id(
810 __isl_keep isl_space *space, enum isl_dim_type type);
811 __isl_give isl_space *isl_space_set_tuple_name(
812 __isl_take isl_space *space,
813 enum isl_dim_type type, const char *s);
814 int isl_space_has_tuple_name(__isl_keep isl_space *space,
815 enum isl_dim_type type);
816 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
817 enum isl_dim_type type);
819 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
820 or C<isl_dim_set>. As with C<isl_space_get_name>,
821 the C<isl_space_get_tuple_name> function returns a pointer to some internal
823 Binary operations require the corresponding spaces of their arguments
824 to have the same name.
826 Spaces can be nested. In particular, the domain of a set or
827 the domain or range of a relation can be a nested relation.
828 The following functions can be used to construct and deconstruct
831 #include <isl/space.h>
832 int isl_space_is_wrapping(__isl_keep isl_space *space);
833 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
834 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
836 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
837 be the space of a set, while that of
838 C<isl_space_wrap> should be the space of a relation.
839 Conversely, the output of C<isl_space_unwrap> is the space
840 of a relation, while that of C<isl_space_wrap> is the space of a set.
842 Spaces can be created from other spaces
843 using the following functions.
845 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
846 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
847 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
848 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
849 __isl_give isl_space *isl_space_params(
850 __isl_take isl_space *space);
851 __isl_give isl_space *isl_space_set_from_params(
852 __isl_take isl_space *space);
853 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
854 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
855 __isl_take isl_space *right);
856 __isl_give isl_space *isl_space_align_params(
857 __isl_take isl_space *space1, __isl_take isl_space *space2)
858 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
859 enum isl_dim_type type, unsigned pos, unsigned n);
860 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
861 enum isl_dim_type type, unsigned n);
862 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
863 enum isl_dim_type type, unsigned first, unsigned n);
864 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
865 enum isl_dim_type dst_type, unsigned dst_pos,
866 enum isl_dim_type src_type, unsigned src_pos,
868 __isl_give isl_space *isl_space_map_from_set(
869 __isl_take isl_space *space);
870 __isl_give isl_space *isl_space_map_from_domain_and_range(
871 __isl_take isl_space *domain,
872 __isl_take isl_space *range);
873 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
874 __isl_give isl_space *isl_space_curry(
875 __isl_take isl_space *space);
876 __isl_give isl_space *isl_space_uncurry(
877 __isl_take isl_space *space);
879 Note that if dimensions are added or removed from a space, then
880 the name and the internal structure are lost.
884 A local space is essentially a space with
885 zero or more existentially quantified variables.
886 The local space of a (constraint of a) basic set or relation can be obtained
887 using the following functions.
889 #include <isl/constraint.h>
890 __isl_give isl_local_space *isl_constraint_get_local_space(
891 __isl_keep isl_constraint *constraint);
894 __isl_give isl_local_space *isl_basic_set_get_local_space(
895 __isl_keep isl_basic_set *bset);
898 __isl_give isl_local_space *isl_basic_map_get_local_space(
899 __isl_keep isl_basic_map *bmap);
901 A new local space can be created from a space using
903 #include <isl/local_space.h>
904 __isl_give isl_local_space *isl_local_space_from_space(
905 __isl_take isl_space *space);
907 They can be inspected, modified, copied and freed using the following functions.
909 #include <isl/local_space.h>
910 isl_ctx *isl_local_space_get_ctx(
911 __isl_keep isl_local_space *ls);
912 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
913 int isl_local_space_dim(__isl_keep isl_local_space *ls,
914 enum isl_dim_type type);
915 int isl_local_space_has_dim_id(
916 __isl_keep isl_local_space *ls,
917 enum isl_dim_type type, unsigned pos);
918 __isl_give isl_id *isl_local_space_get_dim_id(
919 __isl_keep isl_local_space *ls,
920 enum isl_dim_type type, unsigned pos);
921 int isl_local_space_has_dim_name(
922 __isl_keep isl_local_space *ls,
923 enum isl_dim_type type, unsigned pos)
924 const char *isl_local_space_get_dim_name(
925 __isl_keep isl_local_space *ls,
926 enum isl_dim_type type, unsigned pos);
927 __isl_give isl_local_space *isl_local_space_set_dim_name(
928 __isl_take isl_local_space *ls,
929 enum isl_dim_type type, unsigned pos, const char *s);
930 __isl_give isl_local_space *isl_local_space_set_dim_id(
931 __isl_take isl_local_space *ls,
932 enum isl_dim_type type, unsigned pos,
933 __isl_take isl_id *id);
934 __isl_give isl_space *isl_local_space_get_space(
935 __isl_keep isl_local_space *ls);
936 __isl_give isl_aff *isl_local_space_get_div(
937 __isl_keep isl_local_space *ls, int pos);
938 __isl_give isl_local_space *isl_local_space_copy(
939 __isl_keep isl_local_space *ls);
940 void *isl_local_space_free(__isl_take isl_local_space *ls);
942 Two local spaces can be compared using
944 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
945 __isl_keep isl_local_space *ls2);
947 Local spaces can be created from other local spaces
948 using the following functions.
950 __isl_give isl_local_space *isl_local_space_domain(
951 __isl_take isl_local_space *ls);
952 __isl_give isl_local_space *isl_local_space_range(
953 __isl_take isl_local_space *ls);
954 __isl_give isl_local_space *isl_local_space_from_domain(
955 __isl_take isl_local_space *ls);
956 __isl_give isl_local_space *isl_local_space_intersect(
957 __isl_take isl_local_space *ls1,
958 __isl_take isl_local_space *ls2);
959 __isl_give isl_local_space *isl_local_space_add_dims(
960 __isl_take isl_local_space *ls,
961 enum isl_dim_type type, unsigned n);
962 __isl_give isl_local_space *isl_local_space_insert_dims(
963 __isl_take isl_local_space *ls,
964 enum isl_dim_type type, unsigned first, unsigned n);
965 __isl_give isl_local_space *isl_local_space_drop_dims(
966 __isl_take isl_local_space *ls,
967 enum isl_dim_type type, unsigned first, unsigned n);
969 =head2 Input and Output
971 C<isl> supports its own input/output format, which is similar
972 to the C<Omega> format, but also supports the C<PolyLib> format
977 The C<isl> format is similar to that of C<Omega>, but has a different
978 syntax for describing the parameters and allows for the definition
979 of an existentially quantified variable as the integer division
980 of an affine expression.
981 For example, the set of integers C<i> between C<0> and C<n>
982 such that C<i % 10 <= 6> can be described as
984 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
987 A set or relation can have several disjuncts, separated
988 by the keyword C<or>. Each disjunct is either a conjunction
989 of constraints or a projection (C<exists>) of a conjunction
990 of constraints. The constraints are separated by the keyword
993 =head3 C<PolyLib> format
995 If the represented set is a union, then the first line
996 contains a single number representing the number of disjuncts.
997 Otherwise, a line containing the number C<1> is optional.
999 Each disjunct is represented by a matrix of constraints.
1000 The first line contains two numbers representing
1001 the number of rows and columns,
1002 where the number of rows is equal to the number of constraints
1003 and the number of columns is equal to two plus the number of variables.
1004 The following lines contain the actual rows of the constraint matrix.
1005 In each row, the first column indicates whether the constraint
1006 is an equality (C<0>) or inequality (C<1>). The final column
1007 corresponds to the constant term.
1009 If the set is parametric, then the coefficients of the parameters
1010 appear in the last columns before the constant column.
1011 The coefficients of any existentially quantified variables appear
1012 between those of the set variables and those of the parameters.
1014 =head3 Extended C<PolyLib> format
1016 The extended C<PolyLib> format is nearly identical to the
1017 C<PolyLib> format. The only difference is that the line
1018 containing the number of rows and columns of a constraint matrix
1019 also contains four additional numbers:
1020 the number of output dimensions, the number of input dimensions,
1021 the number of local dimensions (i.e., the number of existentially
1022 quantified variables) and the number of parameters.
1023 For sets, the number of ``output'' dimensions is equal
1024 to the number of set dimensions, while the number of ``input''
1029 #include <isl/set.h>
1030 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1031 isl_ctx *ctx, FILE *input);
1032 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1033 isl_ctx *ctx, const char *str);
1034 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1036 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1039 #include <isl/map.h>
1040 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1041 isl_ctx *ctx, FILE *input);
1042 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1043 isl_ctx *ctx, const char *str);
1044 __isl_give isl_map *isl_map_read_from_file(
1045 isl_ctx *ctx, FILE *input);
1046 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1049 #include <isl/union_set.h>
1050 __isl_give isl_union_set *isl_union_set_read_from_file(
1051 isl_ctx *ctx, FILE *input);
1052 __isl_give isl_union_set *isl_union_set_read_from_str(
1053 isl_ctx *ctx, const char *str);
1055 #include <isl/union_map.h>
1056 __isl_give isl_union_map *isl_union_map_read_from_file(
1057 isl_ctx *ctx, FILE *input);
1058 __isl_give isl_union_map *isl_union_map_read_from_str(
1059 isl_ctx *ctx, const char *str);
1061 The input format is autodetected and may be either the C<PolyLib> format
1062 or the C<isl> format.
1066 Before anything can be printed, an C<isl_printer> needs to
1069 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1071 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1072 void *isl_printer_free(__isl_take isl_printer *printer);
1073 __isl_give char *isl_printer_get_str(
1074 __isl_keep isl_printer *printer);
1076 The printer can be inspected using the following functions.
1078 FILE *isl_printer_get_file(
1079 __isl_keep isl_printer *printer);
1080 int isl_printer_get_output_format(
1081 __isl_keep isl_printer *p);
1083 The behavior of the printer can be modified in various ways
1085 __isl_give isl_printer *isl_printer_set_output_format(
1086 __isl_take isl_printer *p, int output_format);
1087 __isl_give isl_printer *isl_printer_set_indent(
1088 __isl_take isl_printer *p, int indent);
1089 __isl_give isl_printer *isl_printer_indent(
1090 __isl_take isl_printer *p, int indent);
1091 __isl_give isl_printer *isl_printer_set_prefix(
1092 __isl_take isl_printer *p, const char *prefix);
1093 __isl_give isl_printer *isl_printer_set_suffix(
1094 __isl_take isl_printer *p, const char *suffix);
1096 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1097 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1098 and defaults to C<ISL_FORMAT_ISL>.
1099 Each line in the output is indented by C<indent> (set by
1100 C<isl_printer_set_indent>) spaces
1101 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1102 In the C<PolyLib> format output,
1103 the coefficients of the existentially quantified variables
1104 appear between those of the set variables and those
1106 The function C<isl_printer_indent> increases the indentation
1107 by the specified amount (which may be negative).
1109 To actually print something, use
1111 #include <isl/printer.h>
1112 __isl_give isl_printer *isl_printer_print_double(
1113 __isl_take isl_printer *p, double d);
1115 #include <isl/set.h>
1116 __isl_give isl_printer *isl_printer_print_basic_set(
1117 __isl_take isl_printer *printer,
1118 __isl_keep isl_basic_set *bset);
1119 __isl_give isl_printer *isl_printer_print_set(
1120 __isl_take isl_printer *printer,
1121 __isl_keep isl_set *set);
1123 #include <isl/map.h>
1124 __isl_give isl_printer *isl_printer_print_basic_map(
1125 __isl_take isl_printer *printer,
1126 __isl_keep isl_basic_map *bmap);
1127 __isl_give isl_printer *isl_printer_print_map(
1128 __isl_take isl_printer *printer,
1129 __isl_keep isl_map *map);
1131 #include <isl/union_set.h>
1132 __isl_give isl_printer *isl_printer_print_union_set(
1133 __isl_take isl_printer *p,
1134 __isl_keep isl_union_set *uset);
1136 #include <isl/union_map.h>
1137 __isl_give isl_printer *isl_printer_print_union_map(
1138 __isl_take isl_printer *p,
1139 __isl_keep isl_union_map *umap);
1141 When called on a file printer, the following function flushes
1142 the file. When called on a string printer, the buffer is cleared.
1144 __isl_give isl_printer *isl_printer_flush(
1145 __isl_take isl_printer *p);
1147 =head2 Creating New Sets and Relations
1149 C<isl> has functions for creating some standard sets and relations.
1153 =item * Empty sets and relations
1155 __isl_give isl_basic_set *isl_basic_set_empty(
1156 __isl_take isl_space *space);
1157 __isl_give isl_basic_map *isl_basic_map_empty(
1158 __isl_take isl_space *space);
1159 __isl_give isl_set *isl_set_empty(
1160 __isl_take isl_space *space);
1161 __isl_give isl_map *isl_map_empty(
1162 __isl_take isl_space *space);
1163 __isl_give isl_union_set *isl_union_set_empty(
1164 __isl_take isl_space *space);
1165 __isl_give isl_union_map *isl_union_map_empty(
1166 __isl_take isl_space *space);
1168 For C<isl_union_set>s and C<isl_union_map>s, the space
1169 is only used to specify the parameters.
1171 =item * Universe sets and relations
1173 __isl_give isl_basic_set *isl_basic_set_universe(
1174 __isl_take isl_space *space);
1175 __isl_give isl_basic_map *isl_basic_map_universe(
1176 __isl_take isl_space *space);
1177 __isl_give isl_set *isl_set_universe(
1178 __isl_take isl_space *space);
1179 __isl_give isl_map *isl_map_universe(
1180 __isl_take isl_space *space);
1181 __isl_give isl_union_set *isl_union_set_universe(
1182 __isl_take isl_union_set *uset);
1183 __isl_give isl_union_map *isl_union_map_universe(
1184 __isl_take isl_union_map *umap);
1186 The sets and relations constructed by the functions above
1187 contain all integer values, while those constructed by the
1188 functions below only contain non-negative values.
1190 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1191 __isl_take isl_space *space);
1192 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1193 __isl_take isl_space *space);
1194 __isl_give isl_set *isl_set_nat_universe(
1195 __isl_take isl_space *space);
1196 __isl_give isl_map *isl_map_nat_universe(
1197 __isl_take isl_space *space);
1199 =item * Identity relations
1201 __isl_give isl_basic_map *isl_basic_map_identity(
1202 __isl_take isl_space *space);
1203 __isl_give isl_map *isl_map_identity(
1204 __isl_take isl_space *space);
1206 The number of input and output dimensions in C<space> needs
1209 =item * Lexicographic order
1211 __isl_give isl_map *isl_map_lex_lt(
1212 __isl_take isl_space *set_space);
1213 __isl_give isl_map *isl_map_lex_le(
1214 __isl_take isl_space *set_space);
1215 __isl_give isl_map *isl_map_lex_gt(
1216 __isl_take isl_space *set_space);
1217 __isl_give isl_map *isl_map_lex_ge(
1218 __isl_take isl_space *set_space);
1219 __isl_give isl_map *isl_map_lex_lt_first(
1220 __isl_take isl_space *space, unsigned n);
1221 __isl_give isl_map *isl_map_lex_le_first(
1222 __isl_take isl_space *space, unsigned n);
1223 __isl_give isl_map *isl_map_lex_gt_first(
1224 __isl_take isl_space *space, unsigned n);
1225 __isl_give isl_map *isl_map_lex_ge_first(
1226 __isl_take isl_space *space, unsigned n);
1228 The first four functions take a space for a B<set>
1229 and return relations that express that the elements in the domain
1230 are lexicographically less
1231 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1232 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1233 than the elements in the range.
1234 The last four functions take a space for a map
1235 and return relations that express that the first C<n> dimensions
1236 in the domain are lexicographically less
1237 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1238 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1239 than the first C<n> dimensions in the range.
1243 A basic set or relation can be converted to a set or relation
1244 using the following functions.
1246 __isl_give isl_set *isl_set_from_basic_set(
1247 __isl_take isl_basic_set *bset);
1248 __isl_give isl_map *isl_map_from_basic_map(
1249 __isl_take isl_basic_map *bmap);
1251 Sets and relations can be converted to union sets and relations
1252 using the following functions.
1254 __isl_give isl_union_set *isl_union_set_from_basic_set(
1255 __isl_take isl_basic_set *bset);
1256 __isl_give isl_union_map *isl_union_map_from_basic_map(
1257 __isl_take isl_basic_map *bmap);
1258 __isl_give isl_union_set *isl_union_set_from_set(
1259 __isl_take isl_set *set);
1260 __isl_give isl_union_map *isl_union_map_from_map(
1261 __isl_take isl_map *map);
1263 The inverse conversions below can only be used if the input
1264 union set or relation is known to contain elements in exactly one
1267 __isl_give isl_set *isl_set_from_union_set(
1268 __isl_take isl_union_set *uset);
1269 __isl_give isl_map *isl_map_from_union_map(
1270 __isl_take isl_union_map *umap);
1272 A zero-dimensional set can be constructed on a given parameter domain
1273 using the following function.
1275 __isl_give isl_set *isl_set_from_params(
1276 __isl_take isl_set *set);
1278 Sets and relations can be copied and freed again using the following
1281 __isl_give isl_basic_set *isl_basic_set_copy(
1282 __isl_keep isl_basic_set *bset);
1283 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1284 __isl_give isl_union_set *isl_union_set_copy(
1285 __isl_keep isl_union_set *uset);
1286 __isl_give isl_basic_map *isl_basic_map_copy(
1287 __isl_keep isl_basic_map *bmap);
1288 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1289 __isl_give isl_union_map *isl_union_map_copy(
1290 __isl_keep isl_union_map *umap);
1291 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1292 void *isl_set_free(__isl_take isl_set *set);
1293 void *isl_union_set_free(__isl_take isl_union_set *uset);
1294 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1295 void *isl_map_free(__isl_take isl_map *map);
1296 void *isl_union_map_free(__isl_take isl_union_map *umap);
1298 Other sets and relations can be constructed by starting
1299 from a universe set or relation, adding equality and/or
1300 inequality constraints and then projecting out the
1301 existentially quantified variables, if any.
1302 Constraints can be constructed, manipulated and
1303 added to (or removed from) (basic) sets and relations
1304 using the following functions.
1306 #include <isl/constraint.h>
1307 __isl_give isl_constraint *isl_equality_alloc(
1308 __isl_take isl_local_space *ls);
1309 __isl_give isl_constraint *isl_inequality_alloc(
1310 __isl_take isl_local_space *ls);
1311 __isl_give isl_constraint *isl_constraint_set_constant(
1312 __isl_take isl_constraint *constraint, isl_int v);
1313 __isl_give isl_constraint *isl_constraint_set_constant_si(
1314 __isl_take isl_constraint *constraint, int v);
1315 __isl_give isl_constraint *isl_constraint_set_coefficient(
1316 __isl_take isl_constraint *constraint,
1317 enum isl_dim_type type, int pos, isl_int v);
1318 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1319 __isl_take isl_constraint *constraint,
1320 enum isl_dim_type type, int pos, int v);
1321 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1322 __isl_take isl_basic_map *bmap,
1323 __isl_take isl_constraint *constraint);
1324 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1325 __isl_take isl_basic_set *bset,
1326 __isl_take isl_constraint *constraint);
1327 __isl_give isl_map *isl_map_add_constraint(
1328 __isl_take isl_map *map,
1329 __isl_take isl_constraint *constraint);
1330 __isl_give isl_set *isl_set_add_constraint(
1331 __isl_take isl_set *set,
1332 __isl_take isl_constraint *constraint);
1333 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1334 __isl_take isl_basic_set *bset,
1335 __isl_take isl_constraint *constraint);
1337 For example, to create a set containing the even integers
1338 between 10 and 42, you would use the following code.
1341 isl_local_space *ls;
1343 isl_basic_set *bset;
1345 space = isl_space_set_alloc(ctx, 0, 2);
1346 bset = isl_basic_set_universe(isl_space_copy(space));
1347 ls = isl_local_space_from_space(space);
1349 c = isl_equality_alloc(isl_local_space_copy(ls));
1350 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1351 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1352 bset = isl_basic_set_add_constraint(bset, c);
1354 c = isl_inequality_alloc(isl_local_space_copy(ls));
1355 c = isl_constraint_set_constant_si(c, -10);
1356 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1357 bset = isl_basic_set_add_constraint(bset, c);
1359 c = isl_inequality_alloc(ls);
1360 c = isl_constraint_set_constant_si(c, 42);
1361 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1362 bset = isl_basic_set_add_constraint(bset, c);
1364 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1368 isl_basic_set *bset;
1369 bset = isl_basic_set_read_from_str(ctx,
1370 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1372 A basic set or relation can also be constructed from two matrices
1373 describing the equalities and the inequalities.
1375 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1376 __isl_take isl_space *space,
1377 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1378 enum isl_dim_type c1,
1379 enum isl_dim_type c2, enum isl_dim_type c3,
1380 enum isl_dim_type c4);
1381 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1382 __isl_take isl_space *space,
1383 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1384 enum isl_dim_type c1,
1385 enum isl_dim_type c2, enum isl_dim_type c3,
1386 enum isl_dim_type c4, enum isl_dim_type c5);
1388 The C<isl_dim_type> arguments indicate the order in which
1389 different kinds of variables appear in the input matrices
1390 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1391 C<isl_dim_set> and C<isl_dim_div> for sets and
1392 of C<isl_dim_cst>, C<isl_dim_param>,
1393 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1395 A (basic or union) set or relation can also be constructed from a
1396 (union) (piecewise) (multiple) affine expression
1397 or a list of affine expressions
1398 (See L<"Piecewise Quasi Affine Expressions"> and
1399 L<"Piecewise Multiple Quasi Affine Expressions">).
1401 __isl_give isl_basic_map *isl_basic_map_from_aff(
1402 __isl_take isl_aff *aff);
1403 __isl_give isl_map *isl_map_from_aff(
1404 __isl_take isl_aff *aff);
1405 __isl_give isl_set *isl_set_from_pw_aff(
1406 __isl_take isl_pw_aff *pwaff);
1407 __isl_give isl_map *isl_map_from_pw_aff(
1408 __isl_take isl_pw_aff *pwaff);
1409 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1410 __isl_take isl_space *domain_space,
1411 __isl_take isl_aff_list *list);
1412 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1413 __isl_take isl_multi_aff *maff)
1414 __isl_give isl_map *isl_map_from_multi_aff(
1415 __isl_take isl_multi_aff *maff)
1416 __isl_give isl_set *isl_set_from_pw_multi_aff(
1417 __isl_take isl_pw_multi_aff *pma);
1418 __isl_give isl_map *isl_map_from_pw_multi_aff(
1419 __isl_take isl_pw_multi_aff *pma);
1420 __isl_give isl_union_map *
1421 isl_union_map_from_union_pw_multi_aff(
1422 __isl_take isl_union_pw_multi_aff *upma);
1424 The C<domain_dim> argument describes the domain of the resulting
1425 basic relation. It is required because the C<list> may consist
1426 of zero affine expressions.
1428 =head2 Inspecting Sets and Relations
1430 Usually, the user should not have to care about the actual constraints
1431 of the sets and maps, but should instead apply the abstract operations
1432 explained in the following sections.
1433 Occasionally, however, it may be required to inspect the individual
1434 coefficients of the constraints. This section explains how to do so.
1435 In these cases, it may also be useful to have C<isl> compute
1436 an explicit representation of the existentially quantified variables.
1438 __isl_give isl_set *isl_set_compute_divs(
1439 __isl_take isl_set *set);
1440 __isl_give isl_map *isl_map_compute_divs(
1441 __isl_take isl_map *map);
1442 __isl_give isl_union_set *isl_union_set_compute_divs(
1443 __isl_take isl_union_set *uset);
1444 __isl_give isl_union_map *isl_union_map_compute_divs(
1445 __isl_take isl_union_map *umap);
1447 This explicit representation defines the existentially quantified
1448 variables as integer divisions of the other variables, possibly
1449 including earlier existentially quantified variables.
1450 An explicitly represented existentially quantified variable therefore
1451 has a unique value when the values of the other variables are known.
1452 If, furthermore, the same existentials, i.e., existentials
1453 with the same explicit representations, should appear in the
1454 same order in each of the disjuncts of a set or map, then the user should call
1455 either of the following functions.
1457 __isl_give isl_set *isl_set_align_divs(
1458 __isl_take isl_set *set);
1459 __isl_give isl_map *isl_map_align_divs(
1460 __isl_take isl_map *map);
1462 Alternatively, the existentially quantified variables can be removed
1463 using the following functions, which compute an overapproximation.
1465 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1466 __isl_take isl_basic_set *bset);
1467 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1468 __isl_take isl_basic_map *bmap);
1469 __isl_give isl_set *isl_set_remove_divs(
1470 __isl_take isl_set *set);
1471 __isl_give isl_map *isl_map_remove_divs(
1472 __isl_take isl_map *map);
1474 It is also possible to only remove those divs that are defined
1475 in terms of a given range of dimensions or only those for which
1476 no explicit representation is known.
1478 __isl_give isl_basic_set *
1479 isl_basic_set_remove_divs_involving_dims(
1480 __isl_take isl_basic_set *bset,
1481 enum isl_dim_type type,
1482 unsigned first, unsigned n);
1483 __isl_give isl_basic_map *
1484 isl_basic_map_remove_divs_involving_dims(
1485 __isl_take isl_basic_map *bmap,
1486 enum isl_dim_type type,
1487 unsigned first, unsigned n);
1488 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1489 __isl_take isl_set *set, enum isl_dim_type type,
1490 unsigned first, unsigned n);
1491 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1492 __isl_take isl_map *map, enum isl_dim_type type,
1493 unsigned first, unsigned n);
1495 __isl_give isl_basic_set *
1496 isl_basic_set_remove_unknown_divs(
1497 __isl_take isl_basic_set *bset);
1498 __isl_give isl_set *isl_set_remove_unknown_divs(
1499 __isl_take isl_set *set);
1500 __isl_give isl_map *isl_map_remove_unknown_divs(
1501 __isl_take isl_map *map);
1503 To iterate over all the sets or maps in a union set or map, use
1505 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1506 int (*fn)(__isl_take isl_set *set, void *user),
1508 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1509 int (*fn)(__isl_take isl_map *map, void *user),
1512 The number of sets or maps in a union set or map can be obtained
1515 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1516 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1518 To extract the set or map in a given space from a union, use
1520 __isl_give isl_set *isl_union_set_extract_set(
1521 __isl_keep isl_union_set *uset,
1522 __isl_take isl_space *space);
1523 __isl_give isl_map *isl_union_map_extract_map(
1524 __isl_keep isl_union_map *umap,
1525 __isl_take isl_space *space);
1527 To iterate over all the basic sets or maps in a set or map, use
1529 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1530 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1532 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1533 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1536 The callback function C<fn> should return 0 if successful and
1537 -1 if an error occurs. In the latter case, or if any other error
1538 occurs, the above functions will return -1.
1540 It should be noted that C<isl> does not guarantee that
1541 the basic sets or maps passed to C<fn> are disjoint.
1542 If this is required, then the user should call one of
1543 the following functions first.
1545 __isl_give isl_set *isl_set_make_disjoint(
1546 __isl_take isl_set *set);
1547 __isl_give isl_map *isl_map_make_disjoint(
1548 __isl_take isl_map *map);
1550 The number of basic sets in a set can be obtained
1553 int isl_set_n_basic_set(__isl_keep isl_set *set);
1555 To iterate over the constraints of a basic set or map, use
1557 #include <isl/constraint.h>
1559 int isl_basic_set_n_constraint(
1560 __isl_keep isl_basic_set *bset);
1561 int isl_basic_set_foreach_constraint(
1562 __isl_keep isl_basic_set *bset,
1563 int (*fn)(__isl_take isl_constraint *c, void *user),
1565 int isl_basic_map_foreach_constraint(
1566 __isl_keep isl_basic_map *bmap,
1567 int (*fn)(__isl_take isl_constraint *c, void *user),
1569 void *isl_constraint_free(__isl_take isl_constraint *c);
1571 Again, the callback function C<fn> should return 0 if successful and
1572 -1 if an error occurs. In the latter case, or if any other error
1573 occurs, the above functions will return -1.
1574 The constraint C<c> represents either an equality or an inequality.
1575 Use the following function to find out whether a constraint
1576 represents an equality. If not, it represents an inequality.
1578 int isl_constraint_is_equality(
1579 __isl_keep isl_constraint *constraint);
1581 The coefficients of the constraints can be inspected using
1582 the following functions.
1584 int isl_constraint_is_lower_bound(
1585 __isl_keep isl_constraint *constraint,
1586 enum isl_dim_type type, unsigned pos);
1587 int isl_constraint_is_upper_bound(
1588 __isl_keep isl_constraint *constraint,
1589 enum isl_dim_type type, unsigned pos);
1590 void isl_constraint_get_constant(
1591 __isl_keep isl_constraint *constraint, isl_int *v);
1592 void isl_constraint_get_coefficient(
1593 __isl_keep isl_constraint *constraint,
1594 enum isl_dim_type type, int pos, isl_int *v);
1595 int isl_constraint_involves_dims(
1596 __isl_keep isl_constraint *constraint,
1597 enum isl_dim_type type, unsigned first, unsigned n);
1599 The explicit representations of the existentially quantified
1600 variables can be inspected using the following function.
1601 Note that the user is only allowed to use this function
1602 if the inspected set or map is the result of a call
1603 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1604 The existentially quantified variable is equal to the floor
1605 of the returned affine expression. The affine expression
1606 itself can be inspected using the functions in
1607 L<"Piecewise Quasi Affine Expressions">.
1609 __isl_give isl_aff *isl_constraint_get_div(
1610 __isl_keep isl_constraint *constraint, int pos);
1612 To obtain the constraints of a basic set or map in matrix
1613 form, use the following functions.
1615 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1616 __isl_keep isl_basic_set *bset,
1617 enum isl_dim_type c1, enum isl_dim_type c2,
1618 enum isl_dim_type c3, enum isl_dim_type c4);
1619 __isl_give isl_mat *isl_basic_set_inequalities_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_map_equalities_matrix(
1624 __isl_keep isl_basic_map *bmap,
1625 enum isl_dim_type c1,
1626 enum isl_dim_type c2, enum isl_dim_type c3,
1627 enum isl_dim_type c4, enum isl_dim_type c5);
1628 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1629 __isl_keep isl_basic_map *bmap,
1630 enum isl_dim_type c1,
1631 enum isl_dim_type c2, enum isl_dim_type c3,
1632 enum isl_dim_type c4, enum isl_dim_type c5);
1634 The C<isl_dim_type> arguments dictate the order in which
1635 different kinds of variables appear in the resulting matrix
1636 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1637 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1639 The number of parameters, input, output or set dimensions can
1640 be obtained using the following functions.
1642 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1643 enum isl_dim_type type);
1644 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1645 enum isl_dim_type type);
1646 unsigned isl_set_dim(__isl_keep isl_set *set,
1647 enum isl_dim_type type);
1648 unsigned isl_map_dim(__isl_keep isl_map *map,
1649 enum isl_dim_type type);
1651 To check whether the description of a set or relation depends
1652 on one or more given dimensions, it is not necessary to iterate over all
1653 constraints. Instead the following functions can be used.
1655 int isl_basic_set_involves_dims(
1656 __isl_keep isl_basic_set *bset,
1657 enum isl_dim_type type, unsigned first, unsigned n);
1658 int isl_set_involves_dims(__isl_keep isl_set *set,
1659 enum isl_dim_type type, unsigned first, unsigned n);
1660 int isl_basic_map_involves_dims(
1661 __isl_keep isl_basic_map *bmap,
1662 enum isl_dim_type type, unsigned first, unsigned n);
1663 int isl_map_involves_dims(__isl_keep isl_map *map,
1664 enum isl_dim_type type, unsigned first, unsigned n);
1666 Similarly, the following functions can be used to check whether
1667 a given dimension is involved in any lower or upper bound.
1669 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1670 enum isl_dim_type type, unsigned pos);
1671 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1672 enum isl_dim_type type, unsigned pos);
1674 The identifiers or names of the domain and range spaces of a set
1675 or relation can be read off or set using the following functions.
1677 __isl_give isl_set *isl_set_set_tuple_id(
1678 __isl_take isl_set *set, __isl_take isl_id *id);
1679 __isl_give isl_set *isl_set_reset_tuple_id(
1680 __isl_take isl_set *set);
1681 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1682 __isl_give isl_id *isl_set_get_tuple_id(
1683 __isl_keep isl_set *set);
1684 __isl_give isl_map *isl_map_set_tuple_id(
1685 __isl_take isl_map *map, enum isl_dim_type type,
1686 __isl_take isl_id *id);
1687 __isl_give isl_map *isl_map_reset_tuple_id(
1688 __isl_take isl_map *map, enum isl_dim_type type);
1689 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1690 enum isl_dim_type type);
1691 __isl_give isl_id *isl_map_get_tuple_id(
1692 __isl_keep isl_map *map, enum isl_dim_type type);
1694 const char *isl_basic_set_get_tuple_name(
1695 __isl_keep isl_basic_set *bset);
1696 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1697 __isl_take isl_basic_set *set, const char *s);
1698 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1699 const char *isl_set_get_tuple_name(
1700 __isl_keep isl_set *set);
1701 const char *isl_basic_map_get_tuple_name(
1702 __isl_keep isl_basic_map *bmap,
1703 enum isl_dim_type type);
1704 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1705 __isl_take isl_basic_map *bmap,
1706 enum isl_dim_type type, const char *s);
1707 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1708 enum isl_dim_type type);
1709 const char *isl_map_get_tuple_name(
1710 __isl_keep isl_map *map,
1711 enum isl_dim_type type);
1713 As with C<isl_space_get_tuple_name>, the value returned points to
1714 an internal data structure.
1715 The identifiers, positions or names of individual dimensions can be
1716 read off using the following functions.
1718 __isl_give isl_id *isl_basic_set_get_dim_id(
1719 __isl_keep isl_basic_set *bset,
1720 enum isl_dim_type type, unsigned pos);
1721 __isl_give isl_set *isl_set_set_dim_id(
1722 __isl_take isl_set *set, enum isl_dim_type type,
1723 unsigned pos, __isl_take isl_id *id);
1724 int isl_set_has_dim_id(__isl_keep isl_set *set,
1725 enum isl_dim_type type, unsigned pos);
1726 __isl_give isl_id *isl_set_get_dim_id(
1727 __isl_keep isl_set *set, enum isl_dim_type type,
1729 int isl_basic_map_has_dim_id(
1730 __isl_keep isl_basic_map *bmap,
1731 enum isl_dim_type type, unsigned pos);
1732 __isl_give isl_map *isl_map_set_dim_id(
1733 __isl_take isl_map *map, enum isl_dim_type type,
1734 unsigned pos, __isl_take isl_id *id);
1735 int isl_map_has_dim_id(__isl_keep isl_map *map,
1736 enum isl_dim_type type, unsigned pos);
1737 __isl_give isl_id *isl_map_get_dim_id(
1738 __isl_keep isl_map *map, enum isl_dim_type type,
1741 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1742 enum isl_dim_type type, __isl_keep isl_id *id);
1743 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1744 enum isl_dim_type type, __isl_keep isl_id *id);
1745 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1746 enum isl_dim_type type, const char *name);
1747 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1748 enum isl_dim_type type, const char *name);
1750 const char *isl_constraint_get_dim_name(
1751 __isl_keep isl_constraint *constraint,
1752 enum isl_dim_type type, unsigned pos);
1753 const char *isl_basic_set_get_dim_name(
1754 __isl_keep isl_basic_set *bset,
1755 enum isl_dim_type type, unsigned pos);
1756 int isl_set_has_dim_name(__isl_keep isl_set *set,
1757 enum isl_dim_type type, unsigned pos);
1758 const char *isl_set_get_dim_name(
1759 __isl_keep isl_set *set,
1760 enum isl_dim_type type, unsigned pos);
1761 const char *isl_basic_map_get_dim_name(
1762 __isl_keep isl_basic_map *bmap,
1763 enum isl_dim_type type, unsigned pos);
1764 int isl_map_has_dim_name(__isl_keep isl_map *map,
1765 enum isl_dim_type type, unsigned pos);
1766 const char *isl_map_get_dim_name(
1767 __isl_keep isl_map *map,
1768 enum isl_dim_type type, unsigned pos);
1770 These functions are mostly useful to obtain the identifiers, positions
1771 or names of the parameters. Identifiers of individual dimensions are
1772 essentially only useful for printing. They are ignored by all other
1773 operations and may not be preserved across those operations.
1777 =head3 Unary Properties
1783 The following functions test whether the given set or relation
1784 contains any integer points. The ``plain'' variants do not perform
1785 any computations, but simply check if the given set or relation
1786 is already known to be empty.
1788 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1789 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1790 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1791 int isl_set_is_empty(__isl_keep isl_set *set);
1792 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1793 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1794 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1795 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1796 int isl_map_is_empty(__isl_keep isl_map *map);
1797 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1799 =item * Universality
1801 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1802 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1803 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1805 =item * Single-valuedness
1807 int isl_basic_map_is_single_valued(
1808 __isl_keep isl_basic_map *bmap);
1809 int isl_map_plain_is_single_valued(
1810 __isl_keep isl_map *map);
1811 int isl_map_is_single_valued(__isl_keep isl_map *map);
1812 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1816 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1817 int isl_map_is_injective(__isl_keep isl_map *map);
1818 int isl_union_map_plain_is_injective(
1819 __isl_keep isl_union_map *umap);
1820 int isl_union_map_is_injective(
1821 __isl_keep isl_union_map *umap);
1825 int isl_map_is_bijective(__isl_keep isl_map *map);
1826 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1830 int isl_basic_map_plain_is_fixed(
1831 __isl_keep isl_basic_map *bmap,
1832 enum isl_dim_type type, unsigned pos,
1834 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1835 enum isl_dim_type type, unsigned pos,
1837 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1838 enum isl_dim_type type, unsigned pos,
1841 Check if the relation obviously lies on a hyperplane where the given dimension
1842 has a fixed value and if so, return that value in C<*val>.
1846 To check whether a set is a parameter domain, use this function:
1848 int isl_set_is_params(__isl_keep isl_set *set);
1849 int isl_union_set_is_params(
1850 __isl_keep isl_union_set *uset);
1854 The following functions check whether the domain of the given
1855 (basic) set is a wrapped relation.
1857 int isl_basic_set_is_wrapping(
1858 __isl_keep isl_basic_set *bset);
1859 int isl_set_is_wrapping(__isl_keep isl_set *set);
1861 =item * Internal Product
1863 int isl_basic_map_can_zip(
1864 __isl_keep isl_basic_map *bmap);
1865 int isl_map_can_zip(__isl_keep isl_map *map);
1867 Check whether the product of domain and range of the given relation
1869 i.e., whether both domain and range are nested relations.
1873 int isl_basic_map_can_curry(
1874 __isl_keep isl_basic_map *bmap);
1875 int isl_map_can_curry(__isl_keep isl_map *map);
1877 Check whether the domain of the (basic) relation is a wrapped relation.
1879 int isl_basic_map_can_uncurry(
1880 __isl_keep isl_basic_map *bmap);
1881 int isl_map_can_uncurry(__isl_keep isl_map *map);
1883 Check whether the range of the (basic) relation is a wrapped relation.
1887 =head3 Binary Properties
1893 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1894 __isl_keep isl_set *set2);
1895 int isl_set_is_equal(__isl_keep isl_set *set1,
1896 __isl_keep isl_set *set2);
1897 int isl_union_set_is_equal(
1898 __isl_keep isl_union_set *uset1,
1899 __isl_keep isl_union_set *uset2);
1900 int isl_basic_map_is_equal(
1901 __isl_keep isl_basic_map *bmap1,
1902 __isl_keep isl_basic_map *bmap2);
1903 int isl_map_is_equal(__isl_keep isl_map *map1,
1904 __isl_keep isl_map *map2);
1905 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1906 __isl_keep isl_map *map2);
1907 int isl_union_map_is_equal(
1908 __isl_keep isl_union_map *umap1,
1909 __isl_keep isl_union_map *umap2);
1911 =item * Disjointness
1913 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1914 __isl_keep isl_set *set2);
1915 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1916 __isl_keep isl_set *set2);
1917 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1918 __isl_keep isl_map *map2);
1922 int isl_basic_set_is_subset(
1923 __isl_keep isl_basic_set *bset1,
1924 __isl_keep isl_basic_set *bset2);
1925 int isl_set_is_subset(__isl_keep isl_set *set1,
1926 __isl_keep isl_set *set2);
1927 int isl_set_is_strict_subset(
1928 __isl_keep isl_set *set1,
1929 __isl_keep isl_set *set2);
1930 int isl_union_set_is_subset(
1931 __isl_keep isl_union_set *uset1,
1932 __isl_keep isl_union_set *uset2);
1933 int isl_union_set_is_strict_subset(
1934 __isl_keep isl_union_set *uset1,
1935 __isl_keep isl_union_set *uset2);
1936 int isl_basic_map_is_subset(
1937 __isl_keep isl_basic_map *bmap1,
1938 __isl_keep isl_basic_map *bmap2);
1939 int isl_basic_map_is_strict_subset(
1940 __isl_keep isl_basic_map *bmap1,
1941 __isl_keep isl_basic_map *bmap2);
1942 int isl_map_is_subset(
1943 __isl_keep isl_map *map1,
1944 __isl_keep isl_map *map2);
1945 int isl_map_is_strict_subset(
1946 __isl_keep isl_map *map1,
1947 __isl_keep isl_map *map2);
1948 int isl_union_map_is_subset(
1949 __isl_keep isl_union_map *umap1,
1950 __isl_keep isl_union_map *umap2);
1951 int isl_union_map_is_strict_subset(
1952 __isl_keep isl_union_map *umap1,
1953 __isl_keep isl_union_map *umap2);
1955 Check whether the first argument is a (strict) subset of the
1960 int isl_set_plain_cmp(__isl_keep isl_set *set1,
1961 __isl_keep isl_set *set2);
1963 This function is useful for sorting C<isl_set>s.
1964 The order depends on the internal representation of the inputs.
1965 The order is fixed over different calls to the function (assuming
1966 the internal representation of the inputs has not changed), but may
1967 change over different versions of C<isl>.
1971 =head2 Unary Operations
1977 __isl_give isl_set *isl_set_complement(
1978 __isl_take isl_set *set);
1979 __isl_give isl_map *isl_map_complement(
1980 __isl_take isl_map *map);
1984 __isl_give isl_basic_map *isl_basic_map_reverse(
1985 __isl_take isl_basic_map *bmap);
1986 __isl_give isl_map *isl_map_reverse(
1987 __isl_take isl_map *map);
1988 __isl_give isl_union_map *isl_union_map_reverse(
1989 __isl_take isl_union_map *umap);
1993 __isl_give isl_basic_set *isl_basic_set_project_out(
1994 __isl_take isl_basic_set *bset,
1995 enum isl_dim_type type, unsigned first, unsigned n);
1996 __isl_give isl_basic_map *isl_basic_map_project_out(
1997 __isl_take isl_basic_map *bmap,
1998 enum isl_dim_type type, unsigned first, unsigned n);
1999 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2000 enum isl_dim_type type, unsigned first, unsigned n);
2001 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2002 enum isl_dim_type type, unsigned first, unsigned n);
2003 __isl_give isl_basic_set *isl_basic_set_params(
2004 __isl_take isl_basic_set *bset);
2005 __isl_give isl_basic_set *isl_basic_map_domain(
2006 __isl_take isl_basic_map *bmap);
2007 __isl_give isl_basic_set *isl_basic_map_range(
2008 __isl_take isl_basic_map *bmap);
2009 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2010 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2011 __isl_give isl_set *isl_map_domain(
2012 __isl_take isl_map *bmap);
2013 __isl_give isl_set *isl_map_range(
2014 __isl_take isl_map *map);
2015 __isl_give isl_set *isl_union_set_params(
2016 __isl_take isl_union_set *uset);
2017 __isl_give isl_set *isl_union_map_params(
2018 __isl_take isl_union_map *umap);
2019 __isl_give isl_union_set *isl_union_map_domain(
2020 __isl_take isl_union_map *umap);
2021 __isl_give isl_union_set *isl_union_map_range(
2022 __isl_take isl_union_map *umap);
2024 __isl_give isl_basic_map *isl_basic_map_domain_map(
2025 __isl_take isl_basic_map *bmap);
2026 __isl_give isl_basic_map *isl_basic_map_range_map(
2027 __isl_take isl_basic_map *bmap);
2028 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2029 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2030 __isl_give isl_union_map *isl_union_map_domain_map(
2031 __isl_take isl_union_map *umap);
2032 __isl_give isl_union_map *isl_union_map_range_map(
2033 __isl_take isl_union_map *umap);
2035 The functions above construct a (basic, regular or union) relation
2036 that maps (a wrapped version of) the input relation to its domain or range.
2040 __isl_give isl_basic_set *isl_basic_set_eliminate(
2041 __isl_take isl_basic_set *bset,
2042 enum isl_dim_type type,
2043 unsigned first, unsigned n);
2044 __isl_give isl_set *isl_set_eliminate(
2045 __isl_take isl_set *set, enum isl_dim_type type,
2046 unsigned first, unsigned n);
2047 __isl_give isl_basic_map *isl_basic_map_eliminate(
2048 __isl_take isl_basic_map *bmap,
2049 enum isl_dim_type type,
2050 unsigned first, unsigned n);
2051 __isl_give isl_map *isl_map_eliminate(
2052 __isl_take isl_map *map, enum isl_dim_type type,
2053 unsigned first, unsigned n);
2055 Eliminate the coefficients for the given dimensions from the constraints,
2056 without removing the dimensions.
2060 __isl_give isl_basic_set *isl_basic_set_fix(
2061 __isl_take isl_basic_set *bset,
2062 enum isl_dim_type type, unsigned pos,
2064 __isl_give isl_basic_set *isl_basic_set_fix_si(
2065 __isl_take isl_basic_set *bset,
2066 enum isl_dim_type type, unsigned pos, int value);
2067 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2068 enum isl_dim_type type, unsigned pos,
2070 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2071 enum isl_dim_type type, unsigned pos, int value);
2072 __isl_give isl_basic_map *isl_basic_map_fix_si(
2073 __isl_take isl_basic_map *bmap,
2074 enum isl_dim_type type, unsigned pos, int value);
2075 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2076 enum isl_dim_type type, unsigned pos,
2078 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2079 enum isl_dim_type type, unsigned pos, int value);
2081 Intersect the set or relation with the hyperplane where the given
2082 dimension has the fixed given value.
2084 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2085 __isl_take isl_basic_map *bmap,
2086 enum isl_dim_type type, unsigned pos, int value);
2087 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2088 __isl_take isl_basic_map *bmap,
2089 enum isl_dim_type type, unsigned pos, int value);
2090 __isl_give isl_set *isl_set_lower_bound(
2091 __isl_take isl_set *set,
2092 enum isl_dim_type type, unsigned pos,
2094 __isl_give isl_set *isl_set_lower_bound_si(
2095 __isl_take isl_set *set,
2096 enum isl_dim_type type, unsigned pos, int value);
2097 __isl_give isl_map *isl_map_lower_bound_si(
2098 __isl_take isl_map *map,
2099 enum isl_dim_type type, unsigned pos, int value);
2100 __isl_give isl_set *isl_set_upper_bound(
2101 __isl_take isl_set *set,
2102 enum isl_dim_type type, unsigned pos,
2104 __isl_give isl_set *isl_set_upper_bound_si(
2105 __isl_take isl_set *set,
2106 enum isl_dim_type type, unsigned pos, int value);
2107 __isl_give isl_map *isl_map_upper_bound_si(
2108 __isl_take isl_map *map,
2109 enum isl_dim_type type, unsigned pos, int value);
2111 Intersect the set or relation with the half-space where the given
2112 dimension has a value bounded by the fixed given value.
2114 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2115 enum isl_dim_type type1, int pos1,
2116 enum isl_dim_type type2, int pos2);
2117 __isl_give isl_basic_map *isl_basic_map_equate(
2118 __isl_take isl_basic_map *bmap,
2119 enum isl_dim_type type1, int pos1,
2120 enum isl_dim_type type2, int pos2);
2121 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2122 enum isl_dim_type type1, int pos1,
2123 enum isl_dim_type type2, int pos2);
2125 Intersect the set or relation with the hyperplane where the given
2126 dimensions are equal to each other.
2128 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2129 enum isl_dim_type type1, int pos1,
2130 enum isl_dim_type type2, int pos2);
2132 Intersect the relation with the hyperplane where the given
2133 dimensions have opposite values.
2135 __isl_give isl_basic_map *isl_basic_map_order_ge(
2136 __isl_take isl_basic_map *bmap,
2137 enum isl_dim_type type1, int pos1,
2138 enum isl_dim_type type2, int pos2);
2139 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2140 enum isl_dim_type type1, int pos1,
2141 enum isl_dim_type type2, int pos2);
2142 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2143 enum isl_dim_type type1, int pos1,
2144 enum isl_dim_type type2, int pos2);
2146 Intersect the relation with the half-space where the given
2147 dimensions satisfy the given ordering.
2151 __isl_give isl_map *isl_set_identity(
2152 __isl_take isl_set *set);
2153 __isl_give isl_union_map *isl_union_set_identity(
2154 __isl_take isl_union_set *uset);
2156 Construct an identity relation on the given (union) set.
2160 __isl_give isl_basic_set *isl_basic_map_deltas(
2161 __isl_take isl_basic_map *bmap);
2162 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2163 __isl_give isl_union_set *isl_union_map_deltas(
2164 __isl_take isl_union_map *umap);
2166 These functions return a (basic) set containing the differences
2167 between image elements and corresponding domain elements in the input.
2169 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2170 __isl_take isl_basic_map *bmap);
2171 __isl_give isl_map *isl_map_deltas_map(
2172 __isl_take isl_map *map);
2173 __isl_give isl_union_map *isl_union_map_deltas_map(
2174 __isl_take isl_union_map *umap);
2176 The functions above construct a (basic, regular or union) relation
2177 that maps (a wrapped version of) the input relation to its delta set.
2181 Simplify the representation of a set or relation by trying
2182 to combine pairs of basic sets or relations into a single
2183 basic set or relation.
2185 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2186 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2187 __isl_give isl_union_set *isl_union_set_coalesce(
2188 __isl_take isl_union_set *uset);
2189 __isl_give isl_union_map *isl_union_map_coalesce(
2190 __isl_take isl_union_map *umap);
2192 One of the methods for combining pairs of basic sets or relations
2193 can result in coefficients that are much larger than those that appear
2194 in the constraints of the input. By default, the coefficients are
2195 not allowed to grow larger, but this can be changed by unsetting
2196 the following option.
2198 int isl_options_set_coalesce_bounded_wrapping(
2199 isl_ctx *ctx, int val);
2200 int isl_options_get_coalesce_bounded_wrapping(
2203 =item * Detecting equalities
2205 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2206 __isl_take isl_basic_set *bset);
2207 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_set *isl_set_detect_equalities(
2210 __isl_take isl_set *set);
2211 __isl_give isl_map *isl_map_detect_equalities(
2212 __isl_take isl_map *map);
2213 __isl_give isl_union_set *isl_union_set_detect_equalities(
2214 __isl_take isl_union_set *uset);
2215 __isl_give isl_union_map *isl_union_map_detect_equalities(
2216 __isl_take isl_union_map *umap);
2218 Simplify the representation of a set or relation by detecting implicit
2221 =item * Removing redundant constraints
2223 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2224 __isl_take isl_basic_set *bset);
2225 __isl_give isl_set *isl_set_remove_redundancies(
2226 __isl_take isl_set *set);
2227 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2228 __isl_take isl_basic_map *bmap);
2229 __isl_give isl_map *isl_map_remove_redundancies(
2230 __isl_take isl_map *map);
2234 __isl_give isl_basic_set *isl_set_convex_hull(
2235 __isl_take isl_set *set);
2236 __isl_give isl_basic_map *isl_map_convex_hull(
2237 __isl_take isl_map *map);
2239 If the input set or relation has any existentially quantified
2240 variables, then the result of these operations is currently undefined.
2244 __isl_give isl_basic_set *
2245 isl_set_unshifted_simple_hull(
2246 __isl_take isl_set *set);
2247 __isl_give isl_basic_map *
2248 isl_map_unshifted_simple_hull(
2249 __isl_take isl_map *map);
2250 __isl_give isl_basic_set *isl_set_simple_hull(
2251 __isl_take isl_set *set);
2252 __isl_give isl_basic_map *isl_map_simple_hull(
2253 __isl_take isl_map *map);
2254 __isl_give isl_union_map *isl_union_map_simple_hull(
2255 __isl_take isl_union_map *umap);
2257 These functions compute a single basic set or relation
2258 that contains the whole input set or relation.
2259 In particular, the output is described by translates
2260 of the constraints describing the basic sets or relations in the input.
2261 In case of C<isl_set_unshifted_simple_hull>, only the original
2262 constraints are used, without any translation.
2266 (See \autoref{s:simple hull}.)
2272 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2273 __isl_take isl_basic_set *bset);
2274 __isl_give isl_basic_set *isl_set_affine_hull(
2275 __isl_take isl_set *set);
2276 __isl_give isl_union_set *isl_union_set_affine_hull(
2277 __isl_take isl_union_set *uset);
2278 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2279 __isl_take isl_basic_map *bmap);
2280 __isl_give isl_basic_map *isl_map_affine_hull(
2281 __isl_take isl_map *map);
2282 __isl_give isl_union_map *isl_union_map_affine_hull(
2283 __isl_take isl_union_map *umap);
2285 In case of union sets and relations, the affine hull is computed
2288 =item * Polyhedral hull
2290 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2291 __isl_take isl_set *set);
2292 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2293 __isl_take isl_map *map);
2294 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2295 __isl_take isl_union_set *uset);
2296 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2297 __isl_take isl_union_map *umap);
2299 These functions compute a single basic set or relation
2300 not involving any existentially quantified variables
2301 that contains the whole input set or relation.
2302 In case of union sets and relations, the polyhedral hull is computed
2307 __isl_give isl_basic_set *isl_basic_set_sample(
2308 __isl_take isl_basic_set *bset);
2309 __isl_give isl_basic_set *isl_set_sample(
2310 __isl_take isl_set *set);
2311 __isl_give isl_basic_map *isl_basic_map_sample(
2312 __isl_take isl_basic_map *bmap);
2313 __isl_give isl_basic_map *isl_map_sample(
2314 __isl_take isl_map *map);
2316 If the input (basic) set or relation is non-empty, then return
2317 a singleton subset of the input. Otherwise, return an empty set.
2319 =item * Optimization
2321 #include <isl/ilp.h>
2322 enum isl_lp_result isl_basic_set_max(
2323 __isl_keep isl_basic_set *bset,
2324 __isl_keep isl_aff *obj, isl_int *opt)
2325 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2326 __isl_keep isl_aff *obj, isl_int *opt);
2327 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2328 __isl_keep isl_aff *obj, isl_int *opt);
2330 Compute the minimum or maximum of the integer affine expression C<obj>
2331 over the points in C<set>, returning the result in C<opt>.
2332 The return value may be one of C<isl_lp_error>,
2333 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2335 =item * Parametric optimization
2337 __isl_give isl_pw_aff *isl_set_dim_min(
2338 __isl_take isl_set *set, int pos);
2339 __isl_give isl_pw_aff *isl_set_dim_max(
2340 __isl_take isl_set *set, int pos);
2341 __isl_give isl_pw_aff *isl_map_dim_max(
2342 __isl_take isl_map *map, int pos);
2344 Compute the minimum or maximum of the given set or output dimension
2345 as a function of the parameters (and input dimensions), but independently
2346 of the other set or output dimensions.
2347 For lexicographic optimization, see L<"Lexicographic Optimization">.
2351 The following functions compute either the set of (rational) coefficient
2352 values of valid constraints for the given set or the set of (rational)
2353 values satisfying the constraints with coefficients from the given set.
2354 Internally, these two sets of functions perform essentially the
2355 same operations, except that the set of coefficients is assumed to
2356 be a cone, while the set of values may be any polyhedron.
2357 The current implementation is based on the Farkas lemma and
2358 Fourier-Motzkin elimination, but this may change or be made optional
2359 in future. In particular, future implementations may use different
2360 dualization algorithms or skip the elimination step.
2362 __isl_give isl_basic_set *isl_basic_set_coefficients(
2363 __isl_take isl_basic_set *bset);
2364 __isl_give isl_basic_set *isl_set_coefficients(
2365 __isl_take isl_set *set);
2366 __isl_give isl_union_set *isl_union_set_coefficients(
2367 __isl_take isl_union_set *bset);
2368 __isl_give isl_basic_set *isl_basic_set_solutions(
2369 __isl_take isl_basic_set *bset);
2370 __isl_give isl_basic_set *isl_set_solutions(
2371 __isl_take isl_set *set);
2372 __isl_give isl_union_set *isl_union_set_solutions(
2373 __isl_take isl_union_set *bset);
2377 __isl_give isl_map *isl_map_fixed_power(
2378 __isl_take isl_map *map, isl_int exp);
2379 __isl_give isl_union_map *isl_union_map_fixed_power(
2380 __isl_take isl_union_map *umap, isl_int exp);
2382 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2383 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2384 of C<map> is computed.
2386 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2388 __isl_give isl_union_map *isl_union_map_power(
2389 __isl_take isl_union_map *umap, int *exact);
2391 Compute a parametric representation for all positive powers I<k> of C<map>.
2392 The result maps I<k> to a nested relation corresponding to the
2393 I<k>th power of C<map>.
2394 The result may be an overapproximation. If the result is known to be exact,
2395 then C<*exact> is set to C<1>.
2397 =item * Transitive closure
2399 __isl_give isl_map *isl_map_transitive_closure(
2400 __isl_take isl_map *map, int *exact);
2401 __isl_give isl_union_map *isl_union_map_transitive_closure(
2402 __isl_take isl_union_map *umap, int *exact);
2404 Compute the transitive closure of C<map>.
2405 The result may be an overapproximation. If the result is known to be exact,
2406 then C<*exact> is set to C<1>.
2408 =item * Reaching path lengths
2410 __isl_give isl_map *isl_map_reaching_path_lengths(
2411 __isl_take isl_map *map, int *exact);
2413 Compute a relation that maps each element in the range of C<map>
2414 to the lengths of all paths composed of edges in C<map> that
2415 end up in the given element.
2416 The result may be an overapproximation. If the result is known to be exact,
2417 then C<*exact> is set to C<1>.
2418 To compute the I<maximal> path length, the resulting relation
2419 should be postprocessed by C<isl_map_lexmax>.
2420 In particular, if the input relation is a dependence relation
2421 (mapping sources to sinks), then the maximal path length corresponds
2422 to the free schedule.
2423 Note, however, that C<isl_map_lexmax> expects the maximum to be
2424 finite, so if the path lengths are unbounded (possibly due to
2425 the overapproximation), then you will get an error message.
2429 __isl_give isl_basic_set *isl_basic_map_wrap(
2430 __isl_take isl_basic_map *bmap);
2431 __isl_give isl_set *isl_map_wrap(
2432 __isl_take isl_map *map);
2433 __isl_give isl_union_set *isl_union_map_wrap(
2434 __isl_take isl_union_map *umap);
2435 __isl_give isl_basic_map *isl_basic_set_unwrap(
2436 __isl_take isl_basic_set *bset);
2437 __isl_give isl_map *isl_set_unwrap(
2438 __isl_take isl_set *set);
2439 __isl_give isl_union_map *isl_union_set_unwrap(
2440 __isl_take isl_union_set *uset);
2444 Remove any internal structure of domain (and range) of the given
2445 set or relation. If there is any such internal structure in the input,
2446 then the name of the space is also removed.
2448 __isl_give isl_basic_set *isl_basic_set_flatten(
2449 __isl_take isl_basic_set *bset);
2450 __isl_give isl_set *isl_set_flatten(
2451 __isl_take isl_set *set);
2452 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2453 __isl_take isl_basic_map *bmap);
2454 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2455 __isl_take isl_basic_map *bmap);
2456 __isl_give isl_map *isl_map_flatten_range(
2457 __isl_take isl_map *map);
2458 __isl_give isl_map *isl_map_flatten_domain(
2459 __isl_take isl_map *map);
2460 __isl_give isl_basic_map *isl_basic_map_flatten(
2461 __isl_take isl_basic_map *bmap);
2462 __isl_give isl_map *isl_map_flatten(
2463 __isl_take isl_map *map);
2465 __isl_give isl_map *isl_set_flatten_map(
2466 __isl_take isl_set *set);
2468 The function above constructs a relation
2469 that maps the input set to a flattened version of the set.
2473 Lift the input set to a space with extra dimensions corresponding
2474 to the existentially quantified variables in the input.
2475 In particular, the result lives in a wrapped map where the domain
2476 is the original space and the range corresponds to the original
2477 existentially quantified variables.
2479 __isl_give isl_basic_set *isl_basic_set_lift(
2480 __isl_take isl_basic_set *bset);
2481 __isl_give isl_set *isl_set_lift(
2482 __isl_take isl_set *set);
2483 __isl_give isl_union_set *isl_union_set_lift(
2484 __isl_take isl_union_set *uset);
2486 Given a local space that contains the existentially quantified
2487 variables of a set, a basic relation that, when applied to
2488 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2489 can be constructed using the following function.
2491 #include <isl/local_space.h>
2492 __isl_give isl_basic_map *isl_local_space_lifting(
2493 __isl_take isl_local_space *ls);
2495 =item * Internal Product
2497 __isl_give isl_basic_map *isl_basic_map_zip(
2498 __isl_take isl_basic_map *bmap);
2499 __isl_give isl_map *isl_map_zip(
2500 __isl_take isl_map *map);
2501 __isl_give isl_union_map *isl_union_map_zip(
2502 __isl_take isl_union_map *umap);
2504 Given a relation with nested relations for domain and range,
2505 interchange the range of the domain with the domain of the range.
2509 __isl_give isl_basic_map *isl_basic_map_curry(
2510 __isl_take isl_basic_map *bmap);
2511 __isl_give isl_basic_map *isl_basic_map_uncurry(
2512 __isl_take isl_basic_map *bmap);
2513 __isl_give isl_map *isl_map_curry(
2514 __isl_take isl_map *map);
2515 __isl_give isl_map *isl_map_uncurry(
2516 __isl_take isl_map *map);
2517 __isl_give isl_union_map *isl_union_map_curry(
2518 __isl_take isl_union_map *umap);
2520 Given a relation with a nested relation for domain,
2521 the C<curry> functions
2522 move the range of the nested relation out of the domain
2523 and use it as the domain of a nested relation in the range,
2524 with the original range as range of this nested relation.
2525 The C<uncurry> functions perform the inverse operation.
2527 =item * Aligning parameters
2529 __isl_give isl_basic_set *isl_basic_set_align_params(
2530 __isl_take isl_basic_set *bset,
2531 __isl_take isl_space *model);
2532 __isl_give isl_set *isl_set_align_params(
2533 __isl_take isl_set *set,
2534 __isl_take isl_space *model);
2535 __isl_give isl_basic_map *isl_basic_map_align_params(
2536 __isl_take isl_basic_map *bmap,
2537 __isl_take isl_space *model);
2538 __isl_give isl_map *isl_map_align_params(
2539 __isl_take isl_map *map,
2540 __isl_take isl_space *model);
2542 Change the order of the parameters of the given set or relation
2543 such that the first parameters match those of C<model>.
2544 This may involve the introduction of extra parameters.
2545 All parameters need to be named.
2547 =item * Dimension manipulation
2549 __isl_give isl_set *isl_set_add_dims(
2550 __isl_take isl_set *set,
2551 enum isl_dim_type type, unsigned n);
2552 __isl_give isl_map *isl_map_add_dims(
2553 __isl_take isl_map *map,
2554 enum isl_dim_type type, unsigned n);
2555 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2556 __isl_take isl_basic_set *bset,
2557 enum isl_dim_type type, unsigned pos,
2559 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2560 __isl_take isl_basic_map *bmap,
2561 enum isl_dim_type type, unsigned pos,
2563 __isl_give isl_set *isl_set_insert_dims(
2564 __isl_take isl_set *set,
2565 enum isl_dim_type type, unsigned pos, unsigned n);
2566 __isl_give isl_map *isl_map_insert_dims(
2567 __isl_take isl_map *map,
2568 enum isl_dim_type type, unsigned pos, unsigned n);
2569 __isl_give isl_basic_set *isl_basic_set_move_dims(
2570 __isl_take isl_basic_set *bset,
2571 enum isl_dim_type dst_type, unsigned dst_pos,
2572 enum isl_dim_type src_type, unsigned src_pos,
2574 __isl_give isl_basic_map *isl_basic_map_move_dims(
2575 __isl_take isl_basic_map *bmap,
2576 enum isl_dim_type dst_type, unsigned dst_pos,
2577 enum isl_dim_type src_type, unsigned src_pos,
2579 __isl_give isl_set *isl_set_move_dims(
2580 __isl_take isl_set *set,
2581 enum isl_dim_type dst_type, unsigned dst_pos,
2582 enum isl_dim_type src_type, unsigned src_pos,
2584 __isl_give isl_map *isl_map_move_dims(
2585 __isl_take isl_map *map,
2586 enum isl_dim_type dst_type, unsigned dst_pos,
2587 enum isl_dim_type src_type, unsigned src_pos,
2590 It is usually not advisable to directly change the (input or output)
2591 space of a set or a relation as this removes the name and the internal
2592 structure of the space. However, the above functions can be useful
2593 to add new parameters, assuming
2594 C<isl_set_align_params> and C<isl_map_align_params>
2599 =head2 Binary Operations
2601 The two arguments of a binary operation not only need to live
2602 in the same C<isl_ctx>, they currently also need to have
2603 the same (number of) parameters.
2605 =head3 Basic Operations
2609 =item * Intersection
2611 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2612 __isl_take isl_basic_set *bset1,
2613 __isl_take isl_basic_set *bset2);
2614 __isl_give isl_basic_set *isl_basic_set_intersect(
2615 __isl_take isl_basic_set *bset1,
2616 __isl_take isl_basic_set *bset2);
2617 __isl_give isl_set *isl_set_intersect_params(
2618 __isl_take isl_set *set,
2619 __isl_take isl_set *params);
2620 __isl_give isl_set *isl_set_intersect(
2621 __isl_take isl_set *set1,
2622 __isl_take isl_set *set2);
2623 __isl_give isl_union_set *isl_union_set_intersect_params(
2624 __isl_take isl_union_set *uset,
2625 __isl_take isl_set *set);
2626 __isl_give isl_union_map *isl_union_map_intersect_params(
2627 __isl_take isl_union_map *umap,
2628 __isl_take isl_set *set);
2629 __isl_give isl_union_set *isl_union_set_intersect(
2630 __isl_take isl_union_set *uset1,
2631 __isl_take isl_union_set *uset2);
2632 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2633 __isl_take isl_basic_map *bmap,
2634 __isl_take isl_basic_set *bset);
2635 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2636 __isl_take isl_basic_map *bmap,
2637 __isl_take isl_basic_set *bset);
2638 __isl_give isl_basic_map *isl_basic_map_intersect(
2639 __isl_take isl_basic_map *bmap1,
2640 __isl_take isl_basic_map *bmap2);
2641 __isl_give isl_map *isl_map_intersect_params(
2642 __isl_take isl_map *map,
2643 __isl_take isl_set *params);
2644 __isl_give isl_map *isl_map_intersect_domain(
2645 __isl_take isl_map *map,
2646 __isl_take isl_set *set);
2647 __isl_give isl_map *isl_map_intersect_range(
2648 __isl_take isl_map *map,
2649 __isl_take isl_set *set);
2650 __isl_give isl_map *isl_map_intersect(
2651 __isl_take isl_map *map1,
2652 __isl_take isl_map *map2);
2653 __isl_give isl_union_map *isl_union_map_intersect_domain(
2654 __isl_take isl_union_map *umap,
2655 __isl_take isl_union_set *uset);
2656 __isl_give isl_union_map *isl_union_map_intersect_range(
2657 __isl_take isl_union_map *umap,
2658 __isl_take isl_union_set *uset);
2659 __isl_give isl_union_map *isl_union_map_intersect(
2660 __isl_take isl_union_map *umap1,
2661 __isl_take isl_union_map *umap2);
2663 The second argument to the C<_params> functions needs to be
2664 a parametric (basic) set. For the other functions, a parametric set
2665 for either argument is only allowed if the other argument is
2666 a parametric set as well.
2670 __isl_give isl_set *isl_basic_set_union(
2671 __isl_take isl_basic_set *bset1,
2672 __isl_take isl_basic_set *bset2);
2673 __isl_give isl_map *isl_basic_map_union(
2674 __isl_take isl_basic_map *bmap1,
2675 __isl_take isl_basic_map *bmap2);
2676 __isl_give isl_set *isl_set_union(
2677 __isl_take isl_set *set1,
2678 __isl_take isl_set *set2);
2679 __isl_give isl_map *isl_map_union(
2680 __isl_take isl_map *map1,
2681 __isl_take isl_map *map2);
2682 __isl_give isl_union_set *isl_union_set_union(
2683 __isl_take isl_union_set *uset1,
2684 __isl_take isl_union_set *uset2);
2685 __isl_give isl_union_map *isl_union_map_union(
2686 __isl_take isl_union_map *umap1,
2687 __isl_take isl_union_map *umap2);
2689 =item * Set difference
2691 __isl_give isl_set *isl_set_subtract(
2692 __isl_take isl_set *set1,
2693 __isl_take isl_set *set2);
2694 __isl_give isl_map *isl_map_subtract(
2695 __isl_take isl_map *map1,
2696 __isl_take isl_map *map2);
2697 __isl_give isl_map *isl_map_subtract_domain(
2698 __isl_take isl_map *map,
2699 __isl_take isl_set *dom);
2700 __isl_give isl_map *isl_map_subtract_range(
2701 __isl_take isl_map *map,
2702 __isl_take isl_set *dom);
2703 __isl_give isl_union_set *isl_union_set_subtract(
2704 __isl_take isl_union_set *uset1,
2705 __isl_take isl_union_set *uset2);
2706 __isl_give isl_union_map *isl_union_map_subtract(
2707 __isl_take isl_union_map *umap1,
2708 __isl_take isl_union_map *umap2);
2709 __isl_give isl_union_map *isl_union_map_subtract_domain(
2710 __isl_take isl_union_map *umap,
2711 __isl_take isl_union_set *dom);
2712 __isl_give isl_union_map *isl_union_map_subtract_range(
2713 __isl_take isl_union_map *umap,
2714 __isl_take isl_union_set *dom);
2718 __isl_give isl_basic_set *isl_basic_set_apply(
2719 __isl_take isl_basic_set *bset,
2720 __isl_take isl_basic_map *bmap);
2721 __isl_give isl_set *isl_set_apply(
2722 __isl_take isl_set *set,
2723 __isl_take isl_map *map);
2724 __isl_give isl_union_set *isl_union_set_apply(
2725 __isl_take isl_union_set *uset,
2726 __isl_take isl_union_map *umap);
2727 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2728 __isl_take isl_basic_map *bmap1,
2729 __isl_take isl_basic_map *bmap2);
2730 __isl_give isl_basic_map *isl_basic_map_apply_range(
2731 __isl_take isl_basic_map *bmap1,
2732 __isl_take isl_basic_map *bmap2);
2733 __isl_give isl_map *isl_map_apply_domain(
2734 __isl_take isl_map *map1,
2735 __isl_take isl_map *map2);
2736 __isl_give isl_union_map *isl_union_map_apply_domain(
2737 __isl_take isl_union_map *umap1,
2738 __isl_take isl_union_map *umap2);
2739 __isl_give isl_map *isl_map_apply_range(
2740 __isl_take isl_map *map1,
2741 __isl_take isl_map *map2);
2742 __isl_give isl_union_map *isl_union_map_apply_range(
2743 __isl_take isl_union_map *umap1,
2744 __isl_take isl_union_map *umap2);
2746 =item * Cartesian Product
2748 __isl_give isl_set *isl_set_product(
2749 __isl_take isl_set *set1,
2750 __isl_take isl_set *set2);
2751 __isl_give isl_union_set *isl_union_set_product(
2752 __isl_take isl_union_set *uset1,
2753 __isl_take isl_union_set *uset2);
2754 __isl_give isl_basic_map *isl_basic_map_domain_product(
2755 __isl_take isl_basic_map *bmap1,
2756 __isl_take isl_basic_map *bmap2);
2757 __isl_give isl_basic_map *isl_basic_map_range_product(
2758 __isl_take isl_basic_map *bmap1,
2759 __isl_take isl_basic_map *bmap2);
2760 __isl_give isl_basic_map *isl_basic_map_product(
2761 __isl_take isl_basic_map *bmap1,
2762 __isl_take isl_basic_map *bmap2);
2763 __isl_give isl_map *isl_map_domain_product(
2764 __isl_take isl_map *map1,
2765 __isl_take isl_map *map2);
2766 __isl_give isl_map *isl_map_range_product(
2767 __isl_take isl_map *map1,
2768 __isl_take isl_map *map2);
2769 __isl_give isl_union_map *isl_union_map_domain_product(
2770 __isl_take isl_union_map *umap1,
2771 __isl_take isl_union_map *umap2);
2772 __isl_give isl_union_map *isl_union_map_range_product(
2773 __isl_take isl_union_map *umap1,
2774 __isl_take isl_union_map *umap2);
2775 __isl_give isl_map *isl_map_product(
2776 __isl_take isl_map *map1,
2777 __isl_take isl_map *map2);
2778 __isl_give isl_union_map *isl_union_map_product(
2779 __isl_take isl_union_map *umap1,
2780 __isl_take isl_union_map *umap2);
2782 The above functions compute the cross product of the given
2783 sets or relations. The domains and ranges of the results
2784 are wrapped maps between domains and ranges of the inputs.
2785 To obtain a ``flat'' product, use the following functions
2788 __isl_give isl_basic_set *isl_basic_set_flat_product(
2789 __isl_take isl_basic_set *bset1,
2790 __isl_take isl_basic_set *bset2);
2791 __isl_give isl_set *isl_set_flat_product(
2792 __isl_take isl_set *set1,
2793 __isl_take isl_set *set2);
2794 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2795 __isl_take isl_basic_map *bmap1,
2796 __isl_take isl_basic_map *bmap2);
2797 __isl_give isl_map *isl_map_flat_domain_product(
2798 __isl_take isl_map *map1,
2799 __isl_take isl_map *map2);
2800 __isl_give isl_map *isl_map_flat_range_product(
2801 __isl_take isl_map *map1,
2802 __isl_take isl_map *map2);
2803 __isl_give isl_union_map *isl_union_map_flat_range_product(
2804 __isl_take isl_union_map *umap1,
2805 __isl_take isl_union_map *umap2);
2806 __isl_give isl_basic_map *isl_basic_map_flat_product(
2807 __isl_take isl_basic_map *bmap1,
2808 __isl_take isl_basic_map *bmap2);
2809 __isl_give isl_map *isl_map_flat_product(
2810 __isl_take isl_map *map1,
2811 __isl_take isl_map *map2);
2813 =item * Simplification
2815 __isl_give isl_basic_set *isl_basic_set_gist(
2816 __isl_take isl_basic_set *bset,
2817 __isl_take isl_basic_set *context);
2818 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2819 __isl_take isl_set *context);
2820 __isl_give isl_set *isl_set_gist_params(
2821 __isl_take isl_set *set,
2822 __isl_take isl_set *context);
2823 __isl_give isl_union_set *isl_union_set_gist(
2824 __isl_take isl_union_set *uset,
2825 __isl_take isl_union_set *context);
2826 __isl_give isl_union_set *isl_union_set_gist_params(
2827 __isl_take isl_union_set *uset,
2828 __isl_take isl_set *set);
2829 __isl_give isl_basic_map *isl_basic_map_gist(
2830 __isl_take isl_basic_map *bmap,
2831 __isl_take isl_basic_map *context);
2832 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2833 __isl_take isl_map *context);
2834 __isl_give isl_map *isl_map_gist_params(
2835 __isl_take isl_map *map,
2836 __isl_take isl_set *context);
2837 __isl_give isl_map *isl_map_gist_domain(
2838 __isl_take isl_map *map,
2839 __isl_take isl_set *context);
2840 __isl_give isl_map *isl_map_gist_range(
2841 __isl_take isl_map *map,
2842 __isl_take isl_set *context);
2843 __isl_give isl_union_map *isl_union_map_gist(
2844 __isl_take isl_union_map *umap,
2845 __isl_take isl_union_map *context);
2846 __isl_give isl_union_map *isl_union_map_gist_params(
2847 __isl_take isl_union_map *umap,
2848 __isl_take isl_set *set);
2849 __isl_give isl_union_map *isl_union_map_gist_domain(
2850 __isl_take isl_union_map *umap,
2851 __isl_take isl_union_set *uset);
2852 __isl_give isl_union_map *isl_union_map_gist_range(
2853 __isl_take isl_union_map *umap,
2854 __isl_take isl_union_set *uset);
2856 The gist operation returns a set or relation that has the
2857 same intersection with the context as the input set or relation.
2858 Any implicit equality in the intersection is made explicit in the result,
2859 while all inequalities that are redundant with respect to the intersection
2861 In case of union sets and relations, the gist operation is performed
2866 =head3 Lexicographic Optimization
2868 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2869 the following functions
2870 compute a set that contains the lexicographic minimum or maximum
2871 of the elements in C<set> (or C<bset>) for those values of the parameters
2872 that satisfy C<dom>.
2873 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2874 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2876 In other words, the union of the parameter values
2877 for which the result is non-empty and of C<*empty>
2880 __isl_give isl_set *isl_basic_set_partial_lexmin(
2881 __isl_take isl_basic_set *bset,
2882 __isl_take isl_basic_set *dom,
2883 __isl_give isl_set **empty);
2884 __isl_give isl_set *isl_basic_set_partial_lexmax(
2885 __isl_take isl_basic_set *bset,
2886 __isl_take isl_basic_set *dom,
2887 __isl_give isl_set **empty);
2888 __isl_give isl_set *isl_set_partial_lexmin(
2889 __isl_take isl_set *set, __isl_take isl_set *dom,
2890 __isl_give isl_set **empty);
2891 __isl_give isl_set *isl_set_partial_lexmax(
2892 __isl_take isl_set *set, __isl_take isl_set *dom,
2893 __isl_give isl_set **empty);
2895 Given a (basic) set C<set> (or C<bset>), the following functions simply
2896 return a set containing the lexicographic minimum or maximum
2897 of the elements in C<set> (or C<bset>).
2898 In case of union sets, the optimum is computed per space.
2900 __isl_give isl_set *isl_basic_set_lexmin(
2901 __isl_take isl_basic_set *bset);
2902 __isl_give isl_set *isl_basic_set_lexmax(
2903 __isl_take isl_basic_set *bset);
2904 __isl_give isl_set *isl_set_lexmin(
2905 __isl_take isl_set *set);
2906 __isl_give isl_set *isl_set_lexmax(
2907 __isl_take isl_set *set);
2908 __isl_give isl_union_set *isl_union_set_lexmin(
2909 __isl_take isl_union_set *uset);
2910 __isl_give isl_union_set *isl_union_set_lexmax(
2911 __isl_take isl_union_set *uset);
2913 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2914 the following functions
2915 compute a relation that maps each element of C<dom>
2916 to the single lexicographic minimum or maximum
2917 of the elements that are associated to that same
2918 element in C<map> (or C<bmap>).
2919 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2920 that contains the elements in C<dom> that do not map
2921 to any elements in C<map> (or C<bmap>).
2922 In other words, the union of the domain of the result and of C<*empty>
2925 __isl_give isl_map *isl_basic_map_partial_lexmax(
2926 __isl_take isl_basic_map *bmap,
2927 __isl_take isl_basic_set *dom,
2928 __isl_give isl_set **empty);
2929 __isl_give isl_map *isl_basic_map_partial_lexmin(
2930 __isl_take isl_basic_map *bmap,
2931 __isl_take isl_basic_set *dom,
2932 __isl_give isl_set **empty);
2933 __isl_give isl_map *isl_map_partial_lexmax(
2934 __isl_take isl_map *map, __isl_take isl_set *dom,
2935 __isl_give isl_set **empty);
2936 __isl_give isl_map *isl_map_partial_lexmin(
2937 __isl_take isl_map *map, __isl_take isl_set *dom,
2938 __isl_give isl_set **empty);
2940 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2941 return a map mapping each element in the domain of
2942 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2943 of all elements associated to that element.
2944 In case of union relations, the optimum is computed per space.
2946 __isl_give isl_map *isl_basic_map_lexmin(
2947 __isl_take isl_basic_map *bmap);
2948 __isl_give isl_map *isl_basic_map_lexmax(
2949 __isl_take isl_basic_map *bmap);
2950 __isl_give isl_map *isl_map_lexmin(
2951 __isl_take isl_map *map);
2952 __isl_give isl_map *isl_map_lexmax(
2953 __isl_take isl_map *map);
2954 __isl_give isl_union_map *isl_union_map_lexmin(
2955 __isl_take isl_union_map *umap);
2956 __isl_give isl_union_map *isl_union_map_lexmax(
2957 __isl_take isl_union_map *umap);
2959 The following functions return their result in the form of
2960 a piecewise multi-affine expression
2961 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2962 but are otherwise equivalent to the corresponding functions
2963 returning a basic set or relation.
2965 __isl_give isl_pw_multi_aff *
2966 isl_basic_map_lexmin_pw_multi_aff(
2967 __isl_take isl_basic_map *bmap);
2968 __isl_give isl_pw_multi_aff *
2969 isl_basic_set_partial_lexmin_pw_multi_aff(
2970 __isl_take isl_basic_set *bset,
2971 __isl_take isl_basic_set *dom,
2972 __isl_give isl_set **empty);
2973 __isl_give isl_pw_multi_aff *
2974 isl_basic_set_partial_lexmax_pw_multi_aff(
2975 __isl_take isl_basic_set *bset,
2976 __isl_take isl_basic_set *dom,
2977 __isl_give isl_set **empty);
2978 __isl_give isl_pw_multi_aff *
2979 isl_basic_map_partial_lexmin_pw_multi_aff(
2980 __isl_take isl_basic_map *bmap,
2981 __isl_take isl_basic_set *dom,
2982 __isl_give isl_set **empty);
2983 __isl_give isl_pw_multi_aff *
2984 isl_basic_map_partial_lexmax_pw_multi_aff(
2985 __isl_take isl_basic_map *bmap,
2986 __isl_take isl_basic_set *dom,
2987 __isl_give isl_set **empty);
2988 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2989 __isl_take isl_map *map);
2990 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2991 __isl_take isl_map *map);
2995 Lists are defined over several element types, including
2996 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
2997 C<isl_basic_set> and C<isl_set>.
2998 Here we take lists of C<isl_set>s as an example.
2999 Lists can be created, copied, modified and freed using the following functions.
3001 #include <isl/list.h>
3002 __isl_give isl_set_list *isl_set_list_from_set(
3003 __isl_take isl_set *el);
3004 __isl_give isl_set_list *isl_set_list_alloc(
3005 isl_ctx *ctx, int n);
3006 __isl_give isl_set_list *isl_set_list_copy(
3007 __isl_keep isl_set_list *list);
3008 __isl_give isl_set_list *isl_set_list_insert(
3009 __isl_take isl_set_list *list, unsigned pos,
3010 __isl_take isl_set *el);
3011 __isl_give isl_set_list *isl_set_list_add(
3012 __isl_take isl_set_list *list,
3013 __isl_take isl_set *el);
3014 __isl_give isl_set_list *isl_set_list_drop(
3015 __isl_take isl_set_list *list,
3016 unsigned first, unsigned n);
3017 __isl_give isl_set_list *isl_set_list_set_set(
3018 __isl_take isl_set_list *list, int index,
3019 __isl_take isl_set *set);
3020 __isl_give isl_set_list *isl_set_list_concat(
3021 __isl_take isl_set_list *list1,
3022 __isl_take isl_set_list *list2);
3023 void *isl_set_list_free(__isl_take isl_set_list *list);
3025 C<isl_set_list_alloc> creates an empty list with a capacity for
3026 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3029 Lists can be inspected using the following functions.
3031 #include <isl/list.h>
3032 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3033 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3034 __isl_give isl_set *isl_set_list_get_set(
3035 __isl_keep isl_set_list *list, int index);
3036 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3037 int (*fn)(__isl_take isl_set *el, void *user),
3040 Lists can be printed using
3042 #include <isl/list.h>
3043 __isl_give isl_printer *isl_printer_print_set_list(
3044 __isl_take isl_printer *p,
3045 __isl_keep isl_set_list *list);
3049 Vectors can be created, copied and freed using the following functions.
3051 #include <isl/vec.h>
3052 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3054 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3055 void *isl_vec_free(__isl_take isl_vec *vec);
3057 Note that the elements of a newly created vector may have arbitrary values.
3058 The elements can be changed and inspected using the following functions.
3060 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3061 int isl_vec_size(__isl_keep isl_vec *vec);
3062 int isl_vec_get_element(__isl_keep isl_vec *vec,
3063 int pos, isl_int *v);
3064 __isl_give isl_vec *isl_vec_set_element(
3065 __isl_take isl_vec *vec, int pos, isl_int v);
3066 __isl_give isl_vec *isl_vec_set_element_si(
3067 __isl_take isl_vec *vec, int pos, int v);
3068 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3070 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3072 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3075 C<isl_vec_get_element> will return a negative value if anything went wrong.
3076 In that case, the value of C<*v> is undefined.
3078 The following function can be used to concatenate two vectors.
3080 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3081 __isl_take isl_vec *vec2);
3085 Matrices can be created, copied and freed using the following functions.
3087 #include <isl/mat.h>
3088 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3089 unsigned n_row, unsigned n_col);
3090 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3091 void isl_mat_free(__isl_take isl_mat *mat);
3093 Note that the elements of a newly created matrix may have arbitrary values.
3094 The elements can be changed and inspected using the following functions.
3096 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3097 int isl_mat_rows(__isl_keep isl_mat *mat);
3098 int isl_mat_cols(__isl_keep isl_mat *mat);
3099 int isl_mat_get_element(__isl_keep isl_mat *mat,
3100 int row, int col, isl_int *v);
3101 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3102 int row, int col, isl_int v);
3103 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3104 int row, int col, int v);
3106 C<isl_mat_get_element> will return a negative value if anything went wrong.
3107 In that case, the value of C<*v> is undefined.
3109 The following function can be used to compute the (right) inverse
3110 of a matrix, i.e., a matrix such that the product of the original
3111 and the inverse (in that order) is a multiple of the identity matrix.
3112 The input matrix is assumed to be of full row-rank.
3114 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3116 The following function can be used to compute the (right) kernel
3117 (or null space) of a matrix, i.e., a matrix such that the product of
3118 the original and the kernel (in that order) is the zero matrix.
3120 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3122 =head2 Piecewise Quasi Affine Expressions
3124 The zero quasi affine expression on a given domain can be created using
3126 __isl_give isl_aff *isl_aff_zero_on_domain(
3127 __isl_take isl_local_space *ls);
3129 Note that the space in which the resulting object lives is a map space
3130 with the given space as domain and a one-dimensional range.
3132 An empty piecewise quasi affine expression (one with no cells)
3133 or a piecewise quasi affine expression with a single cell can
3134 be created using the following functions.
3136 #include <isl/aff.h>
3137 __isl_give isl_pw_aff *isl_pw_aff_empty(
3138 __isl_take isl_space *space);
3139 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3140 __isl_take isl_set *set, __isl_take isl_aff *aff);
3141 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3142 __isl_take isl_aff *aff);
3144 A piecewise quasi affine expression that is equal to 1 on a set
3145 and 0 outside the set can be created using the following function.
3147 #include <isl/aff.h>
3148 __isl_give isl_pw_aff *isl_set_indicator_function(
3149 __isl_take isl_set *set);
3151 Quasi affine expressions can be copied and freed using
3153 #include <isl/aff.h>
3154 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3155 void *isl_aff_free(__isl_take isl_aff *aff);
3157 __isl_give isl_pw_aff *isl_pw_aff_copy(
3158 __isl_keep isl_pw_aff *pwaff);
3159 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3161 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3162 using the following function. The constraint is required to have
3163 a non-zero coefficient for the specified dimension.
3165 #include <isl/constraint.h>
3166 __isl_give isl_aff *isl_constraint_get_bound(
3167 __isl_keep isl_constraint *constraint,
3168 enum isl_dim_type type, int pos);
3170 The entire affine expression of the constraint can also be extracted
3171 using the following function.
3173 #include <isl/constraint.h>
3174 __isl_give isl_aff *isl_constraint_get_aff(
3175 __isl_keep isl_constraint *constraint);
3177 Conversely, an equality constraint equating
3178 the affine expression to zero or an inequality constraint enforcing
3179 the affine expression to be non-negative, can be constructed using
3181 __isl_give isl_constraint *isl_equality_from_aff(
3182 __isl_take isl_aff *aff);
3183 __isl_give isl_constraint *isl_inequality_from_aff(
3184 __isl_take isl_aff *aff);
3186 The expression can be inspected using
3188 #include <isl/aff.h>
3189 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3190 int isl_aff_dim(__isl_keep isl_aff *aff,
3191 enum isl_dim_type type);
3192 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3193 __isl_keep isl_aff *aff);
3194 __isl_give isl_local_space *isl_aff_get_local_space(
3195 __isl_keep isl_aff *aff);
3196 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3197 enum isl_dim_type type, unsigned pos);
3198 const char *isl_pw_aff_get_dim_name(
3199 __isl_keep isl_pw_aff *pa,
3200 enum isl_dim_type type, unsigned pos);
3201 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3202 enum isl_dim_type type, unsigned pos);
3203 __isl_give isl_id *isl_pw_aff_get_dim_id(
3204 __isl_keep isl_pw_aff *pa,
3205 enum isl_dim_type type, unsigned pos);
3206 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3207 __isl_keep isl_pw_aff *pa,
3208 enum isl_dim_type type);
3209 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3211 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3212 enum isl_dim_type type, int pos, isl_int *v);
3213 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3215 __isl_give isl_aff *isl_aff_get_div(
3216 __isl_keep isl_aff *aff, int pos);
3218 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3219 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3220 int (*fn)(__isl_take isl_set *set,
3221 __isl_take isl_aff *aff,
3222 void *user), void *user);
3224 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3225 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3227 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3228 enum isl_dim_type type, unsigned first, unsigned n);
3229 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3230 enum isl_dim_type type, unsigned first, unsigned n);
3232 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3233 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3234 enum isl_dim_type type);
3235 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3237 It can be modified using
3239 #include <isl/aff.h>
3240 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3241 __isl_take isl_pw_aff *pwaff,
3242 enum isl_dim_type type, __isl_take isl_id *id);
3243 __isl_give isl_aff *isl_aff_set_dim_name(
3244 __isl_take isl_aff *aff, enum isl_dim_type type,
3245 unsigned pos, const char *s);
3246 __isl_give isl_aff *isl_aff_set_dim_id(
3247 __isl_take isl_aff *aff, enum isl_dim_type type,
3248 unsigned pos, __isl_take isl_id *id);
3249 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3250 __isl_take isl_pw_aff *pma,
3251 enum isl_dim_type type, unsigned pos,
3252 __isl_take isl_id *id);
3253 __isl_give isl_aff *isl_aff_set_constant(
3254 __isl_take isl_aff *aff, isl_int v);
3255 __isl_give isl_aff *isl_aff_set_constant_si(
3256 __isl_take isl_aff *aff, int v);
3257 __isl_give isl_aff *isl_aff_set_coefficient(
3258 __isl_take isl_aff *aff,
3259 enum isl_dim_type type, int pos, isl_int v);
3260 __isl_give isl_aff *isl_aff_set_coefficient_si(
3261 __isl_take isl_aff *aff,
3262 enum isl_dim_type type, int pos, int v);
3263 __isl_give isl_aff *isl_aff_set_denominator(
3264 __isl_take isl_aff *aff, isl_int v);
3266 __isl_give isl_aff *isl_aff_add_constant(
3267 __isl_take isl_aff *aff, isl_int v);
3268 __isl_give isl_aff *isl_aff_add_constant_si(
3269 __isl_take isl_aff *aff, int v);
3270 __isl_give isl_aff *isl_aff_add_constant_num(
3271 __isl_take isl_aff *aff, isl_int v);
3272 __isl_give isl_aff *isl_aff_add_constant_num_si(
3273 __isl_take isl_aff *aff, int v);
3274 __isl_give isl_aff *isl_aff_add_coefficient(
3275 __isl_take isl_aff *aff,
3276 enum isl_dim_type type, int pos, isl_int v);
3277 __isl_give isl_aff *isl_aff_add_coefficient_si(
3278 __isl_take isl_aff *aff,
3279 enum isl_dim_type type, int pos, int v);
3281 __isl_give isl_aff *isl_aff_insert_dims(
3282 __isl_take isl_aff *aff,
3283 enum isl_dim_type type, unsigned first, unsigned n);
3284 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3285 __isl_take isl_pw_aff *pwaff,
3286 enum isl_dim_type type, unsigned first, unsigned n);
3287 __isl_give isl_aff *isl_aff_add_dims(
3288 __isl_take isl_aff *aff,
3289 enum isl_dim_type type, unsigned n);
3290 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3291 __isl_take isl_pw_aff *pwaff,
3292 enum isl_dim_type type, unsigned n);
3293 __isl_give isl_aff *isl_aff_drop_dims(
3294 __isl_take isl_aff *aff,
3295 enum isl_dim_type type, unsigned first, unsigned n);
3296 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3297 __isl_take isl_pw_aff *pwaff,
3298 enum isl_dim_type type, unsigned first, unsigned n);
3300 Note that the C<set_constant> and C<set_coefficient> functions
3301 set the I<numerator> of the constant or coefficient, while
3302 C<add_constant> and C<add_coefficient> add an integer value to
3303 the possibly rational constant or coefficient.
3304 The C<add_constant_num> functions add an integer value to
3307 To check whether an affine expressions is obviously zero
3308 or obviously equal to some other affine expression, use
3310 #include <isl/aff.h>
3311 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3312 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3313 __isl_keep isl_aff *aff2);
3314 int isl_pw_aff_plain_is_equal(
3315 __isl_keep isl_pw_aff *pwaff1,
3316 __isl_keep isl_pw_aff *pwaff2);
3320 #include <isl/aff.h>
3321 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3322 __isl_take isl_aff *aff2);
3323 __isl_give isl_pw_aff *isl_pw_aff_add(
3324 __isl_take isl_pw_aff *pwaff1,
3325 __isl_take isl_pw_aff *pwaff2);
3326 __isl_give isl_pw_aff *isl_pw_aff_min(
3327 __isl_take isl_pw_aff *pwaff1,
3328 __isl_take isl_pw_aff *pwaff2);
3329 __isl_give isl_pw_aff *isl_pw_aff_max(
3330 __isl_take isl_pw_aff *pwaff1,
3331 __isl_take isl_pw_aff *pwaff2);
3332 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3333 __isl_take isl_aff *aff2);
3334 __isl_give isl_pw_aff *isl_pw_aff_sub(
3335 __isl_take isl_pw_aff *pwaff1,
3336 __isl_take isl_pw_aff *pwaff2);
3337 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3338 __isl_give isl_pw_aff *isl_pw_aff_neg(
3339 __isl_take isl_pw_aff *pwaff);
3340 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3341 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3342 __isl_take isl_pw_aff *pwaff);
3343 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3344 __isl_give isl_pw_aff *isl_pw_aff_floor(
3345 __isl_take isl_pw_aff *pwaff);
3346 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3348 __isl_give isl_pw_aff *isl_pw_aff_mod(
3349 __isl_take isl_pw_aff *pwaff, isl_int mod);
3350 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3352 __isl_give isl_pw_aff *isl_pw_aff_scale(
3353 __isl_take isl_pw_aff *pwaff, isl_int f);
3354 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3356 __isl_give isl_aff *isl_aff_scale_down_ui(
3357 __isl_take isl_aff *aff, unsigned f);
3358 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3359 __isl_take isl_pw_aff *pwaff, isl_int f);
3361 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3362 __isl_take isl_pw_aff_list *list);
3363 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3364 __isl_take isl_pw_aff_list *list);
3366 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3367 __isl_take isl_pw_aff *pwqp);
3369 __isl_give isl_aff *isl_aff_align_params(
3370 __isl_take isl_aff *aff,
3371 __isl_take isl_space *model);
3372 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3373 __isl_take isl_pw_aff *pwaff,
3374 __isl_take isl_space *model);
3376 __isl_give isl_aff *isl_aff_project_domain_on_params(
3377 __isl_take isl_aff *aff);
3379 __isl_give isl_aff *isl_aff_gist_params(
3380 __isl_take isl_aff *aff,
3381 __isl_take isl_set *context);
3382 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3383 __isl_take isl_set *context);
3384 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3385 __isl_take isl_pw_aff *pwaff,
3386 __isl_take isl_set *context);
3387 __isl_give isl_pw_aff *isl_pw_aff_gist(
3388 __isl_take isl_pw_aff *pwaff,
3389 __isl_take isl_set *context);
3391 __isl_give isl_set *isl_pw_aff_domain(
3392 __isl_take isl_pw_aff *pwaff);
3393 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3394 __isl_take isl_pw_aff *pa,
3395 __isl_take isl_set *set);
3396 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3397 __isl_take isl_pw_aff *pa,
3398 __isl_take isl_set *set);
3400 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3401 __isl_take isl_aff *aff2);
3402 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3403 __isl_take isl_aff *aff2);
3404 __isl_give isl_pw_aff *isl_pw_aff_mul(
3405 __isl_take isl_pw_aff *pwaff1,
3406 __isl_take isl_pw_aff *pwaff2);
3407 __isl_give isl_pw_aff *isl_pw_aff_div(
3408 __isl_take isl_pw_aff *pa1,
3409 __isl_take isl_pw_aff *pa2);
3410 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3411 __isl_take isl_pw_aff *pa1,
3412 __isl_take isl_pw_aff *pa2);
3413 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3414 __isl_take isl_pw_aff *pa1,
3415 __isl_take isl_pw_aff *pa2);
3417 When multiplying two affine expressions, at least one of the two needs
3418 to be a constant. Similarly, when dividing an affine expression by another,
3419 the second expression needs to be a constant.
3420 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3421 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3424 #include <isl/aff.h>
3425 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3426 __isl_take isl_aff *aff);
3427 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3428 __isl_take isl_aff *aff);
3429 __isl_give isl_basic_set *isl_aff_le_basic_set(
3430 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3431 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3432 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3433 __isl_give isl_set *isl_pw_aff_eq_set(
3434 __isl_take isl_pw_aff *pwaff1,
3435 __isl_take isl_pw_aff *pwaff2);
3436 __isl_give isl_set *isl_pw_aff_ne_set(
3437 __isl_take isl_pw_aff *pwaff1,
3438 __isl_take isl_pw_aff *pwaff2);
3439 __isl_give isl_set *isl_pw_aff_le_set(
3440 __isl_take isl_pw_aff *pwaff1,
3441 __isl_take isl_pw_aff *pwaff2);
3442 __isl_give isl_set *isl_pw_aff_lt_set(
3443 __isl_take isl_pw_aff *pwaff1,
3444 __isl_take isl_pw_aff *pwaff2);
3445 __isl_give isl_set *isl_pw_aff_ge_set(
3446 __isl_take isl_pw_aff *pwaff1,
3447 __isl_take isl_pw_aff *pwaff2);
3448 __isl_give isl_set *isl_pw_aff_gt_set(
3449 __isl_take isl_pw_aff *pwaff1,
3450 __isl_take isl_pw_aff *pwaff2);
3452 __isl_give isl_set *isl_pw_aff_list_eq_set(
3453 __isl_take isl_pw_aff_list *list1,
3454 __isl_take isl_pw_aff_list *list2);
3455 __isl_give isl_set *isl_pw_aff_list_ne_set(
3456 __isl_take isl_pw_aff_list *list1,
3457 __isl_take isl_pw_aff_list *list2);
3458 __isl_give isl_set *isl_pw_aff_list_le_set(
3459 __isl_take isl_pw_aff_list *list1,
3460 __isl_take isl_pw_aff_list *list2);
3461 __isl_give isl_set *isl_pw_aff_list_lt_set(
3462 __isl_take isl_pw_aff_list *list1,
3463 __isl_take isl_pw_aff_list *list2);
3464 __isl_give isl_set *isl_pw_aff_list_ge_set(
3465 __isl_take isl_pw_aff_list *list1,
3466 __isl_take isl_pw_aff_list *list2);
3467 __isl_give isl_set *isl_pw_aff_list_gt_set(
3468 __isl_take isl_pw_aff_list *list1,
3469 __isl_take isl_pw_aff_list *list2);
3471 The function C<isl_aff_neg_basic_set> returns a basic set
3472 containing those elements in the domain space
3473 of C<aff> where C<aff> is negative.
3474 The function C<isl_aff_ge_basic_set> returns a basic set
3475 containing those elements in the shared space
3476 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3477 The function C<isl_pw_aff_ge_set> returns a set
3478 containing those elements in the shared domain
3479 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3480 The functions operating on C<isl_pw_aff_list> apply the corresponding
3481 C<isl_pw_aff> function to each pair of elements in the two lists.
3483 #include <isl/aff.h>
3484 __isl_give isl_set *isl_pw_aff_nonneg_set(
3485 __isl_take isl_pw_aff *pwaff);
3486 __isl_give isl_set *isl_pw_aff_zero_set(
3487 __isl_take isl_pw_aff *pwaff);
3488 __isl_give isl_set *isl_pw_aff_non_zero_set(
3489 __isl_take isl_pw_aff *pwaff);
3491 The function C<isl_pw_aff_nonneg_set> returns a set
3492 containing those elements in the domain
3493 of C<pwaff> where C<pwaff> is non-negative.
3495 #include <isl/aff.h>
3496 __isl_give isl_pw_aff *isl_pw_aff_cond(
3497 __isl_take isl_pw_aff *cond,
3498 __isl_take isl_pw_aff *pwaff_true,
3499 __isl_take isl_pw_aff *pwaff_false);
3501 The function C<isl_pw_aff_cond> performs a conditional operator
3502 and returns an expression that is equal to C<pwaff_true>
3503 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3504 where C<cond> is zero.
3506 #include <isl/aff.h>
3507 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3508 __isl_take isl_pw_aff *pwaff1,
3509 __isl_take isl_pw_aff *pwaff2);
3510 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3511 __isl_take isl_pw_aff *pwaff1,
3512 __isl_take isl_pw_aff *pwaff2);
3513 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3514 __isl_take isl_pw_aff *pwaff1,
3515 __isl_take isl_pw_aff *pwaff2);
3517 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3518 expression with a domain that is the union of those of C<pwaff1> and
3519 C<pwaff2> and such that on each cell, the quasi-affine expression is
3520 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3521 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3522 associated expression is the defined one.
3524 An expression can be read from input using
3526 #include <isl/aff.h>
3527 __isl_give isl_aff *isl_aff_read_from_str(
3528 isl_ctx *ctx, const char *str);
3529 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3530 isl_ctx *ctx, const char *str);
3532 An expression can be printed using
3534 #include <isl/aff.h>
3535 __isl_give isl_printer *isl_printer_print_aff(
3536 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3538 __isl_give isl_printer *isl_printer_print_pw_aff(
3539 __isl_take isl_printer *p,
3540 __isl_keep isl_pw_aff *pwaff);
3542 =head2 Piecewise Multiple Quasi Affine Expressions
3544 An C<isl_multi_aff> object represents a sequence of
3545 zero or more affine expressions, all defined on the same domain space.
3547 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3550 #include <isl/aff.h>
3551 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3552 __isl_take isl_space *space,
3553 __isl_take isl_aff_list *list);
3555 An empty piecewise multiple quasi affine expression (one with no cells),
3556 the zero piecewise multiple quasi affine expression (with value zero
3557 for each output dimension),
3558 a piecewise multiple quasi affine expression with a single cell (with
3559 either a universe or a specified domain) or
3560 a zero-dimensional piecewise multiple quasi affine expression
3562 can be created using the following functions.
3564 #include <isl/aff.h>
3565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3566 __isl_take isl_space *space);
3567 __isl_give isl_multi_aff *isl_multi_aff_zero(
3568 __isl_take isl_space *space);
3569 __isl_give isl_multi_aff *isl_multi_aff_identity(
3570 __isl_take isl_space *space);
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3572 __isl_take isl_space *space);
3573 __isl_give isl_pw_multi_aff *
3574 isl_pw_multi_aff_from_multi_aff(
3575 __isl_take isl_multi_aff *ma);
3576 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3577 __isl_take isl_set *set,
3578 __isl_take isl_multi_aff *maff);
3579 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3580 __isl_take isl_set *set);
3582 __isl_give isl_union_pw_multi_aff *
3583 isl_union_pw_multi_aff_empty(
3584 __isl_take isl_space *space);
3585 __isl_give isl_union_pw_multi_aff *
3586 isl_union_pw_multi_aff_add_pw_multi_aff(
3587 __isl_take isl_union_pw_multi_aff *upma,
3588 __isl_take isl_pw_multi_aff *pma);
3589 __isl_give isl_union_pw_multi_aff *
3590 isl_union_pw_multi_aff_from_domain(
3591 __isl_take isl_union_set *uset);
3593 A piecewise multiple quasi affine expression can also be initialized
3594 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3595 and the C<isl_map> is single-valued.
3597 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3598 __isl_take isl_set *set);
3599 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3600 __isl_take isl_map *map);
3602 Multiple quasi affine expressions can be copied and freed using
3604 #include <isl/aff.h>
3605 __isl_give isl_multi_aff *isl_multi_aff_copy(
3606 __isl_keep isl_multi_aff *maff);
3607 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3610 __isl_keep isl_pw_multi_aff *pma);
3611 void *isl_pw_multi_aff_free(
3612 __isl_take isl_pw_multi_aff *pma);
3614 __isl_give isl_union_pw_multi_aff *
3615 isl_union_pw_multi_aff_copy(
3616 __isl_keep isl_union_pw_multi_aff *upma);
3617 void *isl_union_pw_multi_aff_free(
3618 __isl_take isl_union_pw_multi_aff *upma);
3620 The expression can be inspected using
3622 #include <isl/aff.h>
3623 isl_ctx *isl_multi_aff_get_ctx(
3624 __isl_keep isl_multi_aff *maff);
3625 isl_ctx *isl_pw_multi_aff_get_ctx(
3626 __isl_keep isl_pw_multi_aff *pma);
3627 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3628 __isl_keep isl_union_pw_multi_aff *upma);
3629 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3630 enum isl_dim_type type);
3631 unsigned isl_pw_multi_aff_dim(
3632 __isl_keep isl_pw_multi_aff *pma,
3633 enum isl_dim_type type);
3634 __isl_give isl_aff *isl_multi_aff_get_aff(
3635 __isl_keep isl_multi_aff *multi, int pos);
3636 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3637 __isl_keep isl_pw_multi_aff *pma, int pos);
3638 const char *isl_pw_multi_aff_get_dim_name(
3639 __isl_keep isl_pw_multi_aff *pma,
3640 enum isl_dim_type type, unsigned pos);
3641 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3642 __isl_keep isl_pw_multi_aff *pma,
3643 enum isl_dim_type type, unsigned pos);
3644 const char *isl_multi_aff_get_tuple_name(
3645 __isl_keep isl_multi_aff *multi,
3646 enum isl_dim_type type);
3647 int isl_pw_multi_aff_has_tuple_name(
3648 __isl_keep isl_pw_multi_aff *pma,
3649 enum isl_dim_type type);
3650 const char *isl_pw_multi_aff_get_tuple_name(
3651 __isl_keep isl_pw_multi_aff *pma,
3652 enum isl_dim_type type);
3653 int isl_pw_multi_aff_has_tuple_id(
3654 __isl_keep isl_pw_multi_aff *pma,
3655 enum isl_dim_type type);
3656 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3657 __isl_keep isl_pw_multi_aff *pma,
3658 enum isl_dim_type type);
3660 int isl_pw_multi_aff_foreach_piece(
3661 __isl_keep isl_pw_multi_aff *pma,
3662 int (*fn)(__isl_take isl_set *set,
3663 __isl_take isl_multi_aff *maff,
3664 void *user), void *user);
3666 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3667 __isl_keep isl_union_pw_multi_aff *upma,
3668 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3669 void *user), void *user);
3671 It can be modified using
3673 #include <isl/aff.h>
3674 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3675 __isl_take isl_multi_aff *multi, int pos,
3676 __isl_take isl_aff *aff);
3677 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3678 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3679 __isl_take isl_pw_aff *pa);
3680 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3681 __isl_take isl_multi_aff *maff,
3682 enum isl_dim_type type, unsigned pos, const char *s);
3683 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3684 __isl_take isl_multi_aff *maff,
3685 enum isl_dim_type type, __isl_take isl_id *id);
3686 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3687 __isl_take isl_pw_multi_aff *pma,
3688 enum isl_dim_type type, __isl_take isl_id *id);
3690 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3691 __isl_take isl_multi_aff *maff,
3692 enum isl_dim_type type, unsigned first, unsigned n);
3693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3694 __isl_take isl_pw_multi_aff *pma,
3695 enum isl_dim_type type, unsigned first, unsigned n);
3697 To check whether two multiple affine expressions are
3698 obviously equal to each other, use
3700 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3701 __isl_keep isl_multi_aff *maff2);
3702 int isl_pw_multi_aff_plain_is_equal(
3703 __isl_keep isl_pw_multi_aff *pma1,
3704 __isl_keep isl_pw_multi_aff *pma2);
3708 #include <isl/aff.h>
3709 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3710 __isl_take isl_pw_multi_aff *pma1,
3711 __isl_take isl_pw_multi_aff *pma2);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3713 __isl_take isl_pw_multi_aff *pma1,
3714 __isl_take isl_pw_multi_aff *pma2);
3715 __isl_give isl_multi_aff *isl_multi_aff_add(
3716 __isl_take isl_multi_aff *maff1,
3717 __isl_take isl_multi_aff *maff2);
3718 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3719 __isl_take isl_pw_multi_aff *pma1,
3720 __isl_take isl_pw_multi_aff *pma2);
3721 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3722 __isl_take isl_union_pw_multi_aff *upma1,
3723 __isl_take isl_union_pw_multi_aff *upma2);
3724 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3725 __isl_take isl_pw_multi_aff *pma1,
3726 __isl_take isl_pw_multi_aff *pma2);
3727 __isl_give isl_multi_aff *isl_multi_aff_scale(
3728 __isl_take isl_multi_aff *maff,
3730 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3731 __isl_take isl_pw_multi_aff *pma,
3732 __isl_take isl_set *set);
3733 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3734 __isl_take isl_pw_multi_aff *pma,
3735 __isl_take isl_set *set);
3736 __isl_give isl_multi_aff *isl_multi_aff_lift(
3737 __isl_take isl_multi_aff *maff,
3738 __isl_give isl_local_space **ls);
3739 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3740 __isl_take isl_pw_multi_aff *pma);
3741 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3742 __isl_take isl_multi_aff *multi,
3743 __isl_take isl_space *model);
3744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3745 __isl_take isl_pw_multi_aff *pma,
3746 __isl_take isl_space *model);
3747 __isl_give isl_pw_multi_aff *
3748 isl_pw_multi_aff_project_domain_on_params(
3749 __isl_take isl_pw_multi_aff *pma);
3750 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3751 __isl_take isl_multi_aff *maff,
3752 __isl_take isl_set *context);
3753 __isl_give isl_multi_aff *isl_multi_aff_gist(
3754 __isl_take isl_multi_aff *maff,
3755 __isl_take isl_set *context);
3756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3757 __isl_take isl_pw_multi_aff *pma,
3758 __isl_take isl_set *set);
3759 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3760 __isl_take isl_pw_multi_aff *pma,
3761 __isl_take isl_set *set);
3762 __isl_give isl_set *isl_pw_multi_aff_domain(
3763 __isl_take isl_pw_multi_aff *pma);
3764 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3765 __isl_take isl_union_pw_multi_aff *upma);
3766 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3767 __isl_take isl_multi_aff *ma1,
3768 __isl_take isl_multi_aff *ma2);
3769 __isl_give isl_multi_aff *isl_multi_aff_product(
3770 __isl_take isl_multi_aff *ma1,
3771 __isl_take isl_multi_aff *ma2);
3772 __isl_give isl_pw_multi_aff *
3773 isl_pw_multi_aff_flat_range_product(
3774 __isl_take isl_pw_multi_aff *pma1,
3775 __isl_take isl_pw_multi_aff *pma2);
3776 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3777 __isl_take isl_pw_multi_aff *pma1,
3778 __isl_take isl_pw_multi_aff *pma2);
3779 __isl_give isl_union_pw_multi_aff *
3780 isl_union_pw_multi_aff_flat_range_product(
3781 __isl_take isl_union_pw_multi_aff *upma1,
3782 __isl_take isl_union_pw_multi_aff *upma2);
3784 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3785 then it is assigned the local space that lies at the basis of
3786 the lifting applied.
3788 __isl_give isl_set *isl_multi_aff_lex_le_set(
3789 __isl_take isl_multi_aff *ma1,
3790 __isl_take isl_multi_aff *ma2);
3791 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3792 __isl_take isl_multi_aff *ma1,
3793 __isl_take isl_multi_aff *ma2);
3795 The function C<isl_multi_aff_lex_le_set> returns a set
3796 containing those elements in the shared domain space
3797 where C<ma1> is lexicographically smaller than or
3800 An expression can be read from input using
3802 #include <isl/aff.h>
3803 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3804 isl_ctx *ctx, const char *str);
3805 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3806 isl_ctx *ctx, const char *str);
3808 An expression can be printed using
3810 #include <isl/aff.h>
3811 __isl_give isl_printer *isl_printer_print_multi_aff(
3812 __isl_take isl_printer *p,
3813 __isl_keep isl_multi_aff *maff);
3814 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3815 __isl_take isl_printer *p,
3816 __isl_keep isl_pw_multi_aff *pma);
3817 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3818 __isl_take isl_printer *p,
3819 __isl_keep isl_union_pw_multi_aff *upma);
3823 Points are elements of a set. They can be used to construct
3824 simple sets (boxes) or they can be used to represent the
3825 individual elements of a set.
3826 The zero point (the origin) can be created using
3828 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3830 The coordinates of a point can be inspected, set and changed
3833 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3834 enum isl_dim_type type, int pos, isl_int *v);
3835 __isl_give isl_point *isl_point_set_coordinate(
3836 __isl_take isl_point *pnt,
3837 enum isl_dim_type type, int pos, isl_int v);
3839 __isl_give isl_point *isl_point_add_ui(
3840 __isl_take isl_point *pnt,
3841 enum isl_dim_type type, int pos, unsigned val);
3842 __isl_give isl_point *isl_point_sub_ui(
3843 __isl_take isl_point *pnt,
3844 enum isl_dim_type type, int pos, unsigned val);
3846 Other properties can be obtained using
3848 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3850 Points can be copied or freed using
3852 __isl_give isl_point *isl_point_copy(
3853 __isl_keep isl_point *pnt);
3854 void isl_point_free(__isl_take isl_point *pnt);
3856 A singleton set can be created from a point using
3858 __isl_give isl_basic_set *isl_basic_set_from_point(
3859 __isl_take isl_point *pnt);
3860 __isl_give isl_set *isl_set_from_point(
3861 __isl_take isl_point *pnt);
3863 and a box can be created from two opposite extremal points using
3865 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3866 __isl_take isl_point *pnt1,
3867 __isl_take isl_point *pnt2);
3868 __isl_give isl_set *isl_set_box_from_points(
3869 __isl_take isl_point *pnt1,
3870 __isl_take isl_point *pnt2);
3872 All elements of a B<bounded> (union) set can be enumerated using
3873 the following functions.
3875 int isl_set_foreach_point(__isl_keep isl_set *set,
3876 int (*fn)(__isl_take isl_point *pnt, void *user),
3878 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3879 int (*fn)(__isl_take isl_point *pnt, void *user),
3882 The function C<fn> is called for each integer point in
3883 C<set> with as second argument the last argument of
3884 the C<isl_set_foreach_point> call. The function C<fn>
3885 should return C<0> on success and C<-1> on failure.
3886 In the latter case, C<isl_set_foreach_point> will stop
3887 enumerating and return C<-1> as well.
3888 If the enumeration is performed successfully and to completion,
3889 then C<isl_set_foreach_point> returns C<0>.
3891 To obtain a single point of a (basic) set, use
3893 __isl_give isl_point *isl_basic_set_sample_point(
3894 __isl_take isl_basic_set *bset);
3895 __isl_give isl_point *isl_set_sample_point(
3896 __isl_take isl_set *set);
3898 If C<set> does not contain any (integer) points, then the
3899 resulting point will be ``void'', a property that can be
3902 int isl_point_is_void(__isl_keep isl_point *pnt);
3904 =head2 Piecewise Quasipolynomials
3906 A piecewise quasipolynomial is a particular kind of function that maps
3907 a parametric point to a rational value.
3908 More specifically, a quasipolynomial is a polynomial expression in greatest
3909 integer parts of affine expressions of parameters and variables.
3910 A piecewise quasipolynomial is a subdivision of a given parametric
3911 domain into disjoint cells with a quasipolynomial associated to
3912 each cell. The value of the piecewise quasipolynomial at a given
3913 point is the value of the quasipolynomial associated to the cell
3914 that contains the point. Outside of the union of cells,
3915 the value is assumed to be zero.
3916 For example, the piecewise quasipolynomial
3918 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3920 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3921 A given piecewise quasipolynomial has a fixed domain dimension.
3922 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3923 defined over different domains.
3924 Piecewise quasipolynomials are mainly used by the C<barvinok>
3925 library for representing the number of elements in a parametric set or map.
3926 For example, the piecewise quasipolynomial above represents
3927 the number of points in the map
3929 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3931 =head3 Input and Output
3933 Piecewise quasipolynomials can be read from input using
3935 __isl_give isl_union_pw_qpolynomial *
3936 isl_union_pw_qpolynomial_read_from_str(
3937 isl_ctx *ctx, const char *str);
3939 Quasipolynomials and piecewise quasipolynomials can be printed
3940 using the following functions.
3942 __isl_give isl_printer *isl_printer_print_qpolynomial(
3943 __isl_take isl_printer *p,
3944 __isl_keep isl_qpolynomial *qp);
3946 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3947 __isl_take isl_printer *p,
3948 __isl_keep isl_pw_qpolynomial *pwqp);
3950 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3951 __isl_take isl_printer *p,
3952 __isl_keep isl_union_pw_qpolynomial *upwqp);
3954 The output format of the printer
3955 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3956 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3958 In case of printing in C<ISL_FORMAT_C>, the user may want
3959 to set the names of all dimensions
3961 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3962 __isl_take isl_qpolynomial *qp,
3963 enum isl_dim_type type, unsigned pos,
3965 __isl_give isl_pw_qpolynomial *
3966 isl_pw_qpolynomial_set_dim_name(
3967 __isl_take isl_pw_qpolynomial *pwqp,
3968 enum isl_dim_type type, unsigned pos,
3971 =head3 Creating New (Piecewise) Quasipolynomials
3973 Some simple quasipolynomials can be created using the following functions.
3974 More complicated quasipolynomials can be created by applying
3975 operations such as addition and multiplication
3976 on the resulting quasipolynomials
3978 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3979 __isl_take isl_space *domain);
3980 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3981 __isl_take isl_space *domain);
3982 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3983 __isl_take isl_space *domain);
3984 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3985 __isl_take isl_space *domain);
3986 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3987 __isl_take isl_space *domain);
3988 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3989 __isl_take isl_space *domain,
3990 const isl_int n, const isl_int d);
3991 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3992 __isl_take isl_space *domain,
3993 enum isl_dim_type type, unsigned pos);
3994 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3995 __isl_take isl_aff *aff);
3997 Note that the space in which a quasipolynomial lives is a map space
3998 with a one-dimensional range. The C<domain> argument in some of
3999 the functions above corresponds to the domain of this map space.
4001 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4002 with a single cell can be created using the following functions.
4003 Multiple of these single cell piecewise quasipolynomials can
4004 be combined to create more complicated piecewise quasipolynomials.
4006 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4007 __isl_take isl_space *space);
4008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4009 __isl_take isl_set *set,
4010 __isl_take isl_qpolynomial *qp);
4011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4012 __isl_take isl_qpolynomial *qp);
4013 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4014 __isl_take isl_pw_aff *pwaff);
4016 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4017 __isl_take isl_space *space);
4018 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4019 __isl_take isl_pw_qpolynomial *pwqp);
4020 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4021 __isl_take isl_union_pw_qpolynomial *upwqp,
4022 __isl_take isl_pw_qpolynomial *pwqp);
4024 Quasipolynomials can be copied and freed again using the following
4027 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4028 __isl_keep isl_qpolynomial *qp);
4029 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4031 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4032 __isl_keep isl_pw_qpolynomial *pwqp);
4033 void *isl_pw_qpolynomial_free(
4034 __isl_take isl_pw_qpolynomial *pwqp);
4036 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4037 __isl_keep isl_union_pw_qpolynomial *upwqp);
4038 void *isl_union_pw_qpolynomial_free(
4039 __isl_take isl_union_pw_qpolynomial *upwqp);
4041 =head3 Inspecting (Piecewise) Quasipolynomials
4043 To iterate over all piecewise quasipolynomials in a union
4044 piecewise quasipolynomial, use the following function
4046 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4047 __isl_keep isl_union_pw_qpolynomial *upwqp,
4048 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4051 To extract the piecewise quasipolynomial in a given space from a union, use
4053 __isl_give isl_pw_qpolynomial *
4054 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4055 __isl_keep isl_union_pw_qpolynomial *upwqp,
4056 __isl_take isl_space *space);
4058 To iterate over the cells in a piecewise quasipolynomial,
4059 use either of the following two functions
4061 int isl_pw_qpolynomial_foreach_piece(
4062 __isl_keep isl_pw_qpolynomial *pwqp,
4063 int (*fn)(__isl_take isl_set *set,
4064 __isl_take isl_qpolynomial *qp,
4065 void *user), void *user);
4066 int isl_pw_qpolynomial_foreach_lifted_piece(
4067 __isl_keep isl_pw_qpolynomial *pwqp,
4068 int (*fn)(__isl_take isl_set *set,
4069 __isl_take isl_qpolynomial *qp,
4070 void *user), void *user);
4072 As usual, the function C<fn> should return C<0> on success
4073 and C<-1> on failure. The difference between
4074 C<isl_pw_qpolynomial_foreach_piece> and
4075 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4076 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4077 compute unique representations for all existentially quantified
4078 variables and then turn these existentially quantified variables
4079 into extra set variables, adapting the associated quasipolynomial
4080 accordingly. This means that the C<set> passed to C<fn>
4081 will not have any existentially quantified variables, but that
4082 the dimensions of the sets may be different for different
4083 invocations of C<fn>.
4085 To iterate over all terms in a quasipolynomial,
4088 int isl_qpolynomial_foreach_term(
4089 __isl_keep isl_qpolynomial *qp,
4090 int (*fn)(__isl_take isl_term *term,
4091 void *user), void *user);
4093 The terms themselves can be inspected and freed using
4096 unsigned isl_term_dim(__isl_keep isl_term *term,
4097 enum isl_dim_type type);
4098 void isl_term_get_num(__isl_keep isl_term *term,
4100 void isl_term_get_den(__isl_keep isl_term *term,
4102 int isl_term_get_exp(__isl_keep isl_term *term,
4103 enum isl_dim_type type, unsigned pos);
4104 __isl_give isl_aff *isl_term_get_div(
4105 __isl_keep isl_term *term, unsigned pos);
4106 void isl_term_free(__isl_take isl_term *term);
4108 Each term is a product of parameters, set variables and
4109 integer divisions. The function C<isl_term_get_exp>
4110 returns the exponent of a given dimensions in the given term.
4111 The C<isl_int>s in the arguments of C<isl_term_get_num>
4112 and C<isl_term_get_den> need to have been initialized
4113 using C<isl_int_init> before calling these functions.
4115 =head3 Properties of (Piecewise) Quasipolynomials
4117 To check whether a quasipolynomial is actually a constant,
4118 use the following function.
4120 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4121 isl_int *n, isl_int *d);
4123 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4124 then the numerator and denominator of the constant
4125 are returned in C<*n> and C<*d>, respectively.
4127 To check whether two union piecewise quasipolynomials are
4128 obviously equal, use
4130 int isl_union_pw_qpolynomial_plain_is_equal(
4131 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4132 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4134 =head3 Operations on (Piecewise) Quasipolynomials
4136 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4137 __isl_take isl_qpolynomial *qp, isl_int v);
4138 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4139 __isl_take isl_qpolynomial *qp);
4140 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4141 __isl_take isl_qpolynomial *qp1,
4142 __isl_take isl_qpolynomial *qp2);
4143 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4144 __isl_take isl_qpolynomial *qp1,
4145 __isl_take isl_qpolynomial *qp2);
4146 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4147 __isl_take isl_qpolynomial *qp1,
4148 __isl_take isl_qpolynomial *qp2);
4149 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4150 __isl_take isl_qpolynomial *qp, unsigned exponent);
4152 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4153 __isl_take isl_pw_qpolynomial *pwqp1,
4154 __isl_take isl_pw_qpolynomial *pwqp2);
4155 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4156 __isl_take isl_pw_qpolynomial *pwqp1,
4157 __isl_take isl_pw_qpolynomial *pwqp2);
4158 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4159 __isl_take isl_pw_qpolynomial *pwqp1,
4160 __isl_take isl_pw_qpolynomial *pwqp2);
4161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4162 __isl_take isl_pw_qpolynomial *pwqp);
4163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4164 __isl_take isl_pw_qpolynomial *pwqp1,
4165 __isl_take isl_pw_qpolynomial *pwqp2);
4166 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4167 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4169 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4170 __isl_take isl_union_pw_qpolynomial *upwqp1,
4171 __isl_take isl_union_pw_qpolynomial *upwqp2);
4172 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4173 __isl_take isl_union_pw_qpolynomial *upwqp1,
4174 __isl_take isl_union_pw_qpolynomial *upwqp2);
4175 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4176 __isl_take isl_union_pw_qpolynomial *upwqp1,
4177 __isl_take isl_union_pw_qpolynomial *upwqp2);
4179 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4180 __isl_take isl_pw_qpolynomial *pwqp,
4181 __isl_take isl_point *pnt);
4183 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4184 __isl_take isl_union_pw_qpolynomial *upwqp,
4185 __isl_take isl_point *pnt);
4187 __isl_give isl_set *isl_pw_qpolynomial_domain(
4188 __isl_take isl_pw_qpolynomial *pwqp);
4189 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4190 __isl_take isl_pw_qpolynomial *pwpq,
4191 __isl_take isl_set *set);
4192 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4193 __isl_take isl_pw_qpolynomial *pwpq,
4194 __isl_take isl_set *set);
4196 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4197 __isl_take isl_union_pw_qpolynomial *upwqp);
4198 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4199 __isl_take isl_union_pw_qpolynomial *upwpq,
4200 __isl_take isl_union_set *uset);
4201 __isl_give isl_union_pw_qpolynomial *
4202 isl_union_pw_qpolynomial_intersect_params(
4203 __isl_take isl_union_pw_qpolynomial *upwpq,
4204 __isl_take isl_set *set);
4206 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4207 __isl_take isl_qpolynomial *qp,
4208 __isl_take isl_space *model);
4210 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4211 __isl_take isl_qpolynomial *qp);
4212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4213 __isl_take isl_pw_qpolynomial *pwqp);
4215 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4216 __isl_take isl_union_pw_qpolynomial *upwqp);
4218 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4219 __isl_take isl_qpolynomial *qp,
4220 __isl_take isl_set *context);
4221 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4222 __isl_take isl_qpolynomial *qp,
4223 __isl_take isl_set *context);
4225 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4226 __isl_take isl_pw_qpolynomial *pwqp,
4227 __isl_take isl_set *context);
4228 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4229 __isl_take isl_pw_qpolynomial *pwqp,
4230 __isl_take isl_set *context);
4232 __isl_give isl_union_pw_qpolynomial *
4233 isl_union_pw_qpolynomial_gist_params(
4234 __isl_take isl_union_pw_qpolynomial *upwqp,
4235 __isl_take isl_set *context);
4236 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4237 __isl_take isl_union_pw_qpolynomial *upwqp,
4238 __isl_take isl_union_set *context);
4240 The gist operation applies the gist operation to each of
4241 the cells in the domain of the input piecewise quasipolynomial.
4242 The context is also exploited
4243 to simplify the quasipolynomials associated to each cell.
4245 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4246 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4247 __isl_give isl_union_pw_qpolynomial *
4248 isl_union_pw_qpolynomial_to_polynomial(
4249 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4251 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4252 the polynomial will be an overapproximation. If C<sign> is negative,
4253 it will be an underapproximation. If C<sign> is zero, the approximation
4254 will lie somewhere in between.
4256 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4258 A piecewise quasipolynomial reduction is a piecewise
4259 reduction (or fold) of quasipolynomials.
4260 In particular, the reduction can be maximum or a minimum.
4261 The objects are mainly used to represent the result of
4262 an upper or lower bound on a quasipolynomial over its domain,
4263 i.e., as the result of the following function.
4265 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4266 __isl_take isl_pw_qpolynomial *pwqp,
4267 enum isl_fold type, int *tight);
4269 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4270 __isl_take isl_union_pw_qpolynomial *upwqp,
4271 enum isl_fold type, int *tight);
4273 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4274 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4275 is the returned bound is known be tight, i.e., for each value
4276 of the parameters there is at least
4277 one element in the domain that reaches the bound.
4278 If the domain of C<pwqp> is not wrapping, then the bound is computed
4279 over all elements in that domain and the result has a purely parametric
4280 domain. If the domain of C<pwqp> is wrapping, then the bound is
4281 computed over the range of the wrapped relation. The domain of the
4282 wrapped relation becomes the domain of the result.
4284 A (piecewise) quasipolynomial reduction can be copied or freed using the
4285 following functions.
4287 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4288 __isl_keep isl_qpolynomial_fold *fold);
4289 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4290 __isl_keep isl_pw_qpolynomial_fold *pwf);
4291 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4292 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4293 void isl_qpolynomial_fold_free(
4294 __isl_take isl_qpolynomial_fold *fold);
4295 void *isl_pw_qpolynomial_fold_free(
4296 __isl_take isl_pw_qpolynomial_fold *pwf);
4297 void *isl_union_pw_qpolynomial_fold_free(
4298 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4300 =head3 Printing Piecewise Quasipolynomial Reductions
4302 Piecewise quasipolynomial reductions can be printed
4303 using the following function.
4305 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4306 __isl_take isl_printer *p,
4307 __isl_keep isl_pw_qpolynomial_fold *pwf);
4308 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4309 __isl_take isl_printer *p,
4310 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4312 For C<isl_printer_print_pw_qpolynomial_fold>,
4313 output format of the printer
4314 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4315 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4316 output format of the printer
4317 needs to be set to C<ISL_FORMAT_ISL>.
4318 In case of printing in C<ISL_FORMAT_C>, the user may want
4319 to set the names of all dimensions
4321 __isl_give isl_pw_qpolynomial_fold *
4322 isl_pw_qpolynomial_fold_set_dim_name(
4323 __isl_take isl_pw_qpolynomial_fold *pwf,
4324 enum isl_dim_type type, unsigned pos,
4327 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4329 To iterate over all piecewise quasipolynomial reductions in a union
4330 piecewise quasipolynomial reduction, use the following function
4332 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4333 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4334 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4335 void *user), void *user);
4337 To iterate over the cells in a piecewise quasipolynomial reduction,
4338 use either of the following two functions
4340 int isl_pw_qpolynomial_fold_foreach_piece(
4341 __isl_keep isl_pw_qpolynomial_fold *pwf,
4342 int (*fn)(__isl_take isl_set *set,
4343 __isl_take isl_qpolynomial_fold *fold,
4344 void *user), void *user);
4345 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4346 __isl_keep isl_pw_qpolynomial_fold *pwf,
4347 int (*fn)(__isl_take isl_set *set,
4348 __isl_take isl_qpolynomial_fold *fold,
4349 void *user), void *user);
4351 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4352 of the difference between these two functions.
4354 To iterate over all quasipolynomials in a reduction, use
4356 int isl_qpolynomial_fold_foreach_qpolynomial(
4357 __isl_keep isl_qpolynomial_fold *fold,
4358 int (*fn)(__isl_take isl_qpolynomial *qp,
4359 void *user), void *user);
4361 =head3 Properties of Piecewise Quasipolynomial Reductions
4363 To check whether two union piecewise quasipolynomial reductions are
4364 obviously equal, use
4366 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4367 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4368 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4370 =head3 Operations on Piecewise Quasipolynomial Reductions
4372 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4373 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4375 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4376 __isl_take isl_pw_qpolynomial_fold *pwf1,
4377 __isl_take isl_pw_qpolynomial_fold *pwf2);
4379 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4380 __isl_take isl_pw_qpolynomial_fold *pwf1,
4381 __isl_take isl_pw_qpolynomial_fold *pwf2);
4383 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4384 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4385 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4387 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4388 __isl_take isl_pw_qpolynomial_fold *pwf,
4389 __isl_take isl_point *pnt);
4391 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4392 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4393 __isl_take isl_point *pnt);
4395 __isl_give isl_pw_qpolynomial_fold *
4396 isl_pw_qpolynomial_fold_intersect_params(
4397 __isl_take isl_pw_qpolynomial_fold *pwf,
4398 __isl_take isl_set *set);
4400 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4401 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4402 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4404 __isl_take isl_union_set *uset);
4405 __isl_give isl_union_pw_qpolynomial_fold *
4406 isl_union_pw_qpolynomial_fold_intersect_params(
4407 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4408 __isl_take isl_set *set);
4410 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4411 __isl_take isl_pw_qpolynomial_fold *pwf);
4413 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4414 __isl_take isl_pw_qpolynomial_fold *pwf);
4416 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4417 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4419 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4420 __isl_take isl_qpolynomial_fold *fold,
4421 __isl_take isl_set *context);
4422 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4423 __isl_take isl_qpolynomial_fold *fold,
4424 __isl_take isl_set *context);
4426 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4427 __isl_take isl_pw_qpolynomial_fold *pwf,
4428 __isl_take isl_set *context);
4429 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4430 __isl_take isl_pw_qpolynomial_fold *pwf,
4431 __isl_take isl_set *context);
4433 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4434 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4435 __isl_take isl_union_set *context);
4436 __isl_give isl_union_pw_qpolynomial_fold *
4437 isl_union_pw_qpolynomial_fold_gist_params(
4438 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4439 __isl_take isl_set *context);
4441 The gist operation applies the gist operation to each of
4442 the cells in the domain of the input piecewise quasipolynomial reduction.
4443 In future, the operation will also exploit the context
4444 to simplify the quasipolynomial reductions associated to each cell.
4446 __isl_give isl_pw_qpolynomial_fold *
4447 isl_set_apply_pw_qpolynomial_fold(
4448 __isl_take isl_set *set,
4449 __isl_take isl_pw_qpolynomial_fold *pwf,
4451 __isl_give isl_pw_qpolynomial_fold *
4452 isl_map_apply_pw_qpolynomial_fold(
4453 __isl_take isl_map *map,
4454 __isl_take isl_pw_qpolynomial_fold *pwf,
4456 __isl_give isl_union_pw_qpolynomial_fold *
4457 isl_union_set_apply_union_pw_qpolynomial_fold(
4458 __isl_take isl_union_set *uset,
4459 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4461 __isl_give isl_union_pw_qpolynomial_fold *
4462 isl_union_map_apply_union_pw_qpolynomial_fold(
4463 __isl_take isl_union_map *umap,
4464 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4467 The functions taking a map
4468 compose the given map with the given piecewise quasipolynomial reduction.
4469 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4470 over all elements in the intersection of the range of the map
4471 and the domain of the piecewise quasipolynomial reduction
4472 as a function of an element in the domain of the map.
4473 The functions taking a set compute a bound over all elements in the
4474 intersection of the set and the domain of the
4475 piecewise quasipolynomial reduction.
4477 =head2 Dependence Analysis
4479 C<isl> contains specialized functionality for performing
4480 array dataflow analysis. That is, given a I<sink> access relation
4481 and a collection of possible I<source> access relations,
4482 C<isl> can compute relations that describe
4483 for each iteration of the sink access, which iteration
4484 of which of the source access relations was the last
4485 to access the same data element before the given iteration
4487 The resulting dependence relations map source iterations
4488 to the corresponding sink iterations.
4489 To compute standard flow dependences, the sink should be
4490 a read, while the sources should be writes.
4491 If any of the source accesses are marked as being I<may>
4492 accesses, then there will be a dependence from the last
4493 I<must> access B<and> from any I<may> access that follows
4494 this last I<must> access.
4495 In particular, if I<all> sources are I<may> accesses,
4496 then memory based dependence analysis is performed.
4497 If, on the other hand, all sources are I<must> accesses,
4498 then value based dependence analysis is performed.
4500 #include <isl/flow.h>
4502 typedef int (*isl_access_level_before)(void *first, void *second);
4504 __isl_give isl_access_info *isl_access_info_alloc(
4505 __isl_take isl_map *sink,
4506 void *sink_user, isl_access_level_before fn,
4508 __isl_give isl_access_info *isl_access_info_add_source(
4509 __isl_take isl_access_info *acc,
4510 __isl_take isl_map *source, int must,
4512 void *isl_access_info_free(__isl_take isl_access_info *acc);
4514 __isl_give isl_flow *isl_access_info_compute_flow(
4515 __isl_take isl_access_info *acc);
4517 int isl_flow_foreach(__isl_keep isl_flow *deps,
4518 int (*fn)(__isl_take isl_map *dep, int must,
4519 void *dep_user, void *user),
4521 __isl_give isl_map *isl_flow_get_no_source(
4522 __isl_keep isl_flow *deps, int must);
4523 void isl_flow_free(__isl_take isl_flow *deps);
4525 The function C<isl_access_info_compute_flow> performs the actual
4526 dependence analysis. The other functions are used to construct
4527 the input for this function or to read off the output.
4529 The input is collected in an C<isl_access_info>, which can
4530 be created through a call to C<isl_access_info_alloc>.
4531 The arguments to this functions are the sink access relation
4532 C<sink>, a token C<sink_user> used to identify the sink
4533 access to the user, a callback function for specifying the
4534 relative order of source and sink accesses, and the number
4535 of source access relations that will be added.
4536 The callback function has type C<int (*)(void *first, void *second)>.
4537 The function is called with two user supplied tokens identifying
4538 either a source or the sink and it should return the shared nesting
4539 level and the relative order of the two accesses.
4540 In particular, let I<n> be the number of loops shared by
4541 the two accesses. If C<first> precedes C<second> textually,
4542 then the function should return I<2 * n + 1>; otherwise,
4543 it should return I<2 * n>.
4544 The sources can be added to the C<isl_access_info> by performing
4545 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4546 C<must> indicates whether the source is a I<must> access
4547 or a I<may> access. Note that a multi-valued access relation
4548 should only be marked I<must> if every iteration in the domain
4549 of the relation accesses I<all> elements in its image.
4550 The C<source_user> token is again used to identify
4551 the source access. The range of the source access relation
4552 C<source> should have the same dimension as the range
4553 of the sink access relation.
4554 The C<isl_access_info_free> function should usually not be
4555 called explicitly, because it is called implicitly by
4556 C<isl_access_info_compute_flow>.
4558 The result of the dependence analysis is collected in an
4559 C<isl_flow>. There may be elements of
4560 the sink access for which no preceding source access could be
4561 found or for which all preceding sources are I<may> accesses.
4562 The relations containing these elements can be obtained through
4563 calls to C<isl_flow_get_no_source>, the first with C<must> set
4564 and the second with C<must> unset.
4565 In the case of standard flow dependence analysis,
4566 with the sink a read and the sources I<must> writes,
4567 the first relation corresponds to the reads from uninitialized
4568 array elements and the second relation is empty.
4569 The actual flow dependences can be extracted using
4570 C<isl_flow_foreach>. This function will call the user-specified
4571 callback function C<fn> for each B<non-empty> dependence between
4572 a source and the sink. The callback function is called
4573 with four arguments, the actual flow dependence relation
4574 mapping source iterations to sink iterations, a boolean that
4575 indicates whether it is a I<must> or I<may> dependence, a token
4576 identifying the source and an additional C<void *> with value
4577 equal to the third argument of the C<isl_flow_foreach> call.
4578 A dependence is marked I<must> if it originates from a I<must>
4579 source and if it is not followed by any I<may> sources.
4581 After finishing with an C<isl_flow>, the user should call
4582 C<isl_flow_free> to free all associated memory.
4584 A higher-level interface to dependence analysis is provided
4585 by the following function.
4587 #include <isl/flow.h>
4589 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4590 __isl_take isl_union_map *must_source,
4591 __isl_take isl_union_map *may_source,
4592 __isl_take isl_union_map *schedule,
4593 __isl_give isl_union_map **must_dep,
4594 __isl_give isl_union_map **may_dep,
4595 __isl_give isl_union_map **must_no_source,
4596 __isl_give isl_union_map **may_no_source);
4598 The arrays are identified by the tuple names of the ranges
4599 of the accesses. The iteration domains by the tuple names
4600 of the domains of the accesses and of the schedule.
4601 The relative order of the iteration domains is given by the
4602 schedule. The relations returned through C<must_no_source>
4603 and C<may_no_source> are subsets of C<sink>.
4604 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4605 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4606 any of the other arguments is treated as an error.
4608 =head3 Interaction with Dependence Analysis
4610 During the dependence analysis, we frequently need to perform
4611 the following operation. Given a relation between sink iterations
4612 and potential source iterations from a particular source domain,
4613 what is the last potential source iteration corresponding to each
4614 sink iteration. It can sometimes be convenient to adjust
4615 the set of potential source iterations before or after each such operation.
4616 The prototypical example is fuzzy array dataflow analysis,
4617 where we need to analyze if, based on data-dependent constraints,
4618 the sink iteration can ever be executed without one or more of
4619 the corresponding potential source iterations being executed.
4620 If so, we can introduce extra parameters and select an unknown
4621 but fixed source iteration from the potential source iterations.
4622 To be able to perform such manipulations, C<isl> provides the following
4625 #include <isl/flow.h>
4627 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4628 __isl_keep isl_map *source_map,
4629 __isl_keep isl_set *sink, void *source_user,
4631 __isl_give isl_access_info *isl_access_info_set_restrict(
4632 __isl_take isl_access_info *acc,
4633 isl_access_restrict fn, void *user);
4635 The function C<isl_access_info_set_restrict> should be called
4636 before calling C<isl_access_info_compute_flow> and registers a callback function
4637 that will be called any time C<isl> is about to compute the last
4638 potential source. The first argument is the (reverse) proto-dependence,
4639 mapping sink iterations to potential source iterations.
4640 The second argument represents the sink iterations for which
4641 we want to compute the last source iteration.
4642 The third argument is the token corresponding to the source
4643 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4644 The callback is expected to return a restriction on either the input or
4645 the output of the operation computing the last potential source.
4646 If the input needs to be restricted then restrictions are needed
4647 for both the source and the sink iterations. The sink iterations
4648 and the potential source iterations will be intersected with these sets.
4649 If the output needs to be restricted then only a restriction on the source
4650 iterations is required.
4651 If any error occurs, the callback should return C<NULL>.
4652 An C<isl_restriction> object can be created, freed and inspected
4653 using the following functions.
4655 #include <isl/flow.h>
4657 __isl_give isl_restriction *isl_restriction_input(
4658 __isl_take isl_set *source_restr,
4659 __isl_take isl_set *sink_restr);
4660 __isl_give isl_restriction *isl_restriction_output(
4661 __isl_take isl_set *source_restr);
4662 __isl_give isl_restriction *isl_restriction_none(
4663 __isl_take isl_map *source_map);
4664 __isl_give isl_restriction *isl_restriction_empty(
4665 __isl_take isl_map *source_map);
4666 void *isl_restriction_free(
4667 __isl_take isl_restriction *restr);
4668 isl_ctx *isl_restriction_get_ctx(
4669 __isl_keep isl_restriction *restr);
4671 C<isl_restriction_none> and C<isl_restriction_empty> are special
4672 cases of C<isl_restriction_input>. C<isl_restriction_none>
4673 is essentially equivalent to
4675 isl_restriction_input(isl_set_universe(
4676 isl_space_range(isl_map_get_space(source_map))),
4678 isl_space_domain(isl_map_get_space(source_map))));
4680 whereas C<isl_restriction_empty> is essentially equivalent to
4682 isl_restriction_input(isl_set_empty(
4683 isl_space_range(isl_map_get_space(source_map))),
4685 isl_space_domain(isl_map_get_space(source_map))));
4689 B<The functionality described in this section is fairly new
4690 and may be subject to change.>
4692 The following function can be used to compute a schedule
4693 for a union of domains.
4694 By default, the algorithm used to construct the schedule is similar
4695 to that of C<Pluto>.
4696 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4698 The generated schedule respects all C<validity> dependences.
4699 That is, all dependence distances over these dependences in the
4700 scheduled space are lexicographically positive.
4701 The default algorithm tries to minimize the dependence distances over
4702 C<proximity> dependences.
4703 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4704 for groups of domains where the dependence distances have only
4705 non-negative values.
4706 When using Feautrier's algorithm, the C<proximity> dependence
4707 distances are only minimized during the extension to a
4708 full-dimensional schedule.
4710 #include <isl/schedule.h>
4711 __isl_give isl_schedule *isl_union_set_compute_schedule(
4712 __isl_take isl_union_set *domain,
4713 __isl_take isl_union_map *validity,
4714 __isl_take isl_union_map *proximity);
4715 void *isl_schedule_free(__isl_take isl_schedule *sched);
4717 A mapping from the domains to the scheduled space can be obtained
4718 from an C<isl_schedule> using the following function.
4720 __isl_give isl_union_map *isl_schedule_get_map(
4721 __isl_keep isl_schedule *sched);
4723 A representation of the schedule can be printed using
4725 __isl_give isl_printer *isl_printer_print_schedule(
4726 __isl_take isl_printer *p,
4727 __isl_keep isl_schedule *schedule);
4729 A representation of the schedule as a forest of bands can be obtained
4730 using the following function.
4732 __isl_give isl_band_list *isl_schedule_get_band_forest(
4733 __isl_keep isl_schedule *schedule);
4735 The individual bands can be visited in depth-first post-order
4736 using the following function.
4738 #include <isl/schedule.h>
4739 int isl_schedule_foreach_band(
4740 __isl_keep isl_schedule *sched,
4741 int (*fn)(__isl_keep isl_band *band, void *user),
4744 The list can be manipulated as explained in L<"Lists">.
4745 The bands inside the list can be copied and freed using the following
4748 #include <isl/band.h>
4749 __isl_give isl_band *isl_band_copy(
4750 __isl_keep isl_band *band);
4751 void *isl_band_free(__isl_take isl_band *band);
4753 Each band contains zero or more scheduling dimensions.
4754 These are referred to as the members of the band.
4755 The section of the schedule that corresponds to the band is
4756 referred to as the partial schedule of the band.
4757 For those nodes that participate in a band, the outer scheduling
4758 dimensions form the prefix schedule, while the inner scheduling
4759 dimensions form the suffix schedule.
4760 That is, if we take a cut of the band forest, then the union of
4761 the concatenations of the prefix, partial and suffix schedules of
4762 each band in the cut is equal to the entire schedule (modulo
4763 some possible padding at the end with zero scheduling dimensions).
4764 The properties of a band can be inspected using the following functions.
4766 #include <isl/band.h>
4767 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4769 int isl_band_has_children(__isl_keep isl_band *band);
4770 __isl_give isl_band_list *isl_band_get_children(
4771 __isl_keep isl_band *band);
4773 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4774 __isl_keep isl_band *band);
4775 __isl_give isl_union_map *isl_band_get_partial_schedule(
4776 __isl_keep isl_band *band);
4777 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4778 __isl_keep isl_band *band);
4780 int isl_band_n_member(__isl_keep isl_band *band);
4781 int isl_band_member_is_zero_distance(
4782 __isl_keep isl_band *band, int pos);
4784 int isl_band_list_foreach_band(
4785 __isl_keep isl_band_list *list,
4786 int (*fn)(__isl_keep isl_band *band, void *user),
4789 Note that a scheduling dimension is considered to be ``zero
4790 distance'' if it does not carry any proximity dependences
4792 That is, if the dependence distances of the proximity
4793 dependences are all zero in that direction (for fixed
4794 iterations of outer bands).
4795 Like C<isl_schedule_foreach_band>,
4796 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4797 in depth-first post-order.
4799 A band can be tiled using the following function.
4801 #include <isl/band.h>
4802 int isl_band_tile(__isl_keep isl_band *band,
4803 __isl_take isl_vec *sizes);
4805 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4807 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4809 The C<isl_band_tile> function tiles the band using the given tile sizes
4810 inside its schedule.
4811 A new child band is created to represent the point loops and it is
4812 inserted between the modified band and its children.
4813 The C<tile_scale_tile_loops> option specifies whether the tile
4814 loops iterators should be scaled by the tile sizes.
4816 A representation of the band can be printed using
4818 #include <isl/band.h>
4819 __isl_give isl_printer *isl_printer_print_band(
4820 __isl_take isl_printer *p,
4821 __isl_keep isl_band *band);
4825 #include <isl/schedule.h>
4826 int isl_options_set_schedule_max_coefficient(
4827 isl_ctx *ctx, int val);
4828 int isl_options_get_schedule_max_coefficient(
4830 int isl_options_set_schedule_max_constant_term(
4831 isl_ctx *ctx, int val);
4832 int isl_options_get_schedule_max_constant_term(
4834 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4835 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4836 int isl_options_set_schedule_maximize_band_depth(
4837 isl_ctx *ctx, int val);
4838 int isl_options_get_schedule_maximize_band_depth(
4840 int isl_options_set_schedule_outer_zero_distance(
4841 isl_ctx *ctx, int val);
4842 int isl_options_get_schedule_outer_zero_distance(
4844 int isl_options_set_schedule_split_scaled(
4845 isl_ctx *ctx, int val);
4846 int isl_options_get_schedule_split_scaled(
4848 int isl_options_set_schedule_algorithm(
4849 isl_ctx *ctx, int val);
4850 int isl_options_get_schedule_algorithm(
4852 int isl_options_set_schedule_separate_components(
4853 isl_ctx *ctx, int val);
4854 int isl_options_get_schedule_separate_components(
4859 =item * schedule_max_coefficient
4861 This option enforces that the coefficients for variable and parameter
4862 dimensions in the calculated schedule are not larger than the specified value.
4863 This option can significantly increase the speed of the scheduling calculation
4864 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4865 this option does not introduce bounds on the variable or parameter
4868 =item * schedule_max_constant_term
4870 This option enforces that the constant coefficients in the calculated schedule
4871 are not larger than the maximal constant term. This option can significantly
4872 increase the speed of the scheduling calculation and may also prevent fusing of
4873 unrelated dimensions. A value of -1 means that this option does not introduce
4874 bounds on the constant coefficients.
4876 =item * schedule_fuse
4878 This option controls the level of fusion.
4879 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4880 resulting schedule will be distributed as much as possible.
4881 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4882 try to fuse loops in the resulting schedule.
4884 =item * schedule_maximize_band_depth
4886 If this option is set, we do not split bands at the point
4887 where we detect splitting is necessary. Instead, we
4888 backtrack and split bands as early as possible. This
4889 reduces the number of splits and maximizes the width of
4890 the bands. Wider bands give more possibilities for tiling.
4891 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4892 then bands will be split as early as possible, even if there is no need.
4893 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4895 =item * schedule_outer_zero_distance
4897 If this option is set, then we try to construct schedules
4898 where the outermost scheduling dimension in each band
4899 results in a zero dependence distance over the proximity
4902 =item * schedule_split_scaled
4904 If this option is set, then we try to construct schedules in which the
4905 constant term is split off from the linear part if the linear parts of
4906 the scheduling rows for all nodes in the graphs have a common non-trivial
4908 The constant term is then placed in a separate band and the linear
4911 =item * schedule_algorithm
4913 Selects the scheduling algorithm to be used.
4914 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4915 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4917 =item * schedule_separate_components
4919 If at any point the dependence graph contains any (weakly connected) components,
4920 then these components are scheduled separately.
4921 If this option is not set, then some iterations of the domains
4922 in these components may be scheduled together.
4923 If this option is set, then the components are given consecutive
4928 =head2 Parametric Vertex Enumeration
4930 The parametric vertex enumeration described in this section
4931 is mainly intended to be used internally and by the C<barvinok>
4934 #include <isl/vertices.h>
4935 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4936 __isl_keep isl_basic_set *bset);
4938 The function C<isl_basic_set_compute_vertices> performs the
4939 actual computation of the parametric vertices and the chamber
4940 decomposition and store the result in an C<isl_vertices> object.
4941 This information can be queried by either iterating over all
4942 the vertices or iterating over all the chambers or cells
4943 and then iterating over all vertices that are active on the chamber.
4945 int isl_vertices_foreach_vertex(
4946 __isl_keep isl_vertices *vertices,
4947 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4950 int isl_vertices_foreach_cell(
4951 __isl_keep isl_vertices *vertices,
4952 int (*fn)(__isl_take isl_cell *cell, void *user),
4954 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4955 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4958 Other operations that can be performed on an C<isl_vertices> object are
4961 isl_ctx *isl_vertices_get_ctx(
4962 __isl_keep isl_vertices *vertices);
4963 int isl_vertices_get_n_vertices(
4964 __isl_keep isl_vertices *vertices);
4965 void isl_vertices_free(__isl_take isl_vertices *vertices);
4967 Vertices can be inspected and destroyed using the following functions.
4969 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4970 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4971 __isl_give isl_basic_set *isl_vertex_get_domain(
4972 __isl_keep isl_vertex *vertex);
4973 __isl_give isl_basic_set *isl_vertex_get_expr(
4974 __isl_keep isl_vertex *vertex);
4975 void isl_vertex_free(__isl_take isl_vertex *vertex);
4977 C<isl_vertex_get_expr> returns a singleton parametric set describing
4978 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4980 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4981 B<rational> basic sets, so they should mainly be used for inspection
4982 and should not be mixed with integer sets.
4984 Chambers can be inspected and destroyed using the following functions.
4986 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4987 __isl_give isl_basic_set *isl_cell_get_domain(
4988 __isl_keep isl_cell *cell);
4989 void isl_cell_free(__isl_take isl_cell *cell);
4993 Although C<isl> is mainly meant to be used as a library,
4994 it also contains some basic applications that use some
4995 of the functionality of C<isl>.
4996 The input may be specified in either the L<isl format>
4997 or the L<PolyLib format>.
4999 =head2 C<isl_polyhedron_sample>
5001 C<isl_polyhedron_sample> takes a polyhedron as input and prints
5002 an integer element of the polyhedron, if there is any.
5003 The first column in the output is the denominator and is always
5004 equal to 1. If the polyhedron contains no integer points,
5005 then a vector of length zero is printed.
5009 C<isl_pip> takes the same input as the C<example> program
5010 from the C<piplib> distribution, i.e., a set of constraints
5011 on the parameters, a line containing only -1 and finally a set
5012 of constraints on a parametric polyhedron.
5013 The coefficients of the parameters appear in the last columns
5014 (but before the final constant column).
5015 The output is the lexicographic minimum of the parametric polyhedron.
5016 As C<isl> currently does not have its own output format, the output
5017 is just a dump of the internal state.
5019 =head2 C<isl_polyhedron_minimize>
5021 C<isl_polyhedron_minimize> computes the minimum of some linear
5022 or affine objective function over the integer points in a polyhedron.
5023 If an affine objective function
5024 is given, then the constant should appear in the last column.
5026 =head2 C<isl_polytope_scan>
5028 Given a polytope, C<isl_polytope_scan> prints
5029 all integer points in the polytope.