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
8 using C<GMP> or C<imath>.
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 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>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
284 =head3 Changes since isl-0.20
288 =item * Several functions that used to return C<unsigned>
289 now return C<isl_size>. This means that these functions may
290 now return a negative value in case an error occurred.
291 The same holds for functions that used to return C<int>,
292 although some of those were already returning
293 a negative value in case of error.
295 =item * The C<isl_ast_op_type> enumeration type has been
296 renamed to C<isl_ast_expr_op_type>. The corresponding
297 enumeration constants have been similarly renamed.
298 The old names are defined to the new names for backward
301 =item * Several functions returning an extra boolean value
302 through an C<int *> argument now do so through an C<isl_bool *>
303 argument. The returned values are the same, only the type
304 of the pointer has been changed.
310 C<isl> is released under the MIT license.
314 Permission is hereby granted, free of charge, to any person obtaining a copy of
315 this software and associated documentation files (the "Software"), to deal in
316 the Software without restriction, including without limitation the rights to
317 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
318 of the Software, and to permit persons to whom the Software is furnished to do
319 so, subject to the following conditions:
321 The above copyright notice and this permission notice shall be included in all
322 copies or substantial portions of the Software.
324 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
325 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
326 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
327 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
328 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
329 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
334 Note that by default C<isl> requires C<GMP>, which is released
335 under the GNU Lesser General Public License (LGPL). This means
336 that code linked against C<isl> is also linked against LGPL code.
338 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
339 will link against C<imath>, a library for exact integer arithmetic released
340 under the MIT license.
344 The source of C<isl> can be obtained either as a tarball
345 or from the git repository. Both are available from
346 L<https://libisl.sourceforge.io/>.
347 The installation process depends on how you obtained
350 =head2 Installation from the git repository
354 =item 1 Clone or update the repository
356 The first time the source is obtained, you need to clone
359 git clone git://repo.or.cz/isl.git
361 To obtain updates, you need to pull in the latest changes
365 =item 2 Optionally get C<imath> submodule
367 To build C<isl> with C<imath>, you need to obtain the C<imath>
368 submodule by running in the git source tree of C<isl>
373 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
375 =item 2 Generate C<configure>
381 After performing the above steps, continue
382 with the L<Common installation instructions>.
384 =head2 Common installation instructions
388 =item 1 Obtain C<GMP>
390 By default, building C<isl> requires C<GMP>, including its headers files.
391 Your distribution may not provide these header files by default
392 and you may need to install a package called C<gmp-devel> or something
393 similar. Alternatively, C<GMP> can be built from
394 source, available from L<http://gmplib.org/>.
395 C<GMP> is not needed if you build C<isl> with C<imath>.
399 C<isl> uses the standard C<autoconf> C<configure> script.
404 optionally followed by some configure options.
405 A complete list of options can be obtained by running
409 Below we discuss some of the more common options.
415 Installation prefix for C<isl>
417 =item C<--with-int=[gmp|imath|imath-32]>
419 Select the integer library to be used by C<isl>, the default is C<gmp>.
420 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
421 for values out of the 32 bit range. In most applications, C<isl> will run
422 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
425 =item C<--with-gmp-prefix=>I<path>
427 Installation prefix for C<GMP> (architecture-independent files).
429 =item C<--with-gmp-exec-prefix=>I<path>
431 Installation prefix for C<GMP> (architecture-dependent files).
439 =item 4 Test (optional)
443 =item 5 Install (optional)
449 =head2 Building the foreign language bindings
451 The tarball already contains the generated foreign language bindings,
452 but they are not included in the git repository.
453 Building the C++ and Python bindings relies on the LLVM/clang libraries,
454 see C<http://clang.llvm.org/get_started.html>.
455 The C<configure> script will not assume that these are available
457 To enable building the foreign language bindings,
458 one of the following options needs to be specified.
462 =item C<--with-clang=system>
464 Use the system clang libraries (installed in a default location).
466 =item C<--with-clang-prefix=>I<path>
468 Use the system clang libraries installed in I<path>.
472 It is best to use the latest release of the clang libraries (12.0),
473 although any release since 2.9 should work as well.
474 Note that if you build the clang libraries from source,
475 then you need to make sure they are also installed (using C<make install>).
476 If the compiler that was used to compile the clang libraries
477 is different from the default C++ compiler, then use C<CXX_FOR_BUILD>
478 to specify this non-default C++ compiler when running C<isl>'s C<./configure>.
480 =head1 Integer Set Library
482 =head2 Memory Management
484 Since a high-level operation on isl objects usually involves
485 several substeps and since the user is usually not interested in
486 the intermediate results, most functions that return a new object
487 will also release all the objects passed as arguments.
488 If the user still wants to use one or more of these arguments
489 after the function call, she should pass along a copy of the
490 object rather than the object itself.
491 The user is then responsible for making sure that the original
492 object gets used somewhere else or is explicitly freed.
494 The arguments and return values of all documented functions are
495 annotated to make clear which arguments are released and which
496 arguments are preserved. In particular, the following annotations
503 C<__isl_give> means that a new object is returned.
504 The user should make sure that the returned pointer is
505 used exactly once as a value for an C<__isl_take> argument.
506 In between, it can be used as a value for as many
507 C<__isl_keep> arguments as the user likes.
508 There is one exception, and that is the case where the
509 pointer returned is C<NULL>. In this case, the user
510 is free to use it as an C<__isl_take> argument or not.
511 When applied to a C<char *>, the returned pointer needs to be
516 C<__isl_null> means that a C<NULL> value is returned.
520 C<__isl_take> means that the object the argument points to
521 is taken over by the function and may no longer be used
522 by the user as an argument to any other function.
523 The pointer value must be one returned by a function
524 returning an C<__isl_give> pointer.
525 If the user passes in a C<NULL> value, then this will
526 be treated as an error in the sense that the function will
527 not perform its usual operation. However, it will still
528 make sure that all the other C<__isl_take> arguments
533 C<__isl_keep> means that the function will only use the object
534 temporarily. After the function has finished, the user
535 can still use it as an argument to other functions.
536 A C<NULL> value will be treated in the same way as
537 a C<NULL> value for an C<__isl_take> argument.
538 This annotation may also be used on return values of
539 type C<const char *>, in which case the returned pointer should
540 not be freed by the user and is only valid until the object
541 from which it was derived is updated or freed.
545 =head2 Initialization
547 All manipulations of integer sets and relations occur within
548 the context of an C<isl_ctx>.
549 A given C<isl_ctx> can only be used within a single thread.
550 All arguments of a function are required to have been allocated
551 within the same context.
552 There are currently no functions available for moving an object
553 from one C<isl_ctx> to another C<isl_ctx>. This means that
554 there is currently no way of safely moving an object from one
555 thread to another, unless the whole C<isl_ctx> is moved.
557 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
558 freed using C<isl_ctx_free>.
559 All objects allocated within an C<isl_ctx> should be freed
560 before the C<isl_ctx> itself is freed.
562 isl_ctx *isl_ctx_alloc();
563 void isl_ctx_free(isl_ctx *ctx);
565 The user can impose a bound on the number of low-level I<operations>
566 that can be performed by an C<isl_ctx>. This bound can be set and
567 retrieved using the following functions. A bound of zero means that
568 no bound is imposed. The number of operations performed can be
569 reset using C<isl_ctx_reset_operations>. Note that the number
570 of low-level operations needed to perform a high-level computation
571 may differ significantly across different versions
572 of C<isl>, but it should be the same across different platforms
573 for the same version of C<isl>.
575 Warning: This feature is experimental. C<isl> has good support to abort and
576 bail out during the computation, but this feature may exercise error code paths
577 that are normally not used that much. Consequently, it is not unlikely that
578 hidden bugs will be exposed.
580 void isl_ctx_set_max_operations(isl_ctx *ctx,
581 unsigned long max_operations);
582 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
583 void isl_ctx_reset_operations(isl_ctx *ctx);
585 In order to be able to create an object in the same context
586 as another object, most object types (described later in
587 this document) provide a function to obtain the context
588 in which the object was created.
591 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
592 isl_ctx *isl_multi_val_get_ctx(
593 __isl_keep isl_multi_val *mv);
596 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
597 isl_ctx *isl_multi_id_get_ctx(
598 __isl_keep isl_multi_id *mi);
600 #include <isl/local_space.h>
601 isl_ctx *isl_local_space_get_ctx(
602 __isl_keep isl_local_space *ls);
605 isl_ctx *isl_set_list_get_ctx(
606 __isl_keep isl_set_list *list);
609 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
610 isl_ctx *isl_multi_aff_get_ctx(
611 __isl_keep isl_multi_aff *maff);
612 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
613 isl_ctx *isl_pw_multi_aff_get_ctx(
614 __isl_keep isl_pw_multi_aff *pma);
615 isl_ctx *isl_multi_pw_aff_get_ctx(
616 __isl_keep isl_multi_pw_aff *mpa);
617 isl_ctx *isl_union_pw_aff_get_ctx(
618 __isl_keep isl_union_pw_aff *upa);
619 isl_ctx *isl_union_pw_multi_aff_get_ctx(
620 __isl_keep isl_union_pw_multi_aff *upma);
621 isl_ctx *isl_multi_union_pw_aff_get_ctx(
622 __isl_keep isl_multi_union_pw_aff *mupa);
624 #include <isl/id_to_ast_expr.h>
625 isl_ctx *isl_id_to_ast_expr_get_ctx(
626 __isl_keep isl_id_to_ast_expr *id2expr);
628 #include <isl/point.h>
629 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
632 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
635 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
637 #include <isl/vertices.h>
638 isl_ctx *isl_vertices_get_ctx(
639 __isl_keep isl_vertices *vertices);
640 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
641 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
643 #include <isl/flow.h>
644 isl_ctx *isl_restriction_get_ctx(
645 __isl_keep isl_restriction *restr);
646 isl_ctx *isl_union_access_info_get_ctx(
647 __isl_keep isl_union_access_info *access);
648 isl_ctx *isl_union_flow_get_ctx(
649 __isl_keep isl_union_flow *flow);
651 #include <isl/schedule.h>
652 isl_ctx *isl_schedule_get_ctx(
653 __isl_keep isl_schedule *sched);
654 isl_ctx *isl_schedule_constraints_get_ctx(
655 __isl_keep isl_schedule_constraints *sc);
657 #include <isl/schedule_node.h>
658 isl_ctx *isl_schedule_node_get_ctx(
659 __isl_keep isl_schedule_node *node);
661 #include <isl/ast_build.h>
662 isl_ctx *isl_ast_build_get_ctx(
663 __isl_keep isl_ast_build *build);
666 isl_ctx *isl_ast_expr_get_ctx(
667 __isl_keep isl_ast_expr *expr);
668 isl_ctx *isl_ast_node_get_ctx(
669 __isl_keep isl_ast_node *node);
671 #include <isl/stride_info.h>
672 isl_ctx *isl_stride_info_get_ctx(
673 __isl_keep isl_stride_info *si);
675 #include <isl/fixed_box.h>
676 isl_ctx *isl_fixed_box_get_ctx(
677 __isl_keep isl_fixed_box *box);
681 C<isl> uses the special return type C<isl_size> for functions
682 that return a non-negative value, typically a number or a position.
683 Besides the regular non-negative return values, a special (negative)
684 value C<isl_size_error> may be returned, indicating that something
687 C<isl> also uses two special return types for functions that either return
688 a boolean or that in principle do not return anything.
689 In particular, the C<isl_bool> type has three possible values:
690 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
691 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
692 C<isl_bool_error> (a negative integer value), indicating that something
693 went wrong. The following operations are defined on C<isl_bool>. The function
694 C<isl_bool_not> can be used to negate an C<isl_bool>, where the negation of
695 C<isl_bool_error> is C<isl_bool_error> again. The function C<isl_bool_ok>
696 converts an integer to an C<isl_bool>. Any non-zero values yields
697 C<isl_bool_true> and zero yields C<isl_bool_false>.
700 isl_bool isl_bool_not(isl_bool b);
701 isl_bool isl_bool_ok(int b);
703 The C<isl_stat> type has two possible values:
704 C<isl_stat_ok> (the integer value zero), indicating a successful
706 C<isl_stat_error> (a negative integer value), indicating that something
708 The function C<isl_stat_non_null> converts an isl object pointer
709 to an C<isl_stat>, returning C<isl_stat_ok> if the object pointer is valid and
710 C<isl_stat_error> if it is C<NULL>.
713 isl_stat isl_stat_non_null(void *obj);
715 See L</"Error Handling"> for more information on
716 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
720 An C<isl_val> represents an integer value, a rational value
721 or one of three special values, infinity, negative infinity and NaN.
722 Some predefined values can be created using the following functions.
725 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
726 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
727 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
728 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
729 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
730 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
732 Specific integer values can be created using the following functions.
735 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
737 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
739 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
740 size_t n, size_t size, const void *chunks);
742 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
743 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
744 The least significant digit is assumed to be stored first.
746 Value objects can be copied and freed using the following functions.
749 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
750 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
752 They can be inspected using the following functions.
755 long isl_val_get_num_si(__isl_keep isl_val *v);
756 long isl_val_get_den_si(__isl_keep isl_val *v);
757 __isl_give isl_val *isl_val_get_den_val(
758 __isl_keep isl_val *v);
759 double isl_val_get_d(__isl_keep isl_val *v);
760 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
762 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
763 size_t size, void *chunks);
765 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
766 of C<size> bytes needed to store the absolute value of the
768 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
769 which is assumed to have been preallocated by the caller.
770 The least significant digit is stored first.
771 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
772 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
773 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
775 An C<isl_val> can be modified using the following function.
778 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
781 The following unary properties are defined on C<isl_val>s.
784 int isl_val_sgn(__isl_keep isl_val *v);
785 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
786 isl_bool isl_val_is_one(__isl_keep isl_val *v);
787 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
788 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
789 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
790 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
791 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
792 isl_bool isl_val_is_int(__isl_keep isl_val *v);
793 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
794 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
795 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
796 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
798 Note that the sign of NaN is undefined.
800 The following binary properties are defined on pairs of C<isl_val>s.
803 isl_bool isl_val_lt(__isl_keep isl_val *v1,
804 __isl_keep isl_val *v2);
805 isl_bool isl_val_le(__isl_keep isl_val *v1,
806 __isl_keep isl_val *v2);
807 isl_bool isl_val_gt(__isl_keep isl_val *v1,
808 __isl_keep isl_val *v2);
809 isl_bool isl_val_ge(__isl_keep isl_val *v1,
810 __isl_keep isl_val *v2);
811 isl_bool isl_val_eq(__isl_keep isl_val *v1,
812 __isl_keep isl_val *v2);
813 isl_bool isl_val_ne(__isl_keep isl_val *v1,
814 __isl_keep isl_val *v2);
815 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
816 __isl_keep isl_val *v2);
818 Comparisons to NaN always return false.
819 That is, a NaN is not considered to hold any relative position
820 with respect to any value. In particular, a NaN
821 is neither considered to be equal to nor to be different from
822 any value (including another NaN).
823 The function C<isl_val_abs_eq> checks whether its two arguments
824 are equal in absolute value.
826 For integer C<isl_val>s we additionally have the following binary property.
829 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
830 __isl_keep isl_val *v2);
832 An C<isl_val> can also be compared to an integer using the following
833 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
836 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
837 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
838 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
840 The following unary operations are available on C<isl_val>s.
843 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
844 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
845 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
846 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
847 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
848 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
850 The following binary operations are available on C<isl_val>s.
853 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
854 __isl_take isl_val *v2);
855 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
856 __isl_take isl_val *v2);
857 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
858 __isl_take isl_val *v2);
859 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
861 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
862 __isl_take isl_val *v2);
863 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
865 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
866 __isl_take isl_val *v2);
867 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
869 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
870 __isl_take isl_val *v2);
871 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
874 On integer values, we additionally have the following operations.
877 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
878 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
879 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
880 __isl_take isl_val *v2);
881 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
882 __isl_take isl_val *v2);
883 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
884 __isl_take isl_val *v2, __isl_give isl_val **x,
885 __isl_give isl_val **y);
887 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
888 The function C<isl_val_gcdext> returns the greatest common divisor g
889 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
890 that C<*x> * C<v1> + C<*y> * C<v2> = g.
892 =head3 GMP specific functions
894 These functions are only available if C<isl> has been compiled with C<GMP>
897 Specific integer and rational values can be created from C<GMP> values using
898 the following functions.
900 #include <isl/val_gmp.h>
901 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
903 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
904 const mpz_t n, const mpz_t d);
906 The numerator and denominator of a rational value can be extracted as
907 C<GMP> values using the following functions.
909 #include <isl/val_gmp.h>
910 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
911 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
913 =head2 Sets and Relations
915 C<isl> uses six types of objects for representing sets and relations,
916 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
917 C<isl_union_set> and C<isl_union_map>.
918 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
919 can be described as a conjunction of affine constraints, while
920 C<isl_set> and C<isl_map> represent unions of
921 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
922 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
923 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
924 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
925 where spaces are considered different if they have a different number
926 of dimensions and/or different names (see L<"Spaces">).
927 The difference between sets and relations (maps) is that sets have
928 one set of variables, while relations have two sets of variables,
929 input variables and output variables.
931 =head2 Error Handling
933 C<isl> supports different ways to react in case a runtime error is triggered.
934 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
935 with two maps that have incompatible spaces. There are three possible ways
936 to react on error: to warn, to continue or to abort.
938 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
939 the last error in the corresponding C<isl_ctx> and the function in which the
940 error was triggered returns a value indicating that some error has
941 occurred. In case of functions returning a pointer, this value is
942 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
943 C<isl_stat>, this value is C<isl_size_error>,
944 C<isl_bool_error> or C<isl_stat_error>.
945 An error does not corrupt internal state,
946 such that isl can continue to be used. C<isl> also provides functions to
947 read the last error, including the specific error message,
948 the isl source file where the error occurred and the line number,
949 and to reset all information about the last error. The
950 last error is only stored for information purposes. Its presence does not
951 change the behavior of C<isl>. Hence, resetting an error is not required to
952 continue to use isl, but only to observe new errors.
955 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
956 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
957 const char *isl_ctx_last_error_file(isl_ctx *ctx);
958 int isl_ctx_last_error_line(isl_ctx *ctx);
959 void isl_ctx_reset_error(isl_ctx *ctx);
961 If no error has occurred since the last call to C<isl_ctx_reset_error>,
962 then the functions C<isl_ctx_last_error_msg> and
963 C<isl_ctx_last_error_file> return C<NULL>.
965 Another option is to continue on error. This is similar to warn on error mode,
966 except that C<isl> does not print any warning. This allows a program to
967 implement its own error reporting.
969 The last option is to directly abort the execution of the program from within
970 the isl library. This makes it obviously impossible to recover from an error,
971 but it allows to directly spot the error location. By aborting on error,
972 debuggers break at the location the error occurred and can provide a stack
973 trace. Other tools that automatically provide stack traces on abort or that do
974 not want to continue execution after an error was triggered may also prefer to
977 The on error behavior of isl can be specified by calling
978 C<isl_options_set_on_error> or by setting the command line option
979 C<--isl-on-error>. Valid arguments for the function call are
980 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
981 choices for the command line option are C<warn>, C<continue> and C<abort>.
982 It is also possible to query the current error mode.
984 #include <isl/options.h>
985 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
986 int isl_options_get_on_error(isl_ctx *ctx);
990 Identifiers are used to identify both individual dimensions
991 and tuples of dimensions. They consist of an optional name and an optional
992 user pointer. The name and the user pointer cannot both be C<NULL>, however.
993 Identifiers with the same name but different pointer values
994 are considered to be distinct.
995 Similarly, identifiers with different names but the same pointer value
996 are also considered to be distinct.
997 Equal identifiers are represented using the same object.
998 Pairs of identifiers can therefore be tested for equality using the
1000 Identifiers can be constructed, copied, freed, inspected and printed
1001 using the following functions.
1004 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
1005 __isl_keep const char *name, void *user);
1006 __isl_give isl_id *isl_id_set_free_user(
1007 __isl_take isl_id *id,
1008 void (*free_user)(void *user));
1009 void (*isl_id_get_free_user(__isl_keep isl_id *id))
1011 __isl_give isl_id *isl_id_copy(isl_id *id);
1012 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
1014 void *isl_id_get_user(__isl_keep isl_id *id);
1015 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
1017 __isl_give isl_printer *isl_printer_print_id(
1018 __isl_take isl_printer *p, __isl_keep isl_id *id);
1020 The callback set by C<isl_id_set_free_user> is called on the user
1021 pointer when the last reference to the C<isl_id> is freed.
1022 This callback can be retrieved using C<isl_id_get_free_user>.
1023 Note that C<isl_id_get_name> returns a pointer to some internal
1024 data structure, so the result can only be used while the
1025 corresponding C<isl_id> is alive.
1029 Whenever a new set, relation or similar object is created from scratch,
1030 the space in which it lives needs to be specified using an C<isl_space>.
1031 Each space involves zero or more parameters and zero, one or two
1032 tuples of set or input/output dimensions. The parameters and dimensions
1033 are identified by an C<isl_dim_type> and a position.
1034 The type C<isl_dim_param> refers to parameters,
1035 the type C<isl_dim_set> refers to set dimensions (for spaces
1036 with a single tuple of dimensions) and the types C<isl_dim_in>
1037 and C<isl_dim_out> refer to input and output dimensions
1038 (for spaces with two tuples of dimensions).
1039 Local spaces (see L</"Local Spaces">) also contain dimensions
1040 of type C<isl_dim_div>.
1041 Note that parameters are only identified by their position within
1042 a given object. Across different objects, parameters are (usually)
1043 identified by their names or identifiers. Only unnamed parameters
1044 are identified by their positions across objects. The use of unnamed
1045 parameters is discouraged.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1049 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1050 unsigned nparam, unsigned n_in, unsigned n_out);
1051 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1053 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1054 unsigned nparam, unsigned dim);
1055 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1056 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1058 The space used for creating a parameter domain
1059 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1060 For other sets, the space
1061 needs to be created using C<isl_space_set_alloc>, while
1062 for a relation, the space
1063 needs to be created using C<isl_space_alloc>.
1064 The use of C<isl_space_params_alloc>,
1065 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1066 for the introduction of unnamed parameters.
1068 To check whether a given space is that of a set or a map
1069 or whether it is a parameter space, use these functions:
1071 #include <isl/space.h>
1072 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1073 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1074 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1076 Spaces can be compared using the following functions:
1078 #include <isl/space.h>
1079 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1080 __isl_keep isl_space *space2);
1081 isl_bool isl_space_has_equal_params(
1082 __isl_keep isl_space *space1,
1083 __isl_keep isl_space *space2);
1084 isl_bool isl_space_has_equal_tuples(
1085 __isl_keep isl_space *space1,
1086 __isl_keep isl_space *space2);
1087 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1088 __isl_keep isl_space *space2);
1089 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1090 __isl_keep isl_space *space2);
1091 isl_bool isl_space_tuple_is_equal(
1092 __isl_keep isl_space *space1,
1093 enum isl_dim_type type1,
1094 __isl_keep isl_space *space2,
1095 enum isl_dim_type type2);
1097 C<isl_space_is_domain> checks whether the first argument is equal
1098 to the domain of the second argument. This requires in particular that
1099 the first argument is a set space and that the second argument
1100 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1101 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1102 spaces are the same. That is, it checks if they have the same
1103 identifier (if any), the same dimension and the same internal structure
1106 C<isl_space_has_equal_params> checks whether two spaces
1107 have the same parameters in the same order.
1108 C<isl_space_has_equal_tuples> check whether two spaces have
1109 the same tuples. In contrast to C<isl_space_is_equal> below,
1110 it does not check the
1111 parameters. This is useful because many C<isl> functions align the
1112 parameters before they perform their operations, such that equivalence
1114 C<isl_space_is_equal> checks whether two spaces are identical,
1115 meaning that they have the same parameters and the same tuples.
1116 That is, it checks whether both C<isl_space_has_equal_params> and
1117 C<isl_space_has_equal_tuples> hold.
1119 It is often useful to create objects that live in the
1120 same space as some other object. This can be accomplished
1121 by creating the new objects
1122 (see L</"Creating New Sets and Relations"> or
1123 L</"Functions">) based on the space
1124 of the original object.
1126 #include <isl/set.h>
1127 __isl_give isl_space *isl_basic_set_get_space(
1128 __isl_keep isl_basic_set *bset);
1129 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1131 #include <isl/union_set.h>
1132 __isl_give isl_space *isl_union_set_get_space(
1133 __isl_keep isl_union_set *uset);
1135 #include <isl/map.h>
1136 __isl_give isl_space *isl_basic_map_get_space(
1137 __isl_keep isl_basic_map *bmap);
1138 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1140 #include <isl/union_map.h>
1141 __isl_give isl_space *isl_union_map_get_space(
1142 __isl_keep isl_union_map *umap);
1144 #include <isl/constraint.h>
1145 __isl_give isl_space *isl_constraint_get_space(
1146 __isl_keep isl_constraint *constraint);
1148 #include <isl/polynomial.h>
1149 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1150 __isl_keep isl_qpolynomial *qp);
1151 __isl_give isl_space *isl_qpolynomial_get_space(
1152 __isl_keep isl_qpolynomial *qp);
1153 __isl_give isl_space *
1154 isl_qpolynomial_fold_get_domain_space(
1155 __isl_keep isl_qpolynomial_fold *fold);
1156 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1157 __isl_keep isl_qpolynomial_fold *fold);
1158 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1159 __isl_keep isl_pw_qpolynomial *pwqp);
1160 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1161 __isl_keep isl_pw_qpolynomial *pwqp);
1162 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1163 __isl_keep isl_pw_qpolynomial_fold *pwf);
1164 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1165 __isl_keep isl_pw_qpolynomial_fold *pwf);
1166 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1167 __isl_keep isl_union_pw_qpolynomial *upwqp);
1168 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1169 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1172 __isl_give isl_space *isl_multi_id_get_space(
1173 __isl_keep isl_multi_id *mi);
1175 #include <isl/val.h>
1176 __isl_give isl_space *isl_multi_val_get_space(
1177 __isl_keep isl_multi_val *mv);
1179 #include <isl/aff.h>
1180 __isl_give isl_space *isl_aff_get_domain_space(
1181 __isl_keep isl_aff *aff);
1182 __isl_give isl_space *isl_aff_get_space(
1183 __isl_keep isl_aff *aff);
1184 __isl_give isl_space *isl_pw_aff_get_domain_space(
1185 __isl_keep isl_pw_aff *pwaff);
1186 __isl_give isl_space *isl_pw_aff_get_space(
1187 __isl_keep isl_pw_aff *pwaff);
1188 __isl_give isl_space *isl_multi_aff_get_domain_space(
1189 __isl_keep isl_multi_aff *maff);
1190 __isl_give isl_space *isl_multi_aff_get_space(
1191 __isl_keep isl_multi_aff *maff);
1192 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1193 __isl_keep isl_pw_multi_aff *pma);
1194 __isl_give isl_space *isl_pw_multi_aff_get_space(
1195 __isl_keep isl_pw_multi_aff *pma);
1196 __isl_give isl_space *isl_union_pw_aff_get_space(
1197 __isl_keep isl_union_pw_aff *upa);
1198 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1199 __isl_keep isl_union_pw_multi_aff *upma);
1200 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1201 __isl_keep isl_multi_pw_aff *mpa);
1202 __isl_give isl_space *isl_multi_pw_aff_get_space(
1203 __isl_keep isl_multi_pw_aff *mpa);
1204 __isl_give isl_space *
1205 isl_multi_union_pw_aff_get_domain_space(
1206 __isl_keep isl_multi_union_pw_aff *mupa);
1207 __isl_give isl_space *
1208 isl_multi_union_pw_aff_get_space(
1209 __isl_keep isl_multi_union_pw_aff *mupa);
1211 #include <isl/point.h>
1212 __isl_give isl_space *isl_point_get_space(
1213 __isl_keep isl_point *pnt);
1215 #include <isl/fixed_box.h>
1216 __isl_give isl_space *isl_fixed_box_get_space(
1217 __isl_keep isl_fixed_box *box);
1219 The number of dimensions of a given type of space
1220 may be read off from a space or an object that lives
1221 in a space using the following functions.
1222 In case of C<isl_space_dim>, type may be
1223 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1224 C<isl_dim_out> (only for relations), C<isl_dim_set>
1225 (only for sets) or C<isl_dim_all>.
1227 #include <isl/space.h>
1228 isl_size isl_space_dim(__isl_keep isl_space *space,
1229 enum isl_dim_type type);
1231 #include <isl/local_space.h>
1232 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1233 enum isl_dim_type type);
1235 #include <isl/set.h>
1236 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1237 enum isl_dim_type type);
1238 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1239 isl_size isl_set_dim(__isl_keep isl_set *set,
1240 enum isl_dim_type type);
1242 #include <isl/union_set.h>
1243 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1244 enum isl_dim_type type);
1246 #include <isl/map.h>
1247 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type);
1249 isl_size isl_map_domain_tuple_dim(
1250 __isl_keep isl_map *map);
1251 isl_size isl_map_range_tuple_dim(
1252 __isl_keep isl_map *map);
1253 isl_size isl_map_dim(__isl_keep isl_map *map,
1254 enum isl_dim_type type);
1256 #include <isl/union_map.h>
1257 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1258 enum isl_dim_type type);
1260 #include <isl/val.h>
1261 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1262 enum isl_dim_type type);
1264 #include <isl/aff.h>
1265 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1266 enum isl_dim_type type);
1267 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1268 enum isl_dim_type type);
1269 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1270 enum isl_dim_type type);
1271 isl_size isl_pw_multi_aff_dim(
1272 __isl_keep isl_pw_multi_aff *pma,
1273 enum isl_dim_type type);
1274 isl_size isl_multi_pw_aff_dim(
1275 __isl_keep isl_multi_pw_aff *mpa,
1276 enum isl_dim_type type);
1277 isl_size isl_union_pw_aff_dim(
1278 __isl_keep isl_union_pw_aff *upa,
1279 enum isl_dim_type type);
1280 isl_size isl_union_pw_multi_aff_dim(
1281 __isl_keep isl_union_pw_multi_aff *upma,
1282 enum isl_dim_type type);
1283 isl_size isl_multi_union_pw_aff_dim(
1284 __isl_keep isl_multi_union_pw_aff *mupa,
1285 enum isl_dim_type type);
1287 #include <isl/polynomial.h>
1288 isl_size isl_union_pw_qpolynomial_dim(
1289 __isl_keep isl_union_pw_qpolynomial *upwqp,
1290 enum isl_dim_type type);
1291 isl_size isl_union_pw_qpolynomial_fold_dim(
1292 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1293 enum isl_dim_type type);
1295 Note that an C<isl_union_set>, an C<isl_union_map>,
1296 an C<isl_union_pw_multi_aff>,
1297 an C<isl_union_pw_qpolynomial> and
1298 an C<isl_union_pw_qpolynomial_fold>
1299 only have parameters.
1301 Additional parameters can be added to a space using the following function.
1303 #include <isl/space.h>
1304 __isl_give isl_space *isl_space_add_param_id(
1305 __isl_take isl_space *space,
1306 __isl_take isl_id *id);
1308 If a parameter with the given identifier already appears in the space,
1309 then it is not added again.
1311 Conversely, all parameters can be removed from a space
1312 using the following function.
1314 #include <isl/space.h>
1315 __isl_give isl_space *isl_space_drop_all_params(
1316 __isl_take isl_space *space);
1318 The identifiers or names of the individual dimensions of spaces
1319 may be set or read off using the following functions on spaces
1320 or objects that live in spaces.
1321 These functions are mostly useful to obtain the identifiers, positions
1322 or names of the parameters. Identifiers of individual dimensions are
1323 essentially only useful for printing. They are ignored by all other
1324 operations and may not be preserved across those operations.
1325 To keep track of a space along with names/identifiers of
1326 the set dimensions, use an C<isl_multi_id> as described in
1329 #include <isl/space.h>
1330 __isl_give isl_space *isl_space_set_dim_id(
1331 __isl_take isl_space *space,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1335 enum isl_dim_type type, unsigned pos);
1336 __isl_give isl_id *isl_space_get_dim_id(
1337 __isl_keep isl_space *space,
1338 enum isl_dim_type type, unsigned pos);
1339 __isl_give isl_space *isl_space_set_dim_name(
1340 __isl_take isl_space *space,
1341 enum isl_dim_type type, unsigned pos,
1342 __isl_keep const char *name);
1343 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1344 enum isl_dim_type type, unsigned pos);
1345 __isl_keep const char *isl_space_get_dim_name(
1346 __isl_keep isl_space *space,
1347 enum isl_dim_type type, unsigned pos);
1349 #include <isl/local_space.h>
1350 __isl_give isl_local_space *isl_local_space_set_dim_id(
1351 __isl_take isl_local_space *ls,
1352 enum isl_dim_type type, unsigned pos,
1353 __isl_take isl_id *id);
1354 isl_bool isl_local_space_has_dim_id(
1355 __isl_keep isl_local_space *ls,
1356 enum isl_dim_type type, unsigned pos);
1357 __isl_give isl_id *isl_local_space_get_dim_id(
1358 __isl_keep isl_local_space *ls,
1359 enum isl_dim_type type, unsigned pos);
1360 __isl_give isl_local_space *isl_local_space_set_dim_name(
1361 __isl_take isl_local_space *ls,
1362 enum isl_dim_type type, unsigned pos, const char *s);
1363 isl_bool isl_local_space_has_dim_name(
1364 __isl_keep isl_local_space *ls,
1365 enum isl_dim_type type, unsigned pos)
1366 const char *isl_local_space_get_dim_name(
1367 __isl_keep isl_local_space *ls,
1368 enum isl_dim_type type, unsigned pos);
1370 #include <isl/constraint.h>
1371 const char *isl_constraint_get_dim_name(
1372 __isl_keep isl_constraint *constraint,
1373 enum isl_dim_type type, unsigned pos);
1375 #include <isl/set.h>
1376 __isl_give isl_id *isl_basic_set_get_dim_id(
1377 __isl_keep isl_basic_set *bset,
1378 enum isl_dim_type type, unsigned pos);
1379 __isl_give isl_set *isl_set_set_dim_id(
1380 __isl_take isl_set *set, enum isl_dim_type type,
1381 unsigned pos, __isl_take isl_id *id);
1382 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_id *isl_set_get_dim_id(
1385 __isl_keep isl_set *set, enum isl_dim_type type,
1387 const char *isl_basic_set_get_dim_name(
1388 __isl_keep isl_basic_set *bset,
1389 enum isl_dim_type type, unsigned pos);
1390 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1391 enum isl_dim_type type, unsigned pos);
1392 const char *isl_set_get_dim_name(
1393 __isl_keep isl_set *set,
1394 enum isl_dim_type type, unsigned pos);
1396 #include <isl/map.h>
1397 __isl_give isl_map *isl_map_set_dim_id(
1398 __isl_take isl_map *map, enum isl_dim_type type,
1399 unsigned pos, __isl_take isl_id *id);
1400 isl_bool isl_basic_map_has_dim_id(
1401 __isl_keep isl_basic_map *bmap,
1402 enum isl_dim_type type, unsigned pos);
1403 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1404 enum isl_dim_type type, unsigned pos);
1405 __isl_give isl_id *isl_map_get_dim_id(
1406 __isl_keep isl_map *map, enum isl_dim_type type,
1408 __isl_give isl_id *isl_union_map_get_dim_id(
1409 __isl_keep isl_union_map *umap,
1410 enum isl_dim_type type, unsigned pos);
1411 const char *isl_basic_map_get_dim_name(
1412 __isl_keep isl_basic_map *bmap,
1413 enum isl_dim_type type, unsigned pos);
1414 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1415 enum isl_dim_type type, unsigned pos);
1416 const char *isl_map_get_dim_name(
1417 __isl_keep isl_map *map,
1418 enum isl_dim_type type, unsigned pos);
1420 #include <isl/val.h>
1421 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1422 __isl_take isl_multi_val *mv,
1423 enum isl_dim_type type, unsigned pos,
1424 __isl_take isl_id *id);
1425 __isl_give isl_id *isl_multi_val_get_dim_id(
1426 __isl_keep isl_multi_val *mv,
1427 enum isl_dim_type type, unsigned pos);
1428 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1429 __isl_take isl_multi_val *mv,
1430 enum isl_dim_type type, unsigned pos, const char *s);
1432 #include <isl/aff.h>
1433 __isl_give isl_aff *isl_aff_set_dim_id(
1434 __isl_take isl_aff *aff, enum isl_dim_type type,
1435 unsigned pos, __isl_take isl_id *id);
1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1437 __isl_take isl_multi_aff *maff,
1438 enum isl_dim_type type, unsigned pos,
1439 __isl_take isl_id *id);
1440 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1441 __isl_take isl_pw_aff *pma,
1442 enum isl_dim_type type, unsigned pos,
1443 __isl_take isl_id *id);
1444 __isl_give isl_multi_pw_aff *
1445 isl_multi_pw_aff_set_dim_id(
1446 __isl_take isl_multi_pw_aff *mpa,
1447 enum isl_dim_type type, unsigned pos,
1448 __isl_take isl_id *id);
1449 __isl_give isl_multi_union_pw_aff *
1450 isl_multi_union_pw_aff_set_dim_id(
1451 __isl_take isl_multi_union_pw_aff *mupa,
1452 enum isl_dim_type type, unsigned pos,
1453 __isl_take isl_id *id);
1454 __isl_give isl_id *isl_multi_aff_get_dim_id(
1455 __isl_keep isl_multi_aff *ma,
1456 enum isl_dim_type type, unsigned pos);
1457 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1458 enum isl_dim_type type, unsigned pos);
1459 __isl_give isl_id *isl_pw_aff_get_dim_id(
1460 __isl_keep isl_pw_aff *pa,
1461 enum isl_dim_type type, unsigned pos);
1462 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type, unsigned pos);
1465 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1466 __isl_keep isl_multi_pw_aff *mpa,
1467 enum isl_dim_type type, unsigned pos);
1468 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1469 __isl_keep isl_multi_union_pw_aff *mupa,
1470 enum isl_dim_type type, unsigned pos);
1471 __isl_give isl_aff *isl_aff_set_dim_name(
1472 __isl_take isl_aff *aff, enum isl_dim_type type,
1473 unsigned pos, const char *s);
1474 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1475 __isl_take isl_multi_aff *maff,
1476 enum isl_dim_type type, unsigned pos, const char *s);
1477 __isl_give isl_multi_pw_aff *
1478 isl_multi_pw_aff_set_dim_name(
1479 __isl_take isl_multi_pw_aff *mpa,
1480 enum isl_dim_type type, unsigned pos, const char *s);
1481 __isl_give isl_union_pw_aff *
1482 isl_union_pw_aff_set_dim_name(
1483 __isl_take isl_union_pw_aff *upa,
1484 enum isl_dim_type type, unsigned pos,
1486 __isl_give isl_union_pw_multi_aff *
1487 isl_union_pw_multi_aff_set_dim_name(
1488 __isl_take isl_union_pw_multi_aff *upma,
1489 enum isl_dim_type type, unsigned pos,
1491 __isl_give isl_multi_union_pw_aff *
1492 isl_multi_union_pw_aff_set_dim_name(
1493 __isl_take isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, unsigned pos,
1496 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_pw_aff_get_dim_name(
1499 __isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_pw_multi_aff_get_dim_name(
1502 __isl_keep isl_pw_multi_aff *pma,
1503 enum isl_dim_type type, unsigned pos);
1505 #include <isl/polynomial.h>
1506 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1507 __isl_take isl_qpolynomial *qp,
1508 enum isl_dim_type type, unsigned pos,
1510 __isl_give isl_pw_qpolynomial *
1511 isl_pw_qpolynomial_set_dim_name(
1512 __isl_take isl_pw_qpolynomial *pwqp,
1513 enum isl_dim_type type, unsigned pos,
1515 __isl_give isl_pw_qpolynomial_fold *
1516 isl_pw_qpolynomial_fold_set_dim_name(
1517 __isl_take isl_pw_qpolynomial_fold *pwf,
1518 enum isl_dim_type type, unsigned pos,
1520 __isl_give isl_union_pw_qpolynomial *
1521 isl_union_pw_qpolynomial_set_dim_name(
1522 __isl_take isl_union_pw_qpolynomial *upwqp,
1523 enum isl_dim_type type, unsigned pos,
1525 __isl_give isl_union_pw_qpolynomial_fold *
1526 isl_union_pw_qpolynomial_fold_set_dim_name(
1527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1528 enum isl_dim_type type, unsigned pos,
1531 Note that C<isl_space_get_name> returns a pointer to some internal
1532 data structure, so the result can only be used while the
1533 corresponding C<isl_space> is alive.
1534 Also note that every function that operates on two sets or relations
1535 requires that both arguments have the same parameters. This also
1536 means that if one of the arguments has named parameters, then the
1537 other needs to have named parameters too and the names need to match.
1538 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1539 arguments may have different parameters (as long as they are named),
1540 in which case the result will have as parameters the union of the parameters of
1543 Given the identifier or name of a dimension (typically a parameter),
1544 its position can be obtained from the following functions.
1546 #include <isl/space.h>
1547 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1550 enum isl_dim_type type, const char *name);
1552 #include <isl/local_space.h>
1553 int isl_local_space_find_dim_by_name(
1554 __isl_keep isl_local_space *ls,
1555 enum isl_dim_type type, const char *name);
1557 #include <isl/val.h>
1558 int isl_multi_val_find_dim_by_id(
1559 __isl_keep isl_multi_val *mv,
1560 enum isl_dim_type type, __isl_keep isl_id *id);
1561 int isl_multi_val_find_dim_by_name(
1562 __isl_keep isl_multi_val *mv,
1563 enum isl_dim_type type, const char *name);
1565 #include <isl/set.h>
1566 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1567 enum isl_dim_type type, __isl_keep isl_id *id);
1568 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1569 enum isl_dim_type type, const char *name);
1571 #include <isl/map.h>
1572 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1573 enum isl_dim_type type, __isl_keep isl_id *id);
1574 int isl_basic_map_find_dim_by_name(
1575 __isl_keep isl_basic_map *bmap,
1576 enum isl_dim_type type, const char *name);
1577 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1578 enum isl_dim_type type, const char *name);
1579 int isl_union_map_find_dim_by_name(
1580 __isl_keep isl_union_map *umap,
1581 enum isl_dim_type type, const char *name);
1583 #include <isl/aff.h>
1584 int isl_multi_aff_find_dim_by_id(
1585 __isl_keep isl_multi_aff *ma,
1586 enum isl_dim_type type, __isl_keep isl_id *id);
1587 int isl_multi_pw_aff_find_dim_by_id(
1588 __isl_keep isl_multi_pw_aff *mpa,
1589 enum isl_dim_type type, __isl_keep isl_id *id);
1590 int isl_multi_union_pw_aff_find_dim_by_id(
1591 __isl_keep isl_multi_union_pw_aff *mupa,
1592 enum isl_dim_type type, __isl_keep isl_id *id);
1593 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1594 enum isl_dim_type type, const char *name);
1595 int isl_multi_aff_find_dim_by_name(
1596 __isl_keep isl_multi_aff *ma,
1597 enum isl_dim_type type, const char *name);
1598 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1599 enum isl_dim_type type, const char *name);
1600 int isl_multi_pw_aff_find_dim_by_name(
1601 __isl_keep isl_multi_pw_aff *mpa,
1602 enum isl_dim_type type, const char *name);
1603 int isl_pw_multi_aff_find_dim_by_name(
1604 __isl_keep isl_pw_multi_aff *pma,
1605 enum isl_dim_type type, const char *name);
1606 int isl_union_pw_aff_find_dim_by_name(
1607 __isl_keep isl_union_pw_aff *upa,
1608 enum isl_dim_type type, const char *name);
1609 int isl_union_pw_multi_aff_find_dim_by_name(
1610 __isl_keep isl_union_pw_multi_aff *upma,
1611 enum isl_dim_type type, const char *name);
1612 int isl_multi_union_pw_aff_find_dim_by_name(
1613 __isl_keep isl_multi_union_pw_aff *mupa,
1614 enum isl_dim_type type, const char *name);
1616 #include <isl/polynomial.h>
1617 int isl_pw_qpolynomial_find_dim_by_name(
1618 __isl_keep isl_pw_qpolynomial *pwqp,
1619 enum isl_dim_type type, const char *name);
1620 int isl_pw_qpolynomial_fold_find_dim_by_name(
1621 __isl_keep isl_pw_qpolynomial_fold *pwf,
1622 enum isl_dim_type type, const char *name);
1623 int isl_union_pw_qpolynomial_find_dim_by_name(
1624 __isl_keep isl_union_pw_qpolynomial *upwqp,
1625 enum isl_dim_type type, const char *name);
1626 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1627 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1628 enum isl_dim_type type, const char *name);
1630 The identifiers or names of entire spaces may be set or read off
1631 using the following functions.
1633 #include <isl/space.h>
1634 __isl_give isl_space *isl_space_set_domain_tuple_id(
1635 __isl_take isl_space *space,
1636 __isl_take isl_id *id);
1637 __isl_give isl_space *isl_space_set_range_tuple_id(
1638 __isl_take isl_space *space,
1639 __isl_take isl_id *id);
1640 __isl_give isl_space *isl_space_set_tuple_id(
1641 __isl_take isl_space *space,
1642 enum isl_dim_type type, __isl_take isl_id *id);
1643 __isl_give isl_space *isl_space_reset_tuple_id(
1644 __isl_take isl_space *space, enum isl_dim_type type);
1645 isl_bool isl_space_has_domain_tuple_id(
1646 __isl_keep isl_space *space);
1647 isl_bool isl_space_has_range_tuple_id(
1648 __isl_keep isl_space *space);
1649 isl_bool isl_space_has_tuple_id(
1650 __isl_keep isl_space *space,
1651 enum isl_dim_type type);
1652 __isl_give isl_id *isl_space_get_domain_tuple_id(
1653 __isl_keep isl_space *space);
1654 __isl_give isl_id *isl_space_get_range_tuple_id(
1655 __isl_keep isl_space *space);
1656 __isl_give isl_id *isl_space_get_tuple_id(
1657 __isl_keep isl_space *space, enum isl_dim_type type);
1658 __isl_give isl_space *isl_space_set_tuple_name(
1659 __isl_take isl_space *space,
1660 enum isl_dim_type type, const char *s);
1661 isl_bool isl_space_has_tuple_name(
1662 __isl_keep isl_space *space,
1663 enum isl_dim_type type);
1664 __isl_keep const char *isl_space_get_tuple_name(
1665 __isl_keep isl_space *space,
1666 enum isl_dim_type type);
1668 #include <isl/local_space.h>
1669 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1670 __isl_take isl_local_space *ls,
1671 enum isl_dim_type type, __isl_take isl_id *id);
1673 #include <isl/set.h>
1674 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1675 __isl_take isl_basic_set *bset,
1676 __isl_take isl_id *id);
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 isl_bool 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_basic_set *isl_basic_set_set_tuple_name(
1685 __isl_take isl_basic_set *set, const char *s);
1686 __isl_give isl_set *isl_set_set_tuple_name(
1687 __isl_take isl_set *set, const char *s);
1688 const char *isl_basic_set_get_tuple_name(
1689 __isl_keep isl_basic_set *bset);
1690 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1691 const char *isl_set_get_tuple_name(
1692 __isl_keep isl_set *set);
1694 #include <isl/map.h>
1695 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, __isl_take isl_id *id);
1698 __isl_give isl_map *isl_map_set_domain_tuple_id(
1699 __isl_take isl_map *map, __isl_take isl_id *id);
1700 __isl_give isl_map *isl_map_set_range_tuple_id(
1701 __isl_take isl_map *map, __isl_take isl_id *id);
1702 __isl_give isl_map *isl_map_set_tuple_id(
1703 __isl_take isl_map *map, enum isl_dim_type type,
1704 __isl_take isl_id *id);
1705 __isl_give isl_map *isl_map_reset_tuple_id(
1706 __isl_take isl_map *map, enum isl_dim_type type);
1707 isl_bool isl_map_has_domain_tuple_id(
1708 __isl_keep isl_map *map);
1709 isl_bool isl_map_has_range_tuple_id(
1710 __isl_keep isl_map *map);
1711 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1712 enum isl_dim_type type);
1713 __isl_give isl_id *isl_map_get_domain_tuple_id(
1714 __isl_keep isl_map *map);
1715 __isl_give isl_id *isl_map_get_range_tuple_id(
1716 __isl_keep isl_map *map);
1717 __isl_give isl_id *isl_map_get_tuple_id(
1718 __isl_keep isl_map *map, enum isl_dim_type type);
1719 __isl_give isl_map *isl_map_set_tuple_name(
1720 __isl_take isl_map *map,
1721 enum isl_dim_type type, const char *s);
1722 const char *isl_basic_map_get_tuple_name(
1723 __isl_keep isl_basic_map *bmap,
1724 enum isl_dim_type type);
1725 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1726 __isl_take isl_basic_map *bmap,
1727 enum isl_dim_type type, const char *s);
1728 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1729 enum isl_dim_type type);
1730 const char *isl_map_get_tuple_name(
1731 __isl_keep isl_map *map,
1732 enum isl_dim_type type);
1734 #include <isl/val.h>
1735 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1736 __isl_take isl_multi_val *mv,
1737 __isl_take isl_id *id);
1738 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1739 __isl_take isl_multi_val *mv,
1740 enum isl_dim_type type, __isl_take isl_id *id);
1741 __isl_give isl_multi_val *
1742 isl_multi_val_reset_range_tuple_id(
1743 __isl_take isl_multi_val *mv);
1744 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1745 __isl_take isl_multi_val *mv,
1746 enum isl_dim_type type);
1747 isl_bool isl_multi_val_has_range_tuple_id(
1748 __isl_keep isl_multi_val *mv);
1749 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1750 __isl_keep isl_multi_val *mv);
1751 isl_bool isl_multi_val_has_tuple_id(
1752 __isl_keep isl_multi_val *mv,
1753 enum isl_dim_type type);
1754 __isl_give isl_id *isl_multi_val_get_tuple_id(
1755 __isl_keep isl_multi_val *mv,
1756 enum isl_dim_type type);
1757 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1758 __isl_take isl_multi_val *mv,
1759 enum isl_dim_type type, const char *s);
1760 const char *isl_multi_val_get_tuple_name(
1761 __isl_keep isl_multi_val *mv,
1762 enum isl_dim_type type);
1764 #include <isl/aff.h>
1765 __isl_give isl_aff *isl_aff_set_tuple_id(
1766 __isl_take isl_aff *aff,
1767 enum isl_dim_type type, __isl_take isl_id *id);
1768 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1769 __isl_take isl_multi_aff *ma,
1770 __isl_take isl_id *id);
1771 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1772 __isl_take isl_multi_aff *maff,
1773 enum isl_dim_type type, __isl_take isl_id *id);
1774 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1775 __isl_take isl_pw_aff *pwaff,
1776 enum isl_dim_type type, __isl_take isl_id *id);
1777 __isl_give isl_pw_multi_aff *
1778 isl_pw_multi_aff_set_range_tuple_id(
1779 __isl_take isl_pw_multi_aff *pma,
1780 __isl_take isl_id *id);
1781 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1782 __isl_take isl_pw_multi_aff *pma,
1783 enum isl_dim_type type, __isl_take isl_id *id);
1784 __isl_give isl_multi_pw_aff *
1785 isl_multi_pw_aff_set_range_tuple_id(
1786 __isl_take isl_multi_pw_aff *mpa,
1787 __isl_take isl_id *id);
1788 __isl_give isl_multi_union_pw_aff *
1789 isl_multi_union_pw_aff_set_range_tuple_id(
1790 __isl_take isl_multi_union_pw_aff *mupa,
1791 __isl_take isl_id *id);
1792 __isl_give isl_multi_union_pw_aff *
1793 isl_multi_union_pw_aff_set_tuple_id(
1794 __isl_take isl_multi_union_pw_aff *mupa,
1795 enum isl_dim_type type, __isl_take isl_id *id);
1796 __isl_give isl_multi_aff *
1797 isl_multi_aff_reset_range_tuple_id(
1798 __isl_take isl_multi_aff *ma);
1799 __isl_give isl_multi_pw_aff *
1800 isl_multi_pw_aff_reset_range_tuple_id(
1801 __isl_take isl_multi_pw_aff *mpa);
1802 __isl_give isl_multi_union_pw_aff *
1803 isl_multi_union_pw_aff_reset_range_tuple_id(
1804 __isl_take isl_multi_union_pw_aff *mupa);
1805 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1806 __isl_take isl_multi_aff *ma,
1807 enum isl_dim_type type);
1808 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1809 __isl_take isl_pw_aff *pa,
1810 enum isl_dim_type type);
1811 __isl_give isl_multi_pw_aff *
1812 isl_multi_pw_aff_reset_tuple_id(
1813 __isl_take isl_multi_pw_aff *mpa,
1814 enum isl_dim_type type);
1815 __isl_give isl_pw_multi_aff *
1816 isl_pw_multi_aff_reset_tuple_id(
1817 __isl_take isl_pw_multi_aff *pma,
1818 enum isl_dim_type type);
1819 __isl_give isl_multi_union_pw_aff *
1820 isl_multi_union_pw_aff_reset_tuple_id(
1821 __isl_take isl_multi_union_pw_aff *mupa,
1822 enum isl_dim_type type);
1823 isl_bool isl_multi_aff_has_range_tuple_id(
1824 __isl_keep isl_multi_aff *ma);
1825 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1826 __isl_keep isl_multi_aff *ma);
1827 isl_bool isl_multi_aff_has_tuple_id(
1828 __isl_keep isl_multi_aff *ma,
1829 enum isl_dim_type type);
1830 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1831 __isl_keep isl_multi_aff *ma,
1832 enum isl_dim_type type);
1833 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1834 enum isl_dim_type type);
1835 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1836 __isl_keep isl_pw_aff *pa,
1837 enum isl_dim_type type);
1838 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1839 __isl_keep isl_pw_multi_aff *pma);
1840 isl_bool isl_pw_multi_aff_has_tuple_id(
1841 __isl_keep isl_pw_multi_aff *pma,
1842 enum isl_dim_type type);
1843 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1844 __isl_keep isl_pw_multi_aff *pma);
1845 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1846 __isl_keep isl_pw_multi_aff *pma,
1847 enum isl_dim_type type);
1848 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1849 __isl_keep isl_multi_pw_aff *mpa);
1850 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1851 __isl_keep isl_multi_pw_aff *mpa);
1852 isl_bool isl_multi_pw_aff_has_tuple_id(
1853 __isl_keep isl_multi_pw_aff *mpa,
1854 enum isl_dim_type type);
1855 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1856 __isl_keep isl_multi_pw_aff *mpa,
1857 enum isl_dim_type type);
1858 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1859 __isl_keep isl_multi_union_pw_aff *mupa);
1861 isl_multi_union_pw_aff_get_range_tuple_id(
1862 __isl_keep isl_multi_union_pw_aff *mupa);
1863 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1864 __isl_keep isl_multi_union_pw_aff *mupa,
1865 enum isl_dim_type type);
1866 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1867 __isl_keep isl_multi_union_pw_aff *mupa,
1868 enum isl_dim_type type);
1869 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1870 __isl_take isl_multi_aff *maff,
1871 enum isl_dim_type type, const char *s);
1872 __isl_give isl_multi_pw_aff *
1873 isl_multi_pw_aff_set_tuple_name(
1874 __isl_take isl_multi_pw_aff *mpa,
1875 enum isl_dim_type type, const char *s);
1876 __isl_give isl_multi_union_pw_aff *
1877 isl_multi_union_pw_aff_set_tuple_name(
1878 __isl_take isl_multi_union_pw_aff *mupa,
1879 enum isl_dim_type type, const char *s);
1880 const char *isl_multi_aff_get_tuple_name(
1881 __isl_keep isl_multi_aff *multi,
1882 enum isl_dim_type type);
1883 isl_bool isl_pw_multi_aff_has_tuple_name(
1884 __isl_keep isl_pw_multi_aff *pma,
1885 enum isl_dim_type type);
1886 const char *isl_pw_multi_aff_get_tuple_name(
1887 __isl_keep isl_pw_multi_aff *pma,
1888 enum isl_dim_type type);
1889 const char *isl_multi_union_pw_aff_get_tuple_name(
1890 __isl_keep isl_multi_union_pw_aff *mupa,
1891 enum isl_dim_type type);
1893 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1894 or C<isl_dim_set>. As with C<isl_space_get_name>,
1895 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1897 Binary operations require the corresponding spaces of their arguments
1898 to have the same name.
1900 To keep the names of all parameters and tuples, but reset the user pointers
1901 of all the corresponding identifiers, use the following function.
1903 #include <isl/space.h>
1904 __isl_give isl_space *isl_space_reset_user(
1905 __isl_take isl_space *space);
1907 #include <isl/set.h>
1908 __isl_give isl_set *isl_set_reset_user(
1909 __isl_take isl_set *set);
1911 #include <isl/map.h>
1912 __isl_give isl_map *isl_map_reset_user(
1913 __isl_take isl_map *map);
1915 #include <isl/union_set.h>
1916 __isl_give isl_union_set *isl_union_set_reset_user(
1917 __isl_take isl_union_set *uset);
1919 #include <isl/union_map.h>
1920 __isl_give isl_union_map *isl_union_map_reset_user(
1921 __isl_take isl_union_map *umap);
1924 __isl_give isl_multi_id *isl_multi_id_reset_user(
1925 __isl_take isl_multi_id *mi);
1927 #include <isl/val.h>
1928 __isl_give isl_multi_val *isl_multi_val_reset_user(
1929 __isl_take isl_multi_val *mv);
1931 #include <isl/aff.h>
1932 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1933 __isl_take isl_multi_aff *ma);
1934 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1935 __isl_take isl_pw_aff *pa);
1936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1937 __isl_take isl_multi_pw_aff *mpa);
1938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1939 __isl_take isl_pw_multi_aff *pma);
1940 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1941 __isl_take isl_union_pw_aff *upa);
1942 __isl_give isl_multi_union_pw_aff *
1943 isl_multi_union_pw_aff_reset_user(
1944 __isl_take isl_multi_union_pw_aff *mupa);
1945 __isl_give isl_union_pw_multi_aff *
1946 isl_union_pw_multi_aff_reset_user(
1947 __isl_take isl_union_pw_multi_aff *upma);
1949 #include <isl/polynomial.h>
1950 __isl_give isl_pw_qpolynomial *
1951 isl_pw_qpolynomial_reset_user(
1952 __isl_take isl_pw_qpolynomial *pwqp);
1953 __isl_give isl_union_pw_qpolynomial *
1954 isl_union_pw_qpolynomial_reset_user(
1955 __isl_take isl_union_pw_qpolynomial *upwqp);
1956 __isl_give isl_pw_qpolynomial_fold *
1957 isl_pw_qpolynomial_fold_reset_user(
1958 __isl_take isl_pw_qpolynomial_fold *pwf);
1959 __isl_give isl_union_pw_qpolynomial_fold *
1960 isl_union_pw_qpolynomial_fold_reset_user(
1961 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1963 Spaces can be nested. In particular, the domain of a set or
1964 the domain or range of a relation can be a nested relation.
1965 This process is also called I<wrapping>.
1966 The functions for detecting, constructing and deconstructing
1967 such nested spaces can be found in the wrapping properties
1968 of L</"Unary Properties">, the wrapping operations
1969 of L</"Unary Operations"> and the Cartesian product operations
1970 of L</"Basic Operations">.
1972 Spaces can be created from other spaces
1973 using the functions described in L</"Unary Operations">
1974 and L</"Binary Operations">.
1978 A local space is essentially a space with
1979 zero or more existentially quantified variables.
1980 The local space of various objects can be obtained
1981 using the following functions.
1983 #include <isl/constraint.h>
1984 __isl_give isl_local_space *isl_constraint_get_local_space(
1985 __isl_keep isl_constraint *constraint);
1987 #include <isl/set.h>
1988 __isl_give isl_local_space *isl_basic_set_get_local_space(
1989 __isl_keep isl_basic_set *bset);
1991 #include <isl/map.h>
1992 __isl_give isl_local_space *isl_basic_map_get_local_space(
1993 __isl_keep isl_basic_map *bmap);
1995 #include <isl/aff.h>
1996 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1997 __isl_keep isl_aff *aff);
1998 __isl_give isl_local_space *isl_aff_get_local_space(
1999 __isl_keep isl_aff *aff);
2001 A new local space can be created from a space using
2003 #include <isl/local_space.h>
2004 __isl_give isl_local_space *isl_local_space_from_space(
2005 __isl_take isl_space *space);
2007 They can be inspected, modified, copied and freed using the following functions.
2009 #include <isl/local_space.h>
2010 isl_bool isl_local_space_is_params(
2011 __isl_keep isl_local_space *ls);
2012 isl_bool isl_local_space_is_set(
2013 __isl_keep isl_local_space *ls);
2014 __isl_give isl_space *isl_local_space_get_space(
2015 __isl_keep isl_local_space *ls);
2016 __isl_give isl_aff *isl_local_space_get_div(
2017 __isl_keep isl_local_space *ls, int pos);
2018 __isl_give isl_local_space *isl_local_space_copy(
2019 __isl_keep isl_local_space *ls);
2020 __isl_null isl_local_space *isl_local_space_free(
2021 __isl_take isl_local_space *ls);
2023 Note that C<isl_local_space_get_div> can only be used on local spaces
2026 Two local spaces can be compared using
2028 isl_bool isl_local_space_is_equal(
2029 __isl_keep isl_local_space *ls1,
2030 __isl_keep isl_local_space *ls2);
2032 Local spaces can be created from other local spaces
2033 using the functions described in L</"Unary Operations">
2034 and L</"Binary Operations">.
2036 =head2 Creating New Sets and Relations
2038 C<isl> has functions for creating some standard sets and relations.
2042 =item * Empty sets and relations
2044 __isl_give isl_basic_set *isl_basic_set_empty(
2045 __isl_take isl_space *space);
2046 __isl_give isl_basic_map *isl_basic_map_empty(
2047 __isl_take isl_space *space);
2048 __isl_give isl_set *isl_set_empty(
2049 __isl_take isl_space *space);
2050 __isl_give isl_map *isl_map_empty(
2051 __isl_take isl_space *space);
2052 __isl_give isl_union_set *isl_union_set_empty_ctx(
2054 __isl_give isl_union_set *isl_union_set_empty_space(
2055 __isl_take isl_space *space);
2056 __isl_give isl_union_set *isl_union_set_empty(
2057 __isl_take isl_space *space);
2058 __isl_give isl_union_map *isl_union_map_empty_ctx(
2060 __isl_give isl_union_map *isl_union_map_empty_space(
2061 __isl_take isl_space *space);
2062 __isl_give isl_union_map *isl_union_map_empty(
2063 __isl_take isl_space *space);
2065 For C<isl_union_set>s and C<isl_union_map>s, the space
2066 is only used to specify the parameters.
2067 C<isl_union_set_empty> is an alternative name for
2068 C<isl_union_set_empty_space>.
2069 Similarly for the other pair of functions.
2071 =item * Universe sets and relations
2073 #include <isl/set.h>
2074 __isl_give isl_basic_set *isl_basic_set_universe(
2075 __isl_take isl_space *space);
2076 __isl_give isl_set *isl_set_universe(
2077 __isl_take isl_space *space);
2078 __isl_give isl_set *isl_space_universe_set(
2079 __isl_take isl_space *space);
2081 #include <isl/map.h>
2082 __isl_give isl_basic_map *isl_basic_map_universe(
2083 __isl_take isl_space *space);
2084 __isl_give isl_map *isl_map_universe(
2085 __isl_take isl_space *space);
2086 __isl_give isl_map *isl_space_universe_map(
2087 __isl_take isl_space *space);
2089 #include <isl/union_set.h>
2090 __isl_give isl_union_set *isl_union_set_universe(
2091 __isl_take isl_union_set *uset);
2093 #include <isl/union_map.h>
2094 __isl_give isl_union_map *isl_union_map_universe(
2095 __isl_take isl_union_map *umap);
2097 C<isl_set_universe> and C<isl_space_universe_set>
2098 perform the same operation.
2100 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2102 The sets and relations constructed by the functions above
2103 contain all integer values, while those constructed by the
2104 functions below only contain non-negative values.
2106 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2107 __isl_take isl_space *space);
2108 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2109 __isl_take isl_space *space);
2110 __isl_give isl_set *isl_set_nat_universe(
2111 __isl_take isl_space *space);
2112 __isl_give isl_map *isl_map_nat_universe(
2113 __isl_take isl_space *space);
2115 =item * Identity relations
2117 __isl_give isl_basic_map *isl_basic_map_identity(
2118 __isl_take isl_space *space);
2119 __isl_give isl_map *isl_map_identity(
2120 __isl_take isl_space *space);
2122 The number of input and output dimensions in C<space> needs
2125 =item * Lexicographic order
2127 __isl_give isl_map *isl_map_lex_lt(
2128 __isl_take isl_space *set_space);
2129 __isl_give isl_map *isl_map_lex_le(
2130 __isl_take isl_space *set_space);
2131 __isl_give isl_map *isl_map_lex_gt(
2132 __isl_take isl_space *set_space);
2133 __isl_give isl_map *isl_map_lex_ge(
2134 __isl_take isl_space *set_space);
2135 __isl_give isl_map *isl_map_lex_lt_first(
2136 __isl_take isl_space *space, unsigned n);
2137 __isl_give isl_map *isl_map_lex_le_first(
2138 __isl_take isl_space *space, unsigned n);
2139 __isl_give isl_map *isl_map_lex_gt_first(
2140 __isl_take isl_space *space, unsigned n);
2141 __isl_give isl_map *isl_map_lex_ge_first(
2142 __isl_take isl_space *space, unsigned n);
2144 The first four functions take a space for a B<set>
2145 and return relations that express that the elements in the domain
2146 are lexicographically less
2147 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2148 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2149 than the elements in the range.
2150 The last four functions take a space for a map
2151 and return relations that express that the first C<n> dimensions
2152 in the domain are lexicographically less
2153 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2154 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2155 than the first C<n> dimensions in the range.
2159 A basic set or relation can be converted to a set or relation
2160 using the following functions.
2162 __isl_give isl_set *isl_basic_set_to_set(
2163 __isl_take isl_basic_set *bset);
2164 __isl_give isl_set *isl_set_from_basic_set(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_map *isl_map_from_basic_map(
2167 __isl_take isl_basic_map *bmap);
2169 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2172 Sets and relations can be converted to union sets and relations
2173 using the following functions.
2175 __isl_give isl_union_set *isl_union_set_from_basic_set(
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_union_map *isl_union_map_from_basic_map(
2178 __isl_take isl_basic_map *bmap);
2179 __isl_give isl_union_set *isl_set_to_union_set(
2180 __isl_take isl_set *set);
2181 __isl_give isl_union_set *isl_union_set_from_set(
2182 __isl_take isl_set *set);
2183 __isl_give isl_union_map *isl_map_to_union_map(
2184 __isl_take isl_map *map);
2185 __isl_give isl_union_map *isl_union_map_from_map(
2186 __isl_take isl_map *map);
2188 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2190 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2192 The inverse conversions below can only be used if the input
2193 union set or relation is known to contain elements in exactly one
2196 #include <isl/union_set.h>
2197 isl_bool isl_union_set_isa_set(
2198 __isl_keep isl_union_set *uset);
2199 __isl_give isl_set *isl_union_set_as_set(
2200 __isl_take isl_union_set *uset);
2201 __isl_give isl_set *isl_set_from_union_set(
2202 __isl_take isl_union_set *uset);
2204 #include <isl/union_map.h>
2205 isl_bool isl_union_map_isa_map(
2206 __isl_keep isl_union_map *umap);
2207 __isl_give isl_map *isl_union_map_as_map(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_map *isl_map_from_union_map(
2210 __isl_take isl_union_map *umap);
2212 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2214 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2216 Sets and relations can be copied and freed again using the following
2219 __isl_give isl_basic_set *isl_basic_set_copy(
2220 __isl_keep isl_basic_set *bset);
2221 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2222 __isl_give isl_union_set *isl_union_set_copy(
2223 __isl_keep isl_union_set *uset);
2224 __isl_give isl_basic_map *isl_basic_map_copy(
2225 __isl_keep isl_basic_map *bmap);
2226 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2227 __isl_give isl_union_map *isl_union_map_copy(
2228 __isl_keep isl_union_map *umap);
2229 __isl_null isl_basic_set *isl_basic_set_free(
2230 __isl_take isl_basic_set *bset);
2231 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2232 __isl_null isl_union_set *isl_union_set_free(
2233 __isl_take isl_union_set *uset);
2234 __isl_null isl_basic_map *isl_basic_map_free(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2237 __isl_null isl_union_map *isl_union_map_free(
2238 __isl_take isl_union_map *umap);
2240 Other sets and relations can be constructed by starting
2241 from a universe set or relation, adding equality and/or
2242 inequality constraints and then projecting out the
2243 existentially quantified variables, if any.
2244 Constraints can be constructed, manipulated and
2245 added to (or removed from) (basic) sets and relations
2246 using the following functions.
2248 #include <isl/constraint.h>
2249 __isl_give isl_constraint *isl_constraint_alloc_equality(
2250 __isl_take isl_local_space *ls);
2251 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2252 __isl_take isl_local_space *ls);
2253 __isl_give isl_constraint *isl_constraint_set_constant_si(
2254 __isl_take isl_constraint *constraint, int v);
2255 __isl_give isl_constraint *isl_constraint_set_constant_val(
2256 __isl_take isl_constraint *constraint,
2257 __isl_take isl_val *v);
2258 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2259 __isl_take isl_constraint *constraint,
2260 enum isl_dim_type type, int pos, int v);
2261 __isl_give isl_constraint *
2262 isl_constraint_set_coefficient_val(
2263 __isl_take isl_constraint *constraint,
2264 enum isl_dim_type type, int pos,
2265 __isl_take isl_val *v);
2266 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2267 __isl_take isl_basic_map *bmap,
2268 __isl_take isl_constraint *constraint);
2269 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2270 __isl_take isl_basic_set *bset,
2271 __isl_take isl_constraint *constraint);
2272 __isl_give isl_map *isl_map_add_constraint(
2273 __isl_take isl_map *map,
2274 __isl_take isl_constraint *constraint);
2275 __isl_give isl_set *isl_set_add_constraint(
2276 __isl_take isl_set *set,
2277 __isl_take isl_constraint *constraint);
2279 For example, to create a set containing the even integers
2280 between 10 and 42, you could use the following code.
2283 isl_local_space *ls;
2285 isl_basic_set *bset;
2287 space = isl_space_set_alloc(ctx, 0, 2);
2288 bset = isl_basic_set_universe(isl_space_copy(space));
2289 ls = isl_local_space_from_space(space);
2291 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2293 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2294 bset = isl_basic_set_add_constraint(bset, c);
2296 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2297 c = isl_constraint_set_constant_si(c, -10);
2298 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2299 bset = isl_basic_set_add_constraint(bset, c);
2301 c = isl_constraint_alloc_inequality(ls);
2302 c = isl_constraint_set_constant_si(c, 42);
2303 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2304 bset = isl_basic_set_add_constraint(bset, c);
2306 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2308 However, this is considered to be a fairly low-level approach.
2309 It is more appropriate to construct a (basic) set by means
2310 of affine expressions (defined below in L</"Functions">).
2311 For example, the same set could be constructed as follows.
2317 isl_basic_set *bset;
2319 space = isl_space_unit(ctx);
2320 space = isl_space_add_unnamed_tuple_ui(space, 1);
2321 ma = isl_multi_aff_identity_on_domain_space(
2322 isl_space_copy(space));
2323 var = isl_multi_aff_get_at(ma, 0);
2324 v = isl_val_int_from_si(ctx, 10);
2325 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2326 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2328 v = isl_val_int_from_si(ctx, 42);
2329 cst = isl_aff_val_on_domain_space(space, v);
2330 bset = isl_basic_set_intersect(bset,
2331 isl_aff_le_basic_set(var, cst));
2333 two = isl_val_int_from_si(ctx, 2);
2334 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2335 bset = isl_basic_set_preimage_multi_aff(bset,
2336 isl_multi_aff_copy(ma));
2337 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2338 ma = isl_multi_aff_scale_down_val(ma, two);
2339 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2341 Alternatively, the set can be parsed from a string representation.
2343 isl_basic_set *bset;
2344 bset = isl_basic_set_read_from_str(ctx,
2345 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2347 A basic set or relation can also be constructed from two matrices
2348 describing the equalities and the inequalities.
2350 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2351 __isl_take isl_space *space,
2352 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2353 enum isl_dim_type c1,
2354 enum isl_dim_type c2, enum isl_dim_type c3,
2355 enum isl_dim_type c4);
2356 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2357 __isl_take isl_space *space,
2358 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2359 enum isl_dim_type c1,
2360 enum isl_dim_type c2, enum isl_dim_type c3,
2361 enum isl_dim_type c4, enum isl_dim_type c5);
2363 The C<isl_dim_type> arguments indicate the order in which
2364 different kinds of variables appear in the input matrices
2365 and should be a permutation of C<isl_dim_cst> (the constant term),
2366 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2367 of C<isl_dim_cst>, C<isl_dim_param>,
2368 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2370 A (basic or union) set or relation can also be constructed from a
2371 (union) (piecewise) (multiple) affine expression
2372 or a list of affine expressions
2373 (See L</"Functions">), provided these affine expressions do not
2376 #include <isl/set.h>
2377 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2378 __isl_take isl_multi_aff *ma);
2379 __isl_give isl_set *isl_multi_aff_as_set(
2380 __isl_take isl_multi_aff *ma);
2381 __isl_give isl_set *isl_set_from_multi_aff(
2382 __isl_take isl_multi_aff *ma);
2384 #include <isl/map.h>
2385 __isl_give isl_basic_map *isl_basic_map_from_aff(
2386 __isl_take isl_aff *aff);
2387 __isl_give isl_map *isl_map_from_aff(
2388 __isl_take isl_aff *aff);
2389 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2390 __isl_take isl_space *domain_space,
2391 __isl_take isl_aff_list *list);
2392 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2393 __isl_take isl_multi_aff *maff)
2394 __isl_give isl_map *isl_multi_aff_as_map(
2395 __isl_take isl_multi_aff *ma);
2396 __isl_give isl_map *isl_map_from_multi_aff(
2397 __isl_take isl_multi_aff *maff)
2399 #include <isl/aff.h>
2400 __isl_give isl_set *isl_set_from_pw_aff(
2401 __isl_take isl_pw_aff *pwaff);
2402 __isl_give isl_map *isl_pw_aff_as_map(
2403 __isl_take isl_pw_aff *pa);
2404 __isl_give isl_map *isl_map_from_pw_aff(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_set *isl_pw_multi_aff_as_set(
2407 __isl_take isl_pw_multi_aff *pma);
2408 __isl_give isl_set *isl_set_from_pw_multi_aff(
2409 __isl_take isl_pw_multi_aff *pma);
2410 __isl_give isl_map *isl_pw_multi_aff_as_map(
2411 __isl_take isl_pw_multi_aff *pma);
2412 __isl_give isl_map *isl_map_from_pw_multi_aff(
2413 __isl_take isl_pw_multi_aff *pma);
2414 __isl_give isl_set *isl_multi_pw_aff_as_set(
2415 __isl_take isl_multi_pw_aff *mpa);
2416 __isl_give isl_set *isl_set_from_multi_pw_aff(
2417 __isl_take isl_multi_pw_aff *mpa);
2418 __isl_give isl_map *isl_multi_pw_aff_as_map(
2419 __isl_take isl_multi_pw_aff *mpa);
2420 __isl_give isl_map *isl_map_from_multi_pw_aff(
2421 __isl_take isl_multi_pw_aff *mpa);
2422 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2423 __isl_take isl_union_pw_aff *upa);
2424 __isl_give isl_union_map *
2425 isl_union_pw_multi_aff_as_union_map(
2426 __isl_take isl_union_pw_multi_aff *upma);
2427 __isl_give isl_union_map *
2428 isl_union_map_from_union_pw_multi_aff(
2429 __isl_take isl_union_pw_multi_aff *upma);
2430 __isl_give isl_union_map *
2431 isl_union_map_from_multi_union_pw_aff(
2432 __isl_take isl_multi_union_pw_aff *mupa);
2434 The C<domain_space> argument describes the domain of the resulting
2435 basic relation. It is required because the C<list> may consist
2436 of zero affine expressions.
2437 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2438 is not allowed to be zero-dimensional. The domain of the result
2439 is the shared domain of the union piecewise affine elements.
2440 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2442 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2443 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2444 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2445 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2446 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2447 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2449 C<isl_union_pw_multi_aff_as_union_map> and
2450 C<isl_union_map_from_union_pw_multi_aff>.
2452 =head2 Inspecting Sets and Relations
2454 Usually, the user should not have to care about the actual constraints
2455 of the sets and maps, but should instead apply the abstract operations
2456 explained in the following sections.
2457 Occasionally, however, it may be required to inspect the individual
2458 coefficients of the constraints. This section explains how to do so.
2459 In these cases, it may also be useful to have C<isl> compute
2460 an explicit representation of the existentially quantified variables.
2462 __isl_give isl_set *isl_set_compute_divs(
2463 __isl_take isl_set *set);
2464 __isl_give isl_map *isl_map_compute_divs(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_set *isl_union_set_compute_divs(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_union_map *isl_union_map_compute_divs(
2469 __isl_take isl_union_map *umap);
2471 This explicit representation defines the existentially quantified
2472 variables as integer divisions of the other variables, possibly
2473 including earlier existentially quantified variables.
2474 An explicitly represented existentially quantified variable therefore
2475 has a unique value when the values of the other variables are known.
2477 Alternatively, the existentially quantified variables can be removed
2478 using the following functions, which compute an overapproximation.
2480 #include <isl/set.h>
2481 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2482 __isl_take isl_basic_set *bset);
2483 __isl_give isl_set *isl_set_remove_divs(
2484 __isl_take isl_set *set);
2486 #include <isl/map.h>
2487 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2488 __isl_take isl_basic_map *bmap);
2489 __isl_give isl_map *isl_map_remove_divs(
2490 __isl_take isl_map *map);
2492 #include <isl/union_set.h>
2493 __isl_give isl_union_set *isl_union_set_remove_divs(
2494 __isl_take isl_union_set *bset);
2496 #include <isl/union_map.h>
2497 __isl_give isl_union_map *isl_union_map_remove_divs(
2498 __isl_take isl_union_map *bmap);
2500 It is also possible to only remove those divs that are defined
2501 in terms of a given range of dimensions or only those for which
2502 no explicit representation is known.
2504 __isl_give isl_basic_set *
2505 isl_basic_set_remove_divs_involving_dims(
2506 __isl_take isl_basic_set *bset,
2507 enum isl_dim_type type,
2508 unsigned first, unsigned n);
2509 __isl_give isl_basic_map *
2510 isl_basic_map_remove_divs_involving_dims(
2511 __isl_take isl_basic_map *bmap,
2512 enum isl_dim_type type,
2513 unsigned first, unsigned n);
2514 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2515 __isl_take isl_set *set, enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2518 __isl_take isl_map *map, enum isl_dim_type type,
2519 unsigned first, unsigned n);
2521 __isl_give isl_basic_set *
2522 isl_basic_set_remove_unknown_divs(
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_set *isl_set_remove_unknown_divs(
2525 __isl_take isl_set *set);
2526 __isl_give isl_map *isl_map_remove_unknown_divs(
2527 __isl_take isl_map *map);
2529 To iterate over all the sets or maps in a union set or map, use
2531 #include <isl/union_set.h>
2532 isl_stat isl_union_set_foreach_set(
2533 __isl_keep isl_union_set *uset,
2534 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2536 isl_bool isl_union_set_every_set(
2537 __isl_keep isl_union_set *uset,
2538 isl_bool (*test)(__isl_keep isl_set *set,
2542 #include <isl/union_map.h>
2543 isl_stat isl_union_map_foreach_map(
2544 __isl_keep isl_union_map *umap,
2545 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2547 isl_bool isl_union_map_every_map(
2548 __isl_keep isl_union_map *umap,
2549 isl_bool (*test)(__isl_keep isl_map *map,
2553 These functions call the callback function once for each
2554 (pair of) space(s) for which there are elements in the input.
2555 The argument to the callback contains all elements in the input
2556 with that (pair of) space(s).
2557 The C<isl_union_set_every_set> and
2558 C<isl_union_map_every_map> variants check whether each
2559 call to the callback returns true and stops checking as soon as one
2560 of these calls returns false.
2562 The number of sets or maps in a union set or map can be obtained
2565 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2566 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2568 To extract the set or map in a given space from a union, use
2570 __isl_give isl_set *isl_union_set_extract_set(
2571 __isl_keep isl_union_set *uset,
2572 __isl_take isl_space *space);
2573 __isl_give isl_map *isl_union_map_extract_map(
2574 __isl_keep isl_union_map *umap,
2575 __isl_take isl_space *space);
2577 To iterate over all the basic sets or maps in a set or map, use
2579 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2580 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2583 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2584 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2588 The callback function C<fn> should return C<isl_stat_ok> if successful and
2589 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2590 occurs, the above functions will return C<isl_stat_error>.
2592 It should be noted that C<isl> does not guarantee that
2593 the basic sets or maps passed to C<fn> are disjoint.
2594 If this is required, then the user should call one of
2595 the following functions first.
2597 __isl_give isl_set *isl_set_make_disjoint(
2598 __isl_take isl_set *set);
2599 __isl_give isl_map *isl_map_make_disjoint(
2600 __isl_take isl_map *map);
2602 The number of basic sets in a set can be obtained
2603 or the number of basic maps in a map can be obtained
2606 #include <isl/set.h>
2607 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2609 #include <isl/map.h>
2610 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2612 It is also possible to obtain a list of (basic) sets from a set
2613 or union set, a list of basic maps from a map and a list of maps from a union
2616 #include <isl/set.h>
2617 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2618 __isl_keep isl_set *set);
2620 #include <isl/union_set.h>
2621 __isl_give isl_basic_set_list *
2622 isl_union_set_get_basic_set_list(
2623 __isl_keep isl_union_set *uset);
2624 __isl_give isl_set_list *isl_union_set_get_set_list(
2625 __isl_keep isl_union_set *uset);
2627 #include <isl/map.h>
2628 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2629 __isl_keep isl_map *map);
2631 #include <isl/union_map.h>
2632 __isl_give isl_map_list *isl_union_map_get_map_list(
2633 __isl_keep isl_union_map *umap);
2635 The returned list can be manipulated using the functions in L<"Lists">.
2637 To iterate over the constraints of a basic set or map, use
2639 #include <isl/constraint.h>
2641 isl_size isl_basic_set_n_constraint(
2642 __isl_keep isl_basic_set *bset);
2643 isl_stat isl_basic_set_foreach_constraint(
2644 __isl_keep isl_basic_set *bset,
2645 isl_stat (*fn)(__isl_take isl_constraint *c,
2648 isl_size isl_basic_map_n_constraint(
2649 __isl_keep isl_basic_map *bmap);
2650 isl_stat isl_basic_map_foreach_constraint(
2651 __isl_keep isl_basic_map *bmap,
2652 isl_stat (*fn)(__isl_take isl_constraint *c,
2655 __isl_null isl_constraint *isl_constraint_free(
2656 __isl_take isl_constraint *c);
2658 Again, the callback function C<fn> should return C<isl_stat_ok>
2660 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2661 occurs, the above functions will return C<isl_stat_error>.
2662 The constraint C<c> represents either an equality or an inequality.
2663 Use the following function to find out whether a constraint
2664 represents an equality. If not, it represents an inequality.
2666 isl_bool isl_constraint_is_equality(
2667 __isl_keep isl_constraint *constraint);
2669 It is also possible to obtain a list of constraints from a basic
2672 #include <isl/constraint.h>
2673 __isl_give isl_constraint_list *
2674 isl_basic_map_get_constraint_list(
2675 __isl_keep isl_basic_map *bmap);
2676 __isl_give isl_constraint_list *
2677 isl_basic_set_get_constraint_list(
2678 __isl_keep isl_basic_set *bset);
2680 These functions require that all existentially quantified variables
2681 have an explicit representation.
2682 The returned list can be manipulated using the functions in L<"Lists">.
2684 The coefficients of the constraints can be inspected using
2685 the following functions.
2687 isl_bool isl_constraint_is_lower_bound(
2688 __isl_keep isl_constraint *constraint,
2689 enum isl_dim_type type, unsigned pos);
2690 isl_bool isl_constraint_is_upper_bound(
2691 __isl_keep isl_constraint *constraint,
2692 enum isl_dim_type type, unsigned pos);
2693 __isl_give isl_val *isl_constraint_get_constant_val(
2694 __isl_keep isl_constraint *constraint);
2695 __isl_give isl_val *isl_constraint_get_coefficient_val(
2696 __isl_keep isl_constraint *constraint,
2697 enum isl_dim_type type, int pos);
2699 The explicit representations of the existentially quantified
2700 variables can be inspected using the following function.
2701 Note that the user is only allowed to use this function
2702 if the inspected set or map is the result of a call
2703 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2704 The existentially quantified variable is equal to the floor
2705 of the returned affine expression. The affine expression
2706 itself can be inspected using the functions in
2709 __isl_give isl_aff *isl_constraint_get_div(
2710 __isl_keep isl_constraint *constraint, int pos);
2712 To obtain the constraints of a basic set or map in matrix
2713 form, use the following functions.
2715 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2716 __isl_keep isl_basic_set *bset,
2717 enum isl_dim_type c1, enum isl_dim_type c2,
2718 enum isl_dim_type c3, enum isl_dim_type c4);
2719 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2720 __isl_keep isl_basic_set *bset,
2721 enum isl_dim_type c1, enum isl_dim_type c2,
2722 enum isl_dim_type c3, enum isl_dim_type c4);
2723 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2724 __isl_keep isl_basic_map *bmap,
2725 enum isl_dim_type c1,
2726 enum isl_dim_type c2, enum isl_dim_type c3,
2727 enum isl_dim_type c4, enum isl_dim_type c5);
2728 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2729 __isl_keep isl_basic_map *bmap,
2730 enum isl_dim_type c1,
2731 enum isl_dim_type c2, enum isl_dim_type c3,
2732 enum isl_dim_type c4, enum isl_dim_type c5);
2734 The C<isl_dim_type> arguments dictate the order in which
2735 different kinds of variables appear in the resulting matrix.
2736 For set inputs, they should be a permutation of
2737 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2739 For map inputs, they should be a permutation of
2740 C<isl_dim_cst>, C<isl_dim_param>,
2741 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2745 Points are elements of a set. They can be used to construct
2746 simple sets (boxes) or they can be used to represent the
2747 individual elements of a set.
2748 The zero point (the origin) can be created using
2750 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2752 The coordinates of a point can be inspected, set and changed
2755 #include <isl/point.h>
2756 __isl_give isl_multi_val *isl_point_get_multi_val(
2757 __isl_keep isl_point *pnt);
2758 __isl_give isl_val *isl_point_get_coordinate_val(
2759 __isl_keep isl_point *pnt,
2760 enum isl_dim_type type, int pos);
2761 __isl_give isl_point *isl_point_set_coordinate_val(
2762 __isl_take isl_point *pnt,
2763 enum isl_dim_type type, int pos,
2764 __isl_take isl_val *v);
2766 __isl_give isl_point *isl_point_add_ui(
2767 __isl_take isl_point *pnt,
2768 enum isl_dim_type type, int pos, unsigned val);
2769 __isl_give isl_point *isl_point_sub_ui(
2770 __isl_take isl_point *pnt,
2771 enum isl_dim_type type, int pos, unsigned val);
2773 Points can be copied or freed using
2775 __isl_give isl_point *isl_point_copy(
2776 __isl_keep isl_point *pnt);
2777 __isl_null isl_point *isl_point_free(
2778 __isl_take isl_point *pnt);
2780 A singleton set can be created from a point using the following functions.
2782 __isl_give isl_basic_set *isl_basic_set_from_point(
2783 __isl_take isl_point *pnt);
2784 __isl_give isl_set *isl_point_to_set(
2785 __isl_take isl_point *pnt);
2786 __isl_give isl_set *isl_set_from_point(
2787 __isl_take isl_point *pnt);
2788 __isl_give isl_union_set *isl_union_set_from_point(
2789 __isl_take isl_point *pnt);
2791 C<isl_point_to_set> and C<isl_set_from_point> perform
2794 A box can be created from two opposite extremal points using
2796 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2797 __isl_take isl_point *pnt1,
2798 __isl_take isl_point *pnt2);
2799 __isl_give isl_set *isl_set_box_from_points(
2800 __isl_take isl_point *pnt1,
2801 __isl_take isl_point *pnt2);
2803 All elements of a B<bounded> (union) set can be enumerated using
2804 the following functions.
2806 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2807 isl_stat (*fn)(__isl_take isl_point *pnt,
2810 isl_stat isl_union_set_foreach_point(
2811 __isl_keep isl_union_set *uset,
2812 isl_stat (*fn)(__isl_take isl_point *pnt,
2816 The function C<fn> is called for each integer point in
2817 C<set> with as second argument the last argument of
2818 the C<isl_set_foreach_point> call. The function C<fn>
2819 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2820 In the latter case, C<isl_set_foreach_point> will stop
2821 enumerating and return C<isl_stat_error> as well.
2822 If the enumeration is performed successfully and to completion,
2823 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2825 To obtain a single point of a (basic or union) set, use
2827 __isl_give isl_point *isl_basic_set_sample_point(
2828 __isl_take isl_basic_set *bset);
2829 __isl_give isl_point *isl_set_sample_point(
2830 __isl_take isl_set *set);
2831 __isl_give isl_point *isl_union_set_sample_point(
2832 __isl_take isl_union_set *uset);
2834 If C<set> does not contain any (integer) points, then the
2835 resulting point will be ``void'', a property that can be
2838 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2842 Besides sets and relation, C<isl> also supports various types of functions.
2843 Each of these types is derived from the value type (see L</"Values">)
2844 or from one of two primitive function types
2845 through the application of zero or more type constructors.
2846 As a special case, a multiple expression can also be derived
2847 from an identifier (see L</"Identifiers">) although the result
2848 is not really a function.
2849 We first describe the primitive type and then we describe
2850 the types derived from these primitive types.
2852 =head3 Primitive Functions
2854 C<isl> support two primitive function types, quasi-affine
2855 expressions and quasipolynomials.
2856 A quasi-affine expression is defined either over a parameter
2857 space or over a set and is composed of integer constants,
2858 parameters and set variables, addition, subtraction and
2859 integer division by an integer constant.
2860 For example, the quasi-affine expression
2862 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2864 maps C<x> to C<2*floor((4 n + x)/9>.
2865 A quasipolynomial is a polynomial expression in quasi-affine
2866 expression. That is, it additionally allows for multiplication.
2867 Note, though, that it is not allowed to construct an integer
2868 division of an expression involving multiplications.
2869 Here is an example of a quasipolynomial that is not
2870 quasi-affine expression
2872 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2874 Note that the external representations of quasi-affine expressions
2875 and quasipolynomials are different. Quasi-affine expressions
2876 use a notation with square brackets just like binary relations,
2877 while quasipolynomials do not. This might change at some point.
2879 If a primitive function is defined over a parameter space,
2880 then the space of the function itself is that of a set.
2881 If it is defined over a set, then the space of the function
2882 is that of a relation. In both cases, the set space (or
2883 the output space) is single-dimensional, anonymous and unstructured.
2884 To create functions with multiple dimensions or with other kinds
2885 of set or output spaces, use multiple expressions
2886 (see L</"Multiple Expressions">).
2890 =item * Quasi-affine Expressions
2892 Besides the expressions described above, a quasi-affine
2893 expression can also be set to NaN. Such expressions
2894 typically represent a failure to represent a result
2895 as a quasi-affine expression.
2897 The zero quasi affine expression or the quasi affine expression
2898 that is equal to a given value, parameter or
2899 a specified dimension on a given domain can be created using
2901 #include <isl/aff.h>
2902 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2903 __isl_take isl_space *space);
2904 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2905 __isl_take isl_space *space);
2906 __isl_give isl_aff *isl_aff_zero_on_domain(
2907 __isl_take isl_local_space *ls);
2908 __isl_give isl_aff *isl_aff_val_on_domain_space(
2909 __isl_take isl_space *space,
2910 __isl_take isl_val *val);
2911 __isl_give isl_aff *isl_aff_val_on_domain(
2912 __isl_take isl_local_space *ls,
2913 __isl_take isl_val *val);
2914 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2915 __isl_take isl_space *space,
2916 __isl_take isl_id *id);
2917 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2918 __isl_take isl_space *space,
2919 __isl_take isl_id *id);
2920 __isl_give isl_aff *isl_aff_var_on_domain(
2921 __isl_take isl_local_space *ls,
2922 enum isl_dim_type type, unsigned pos);
2923 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2924 __isl_take isl_space *space);
2925 __isl_give isl_aff *isl_aff_nan_on_domain(
2926 __isl_take isl_local_space *ls);
2928 The space passed to C<isl_aff_param_on_domain_space_id>
2929 is required to have a parameter with the given identifier.
2930 C<isl_aff_param_on_domain_space_id> and
2931 C<isl_space_param_aff_on_domain_id> perform the same operation.
2933 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2934 perform the same operation.
2936 Quasi affine expressions can be copied and freed using
2938 #include <isl/aff.h>
2939 __isl_give isl_aff *isl_aff_copy(
2940 __isl_keep isl_aff *aff);
2941 __isl_null isl_aff *isl_aff_free(
2942 __isl_take isl_aff *aff);
2944 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2945 using the following function. The constraint is required to have
2946 a non-zero coefficient for the specified dimension.
2948 #include <isl/constraint.h>
2949 __isl_give isl_aff *isl_constraint_get_bound(
2950 __isl_keep isl_constraint *constraint,
2951 enum isl_dim_type type, int pos);
2953 The entire affine expression of the constraint can also be extracted
2954 using the following function.
2956 #include <isl/constraint.h>
2957 __isl_give isl_aff *isl_constraint_get_aff(
2958 __isl_keep isl_constraint *constraint);
2960 Conversely, an equality constraint equating
2961 the affine expression to zero or an inequality constraint enforcing
2962 the affine expression to be non-negative, can be constructed using
2964 __isl_give isl_constraint *isl_equality_from_aff(
2965 __isl_take isl_aff *aff);
2966 __isl_give isl_constraint *isl_inequality_from_aff(
2967 __isl_take isl_aff *aff);
2969 The coefficients and the integer divisions of an affine expression
2970 can be inspected using the following functions.
2972 #include <isl/aff.h>
2973 __isl_give isl_val *isl_aff_get_constant_val(
2974 __isl_keep isl_aff *aff);
2975 __isl_give isl_val *isl_aff_get_coefficient_val(
2976 __isl_keep isl_aff *aff,
2977 enum isl_dim_type type, int pos);
2978 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2979 enum isl_dim_type type, int pos);
2980 __isl_give isl_val *isl_aff_get_denominator_val(
2981 __isl_keep isl_aff *aff);
2982 __isl_give isl_aff *isl_aff_get_div(
2983 __isl_keep isl_aff *aff, int pos);
2985 They can be modified using the following functions.
2987 #include <isl/aff.h>
2988 __isl_give isl_aff *isl_aff_set_constant_si(
2989 __isl_take isl_aff *aff, int v);
2990 __isl_give isl_aff *isl_aff_set_constant_val(
2991 __isl_take isl_aff *aff, __isl_take isl_val *v);
2992 __isl_give isl_aff *isl_aff_set_coefficient_si(
2993 __isl_take isl_aff *aff,
2994 enum isl_dim_type type, int pos, int v);
2995 __isl_give isl_aff *isl_aff_set_coefficient_val(
2996 __isl_take isl_aff *aff,
2997 enum isl_dim_type type, int pos,
2998 __isl_take isl_val *v);
3000 __isl_give isl_aff *isl_aff_add_constant_si(
3001 __isl_take isl_aff *aff, int v);
3002 __isl_give isl_aff *isl_aff_add_constant_val(
3003 __isl_take isl_aff *aff, __isl_take isl_val *v);
3004 __isl_give isl_aff *isl_aff_add_constant_num_si(
3005 __isl_take isl_aff *aff, int v);
3006 __isl_give isl_aff *isl_aff_add_coefficient_si(
3007 __isl_take isl_aff *aff,
3008 enum isl_dim_type type, int pos, int v);
3009 __isl_give isl_aff *isl_aff_add_coefficient_val(
3010 __isl_take isl_aff *aff,
3011 enum isl_dim_type type, int pos,
3012 __isl_take isl_val *v);
3014 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3015 set the I<numerator> of the constant or coefficient, while
3016 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3017 the constant or coefficient as a whole.
3018 The C<add_constant> and C<add_coefficient> functions add an integer
3019 or rational value to
3020 the possibly rational constant or coefficient.
3021 The C<add_constant_num> functions add an integer value to
3024 =item * Quasipolynomials
3026 Some simple quasipolynomials can be created using the following functions.
3028 #include <isl/polynomial.h>
3029 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3030 __isl_take isl_space *domain);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3032 __isl_take isl_space *domain);
3033 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3034 __isl_take isl_space *domain);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3036 __isl_take isl_space *domain);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3038 __isl_take isl_space *domain);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3040 __isl_take isl_space *domain,
3041 __isl_take isl_val *val);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3043 __isl_take isl_space *domain,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3046 __isl_take isl_aff *aff);
3048 Recall that the space in which a quasipolynomial lives is a map space
3049 with a one-dimensional range. The C<domain> argument in some of
3050 the functions above corresponds to the domain of this map space.
3052 Quasipolynomials can be copied and freed again using the following
3055 #include <isl/polynomial.h>
3056 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3057 __isl_keep isl_qpolynomial *qp);
3058 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3059 __isl_take isl_qpolynomial *qp);
3061 The constant term of a quasipolynomial can be extracted using
3063 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3064 __isl_keep isl_qpolynomial *qp);
3066 To iterate over all terms in a quasipolynomial,
3069 isl_stat isl_qpolynomial_foreach_term(
3070 __isl_keep isl_qpolynomial *qp,
3071 isl_stat (*fn)(__isl_take isl_term *term,
3072 void *user), void *user);
3074 The terms themselves can be inspected and freed using
3077 isl_size isl_term_dim(__isl_keep isl_term *term,
3078 enum isl_dim_type type);
3079 __isl_give isl_val *isl_term_get_coefficient_val(
3080 __isl_keep isl_term *term);
3081 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3082 enum isl_dim_type type, unsigned pos);
3083 __isl_give isl_aff *isl_term_get_div(
3084 __isl_keep isl_term *term, unsigned pos);
3085 __isl_null isl_term *isl_term_free(
3086 __isl_take isl_term *term);
3088 Each term is a product of parameters, set variables and
3089 integer divisions. The function C<isl_term_get_exp>
3090 returns the exponent of a given dimensions in the given term.
3096 A reduction represents a maximum or a minimum of its
3098 The only reduction type defined by C<isl> is
3099 C<isl_qpolynomial_fold>.
3101 There are currently no functions to directly create such
3102 objects, but they do appear in the piecewise quasipolynomial
3103 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3105 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3107 Reductions can be copied and freed using
3108 the following functions.
3110 #include <isl/polynomial.h>
3111 __isl_give isl_qpolynomial_fold *
3112 isl_qpolynomial_fold_copy(
3113 __isl_keep isl_qpolynomial_fold *fold);
3114 __isl_null isl_qpolynomial_fold *
3115 isl_qpolynomial_fold_free(
3116 __isl_take isl_qpolynomial_fold *fold);
3118 The type of a (union piecewise) reduction
3119 can be obtained using the following functions.
3121 #include <isl/polynomial.h>
3122 enum isl_fold isl_qpolynomial_fold_get_type(
3123 __isl_keep isl_qpolynomial_fold *fold);
3124 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3125 __isl_keep isl_pw_qpolynomial_fold *pwf);
3126 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3127 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3129 The type may be either C<isl_fold_min> or C<isl_fold_max>
3130 (or C<isl_fold_error> in case of error).
3132 To iterate over all quasipolynomials in a reduction, use
3134 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3135 __isl_keep isl_qpolynomial_fold *fold,
3136 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3137 void *user), void *user);
3139 =head3 Multiple Expressions
3141 A multiple expression represents a sequence of zero or
3142 more base expressions, all defined on the same domain space.
3143 The domain space of the multiple expression is the same
3144 as that of the base expressions, but the range space
3145 can be any space. In case the base expressions have
3146 a set space, the corresponding multiple expression
3147 also has a set space.
3148 Objects of the value or identifier type do not have an associated space.
3149 The space of a multiple value or
3150 multiple identifier is therefore always a set space.
3151 Similarly, the space of a multiple union piecewise
3152 affine expression is always a set space.
3153 If the base expressions are not total, then
3154 a corresponding zero-dimensional multiple expression may
3155 have an explicit domain that keeps track of the domain
3156 outside of any base expressions.
3158 The multiple expression types defined by C<isl>
3159 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3160 C<isl_multi_union_pw_aff>.
3162 A multiple expression with the value zero for
3163 each output (or set) dimension can be created
3164 using the following functions.
3166 #include <isl/val.h>
3167 __isl_give isl_multi_val *isl_multi_val_zero(
3168 __isl_take isl_space *space);
3169 __isl_give isl_multi_val *isl_space_zero_multi_val(
3170 __isl_take isl_space *space);
3172 #include <isl/aff.h>
3173 __isl_give isl_multi_aff *isl_multi_aff_zero(
3174 __isl_take isl_space *space);
3175 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3176 __isl_take isl_space *space);
3177 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3178 __isl_take isl_space *space);
3179 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3180 __isl_take isl_space *space);
3181 __isl_give isl_multi_union_pw_aff *
3182 isl_multi_union_pw_aff_zero(
3183 __isl_take isl_space *space);
3184 __isl_give isl_multi_union_pw_aff *
3185 isl_space_zero_multi_union_pw_aff(
3186 __isl_take isl_space *space);
3188 Since there is no canonical way of representing a zero
3189 value of type C<isl_union_pw_aff>, the space passed
3190 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3191 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3192 perform the same operation.
3194 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3195 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3196 for the pair C<isl_multi_union_pw_aff_zero> and
3197 C<isl_space_zero_multi_union_pw_aff>.
3200 An identity function can be created using the following
3202 For the first group of functions, the space needs to be that of a set.
3203 For the second group,
3204 the space needs to be that of a relation
3205 with the same number of input and output dimensions.
3206 For the third group, the input function needs to live in a space
3207 with the same number of input and output dimensions and
3208 the identity function is created in that space.
3210 #include <isl/aff.h>
3211 __isl_give isl_multi_aff *
3212 isl_multi_aff_identity_on_domain_space(
3213 __isl_take isl_space *space);
3214 __isl_give isl_multi_aff *
3215 isl_space_identity_multi_aff_on_domain(
3216 __isl_take isl_space *space);
3217 __isl_give isl_multi_pw_aff *
3218 isl_multi_pw_aff_identity_on_domain_space(
3219 __isl_take isl_space *space);
3220 __isl_give isl_multi_pw_aff *
3221 isl_space_identity_multi_pw_aff_on_domain(
3222 __isl_take isl_space *space);
3223 __isl_give isl_multi_aff *isl_multi_aff_identity(
3224 __isl_take isl_space *space);
3225 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3226 __isl_take isl_space *space);
3227 __isl_give isl_multi_aff *
3228 isl_multi_aff_identity_multi_aff(
3229 __isl_take isl_multi_aff *ma);
3230 __isl_give isl_multi_pw_aff *
3231 isl_multi_pw_aff_identity_multi_pw_aff(
3232 __isl_take isl_multi_pw_aff *mpa);
3234 C<isl_multi_aff_identity_on_domain_space> and
3235 C<isl_space_identity_multi_aff_on_domain>
3236 perform the same operation.
3238 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3239 C<isl_space_identity_multi_pw_aff_on_domain>.
3241 A function that performs a projection on a universe
3242 relation or set can be created using the following functions.
3243 See also the corresponding
3244 projection operations in L</"Unary Operations">.
3246 #include <isl/aff.h>
3247 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3248 __isl_take isl_space *space);
3249 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3250 __isl_take isl_space *space);
3251 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3252 __isl_take isl_space *space);
3253 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3254 __isl_take isl_space *space);
3255 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3256 __isl_take isl_space *space,
3257 enum isl_dim_type type,
3258 unsigned first, unsigned n);
3260 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3263 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3265 A multiple expression can be created from a single
3266 base expression using the following functions.
3267 The space of the created multiple expression is the same
3268 as that of the base expression, except for
3269 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3270 lives in a parameter space and the output lives
3271 in a single-dimensional set space.
3273 #include <isl/aff.h>
3274 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3275 __isl_take isl_aff *aff);
3276 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3277 __isl_take isl_pw_aff *pa);
3278 __isl_give isl_multi_union_pw_aff *
3279 isl_multi_union_pw_aff_from_union_pw_aff(
3280 __isl_take isl_union_pw_aff *upa);
3282 A multiple expression can be created from a list
3283 of base expression in a specified space.
3284 The domain of this space needs to be the same
3285 as the domains of the base expressions in the list.
3286 If the base expressions have a set space (or no associated space),
3287 then this space also needs to be a set space.
3290 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3291 __isl_take isl_space *space,
3292 __isl_take isl_id_list *list);
3293 __isl_give isl_multi_id *isl_space_multi_id(
3294 __isl_take isl_space *space,
3295 __isl_take isl_id_list *list);
3297 #include <isl/val.h>
3298 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3299 __isl_take isl_space *space,
3300 __isl_take isl_val_list *list);
3301 __isl_give isl_multi_val *isl_space_multi_val(
3302 __isl_take isl_space *space,
3303 __isl_take isl_val_list *list);
3305 #include <isl/aff.h>
3306 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3307 __isl_take isl_space *space,
3308 __isl_take isl_aff_list *list);
3309 __isl_give isl_multi_aff *isl_space_multi_aff(
3310 __isl_take isl_space *space,
3311 __isl_take isl_aff_list *list);
3312 __isl_give isl_multi_pw_aff *
3313 isl_multi_pw_aff_from_pw_aff_list(
3314 __isl_take isl_space *space,
3315 __isl_take isl_pw_aff_list *list);
3316 __isl_give isl_multi_pw_aff *
3317 isl_space_multi_pw_aff(
3318 __isl_take isl_space *space,
3319 __isl_take isl_pw_aff_list *list);
3320 __isl_give isl_multi_union_pw_aff *
3321 isl_multi_union_pw_aff_from_union_pw_aff_list(
3322 __isl_take isl_space *space,
3323 __isl_take isl_union_pw_aff_list *list);
3324 __isl_give isl_multi_union_pw_aff *
3325 isl_space_multi_union_pw_aff(
3326 __isl_take isl_space *space,
3327 __isl_take isl_union_pw_aff_list *list);
3329 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3331 Similarly for the pair C<isl_multi_val_from_val_list> and
3332 C<isl_space_multi_val>,
3333 for the pair C<isl_multi_aff_from_aff_list> and
3334 C<isl_space_multi_aff>,
3335 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3336 C<isl_space_multi_pw_aff> and
3337 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3338 C<isl_space_multi_union_pw_aff>.
3340 As a convenience, a multiple piecewise expression can
3341 also be created from a multiple expression,
3342 or even directly from a single base expression.
3343 Each piecewise expression in the result has a single
3346 #include <isl/aff.h>
3347 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3348 __isl_take isl_aff *aff);
3349 __isl_give isl_multi_pw_aff *
3350 isl_multi_aff_to_multi_pw_aff(
3351 __isl_take isl_multi_aff *ma);
3352 __isl_give isl_multi_pw_aff *
3353 isl_multi_pw_aff_from_multi_aff(
3354 __isl_take isl_multi_aff *ma);
3356 C<isl_multi_aff_to_multi_pw_aff> and
3357 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3359 Similarly, a multiple union expression can be
3360 created from a multiple expression.
3362 #include <isl/aff.h>
3363 __isl_give isl_multi_union_pw_aff *
3364 isl_multi_union_pw_aff_from_multi_aff(
3365 __isl_take isl_multi_aff *ma);
3366 __isl_give isl_multi_union_pw_aff *
3367 isl_multi_aff_to_multi_union_pw_aff(
3368 __isl_take isl_multi_aff *ma);
3369 __isl_give isl_multi_union_pw_aff *
3370 isl_multi_union_pw_aff_from_multi_pw_aff(
3371 __isl_take isl_multi_pw_aff *mpa);
3373 C<isl_multi_aff_to_multi_union_pw_aff> and
3374 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3376 A multiple quasi-affine expression can be created from
3377 a multiple value with a given domain space using the following
3380 #include <isl/aff.h>
3381 __isl_give isl_multi_aff *
3382 isl_multi_aff_multi_val_on_domain_space(
3383 __isl_take isl_space *space,
3384 __isl_take isl_multi_val *mv);
3385 __isl_give isl_multi_aff *
3386 isl_space_multi_aff_on_domain_multi_val(
3387 __isl_take isl_space *space,
3388 __isl_take isl_multi_val *mv);
3389 __isl_give isl_multi_aff *
3390 isl_multi_aff_multi_val_on_space(
3391 __isl_take isl_space *space,
3392 __isl_take isl_multi_val *mv);
3394 C<isl_space_multi_aff_on_domain_multi_val> and
3395 C<isl_multi_aff_multi_val_on_space> are alternative names
3396 for C<isl_multi_aff_multi_val_on_domain_space>.
3399 a multiple union piecewise affine expression can be created from
3400 a multiple value with a given domain or
3401 a (piecewise) multiple affine expression with a given domain
3402 using the following functions.
3404 #include <isl/aff.h>
3405 __isl_give isl_multi_union_pw_aff *
3406 isl_multi_union_pw_aff_multi_val_on_domain(
3407 __isl_take isl_union_set *domain,
3408 __isl_take isl_multi_val *mv);
3409 __isl_give isl_multi_union_pw_aff *
3410 isl_multi_union_pw_aff_multi_aff_on_domain(
3411 __isl_take isl_union_set *domain,
3412 __isl_take isl_multi_aff *ma);
3413 __isl_give isl_multi_union_pw_aff *
3414 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3415 __isl_take isl_union_set *domain,
3416 __isl_take isl_pw_multi_aff *pma);
3418 Multiple expressions can be copied and freed using
3419 the following functions.
3422 __isl_give isl_multi_id *isl_multi_id_copy(
3423 __isl_keep isl_multi_id *mi);
3424 __isl_null isl_multi_id *isl_multi_id_free(
3425 __isl_take isl_multi_id *mi);
3427 #include <isl/val.h>
3428 __isl_give isl_multi_val *isl_multi_val_copy(
3429 __isl_keep isl_multi_val *mv);
3430 __isl_null isl_multi_val *isl_multi_val_free(
3431 __isl_take isl_multi_val *mv);
3433 #include <isl/aff.h>
3434 __isl_give isl_multi_aff *isl_multi_aff_copy(
3435 __isl_keep isl_multi_aff *maff);
3436 __isl_null isl_multi_aff *isl_multi_aff_free(
3437 __isl_take isl_multi_aff *maff);
3438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3439 __isl_keep isl_multi_pw_aff *mpa);
3440 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3441 __isl_take isl_multi_pw_aff *mpa);
3442 __isl_give isl_multi_union_pw_aff *
3443 isl_multi_union_pw_aff_copy(
3444 __isl_keep isl_multi_union_pw_aff *mupa);
3445 __isl_null isl_multi_union_pw_aff *
3446 isl_multi_union_pw_aff_free(
3447 __isl_take isl_multi_union_pw_aff *mupa);
3449 The number of base expressions in a multiple
3450 expression can be obtained using the following functions.
3453 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3455 #include <isl/val.h>
3456 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3458 #include <isl/aff.h>
3459 isl_size isl_multi_aff_size(
3460 __isl_keep isl_multi_aff *multi);
3461 isl_size isl_multi_pw_aff_size(
3462 __isl_keep isl_multi_pw_aff *mpa);
3463 isl_size isl_multi_union_pw_aff_size(
3464 __isl_keep isl_multi_union_pw_aff *mupa);
3466 The base expression at a given position of a multiple
3467 expression can be extracted using the following functions.
3470 __isl_give isl_id *isl_multi_id_get_at(
3471 __isl_keep isl_multi_id *mi, int pos);
3472 __isl_give isl_id *isl_multi_id_get_id(
3473 __isl_keep isl_multi_id *mi, int pos);
3475 #include <isl/val.h>
3476 __isl_give isl_val *isl_multi_val_get_at(
3477 __isl_keep isl_multi_val *mv, int pos);
3478 __isl_give isl_val *isl_multi_val_get_val(
3479 __isl_keep isl_multi_val *mv, int pos);
3481 #include <isl/aff.h>
3482 __isl_give isl_aff *isl_multi_aff_get_at(
3483 __isl_keep isl_multi_aff *ma, int pos);
3484 __isl_give isl_aff *isl_multi_aff_get_aff(
3485 __isl_keep isl_multi_aff *multi, int pos);
3486 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3487 __isl_keep isl_multi_pw_aff *mpa, int pos);
3488 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3489 __isl_keep isl_multi_pw_aff *mpa, int pos);
3490 __isl_give isl_union_pw_aff *
3491 isl_multi_union_pw_aff_get_at(
3492 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3493 __isl_give isl_union_pw_aff *
3494 isl_multi_union_pw_aff_get_union_pw_aff(
3495 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3497 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3498 Similarly for the other pairs of functions.
3500 The base expression can be replaced using the following functions.
3503 __isl_give isl_multi_id *isl_multi_id_set_at(
3504 __isl_take isl_multi_id *mi, int pos,
3505 __isl_take isl_id *id);
3506 __isl_give isl_multi_id *isl_multi_id_set_id(
3507 __isl_take isl_multi_id *mi, int pos,
3508 __isl_take isl_id *id);
3510 #include <isl/val.h>
3511 __isl_give isl_multi_val *isl_multi_val_set_at(
3512 __isl_take isl_multi_val *mv, int pos,
3513 __isl_take isl_val *val);
3514 __isl_give isl_multi_val *isl_multi_val_set_val(
3515 __isl_take isl_multi_val *mv, int pos,
3516 __isl_take isl_val *val);
3518 #include <isl/aff.h>
3519 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3520 __isl_take isl_multi_aff *ma, int pos,
3521 __isl_take isl_aff *aff);
3522 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3523 __isl_take isl_multi_aff *multi, int pos,
3524 __isl_take isl_aff *aff);
3525 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3526 __isl_take isl_multi_pw_aff *mpa, int pos,
3527 __isl_take isl_pw_aff *pa);
3528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3529 __isl_take isl_multi_pw_aff *mpa, int pos,
3530 __isl_take isl_pw_aff *pa);
3531 __isl_give isl_multi_union_pw_aff *
3532 isl_multi_union_pw_aff_set_at(
3533 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3534 __isl_take isl_union_pw_aff *upa);
3535 __isl_give isl_multi_union_pw_aff *
3536 isl_multi_union_pw_aff_set_union_pw_aff(
3537 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3538 __isl_take isl_union_pw_aff *upa);
3540 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3541 Similarly for the other pairs of functions.
3543 A list of all base expressions of a multiple
3544 expression can be extracted using the following functions.
3547 __isl_give isl_id_list *isl_multi_id_get_list(
3548 __isl_keep isl_multi_id *mi);
3550 #include <isl/val.h>
3551 __isl_give isl_val_list *isl_multi_val_get_list(
3552 __isl_keep isl_multi_val *mv);
3554 #include <isl/aff.h>
3555 __isl_give isl_aff_list *isl_multi_aff_get_list(
3556 __isl_keep isl_multi_aff *multi);
3557 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3558 __isl_keep isl_multi_pw_aff *mpa);
3559 __isl_give isl_union_pw_aff_list *
3560 isl_multi_union_pw_aff_list(
3561 __isl_keep isl_multi_union_pw_aff *mupa);
3563 The constant terms of the base expressions can be obtained using
3564 the following function.
3566 #include <isl/aff.h>
3567 __isl_give isl_multi_val *
3568 isl_multi_aff_get_constant_multi_val(
3569 __isl_keep isl_multi_aff *ma);
3571 As a convenience, a sequence of base expressions that have
3572 their domains in a given space can be extracted from a sequence
3573 of union expressions using the following function.
3575 #include <isl/aff.h>
3576 __isl_give isl_multi_pw_aff *
3577 isl_multi_union_pw_aff_extract_multi_pw_aff(
3578 __isl_keep isl_multi_union_pw_aff *mupa,
3579 __isl_take isl_space *space);
3581 Note that there is a difference between C<isl_multi_union_pw_aff>
3582 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3583 of unions of piecewise expressions, while the second is a union
3584 of piecewise sequences. In particular, multiple affine expressions
3585 in an C<isl_union_pw_multi_aff> may live in different spaces,
3586 while there is only a single multiple expression in
3587 an C<isl_multi_union_pw_aff>, which can therefore only live
3588 in a single space. This means that not every
3589 C<isl_union_pw_multi_aff> can be converted to
3590 an C<isl_multi_union_pw_aff>. Conversely, the elements
3591 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3592 while each multiple expression inside an C<isl_union_pw_multi_aff>
3593 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3594 of dimension greater than one may therefore not be exact.
3595 The following functions can
3596 be used to perform these conversions when they are possible.
3598 #include <isl/aff.h>
3599 __isl_give isl_multi_union_pw_aff *
3600 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3601 __isl_take isl_union_pw_multi_aff *upma);
3602 __isl_give isl_multi_union_pw_aff *
3603 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3604 __isl_take isl_union_pw_multi_aff *upma);
3605 __isl_give isl_union_pw_multi_aff *
3606 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3607 __isl_take isl_multi_union_pw_aff *mupa);
3609 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3610 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3611 perform the same operation.
3613 =head3 Piecewise Expressions
3615 A piecewise expression is an expression that is described
3616 using zero or more base expression defined over the same
3617 number of cells in the domain space of the base expressions.
3618 All base expressions are defined over the same
3619 domain space and the cells are disjoint.
3620 The space of a piecewise expression is the same as
3621 that of the base expressions.
3622 If the union of the cells is a strict subset of the domain
3623 space, then the value of the piecewise expression outside
3624 this union is different for types derived from quasi-affine
3625 expressions and those derived from quasipolynomials.
3626 Piecewise expressions derived from quasi-affine expressions
3627 are considered to be undefined outside the union of their cells.
3628 Piecewise expressions derived from quasipolynomials
3629 are considered to be zero outside the union of their cells.
3631 Piecewise quasipolynomials are mainly used by the C<barvinok>
3632 library for representing the number of elements in a parametric set or map.
3633 For example, the piecewise quasipolynomial
3635 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3637 represents the number of points in the map
3639 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3641 The piecewise expression types defined by C<isl>
3642 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3643 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3645 A piecewise expression with no cells can be created using
3646 the following functions.
3648 #include <isl/aff.h>
3649 __isl_give isl_pw_aff *isl_pw_aff_empty(
3650 __isl_take isl_space *space);
3651 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3652 __isl_take isl_space *space);
3654 A piecewise expression with a single universe cell can be
3655 created using the following functions.
3657 #include <isl/aff.h>
3658 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3659 __isl_take isl_aff *aff);
3660 __isl_give isl_pw_multi_aff *
3661 isl_multi_aff_to_pw_multi_aff(
3662 __isl_take isl_multi_aff *ma);
3663 __isl_give isl_pw_multi_aff *
3664 isl_pw_multi_aff_from_multi_aff(
3665 __isl_take isl_multi_aff *ma);
3667 #include <isl/polynomial.h>
3668 __isl_give isl_pw_qpolynomial *
3669 isl_pw_qpolynomial_from_qpolynomial(
3670 __isl_take isl_qpolynomial *qp);
3671 __isl_give isl_pw_qpolynomial_fold *
3672 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3673 __isl_take isl_qpolynomial_fold *fold);
3675 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3678 The inverse conversions below can only be used if the input
3679 expression is known to be defined over a single universe domain.
3681 #include <isl/aff.h>
3682 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3683 __isl_give isl_aff *isl_pw_aff_as_aff(
3684 __isl_take isl_pw_aff *pa);
3685 isl_bool isl_multi_pw_aff_isa_multi_aff(
3686 __isl_keep isl_multi_pw_aff *mpa);
3687 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3688 __isl_take isl_multi_pw_aff *mpa);
3689 isl_bool isl_pw_multi_aff_isa_multi_aff(
3690 __isl_keep isl_pw_multi_aff *pma);
3691 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3692 __isl_take isl_pw_multi_aff *pma);
3694 #include <isl/polynomial.h>
3695 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3696 __isl_keep isl_pw_qpolynomial *pwqp);
3697 __isl_give isl_qpolynomial *
3698 isl_pw_qpolynomial_as_qpolynomial(
3699 __isl_take isl_pw_qpolynomial *pwqp);
3700 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3701 __isl_keep isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_qpolynomial_fold *
3703 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3704 __isl_take isl_pw_qpolynomial_fold *pwf);
3706 A piecewise expression with a single specified cell can be
3707 created using the following functions.
3709 #include <isl/aff.h>
3710 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3711 __isl_take isl_set *set, __isl_take isl_aff *aff);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3713 __isl_take isl_set *set,
3714 __isl_take isl_multi_aff *maff);
3716 #include <isl/polynomial.h>
3717 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3718 __isl_take isl_set *set,
3719 __isl_take isl_qpolynomial *qp);
3721 The following convenience functions first create a base expression and
3722 then create a piecewise expression over a universe domain.
3724 #include <isl/aff.h>
3725 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3726 __isl_take isl_local_space *ls);
3727 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3728 __isl_take isl_local_space *ls,
3729 enum isl_dim_type type, unsigned pos);
3730 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3731 __isl_take isl_space *space);
3732 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3733 __isl_take isl_local_space *ls);
3734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3735 __isl_take isl_space *space);
3736 __isl_give isl_pw_multi_aff *
3737 isl_pw_multi_aff_identity_on_domain_space(
3738 __isl_take isl_space *space)
3739 __isl_give isl_pw_multi_aff *
3740 isl_space_identity_pw_multi_aff_on_domain(
3741 __isl_take isl_space *space)
3742 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3743 __isl_take isl_space *space);
3744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3745 __isl_take isl_space *space);
3746 __isl_give isl_pw_multi_aff *
3747 isl_space_domain_map_pw_multi_aff(
3748 __isl_take isl_space *space);
3749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3750 __isl_take isl_space *space);
3751 __isl_give isl_pw_multi_aff *
3752 isl_space_range_map_pw_multi_aff(
3753 __isl_take isl_space *space);
3754 __isl_give isl_pw_multi_aff *
3755 isl_pw_multi_aff_project_out_map(
3756 __isl_take isl_space *space,
3757 enum isl_dim_type type,
3758 unsigned first, unsigned n);
3760 #include <isl/polynomial.h>
3761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3762 __isl_take isl_space *space);
3764 C<isl_pw_multi_aff_identity_on_domain_space> and
3765 C<isl_space_identity_pw_multi_aff_on_domain>
3766 perform the same operation.
3768 for the pair C<isl_pw_multi_aff_domain_map> and
3769 C<isl_space_domain_map_pw_multi_aff> and
3770 for the pair C<isl_pw_multi_aff_range_map> and
3771 C<isl_space_range_map_pw_multi_aff>.
3773 The following convenience functions first create a base expression and
3774 then create a piecewise expression over a given domain.
3776 #include <isl/aff.h>
3777 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3778 __isl_take isl_set *domain,
3779 __isl_take isl_val *v);
3780 __isl_give isl_pw_aff *isl_set_pw_aff_on_domain_val(
3781 __isl_take isl_set *domain,
3782 __isl_take isl_val *v);
3783 __isl_give isl_pw_multi_aff *
3784 isl_pw_multi_aff_multi_val_on_domain(
3785 __isl_take isl_set *domain,
3786 __isl_take isl_multi_val *mv);
3787 __isl_give isl_pw_multi_aff *
3788 isl_set_pw_multi_aff_on_domain_multi_val(
3789 __isl_take isl_set *domain,
3790 __isl_take isl_multi_val *mv);
3791 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3792 __isl_take isl_set *domain,
3793 __isl_take isl_id *id);
3794 __isl_give isl_pw_aff *isl_set_param_pw_aff_on_domain_id(
3795 __isl_take isl_set *domain,
3796 __isl_take isl_id *id);
3798 C<isl_set_pw_aff_on_domain_val> is an alternative name
3799 for C<isl_pw_aff_val_on_domain>.
3800 Similarly for the pair
3801 C<isl_set_pw_multi_aff_on_domain_multi_val> and
3802 C<isl_pw_multi_aff_multi_val_on_domain> and
3803 for the pair C<isl_set_param_pw_aff_on_domain_id> and
3804 C<isl_pw_aff_param_on_domain_id>.
3806 As a convenience, a piecewise multiple expression can
3807 also be created from a piecewise expression.
3808 Each multiple expression in the result is derived
3809 from the corresponding base expression.
3811 #include <isl/aff.h>
3812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3813 __isl_take isl_pw_aff *pa);
3815 Similarly, a piecewise quasipolynomial can be
3816 created from a piecewise quasi-affine expression using
3817 the following function.
3819 #include <isl/polynomial.h>
3820 __isl_give isl_pw_qpolynomial *
3821 isl_pw_qpolynomial_from_pw_aff(
3822 __isl_take isl_pw_aff *pwaff);
3824 Piecewise expressions can be copied and freed using the following functions.
3826 #include <isl/aff.h>
3827 __isl_give isl_pw_aff *isl_pw_aff_copy(
3828 __isl_keep isl_pw_aff *pwaff);
3829 __isl_null isl_pw_aff *isl_pw_aff_free(
3830 __isl_take isl_pw_aff *pwaff);
3831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3832 __isl_keep isl_pw_multi_aff *pma);
3833 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3834 __isl_take isl_pw_multi_aff *pma);
3836 #include <isl/polynomial.h>
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3838 __isl_keep isl_pw_qpolynomial *pwqp);
3839 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3840 __isl_take isl_pw_qpolynomial *pwqp);
3841 __isl_give isl_pw_qpolynomial_fold *
3842 isl_pw_qpolynomial_fold_copy(
3843 __isl_keep isl_pw_qpolynomial_fold *pwf);
3844 __isl_null isl_pw_qpolynomial_fold *
3845 isl_pw_qpolynomial_fold_free(
3846 __isl_take isl_pw_qpolynomial_fold *pwf);
3848 To iterate over the different cells of a piecewise expression,
3849 use the following functions.
3851 #include <isl/aff.h>
3852 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3853 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3854 isl_stat isl_pw_aff_foreach_piece(
3855 __isl_keep isl_pw_aff *pwaff,
3856 isl_stat (*fn)(__isl_take isl_set *set,
3857 __isl_take isl_aff *aff,
3858 void *user), void *user);
3859 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3860 isl_bool (*test)(__isl_keep isl_set *set,
3861 __isl_keep isl_aff *aff, void *user),
3863 isl_size isl_pw_multi_aff_n_piece(
3864 __isl_keep isl_pw_multi_aff *pma);
3865 isl_stat isl_pw_multi_aff_foreach_piece(
3866 __isl_keep isl_pw_multi_aff *pma,
3867 isl_stat (*fn)(__isl_take isl_set *set,
3868 __isl_take isl_multi_aff *maff,
3869 void *user), void *user);
3870 isl_bool isl_pw_multi_aff_every_piece(
3871 __isl_keep isl_pw_multi_aff *pma,
3872 isl_bool (*test)(__isl_keep isl_set *set,
3873 __isl_keep isl_multi_aff *ma, void *user),
3876 #include <isl/polynomial.h>
3877 isl_size isl_pw_qpolynomial_n_piece(
3878 __isl_keep isl_pw_qpolynomial *pwqp);
3879 isl_stat isl_pw_qpolynomial_foreach_piece(
3880 __isl_keep isl_pw_qpolynomial *pwqp,
3881 isl_stat (*fn)(__isl_take isl_set *set,
3882 __isl_take isl_qpolynomial *qp,
3883 void *user), void *user);
3884 isl_bool isl_pw_qpolynomial_every_piece(
3885 __isl_keep isl_pw_qpolynomial *pwqp,
3886 isl_bool (*test)(__isl_keep isl_set *set,
3887 __isl_keep isl_qpolynomial *qp,
3888 void *user), void *user);
3889 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3890 __isl_keep isl_pw_qpolynomial *pwqp,
3891 isl_stat (*fn)(__isl_take isl_set *set,
3892 __isl_take isl_qpolynomial *qp,
3893 void *user), void *user);
3894 isl_size isl_pw_qpolynomial_fold_n_piece(
3895 __isl_keep isl_pw_qpolynomial_fold *pwf);
3896 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3897 __isl_keep isl_pw_qpolynomial_fold *pwf,
3898 isl_stat (*fn)(__isl_take isl_set *set,
3899 __isl_take isl_qpolynomial_fold *fold,
3900 void *user), void *user);
3901 isl_bool isl_pw_qpolynomial_fold_every_piece(
3902 __isl_keep isl_pw_qpolynomial_fold *pwf,
3903 isl_bool (*test)(__isl_keep isl_set *set,
3904 __isl_keep isl_qpolynomial_fold *fold,
3905 void *user), void *user);
3906 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3907 __isl_keep isl_pw_qpolynomial_fold *pwf,
3908 isl_stat (*fn)(__isl_take isl_set *set,
3909 __isl_take isl_qpolynomial_fold *fold,
3910 void *user), void *user);
3912 As usual, the function C<fn> should return C<isl_stat_ok> on success
3913 and C<isl_stat_error> on failure. The difference between
3914 C<isl_pw_qpolynomial_foreach_piece> and
3915 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3916 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3917 compute unique representations for all existentially quantified
3918 variables and then turn these existentially quantified variables
3919 into extra set variables, adapting the associated quasipolynomial
3920 accordingly. This means that the C<set> passed to C<fn>
3921 will not have any existentially quantified variables, but that
3922 the dimensions of the sets may be different for different
3923 invocations of C<fn>.
3924 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3925 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3926 The function C<isl_pw_aff_every_piece> and its variants
3927 check whether each call to the callback returns true and
3928 stop checking as soon as one of these calls returns false (or error).
3930 A piecewise expression consisting of the expressions at a given
3931 position of a piecewise multiple expression can be extracted
3932 using the following function.
3934 #include <isl/aff.h>
3935 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3936 __isl_keep isl_pw_multi_aff *pma, int pos);
3937 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3938 __isl_keep isl_pw_multi_aff *pma, int pos);
3940 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3941 C<isl_pw_multi_aff_get_at>.
3943 These expressions can be replaced using the following function.
3945 #include <isl/aff.h>
3946 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3947 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3948 __isl_take isl_pw_aff *pa);
3950 Note that there is a difference between C<isl_multi_pw_aff> and
3951 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3952 affine expressions, while the second is a piecewise sequence
3953 of affine expressions. In particular, each of the piecewise
3954 affine expressions in an C<isl_multi_pw_aff> may have a different
3955 domain, while all multiple expressions associated to a cell
3956 in an C<isl_pw_multi_aff> have the same domain.
3957 It is possible to convert between the two, but when converting
3958 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3959 of the result is the intersection of the domains of the input.
3960 The reverse conversion is exact.
3962 #include <isl/aff.h>
3963 __isl_give isl_pw_multi_aff *
3964 isl_pw_multi_aff_from_multi_pw_aff(
3965 __isl_take isl_multi_pw_aff *mpa);
3966 __isl_give isl_multi_pw_aff *
3967 isl_pw_multi_aff_to_multi_pw_aff(
3968 __isl_take isl_pw_multi_aff *pma);
3969 __isl_give isl_multi_pw_aff *
3970 isl_multi_pw_aff_from_pw_multi_aff(
3971 __isl_take isl_pw_multi_aff *pma);
3973 C<isl_pw_multi_aff_to_multi_pw_aff> and
3974 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3976 =head3 Union Expressions
3978 A union expression collects base expressions defined
3979 over different domains. The space of a union expression
3980 is that of the shared parameter space.
3982 The union expression types defined by C<isl>
3983 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3984 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3986 C<isl_union_pw_aff>,
3987 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3988 there can be at most one base expression for a given domain space.
3990 C<isl_union_pw_multi_aff>,
3991 there can be multiple such expressions for a given domain space,
3992 but the domains of these expressions need to be disjoint.
3994 An empty union expression can be created using the following functions.
3996 #include <isl/aff.h>
3997 __isl_give isl_union_pw_aff *
3998 isl_union_pw_aff_empty_ctx(
4000 __isl_give isl_union_pw_aff *
4001 isl_union_pw_aff_empty_space(
4002 __isl_take isl_space *space);
4003 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
4004 __isl_take isl_space *space);
4005 __isl_give isl_union_pw_multi_aff *
4006 isl_union_pw_multi_aff_empty_ctx(
4008 __isl_give isl_union_pw_multi_aff *
4009 isl_union_pw_multi_aff_empty_space(
4010 __isl_take isl_space *space);
4011 __isl_give isl_union_pw_multi_aff *
4012 isl_union_pw_multi_aff_empty(
4013 __isl_take isl_space *space);
4015 #include <isl/polynomial.h>
4016 __isl_give isl_union_pw_qpolynomial *
4017 isl_union_pw_qpolynomial_zero_ctx(
4019 __isl_give isl_union_pw_qpolynomial *
4020 isl_union_pw_qpolynomial_zero_space(
4021 __isl_take isl_space *space);
4022 __isl_give isl_union_pw_qpolynomial *
4023 isl_union_pw_qpolynomial_zero(
4024 __isl_take isl_space *space);
4026 C<isl_union_pw_aff_empty> is an alternative name for
4027 C<isl_union_pw_aff_empty_space>.
4028 Similarly for the other pairs of functions.
4030 A union expression containing a single base expression
4031 can be created using the following functions.
4033 #include <isl/aff.h>
4034 __isl_give isl_union_pw_aff *
4035 isl_pw_aff_to_union_pw_aff(
4036 __isl_take isl_pw_aff *pa);
4037 __isl_give isl_union_pw_aff *
4038 isl_union_pw_aff_from_pw_aff(
4039 __isl_take isl_pw_aff *pa);
4040 __isl_give isl_union_pw_multi_aff *
4041 isl_union_pw_multi_aff_from_aff(
4042 __isl_take isl_aff *aff);
4043 __isl_give isl_union_pw_multi_aff *
4044 isl_pw_multi_aff_to_union_pw_multi_aff(
4045 __isl_take isl_pw_multi_aff *pma);
4046 __isl_give isl_union_pw_multi_aff *
4047 isl_union_pw_multi_aff_from_pw_multi_aff(
4048 __isl_take isl_pw_multi_aff *pma);
4050 #include <isl/polynomial.h>
4051 __isl_give isl_union_pw_qpolynomial *
4052 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4053 __isl_take isl_pw_qpolynomial *pwqp);
4054 __isl_give isl_union_pw_qpolynomial *
4055 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4056 __isl_take isl_pw_qpolynomial *pwqp);
4057 __isl_give isl_union_pw_qpolynomial_fold *
4058 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4059 __isl_take isl_pw_qpolynomial_fold *pwf);
4060 __isl_give isl_union_pw_qpolynomial_fold *
4061 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4062 __isl_take isl_pw_qpolynomial_fold *pwf);
4064 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4066 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4067 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4069 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4070 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4072 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4073 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4075 The inverse conversions below can only be used if the input
4076 expression is known to live in exactly one space.
4078 #include <isl/aff.h>
4079 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4080 __isl_keep isl_union_pw_multi_aff *upma);
4081 __isl_give isl_pw_multi_aff *
4082 isl_union_pw_multi_aff_as_pw_multi_aff(
4083 __isl_take isl_union_pw_multi_aff *upma);
4085 A union piecewise expression containing a single base expression
4086 on a universe domain can also be created directly from
4087 a base expression using the following functions.
4089 #include <isl/aff.h>
4090 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4091 __isl_take isl_aff *aff);
4092 __isl_give isl_union_pw_multi_aff *
4093 isl_union_pw_multi_aff_from_multi_aff(
4094 __isl_take isl_multi_aff *ma);
4096 The following functions create a base expression on each
4097 of the sets in the union set and collect the results.
4099 #include <isl/aff.h>
4100 __isl_give isl_union_pw_multi_aff *
4101 isl_union_pw_multi_aff_from_union_pw_aff(
4102 __isl_take isl_union_pw_aff *upa);
4103 __isl_give isl_union_pw_aff *
4104 isl_union_pw_multi_aff_get_union_pw_aff(
4105 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4106 __isl_give isl_union_pw_aff *
4107 isl_union_pw_aff_val_on_domain(
4108 __isl_take isl_union_set *domain,
4109 __isl_take isl_val *v);
4110 __isl_give isl_union_pw_multi_aff *
4111 isl_union_pw_multi_aff_multi_val_on_domain(
4112 __isl_take isl_union_set *domain,
4113 __isl_take isl_multi_val *mv);
4114 __isl_give isl_union_pw_aff *
4115 isl_union_pw_aff_param_on_domain_id(
4116 __isl_take isl_union_set *domain,
4117 __isl_take isl_id *id);
4119 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4120 is the identifier of a parameter that may or may not already
4121 be present in C<domain>.
4123 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4125 expression on a given domain can be created using the following
4128 #include <isl/aff.h>
4129 __isl_give isl_union_pw_aff *
4130 isl_union_pw_aff_aff_on_domain(
4131 __isl_take isl_union_set *domain,
4132 __isl_take isl_aff *aff);
4133 __isl_give isl_union_pw_aff *
4134 isl_union_pw_aff_pw_aff_on_domain(
4135 __isl_take isl_union_set *domain,
4136 __isl_take isl_pw_aff *pa);
4138 A base expression can be added to a union expression using
4139 the following functions.
4141 #include <isl/aff.h>
4142 __isl_give isl_union_pw_aff *
4143 isl_union_pw_aff_add_pw_aff(
4144 __isl_take isl_union_pw_aff *upa,
4145 __isl_take isl_pw_aff *pa);
4146 __isl_give isl_union_pw_multi_aff *
4147 isl_union_pw_multi_aff_add_pw_multi_aff(
4148 __isl_take isl_union_pw_multi_aff *upma,
4149 __isl_take isl_pw_multi_aff *pma);
4151 #include <isl/polynomial.h>
4152 __isl_give isl_union_pw_qpolynomial *
4153 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4154 __isl_take isl_union_pw_qpolynomial *upwqp,
4155 __isl_take isl_pw_qpolynomial *pwqp);
4157 Union expressions can be copied and freed using
4158 the following functions.
4160 #include <isl/aff.h>
4161 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4162 __isl_keep isl_union_pw_aff *upa);
4163 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4164 __isl_take isl_union_pw_aff *upa);
4165 __isl_give isl_union_pw_multi_aff *
4166 isl_union_pw_multi_aff_copy(
4167 __isl_keep isl_union_pw_multi_aff *upma);
4168 __isl_null isl_union_pw_multi_aff *
4169 isl_union_pw_multi_aff_free(
4170 __isl_take isl_union_pw_multi_aff *upma);
4172 #include <isl/polynomial.h>
4173 __isl_give isl_union_pw_qpolynomial *
4174 isl_union_pw_qpolynomial_copy(
4175 __isl_keep isl_union_pw_qpolynomial *upwqp);
4176 __isl_null isl_union_pw_qpolynomial *
4177 isl_union_pw_qpolynomial_free(
4178 __isl_take isl_union_pw_qpolynomial *upwqp);
4179 __isl_give isl_union_pw_qpolynomial_fold *
4180 isl_union_pw_qpolynomial_fold_copy(
4181 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4182 __isl_null isl_union_pw_qpolynomial_fold *
4183 isl_union_pw_qpolynomial_fold_free(
4184 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4186 To iterate over the base expressions in a union expression,
4187 use the following functions.
4189 #include <isl/aff.h>
4190 isl_size isl_union_pw_aff_n_pw_aff(
4191 __isl_keep isl_union_pw_aff *upa);
4192 isl_stat isl_union_pw_aff_foreach_pw_aff(
4193 __isl_keep isl_union_pw_aff *upa,
4194 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4195 void *user), void *user);
4196 isl_bool isl_union_pw_aff_every_pw_aff(
4197 __isl_keep isl_union_pw_aff *upa,
4198 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4199 void *user), void *user);
4200 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4201 __isl_keep isl_union_pw_multi_aff *upma);
4202 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4203 __isl_keep isl_union_pw_multi_aff *upma,
4204 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4205 void *user), void *user);
4206 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4207 __isl_keep isl_union_pw_multi_aff *upma,
4209 __isl_keep isl_pw_multi_aff *pma,
4210 void *user), void *user);
4212 #include <isl/polynomial.h>
4213 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4214 __isl_keep isl_union_pw_qpolynomial *upwqp);
4215 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4216 __isl_keep isl_union_pw_qpolynomial *upwqp,
4217 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4218 void *user), void *user);
4219 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4220 __isl_keep isl_union_pw_qpolynomial *upwqp,
4222 __isl_keep isl_pw_qpolynomial *pwqp,
4223 void *user), void *user);
4224 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4225 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4226 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4227 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4228 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4229 void *user), void *user);
4231 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4232 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4234 __isl_keep isl_pw_qpolynomial_fold *pwf,
4235 void *user), void *user);
4237 To extract the base expression in a given space from a union, use
4238 the following functions.
4240 #include <isl/aff.h>
4241 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4242 __isl_keep isl_union_pw_aff *upa,
4243 __isl_take isl_space *space);
4244 __isl_give isl_pw_multi_aff *
4245 isl_union_pw_multi_aff_extract_pw_multi_aff(
4246 __isl_keep isl_union_pw_multi_aff *upma,
4247 __isl_take isl_space *space);
4249 #include <isl/polynomial.h>
4250 __isl_give isl_pw_qpolynomial *
4251 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4252 __isl_keep isl_union_pw_qpolynomial *upwqp,
4253 __isl_take isl_space *space);
4255 It is also possible to obtain a list of the base expressions using
4256 the following functions.
4258 #include <isl/aff.h>
4259 __isl_give isl_pw_aff_list *
4260 isl_union_pw_aff_get_pw_aff_list(
4261 __isl_keep isl_union_pw_aff *upa);
4262 __isl_give isl_pw_multi_aff_list *
4263 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4264 __isl_keep isl_union_pw_multi_aff *upma);
4266 #include <isl/polynomial.h>
4267 __isl_give isl_pw_qpolynomial_list *
4268 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4269 __isl_keep isl_union_pw_qpolynomial *upwqp);
4270 __isl_give isl_pw_qpolynomial_fold_list *
4271 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4272 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4274 The returned list can be manipulated using the functions in L<"Lists">.
4276 =head2 Input and Output
4278 For set and relation,
4279 C<isl> supports its own input/output format, which is similar
4280 to the C<Omega> format, but also supports the C<PolyLib> format
4282 For other object types, typically only an C<isl> format is supported.
4284 =head3 C<isl> format
4286 The C<isl> format is similar to that of C<Omega>, but has a different
4287 syntax for describing the parameters and allows for the definition
4288 of an existentially quantified variable as the integer division
4289 of an affine expression.
4290 For example, the set of integers C<i> between C<0> and C<n>
4291 such that C<i % 10 <= 6> can be described as
4293 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4296 A set or relation can have several disjuncts, separated
4297 by the keyword C<or>. Each disjunct is either a conjunction
4298 of constraints or a projection (C<exists>) of a conjunction
4299 of constraints. The constraints are separated by the keyword
4302 =head3 C<PolyLib> format
4304 If the represented set is a union, then the first line
4305 contains a single number representing the number of disjuncts.
4306 Otherwise, a line containing the number C<1> is optional.
4308 Each disjunct is represented by a matrix of constraints.
4309 The first line contains two numbers representing
4310 the number of rows and columns,
4311 where the number of rows is equal to the number of constraints
4312 and the number of columns is equal to two plus the number of variables.
4313 The following lines contain the actual rows of the constraint matrix.
4314 In each row, the first column indicates whether the constraint
4315 is an equality (C<0>) or inequality (C<1>). The final column
4316 corresponds to the constant term.
4318 If the set is parametric, then the coefficients of the parameters
4319 appear in the last columns before the constant column.
4320 The coefficients of any existentially quantified variables appear
4321 between those of the set variables and those of the parameters.
4323 =head3 Extended C<PolyLib> format
4325 The extended C<PolyLib> format is nearly identical to the
4326 C<PolyLib> format. The only difference is that the line
4327 containing the number of rows and columns of a constraint matrix
4328 also contains four additional numbers:
4329 the number of output dimensions, the number of input dimensions,
4330 the number of local dimensions (i.e., the number of existentially
4331 quantified variables) and the number of parameters.
4332 For sets, the number of ``output'' dimensions is equal
4333 to the number of set dimensions, while the number of ``input''
4338 Objects can be read from input using the following functions.
4341 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4343 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4344 isl_ctx *ctx, const char *str);
4346 #include <isl/val.h>
4347 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4349 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4350 isl_ctx *ctx, const char *str);
4352 #include <isl/set.h>
4353 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4354 isl_ctx *ctx, FILE *input);
4355 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4356 isl_ctx *ctx, const char *str);
4357 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4359 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4362 #include <isl/map.h>
4363 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4364 isl_ctx *ctx, FILE *input);
4365 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4366 isl_ctx *ctx, const char *str);
4367 __isl_give isl_map *isl_map_read_from_file(
4368 isl_ctx *ctx, FILE *input);
4369 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4372 #include <isl/union_set.h>
4373 __isl_give isl_union_set *isl_union_set_read_from_file(
4374 isl_ctx *ctx, FILE *input);
4375 __isl_give isl_union_set *isl_union_set_read_from_str(
4376 isl_ctx *ctx, const char *str);
4378 #include <isl/union_map.h>
4379 __isl_give isl_union_map *isl_union_map_read_from_file(
4380 isl_ctx *ctx, FILE *input);
4381 __isl_give isl_union_map *isl_union_map_read_from_str(
4382 isl_ctx *ctx, const char *str);
4384 #include <isl/aff.h>
4385 __isl_give isl_aff *isl_aff_read_from_str(
4386 isl_ctx *ctx, const char *str);
4387 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4388 isl_ctx *ctx, const char *str);
4389 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4390 isl_ctx *ctx, const char *str);
4391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4392 isl_ctx *ctx, const char *str);
4393 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4394 isl_ctx *ctx, const char *str);
4395 __isl_give isl_union_pw_aff *
4396 isl_union_pw_aff_read_from_str(
4397 isl_ctx *ctx, const char *str);
4398 __isl_give isl_union_pw_multi_aff *
4399 isl_union_pw_multi_aff_read_from_str(
4400 isl_ctx *ctx, const char *str);
4401 __isl_give isl_multi_union_pw_aff *
4402 isl_multi_union_pw_aff_read_from_str(
4403 isl_ctx *ctx, const char *str);
4405 #include <isl/polynomial.h>
4406 __isl_give isl_union_pw_qpolynomial *
4407 isl_union_pw_qpolynomial_read_from_str(
4408 isl_ctx *ctx, const char *str);
4410 __isl_give isl_pw_qpolynomial_fold *
4411 isl_pw_qpolynomial_fold_read_from_str(
4412 isl_ctx *ctx, const char *str);
4414 For sets and relations,
4415 the input format is autodetected and may be either the C<PolyLib> format
4416 or the C<isl> format.
4420 Before anything can be printed, an C<isl_printer> needs to
4423 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4425 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4426 __isl_null isl_printer *isl_printer_free(
4427 __isl_take isl_printer *printer);
4429 C<isl_printer_to_file> prints to the given file, while
4430 C<isl_printer_to_str> prints to a string that can be extracted
4431 using the following function.
4433 #include <isl/printer.h>
4434 __isl_give char *isl_printer_get_str(
4435 __isl_keep isl_printer *printer);
4437 The printer can be inspected using the following functions.
4439 FILE *isl_printer_get_file(
4440 __isl_keep isl_printer *printer);
4441 int isl_printer_get_output_format(
4442 __isl_keep isl_printer *p);
4443 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4445 The behavior of the printer can be modified in various ways
4447 __isl_give isl_printer *isl_printer_set_output_format(
4448 __isl_take isl_printer *p, int output_format);
4449 __isl_give isl_printer *isl_printer_set_indent(
4450 __isl_take isl_printer *p, int indent);
4451 __isl_give isl_printer *isl_printer_set_indent_prefix(
4452 __isl_take isl_printer *p, const char *prefix);
4453 __isl_give isl_printer *isl_printer_indent(
4454 __isl_take isl_printer *p, int indent);
4455 __isl_give isl_printer *isl_printer_set_prefix(
4456 __isl_take isl_printer *p, const char *prefix);
4457 __isl_give isl_printer *isl_printer_set_suffix(
4458 __isl_take isl_printer *p, const char *suffix);
4459 __isl_give isl_printer *isl_printer_set_yaml_style(
4460 __isl_take isl_printer *p, int yaml_style);
4462 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4463 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4464 and defaults to C<ISL_FORMAT_ISL>.
4465 Each line in the output is prefixed by C<indent_prefix>,
4466 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4467 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4468 In the C<PolyLib> format output,
4469 the coefficients of the existentially quantified variables
4470 appear between those of the set variables and those
4472 The function C<isl_printer_indent> increases the indentation
4473 by the specified amount (which may be negative).
4474 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4475 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4478 To actually print something, use
4480 #include <isl/printer.h>
4481 __isl_give isl_printer *isl_printer_print_double(
4482 __isl_take isl_printer *p, double d);
4484 #include <isl/val.h>
4485 __isl_give isl_printer *isl_printer_print_val(
4486 __isl_take isl_printer *p, __isl_keep isl_val *v);
4488 #include <isl/set.h>
4489 __isl_give isl_printer *isl_printer_print_basic_set(
4490 __isl_take isl_printer *printer,
4491 __isl_keep isl_basic_set *bset);
4492 __isl_give isl_printer *isl_printer_print_set(
4493 __isl_take isl_printer *printer,
4494 __isl_keep isl_set *set);
4496 #include <isl/map.h>
4497 __isl_give isl_printer *isl_printer_print_basic_map(
4498 __isl_take isl_printer *printer,
4499 __isl_keep isl_basic_map *bmap);
4500 __isl_give isl_printer *isl_printer_print_map(
4501 __isl_take isl_printer *printer,
4502 __isl_keep isl_map *map);
4504 #include <isl/union_set.h>
4505 __isl_give isl_printer *isl_printer_print_union_set(
4506 __isl_take isl_printer *p,
4507 __isl_keep isl_union_set *uset);
4509 #include <isl/union_map.h>
4510 __isl_give isl_printer *isl_printer_print_union_map(
4511 __isl_take isl_printer *p,
4512 __isl_keep isl_union_map *umap);
4514 #include <isl/val.h>
4515 __isl_give isl_printer *isl_printer_print_multi_val(
4516 __isl_take isl_printer *p,
4517 __isl_keep isl_multi_val *mv);
4520 __isl_give isl_printer *isl_printer_print_multi_id(
4521 __isl_take isl_printer *p,
4522 __isl_keep isl_multi_id *mi);
4524 #include <isl/aff.h>
4525 __isl_give isl_printer *isl_printer_print_aff(
4526 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4527 __isl_give isl_printer *isl_printer_print_multi_aff(
4528 __isl_take isl_printer *p,
4529 __isl_keep isl_multi_aff *maff);
4530 __isl_give isl_printer *isl_printer_print_pw_aff(
4531 __isl_take isl_printer *p,
4532 __isl_keep isl_pw_aff *pwaff);
4533 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4534 __isl_take isl_printer *p,
4535 __isl_keep isl_pw_multi_aff *pma);
4536 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4537 __isl_take isl_printer *p,
4538 __isl_keep isl_multi_pw_aff *mpa);
4539 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4540 __isl_take isl_printer *p,
4541 __isl_keep isl_union_pw_aff *upa);
4542 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4543 __isl_take isl_printer *p,
4544 __isl_keep isl_union_pw_multi_aff *upma);
4545 __isl_give isl_printer *
4546 isl_printer_print_multi_union_pw_aff(
4547 __isl_take isl_printer *p,
4548 __isl_keep isl_multi_union_pw_aff *mupa);
4550 #include <isl/polynomial.h>
4551 __isl_give isl_printer *isl_printer_print_qpolynomial(
4552 __isl_take isl_printer *p,
4553 __isl_keep isl_qpolynomial *qp);
4554 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4555 __isl_take isl_printer *p,
4556 __isl_keep isl_pw_qpolynomial *pwqp);
4557 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_union_pw_qpolynomial *upwqp);
4561 __isl_give isl_printer *
4562 isl_printer_print_pw_qpolynomial_fold(
4563 __isl_take isl_printer *p,
4564 __isl_keep isl_pw_qpolynomial_fold *pwf);
4565 __isl_give isl_printer *
4566 isl_printer_print_union_pw_qpolynomial_fold(
4567 __isl_take isl_printer *p,
4568 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4570 For C<isl_printer_print_qpolynomial>,
4571 C<isl_printer_print_pw_qpolynomial> and
4572 C<isl_printer_print_pw_qpolynomial_fold>,
4573 the output format of the printer
4574 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4575 For C<isl_printer_print_union_pw_qpolynomial> and
4576 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4578 In case of printing in C<ISL_FORMAT_C>, the user may want
4579 to set the names of all dimensions first.
4581 C<isl> also provides limited support for printing YAML documents,
4582 just enough for the internal use for printing such documents.
4584 #include <isl/printer.h>
4585 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4586 __isl_take isl_printer *p);
4587 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4588 __isl_take isl_printer *p);
4589 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4590 __isl_take isl_printer *p);
4591 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4592 __isl_take isl_printer *p);
4593 __isl_give isl_printer *isl_printer_yaml_next(
4594 __isl_take isl_printer *p);
4596 A document is started by a call to either
4597 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4598 Anything printed to the printer after such a call belong to the
4599 first key of the mapping or the first element in the sequence.
4600 The function C<isl_printer_yaml_next> moves to the value if
4601 we are currently printing a mapping key, the next key if we
4602 are printing a value or the next element if we are printing
4603 an element in a sequence.
4604 Nested mappings and sequences are initiated by the same
4605 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4606 Each call to these functions needs to have a corresponding call to
4607 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4609 When called on a file printer, the following function flushes
4610 the file. When called on a string printer, the buffer is cleared.
4612 __isl_give isl_printer *isl_printer_flush(
4613 __isl_take isl_printer *p);
4615 The following functions allow the user to attach
4616 notes to a printer in order to keep track of additional state.
4618 #include <isl/printer.h>
4619 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4620 __isl_keep isl_id *id);
4621 __isl_give isl_id *isl_printer_get_note(
4622 __isl_keep isl_printer *p, __isl_take isl_id *id);
4623 __isl_give isl_printer *isl_printer_set_note(
4624 __isl_take isl_printer *p,
4625 __isl_take isl_id *id, __isl_take isl_id *note);
4627 C<isl_printer_set_note> associates the given note to the given
4628 identifier in the printer.
4629 C<isl_printer_get_note> retrieves a note associated to an
4631 C<isl_printer_has_note> checks if there is such a note.
4632 C<isl_printer_get_note> fails if the requested note does not exist.
4634 Alternatively, a string representation can be obtained
4635 directly using the following functions, which always print
4639 __isl_give char *isl_id_to_str(
4640 __isl_keep isl_id *id);
4641 __isl_give char *isl_multi_id_to_str(
4642 __isl_keep isl_multi_id *mi);
4644 #include <isl/space.h>
4645 __isl_give char *isl_space_to_str(
4646 __isl_keep isl_space *space);
4648 #include <isl/val.h>
4649 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4650 __isl_give char *isl_multi_val_to_str(
4651 __isl_keep isl_multi_val *mv);
4653 #include <isl/set.h>
4654 __isl_give char *isl_basic_set_to_str(
4655 __isl_keep isl_basic_set *bset);
4656 __isl_give char *isl_set_to_str(
4657 __isl_keep isl_set *set);
4659 #include <isl/union_set.h>
4660 __isl_give char *isl_union_set_to_str(
4661 __isl_keep isl_union_set *uset);
4663 #include <isl/map.h>
4664 __isl_give char *isl_basic_map_to_str(
4665 __isl_keep isl_basic_map *bmap);
4666 __isl_give char *isl_map_to_str(
4667 __isl_keep isl_map *map);
4669 #include <isl/union_map.h>
4670 __isl_give char *isl_union_map_to_str(
4671 __isl_keep isl_union_map *umap);
4673 #include <isl/aff.h>
4674 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4675 __isl_give char *isl_pw_aff_to_str(
4676 __isl_keep isl_pw_aff *pa);
4677 __isl_give char *isl_multi_aff_to_str(
4678 __isl_keep isl_multi_aff *ma);
4679 __isl_give char *isl_pw_multi_aff_to_str(
4680 __isl_keep isl_pw_multi_aff *pma);
4681 __isl_give char *isl_multi_pw_aff_to_str(
4682 __isl_keep isl_multi_pw_aff *mpa);
4683 __isl_give char *isl_union_pw_aff_to_str(
4684 __isl_keep isl_union_pw_aff *upa);
4685 __isl_give char *isl_union_pw_multi_aff_to_str(
4686 __isl_keep isl_union_pw_multi_aff *upma);
4687 __isl_give char *isl_multi_union_pw_aff_to_str(
4688 __isl_keep isl_multi_union_pw_aff *mupa);
4690 #include <isl/point.h>
4691 __isl_give char *isl_point_to_str(
4692 __isl_keep isl_point *pnt);
4694 #include <isl/polynomial.h>
4695 __isl_give char *isl_pw_qpolynomial_to_str(
4696 __isl_keep isl_pw_qpolynomial *pwqp);
4697 __isl_give char *isl_union_pw_qpolynomial_to_str(
4698 __isl_keep isl_union_pw_qpolynomial *upwqp);
4702 =head3 Unary Properties
4708 The following functions test whether the given set or relation
4709 contains any integer points. The ``plain'' variants do not perform
4710 any computations, but simply check if the given set or relation
4711 is already known to be empty.
4713 #include <isl/set.h>
4714 isl_bool isl_basic_set_plain_is_empty(
4715 __isl_keep isl_basic_set *bset);
4716 isl_bool isl_basic_set_is_empty(
4717 __isl_keep isl_basic_set *bset);
4718 isl_bool isl_set_plain_is_empty(
4719 __isl_keep isl_set *set);
4720 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4722 #include <isl/union_set.h>
4723 isl_bool isl_union_set_is_empty(
4724 __isl_keep isl_union_set *uset);
4726 #include <isl/map.h>
4727 isl_bool isl_basic_map_plain_is_empty(
4728 __isl_keep isl_basic_map *bmap);
4729 isl_bool isl_basic_map_is_empty(
4730 __isl_keep isl_basic_map *bmap);
4731 isl_bool isl_map_plain_is_empty(
4732 __isl_keep isl_map *map);
4733 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4735 #include <isl/union_map.h>
4736 isl_bool isl_union_map_plain_is_empty(
4737 __isl_keep isl_union_map *umap);
4738 isl_bool isl_union_map_is_empty(
4739 __isl_keep isl_union_map *umap);
4741 #include <isl/aff.h>
4742 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4743 __isl_keep isl_union_pw_multi_aff *upma);
4745 =item * Universality
4747 isl_bool isl_basic_set_plain_is_universe(
4748 __isl_keep isl_basic_set *bset);
4749 isl_bool isl_basic_set_is_universe(
4750 __isl_keep isl_basic_set *bset);
4751 isl_bool isl_basic_map_plain_is_universe(
4752 __isl_keep isl_basic_map *bmap);
4753 isl_bool isl_basic_map_is_universe(
4754 __isl_keep isl_basic_map *bmap);
4755 isl_bool isl_set_plain_is_universe(
4756 __isl_keep isl_set *set);
4757 isl_bool isl_map_plain_is_universe(
4758 __isl_keep isl_map *map);
4760 =item * Single-valuedness
4762 #include <isl/set.h>
4763 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4765 #include <isl/map.h>
4766 isl_bool isl_basic_map_is_single_valued(
4767 __isl_keep isl_basic_map *bmap);
4768 isl_bool isl_map_plain_is_single_valued(
4769 __isl_keep isl_map *map);
4770 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4772 #include <isl/union_map.h>
4773 isl_bool isl_union_map_is_single_valued(
4774 __isl_keep isl_union_map *umap);
4778 isl_bool isl_map_plain_is_injective(
4779 __isl_keep isl_map *map);
4780 isl_bool isl_map_is_injective(
4781 __isl_keep isl_map *map);
4782 isl_bool isl_union_map_plain_is_injective(
4783 __isl_keep isl_union_map *umap);
4784 isl_bool isl_union_map_is_injective(
4785 __isl_keep isl_union_map *umap);
4789 isl_bool isl_map_is_bijective(
4790 __isl_keep isl_map *map);
4791 isl_bool isl_union_map_is_bijective(
4792 __isl_keep isl_union_map *umap);
4796 The following functions test whether the given relation
4797 only maps elements to themselves.
4799 #include <isl/map.h>
4800 isl_bool isl_map_is_identity(
4801 __isl_keep isl_map *map);
4803 #include <isl/union_map.h>
4804 isl_bool isl_union_map_is_identity(
4805 __isl_keep isl_union_map *umap);
4809 __isl_give isl_val *
4810 isl_basic_map_plain_get_val_if_fixed(
4811 __isl_keep isl_basic_map *bmap,
4812 enum isl_dim_type type, unsigned pos);
4813 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4814 __isl_keep isl_set *set,
4815 enum isl_dim_type type, unsigned pos);
4816 __isl_give isl_multi_val *
4817 isl_set_get_plain_multi_val_if_fixed(
4818 __isl_keep isl_set *set);
4819 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4820 __isl_keep isl_map *map,
4821 enum isl_dim_type type, unsigned pos);
4823 If the set or relation obviously lies on a hyperplane where the given dimension
4824 has a fixed value, then return that value.
4825 Otherwise return NaN.
4826 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4831 Stride detection is based on heuristics.
4832 The strides returned by the functions below are always valid,
4833 but there may be larger valid strides that are not detected.
4835 isl_stat isl_set_dim_residue_class_val(
4836 __isl_keep isl_set *set,
4837 int pos, __isl_give isl_val **modulo,
4838 __isl_give isl_val **residue);
4840 Check if the values of the given set dimension are equal to a fixed
4841 value modulo some integer value. If so, assign the modulo to C<*modulo>
4842 and the fixed value to C<*residue>. If the given dimension attains only
4843 a single value, then assign C<0> to C<*modulo> and the fixed value to
4845 If the dimension does not attain only a single value and if no modulo
4846 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4848 #include <isl/set.h>
4849 __isl_give isl_stride_info *isl_set_get_stride_info(
4850 __isl_keep isl_set *set, int pos);
4851 __isl_give isl_val *isl_set_get_stride(
4852 __isl_keep isl_set *set, int pos);
4853 __isl_give isl_fixed_box *isl_set_get_lattice_tile(
4854 __isl_keep isl_set *set);
4856 #include <isl/map.h>
4857 __isl_give isl_stride_info *
4858 isl_map_get_range_stride_info(
4859 __isl_keep isl_map *map, int pos);
4860 __isl_give isl_fixed_box *
4861 isl_map_get_range_lattice_tile(
4862 __isl_keep isl_map *map);
4864 Check if the values of the given set dimension are equal to
4865 some affine expression of the other dimensions (the offset)
4866 modulo some integer stride or
4867 check if the values of the given output dimensions are equal to
4868 some affine expression of the input dimensions (the offset)
4869 modulo some integer stride.
4870 If no more specific information can be found, then the stride
4871 is taken to be one and the offset is taken to be the zero expression.
4872 The function C<isl_set_get_stride> performs the same
4873 computation as C<isl_set_get_stride_info> but only returns the stride.
4874 The function C<isl_map_get_range_lattice_tile> collects the stride
4875 information over all output dimensions.
4876 In particular, it returns a tile of a rectangular lattice
4877 (possibly of size 1 in all directions)
4878 containing the output in terms of the parameters and the input dimensions.
4879 The size and the offset of this tile correspond to
4880 the strides and the offsets of the stride information and
4881 can be extracted from the returned
4882 C<isl_fixed_box> using the functions described under "Box hull" in
4883 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4884 C<isl_map_get_range_lattice_tile> is always valid.
4885 The function C<isl_set_get_lattice_tile> collects the same stride
4886 information over all set dimensions.
4887 For the other functions,
4888 the stride and offset can be extracted from the returned object
4889 using the following functions.
4891 #include <isl/stride_info.h>
4892 __isl_give isl_val *isl_stride_info_get_stride(
4893 __isl_keep isl_stride_info *si);
4894 __isl_give isl_aff *isl_stride_info_get_offset(
4895 __isl_keep isl_stride_info *si);
4897 The stride info object can be copied and released using the following
4900 #include <isl/stride_info.h>
4901 __isl_give isl_stride_info *isl_stride_info_copy(
4902 __isl_keep isl_stride_info *si);
4903 __isl_null isl_stride_info *isl_stride_info_free(
4904 __isl_take isl_stride_info *si);
4908 To check whether a function involves any local variables,
4909 i.e., integer divisions,
4910 the following functions can be used.
4912 #include <isl/set.h>
4913 isl_bool isl_set_involves_locals(
4914 __isl_keep isl_set *set);
4916 #include <isl/aff.h>
4917 isl_bool isl_aff_involves_locals(
4918 __isl_keep isl_aff *aff);
4919 isl_bool isl_multi_aff_involves_locals(
4920 __isl_keep isl_multi_aff *ma);
4921 isl_bool isl_pw_multi_aff_involves_locals(
4922 __isl_keep isl_pw_multi_aff *pma);
4923 isl_bool isl_union_pw_multi_aff_involves_locals(
4924 __isl_keep isl_union_pw_multi_aff *upma);
4926 To check whether the description of a set, relation or function depends
4927 on a parameter or one or more given dimensions,
4928 the following functions can be used.
4930 #include <isl/constraint.h>
4931 isl_bool isl_constraint_involves_dims(
4932 __isl_keep isl_constraint *constraint,
4933 enum isl_dim_type type, unsigned first, unsigned n);
4935 #include <isl/set.h>
4936 isl_bool isl_basic_set_involves_dims(
4937 __isl_keep isl_basic_set *bset,
4938 enum isl_dim_type type, unsigned first, unsigned n);
4939 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4940 enum isl_dim_type type, unsigned first, unsigned n);
4942 #include <isl/map.h>
4943 isl_bool isl_basic_map_involves_dims(
4944 __isl_keep isl_basic_map *bmap,
4945 enum isl_dim_type type, unsigned first, unsigned n);
4946 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4947 enum isl_dim_type type, unsigned first, unsigned n);
4949 #include <isl/union_map.h>
4950 isl_bool isl_union_map_involves_dims(
4951 __isl_keep isl_union_map *umap,
4952 enum isl_dim_type type, unsigned first, unsigned n);
4954 #include <isl/aff.h>
4955 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4956 enum isl_dim_type type, unsigned first, unsigned n);
4957 isl_bool isl_pw_aff_involves_param_id(
4958 __isl_keep isl_pw_aff *pa,
4959 __isl_keep isl_id *id);
4960 isl_bool isl_pw_aff_involves_dims(
4961 __isl_keep isl_pw_aff *pwaff,
4962 enum isl_dim_type type, unsigned first, unsigned n);
4963 isl_bool isl_multi_aff_involves_dims(
4964 __isl_keep isl_multi_aff *ma,
4965 enum isl_dim_type type, unsigned first, unsigned n);
4966 isl_bool isl_pw_multi_aff_involves_param_id(
4967 __isl_keep isl_pw_multi_aff *pma,
4968 __isl_keep isl_id *id);
4969 isl_bool isl_pw_multi_aff_involves_dims(
4970 __isl_keep isl_pw_multi_aff *pma,
4971 enum isl_dim_type type, unsigned first, unsigned n);
4972 isl_bool isl_multi_pw_aff_involves_dims(
4973 __isl_keep isl_multi_pw_aff *mpa,
4974 enum isl_dim_type type, unsigned first, unsigned n);
4975 isl_bool isl_multi_pw_aff_involves_param_id(
4976 __isl_keep isl_multi_pw_aff *mpa,
4977 __isl_keep isl_id *id);
4978 isl_bool isl_multi_pw_aff_involves_param_id_list(
4979 __isl_keep isl_multi_pw_aff *mpa,
4980 __isl_keep isl_id_list *list);
4982 #include <isl/polynomial.h>
4983 isl_bool isl_qpolynomial_involves_dims(
4984 __isl_keep isl_qpolynomial *qp,
4985 enum isl_dim_type type, unsigned first, unsigned n);
4986 isl_bool isl_pw_qpolynomial_involves_param_id(
4987 __isl_keep isl_pw_qpolynomial *pwqp,
4988 __isl_keep isl_id *id);
4989 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
4990 __isl_keep isl_pw_qpolynomial_fold *pwf,
4991 __isl_keep isl_id *id);
4993 Similarly, the following functions can be used to check whether
4994 a given dimension is involved in any lower or upper bound.
4996 #include <isl/set.h>
4997 isl_bool isl_set_dim_has_any_lower_bound(
4998 __isl_keep isl_set *set,
4999 enum isl_dim_type type, unsigned pos);
5000 isl_bool isl_set_dim_has_any_upper_bound(
5001 __isl_keep isl_set *set,
5002 enum isl_dim_type type, unsigned pos);
5004 Note that these functions return true even if there is a bound on
5005 the dimension on only some of the basic sets of C<set>.
5006 To check if they have a bound for all of the basic sets in C<set>,
5007 use the following functions instead.
5009 #include <isl/set.h>
5010 isl_bool isl_set_dim_has_lower_bound(
5011 __isl_keep isl_set *set,
5012 enum isl_dim_type type, unsigned pos);
5013 isl_bool isl_set_dim_has_upper_bound(
5014 __isl_keep isl_set *set,
5015 enum isl_dim_type type, unsigned pos);
5019 To check whether a set is a parameter domain, use this function:
5021 isl_bool isl_set_is_params(__isl_keep isl_set *set);
5022 isl_bool isl_union_set_is_params(
5023 __isl_keep isl_union_set *uset);
5027 The following functions check whether the space of the given
5028 (basic) set or relation domain and/or range is a wrapped relation.
5030 #include <isl/space.h>
5031 isl_bool isl_space_is_wrapping(
5032 __isl_keep isl_space *space);
5033 isl_bool isl_space_domain_is_wrapping(
5034 __isl_keep isl_space *space);
5035 isl_bool isl_space_range_is_wrapping(
5036 __isl_keep isl_space *space);
5037 isl_bool isl_space_is_product(
5038 __isl_keep isl_space *space);
5040 #include <isl/set.h>
5041 isl_bool isl_basic_set_is_wrapping(
5042 __isl_keep isl_basic_set *bset);
5043 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
5045 #include <isl/map.h>
5046 isl_bool isl_map_domain_is_wrapping(
5047 __isl_keep isl_map *map);
5048 isl_bool isl_map_range_is_wrapping(
5049 __isl_keep isl_map *map);
5050 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5053 isl_bool isl_multi_id_range_is_wrapping(
5054 __isl_keep isl_multi_id *mi);
5056 #include <isl/val.h>
5057 isl_bool isl_multi_val_range_is_wrapping(
5058 __isl_keep isl_multi_val *mv);
5060 #include <isl/aff.h>
5061 isl_bool isl_multi_aff_range_is_wrapping(
5062 __isl_keep isl_multi_aff *ma);
5063 isl_bool isl_multi_pw_aff_range_is_wrapping(
5064 __isl_keep isl_multi_pw_aff *mpa);
5065 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5066 __isl_keep isl_multi_union_pw_aff *mupa);
5068 The input to C<isl_space_is_wrapping> should
5069 be the space of a set, while that of
5070 C<isl_space_domain_is_wrapping> and
5071 C<isl_space_range_is_wrapping> should be the space of a relation.
5072 The input to C<isl_space_is_product> can be either the space
5073 of a set or that of a binary relation.
5074 In case the input is the space of a binary relation, it checks
5075 whether both domain and range are wrapping.
5077 =item * Internal Product
5079 isl_bool isl_basic_map_can_zip(
5080 __isl_keep isl_basic_map *bmap);
5081 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5083 Check whether the product of domain and range of the given relation
5085 i.e., whether both domain and range are nested relations.
5089 #include <isl/space.h>
5090 isl_bool isl_space_can_curry(
5091 __isl_keep isl_space *space);
5093 #include <isl/map.h>
5094 isl_bool isl_basic_map_can_curry(
5095 __isl_keep isl_basic_map *bmap);
5096 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5098 Check whether the domain of the (basic) relation is a wrapped relation.
5100 #include <isl/space.h>
5101 isl_bool isl_space_can_uncurry(
5102 __isl_keep isl_space *space);
5104 #include <isl/map.h>
5105 isl_bool isl_basic_map_can_uncurry(
5106 __isl_keep isl_basic_map *bmap);
5107 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5109 Check whether the range of the (basic) relation is a wrapped relation.
5111 #include <isl/space.h>
5112 isl_bool isl_space_can_range_curry(
5113 __isl_keep isl_space *space);
5115 #include <isl/map.h>
5116 isl_bool isl_map_can_range_curry(
5117 __isl_keep isl_map *map);
5119 Check whether the domain of the relation wrapped in the range of
5120 the input is itself a wrapped relation.
5122 =item * Special Values
5124 #include <isl/aff.h>
5125 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5126 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5127 isl_bool isl_multi_pw_aff_is_cst(
5128 __isl_keep isl_multi_pw_aff *mpa);
5130 Check whether the given expression is a constant.
5132 #include <isl/val.h>
5133 isl_bool isl_multi_val_involves_nan(
5134 __isl_keep isl_multi_val *mv);
5136 #include <isl/aff.h>
5137 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5138 isl_bool isl_multi_aff_involves_nan(
5139 __isl_keep isl_multi_aff *ma);
5140 isl_bool isl_pw_aff_involves_nan(
5141 __isl_keep isl_pw_aff *pa);
5142 isl_bool isl_pw_multi_aff_involves_nan(
5143 __isl_keep isl_pw_multi_aff *pma);
5144 isl_bool isl_multi_pw_aff_involves_nan(
5145 __isl_keep isl_multi_pw_aff *mpa);
5146 isl_bool isl_union_pw_aff_involves_nan(
5147 __isl_keep isl_union_pw_aff *upa);
5148 isl_bool isl_union_pw_multi_aff_involves_nan(
5149 __isl_keep isl_union_pw_multi_aff *upma);
5150 isl_bool isl_multi_union_pw_aff_involves_nan(
5151 __isl_keep isl_multi_union_pw_aff *mupa);
5153 #include <isl/polynomial.h>
5154 isl_bool isl_qpolynomial_is_nan(
5155 __isl_keep isl_qpolynomial *qp);
5156 isl_bool isl_qpolynomial_fold_is_nan(
5157 __isl_keep isl_qpolynomial_fold *fold);
5158 isl_bool isl_pw_qpolynomial_involves_nan(
5159 __isl_keep isl_pw_qpolynomial *pwqp);
5160 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5161 __isl_keep isl_pw_qpolynomial_fold *pwf);
5162 isl_bool isl_union_pw_qpolynomial_involves_nan(
5163 __isl_keep isl_union_pw_qpolynomial *upwqp);
5164 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5165 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5167 Check whether the given expression is equal to or involves NaN.
5169 #include <isl/val.h>
5170 isl_bool isl_multi_val_is_zero(
5171 __isl_keep isl_multi_val *mv);
5173 Check whether the multiple value is zero.
5175 #include <isl/aff.h>
5176 isl_bool isl_aff_plain_is_zero(
5177 __isl_keep isl_aff *aff);
5179 Check whether the affine expression is obviously zero.
5183 =head3 Binary Properties
5189 The following functions check whether two objects
5190 represent the same set, relation or function.
5191 The C<plain> variants only return true if the objects
5192 are obviously the same. That is, they may return false
5193 even if the objects are the same, but they will never
5194 return true if the objects are not the same.
5196 #include <isl/set.h>
5197 isl_bool isl_basic_set_plain_is_equal(
5198 __isl_keep isl_basic_set *bset1,
5199 __isl_keep isl_basic_set *bset2);
5200 isl_bool isl_basic_set_is_equal(
5201 __isl_keep isl_basic_set *bset1,
5202 __isl_keep isl_basic_set *bset2);
5203 isl_bool isl_set_plain_is_equal(
5204 __isl_keep isl_set *set1,
5205 __isl_keep isl_set *set2);
5206 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5207 __isl_keep isl_set *set2);
5209 #include <isl/map.h>
5210 isl_bool isl_basic_map_is_equal(
5211 __isl_keep isl_basic_map *bmap1,
5212 __isl_keep isl_basic_map *bmap2);
5213 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5214 __isl_keep isl_map *map2);
5215 isl_bool isl_map_plain_is_equal(
5216 __isl_keep isl_map *map1,
5217 __isl_keep isl_map *map2);
5219 #include <isl/union_set.h>
5220 isl_bool isl_union_set_is_equal(
5221 __isl_keep isl_union_set *uset1,
5222 __isl_keep isl_union_set *uset2);
5224 #include <isl/union_map.h>
5225 isl_bool isl_union_map_is_equal(
5226 __isl_keep isl_union_map *umap1,
5227 __isl_keep isl_union_map *umap2);
5230 isl_bool isl_multi_id_plain_is_equal(
5231 __isl_keep isl_multi_id *mi1,
5232 __isl_keep isl_multi_id *mi2);
5234 #include <isl/val.h>
5235 isl_bool isl_multi_val_plain_is_equal(
5236 __isl_keep isl_multi_val *mv1,
5237 __isl_keep isl_multi_val *mv2);
5239 #include <isl/aff.h>
5240 isl_bool isl_aff_plain_is_equal(
5241 __isl_keep isl_aff *aff1,
5242 __isl_keep isl_aff *aff2);
5243 isl_bool isl_multi_aff_plain_is_equal(
5244 __isl_keep isl_multi_aff *maff1,
5245 __isl_keep isl_multi_aff *maff2);
5246 isl_bool isl_pw_aff_plain_is_equal(
5247 __isl_keep isl_pw_aff *pwaff1,
5248 __isl_keep isl_pw_aff *pwaff2);
5249 isl_bool isl_pw_aff_is_equal(
5250 __isl_keep isl_pw_aff *pa1,
5251 __isl_keep isl_pw_aff *pa2);
5252 isl_bool isl_pw_multi_aff_plain_is_equal(
5253 __isl_keep isl_pw_multi_aff *pma1,
5254 __isl_keep isl_pw_multi_aff *pma2);
5255 isl_bool isl_pw_multi_aff_is_equal(
5256 __isl_keep isl_pw_multi_aff *pma1,
5257 __isl_keep isl_pw_multi_aff *pma2);
5258 isl_bool isl_multi_pw_aff_plain_is_equal(
5259 __isl_keep isl_multi_pw_aff *mpa1,
5260 __isl_keep isl_multi_pw_aff *mpa2);
5261 isl_bool isl_multi_pw_aff_is_equal(
5262 __isl_keep isl_multi_pw_aff *mpa1,
5263 __isl_keep isl_multi_pw_aff *mpa2);
5264 isl_bool isl_union_pw_aff_plain_is_equal(
5265 __isl_keep isl_union_pw_aff *upa1,
5266 __isl_keep isl_union_pw_aff *upa2);
5267 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5268 __isl_keep isl_union_pw_multi_aff *upma1,
5269 __isl_keep isl_union_pw_multi_aff *upma2);
5270 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5271 __isl_keep isl_multi_union_pw_aff *mupa1,
5272 __isl_keep isl_multi_union_pw_aff *mupa2);
5274 #include <isl/polynomial.h>
5275 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5276 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5277 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5278 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5279 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5280 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5282 =item * Disjointness
5284 #include <isl/set.h>
5285 isl_bool isl_basic_set_is_disjoint(
5286 __isl_keep isl_basic_set *bset1,
5287 __isl_keep isl_basic_set *bset2);
5288 isl_bool isl_set_plain_is_disjoint(
5289 __isl_keep isl_set *set1,
5290 __isl_keep isl_set *set2);
5291 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5292 __isl_keep isl_set *set2);
5294 #include <isl/map.h>
5295 isl_bool isl_basic_map_is_disjoint(
5296 __isl_keep isl_basic_map *bmap1,
5297 __isl_keep isl_basic_map *bmap2);
5298 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5299 __isl_keep isl_map *map2);
5301 #include <isl/union_set.h>
5302 isl_bool isl_union_set_is_disjoint(
5303 __isl_keep isl_union_set *uset1,
5304 __isl_keep isl_union_set *uset2);
5306 #include <isl/union_map.h>
5307 isl_bool isl_union_map_is_disjoint(
5308 __isl_keep isl_union_map *umap1,
5309 __isl_keep isl_union_map *umap2);
5313 isl_bool isl_basic_set_is_subset(
5314 __isl_keep isl_basic_set *bset1,
5315 __isl_keep isl_basic_set *bset2);
5316 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5317 __isl_keep isl_set *set2);
5318 isl_bool isl_set_is_strict_subset(
5319 __isl_keep isl_set *set1,
5320 __isl_keep isl_set *set2);
5321 isl_bool isl_union_set_is_subset(
5322 __isl_keep isl_union_set *uset1,
5323 __isl_keep isl_union_set *uset2);
5324 isl_bool isl_union_set_is_strict_subset(
5325 __isl_keep isl_union_set *uset1,
5326 __isl_keep isl_union_set *uset2);
5327 isl_bool isl_basic_map_is_subset(
5328 __isl_keep isl_basic_map *bmap1,
5329 __isl_keep isl_basic_map *bmap2);
5330 isl_bool isl_basic_map_is_strict_subset(
5331 __isl_keep isl_basic_map *bmap1,
5332 __isl_keep isl_basic_map *bmap2);
5333 isl_bool isl_map_is_subset(
5334 __isl_keep isl_map *map1,
5335 __isl_keep isl_map *map2);
5336 isl_bool isl_map_is_strict_subset(
5337 __isl_keep isl_map *map1,
5338 __isl_keep isl_map *map2);
5339 isl_bool isl_union_map_is_subset(
5340 __isl_keep isl_union_map *umap1,
5341 __isl_keep isl_union_map *umap2);
5342 isl_bool isl_union_map_is_strict_subset(
5343 __isl_keep isl_union_map *umap1,
5344 __isl_keep isl_union_map *umap2);
5346 Check whether the first argument is a (strict) subset of the
5351 Every comparison function returns a negative value if the first
5352 argument is considered smaller than the second, a positive value
5353 if the first argument is considered greater and zero if the two
5354 constraints are considered the same by the comparison criterion.
5356 #include <isl/constraint.h>
5357 int isl_constraint_plain_cmp(
5358 __isl_keep isl_constraint *c1,
5359 __isl_keep isl_constraint *c2);
5361 This function is useful for sorting C<isl_constraint>s.
5362 The order depends on the internal representation of the inputs.
5363 The order is fixed over different calls to the function (assuming
5364 the internal representation of the inputs has not changed), but may
5365 change over different versions of C<isl>.
5367 #include <isl/constraint.h>
5368 int isl_constraint_cmp_last_non_zero(
5369 __isl_keep isl_constraint *c1,
5370 __isl_keep isl_constraint *c2);
5372 This function can be used to sort constraints that live in the same
5373 local space. Constraints that involve ``earlier'' dimensions or
5374 that have a smaller coefficient for the shared latest dimension
5375 are considered smaller than other constraints.
5376 This function only defines a B<partial> order.
5378 #include <isl/set.h>
5379 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5380 __isl_keep isl_set *set2);
5382 This function is useful for sorting C<isl_set>s.
5383 The order depends on the internal representation of the inputs.
5384 The order is fixed over different calls to the function (assuming
5385 the internal representation of the inputs has not changed), but may
5386 change over different versions of C<isl>.
5388 #include <isl/aff.h>
5389 int isl_multi_aff_plain_cmp(
5390 __isl_keep isl_multi_aff *ma1,
5391 __isl_keep isl_multi_aff *ma2);
5392 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5393 __isl_keep isl_pw_aff *pa2);
5395 The functions C<isl_multi_aff_plain_cmp> and
5396 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5397 C<isl_pw_aff>s. The order is not strictly defined.
5398 The current order sorts expressions that only involve
5399 earlier dimensions before those that involve later dimensions.
5403 =head2 Unary Operations
5409 __isl_give isl_set *isl_set_complement(
5410 __isl_take isl_set *set);
5411 __isl_give isl_map *isl_map_complement(
5412 __isl_take isl_map *map);
5416 #include <isl/space.h>
5417 __isl_give isl_space *isl_space_reverse(
5418 __isl_take isl_space *space);
5419 __isl_give isl_space *isl_space_range_reverse(
5420 __isl_take isl_space *space);
5422 #include <isl/map.h>
5423 __isl_give isl_basic_map *isl_basic_map_reverse(
5424 __isl_take isl_basic_map *bmap);
5425 __isl_give isl_map *isl_map_reverse(
5426 __isl_take isl_map *map);
5427 __isl_give isl_map *isl_map_range_reverse(
5428 __isl_take isl_map *map);
5430 #include <isl/union_map.h>
5431 __isl_give isl_union_map *isl_union_map_reverse(
5432 __isl_take isl_union_map *umap);
5433 __isl_give isl_union_map *isl_union_map_range_reverse(
5434 __isl_take isl_union_map *umap);
5436 The function C<isl_space_range_reverse> reverses the relation
5437 that is embedded in the range of the input map space.
5438 The identifier of the range, if any, is only preserved
5439 if this embedded relation has identical input and output tuples.
5441 =item * Tuple binding
5443 The following function binds
5444 a tuple to a sequence of parameter identifiers, equating
5445 the tuple dimensions to the parameters with those identifiers and
5446 subsequently projecting out the tuple.
5447 If the original object did not reference any such parameters,
5448 then this means that the tuple dimensions are reinterpreted
5450 The space of C<tuple> needs to match that of the bound tuple.
5452 #include <isl/set.h>
5453 __isl_give isl_set *isl_set_bind(
5454 __isl_take isl_set *set,
5455 __isl_take isl_multi_id *tuple);
5457 #include <isl/map.h>
5458 __isl_give isl_set *isl_map_bind_domain(
5459 __isl_take isl_map *map,
5460 __isl_take isl_multi_id *tuple);
5461 __isl_give isl_set *isl_map_bind_range(
5462 __isl_take isl_map *map,
5463 __isl_take isl_multi_id *tuple);
5465 #include <isl/union_map.h>
5466 __isl_give isl_union_set *isl_union_map_bind_range(
5467 __isl_take isl_union_map *umap,
5468 __isl_take isl_multi_id *tuple);
5470 #include <isl/aff.h>
5471 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5472 __isl_take isl_pw_aff *pa,
5473 __isl_take isl_multi_id *tuple);
5474 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5475 __isl_take isl_multi_aff *ma,
5476 __isl_take isl_multi_id *tuple);
5477 __isl_give isl_pw_multi_aff *
5478 isl_pw_multi_aff_bind_domain(
5479 __isl_take isl_pw_multi_aff *pma,
5480 __isl_take isl_multi_id *tuple);
5481 __isl_give isl_multi_pw_aff *
5482 isl_multi_pw_aff_bind_domain(
5483 __isl_take isl_multi_pw_aff *mpa,
5484 __isl_take isl_multi_id *tuple);
5485 __isl_give isl_pw_aff *
5486 isl_pw_aff_bind_domain_wrapped_domain(
5487 __isl_take isl_pw_aff *pa,
5488 __isl_take isl_multi_id *tuple);
5489 __isl_give isl_multi_aff *
5490 isl_multi_aff_bind_domain_wrapped_domain(
5491 __isl_take isl_multi_aff *ma,
5492 __isl_take isl_multi_id *tuple);
5493 __isl_give isl_pw_multi_aff *
5494 isl_pw_multi_aff_bind_domain_wrapped_domain(
5495 __isl_take isl_pw_multi_aff *pma,
5496 __isl_take isl_multi_id *tuple);
5497 __isl_give isl_multi_pw_aff *
5498 isl_multi_pw_aff_bind_domain_wrapped_domain(
5499 __isl_take isl_multi_pw_aff *mpa,
5500 __isl_take isl_multi_id *tuple);
5501 __isl_give isl_basic_set *isl_aff_bind_id(
5502 __isl_take isl_aff *aff,
5503 __isl_take isl_id *id);
5504 __isl_give isl_set *isl_pw_aff_bind_id(
5505 __isl_take isl_pw_aff *pa,
5506 __isl_take isl_id *id);
5507 __isl_give isl_basic_set *isl_multi_aff_bind(
5508 __isl_take isl_multi_aff *ma,
5509 __isl_take isl_multi_id *tuple);
5510 __isl_give isl_set *isl_multi_pw_aff_bind(
5511 __isl_take isl_multi_pw_aff *mpa,
5512 __isl_take isl_multi_id *tuple);
5513 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5514 __isl_take isl_union_pw_aff *upa,
5515 __isl_take isl_id *id);
5516 __isl_give isl_union_set *
5517 isl_multi_union_pw_aff_bind(
5518 __isl_take isl_multi_union_pw_aff *mupa,
5519 __isl_take isl_multi_id *tuple);
5521 Projecting out the domain of the wrapped relation in the domain
5522 of a function leaves the range of that wrapped relation
5523 in the domain of the resulting function.
5524 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5525 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5526 C<isl_union_pw_aff_bind_id> and
5527 C<isl_multi_union_pw_aff_bind>, the parameters
5528 are bound to the function values and the result lives
5529 in the domain of the input function.
5533 #include <isl/space.h>
5534 __isl_give isl_space *isl_space_domain(
5535 __isl_take isl_space *space);
5536 __isl_give isl_space *isl_space_range(
5537 __isl_take isl_space *space);
5538 __isl_give isl_space *isl_space_params(
5539 __isl_take isl_space *space);
5540 __isl_give isl_space *
5541 isl_space_domain_wrapped_domain(
5542 __isl_take isl_space *space);
5543 __isl_give isl_space *
5544 isl_space_domain_wrapped_range(
5545 __isl_take isl_space *space);
5546 __isl_give isl_space *
5547 isl_space_range_wrapped_domain(
5548 __isl_take isl_space *space);
5549 __isl_give isl_space *
5550 isl_space_range_wrapped_range(
5551 __isl_take isl_space *space);
5553 #include <isl/local_space.h>
5554 __isl_give isl_local_space *isl_local_space_domain(
5555 __isl_take isl_local_space *ls);
5556 __isl_give isl_local_space *isl_local_space_range(
5557 __isl_take isl_local_space *ls);
5559 #include <isl/set.h>
5560 __isl_give isl_basic_set *isl_basic_set_project_out(
5561 __isl_take isl_basic_set *bset,
5562 enum isl_dim_type type, unsigned first, unsigned n);
5563 __isl_give isl_set *isl_set_project_out_param_id(
5564 __isl_take isl_set *set,
5565 __isl_take isl_id *id);
5566 __isl_give isl_set *
5567 isl_set_project_out_param_id_list(
5568 __isl_take isl_set *set,
5569 __isl_take isl_id_list *list);
5570 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5571 enum isl_dim_type type, unsigned first, unsigned n);
5572 __isl_give isl_set *isl_set_project_out_all_params(
5573 __isl_take isl_set *set);
5574 __isl_give isl_map *isl_set_project_onto_map(
5575 __isl_take isl_set *set,
5576 enum isl_dim_type type, unsigned first,
5578 __isl_give isl_basic_set *isl_basic_set_params(
5579 __isl_take isl_basic_set *bset);
5580 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5582 The function C<isl_space_domain_wrapped_domain> returns the domain
5583 of the binary relation wrapped inside the domain of the input.
5584 The function C<isl_set_project_onto_map> returns a relation
5585 that projects the input set onto the given set dimensions.
5587 #include <isl/map.h>
5588 __isl_give isl_basic_map *isl_basic_map_project_out(
5589 __isl_take isl_basic_map *bmap,
5590 enum isl_dim_type type, unsigned first, unsigned n);
5591 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5592 enum isl_dim_type type, unsigned first, unsigned n);
5593 __isl_give isl_map *isl_map_project_out_all_params(
5594 __isl_take isl_map *map);
5595 __isl_give isl_basic_set *isl_basic_map_domain(
5596 __isl_take isl_basic_map *bmap);
5597 __isl_give isl_basic_set *isl_basic_map_range(
5598 __isl_take isl_basic_map *bmap);
5599 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5600 __isl_give isl_set *isl_map_domain(
5601 __isl_take isl_map *bmap);
5602 __isl_give isl_set *isl_map_range(
5603 __isl_take isl_map *map);
5605 #include <isl/union_set.h>
5606 __isl_give isl_union_set *isl_union_set_project_out(
5607 __isl_take isl_union_set *uset,
5608 enum isl_dim_type type,
5609 unsigned first, unsigned n);
5610 __isl_give isl_union_set *
5611 isl_union_set_project_out_all_params(
5612 __isl_take isl_union_set *uset);
5613 __isl_give isl_set *isl_union_set_params(
5614 __isl_take isl_union_set *uset);
5616 The function C<isl_union_set_project_out> can only project out
5619 #include <isl/union_map.h>
5620 __isl_give isl_union_map *isl_union_map_project_out(
5621 __isl_take isl_union_map *umap,
5622 enum isl_dim_type type, unsigned first, unsigned n);
5623 __isl_give isl_union_map *
5624 isl_union_map_project_out_all_params(
5625 __isl_take isl_union_map *umap);
5626 __isl_give isl_set *isl_union_map_params(
5627 __isl_take isl_union_map *umap);
5628 __isl_give isl_union_set *isl_union_map_domain(
5629 __isl_take isl_union_map *umap);
5630 __isl_give isl_union_set *isl_union_map_range(
5631 __isl_take isl_union_map *umap);
5633 The function C<isl_union_map_project_out> can only project out
5636 #include <isl/aff.h>
5637 __isl_give isl_aff *isl_aff_project_domain_on_params(
5638 __isl_take isl_aff *aff);
5639 __isl_give isl_multi_aff *
5640 isl_multi_aff_project_domain_on_params(
5641 __isl_take isl_multi_aff *ma);
5642 __isl_give isl_pw_aff *
5643 isl_pw_aff_project_domain_on_params(
5644 __isl_take isl_pw_aff *pa);
5645 __isl_give isl_multi_pw_aff *
5646 isl_multi_pw_aff_project_domain_on_params(
5647 __isl_take isl_multi_pw_aff *mpa);
5648 __isl_give isl_pw_multi_aff *
5649 isl_pw_multi_aff_project_domain_on_params(
5650 __isl_take isl_pw_multi_aff *pma);
5651 __isl_give isl_set *isl_pw_aff_domain(
5652 __isl_take isl_pw_aff *pwaff);
5653 __isl_give isl_set *isl_pw_multi_aff_domain(
5654 __isl_take isl_pw_multi_aff *pma);
5655 __isl_give isl_set *isl_multi_pw_aff_domain(
5656 __isl_take isl_multi_pw_aff *mpa);
5657 __isl_give isl_union_set *isl_union_pw_aff_domain(
5658 __isl_take isl_union_pw_aff *upa);
5659 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5660 __isl_take isl_union_pw_multi_aff *upma);
5661 __isl_give isl_union_set *
5662 isl_multi_union_pw_aff_domain(
5663 __isl_take isl_multi_union_pw_aff *mupa);
5664 __isl_give isl_set *isl_pw_aff_params(
5665 __isl_take isl_pw_aff *pwa);
5667 If no explicit domain was set on a zero-dimensional input to
5668 C<isl_multi_union_pw_aff_domain>, then this function will
5669 return a parameter set.
5671 #include <isl/polynomial.h>
5672 __isl_give isl_qpolynomial *
5673 isl_qpolynomial_project_domain_on_params(
5674 __isl_take isl_qpolynomial *qp);
5675 __isl_give isl_pw_qpolynomial *
5676 isl_pw_qpolynomial_project_domain_on_params(
5677 __isl_take isl_pw_qpolynomial *pwqp);
5678 __isl_give isl_pw_qpolynomial_fold *
5679 isl_pw_qpolynomial_fold_project_domain_on_params(
5680 __isl_take isl_pw_qpolynomial_fold *pwf);
5681 __isl_give isl_set *isl_pw_qpolynomial_domain(
5682 __isl_take isl_pw_qpolynomial *pwqp);
5683 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5684 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5685 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5686 __isl_take isl_union_pw_qpolynomial *upwqp);
5688 #include <isl/space.h>
5689 __isl_give isl_space *isl_space_domain_map(
5690 __isl_take isl_space *space);
5691 __isl_give isl_space *isl_space_range_map(
5692 __isl_take isl_space *space);
5694 #include <isl/map.h>
5695 __isl_give isl_map *isl_set_wrapped_domain_map(
5696 __isl_take isl_set *set);
5697 __isl_give isl_basic_map *isl_basic_map_domain_map(
5698 __isl_take isl_basic_map *bmap);
5699 __isl_give isl_basic_map *isl_basic_map_range_map(
5700 __isl_take isl_basic_map *bmap);
5701 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5702 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5704 #include <isl/union_map.h>
5705 __isl_give isl_union_map *isl_union_map_domain_map(
5706 __isl_take isl_union_map *umap);
5707 __isl_give isl_union_pw_multi_aff *
5708 isl_union_map_domain_map_union_pw_multi_aff(
5709 __isl_take isl_union_map *umap);
5710 __isl_give isl_union_map *isl_union_map_range_map(
5711 __isl_take isl_union_map *umap);
5712 __isl_give isl_union_map *
5713 isl_union_set_wrapped_domain_map(
5714 __isl_take isl_union_set *uset);
5716 The functions above construct a (basic, regular or union) relation
5717 that maps (a wrapped version of) the input relation to its domain or range.
5718 C<isl_set_wrapped_domain_map> maps the input set to the domain
5719 of its wrapped relation.
5723 __isl_give isl_basic_set *isl_basic_set_eliminate(
5724 __isl_take isl_basic_set *bset,
5725 enum isl_dim_type type,
5726 unsigned first, unsigned n);
5727 __isl_give isl_set *isl_set_eliminate(
5728 __isl_take isl_set *set, enum isl_dim_type type,
5729 unsigned first, unsigned n);
5730 __isl_give isl_basic_map *isl_basic_map_eliminate(
5731 __isl_take isl_basic_map *bmap,
5732 enum isl_dim_type type,
5733 unsigned first, unsigned n);
5734 __isl_give isl_map *isl_map_eliminate(
5735 __isl_take isl_map *map, enum isl_dim_type type,
5736 unsigned first, unsigned n);
5738 Eliminate the coefficients for the given dimensions from the constraints,
5739 without removing the dimensions.
5741 =item * Constructing a set from a parameter domain
5743 A set space of a given dimension and with an optional name
5744 can be created from a parameter space using the following functions.
5746 #include <isl/space.h>
5747 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5748 __isl_take isl_space *space, unsigned dim);
5749 __isl_give isl_space *
5750 isl_space_add_named_tuple_id_ui(
5751 __isl_take isl_space *space,
5752 __isl_take isl_id *tuple_id, unsigned dim);
5754 A set with a given tuple can be created from a parameter domain
5755 using the following function.
5757 #include <isl/set.h>
5758 __isl_give isl_set *isl_set_unbind_params(
5759 __isl_take isl_set *set,
5760 __isl_take isl_multi_id *tuple);
5762 Any parameters with identifiers in C<tuple> are reinterpreted
5763 as the corresponding set dimensions.
5765 A zero-dimensional (local) space or (basic) set can be constructed
5766 on a given parameter domain using the following functions.
5768 #include <isl/space.h>
5769 __isl_give isl_space *isl_space_set_from_params(
5770 __isl_take isl_space *space);
5772 #include <isl/local_space.h>
5773 __isl_give isl_local_space *
5774 isl_local_space_set_from_params(
5775 __isl_take isl_local_space *ls);
5777 #include <isl/set.h>
5778 __isl_give isl_basic_set *isl_basic_set_from_params(
5779 __isl_take isl_basic_set *bset);
5780 __isl_give isl_set *isl_set_from_params(
5781 __isl_take isl_set *set);
5783 =item * Constructing a relation from one or two sets
5785 A map space with a range of a given dimension and with an optional name
5786 can be created from a domain space using the functions
5787 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5790 A relation with a given domain tuple can be created from a set
5791 that will become the range of the relation
5792 using the following function.
5794 #include <isl/set.h>
5795 __isl_give isl_map *
5796 isl_set_unbind_params_insert_domain(
5797 __isl_take isl_set *set,
5798 __isl_take isl_multi_id *domain);
5800 Any parameters with identifiers in C<domain> are reinterpreted
5801 as the corresponding input dimensions.
5803 Similarly, a function defined over a parameter domain can
5804 be converted into one defined over a set domain
5805 using the following functions.
5807 #include <isl/aff.h>
5808 __isl_give isl_aff *
5809 isl_aff_unbind_params_insert_domain(
5810 __isl_take isl_aff *aff,
5811 __isl_take isl_multi_id *domain);
5812 __isl_give isl_multi_aff *
5813 isl_multi_aff_unbind_params_insert_domain(
5814 __isl_take isl_multi_aff *ma,
5815 __isl_take isl_multi_id *domain);
5816 __isl_give isl_multi_pw_aff *
5817 isl_multi_pw_aff_unbind_params_insert_domain(
5818 __isl_take isl_multi_pw_aff *mpa,
5819 __isl_take isl_multi_id *domain);
5822 any parameters with identifiers in C<domain> are reinterpreted
5823 as the corresponding input dimensions.
5825 Create a relation with the given set(s) as domain and/or range.
5826 If only the domain or the range is specified, then
5827 the range or domain of the created relation is a zero-dimensional
5828 flat anonymous space.
5829 If the case of C<isl_space_map_from_set>, the input space
5830 specifies both the domain and the range of the result.
5832 #include <isl/space.h>
5833 __isl_give isl_space *isl_space_from_domain(
5834 __isl_take isl_space *space);
5835 __isl_give isl_space *isl_space_from_range(
5836 __isl_take isl_space *space);
5837 __isl_give isl_space *isl_space_map_from_set(
5838 __isl_take isl_space *space);
5839 __isl_give isl_space *isl_space_map_from_domain_and_range(
5840 __isl_take isl_space *domain,
5841 __isl_take isl_space *range);
5843 #include <isl/local_space.h>
5844 __isl_give isl_local_space *isl_local_space_from_domain(
5845 __isl_take isl_local_space *ls);
5847 #include <isl/map.h>
5848 __isl_give isl_map *isl_set_insert_domain(
5849 __isl_take isl_set *set,
5850 __isl_take isl_space *domain);
5851 __isl_give isl_map *isl_map_from_domain(
5852 __isl_take isl_set *set);
5853 __isl_give isl_map *isl_map_from_range(
5854 __isl_take isl_set *set);
5856 #include <isl/union_map.h>
5857 __isl_give isl_union_map *isl_union_map_from_domain(
5858 __isl_take isl_union_set *uset);
5859 __isl_give isl_union_map *isl_union_map_from_range(
5860 __isl_take isl_union_set *uset);
5861 __isl_give isl_union_map *
5862 isl_union_map_from_domain_and_range(
5863 __isl_take isl_union_set *domain,
5864 __isl_take isl_union_set *range);
5867 __isl_give isl_multi_id *isl_multi_id_from_range(
5868 __isl_take isl_multi_id *mi);
5870 #include <isl/val.h>
5871 __isl_give isl_multi_val *isl_multi_val_from_range(
5872 __isl_take isl_multi_val *mv);
5874 #include <isl/aff.h>
5875 __isl_give isl_multi_aff *
5876 isl_multi_aff_insert_domain(
5877 __isl_take isl_multi_aff *ma,
5878 __isl_take isl_space *domain);
5879 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5880 __isl_take isl_pw_aff *pa,
5881 __isl_take isl_space *domain);
5882 __isl_give isl_pw_multi_aff *
5883 isl_pw_multi_aff_insert_domain(
5884 __isl_take isl_pw_multi_aff *pma,
5885 __isl_take isl_space *domain);
5886 __isl_give isl_multi_pw_aff *
5887 isl_multi_pw_aff_insert_domain(
5888 __isl_take isl_multi_pw_aff *mpa,
5889 __isl_take isl_space *domain);
5890 __isl_give isl_aff *isl_aff_from_range(
5891 __isl_take isl_aff *aff);
5892 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5893 __isl_take isl_multi_aff *ma);
5894 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5895 __isl_take isl_pw_aff *pwa);
5896 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5897 __isl_take isl_multi_pw_aff *mpa);
5898 __isl_give isl_multi_union_pw_aff *
5899 isl_multi_union_pw_aff_from_range(
5900 __isl_take isl_multi_union_pw_aff *mupa);
5901 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5902 __isl_take isl_set *set);
5903 __isl_give isl_union_pw_multi_aff *
5904 isl_union_pw_multi_aff_from_domain(
5905 __isl_take isl_union_set *uset);
5907 #include <isl/polynomial.h>
5908 __isl_give isl_pw_qpolynomial *
5909 isl_pw_qpolynomial_from_range(
5910 __isl_take isl_pw_qpolynomial *pwqp);
5911 __isl_give isl_pw_qpolynomial_fold *
5912 isl_pw_qpolynomial_fold_from_range(
5913 __isl_take isl_pw_qpolynomial_fold *pwf);
5917 #include <isl/set.h>
5918 __isl_give isl_basic_set *isl_basic_set_fix_si(
5919 __isl_take isl_basic_set *bset,
5920 enum isl_dim_type type, unsigned pos, int value);
5921 __isl_give isl_basic_set *isl_basic_set_fix_val(
5922 __isl_take isl_basic_set *bset,
5923 enum isl_dim_type type, unsigned pos,
5924 __isl_take isl_val *v);
5925 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5926 enum isl_dim_type type, unsigned pos, int value);
5927 __isl_give isl_set *isl_set_fix_val(
5928 __isl_take isl_set *set,
5929 enum isl_dim_type type, unsigned pos,
5930 __isl_take isl_val *v);
5932 #include <isl/map.h>
5933 __isl_give isl_basic_map *isl_basic_map_fix_si(
5934 __isl_take isl_basic_map *bmap,
5935 enum isl_dim_type type, unsigned pos, int value);
5936 __isl_give isl_basic_map *isl_basic_map_fix_val(
5937 __isl_take isl_basic_map *bmap,
5938 enum isl_dim_type type, unsigned pos,
5939 __isl_take isl_val *v);
5940 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5941 enum isl_dim_type type, unsigned pos, int value);
5942 __isl_give isl_map *isl_map_fix_val(
5943 __isl_take isl_map *map,
5944 enum isl_dim_type type, unsigned pos,
5945 __isl_take isl_val *v);
5947 #include <isl/aff.h>
5948 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5949 __isl_take isl_pw_multi_aff *pma,
5950 enum isl_dim_type type, unsigned pos, int value);
5952 #include <isl/polynomial.h>
5953 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5954 __isl_take isl_pw_qpolynomial *pwqp,
5955 enum isl_dim_type type, unsigned n,
5956 __isl_take isl_val *v);
5957 __isl_give isl_pw_qpolynomial_fold *
5958 isl_pw_qpolynomial_fold_fix_val(
5959 __isl_take isl_pw_qpolynomial_fold *pwf,
5960 enum isl_dim_type type, unsigned n,
5961 __isl_take isl_val *v);
5963 Intersect the set, relation or function domain
5964 with the hyperplane where the given
5965 dimension has the fixed given value.
5967 #include <isl/set.h>
5968 __isl_give isl_basic_set *
5969 isl_basic_set_lower_bound_val(
5970 __isl_take isl_basic_set *bset,
5971 enum isl_dim_type type, unsigned pos,
5972 __isl_take isl_val *value);
5973 __isl_give isl_basic_set *
5974 isl_basic_set_upper_bound_val(
5975 __isl_take isl_basic_set *bset,
5976 enum isl_dim_type type, unsigned pos,
5977 __isl_take isl_val *value);
5978 __isl_give isl_set *isl_set_lower_bound_si(
5979 __isl_take isl_set *set,
5980 enum isl_dim_type type, unsigned pos, int value);
5981 __isl_give isl_set *isl_set_lower_bound_val(
5982 __isl_take isl_set *set,
5983 enum isl_dim_type type, unsigned pos,
5984 __isl_take isl_val *value);
5985 __isl_give isl_set *isl_set_upper_bound_si(
5986 __isl_take isl_set *set,
5987 enum isl_dim_type type, unsigned pos, int value);
5988 __isl_give isl_set *isl_set_upper_bound_val(
5989 __isl_take isl_set *set,
5990 enum isl_dim_type type, unsigned pos,
5991 __isl_take isl_val *value);
5992 __isl_give isl_set *isl_set_lower_bound_multi_val(
5993 __isl_take isl_set *set,
5994 __isl_take isl_multi_val *lower);
5995 __isl_give isl_set *isl_set_upper_bound_multi_val(
5996 __isl_take isl_set *set,
5997 __isl_take isl_multi_val *upper);
5998 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
5999 __isl_take isl_set *set,
6000 __isl_take isl_multi_pw_aff *lower);
6001 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6002 __isl_take isl_set *set,
6003 __isl_take isl_multi_pw_aff *upper);
6005 #include <isl/map.h>
6006 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6007 __isl_take isl_basic_map *bmap,
6008 enum isl_dim_type type, unsigned pos, int value);
6009 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6010 __isl_take isl_basic_map *bmap,
6011 enum isl_dim_type type, unsigned pos, int value);
6012 __isl_give isl_map *isl_map_lower_bound_si(
6013 __isl_take isl_map *map,
6014 enum isl_dim_type type, unsigned pos, int value);
6015 __isl_give isl_map *isl_map_upper_bound_si(
6016 __isl_take isl_map *map,
6017 enum isl_dim_type type, unsigned pos, int value);
6018 __isl_give isl_map *isl_map_lower_bound_val(
6019 __isl_take isl_map *map,
6020 enum isl_dim_type type, unsigned pos,
6021 __isl_take isl_val *value);
6022 __isl_give isl_map *isl_map_upper_bound_val(
6023 __isl_take isl_map *map,
6024 enum isl_dim_type type, unsigned pos,
6025 __isl_take isl_val *value);
6026 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6027 __isl_take isl_map *map,
6028 __isl_take isl_multi_pw_aff *lower);
6029 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6030 __isl_take isl_map *map,
6031 __isl_take isl_multi_pw_aff *upper);
6033 Intersect the set or relation with the half-space where the given
6034 dimension has a value bounded by the given fixed integer value or
6035 symbolic constant expression.
6036 For functions taking a multi expression,
6037 this applies to all set dimensions.
6038 Those that bound a map, bound the range of that map.
6039 If the multi expression is zero-dimensional but has an explicit domain,
6040 then the (parameter) domain of the set or map is intersected
6041 with this explicit domain.
6043 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6044 enum isl_dim_type type1, int pos1,
6045 enum isl_dim_type type2, int pos2);
6046 __isl_give isl_basic_map *isl_basic_map_equate(
6047 __isl_take isl_basic_map *bmap,
6048 enum isl_dim_type type1, int pos1,
6049 enum isl_dim_type type2, int pos2);
6050 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6051 enum isl_dim_type type1, int pos1,
6052 enum isl_dim_type type2, int pos2);
6054 Intersect the set or relation with the hyperplane where the given
6055 dimensions are equal to each other.
6057 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6058 enum isl_dim_type type1, int pos1,
6059 enum isl_dim_type type2, int pos2);
6061 Intersect the relation with the hyperplane where the given
6062 dimensions have opposite values.
6064 __isl_give isl_map *isl_map_order_le(
6065 __isl_take isl_map *map,
6066 enum isl_dim_type type1, int pos1,
6067 enum isl_dim_type type2, int pos2);
6068 __isl_give isl_basic_map *isl_basic_map_order_ge(
6069 __isl_take isl_basic_map *bmap,
6070 enum isl_dim_type type1, int pos1,
6071 enum isl_dim_type type2, int pos2);
6072 __isl_give isl_map *isl_map_order_ge(
6073 __isl_take isl_map *map,
6074 enum isl_dim_type type1, int pos1,
6075 enum isl_dim_type type2, int pos2);
6076 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6077 enum isl_dim_type type1, int pos1,
6078 enum isl_dim_type type2, int pos2);
6079 __isl_give isl_basic_map *isl_basic_map_order_gt(
6080 __isl_take isl_basic_map *bmap,
6081 enum isl_dim_type type1, int pos1,
6082 enum isl_dim_type type2, int pos2);
6083 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6084 enum isl_dim_type type1, int pos1,
6085 enum isl_dim_type type2, int pos2);
6087 Intersect the relation with the half-space where the given
6088 dimensions satisfy the given ordering.
6090 #include <isl/union_set.h>
6091 __isl_give isl_union_map *isl_union_map_remove_map_if(
6092 __isl_take isl_union_map *umap,
6093 isl_bool (*fn)(__isl_keep isl_map *map,
6094 void *user), void *user);
6096 This function calls the callback function once for each
6097 pair of spaces for which there are elements in the input.
6098 If the callback returns C<isl_bool_true>, then all those elements
6099 are removed from the result. The only remaining elements in the output
6100 are then those for which the callback returns C<isl_bool_false>.
6104 #include <isl/aff.h>
6105 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6106 __isl_take isl_aff *aff);
6107 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6108 __isl_take isl_aff *aff);
6109 __isl_give isl_set *isl_pw_aff_pos_set(
6110 __isl_take isl_pw_aff *pa);
6111 __isl_give isl_set *isl_pw_aff_nonneg_set(
6112 __isl_take isl_pw_aff *pwaff);
6113 __isl_give isl_set *isl_pw_aff_zero_set(
6114 __isl_take isl_pw_aff *pwaff);
6115 __isl_give isl_set *isl_pw_aff_non_zero_set(
6116 __isl_take isl_pw_aff *pwaff);
6117 __isl_give isl_union_set *
6118 isl_union_pw_aff_zero_union_set(
6119 __isl_take isl_union_pw_aff *upa);
6120 __isl_give isl_union_set *
6121 isl_multi_union_pw_aff_zero_union_set(
6122 __isl_take isl_multi_union_pw_aff *mupa);
6124 The function C<isl_aff_neg_basic_set> returns a basic set
6125 containing those elements in the domain space
6126 of C<aff> where C<aff> is negative.
6127 The function C<isl_pw_aff_nonneg_set> returns a set
6128 containing those elements in the domain
6129 of C<pwaff> where C<pwaff> is non-negative.
6130 The function C<isl_multi_union_pw_aff_zero_union_set>
6131 returns a union set containing those elements
6132 in the domains of its elements where they are all zero.
6136 __isl_give isl_map *isl_set_identity(
6137 __isl_take isl_set *set);
6138 __isl_give isl_union_map *isl_union_set_identity(
6139 __isl_take isl_union_set *uset);
6140 __isl_give isl_union_pw_multi_aff *
6141 isl_union_set_identity_union_pw_multi_aff(
6142 __isl_take isl_union_set *uset);
6144 Construct an identity relation on the given (union) set.
6146 =item * Function Extraction
6148 A piecewise quasi affine expression that is equal to 1 on a set
6149 and 0 outside the set can be created using the following function.
6151 #include <isl/aff.h>
6152 __isl_give isl_pw_aff *isl_set_indicator_function(
6153 __isl_take isl_set *set);
6155 A piecewise multiple quasi affine expression can be extracted
6156 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6157 and the C<isl_map> is single-valued.
6158 In case of a conversion from an C<isl_union_map>
6159 to an C<isl_union_pw_multi_aff>, these properties need to hold
6160 in each domain space.
6161 A conversion to a C<isl_multi_union_pw_aff> additionally
6162 requires that the input is non-empty and involves only a single
6165 #include <isl/aff.h>
6166 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6167 __isl_take isl_set *set);
6168 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6169 __isl_take isl_set *set);
6170 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6171 __isl_take isl_map *map);
6172 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6173 __isl_take isl_map *map);
6175 __isl_give isl_union_pw_multi_aff *
6176 isl_union_pw_multi_aff_from_union_set(
6177 __isl_take isl_union_set *uset);
6178 __isl_give isl_union_pw_multi_aff *
6179 isl_union_map_as_union_pw_multi_aff(
6180 __isl_take isl_union_map *umap);
6181 __isl_give isl_union_pw_multi_aff *
6182 isl_union_pw_multi_aff_from_union_map(
6183 __isl_take isl_union_map *umap);
6185 __isl_give isl_multi_union_pw_aff *
6186 isl_union_map_as_multi_union_pw_aff(
6187 __isl_take isl_union_map *umap);
6188 __isl_give isl_multi_union_pw_aff *
6189 isl_multi_union_pw_aff_from_union_map(
6190 __isl_take isl_union_map *umap);
6192 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6194 Similarly for C<isl_set_as_pw_multi_aff> and
6195 C<isl_pw_multi_aff_from_set>,
6196 for C<isl_union_map_as_union_pw_multi_aff> and
6197 C<isl_union_pw_multi_aff_from_union_map> and
6198 for C<isl_union_map_as_multi_union_pw_aff> and
6199 C<isl_multi_union_pw_aff_from_union_map>.
6203 __isl_give isl_basic_set *isl_basic_map_deltas(
6204 __isl_take isl_basic_map *bmap);
6205 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6206 __isl_give isl_union_set *isl_union_map_deltas(
6207 __isl_take isl_union_map *umap);
6209 These functions return a (basic) set containing the differences
6210 between image elements and corresponding domain elements in the input.
6212 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6213 __isl_take isl_basic_map *bmap);
6214 __isl_give isl_map *isl_map_deltas_map(
6215 __isl_take isl_map *map);
6216 __isl_give isl_union_map *isl_union_map_deltas_map(
6217 __isl_take isl_union_map *umap);
6219 The functions above construct a (basic, regular or union) relation
6220 that maps (a wrapped version of) the input relation to its delta set.
6224 #include <isl/map.h>
6225 __isl_give isl_map *isl_set_translation(
6226 __isl_take isl_set *deltas);
6228 This function performs essentially the opposite operation
6229 of C<isl_map_deltas>. In particular, it returns pairs
6230 of elements in the same space that have a difference in C<deltas>.
6234 Simplify the representation of a set, relation or functions by trying
6235 to combine pairs of basic sets or relations into a single
6236 basic set or relation.
6238 #include <isl/set.h>
6239 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6241 #include <isl/map.h>
6242 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6244 #include <isl/union_set.h>
6245 __isl_give isl_union_set *isl_union_set_coalesce(
6246 __isl_take isl_union_set *uset);
6248 #include <isl/union_map.h>
6249 __isl_give isl_union_map *isl_union_map_coalesce(
6250 __isl_take isl_union_map *umap);
6252 #include <isl/aff.h>
6253 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6254 __isl_take isl_pw_aff *pa);
6255 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6256 __isl_take isl_pw_multi_aff *pma);
6257 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6258 __isl_take isl_multi_pw_aff *mpa);
6259 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6260 __isl_take isl_union_pw_aff *upa);
6261 __isl_give isl_union_pw_multi_aff *
6262 isl_union_pw_multi_aff_coalesce(
6263 __isl_take isl_union_pw_multi_aff *upma);
6264 __isl_give isl_multi_union_pw_aff *
6265 isl_multi_union_pw_aff_coalesce(
6266 __isl_take isl_multi_union_pw_aff *mupa);
6268 #include <isl/polynomial.h>
6269 __isl_give isl_pw_qpolynomial_fold *
6270 isl_pw_qpolynomial_fold_coalesce(
6271 __isl_take isl_pw_qpolynomial_fold *pwf);
6272 __isl_give isl_union_pw_qpolynomial *
6273 isl_union_pw_qpolynomial_coalesce(
6274 __isl_take isl_union_pw_qpolynomial *upwqp);
6275 __isl_give isl_union_pw_qpolynomial_fold *
6276 isl_union_pw_qpolynomial_fold_coalesce(
6277 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6279 One of the methods for combining pairs of basic sets or relations
6280 can result in coefficients that are much larger than those that appear
6281 in the constraints of the input. By default, the coefficients are
6282 not allowed to grow larger, but this can be changed by unsetting
6283 the following option.
6285 isl_stat isl_options_set_coalesce_bounded_wrapping(
6286 isl_ctx *ctx, int val);
6287 int isl_options_get_coalesce_bounded_wrapping(
6290 One of the other methods tries to combine pairs of basic sets
6291 with different local variables, treating them as existentially
6292 quantified variables even if they have known (but different)
6293 integer division expressions. The result may then also have
6294 existentially quantified variables. Turning on the following
6295 option prevents this from happening.
6297 isl_stat isl_options_set_coalesce_preserve_locals(
6298 isl_ctx *ctx, int val);
6299 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6301 =item * Detecting equalities
6303 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6304 __isl_take isl_basic_set *bset);
6305 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6306 __isl_take isl_basic_map *bmap);
6307 __isl_give isl_set *isl_set_detect_equalities(
6308 __isl_take isl_set *set);
6309 __isl_give isl_map *isl_map_detect_equalities(
6310 __isl_take isl_map *map);
6311 __isl_give isl_union_set *isl_union_set_detect_equalities(
6312 __isl_take isl_union_set *uset);
6313 __isl_give isl_union_map *isl_union_map_detect_equalities(
6314 __isl_take isl_union_map *umap);
6316 Simplify the representation of a set or relation by detecting implicit
6319 =item * Removing redundant constraints
6321 #include <isl/set.h>
6322 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6323 __isl_take isl_basic_set *bset);
6324 __isl_give isl_set *isl_set_remove_redundancies(
6325 __isl_take isl_set *set);
6327 #include <isl/union_set.h>
6328 __isl_give isl_union_set *
6329 isl_union_set_remove_redundancies(
6330 __isl_take isl_union_set *uset);
6332 #include <isl/map.h>
6333 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6334 __isl_take isl_basic_map *bmap);
6335 __isl_give isl_map *isl_map_remove_redundancies(
6336 __isl_take isl_map *map);
6338 #include <isl/union_map.h>
6339 __isl_give isl_union_map *
6340 isl_union_map_remove_redundancies(
6341 __isl_take isl_union_map *umap);
6345 __isl_give isl_basic_set *isl_set_convex_hull(
6346 __isl_take isl_set *set);
6347 __isl_give isl_basic_map *isl_map_convex_hull(
6348 __isl_take isl_map *map);
6350 If the input set or relation has any existentially quantified
6351 variables, then the result of these operations is currently undefined.
6355 #include <isl/set.h>
6356 __isl_give isl_basic_set *
6357 isl_set_unshifted_simple_hull(
6358 __isl_take isl_set *set);
6359 __isl_give isl_basic_set *isl_set_simple_hull(
6360 __isl_take isl_set *set);
6361 __isl_give isl_basic_set *
6362 isl_set_plain_unshifted_simple_hull(
6363 __isl_take isl_set *set);
6364 __isl_give isl_basic_set *
6365 isl_set_unshifted_simple_hull_from_set_list(
6366 __isl_take isl_set *set,
6367 __isl_take isl_set_list *list);
6369 #include <isl/map.h>
6370 __isl_give isl_basic_map *
6371 isl_map_unshifted_simple_hull(
6372 __isl_take isl_map *map);
6373 __isl_give isl_basic_map *isl_map_simple_hull(
6374 __isl_take isl_map *map);
6375 __isl_give isl_basic_map *
6376 isl_map_plain_unshifted_simple_hull(
6377 __isl_take isl_map *map);
6378 __isl_give isl_basic_map *
6379 isl_map_unshifted_simple_hull_from_map_list(
6380 __isl_take isl_map *map,
6381 __isl_take isl_map_list *list);
6383 #include <isl/union_map.h>
6384 __isl_give isl_union_map *isl_union_map_simple_hull(
6385 __isl_take isl_union_map *umap);
6387 These functions compute a single basic set or relation
6388 that contains the whole input set or relation.
6389 In particular, the output is described by translates
6390 of the constraints describing the basic sets or relations in the input.
6391 In case of C<isl_set_unshifted_simple_hull>, only the original
6392 constraints are used, without any translation.
6393 In case of C<isl_set_plain_unshifted_simple_hull> and
6394 C<isl_map_plain_unshifted_simple_hull>, the result is described
6395 by original constraints that are obviously satisfied
6396 by the entire input set or relation.
6397 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6398 C<isl_map_unshifted_simple_hull_from_map_list>, the
6399 constraints are taken from the elements of the second argument.
6403 (See \autoref{s:simple hull}.)
6409 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6410 __isl_take isl_basic_set *bset);
6411 __isl_give isl_basic_set *isl_set_affine_hull(
6412 __isl_take isl_set *set);
6413 __isl_give isl_union_set *isl_union_set_affine_hull(
6414 __isl_take isl_union_set *uset);
6415 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6416 __isl_take isl_basic_map *bmap);
6417 __isl_give isl_basic_map *isl_map_affine_hull(
6418 __isl_take isl_map *map);
6419 __isl_give isl_union_map *isl_union_map_affine_hull(
6420 __isl_take isl_union_map *umap);
6422 In case of union sets and relations, the affine hull is computed
6425 =item * Polyhedral hull
6427 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6428 __isl_take isl_set *set);
6429 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6430 __isl_take isl_map *map);
6431 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6432 __isl_take isl_union_set *uset);
6433 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6434 __isl_take isl_union_map *umap);
6436 These functions compute a single basic set or relation
6437 not involving any existentially quantified variables
6438 that contains the whole input set or relation.
6439 In case of union sets and relations, the polyhedral hull is computed
6444 #include <isl/set.h>
6445 __isl_give isl_fixed_box *
6446 isl_set_get_simple_fixed_box_hull(
6447 __isl_keep isl_set *set)
6449 #include <isl/map.h>
6450 __isl_give isl_fixed_box *
6451 isl_map_get_range_simple_fixed_box_hull(
6452 __isl_keep isl_map *map);
6454 These functions try to approximate the set or
6455 the range of the map by a box of fixed size.
6456 The box is described in terms of an offset living in the same space as
6457 the input and a size living in the set or range space. For any element
6458 in the input map, the range value is greater than or equal to
6459 the offset applied to the domain value and the difference with
6460 this offset is strictly smaller than the size.
6461 The same holds for the elements of the input set, where
6462 the offset is a parametric constant value.
6463 If no fixed-size approximation can be found,
6464 an I<invalid> box is returned, i.e., one for which
6465 C<isl_fixed_box_is_valid> below returns false.
6467 The validity, the offset and the size of the box can be obtained using
6468 the following functions.
6470 #include <isl/fixed_box.h>
6471 isl_bool isl_fixed_box_is_valid(
6472 __isl_keep isl_fixed_box *box);
6473 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6474 __isl_keep isl_fixed_box *box);
6475 __isl_give isl_multi_val *isl_fixed_box_get_size(
6476 __isl_keep isl_fixed_box *box);
6478 The box can be copied and freed using the following functions.
6480 #include <isl/fixed_box.h>
6481 __isl_give isl_fixed_box *isl_fixed_box_copy(
6482 __isl_keep isl_fixed_box *box);
6483 __isl_null isl_fixed_box *isl_fixed_box_free(
6484 __isl_take isl_fixed_box *box);
6486 A representation of the information contained in an object
6487 of type C<isl_fixed_box> can be obtained using
6489 #include <isl/fixed_box.h>
6490 __isl_give isl_printer *isl_printer_print_fixed_box(
6491 __isl_take isl_printer *p,
6492 __isl_keep isl_fixed_box *box);
6493 __isl_give char *isl_fixed_box_to_str(
6494 __isl_keep isl_fixed_box *box);
6496 C<isl_fixed_box_to_str> prints the information in flow format.
6498 =item * Other approximations
6500 #include <isl/set.h>
6501 __isl_give isl_basic_set *
6502 isl_basic_set_drop_constraints_involving_dims(
6503 __isl_take isl_basic_set *bset,
6504 enum isl_dim_type type,
6505 unsigned first, unsigned n);
6506 __isl_give isl_basic_set *
6507 isl_basic_set_drop_constraints_not_involving_dims(
6508 __isl_take isl_basic_set *bset,
6509 enum isl_dim_type type,
6510 unsigned first, unsigned n);
6511 __isl_give isl_set *
6512 isl_set_drop_constraints_involving_dims(
6513 __isl_take isl_set *set,
6514 enum isl_dim_type type,
6515 unsigned first, unsigned n);
6516 __isl_give isl_set *
6517 isl_set_drop_constraints_not_involving_dims(
6518 __isl_take isl_set *set,
6519 enum isl_dim_type type,
6520 unsigned first, unsigned n);
6522 #include <isl/map.h>
6523 __isl_give isl_basic_map *
6524 isl_basic_map_drop_constraints_involving_dims(
6525 __isl_take isl_basic_map *bmap,
6526 enum isl_dim_type type,
6527 unsigned first, unsigned n);
6528 __isl_give isl_basic_map *
6529 isl_basic_map_drop_constraints_not_involving_dims(
6530 __isl_take isl_basic_map *bmap,
6531 enum isl_dim_type type,
6532 unsigned first, unsigned n);
6533 __isl_give isl_map *
6534 isl_map_drop_constraints_involving_dims(
6535 __isl_take isl_map *map,
6536 enum isl_dim_type type,
6537 unsigned first, unsigned n);
6538 __isl_give isl_map *
6539 isl_map_drop_constraints_not_involving_dims(
6540 __isl_take isl_map *map,
6541 enum isl_dim_type type,
6542 unsigned first, unsigned n);
6544 These functions drop any constraints (not) involving the specified dimensions.
6545 Note that the result depends on the representation of the input.
6547 #include <isl/polynomial.h>
6548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6549 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6550 __isl_give isl_union_pw_qpolynomial *
6551 isl_union_pw_qpolynomial_to_polynomial(
6552 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6554 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6555 the polynomial will be an overapproximation. If C<sign> is negative,
6556 it will be an underapproximation. If C<sign> is zero, the approximation
6557 will lie somewhere in between.
6561 __isl_give isl_basic_set *isl_basic_set_sample(
6562 __isl_take isl_basic_set *bset);
6563 __isl_give isl_basic_set *isl_set_sample(
6564 __isl_take isl_set *set);
6565 __isl_give isl_basic_map *isl_basic_map_sample(
6566 __isl_take isl_basic_map *bmap);
6567 __isl_give isl_basic_map *isl_map_sample(
6568 __isl_take isl_map *map);
6570 If the input (basic) set or relation is non-empty, then return
6571 a singleton subset of the input. Otherwise, return an empty set.
6573 =item * Optimization
6575 #include <isl/ilp.h>
6576 __isl_give isl_val *isl_basic_set_max_val(
6577 __isl_keep isl_basic_set *bset,
6578 __isl_keep isl_aff *obj);
6579 __isl_give isl_val *isl_set_min_val(
6580 __isl_keep isl_set *set,
6581 __isl_keep isl_aff *obj);
6582 __isl_give isl_val *isl_set_max_val(
6583 __isl_keep isl_set *set,
6584 __isl_keep isl_aff *obj);
6585 __isl_give isl_multi_val *
6586 isl_union_set_min_multi_union_pw_aff(
6587 __isl_keep isl_union_set *uset,
6588 __isl_keep isl_multi_union_pw_aff *obj);
6590 Compute the minimum or maximum of the integer affine expression C<obj>
6591 over the points in C<set>.
6592 The result is C<NULL> in case of an error, the optimal value in case
6593 there is one, negative infinity or infinity if the problem is unbounded and
6594 NaN if the problem is empty.
6596 #include <isl/ilp.h>
6597 __isl_give isl_val *isl_pw_aff_min_val(
6598 __isl_take isl_pw_aff *pa);
6599 __isl_give isl_val *isl_pw_aff_max_val(
6600 __isl_take isl_pw_aff *pa);
6601 __isl_give isl_multi_val *
6602 isl_pw_multi_aff_min_multi_val(
6603 __isl_take isl_pw_multi_aff *pma);
6604 __isl_give isl_multi_val *
6605 isl_pw_multi_aff_max_multi_val(
6606 __isl_take isl_pw_multi_aff *pma);
6607 __isl_give isl_multi_val *
6608 isl_multi_pw_aff_min_multi_val(
6609 __isl_take isl_multi_pw_aff *mpa);
6610 __isl_give isl_multi_val *
6611 isl_multi_pw_aff_max_multi_val(
6612 __isl_take isl_multi_pw_aff *mpa);
6613 __isl_give isl_val *isl_union_pw_aff_min_val(
6614 __isl_take isl_union_pw_aff *upa);
6615 __isl_give isl_val *isl_union_pw_aff_max_val(
6616 __isl_take isl_union_pw_aff *upa);
6617 __isl_give isl_multi_val *
6618 isl_multi_union_pw_aff_min_multi_val(
6619 __isl_take isl_multi_union_pw_aff *mupa);
6620 __isl_give isl_multi_val *
6621 isl_multi_union_pw_aff_max_multi_val(
6622 __isl_take isl_multi_union_pw_aff *mupa);
6624 Compute the minimum or maximum of the integer affine expression
6625 over its definition domain.
6626 The result is C<NULL> in case of an error, the optimal value in case
6627 there is one, negative infinity or infinity if the problem is unbounded and
6628 NaN if the problem is empty.
6630 #include <isl/ilp.h>
6631 __isl_give isl_val *isl_basic_set_dim_max_val(
6632 __isl_take isl_basic_set *bset, int pos);
6633 __isl_give isl_val *isl_set_dim_min_val(
6634 __isl_take isl_set *set, int pos);
6635 __isl_give isl_val *isl_set_dim_max_val(
6636 __isl_take isl_set *set, int pos);
6638 Return the minimal or maximal value attained by the given set dimension,
6639 independently of the parameter values and of any other dimensions.
6640 The result is C<NULL> in case of an error, the optimal value in case
6641 there is one, (negative) infinity if the problem is unbounded and
6642 NaN if the input is empty.
6644 =item * Parametric optimization
6646 __isl_give isl_pw_aff *isl_set_dim_min(
6647 __isl_take isl_set *set, int pos);
6648 __isl_give isl_pw_aff *isl_set_dim_max(
6649 __isl_take isl_set *set, int pos);
6650 __isl_give isl_pw_aff *isl_map_dim_min(
6651 __isl_take isl_map *map, int pos);
6652 __isl_give isl_pw_aff *isl_map_dim_max(
6653 __isl_take isl_map *map, int pos);
6654 __isl_give isl_multi_pw_aff *
6655 isl_set_min_multi_pw_aff(
6656 __isl_take isl_set *set);
6657 __isl_give isl_multi_pw_aff *
6658 isl_set_max_multi_pw_aff(
6659 __isl_take isl_set *set);
6660 __isl_give isl_multi_pw_aff *
6661 isl_map_min_multi_pw_aff(
6662 __isl_take isl_map *map);
6663 __isl_give isl_multi_pw_aff *
6664 isl_map_max_multi_pw_aff(
6665 __isl_take isl_map *map);
6667 Compute the minimum or maximum of the (given) set or output dimension(s)
6668 as a function of the parameters (and input dimensions), but independently
6669 of the other set or output dimensions.
6670 For lexicographic optimization, see L<"Lexicographic Optimization">.
6674 The following functions compute either the set of (rational) coefficient
6675 values of valid constraints for the given set or the set of (rational)
6676 values satisfying the constraints with coefficients from the given set.
6677 Internally, these two sets of functions perform essentially the
6678 same operations, except that the set of coefficients is assumed to
6679 be a cone, while the set of values may be any polyhedron.
6680 The current implementation is based on the Farkas lemma and
6681 Fourier-Motzkin elimination, but this may change or be made optional
6682 in future. In particular, future implementations may use different
6683 dualization algorithms or skip the elimination step.
6685 #include <isl/set.h>
6686 __isl_give isl_basic_set *isl_basic_set_coefficients(
6687 __isl_take isl_basic_set *bset);
6688 __isl_give isl_basic_set_list *
6689 isl_basic_set_list_coefficients(
6690 __isl_take isl_basic_set_list *list);
6691 __isl_give isl_basic_set *isl_set_coefficients(
6692 __isl_take isl_set *set);
6693 __isl_give isl_union_set *isl_union_set_coefficients(
6694 __isl_take isl_union_set *bset);
6695 __isl_give isl_basic_set *isl_basic_set_solutions(
6696 __isl_take isl_basic_set *bset);
6697 __isl_give isl_basic_set *isl_set_solutions(
6698 __isl_take isl_set *set);
6699 __isl_give isl_union_set *isl_union_set_solutions(
6700 __isl_take isl_union_set *bset);
6704 __isl_give isl_map *isl_map_fixed_power_val(
6705 __isl_take isl_map *map,
6706 __isl_take isl_val *exp);
6707 __isl_give isl_union_map *
6708 isl_union_map_fixed_power_val(
6709 __isl_take isl_union_map *umap,
6710 __isl_take isl_val *exp);
6712 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6713 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6714 of C<map> is computed.
6716 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6718 __isl_give isl_union_map *isl_union_map_power(
6719 __isl_take isl_union_map *umap, isl_bool *exact);
6721 Compute a parametric representation for all positive powers I<k> of C<map>.
6722 The result maps I<k> to a nested relation corresponding to the
6723 I<k>th power of C<map>.
6724 The result may be an overapproximation. If the result is known to be exact,
6725 then C<*exact> is set to C<1>.
6727 =item * Transitive closure
6729 __isl_give isl_map *isl_map_transitive_closure(
6730 __isl_take isl_map *map, isl_bool *exact);
6731 __isl_give isl_union_map *isl_union_map_transitive_closure(
6732 __isl_take isl_union_map *umap, isl_bool *exact);
6734 Compute the transitive closure of C<map>.
6735 The result may be an overapproximation. If the result is known to be exact,
6736 then C<*exact> is set to C<1>.
6738 =item * Reaching path lengths
6740 __isl_give isl_map *isl_map_reaching_path_lengths(
6741 __isl_take isl_map *map, isl_bool *exact);
6743 Compute a relation that maps each element in the range of C<map>
6744 to the lengths of all paths composed of edges in C<map> that
6745 end up in the given element.
6746 The result may be an overapproximation. If the result is known to be exact,
6747 then C<*exact> is set to C<1>.
6748 To compute the I<maximal> path length, the resulting relation
6749 should be postprocessed by C<isl_map_lexmax>.
6750 In particular, if the input relation is a dependence relation
6751 (mapping sources to sinks), then the maximal path length corresponds
6752 to the free schedule.
6753 Note, however, that C<isl_map_lexmax> expects the maximum to be
6754 finite, so if the path lengths are unbounded (possibly due to
6755 the overapproximation), then you will get an error message.
6759 #include <isl/space.h>
6760 __isl_give isl_space *isl_space_wrap(
6761 __isl_take isl_space *space);
6762 __isl_give isl_space *isl_space_unwrap(
6763 __isl_take isl_space *space);
6765 #include <isl/local_space.h>
6766 __isl_give isl_local_space *isl_local_space_wrap(
6767 __isl_take isl_local_space *ls);
6769 #include <isl/set.h>
6770 __isl_give isl_basic_map *isl_basic_set_unwrap(
6771 __isl_take isl_basic_set *bset);
6772 __isl_give isl_map *isl_set_unwrap(
6773 __isl_take isl_set *set);
6775 #include <isl/map.h>
6776 __isl_give isl_basic_set *isl_basic_map_wrap(
6777 __isl_take isl_basic_map *bmap);
6778 __isl_give isl_set *isl_map_wrap(
6779 __isl_take isl_map *map);
6781 #include <isl/union_set.h>
6782 __isl_give isl_union_map *isl_union_set_unwrap(
6783 __isl_take isl_union_set *uset);
6785 #include <isl/union_map.h>
6786 __isl_give isl_union_set *isl_union_map_wrap(
6787 __isl_take isl_union_map *umap);
6789 The input to C<isl_space_unwrap> should
6790 be the space of a set, while that of
6791 C<isl_space_wrap> should be the space of a relation.
6792 Conversely, the output of C<isl_space_unwrap> is the space
6793 of a relation, while that of C<isl_space_wrap> is the space of a set.
6797 Remove any internal structure of domain (and range) of the given
6798 set or relation. If there is any such internal structure in the input,
6799 then the name of the space is also removed.
6801 #include <isl/space.h>
6802 __isl_give isl_space *isl_space_flatten_domain(
6803 __isl_take isl_space *space);
6804 __isl_give isl_space *isl_space_flatten_range(
6805 __isl_take isl_space *space);
6807 #include <isl/local_space.h>
6808 __isl_give isl_local_space *
6809 isl_local_space_flatten_domain(
6810 __isl_take isl_local_space *ls);
6811 __isl_give isl_local_space *
6812 isl_local_space_flatten_range(
6813 __isl_take isl_local_space *ls);
6815 #include <isl/set.h>
6816 __isl_give isl_basic_set *isl_basic_set_flatten(
6817 __isl_take isl_basic_set *bset);
6818 __isl_give isl_set *isl_set_flatten(
6819 __isl_take isl_set *set);
6821 #include <isl/map.h>
6822 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6823 __isl_take isl_basic_map *bmap);
6824 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6825 __isl_take isl_basic_map *bmap);
6826 __isl_give isl_map *isl_map_flatten_range(
6827 __isl_take isl_map *map);
6828 __isl_give isl_map *isl_map_flatten_domain(
6829 __isl_take isl_map *map);
6830 __isl_give isl_basic_map *isl_basic_map_flatten(
6831 __isl_take isl_basic_map *bmap);
6832 __isl_give isl_map *isl_map_flatten(
6833 __isl_take isl_map *map);
6836 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6837 __isl_take isl_multi_id *mi);
6839 #include <isl/val.h>
6840 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6841 __isl_take isl_multi_val *mv);
6843 #include <isl/aff.h>
6844 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6845 __isl_take isl_multi_aff *ma);
6846 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6847 __isl_take isl_multi_aff *ma);
6848 __isl_give isl_multi_pw_aff *
6849 isl_multi_pw_aff_flatten_range(
6850 __isl_take isl_multi_pw_aff *mpa);
6851 __isl_give isl_multi_union_pw_aff *
6852 isl_multi_union_pw_aff_flatten_range(
6853 __isl_take isl_multi_union_pw_aff *mupa);
6855 #include <isl/map.h>
6856 __isl_give isl_map *isl_set_flatten_map(
6857 __isl_take isl_set *set);
6859 The function above constructs a relation
6860 that maps the input set to a flattened version of the set.
6864 Lift the input set to a space with extra dimensions corresponding
6865 to the existentially quantified variables in the input.
6866 In particular, the result lives in a wrapped map where the domain
6867 is the original space and the range corresponds to the original
6868 existentially quantified variables.
6870 #include <isl/set.h>
6871 __isl_give isl_basic_set *isl_basic_set_lift(
6872 __isl_take isl_basic_set *bset);
6873 __isl_give isl_set *isl_set_lift(
6874 __isl_take isl_set *set);
6875 __isl_give isl_union_set *isl_union_set_lift(
6876 __isl_take isl_union_set *uset);
6878 Given a local space that contains the existentially quantified
6879 variables of a set, a basic relation that, when applied to
6880 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6881 can be constructed using the following function.
6883 #include <isl/local_space.h>
6884 __isl_give isl_basic_map *isl_local_space_lifting(
6885 __isl_take isl_local_space *ls);
6887 #include <isl/aff.h>
6888 __isl_give isl_multi_aff *isl_multi_aff_lift(
6889 __isl_take isl_multi_aff *maff,
6890 __isl_give isl_local_space **ls);
6892 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6893 then it is assigned the local space that lies at the basis of
6894 the lifting applied.
6896 =item * Internal Product
6898 #include <isl/space.h>
6899 __isl_give isl_space *isl_space_zip(
6900 __isl_take isl_space *space);
6902 #include <isl/map.h>
6903 __isl_give isl_basic_map *isl_basic_map_zip(
6904 __isl_take isl_basic_map *bmap);
6905 __isl_give isl_map *isl_map_zip(
6906 __isl_take isl_map *map);
6908 #include <isl/union_map.h>
6909 __isl_give isl_union_map *isl_union_map_zip(
6910 __isl_take isl_union_map *umap);
6912 Given a relation with nested relations for domain and range,
6913 interchange the range of the domain with the domain of the range.
6917 #include <isl/space.h>
6918 __isl_give isl_space *isl_space_curry(
6919 __isl_take isl_space *space);
6920 __isl_give isl_space *isl_space_uncurry(
6921 __isl_take isl_space *space);
6923 #include <isl/map.h>
6924 __isl_give isl_basic_map *isl_basic_map_curry(
6925 __isl_take isl_basic_map *bmap);
6926 __isl_give isl_basic_map *isl_basic_map_uncurry(
6927 __isl_take isl_basic_map *bmap);
6928 __isl_give isl_map *isl_map_curry(
6929 __isl_take isl_map *map);
6930 __isl_give isl_map *isl_map_uncurry(
6931 __isl_take isl_map *map);
6933 #include <isl/union_map.h>
6934 __isl_give isl_union_map *isl_union_map_curry(
6935 __isl_take isl_union_map *umap);
6936 __isl_give isl_union_map *isl_union_map_uncurry(
6937 __isl_take isl_union_map *umap);
6939 Given a relation with a nested relation for domain,
6940 the C<curry> functions
6941 move the range of the nested relation out of the domain
6942 and use it as the domain of a nested relation in the range,
6943 with the original range as range of this nested relation.
6944 The C<uncurry> functions perform the inverse operation.
6946 #include <isl/space.h>
6947 __isl_give isl_space *isl_space_range_curry(
6948 __isl_take isl_space *space);
6950 #include <isl/map.h>
6951 __isl_give isl_map *isl_map_range_curry(
6952 __isl_take isl_map *map);
6954 #include <isl/union_map.h>
6955 __isl_give isl_union_map *isl_union_map_range_curry(
6956 __isl_take isl_union_map *umap);
6958 These functions apply the currying to the relation that
6959 is nested inside the range of the input.
6961 =item * Aligning parameters
6963 Change the order of the parameters of the given set, relation
6965 such that the first parameters match those of C<model>.
6966 This may involve the introduction of extra parameters.
6967 All parameters need to be named.
6969 #include <isl/space.h>
6970 __isl_give isl_space *isl_space_align_params(
6971 __isl_take isl_space *space1,
6972 __isl_take isl_space *space2)
6974 #include <isl/set.h>
6975 __isl_give isl_basic_set *isl_basic_set_align_params(
6976 __isl_take isl_basic_set *bset,
6977 __isl_take isl_space *model);
6978 __isl_give isl_set *isl_set_align_params(
6979 __isl_take isl_set *set,
6980 __isl_take isl_space *model);
6982 #include <isl/map.h>
6983 __isl_give isl_basic_map *isl_basic_map_align_params(
6984 __isl_take isl_basic_map *bmap,
6985 __isl_take isl_space *model);
6986 __isl_give isl_map *isl_map_align_params(
6987 __isl_take isl_map *map,
6988 __isl_take isl_space *model);
6991 __isl_give isl_multi_id *isl_multi_id_align_params(
6992 __isl_take isl_multi_id *mi,
6993 __isl_take isl_space *model);
6995 #include <isl/val.h>
6996 __isl_give isl_multi_val *isl_multi_val_align_params(
6997 __isl_take isl_multi_val *mv,
6998 __isl_take isl_space *model);
7000 #include <isl/aff.h>
7001 __isl_give isl_aff *isl_aff_align_params(
7002 __isl_take isl_aff *aff,
7003 __isl_take isl_space *model);
7004 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7005 __isl_take isl_multi_aff *multi,
7006 __isl_take isl_space *model);
7007 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7008 __isl_take isl_pw_aff *pwaff,
7009 __isl_take isl_space *model);
7010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7011 __isl_take isl_pw_multi_aff *pma,
7012 __isl_take isl_space *model);
7013 __isl_give isl_union_pw_aff *
7014 isl_union_pw_aff_align_params(
7015 __isl_take isl_union_pw_aff *upa,
7016 __isl_take isl_space *model);
7017 __isl_give isl_union_pw_multi_aff *
7018 isl_union_pw_multi_aff_align_params(
7019 __isl_take isl_union_pw_multi_aff *upma,
7020 __isl_take isl_space *model);
7021 __isl_give isl_multi_union_pw_aff *
7022 isl_multi_union_pw_aff_align_params(
7023 __isl_take isl_multi_union_pw_aff *mupa,
7024 __isl_take isl_space *model);
7026 #include <isl/polynomial.h>
7027 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7028 __isl_take isl_qpolynomial *qp,
7029 __isl_take isl_space *model);
7031 =item * Drop unused parameters
7033 Drop parameters that are not referenced by the isl object.
7034 All parameters need to be named.
7036 #include <isl/set.h>
7037 __isl_give isl_basic_set *
7038 isl_basic_set_drop_unused_params(
7039 __isl_take isl_basic_set *bset);
7040 __isl_give isl_set *isl_set_drop_unused_params(
7041 __isl_take isl_set *set);
7043 #include <isl/map.h>
7044 __isl_give isl_basic_map *
7045 isl_basic_map_drop_unused_params(
7046 __isl_take isl_basic_map *bmap);
7047 __isl_give isl_map *isl_map_drop_unused_params(
7048 __isl_take isl_map *map);
7050 #include <isl/aff.h>
7051 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7052 __isl_take isl_pw_aff *pa);
7053 __isl_give isl_pw_multi_aff *
7054 isl_pw_multi_aff_drop_unused_params(
7055 __isl_take isl_pw_multi_aff *pma);
7057 #include <isl/polynomial.h>
7058 __isl_give isl_pw_qpolynomial *
7059 isl_pw_qpolynomial_drop_unused_params(
7060 __isl_take isl_pw_qpolynomial *pwqp);
7061 __isl_give isl_pw_qpolynomial_fold *
7062 isl_pw_qpolynomial_fold_drop_unused_params(
7063 __isl_take isl_pw_qpolynomial_fold *pwf);
7065 =item * Unary Arithmetic Operations
7067 #include <isl/set.h>
7068 __isl_give isl_set *isl_set_neg(
7069 __isl_take isl_set *set);
7070 #include <isl/map.h>
7071 __isl_give isl_map *isl_map_neg(
7072 __isl_take isl_map *map);
7074 C<isl_set_neg> constructs a set containing the opposites of
7075 the elements in its argument.
7076 The domain of the result of C<isl_map_neg> is the same
7077 as the domain of its argument. The corresponding range
7078 elements are the opposites of the corresponding range
7079 elements in the argument.
7081 #include <isl/val.h>
7082 __isl_give isl_multi_val *isl_multi_val_neg(
7083 __isl_take isl_multi_val *mv);
7085 #include <isl/aff.h>
7086 __isl_give isl_aff *isl_aff_neg(
7087 __isl_take isl_aff *aff);
7088 __isl_give isl_multi_aff *isl_multi_aff_neg(
7089 __isl_take isl_multi_aff *ma);
7090 __isl_give isl_pw_aff *isl_pw_aff_neg(
7091 __isl_take isl_pw_aff *pwaff);
7092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7093 __isl_take isl_pw_multi_aff *pma);
7094 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7095 __isl_take isl_multi_pw_aff *mpa);
7096 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7097 __isl_take isl_union_pw_aff *upa);
7098 __isl_give isl_union_pw_multi_aff *
7099 isl_union_pw_multi_aff_neg(
7100 __isl_take isl_union_pw_multi_aff *upma);
7101 __isl_give isl_multi_union_pw_aff *
7102 isl_multi_union_pw_aff_neg(
7103 __isl_take isl_multi_union_pw_aff *mupa);
7104 __isl_give isl_aff *isl_aff_ceil(
7105 __isl_take isl_aff *aff);
7106 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7107 __isl_take isl_pw_aff *pwaff);
7108 __isl_give isl_aff *isl_aff_floor(
7109 __isl_take isl_aff *aff);
7110 __isl_give isl_multi_aff *isl_multi_aff_floor(
7111 __isl_take isl_multi_aff *ma);
7112 __isl_give isl_pw_aff *isl_pw_aff_floor(
7113 __isl_take isl_pw_aff *pwaff);
7114 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7115 __isl_take isl_union_pw_aff *upa);
7116 __isl_give isl_multi_union_pw_aff *
7117 isl_multi_union_pw_aff_floor(
7118 __isl_take isl_multi_union_pw_aff *mupa);
7120 #include <isl/aff.h>
7121 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7122 __isl_take isl_pw_aff_list *list);
7123 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7124 __isl_take isl_pw_aff_list *list);
7126 #include <isl/polynomial.h>
7127 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7128 __isl_take isl_qpolynomial *qp);
7129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7130 __isl_take isl_pw_qpolynomial *pwqp);
7131 __isl_give isl_union_pw_qpolynomial *
7132 isl_union_pw_qpolynomial_neg(
7133 __isl_take isl_union_pw_qpolynomial *upwqp);
7134 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7135 __isl_take isl_qpolynomial *qp,
7137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7138 __isl_take isl_pw_qpolynomial *pwqp,
7143 The following functions evaluate a function in a point.
7145 #include <isl/aff.h>
7146 __isl_give isl_val *isl_aff_eval(
7147 __isl_take isl_aff *aff,
7148 __isl_take isl_point *pnt);
7149 __isl_give isl_val *isl_pw_aff_eval(
7150 __isl_take isl_pw_aff *pa,
7151 __isl_take isl_point *pnt);
7153 #include <isl/polynomial.h>
7154 __isl_give isl_val *isl_pw_qpolynomial_eval(
7155 __isl_take isl_pw_qpolynomial *pwqp,
7156 __isl_take isl_point *pnt);
7157 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7158 __isl_take isl_pw_qpolynomial_fold *pwf,
7159 __isl_take isl_point *pnt);
7160 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7161 __isl_take isl_union_pw_qpolynomial *upwqp,
7162 __isl_take isl_point *pnt);
7163 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7164 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7165 __isl_take isl_point *pnt);
7167 These functions return NaN when evaluated at a void point.
7168 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7169 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7170 when the function is evaluated outside its explicit domain.
7172 =item * Dimension manipulation
7174 It is usually not advisable to directly change the (input or output)
7175 space of a set or a relation as this removes the name and the internal
7176 structure of the space. However, the functions below can be useful
7177 to add new parameters, assuming
7178 C<isl_set_align_params> and C<isl_map_align_params>
7181 #include <isl/space.h>
7182 __isl_give isl_space *isl_space_add_dims(
7183 __isl_take isl_space *space,
7184 enum isl_dim_type type, unsigned n);
7185 __isl_give isl_space *isl_space_insert_dims(
7186 __isl_take isl_space *space,
7187 enum isl_dim_type type, unsigned pos, unsigned n);
7188 __isl_give isl_space *isl_space_drop_dims(
7189 __isl_take isl_space *space,
7190 enum isl_dim_type type, unsigned first, unsigned n);
7191 __isl_give isl_space *isl_space_move_dims(
7192 __isl_take isl_space *space,
7193 enum isl_dim_type dst_type, unsigned dst_pos,
7194 enum isl_dim_type src_type, unsigned src_pos,
7197 #include <isl/local_space.h>
7198 __isl_give isl_local_space *isl_local_space_add_dims(
7199 __isl_take isl_local_space *ls,
7200 enum isl_dim_type type, unsigned n);
7201 __isl_give isl_local_space *isl_local_space_insert_dims(
7202 __isl_take isl_local_space *ls,
7203 enum isl_dim_type type, unsigned first, unsigned n);
7204 __isl_give isl_local_space *isl_local_space_drop_dims(
7205 __isl_take isl_local_space *ls,
7206 enum isl_dim_type type, unsigned first, unsigned n);
7208 #include <isl/set.h>
7209 __isl_give isl_basic_set *isl_basic_set_add_dims(
7210 __isl_take isl_basic_set *bset,
7211 enum isl_dim_type type, unsigned n);
7212 __isl_give isl_set *isl_set_add_dims(
7213 __isl_take isl_set *set,
7214 enum isl_dim_type type, unsigned n);
7215 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7216 __isl_take isl_basic_set *bset,
7217 enum isl_dim_type type, unsigned pos,
7219 __isl_give isl_set *isl_set_insert_dims(
7220 __isl_take isl_set *set,
7221 enum isl_dim_type type, unsigned pos, unsigned n);
7222 __isl_give isl_basic_set *isl_basic_set_move_dims(
7223 __isl_take isl_basic_set *bset,
7224 enum isl_dim_type dst_type, unsigned dst_pos,
7225 enum isl_dim_type src_type, unsigned src_pos,
7227 __isl_give isl_set *isl_set_move_dims(
7228 __isl_take isl_set *set,
7229 enum isl_dim_type dst_type, unsigned dst_pos,
7230 enum isl_dim_type src_type, unsigned src_pos,
7233 #include <isl/map.h>
7234 __isl_give isl_basic_map *isl_basic_map_add_dims(
7235 __isl_take isl_basic_map *bmap,
7236 enum isl_dim_type type, unsigned n);
7237 __isl_give isl_map *isl_map_add_dims(
7238 __isl_take isl_map *map,
7239 enum isl_dim_type type, unsigned n);
7240 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7241 __isl_take isl_basic_map *bmap,
7242 enum isl_dim_type type, unsigned pos,
7244 __isl_give isl_map *isl_map_insert_dims(
7245 __isl_take isl_map *map,
7246 enum isl_dim_type type, unsigned pos, unsigned n);
7247 __isl_give isl_basic_map *isl_basic_map_move_dims(
7248 __isl_take isl_basic_map *bmap,
7249 enum isl_dim_type dst_type, unsigned dst_pos,
7250 enum isl_dim_type src_type, unsigned src_pos,
7252 __isl_give isl_map *isl_map_move_dims(
7253 __isl_take isl_map *map,
7254 enum isl_dim_type dst_type, unsigned dst_pos,
7255 enum isl_dim_type src_type, unsigned src_pos,
7258 #include <isl/val.h>
7259 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7260 __isl_take isl_multi_val *mv,
7261 enum isl_dim_type type, unsigned first, unsigned n);
7262 __isl_give isl_multi_val *isl_multi_val_add_dims(
7263 __isl_take isl_multi_val *mv,
7264 enum isl_dim_type type, unsigned n);
7265 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7266 __isl_take isl_multi_val *mv,
7267 enum isl_dim_type type, unsigned first, unsigned n);
7269 #include <isl/aff.h>
7270 __isl_give isl_aff *isl_aff_insert_dims(
7271 __isl_take isl_aff *aff,
7272 enum isl_dim_type type, unsigned first, unsigned n);
7273 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7274 __isl_take isl_multi_aff *ma,
7275 enum isl_dim_type type, unsigned first, unsigned n);
7276 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7277 __isl_take isl_pw_aff *pwaff,
7278 enum isl_dim_type type, unsigned first, unsigned n);
7279 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7280 __isl_take isl_multi_pw_aff *mpa,
7281 enum isl_dim_type type, unsigned first, unsigned n);
7282 __isl_give isl_aff *isl_aff_add_dims(
7283 __isl_take isl_aff *aff,
7284 enum isl_dim_type type, unsigned n);
7285 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7286 __isl_take isl_multi_aff *ma,
7287 enum isl_dim_type type, unsigned n);
7288 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7289 __isl_take isl_pw_aff *pwaff,
7290 enum isl_dim_type type, unsigned n);
7291 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7292 __isl_take isl_multi_pw_aff *mpa,
7293 enum isl_dim_type type, unsigned n);
7294 __isl_give isl_aff *isl_aff_drop_dims(
7295 __isl_take isl_aff *aff,
7296 enum isl_dim_type type, unsigned first, unsigned n);
7297 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7298 __isl_take isl_multi_aff *maff,
7299 enum isl_dim_type type, unsigned first, unsigned n);
7300 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7301 __isl_take isl_pw_aff *pwaff,
7302 enum isl_dim_type type, unsigned first, unsigned n);
7303 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7304 __isl_take isl_pw_multi_aff *pma,
7305 enum isl_dim_type type, unsigned first, unsigned n);
7306 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7307 __isl_take isl_union_pw_aff *upa,
7308 enum isl_dim_type type, unsigned first, unsigned n);
7309 __isl_give isl_union_pw_multi_aff *
7310 isl_union_pw_multi_aff_drop_dims(
7311 __isl_take isl_union_pw_multi_aff *upma,
7312 enum isl_dim_type type,
7313 unsigned first, unsigned n);
7314 __isl_give isl_multi_union_pw_aff *
7315 isl_multi_union_pw_aff_drop_dims(
7316 __isl_take isl_multi_union_pw_aff *mupa,
7317 enum isl_dim_type type, unsigned first,
7319 __isl_give isl_aff *isl_aff_move_dims(
7320 __isl_take isl_aff *aff,
7321 enum isl_dim_type dst_type, unsigned dst_pos,
7322 enum isl_dim_type src_type, unsigned src_pos,
7324 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7325 __isl_take isl_multi_aff *ma,
7326 enum isl_dim_type dst_type, unsigned dst_pos,
7327 enum isl_dim_type src_type, unsigned src_pos,
7329 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7330 __isl_take isl_pw_aff *pa,
7331 enum isl_dim_type dst_type, unsigned dst_pos,
7332 enum isl_dim_type src_type, unsigned src_pos,
7334 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7335 __isl_take isl_multi_pw_aff *pma,
7336 enum isl_dim_type dst_type, unsigned dst_pos,
7337 enum isl_dim_type src_type, unsigned src_pos,
7340 #include <isl/polynomial.h>
7341 __isl_give isl_union_pw_qpolynomial *
7342 isl_union_pw_qpolynomial_drop_dims(
7343 __isl_take isl_union_pw_qpolynomial *upwqp,
7344 enum isl_dim_type type,
7345 unsigned first, unsigned n);
7346 __isl_give isl_union_pw_qpolynomial_fold *
7347 isl_union_pw_qpolynomial_fold_drop_dims(
7348 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7349 enum isl_dim_type type,
7350 unsigned first, unsigned n);
7352 The operations on union expressions can only manipulate parameters.
7356 =head2 Binary Operations
7358 The two arguments of a binary operation not only need to live
7359 in the same C<isl_ctx>, they currently also need to have
7360 the same (number of) parameters.
7362 =head3 Basic Operations
7366 =item * Intersection
7368 #include <isl/local_space.h>
7369 __isl_give isl_local_space *isl_local_space_intersect(
7370 __isl_take isl_local_space *ls1,
7371 __isl_take isl_local_space *ls2);
7373 #include <isl/set.h>
7374 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7375 __isl_take isl_basic_set *bset1,
7376 __isl_take isl_basic_set *bset2);
7377 __isl_give isl_basic_set *isl_basic_set_intersect(
7378 __isl_take isl_basic_set *bset1,
7379 __isl_take isl_basic_set *bset2);
7380 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7381 __isl_take struct isl_basic_set_list *list);
7382 __isl_give isl_set *isl_set_intersect_params(
7383 __isl_take isl_set *set,
7384 __isl_take isl_set *params);
7385 __isl_give isl_set *isl_set_intersect(
7386 __isl_take isl_set *set1,
7387 __isl_take isl_set *set2);
7388 __isl_give isl_set *isl_set_intersect_factor_domain(
7389 __isl_take isl_set *set,
7390 __isl_take isl_set *domain);
7391 __isl_give isl_set *isl_set_intersect_factor_range(
7392 __isl_take isl_set *set,
7393 __isl_take isl_set *range);
7395 #include <isl/map.h>
7396 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7397 __isl_take isl_basic_map *bmap,
7398 __isl_take isl_basic_set *bset);
7399 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7400 __isl_take isl_basic_map *bmap,
7401 __isl_take isl_basic_set *bset);
7402 __isl_give isl_basic_map *isl_basic_map_intersect(
7403 __isl_take isl_basic_map *bmap1,
7404 __isl_take isl_basic_map *bmap2);
7405 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7406 __isl_take isl_basic_map_list *list);
7407 __isl_give isl_map *isl_map_intersect_params(
7408 __isl_take isl_map *map,
7409 __isl_take isl_set *params);
7410 __isl_give isl_map *isl_map_intersect_domain(
7411 __isl_take isl_map *map,
7412 __isl_take isl_set *set);
7413 __isl_give isl_map *isl_map_intersect_range(
7414 __isl_take isl_map *map,
7415 __isl_take isl_set *set);
7416 __isl_give isl_map *isl_map_intersect(
7417 __isl_take isl_map *map1,
7418 __isl_take isl_map *map2);
7419 __isl_give isl_map *
7420 isl_map_intersect_domain_factor_domain(
7421 __isl_take isl_map *map,
7422 __isl_take isl_map *factor);
7423 __isl_give isl_map *
7424 isl_map_intersect_domain_factor_range(
7425 __isl_take isl_map *map,
7426 __isl_take isl_map *factor);
7427 __isl_give isl_map *
7428 isl_map_intersect_range_factor_domain(
7429 __isl_take isl_map *map,
7430 __isl_take isl_map *factor);
7431 __isl_give isl_map *
7432 isl_map_intersect_range_factor_range(
7433 __isl_take isl_map *map,
7434 __isl_take isl_map *factor);
7435 __isl_give isl_map *
7436 isl_map_intersect_domain_wrapped_domain(
7437 __isl_take isl_map *map,
7438 __isl_take isl_set *domain);
7439 __isl_give isl_map *
7440 isl_map_intersect_range_wrapped_domain(
7441 __isl_take isl_map *map,
7442 __isl_take isl_set *domain);
7444 #include <isl/union_set.h>
7445 __isl_give isl_union_set *isl_union_set_intersect_params(
7446 __isl_take isl_union_set *uset,
7447 __isl_take isl_set *set);
7448 __isl_give isl_union_set *isl_union_set_intersect(
7449 __isl_take isl_union_set *uset1,
7450 __isl_take isl_union_set *uset2);
7452 #include <isl/union_map.h>
7453 __isl_give isl_union_map *isl_union_map_intersect_params(
7454 __isl_take isl_union_map *umap,
7455 __isl_take isl_set *set);
7456 __isl_give isl_union_map *
7457 isl_union_map_intersect_domain_union_set(
7458 __isl_take isl_union_map *umap,
7459 __isl_take isl_union_set *uset);
7460 __isl_give isl_union_map *
7461 isl_union_map_intersect_domain_space(
7462 __isl_take isl_union_map *umap,
7463 __isl_take isl_space *space);
7464 __isl_give isl_union_map *isl_union_map_intersect_domain(
7465 __isl_take isl_union_map *umap,
7466 __isl_take isl_union_set *uset);
7467 __isl_give isl_union_map *
7468 isl_union_map_intersect_range_union_set(
7469 __isl_take isl_union_map *umap,
7470 __isl_take isl_union_set *uset);
7471 __isl_give isl_union_map *
7472 isl_union_map_intersect_range_space(
7473 __isl_take isl_union_map *umap,
7474 __isl_take isl_space *space);
7475 __isl_give isl_union_map *isl_union_map_intersect_range(
7476 __isl_take isl_union_map *umap,
7477 __isl_take isl_union_set *uset);
7478 __isl_give isl_union_map *isl_union_map_intersect(
7479 __isl_take isl_union_map *umap1,
7480 __isl_take isl_union_map *umap2);
7481 __isl_give isl_union_map *
7482 isl_union_map_intersect_domain_factor_domain(
7483 __isl_take isl_union_map *umap,
7484 __isl_take isl_union_map *factor);
7485 __isl_give isl_union_map *
7486 isl_union_map_intersect_domain_factor_range(
7487 __isl_take isl_union_map *umap,
7488 __isl_take isl_union_map *factor);
7489 __isl_give isl_union_map *
7490 isl_union_map_intersect_range_factor_domain(
7491 __isl_take isl_union_map *umap,
7492 __isl_take isl_union_map *factor);
7493 __isl_give isl_union_map *
7494 isl_union_map_intersect_range_factor_range(
7495 __isl_take isl_union_map *umap,
7496 __isl_take isl_union_map *factor);
7497 __isl_give isl_union_map *
7498 isl_union_map_intersect_domain_wrapped_domain_union_set(
7499 __isl_take isl_union_map *umap,
7500 __isl_take isl_union_set *domain);
7501 __isl_give isl_union_map *
7502 isl_union_map_intersect_range_wrapped_domain_union_set(
7503 __isl_take isl_union_map *umap,
7504 __isl_take isl_union_set *domain);
7506 #include <isl/aff.h>
7507 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7508 __isl_take isl_pw_aff *pa,
7509 __isl_take isl_set *set);
7510 __isl_give isl_multi_pw_aff *
7511 isl_multi_pw_aff_intersect_domain(
7512 __isl_take isl_multi_pw_aff *mpa,
7513 __isl_take isl_set *domain);
7514 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7515 __isl_take isl_pw_multi_aff *pma,
7516 __isl_take isl_set *set);
7517 __isl_give isl_union_pw_aff *
7518 isl_union_pw_aff_intersect_domain_space(
7519 __isl_take isl_union_pw_aff *upa,
7520 __isl_take isl_space *space);
7521 __isl_give isl_union_pw_aff *
7522 isl_union_pw_aff_intersect_domain_union_set(
7523 __isl_take isl_union_pw_aff *upa,
7524 __isl_take isl_union_set *uset);
7525 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7526 __isl_take isl_union_pw_aff *upa,
7527 __isl_take isl_union_set *uset);
7528 __isl_give isl_union_pw_multi_aff *
7529 isl_union_pw_multi_aff_intersect_domain_space(
7530 __isl_take isl_union_pw_multi_aff *upma,
7531 __isl_take isl_space *space);
7532 __isl_give isl_union_pw_multi_aff *
7533 isl_union_pw_multi_aff_intersect_domain_union_set(
7534 __isl_take isl_union_pw_multi_aff *upma,
7535 __isl_take isl_union_set *uset);
7536 __isl_give isl_union_pw_multi_aff *
7537 isl_union_pw_multi_aff_intersect_domain(
7538 __isl_take isl_union_pw_multi_aff *upma,
7539 __isl_take isl_union_set *uset);
7540 __isl_give isl_multi_union_pw_aff *
7541 isl_multi_union_pw_aff_intersect_domain(
7542 __isl_take isl_multi_union_pw_aff *mupa,
7543 __isl_take isl_union_set *uset);
7544 __isl_give isl_pw_aff *
7545 isl_pw_aff_intersect_domain_wrapped_domain(
7546 __isl_take isl_pw_aff *pa,
7547 __isl_take isl_set *set);
7548 __isl_give isl_pw_multi_aff *
7549 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7550 __isl_take isl_pw_multi_aff *pma,
7551 __isl_take isl_set *set);
7552 __isl_give isl_union_pw_aff *
7553 isl_union_pw_aff_intersect_domain_wrapped_domain(
7554 __isl_take isl_union_pw_aff *upa,
7555 __isl_take isl_union_set *uset);
7556 __isl_give isl_union_pw_multi_aff *
7557 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7558 __isl_take isl_union_pw_multi_aff *upma,
7559 __isl_take isl_union_set *uset);
7560 __isl_give isl_pw_aff *
7561 isl_pw_aff_intersect_domain_wrapped_range(
7562 __isl_take isl_pw_aff *pa,
7563 __isl_take isl_set *set);
7564 __isl_give isl_pw_multi_aff *
7565 isl_pw_multi_aff_intersect_domain_wrapped_range(
7566 __isl_take isl_pw_multi_aff *pma,
7567 __isl_take isl_set *set);
7568 __isl_give isl_union_pw_multi_aff *
7569 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7570 __isl_take isl_union_pw_multi_aff *upma,
7571 __isl_take isl_union_set *uset);
7572 __isl_give isl_union_pw_aff *
7573 isl_union_pw_aff_intersect_domain_wrapped_range(
7574 __isl_take isl_union_pw_aff *upa,
7575 __isl_take isl_union_set *uset);
7576 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7577 __isl_take isl_pw_aff *pa,
7578 __isl_take isl_set *set);
7579 __isl_give isl_multi_pw_aff *
7580 isl_multi_pw_aff_intersect_params(
7581 __isl_take isl_multi_pw_aff *mpa,
7582 __isl_take isl_set *set);
7583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7584 __isl_take isl_pw_multi_aff *pma,
7585 __isl_take isl_set *set);
7586 __isl_give isl_union_pw_aff *
7587 isl_union_pw_aff_intersect_params(
7588 __isl_take isl_union_pw_aff *upa,
7589 __isl_take isl_set *set);
7590 __isl_give isl_union_pw_multi_aff *
7591 isl_union_pw_multi_aff_intersect_params(
7592 __isl_take isl_union_pw_multi_aff *upma,
7593 __isl_take isl_set *set);
7594 __isl_give isl_multi_union_pw_aff *
7595 isl_multi_union_pw_aff_intersect_params(
7596 __isl_take isl_multi_union_pw_aff *mupa,
7597 __isl_take isl_set *params);
7598 __isl_give isl_multi_union_pw_aff *
7599 isl_multi_union_pw_aff_intersect_range(
7600 __isl_take isl_multi_union_pw_aff *mupa,
7601 __isl_take isl_set *set);
7603 #include <isl/polynomial.h>
7604 __isl_give isl_pw_qpolynomial *
7605 isl_pw_qpolynomial_intersect_domain(
7606 __isl_take isl_pw_qpolynomial *pwpq,
7607 __isl_take isl_set *set);
7608 __isl_give isl_union_pw_qpolynomial *
7609 isl_union_pw_qpolynomial_intersect_domain_space(
7610 __isl_take isl_union_pw_qpolynomial *upwpq,
7611 __isl_take isl_space *space);
7612 __isl_give isl_union_pw_qpolynomial *
7613 isl_union_pw_qpolynomial_intersect_domain_union_set(
7614 __isl_take isl_union_pw_qpolynomial *upwpq,
7615 __isl_take isl_union_set *uset);
7616 __isl_give isl_union_pw_qpolynomial *
7617 isl_union_pw_qpolynomial_intersect_domain(
7618 __isl_take isl_union_pw_qpolynomial *upwpq,
7619 __isl_take isl_union_set *uset);
7620 __isl_give isl_union_pw_qpolynomial_fold *
7621 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7622 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7623 __isl_take isl_space *space);
7624 __isl_give isl_union_pw_qpolynomial_fold *
7625 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7626 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7627 __isl_take isl_union_set *uset);
7628 __isl_give isl_union_pw_qpolynomial_fold *
7629 isl_union_pw_qpolynomial_fold_intersect_domain(
7630 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7631 __isl_take isl_union_set *uset);
7632 __isl_give isl_pw_qpolynomial *
7633 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7634 __isl_take isl_pw_qpolynomial *pwpq,
7635 __isl_take isl_set *set);
7636 __isl_give isl_pw_qpolynomial_fold *
7637 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7638 __isl_take isl_pw_qpolynomial_fold *pwf,
7639 __isl_take isl_set *set);
7640 __isl_give isl_union_pw_qpolynomial *
7641 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7642 __isl_take isl_union_pw_qpolynomial *upwpq,
7643 __isl_take isl_union_set *uset);
7644 __isl_give isl_union_pw_qpolynomial_fold *
7645 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7646 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7647 __isl_take isl_union_set *uset);
7648 __isl_give isl_pw_qpolynomial *
7649 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7650 __isl_take isl_pw_qpolynomial *pwpq,
7651 __isl_take isl_set *set);
7652 __isl_give isl_pw_qpolynomial_fold *
7653 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7654 __isl_take isl_pw_qpolynomial_fold *pwf,
7655 __isl_take isl_set *set);
7656 __isl_give isl_union_pw_qpolynomial *
7657 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7658 __isl_take isl_union_pw_qpolynomial *upwpq,
7659 __isl_take isl_union_set *uset);
7660 __isl_give isl_union_pw_qpolynomial_fold *
7661 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7662 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7663 __isl_take isl_union_set *uset);
7664 __isl_give isl_pw_qpolynomial *
7665 isl_pw_qpolynomial_intersect_params(
7666 __isl_take isl_pw_qpolynomial *pwpq,
7667 __isl_take isl_set *set);
7668 __isl_give isl_pw_qpolynomial_fold *
7669 isl_pw_qpolynomial_fold_intersect_params(
7670 __isl_take isl_pw_qpolynomial_fold *pwf,
7671 __isl_take isl_set *set);
7672 __isl_give isl_union_pw_qpolynomial *
7673 isl_union_pw_qpolynomial_intersect_params(
7674 __isl_take isl_union_pw_qpolynomial *upwpq,
7675 __isl_take isl_set *set);
7676 __isl_give isl_union_pw_qpolynomial_fold *
7677 isl_union_pw_qpolynomial_fold_intersect_params(
7678 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7679 __isl_take isl_set *set);
7681 The second argument to the C<_params> functions needs to be
7682 a parametric (basic) set. For the other functions, a parametric set
7683 for either argument is only allowed if the other argument is
7684 a parametric set as well.
7685 The list passed to C<isl_basic_set_list_intersect> needs to have
7686 at least one element and all elements need to live in the same space.
7687 The function C<isl_multi_union_pw_aff_intersect_range>
7688 restricts the input function to those shared domain elements
7689 that map to the specified range.
7690 C<isl_union_map_intersect_domain> is an alternative name for
7691 C<isl_union_map_intersect_domain_union_set>.
7692 Similarly for the other pairs of functions.
7696 #include <isl/set.h>
7697 __isl_give isl_set *isl_basic_set_union(
7698 __isl_take isl_basic_set *bset1,
7699 __isl_take isl_basic_set *bset2);
7700 __isl_give isl_set *isl_set_union(
7701 __isl_take isl_set *set1,
7702 __isl_take isl_set *set2);
7703 __isl_give isl_set *isl_set_list_union(
7704 __isl_take isl_set_list *list);
7706 #include <isl/map.h>
7707 __isl_give isl_map *isl_basic_map_union(
7708 __isl_take isl_basic_map *bmap1,
7709 __isl_take isl_basic_map *bmap2);
7710 __isl_give isl_map *isl_map_union(
7711 __isl_take isl_map *map1,
7712 __isl_take isl_map *map2);
7714 #include <isl/union_set.h>
7715 __isl_give isl_union_set *isl_union_set_union(
7716 __isl_take isl_union_set *uset1,
7717 __isl_take isl_union_set *uset2);
7718 __isl_give isl_union_set *isl_union_set_list_union(
7719 __isl_take isl_union_set_list *list);
7721 #include <isl/union_map.h>
7722 __isl_give isl_union_map *isl_union_map_union(
7723 __isl_take isl_union_map *umap1,
7724 __isl_take isl_union_map *umap2);
7726 The list passed to C<isl_set_list_union> needs to have
7727 at least one element and all elements need to live in the same space.
7729 =item * Set difference
7731 #include <isl/set.h>
7732 __isl_give isl_set *isl_set_subtract(
7733 __isl_take isl_set *set1,
7734 __isl_take isl_set *set2);
7736 #include <isl/map.h>
7737 __isl_give isl_map *isl_map_subtract(
7738 __isl_take isl_map *map1,
7739 __isl_take isl_map *map2);
7740 __isl_give isl_map *isl_map_subtract_domain(
7741 __isl_take isl_map *map,
7742 __isl_take isl_set *dom);
7743 __isl_give isl_map *isl_map_subtract_range(
7744 __isl_take isl_map *map,
7745 __isl_take isl_set *dom);
7747 #include <isl/union_set.h>
7748 __isl_give isl_union_set *isl_union_set_subtract(
7749 __isl_take isl_union_set *uset1,
7750 __isl_take isl_union_set *uset2);
7752 #include <isl/union_map.h>
7753 __isl_give isl_union_map *isl_union_map_subtract(
7754 __isl_take isl_union_map *umap1,
7755 __isl_take isl_union_map *umap2);
7756 __isl_give isl_union_map *isl_union_map_subtract_domain(
7757 __isl_take isl_union_map *umap,
7758 __isl_take isl_union_set *dom);
7759 __isl_give isl_union_map *isl_union_map_subtract_range(
7760 __isl_take isl_union_map *umap,
7761 __isl_take isl_union_set *dom);
7763 #include <isl/aff.h>
7764 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7765 __isl_take isl_pw_aff *pa,
7766 __isl_take isl_set *set);
7767 __isl_give isl_pw_multi_aff *
7768 isl_pw_multi_aff_subtract_domain(
7769 __isl_take isl_pw_multi_aff *pma,
7770 __isl_take isl_set *set);
7771 __isl_give isl_union_pw_aff *
7772 isl_union_pw_aff_subtract_domain_union_set(
7773 __isl_take isl_union_pw_aff *upa,
7774 __isl_take isl_union_set *uset);
7775 __isl_give isl_union_pw_aff *
7776 isl_union_pw_aff_subtract_domain_space(
7777 __isl_take isl_union_pw_aff *upa,
7778 __isl_take isl_space *space);
7779 __isl_give isl_union_pw_aff *
7780 isl_union_pw_aff_subtract_domain(
7781 __isl_take isl_union_pw_aff *upa,
7782 __isl_take isl_union_set *uset);
7783 __isl_give isl_union_pw_multi_aff *
7784 isl_union_pw_multi_aff_subtract_domain_union_set(
7785 __isl_take isl_union_pw_multi_aff *upma,
7786 __isl_take isl_set *set);
7787 __isl_give isl_union_pw_multi_aff *
7788 isl_union_pw_multi_aff_subtract_domain_space(
7789 __isl_take isl_union_pw_multi_aff *upma,
7790 __isl_take isl_space *space);
7791 __isl_give isl_union_pw_multi_aff *
7792 isl_union_pw_multi_aff_subtract_domain(
7793 __isl_take isl_union_pw_multi_aff *upma,
7794 __isl_take isl_union_set *uset);
7796 #include <isl/polynomial.h>
7797 __isl_give isl_pw_qpolynomial *
7798 isl_pw_qpolynomial_subtract_domain(
7799 __isl_take isl_pw_qpolynomial *pwpq,
7800 __isl_take isl_set *set);
7801 __isl_give isl_pw_qpolynomial_fold *
7802 isl_pw_qpolynomial_fold_subtract_domain(
7803 __isl_take isl_pw_qpolynomial_fold *pwf,
7804 __isl_take isl_set *set);
7805 __isl_give isl_union_pw_qpolynomial *
7806 isl_union_pw_qpolynomial_subtract_domain_union_set(
7807 __isl_take isl_union_pw_qpolynomial *upwpq,
7808 __isl_take isl_union_set *uset);
7809 __isl_give isl_union_pw_qpolynomial *
7810 isl_union_pw_qpolynomial_subtract_domain_space(
7811 __isl_take isl_union_pw_qpolynomial *upwpq,
7812 __isl_take isl_space *space);
7813 __isl_give isl_union_pw_qpolynomial *
7814 isl_union_pw_qpolynomial_subtract_domain(
7815 __isl_take isl_union_pw_qpolynomial *upwpq,
7816 __isl_take isl_union_set *uset);
7817 __isl_give isl_union_pw_qpolynomial_fold *
7818 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7819 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7820 __isl_take isl_union_set *uset);
7821 __isl_give isl_union_pw_qpolynomial_fold *
7822 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7823 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7824 __isl_take isl_space *space);
7825 __isl_give isl_union_pw_qpolynomial_fold *
7826 isl_union_pw_qpolynomial_fold_subtract_domain(
7827 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7828 __isl_take isl_union_set *uset);
7830 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7831 C<isl_union_pw_aff_subtract_domain_union_set>.
7832 Similarly for the other pairs of functions.
7836 #include <isl/space.h>
7837 __isl_give isl_space *isl_space_join(
7838 __isl_take isl_space *left,
7839 __isl_take isl_space *right);
7841 #include <isl/set.h>
7842 __isl_give isl_basic_set *isl_basic_set_apply(
7843 __isl_take isl_basic_set *bset,
7844 __isl_take isl_basic_map *bmap);
7845 __isl_give isl_set *isl_set_apply(
7846 __isl_take isl_set *set,
7847 __isl_take isl_map *map);
7849 #include <isl/union_set.h>
7850 __isl_give isl_union_set *isl_union_set_apply(
7851 __isl_take isl_union_set *uset,
7852 __isl_take isl_union_map *umap);
7854 #include <isl/map.h>
7855 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7856 __isl_take isl_basic_map *bmap1,
7857 __isl_take isl_basic_map *bmap2);
7858 __isl_give isl_basic_map *isl_basic_map_apply_range(
7859 __isl_take isl_basic_map *bmap1,
7860 __isl_take isl_basic_map *bmap2);
7861 __isl_give isl_map *isl_map_apply_domain(
7862 __isl_take isl_map *map1,
7863 __isl_take isl_map *map2);
7864 __isl_give isl_map *isl_map_apply_range(
7865 __isl_take isl_map *map1,
7866 __isl_take isl_map *map2);
7868 #include <isl/union_map.h>
7869 __isl_give isl_union_map *isl_union_map_apply_domain(
7870 __isl_take isl_union_map *umap1,
7871 __isl_take isl_union_map *umap2);
7872 __isl_give isl_union_map *isl_union_map_apply_range(
7873 __isl_take isl_union_map *umap1,
7874 __isl_take isl_union_map *umap2);
7876 #include <isl/aff.h>
7877 __isl_give isl_union_pw_multi_aff *
7878 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7879 __isl_take isl_union_pw_multi_aff *upma1,
7880 __isl_take isl_union_pw_multi_aff *upma2);
7881 __isl_give isl_union_pw_aff *
7882 isl_multi_union_pw_aff_apply_aff(
7883 __isl_take isl_multi_union_pw_aff *mupa,
7884 __isl_take isl_aff *aff);
7885 __isl_give isl_union_pw_aff *
7886 isl_multi_union_pw_aff_apply_pw_aff(
7887 __isl_take isl_multi_union_pw_aff *mupa,
7888 __isl_take isl_pw_aff *pa);
7889 __isl_give isl_multi_union_pw_aff *
7890 isl_multi_union_pw_aff_apply_multi_aff(
7891 __isl_take isl_multi_union_pw_aff *mupa,
7892 __isl_take isl_multi_aff *ma);
7893 __isl_give isl_multi_union_pw_aff *
7894 isl_multi_union_pw_aff_apply_pw_multi_aff(
7895 __isl_take isl_multi_union_pw_aff *mupa,
7896 __isl_take isl_pw_multi_aff *pma);
7898 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7899 over the shared domain of the elements of the input. The dimension is
7900 required to be greater than zero.
7901 The C<isl_multi_union_pw_aff> argument of
7902 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7903 but only if the range of the C<isl_multi_aff> argument
7904 is also zero-dimensional.
7905 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7907 #include <isl/polynomial.h>
7908 __isl_give isl_pw_qpolynomial_fold *
7909 isl_set_apply_pw_qpolynomial_fold(
7910 __isl_take isl_set *set,
7911 __isl_take isl_pw_qpolynomial_fold *pwf,
7913 __isl_give isl_pw_qpolynomial_fold *
7914 isl_map_apply_pw_qpolynomial_fold(
7915 __isl_take isl_map *map,
7916 __isl_take isl_pw_qpolynomial_fold *pwf,
7918 __isl_give isl_union_pw_qpolynomial_fold *
7919 isl_union_set_apply_union_pw_qpolynomial_fold(
7920 __isl_take isl_union_set *uset,
7921 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7923 __isl_give isl_union_pw_qpolynomial_fold *
7924 isl_union_map_apply_union_pw_qpolynomial_fold(
7925 __isl_take isl_union_map *umap,
7926 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7929 The functions taking a map
7930 compose the given map with the given piecewise quasipolynomial reduction.
7931 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7932 over all elements in the intersection of the range of the map
7933 and the domain of the piecewise quasipolynomial reduction
7934 as a function of an element in the domain of the map.
7935 The functions taking a set compute a bound over all elements in the
7936 intersection of the set and the domain of the
7937 piecewise quasipolynomial reduction.
7941 #include <isl/set.h>
7942 __isl_give isl_basic_set *
7943 isl_basic_set_preimage_multi_aff(
7944 __isl_take isl_basic_set *bset,
7945 __isl_take isl_multi_aff *ma);
7946 __isl_give isl_set *isl_set_preimage_multi_aff(
7947 __isl_take isl_set *set,
7948 __isl_take isl_multi_aff *ma);
7949 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
7950 __isl_take isl_set *set,
7951 __isl_take isl_pw_multi_aff *pma);
7952 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
7953 __isl_take isl_set *set,
7954 __isl_take isl_multi_pw_aff *mpa);
7956 #include <isl/union_set.h>
7957 __isl_give isl_union_set *
7958 isl_union_set_preimage_multi_aff(
7959 __isl_take isl_union_set *uset,
7960 __isl_take isl_multi_aff *ma);
7961 __isl_give isl_union_set *
7962 isl_union_set_preimage_pw_multi_aff(
7963 __isl_take isl_union_set *uset,
7964 __isl_take isl_pw_multi_aff *pma);
7965 __isl_give isl_union_set *
7966 isl_union_set_preimage_union_pw_multi_aff(
7967 __isl_take isl_union_set *uset,
7968 __isl_take isl_union_pw_multi_aff *upma);
7970 #include <isl/map.h>
7971 __isl_give isl_basic_map *
7972 isl_basic_map_preimage_domain_multi_aff(
7973 __isl_take isl_basic_map *bmap,
7974 __isl_take isl_multi_aff *ma);
7975 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
7976 __isl_take isl_map *map,
7977 __isl_take isl_multi_aff *ma);
7978 __isl_give isl_map *isl_map_preimage_range_multi_aff(
7979 __isl_take isl_map *map,
7980 __isl_take isl_multi_aff *ma);
7981 __isl_give isl_map *
7982 isl_map_preimage_domain_pw_multi_aff(
7983 __isl_take isl_map *map,
7984 __isl_take isl_pw_multi_aff *pma);
7985 __isl_give isl_map *
7986 isl_map_preimage_range_pw_multi_aff(
7987 __isl_take isl_map *map,
7988 __isl_take isl_pw_multi_aff *pma);
7989 __isl_give isl_map *
7990 isl_map_preimage_domain_multi_pw_aff(
7991 __isl_take isl_map *map,
7992 __isl_take isl_multi_pw_aff *mpa);
7993 __isl_give isl_basic_map *
7994 isl_basic_map_preimage_range_multi_aff(
7995 __isl_take isl_basic_map *bmap,
7996 __isl_take isl_multi_aff *ma);
7998 #include <isl/union_map.h>
7999 __isl_give isl_union_map *
8000 isl_union_map_preimage_domain_multi_aff(
8001 __isl_take isl_union_map *umap,
8002 __isl_take isl_multi_aff *ma);
8003 __isl_give isl_union_map *
8004 isl_union_map_preimage_range_multi_aff(
8005 __isl_take isl_union_map *umap,
8006 __isl_take isl_multi_aff *ma);
8007 __isl_give isl_union_map *
8008 isl_union_map_preimage_domain_pw_multi_aff(
8009 __isl_take isl_union_map *umap,
8010 __isl_take isl_pw_multi_aff *pma);
8011 __isl_give isl_union_map *
8012 isl_union_map_preimage_range_pw_multi_aff(
8013 __isl_take isl_union_map *umap,
8014 __isl_take isl_pw_multi_aff *pma);
8015 __isl_give isl_union_map *
8016 isl_union_map_preimage_domain_union_pw_multi_aff(
8017 __isl_take isl_union_map *umap,
8018 __isl_take isl_union_pw_multi_aff *upma);
8019 __isl_give isl_union_map *
8020 isl_union_map_preimage_range_union_pw_multi_aff(
8021 __isl_take isl_union_map *umap,
8022 __isl_take isl_union_pw_multi_aff *upma);
8024 #include <isl/aff.h>
8025 __isl_give isl_pw_multi_aff *
8026 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8027 __isl_take isl_pw_multi_aff *pma1,
8028 __isl_take isl_pw_multi_aff *pma2);
8029 __isl_give isl_union_pw_multi_aff *
8030 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8031 __isl_take isl_union_pw_multi_aff *upma1,
8032 __isl_take isl_union_pw_multi_aff *upma2);
8034 These functions compute the preimage of the given set or map domain/range under
8035 the given function. In other words, the expression is plugged
8036 into the set description or into the domain/range of the map or function.
8040 #include <isl/aff.h>
8041 __isl_give isl_aff *isl_aff_pullback_aff(
8042 __isl_take isl_aff *aff1,
8043 __isl_take isl_aff *aff2);
8044 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8045 __isl_take isl_aff *aff,
8046 __isl_take isl_multi_aff *ma);
8047 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8048 __isl_take isl_pw_aff *pa,
8049 __isl_take isl_multi_aff *ma);
8050 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8051 __isl_take isl_pw_aff *pa,
8052 __isl_take isl_pw_multi_aff *pma);
8053 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8054 __isl_take isl_pw_aff *pa,
8055 __isl_take isl_multi_pw_aff *mpa);
8056 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8057 __isl_take isl_multi_aff *ma1,
8058 __isl_take isl_multi_aff *ma2);
8059 __isl_give isl_pw_multi_aff *
8060 isl_pw_multi_aff_pullback_multi_aff(
8061 __isl_take isl_pw_multi_aff *pma,
8062 __isl_take isl_multi_aff *ma);
8063 __isl_give isl_multi_pw_aff *
8064 isl_multi_pw_aff_pullback_multi_aff(
8065 __isl_take isl_multi_pw_aff *mpa,
8066 __isl_take isl_multi_aff *ma);
8067 __isl_give isl_pw_multi_aff *
8068 isl_pw_multi_aff_pullback_pw_multi_aff(
8069 __isl_take isl_pw_multi_aff *pma1,
8070 __isl_take isl_pw_multi_aff *pma2);
8071 __isl_give isl_multi_pw_aff *
8072 isl_multi_pw_aff_pullback_pw_multi_aff(
8073 __isl_take isl_multi_pw_aff *mpa,
8074 __isl_take isl_pw_multi_aff *pma);
8075 __isl_give isl_multi_pw_aff *
8076 isl_multi_pw_aff_pullback_multi_pw_aff(
8077 __isl_take isl_multi_pw_aff *mpa1,
8078 __isl_take isl_multi_pw_aff *mpa2);
8079 __isl_give isl_union_pw_aff *
8080 isl_union_pw_aff_pullback_union_pw_multi_aff(
8081 __isl_take isl_union_pw_aff *upa,
8082 __isl_take isl_union_pw_multi_aff *upma);
8083 __isl_give isl_union_pw_multi_aff *
8084 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8085 __isl_take isl_union_pw_multi_aff *upma1,
8086 __isl_take isl_union_pw_multi_aff *upma2);
8087 __isl_give isl_multi_union_pw_aff *
8088 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8089 __isl_take isl_multi_union_pw_aff *mupa,
8090 __isl_take isl_union_pw_multi_aff *upma);
8092 These functions precompose the first expression by the second function.
8093 In other words, the second function is plugged
8094 into the first expression.
8098 #include <isl/aff.h>
8099 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8100 __isl_take isl_aff *aff1,
8101 __isl_take isl_aff *aff2);
8102 __isl_give isl_set *isl_aff_eq_set(
8103 __isl_take isl_aff *aff1,
8104 __isl_take isl_aff *aff2);
8105 __isl_give isl_set *isl_aff_ne_set(
8106 __isl_take isl_aff *aff1,
8107 __isl_take isl_aff *aff2);
8108 __isl_give isl_basic_set *isl_aff_le_basic_set(
8109 __isl_take isl_aff *aff1,
8110 __isl_take isl_aff *aff2);
8111 __isl_give isl_set *isl_aff_le_set(
8112 __isl_take isl_aff *aff1,
8113 __isl_take isl_aff *aff2);
8114 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8115 __isl_take isl_aff *aff1,
8116 __isl_take isl_aff *aff2);
8117 __isl_give isl_set *isl_aff_lt_set(
8118 __isl_take isl_aff *aff1,
8119 __isl_take isl_aff *aff2);
8120 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8121 __isl_take isl_aff *aff1,
8122 __isl_take isl_aff *aff2);
8123 __isl_give isl_set *isl_aff_ge_set(
8124 __isl_take isl_aff *aff1,
8125 __isl_take isl_aff *aff2);
8126 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8127 __isl_take isl_aff *aff1,
8128 __isl_take isl_aff *aff2);
8129 __isl_give isl_set *isl_aff_gt_set(
8130 __isl_take isl_aff *aff1,
8131 __isl_take isl_aff *aff2);
8132 __isl_give isl_set *isl_pw_aff_eq_set(
8133 __isl_take isl_pw_aff *pwaff1,
8134 __isl_take isl_pw_aff *pwaff2);
8135 __isl_give isl_set *isl_pw_aff_ne_set(
8136 __isl_take isl_pw_aff *pwaff1,
8137 __isl_take isl_pw_aff *pwaff2);
8138 __isl_give isl_set *isl_pw_aff_le_set(
8139 __isl_take isl_pw_aff *pwaff1,
8140 __isl_take isl_pw_aff *pwaff2);
8141 __isl_give isl_set *isl_pw_aff_lt_set(
8142 __isl_take isl_pw_aff *pwaff1,
8143 __isl_take isl_pw_aff *pwaff2);
8144 __isl_give isl_set *isl_pw_aff_ge_set(
8145 __isl_take isl_pw_aff *pwaff1,
8146 __isl_take isl_pw_aff *pwaff2);
8147 __isl_give isl_set *isl_pw_aff_gt_set(
8148 __isl_take isl_pw_aff *pwaff1,
8149 __isl_take isl_pw_aff *pwaff2);
8151 __isl_give isl_set *isl_multi_aff_lex_le_set(
8152 __isl_take isl_multi_aff *ma1,
8153 __isl_take isl_multi_aff *ma2);
8154 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8155 __isl_take isl_multi_aff *ma1,
8156 __isl_take isl_multi_aff *ma2);
8157 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8158 __isl_take isl_multi_aff *ma1,
8159 __isl_take isl_multi_aff *ma2);
8160 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8161 __isl_take isl_multi_aff *ma1,
8162 __isl_take isl_multi_aff *ma2);
8164 __isl_give isl_set *isl_pw_aff_list_eq_set(
8165 __isl_take isl_pw_aff_list *list1,
8166 __isl_take isl_pw_aff_list *list2);
8167 __isl_give isl_set *isl_pw_aff_list_ne_set(
8168 __isl_take isl_pw_aff_list *list1,
8169 __isl_take isl_pw_aff_list *list2);
8170 __isl_give isl_set *isl_pw_aff_list_le_set(
8171 __isl_take isl_pw_aff_list *list1,
8172 __isl_take isl_pw_aff_list *list2);
8173 __isl_give isl_set *isl_pw_aff_list_lt_set(
8174 __isl_take isl_pw_aff_list *list1,
8175 __isl_take isl_pw_aff_list *list2);
8176 __isl_give isl_set *isl_pw_aff_list_ge_set(
8177 __isl_take isl_pw_aff_list *list1,
8178 __isl_take isl_pw_aff_list *list2);
8179 __isl_give isl_set *isl_pw_aff_list_gt_set(
8180 __isl_take isl_pw_aff_list *list1,
8181 __isl_take isl_pw_aff_list *list2);
8183 The function C<isl_aff_ge_basic_set> returns a basic set
8184 containing those elements in the shared space
8185 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8186 The function C<isl_pw_aff_ge_set> returns a set
8187 containing those elements in the shared domain
8188 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8189 greater than or equal to C<pwaff2>.
8190 The function C<isl_multi_aff_lex_le_set> returns a set
8191 containing those elements in the shared domain space
8192 where C<ma1> is lexicographically smaller than or
8194 The functions operating on C<isl_pw_aff_list> apply the corresponding
8195 C<isl_pw_aff> function to each pair of elements in the two lists.
8197 #include <isl/aff.h>
8198 __isl_give isl_map *isl_pw_aff_eq_map(
8199 __isl_take isl_pw_aff *pa1,
8200 __isl_take isl_pw_aff *pa2);
8201 __isl_give isl_map *isl_pw_aff_le_map(
8202 __isl_take isl_pw_aff *pa1,
8203 __isl_take isl_pw_aff *pa2);
8204 __isl_give isl_map *isl_pw_aff_lt_map(
8205 __isl_take isl_pw_aff *pa1,
8206 __isl_take isl_pw_aff *pa2);
8207 __isl_give isl_map *isl_pw_aff_ge_map(
8208 __isl_take isl_pw_aff *pa1,
8209 __isl_take isl_pw_aff *pa2);
8210 __isl_give isl_map *isl_pw_aff_gt_map(
8211 __isl_take isl_pw_aff *pa1,
8212 __isl_take isl_pw_aff *pa2);
8214 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8215 __isl_take isl_multi_pw_aff *mpa1,
8216 __isl_take isl_multi_pw_aff *mpa2);
8217 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8218 __isl_take isl_multi_pw_aff *mpa1,
8219 __isl_take isl_multi_pw_aff *mpa2);
8220 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8221 __isl_take isl_multi_pw_aff *mpa1,
8222 __isl_take isl_multi_pw_aff *mpa2);
8223 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8224 __isl_take isl_multi_pw_aff *mpa1,
8225 __isl_take isl_multi_pw_aff *mpa2);
8226 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8227 __isl_take isl_multi_pw_aff *mpa1,
8228 __isl_take isl_multi_pw_aff *mpa2);
8230 These functions return a map between domain elements of the arguments
8231 where the function values satisfy the given relation.
8233 #include <isl/map.h>
8234 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8235 __isl_take isl_map *map,
8236 __isl_take isl_multi_pw_aff *mpa);
8237 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8238 __isl_take isl_map *map,
8239 __isl_take isl_multi_pw_aff *mpa);
8240 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8241 __isl_take isl_map *map,
8242 __isl_take isl_multi_pw_aff *mpa);
8243 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8244 __isl_take isl_map *map,
8245 __isl_take isl_multi_pw_aff *mpa);
8246 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8247 __isl_take isl_map *map,
8248 __isl_take isl_multi_pw_aff *mpa);
8250 #include <isl/union_map.h>
8251 __isl_give isl_union_map *
8252 isl_union_map_eq_at_multi_union_pw_aff(
8253 __isl_take isl_union_map *umap,
8254 __isl_take isl_multi_union_pw_aff *mupa);
8255 __isl_give isl_union_map *
8256 isl_union_map_lex_lt_at_multi_union_pw_aff(
8257 __isl_take isl_union_map *umap,
8258 __isl_take isl_multi_union_pw_aff *mupa);
8259 __isl_give isl_union_map *
8260 isl_union_map_lex_le_at_multi_union_pw_aff(
8261 __isl_take isl_union_map *umap,
8262 __isl_take isl_multi_union_pw_aff *mupa);
8263 __isl_give isl_union_map *
8264 isl_union_map_lex_gt_at_multi_union_pw_aff(
8265 __isl_take isl_union_map *umap,
8266 __isl_take isl_multi_union_pw_aff *mupa);
8267 __isl_give isl_union_map *
8268 isl_union_map_lex_ge_at_multi_union_pw_aff(
8269 __isl_take isl_union_map *umap,
8270 __isl_take isl_multi_union_pw_aff *mupa);
8272 These functions select the subset of elements in the union map
8273 that have an equal or lexicographically smaller or greater function value.
8275 =item * Cartesian Product
8277 #include <isl/space.h>
8278 __isl_give isl_space *isl_space_product(
8279 __isl_take isl_space *space1,
8280 __isl_take isl_space *space2);
8281 __isl_give isl_space *isl_space_domain_product(
8282 __isl_take isl_space *space1,
8283 __isl_take isl_space *space2);
8284 __isl_give isl_space *isl_space_range_product(
8285 __isl_take isl_space *space1,
8286 __isl_take isl_space *space2);
8289 C<isl_space_product>, C<isl_space_domain_product>
8290 and C<isl_space_range_product> take pairs or relation spaces and
8291 produce a single relations space, where either the domain, the range
8292 or both domain and range are wrapped spaces of relations between
8293 the domains and/or ranges of the input spaces.
8294 If the product is only constructed over the domain or the range
8295 then the ranges or the domains of the inputs should be the same.
8296 The function C<isl_space_product> also accepts a pair of set spaces,
8297 in which case it returns a wrapped space of a relation between the
8300 #include <isl/set.h>
8301 __isl_give isl_set *isl_set_product(
8302 __isl_take isl_set *set1,
8303 __isl_take isl_set *set2);
8305 #include <isl/map.h>
8306 __isl_give isl_basic_map *isl_basic_map_domain_product(
8307 __isl_take isl_basic_map *bmap1,
8308 __isl_take isl_basic_map *bmap2);
8309 __isl_give isl_basic_map *isl_basic_map_range_product(
8310 __isl_take isl_basic_map *bmap1,
8311 __isl_take isl_basic_map *bmap2);
8312 __isl_give isl_basic_map *isl_basic_map_product(
8313 __isl_take isl_basic_map *bmap1,
8314 __isl_take isl_basic_map *bmap2);
8315 __isl_give isl_map *isl_map_domain_product(
8316 __isl_take isl_map *map1,
8317 __isl_take isl_map *map2);
8318 __isl_give isl_map *isl_map_range_product(
8319 __isl_take isl_map *map1,
8320 __isl_take isl_map *map2);
8321 __isl_give isl_map *isl_map_product(
8322 __isl_take isl_map *map1,
8323 __isl_take isl_map *map2);
8325 #include <isl/union_set.h>
8326 __isl_give isl_union_set *isl_union_set_product(
8327 __isl_take isl_union_set *uset1,
8328 __isl_take isl_union_set *uset2);
8330 #include <isl/union_map.h>
8331 __isl_give isl_union_map *isl_union_map_domain_product(
8332 __isl_take isl_union_map *umap1,
8333 __isl_take isl_union_map *umap2);
8334 __isl_give isl_union_map *isl_union_map_range_product(
8335 __isl_take isl_union_map *umap1,
8336 __isl_take isl_union_map *umap2);
8337 __isl_give isl_union_map *isl_union_map_product(
8338 __isl_take isl_union_map *umap1,
8339 __isl_take isl_union_map *umap2);
8342 __isl_give isl_multi_id *isl_multi_id_range_product(
8343 __isl_take isl_multi_id *mi1,
8344 __isl_take isl_multi_id *mi2);
8346 #include <isl/val.h>
8347 __isl_give isl_multi_val *isl_multi_val_range_product(
8348 __isl_take isl_multi_val *mv1,
8349 __isl_take isl_multi_val *mv2);
8350 __isl_give isl_multi_val *isl_multi_val_product(
8351 __isl_take isl_multi_val *mv1,
8352 __isl_take isl_multi_val *mv2);
8354 #include <isl/aff.h>
8355 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8356 __isl_take isl_multi_aff *ma1,
8357 __isl_take isl_multi_aff *ma2);
8358 __isl_give isl_multi_aff *isl_multi_aff_product(
8359 __isl_take isl_multi_aff *ma1,
8360 __isl_take isl_multi_aff *ma2);
8361 __isl_give isl_multi_pw_aff *
8362 isl_multi_pw_aff_range_product(
8363 __isl_take isl_multi_pw_aff *mpa1,
8364 __isl_take isl_multi_pw_aff *mpa2);
8365 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8366 __isl_take isl_multi_pw_aff *mpa1,
8367 __isl_take isl_multi_pw_aff *mpa2);
8368 __isl_give isl_pw_multi_aff *
8369 isl_pw_multi_aff_range_product(
8370 __isl_take isl_pw_multi_aff *pma1,
8371 __isl_take isl_pw_multi_aff *pma2);
8372 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8373 __isl_take isl_pw_multi_aff *pma1,
8374 __isl_take isl_pw_multi_aff *pma2);
8375 __isl_give isl_union_pw_multi_aff *
8376 isl_union_pw_multi_aff_range_product(
8377 __isl_take isl_union_pw_multi_aff *upma1,
8378 __isl_take isl_union_pw_multi_aff *upma2);
8379 __isl_give isl_multi_union_pw_aff *
8380 isl_multi_union_pw_aff_range_product(
8381 __isl_take isl_multi_union_pw_aff *mupa1,
8382 __isl_take isl_multi_union_pw_aff *mupa2);
8384 The above functions compute the cross product of the given
8385 sets, relations or functions. The domains and ranges of the results
8386 are wrapped maps between domains and ranges of the inputs.
8387 To obtain a ``flat'' product, use the following functions
8390 #include <isl/set.h>
8391 __isl_give isl_basic_set *isl_basic_set_flat_product(
8392 __isl_take isl_basic_set *bset1,
8393 __isl_take isl_basic_set *bset2);
8394 __isl_give isl_set *isl_set_flat_product(
8395 __isl_take isl_set *set1,
8396 __isl_take isl_set *set2);
8398 #include <isl/map.h>
8399 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8400 __isl_take isl_basic_map *bmap1,
8401 __isl_take isl_basic_map *bmap2);
8402 __isl_give isl_map *isl_map_flat_domain_product(
8403 __isl_take isl_map *map1,
8404 __isl_take isl_map *map2);
8405 __isl_give isl_map *isl_map_flat_range_product(
8406 __isl_take isl_map *map1,
8407 __isl_take isl_map *map2);
8408 __isl_give isl_basic_map *isl_basic_map_flat_product(
8409 __isl_take isl_basic_map *bmap1,
8410 __isl_take isl_basic_map *bmap2);
8411 __isl_give isl_map *isl_map_flat_product(
8412 __isl_take isl_map *map1,
8413 __isl_take isl_map *map2);
8415 #include <isl/union_map.h>
8416 __isl_give isl_union_map *
8417 isl_union_map_flat_domain_product(
8418 __isl_take isl_union_map *umap1,
8419 __isl_take isl_union_map *umap2);
8420 __isl_give isl_union_map *
8421 isl_union_map_flat_range_product(
8422 __isl_take isl_union_map *umap1,
8423 __isl_take isl_union_map *umap2);
8426 __isl_give isl_multi_id *
8427 isl_multi_id_flat_range_product(
8428 __isl_take isl_multi_id *mi1,
8429 __isl_take isl_multi_id *mi2);
8431 #include <isl/val.h>
8432 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8433 __isl_take isl_multi_val *mv1,
8434 __isl_take isl_multi_val *mv2);
8436 #include <isl/aff.h>
8437 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8438 __isl_take isl_multi_aff *ma1,
8439 __isl_take isl_multi_aff *ma2);
8440 __isl_give isl_pw_multi_aff *
8441 isl_pw_multi_aff_flat_range_product(
8442 __isl_take isl_pw_multi_aff *pma1,
8443 __isl_take isl_pw_multi_aff *pma2);
8444 __isl_give isl_multi_pw_aff *
8445 isl_multi_pw_aff_flat_range_product(
8446 __isl_take isl_multi_pw_aff *mpa1,
8447 __isl_take isl_multi_pw_aff *mpa2);
8448 __isl_give isl_union_pw_multi_aff *
8449 isl_union_pw_multi_aff_flat_range_product(
8450 __isl_take isl_union_pw_multi_aff *upma1,
8451 __isl_take isl_union_pw_multi_aff *upma2);
8452 __isl_give isl_multi_union_pw_aff *
8453 isl_multi_union_pw_aff_flat_range_product(
8454 __isl_take isl_multi_union_pw_aff *mupa1,
8455 __isl_take isl_multi_union_pw_aff *mupa2);
8457 #include <isl/space.h>
8458 __isl_give isl_space *isl_space_factor_domain(
8459 __isl_take isl_space *space);
8460 __isl_give isl_space *isl_space_factor_range(
8461 __isl_take isl_space *space);
8462 __isl_give isl_space *isl_space_domain_factor_domain(
8463 __isl_take isl_space *space);
8464 __isl_give isl_space *isl_space_domain_factor_range(
8465 __isl_take isl_space *space);
8466 __isl_give isl_space *isl_space_range_factor_domain(
8467 __isl_take isl_space *space);
8468 __isl_give isl_space *isl_space_range_factor_range(
8469 __isl_take isl_space *space);
8471 The functions C<isl_space_range_factor_domain> and
8472 C<isl_space_range_factor_range> extract the two arguments from
8473 the result of a call to C<isl_space_range_product>.
8475 The arguments of a call to a product can be extracted
8476 from the result using the following functions.
8478 #include <isl/map.h>
8479 __isl_give isl_map *isl_map_factor_domain(
8480 __isl_take isl_map *map);
8481 __isl_give isl_map *isl_map_factor_range(
8482 __isl_take isl_map *map);
8483 __isl_give isl_map *isl_map_domain_factor_domain(
8484 __isl_take isl_map *map);
8485 __isl_give isl_map *isl_map_domain_factor_range(
8486 __isl_take isl_map *map);
8487 __isl_give isl_map *isl_map_range_factor_domain(
8488 __isl_take isl_map *map);
8489 __isl_give isl_map *isl_map_range_factor_range(
8490 __isl_take isl_map *map);
8492 #include <isl/union_map.h>
8493 __isl_give isl_union_map *isl_union_map_factor_domain(
8494 __isl_take isl_union_map *umap);
8495 __isl_give isl_union_map *isl_union_map_factor_range(
8496 __isl_take isl_union_map *umap);
8497 __isl_give isl_union_map *
8498 isl_union_map_domain_factor_domain(
8499 __isl_take isl_union_map *umap);
8500 __isl_give isl_union_map *
8501 isl_union_map_domain_factor_range(
8502 __isl_take isl_union_map *umap);
8503 __isl_give isl_union_map *
8504 isl_union_map_range_factor_domain(
8505 __isl_take isl_union_map *umap);
8506 __isl_give isl_union_map *
8507 isl_union_map_range_factor_range(
8508 __isl_take isl_union_map *umap);
8511 __isl_give isl_multi_id *isl_multi_id_factor_range(
8512 __isl_take isl_multi_id *mi);
8513 __isl_give isl_multi_id *
8514 isl_multi_id_range_factor_domain(
8515 __isl_take isl_multi_id *mi);
8516 __isl_give isl_multi_id *
8517 isl_multi_id_range_factor_range(
8518 __isl_take isl_multi_id *mi);
8520 #include <isl/val.h>
8521 __isl_give isl_multi_val *isl_multi_val_factor_range(
8522 __isl_take isl_multi_val *mv);
8523 __isl_give isl_multi_val *
8524 isl_multi_val_range_factor_domain(
8525 __isl_take isl_multi_val *mv);
8526 __isl_give isl_multi_val *
8527 isl_multi_val_range_factor_range(
8528 __isl_take isl_multi_val *mv);
8530 #include <isl/aff.h>
8531 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8532 __isl_take isl_multi_aff *ma);
8533 __isl_give isl_multi_aff *
8534 isl_multi_aff_range_factor_domain(
8535 __isl_take isl_multi_aff *ma);
8536 __isl_give isl_multi_aff *
8537 isl_multi_aff_range_factor_range(
8538 __isl_take isl_multi_aff *ma);
8539 __isl_give isl_multi_pw_aff *
8540 isl_multi_pw_aff_factor_range(
8541 __isl_take isl_multi_pw_aff *mpa);
8542 __isl_give isl_multi_pw_aff *
8543 isl_multi_pw_aff_range_factor_domain(
8544 __isl_take isl_multi_pw_aff *mpa);
8545 __isl_give isl_multi_pw_aff *
8546 isl_multi_pw_aff_range_factor_range(
8547 __isl_take isl_multi_pw_aff *mpa);
8548 __isl_give isl_pw_multi_aff *
8549 isl_pw_multi_aff_range_factor_domain(
8550 __isl_take isl_pw_multi_aff *pma);
8551 __isl_give isl_pw_multi_aff *
8552 isl_pw_multi_aff_range_factor_range(
8553 __isl_take isl_pw_multi_aff *pma);
8554 __isl_give isl_union_pw_multi_aff *
8555 isl_union_pw_multi_aff_range_factor_domain(
8556 __isl_take isl_union_pw_multi_aff *upma);
8557 __isl_give isl_union_pw_multi_aff *
8558 isl_union_pw_multi_aff_range_factor_range(
8559 __isl_take isl_union_pw_multi_aff *upma);
8560 __isl_give isl_multi_union_pw_aff *
8561 isl_multi_union_pw_aff_factor_range(
8562 __isl_take isl_multi_union_pw_aff *mupa);
8563 __isl_give isl_multi_union_pw_aff *
8564 isl_multi_union_pw_aff_range_factor_domain(
8565 __isl_take isl_multi_union_pw_aff *mupa);
8566 __isl_give isl_multi_union_pw_aff *
8567 isl_multi_union_pw_aff_range_factor_range(
8568 __isl_take isl_multi_union_pw_aff *mupa);
8570 The splice functions are a generalization of the flat product functions,
8571 where the second argument may be inserted at any position inside
8572 the first argument rather than being placed at the end.
8573 The functions C<isl_multi_val_factor_range>,
8574 C<isl_multi_aff_factor_range>,
8575 C<isl_multi_pw_aff_factor_range> and
8576 C<isl_multi_union_pw_aff_factor_range>
8577 take functions that live in a set space.
8580 __isl_give isl_multi_id *isl_multi_id_range_splice(
8581 __isl_take isl_multi_id *mi1, unsigned pos,
8582 __isl_take isl_multi_id *mi2);
8584 #include <isl/val.h>
8585 __isl_give isl_multi_val *isl_multi_val_range_splice(
8586 __isl_take isl_multi_val *mv1, unsigned pos,
8587 __isl_take isl_multi_val *mv2);
8589 #include <isl/aff.h>
8590 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8591 __isl_take isl_multi_aff *ma1, unsigned pos,
8592 __isl_take isl_multi_aff *ma2);
8593 __isl_give isl_multi_aff *isl_multi_aff_splice(
8594 __isl_take isl_multi_aff *ma1,
8595 unsigned in_pos, unsigned out_pos,
8596 __isl_take isl_multi_aff *ma2);
8597 __isl_give isl_multi_pw_aff *
8598 isl_multi_pw_aff_range_splice(
8599 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8600 __isl_take isl_multi_pw_aff *mpa2);
8601 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8602 __isl_take isl_multi_pw_aff *mpa1,
8603 unsigned in_pos, unsigned out_pos,
8604 __isl_take isl_multi_pw_aff *mpa2);
8605 __isl_give isl_multi_union_pw_aff *
8606 isl_multi_union_pw_aff_range_splice(
8607 __isl_take isl_multi_union_pw_aff *mupa1,
8609 __isl_take isl_multi_union_pw_aff *mupa2);
8611 =item * Simplification
8613 When applied to a set or relation,
8614 the gist operation returns a set or relation that has the
8615 same intersection with the context as the input set or relation.
8616 Any implicit equality in the intersection is made explicit in the result,
8617 while all inequalities that are redundant with respect to the intersection
8619 In case of union sets and relations, the gist operation is performed
8622 When applied to a function,
8623 the gist operation applies the set gist operation to each of
8624 the cells in the domain of the input piecewise expression.
8625 The context is also exploited
8626 to simplify the expression associated to each cell.
8628 #include <isl/set.h>
8629 __isl_give isl_basic_set *isl_basic_set_gist(
8630 __isl_take isl_basic_set *bset,
8631 __isl_take isl_basic_set *context);
8632 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8633 __isl_take isl_set *context);
8634 __isl_give isl_set *isl_set_gist_params(
8635 __isl_take isl_set *set,
8636 __isl_take isl_set *context);
8638 #include <isl/map.h>
8639 __isl_give isl_basic_map *isl_basic_map_gist(
8640 __isl_take isl_basic_map *bmap,
8641 __isl_take isl_basic_map *context);
8642 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8643 __isl_take isl_basic_map *bmap,
8644 __isl_take isl_basic_set *context);
8645 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8646 __isl_take isl_map *context);
8647 __isl_give isl_map *isl_map_gist_params(
8648 __isl_take isl_map *map,
8649 __isl_take isl_set *context);
8650 __isl_give isl_map *isl_map_gist_domain(
8651 __isl_take isl_map *map,
8652 __isl_take isl_set *context);
8653 __isl_give isl_map *isl_map_gist_range(
8654 __isl_take isl_map *map,
8655 __isl_take isl_set *context);
8657 #include <isl/union_set.h>
8658 __isl_give isl_union_set *isl_union_set_gist(
8659 __isl_take isl_union_set *uset,
8660 __isl_take isl_union_set *context);
8661 __isl_give isl_union_set *isl_union_set_gist_params(
8662 __isl_take isl_union_set *uset,
8663 __isl_take isl_set *set);
8665 #include <isl/union_map.h>
8666 __isl_give isl_union_map *isl_union_map_gist(
8667 __isl_take isl_union_map *umap,
8668 __isl_take isl_union_map *context);
8669 __isl_give isl_union_map *isl_union_map_gist_params(
8670 __isl_take isl_union_map *umap,
8671 __isl_take isl_set *set);
8672 __isl_give isl_union_map *isl_union_map_gist_domain(
8673 __isl_take isl_union_map *umap,
8674 __isl_take isl_union_set *uset);
8675 __isl_give isl_union_map *isl_union_map_gist_range(
8676 __isl_take isl_union_map *umap,
8677 __isl_take isl_union_set *uset);
8679 #include <isl/aff.h>
8680 __isl_give isl_aff *isl_aff_gist_params(
8681 __isl_take isl_aff *aff,
8682 __isl_take isl_set *context);
8683 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8684 __isl_take isl_set *context);
8685 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8686 __isl_take isl_multi_aff *maff,
8687 __isl_take isl_set *context);
8688 __isl_give isl_multi_aff *isl_multi_aff_gist(
8689 __isl_take isl_multi_aff *maff,
8690 __isl_take isl_set *context);
8691 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8692 __isl_take isl_pw_aff *pwaff,
8693 __isl_take isl_set *context);
8694 __isl_give isl_pw_aff *isl_pw_aff_gist(
8695 __isl_take isl_pw_aff *pwaff,
8696 __isl_take isl_set *context);
8697 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8698 __isl_take isl_pw_multi_aff *pma,
8699 __isl_take isl_set *set);
8700 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8701 __isl_take isl_pw_multi_aff *pma,
8702 __isl_take isl_set *set);
8703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8704 __isl_take isl_multi_pw_aff *mpa,
8705 __isl_take isl_set *set);
8706 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8707 __isl_take isl_multi_pw_aff *mpa,
8708 __isl_take isl_set *set);
8709 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8710 __isl_take isl_union_pw_aff *upa,
8711 __isl_take isl_union_set *context);
8712 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8713 __isl_take isl_union_pw_aff *upa,
8714 __isl_take isl_set *context);
8715 __isl_give isl_union_pw_multi_aff *
8716 isl_union_pw_multi_aff_gist_params(
8717 __isl_take isl_union_pw_multi_aff *upma,
8718 __isl_take isl_set *context);
8719 __isl_give isl_union_pw_multi_aff *
8720 isl_union_pw_multi_aff_gist(
8721 __isl_take isl_union_pw_multi_aff *upma,
8722 __isl_take isl_union_set *context);
8723 __isl_give isl_multi_union_pw_aff *
8724 isl_multi_union_pw_aff_gist_params(
8725 __isl_take isl_multi_union_pw_aff *mupa,
8726 __isl_take isl_set *context);
8727 __isl_give isl_multi_union_pw_aff *
8728 isl_multi_union_pw_aff_gist(
8729 __isl_take isl_multi_union_pw_aff *mupa,
8730 __isl_take isl_union_set *context);
8732 #include <isl/polynomial.h>
8733 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8734 __isl_take isl_qpolynomial *qp,
8735 __isl_take isl_set *context);
8736 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8737 __isl_take isl_qpolynomial *qp,
8738 __isl_take isl_set *context);
8739 __isl_give isl_qpolynomial_fold *
8740 isl_qpolynomial_fold_gist_params(
8741 __isl_take isl_qpolynomial_fold *fold,
8742 __isl_take isl_set *context);
8743 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8744 __isl_take isl_qpolynomial_fold *fold,
8745 __isl_take isl_set *context);
8746 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8747 __isl_take isl_pw_qpolynomial *pwqp,
8748 __isl_take isl_set *context);
8749 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8750 __isl_take isl_pw_qpolynomial *pwqp,
8751 __isl_take isl_set *context);
8752 __isl_give isl_pw_qpolynomial_fold *
8753 isl_pw_qpolynomial_fold_gist(
8754 __isl_take isl_pw_qpolynomial_fold *pwf,
8755 __isl_take isl_set *context);
8756 __isl_give isl_pw_qpolynomial_fold *
8757 isl_pw_qpolynomial_fold_gist_params(
8758 __isl_take isl_pw_qpolynomial_fold *pwf,
8759 __isl_take isl_set *context);
8760 __isl_give isl_union_pw_qpolynomial *
8761 isl_union_pw_qpolynomial_gist_params(
8762 __isl_take isl_union_pw_qpolynomial *upwqp,
8763 __isl_take isl_set *context);
8764 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8765 __isl_take isl_union_pw_qpolynomial *upwqp,
8766 __isl_take isl_union_set *context);
8767 __isl_give isl_union_pw_qpolynomial_fold *
8768 isl_union_pw_qpolynomial_fold_gist(
8769 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8770 __isl_take isl_union_set *context);
8771 __isl_give isl_union_pw_qpolynomial_fold *
8772 isl_union_pw_qpolynomial_fold_gist_params(
8773 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8774 __isl_take isl_set *context);
8776 =item * Binary Arithmetic Operations
8778 #include <isl/set.h>
8779 __isl_give isl_set *isl_set_sum(
8780 __isl_take isl_set *set1,
8781 __isl_take isl_set *set2);
8782 #include <isl/map.h>
8783 __isl_give isl_map *isl_map_sum(
8784 __isl_take isl_map *map1,
8785 __isl_take isl_map *map2);
8787 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8788 i.e., the set containing the sums of pairs of elements from
8789 C<set1> and C<set2>.
8790 The domain of the result of C<isl_map_sum> is the intersection
8791 of the domains of its two arguments. The corresponding range
8792 elements are the sums of the corresponding range elements
8793 in the two arguments.
8795 #include <isl/val.h>
8796 __isl_give isl_multi_val *isl_multi_val_add(
8797 __isl_take isl_multi_val *mv1,
8798 __isl_take isl_multi_val *mv2);
8799 __isl_give isl_multi_val *isl_multi_val_sub(
8800 __isl_take isl_multi_val *mv1,
8801 __isl_take isl_multi_val *mv2);
8802 __isl_give isl_multi_val *isl_multi_val_min(
8803 __isl_take isl_multi_val *mv1,
8804 __isl_take isl_multi_val *mv2);
8805 __isl_give isl_multi_val *isl_multi_val_max(
8806 __isl_take isl_multi_val *mv1,
8807 __isl_take isl_multi_val *mv2);
8809 #include <isl/aff.h>
8810 __isl_give isl_aff *isl_aff_add(
8811 __isl_take isl_aff *aff1,
8812 __isl_take isl_aff *aff2);
8813 __isl_give isl_multi_aff *isl_multi_aff_add(
8814 __isl_take isl_multi_aff *maff1,
8815 __isl_take isl_multi_aff *maff2);
8816 __isl_give isl_pw_aff *isl_pw_aff_add(
8817 __isl_take isl_pw_aff *pwaff1,
8818 __isl_take isl_pw_aff *pwaff2);
8819 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8820 __isl_take isl_multi_pw_aff *mpa1,
8821 __isl_take isl_multi_pw_aff *mpa2);
8822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8823 __isl_take isl_pw_multi_aff *pma1,
8824 __isl_take isl_pw_multi_aff *pma2);
8825 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8826 __isl_take isl_union_pw_aff *upa1,
8827 __isl_take isl_union_pw_aff *upa2);
8828 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8829 __isl_take isl_union_pw_multi_aff *upma1,
8830 __isl_take isl_union_pw_multi_aff *upma2);
8831 __isl_give isl_multi_union_pw_aff *
8832 isl_multi_union_pw_aff_add(
8833 __isl_take isl_multi_union_pw_aff *mupa1,
8834 __isl_take isl_multi_union_pw_aff *mupa2);
8835 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8836 __isl_take isl_pw_aff *pa,
8837 __isl_take isl_val *v);
8838 __isl_give isl_multi_aff *
8839 isl_multi_aff_add_constant_val(
8840 __isl_take isl_multi_aff *pa,
8841 __isl_take isl_val *v);
8842 __isl_give isl_pw_multi_aff *
8843 isl_pw_multi_aff_add_constant_val(
8844 __isl_take isl_pw_multi_aff *pma,
8845 __isl_take isl_val *v);
8846 __isl_give isl_pw_multi_aff *
8847 isl_pw_multi_aff_add_constant_multi_val(
8848 __isl_take isl_pw_multi_aff *pma,
8849 __isl_take isl_multi_val *mv);
8850 __isl_give isl_multi_pw_aff *
8851 isl_multi_pw_aff_add_constant_val(
8852 __isl_take isl_multi_pw_aff *mpa,
8853 __isl_take isl_val *v);
8854 __isl_give isl_multi_aff *
8855 isl_multi_aff_add_constant_multi_val(
8856 __isl_take isl_multi_aff *pa,
8857 __isl_take isl_multi_val *mv);
8858 __isl_give isl_multi_pw_aff *
8859 isl_multi_pw_aff_add_constant_multi_val(
8860 __isl_take isl_multi_pw_aff *mpa,
8861 __isl_take isl_multi_val *mv);
8862 __isl_give isl_pw_aff *isl_pw_aff_min(
8863 __isl_take isl_pw_aff *pwaff1,
8864 __isl_take isl_pw_aff *pwaff2);
8865 __isl_give isl_pw_aff *isl_pw_aff_max(
8866 __isl_take isl_pw_aff *pwaff1,
8867 __isl_take isl_pw_aff *pwaff2);
8868 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8869 __isl_take isl_multi_pw_aff *mpa1,
8870 __isl_take isl_multi_pw_aff *mpa2);
8871 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8872 __isl_take isl_multi_pw_aff *mpa1,
8873 __isl_take isl_multi_pw_aff *mpa2);
8874 __isl_give isl_aff *isl_aff_sub(
8875 __isl_take isl_aff *aff1,
8876 __isl_take isl_aff *aff2);
8877 __isl_give isl_multi_aff *isl_multi_aff_sub(
8878 __isl_take isl_multi_aff *ma1,
8879 __isl_take isl_multi_aff *ma2);
8880 __isl_give isl_pw_aff *isl_pw_aff_sub(
8881 __isl_take isl_pw_aff *pwaff1,
8882 __isl_take isl_pw_aff *pwaff2);
8883 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8884 __isl_take isl_multi_pw_aff *mpa1,
8885 __isl_take isl_multi_pw_aff *mpa2);
8886 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8887 __isl_take isl_pw_multi_aff *pma1,
8888 __isl_take isl_pw_multi_aff *pma2);
8889 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8890 __isl_take isl_union_pw_aff *upa1,
8891 __isl_take isl_union_pw_aff *upa2);
8892 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8893 __isl_take isl_union_pw_multi_aff *upma1,
8894 __isl_take isl_union_pw_multi_aff *upma2);
8895 __isl_give isl_multi_union_pw_aff *
8896 isl_multi_union_pw_aff_sub(
8897 __isl_take isl_multi_union_pw_aff *mupa1,
8898 __isl_take isl_multi_union_pw_aff *mupa2);
8900 C<isl_aff_sub> subtracts the second argument from the first.
8902 #include <isl/polynomial.h>
8903 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8904 __isl_take isl_qpolynomial *qp1,
8905 __isl_take isl_qpolynomial *qp2);
8906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8907 __isl_take isl_pw_qpolynomial *pwqp1,
8908 __isl_take isl_pw_qpolynomial *pwqp2);
8909 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8910 __isl_take isl_pw_qpolynomial *pwqp1,
8911 __isl_take isl_pw_qpolynomial *pwqp2);
8912 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8913 __isl_take isl_pw_qpolynomial_fold *pwf1,
8914 __isl_take isl_pw_qpolynomial_fold *pwf2);
8915 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8916 __isl_take isl_union_pw_qpolynomial *upwqp1,
8917 __isl_take isl_union_pw_qpolynomial *upwqp2);
8918 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8919 __isl_take isl_qpolynomial *qp1,
8920 __isl_take isl_qpolynomial *qp2);
8921 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8922 __isl_take isl_pw_qpolynomial *pwqp1,
8923 __isl_take isl_pw_qpolynomial *pwqp2);
8924 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8925 __isl_take isl_union_pw_qpolynomial *upwqp1,
8926 __isl_take isl_union_pw_qpolynomial *upwqp2);
8927 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8928 __isl_take isl_pw_qpolynomial_fold *pwf1,
8929 __isl_take isl_pw_qpolynomial_fold *pwf2);
8930 __isl_give isl_union_pw_qpolynomial_fold *
8931 isl_union_pw_qpolynomial_fold_fold(
8932 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8933 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
8935 #include <isl/aff.h>
8936 __isl_give isl_pw_aff *isl_pw_aff_union_add(
8937 __isl_take isl_pw_aff *pwaff1,
8938 __isl_take isl_pw_aff *pwaff2);
8939 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
8940 __isl_take isl_multi_pw_aff *mpa1,
8941 __isl_take isl_multi_pw_aff *mpa2);
8942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
8943 __isl_take isl_pw_multi_aff *pma1,
8944 __isl_take isl_pw_multi_aff *pma2);
8945 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
8946 __isl_take isl_union_pw_aff *upa1,
8947 __isl_take isl_union_pw_aff *upa2);
8948 __isl_give isl_union_pw_multi_aff *
8949 isl_union_pw_multi_aff_union_add(
8950 __isl_take isl_union_pw_multi_aff *upma1,
8951 __isl_take isl_union_pw_multi_aff *upma2);
8952 __isl_give isl_multi_union_pw_aff *
8953 isl_multi_union_pw_aff_union_add(
8954 __isl_take isl_multi_union_pw_aff *mupa1,
8955 __isl_take isl_multi_union_pw_aff *mupa2);
8956 __isl_give isl_pw_aff *isl_pw_aff_union_min(
8957 __isl_take isl_pw_aff *pwaff1,
8958 __isl_take isl_pw_aff *pwaff2);
8959 __isl_give isl_pw_aff *isl_pw_aff_union_max(
8960 __isl_take isl_pw_aff *pwaff1,
8961 __isl_take isl_pw_aff *pwaff2);
8963 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
8964 expression with a domain that is the union of those of C<pwaff1> and
8965 C<pwaff2> and such that on each cell, the quasi-affine expression is
8966 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
8967 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
8968 associated expression is the defined one.
8969 This in contrast to the C<isl_pw_aff_max> function, which is
8970 only defined on the shared definition domain of the arguments.
8972 #include <isl/val.h>
8973 __isl_give isl_multi_val *isl_multi_val_add_val(
8974 __isl_take isl_multi_val *mv,
8975 __isl_take isl_val *v);
8976 __isl_give isl_multi_val *isl_multi_val_mod_val(
8977 __isl_take isl_multi_val *mv,
8978 __isl_take isl_val *v);
8979 __isl_give isl_multi_val *isl_multi_val_scale_val(
8980 __isl_take isl_multi_val *mv,
8981 __isl_take isl_val *v);
8982 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
8983 __isl_take isl_multi_val *mv,
8984 __isl_take isl_val *v);
8986 #include <isl/aff.h>
8987 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
8988 __isl_take isl_val *mod);
8989 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
8990 __isl_take isl_pw_aff *pa,
8991 __isl_take isl_val *mod);
8992 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
8993 __isl_take isl_union_pw_aff *upa,
8994 __isl_take isl_val *f);
8995 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
8996 __isl_take isl_val *v);
8997 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
8998 __isl_take isl_multi_aff *ma,
8999 __isl_take isl_val *v);
9000 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9001 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9002 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9003 __isl_take isl_multi_pw_aff *mpa,
9004 __isl_take isl_val *v);
9005 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9006 __isl_take isl_pw_multi_aff *pma,
9007 __isl_take isl_val *v);
9008 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9009 __isl_take isl_union_pw_aff *upa,
9010 __isl_take isl_val *f);
9011 __isl_give isl_union_pw_multi_aff *
9012 isl_union_pw_multi_aff_scale_val(
9013 __isl_take isl_union_pw_multi_aff *upma,
9014 __isl_take isl_val *val);
9015 __isl_give isl_multi_union_pw_aff *
9016 isl_multi_union_pw_aff_scale_val(
9017 __isl_take isl_multi_union_pw_aff *mupa,
9018 __isl_take isl_val *v);
9019 __isl_give isl_aff *isl_aff_scale_down_ui(
9020 __isl_take isl_aff *aff, unsigned f);
9021 __isl_give isl_aff *isl_aff_scale_down_val(
9022 __isl_take isl_aff *aff, __isl_take isl_val *v);
9023 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9024 __isl_take isl_multi_aff *ma,
9025 __isl_take isl_val *v);
9026 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9027 __isl_take isl_pw_aff *pa,
9028 __isl_take isl_val *f);
9029 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9030 __isl_take isl_multi_pw_aff *mpa,
9031 __isl_take isl_val *v);
9032 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9033 __isl_take isl_pw_multi_aff *pma,
9034 __isl_take isl_val *v);
9035 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9036 __isl_take isl_union_pw_aff *upa,
9037 __isl_take isl_val *v);
9038 __isl_give isl_union_pw_multi_aff *
9039 isl_union_pw_multi_aff_scale_down_val(
9040 __isl_take isl_union_pw_multi_aff *upma,
9041 __isl_take isl_val *val);
9042 __isl_give isl_multi_union_pw_aff *
9043 isl_multi_union_pw_aff_scale_down_val(
9044 __isl_take isl_multi_union_pw_aff *mupa,
9045 __isl_take isl_val *v);
9047 #include <isl/polynomial.h>
9048 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9049 __isl_take isl_qpolynomial *qp,
9050 __isl_take isl_val *v);
9051 __isl_give isl_qpolynomial_fold *
9052 isl_qpolynomial_fold_scale_val(
9053 __isl_take isl_qpolynomial_fold *fold,
9054 __isl_take isl_val *v);
9055 __isl_give isl_pw_qpolynomial *
9056 isl_pw_qpolynomial_scale_val(
9057 __isl_take isl_pw_qpolynomial *pwqp,
9058 __isl_take isl_val *v);
9059 __isl_give isl_pw_qpolynomial_fold *
9060 isl_pw_qpolynomial_fold_scale_val(
9061 __isl_take isl_pw_qpolynomial_fold *pwf,
9062 __isl_take isl_val *v);
9063 __isl_give isl_union_pw_qpolynomial *
9064 isl_union_pw_qpolynomial_scale_val(
9065 __isl_take isl_union_pw_qpolynomial *upwqp,
9066 __isl_take isl_val *v);
9067 __isl_give isl_union_pw_qpolynomial_fold *
9068 isl_union_pw_qpolynomial_fold_scale_val(
9069 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9070 __isl_take isl_val *v);
9071 __isl_give isl_qpolynomial *
9072 isl_qpolynomial_scale_down_val(
9073 __isl_take isl_qpolynomial *qp,
9074 __isl_take isl_val *v);
9075 __isl_give isl_qpolynomial_fold *
9076 isl_qpolynomial_fold_scale_down_val(
9077 __isl_take isl_qpolynomial_fold *fold,
9078 __isl_take isl_val *v);
9079 __isl_give isl_pw_qpolynomial *
9080 isl_pw_qpolynomial_scale_down_val(
9081 __isl_take isl_pw_qpolynomial *pwqp,
9082 __isl_take isl_val *v);
9083 __isl_give isl_pw_qpolynomial_fold *
9084 isl_pw_qpolynomial_fold_scale_down_val(
9085 __isl_take isl_pw_qpolynomial_fold *pwf,
9086 __isl_take isl_val *v);
9087 __isl_give isl_union_pw_qpolynomial *
9088 isl_union_pw_qpolynomial_scale_down_val(
9089 __isl_take isl_union_pw_qpolynomial *upwqp,
9090 __isl_take isl_val *v);
9091 __isl_give isl_union_pw_qpolynomial_fold *
9092 isl_union_pw_qpolynomial_fold_scale_down_val(
9093 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9094 __isl_take isl_val *v);
9096 #include <isl/val.h>
9097 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9098 __isl_take isl_multi_val *mv1,
9099 __isl_take isl_multi_val *mv2);
9100 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9101 __isl_take isl_multi_val *mv1,
9102 __isl_take isl_multi_val *mv2);
9103 __isl_give isl_multi_val *
9104 isl_multi_val_scale_down_multi_val(
9105 __isl_take isl_multi_val *mv1,
9106 __isl_take isl_multi_val *mv2);
9108 #include <isl/aff.h>
9109 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9110 __isl_take isl_multi_aff *ma,
9111 __isl_take isl_multi_val *mv);
9112 __isl_give isl_multi_union_pw_aff *
9113 isl_multi_union_pw_aff_mod_multi_val(
9114 __isl_take isl_multi_union_pw_aff *upma,
9115 __isl_take isl_multi_val *mv);
9116 __isl_give isl_multi_pw_aff *
9117 isl_multi_pw_aff_mod_multi_val(
9118 __isl_take isl_multi_pw_aff *mpa,
9119 __isl_take isl_multi_val *mv);
9120 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9121 __isl_take isl_multi_aff *ma,
9122 __isl_take isl_multi_val *mv);
9123 __isl_give isl_pw_multi_aff *
9124 isl_pw_multi_aff_scale_multi_val(
9125 __isl_take isl_pw_multi_aff *pma,
9126 __isl_take isl_multi_val *mv);
9127 __isl_give isl_multi_pw_aff *
9128 isl_multi_pw_aff_scale_multi_val(
9129 __isl_take isl_multi_pw_aff *mpa,
9130 __isl_take isl_multi_val *mv);
9131 __isl_give isl_multi_union_pw_aff *
9132 isl_multi_union_pw_aff_scale_multi_val(
9133 __isl_take isl_multi_union_pw_aff *mupa,
9134 __isl_take isl_multi_val *mv);
9135 __isl_give isl_union_pw_multi_aff *
9136 isl_union_pw_multi_aff_scale_multi_val(
9137 __isl_take isl_union_pw_multi_aff *upma,
9138 __isl_take isl_multi_val *mv);
9139 __isl_give isl_multi_aff *
9140 isl_multi_aff_scale_down_multi_val(
9141 __isl_take isl_multi_aff *ma,
9142 __isl_take isl_multi_val *mv);
9143 __isl_give isl_pw_multi_aff *
9144 isl_pw_multi_aff_scale_down_multi_val(
9145 __isl_take isl_pw_multi_aff *pma,
9146 __isl_take isl_multi_val *mv);
9147 __isl_give isl_multi_pw_aff *
9148 isl_multi_pw_aff_scale_down_multi_val(
9149 __isl_take isl_multi_pw_aff *mpa,
9150 __isl_take isl_multi_val *mv);
9151 __isl_give isl_multi_union_pw_aff *
9152 isl_multi_union_pw_aff_scale_down_multi_val(
9153 __isl_take isl_multi_union_pw_aff *mupa,
9154 __isl_take isl_multi_val *mv);
9156 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9157 by the corresponding elements of C<mv>.
9159 #include <isl/aff.h>
9160 __isl_give isl_aff *isl_aff_mul(
9161 __isl_take isl_aff *aff1,
9162 __isl_take isl_aff *aff2);
9163 __isl_give isl_aff *isl_aff_div(
9164 __isl_take isl_aff *aff1,
9165 __isl_take isl_aff *aff2);
9166 __isl_give isl_pw_aff *isl_pw_aff_mul(
9167 __isl_take isl_pw_aff *pwaff1,
9168 __isl_take isl_pw_aff *pwaff2);
9169 __isl_give isl_pw_aff *isl_pw_aff_div(
9170 __isl_take isl_pw_aff *pa1,
9171 __isl_take isl_pw_aff *pa2);
9172 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9173 __isl_take isl_pw_aff *pa1,
9174 __isl_take isl_pw_aff *pa2);
9175 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9176 __isl_take isl_pw_aff *pa1,
9177 __isl_take isl_pw_aff *pa2);
9179 When multiplying two affine expressions, at least one of the two needs
9180 to be a constant. Similarly, when dividing an affine expression by another,
9181 the second expression needs to be a constant.
9182 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9183 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9186 #include <isl/polynomial.h>
9187 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9188 __isl_take isl_qpolynomial *qp1,
9189 __isl_take isl_qpolynomial *qp2);
9190 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9191 __isl_take isl_pw_qpolynomial *pwqp1,
9192 __isl_take isl_pw_qpolynomial *pwqp2);
9193 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9194 __isl_take isl_union_pw_qpolynomial *upwqp1,
9195 __isl_take isl_union_pw_qpolynomial *upwqp2);
9199 =head3 Lexicographic Optimization
9201 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9202 the following functions
9203 compute a set that contains the lexicographic minimum or maximum
9204 of the elements in C<set> (or C<bset>) for those values of the parameters
9205 that satisfy C<dom>.
9206 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9207 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9209 In other words, the union of the parameter values
9210 for which the result is non-empty and of C<*empty>
9213 #include <isl/set.h>
9214 __isl_give isl_set *isl_basic_set_partial_lexmin(
9215 __isl_take isl_basic_set *bset,
9216 __isl_take isl_basic_set *dom,
9217 __isl_give isl_set **empty);
9218 __isl_give isl_set *isl_basic_set_partial_lexmax(
9219 __isl_take isl_basic_set *bset,
9220 __isl_take isl_basic_set *dom,
9221 __isl_give isl_set **empty);
9222 __isl_give isl_set *isl_set_partial_lexmin(
9223 __isl_take isl_set *set, __isl_take isl_set *dom,
9224 __isl_give isl_set **empty);
9225 __isl_give isl_set *isl_set_partial_lexmax(
9226 __isl_take isl_set *set, __isl_take isl_set *dom,
9227 __isl_give isl_set **empty);
9229 Given a (basic) set C<set> (or C<bset>), the following functions simply
9230 return a set containing the lexicographic minimum or maximum
9231 of the elements in C<set> (or C<bset>).
9232 In case of union sets, the optimum is computed per space.
9234 #include <isl/set.h>
9235 __isl_give isl_set *isl_basic_set_lexmin(
9236 __isl_take isl_basic_set *bset);
9237 __isl_give isl_set *isl_basic_set_lexmax(
9238 __isl_take isl_basic_set *bset);
9239 __isl_give isl_set *isl_set_lexmin(
9240 __isl_take isl_set *set);
9241 __isl_give isl_set *isl_set_lexmax(
9242 __isl_take isl_set *set);
9243 __isl_give isl_union_set *isl_union_set_lexmin(
9244 __isl_take isl_union_set *uset);
9245 __isl_give isl_union_set *isl_union_set_lexmax(
9246 __isl_take isl_union_set *uset);
9248 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9249 the following functions
9250 compute a relation that maps each element of C<dom>
9251 to the single lexicographic minimum or maximum
9252 of the elements that are associated to that same
9253 element in C<map> (or C<bmap>).
9254 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9255 that contains the elements in C<dom> that do not map
9256 to any elements in C<map> (or C<bmap>).
9257 In other words, the union of the domain of the result and of C<*empty>
9260 #include <isl/map.h>
9261 __isl_give isl_map *isl_basic_map_partial_lexmax(
9262 __isl_take isl_basic_map *bmap,
9263 __isl_take isl_basic_set *dom,
9264 __isl_give isl_set **empty);
9265 __isl_give isl_map *isl_basic_map_partial_lexmin(
9266 __isl_take isl_basic_map *bmap,
9267 __isl_take isl_basic_set *dom,
9268 __isl_give isl_set **empty);
9269 __isl_give isl_map *isl_map_partial_lexmax(
9270 __isl_take isl_map *map, __isl_take isl_set *dom,
9271 __isl_give isl_set **empty);
9272 __isl_give isl_map *isl_map_partial_lexmin(
9273 __isl_take isl_map *map, __isl_take isl_set *dom,
9274 __isl_give isl_set **empty);
9276 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9277 return a map mapping each element in the domain of
9278 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9279 of all elements associated to that element.
9280 In case of union relations, the optimum is computed per space.
9282 #include <isl/map.h>
9283 __isl_give isl_map *isl_basic_map_lexmin(
9284 __isl_take isl_basic_map *bmap);
9285 __isl_give isl_map *isl_basic_map_lexmax(
9286 __isl_take isl_basic_map *bmap);
9287 __isl_give isl_map *isl_map_lexmin(
9288 __isl_take isl_map *map);
9289 __isl_give isl_map *isl_map_lexmax(
9290 __isl_take isl_map *map);
9291 __isl_give isl_union_map *isl_union_map_lexmin(
9292 __isl_take isl_union_map *umap);
9293 __isl_give isl_union_map *isl_union_map_lexmax(
9294 __isl_take isl_union_map *umap);
9296 The following functions return their result in the form of
9297 a piecewise multi-affine expression,
9298 but are otherwise equivalent to the corresponding functions
9299 returning a basic set or relation.
9301 #include <isl/set.h>
9302 __isl_give isl_pw_multi_aff *
9303 isl_basic_set_partial_lexmin_pw_multi_aff(
9304 __isl_take isl_basic_set *bset,
9305 __isl_take isl_basic_set *dom,
9306 __isl_give isl_set **empty);
9307 __isl_give isl_pw_multi_aff *
9308 isl_basic_set_partial_lexmax_pw_multi_aff(
9309 __isl_take isl_basic_set *bset,
9310 __isl_take isl_basic_set *dom,
9311 __isl_give isl_set **empty);
9312 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9313 __isl_take isl_set *set);
9314 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9315 __isl_take isl_set *set);
9317 #include <isl/map.h>
9318 __isl_give isl_pw_multi_aff *
9319 isl_basic_map_lexmin_pw_multi_aff(
9320 __isl_take isl_basic_map *bmap);
9321 __isl_give isl_pw_multi_aff *
9322 isl_basic_map_partial_lexmin_pw_multi_aff(
9323 __isl_take isl_basic_map *bmap,
9324 __isl_take isl_basic_set *dom,
9325 __isl_give isl_set **empty);
9326 __isl_give isl_pw_multi_aff *
9327 isl_basic_map_partial_lexmax_pw_multi_aff(
9328 __isl_take isl_basic_map *bmap,
9329 __isl_take isl_basic_set *dom,
9330 __isl_give isl_set **empty);
9331 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9332 __isl_take isl_map *map);
9333 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9334 __isl_take isl_map *map);
9336 The following functions return the lexicographic minimum or maximum
9337 on the shared domain of the inputs and the single defined function
9338 on those parts of the domain where only a single function is defined.
9340 #include <isl/aff.h>
9341 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9342 __isl_take isl_pw_multi_aff *pma1,
9343 __isl_take isl_pw_multi_aff *pma2);
9344 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9345 __isl_take isl_pw_multi_aff *pma1,
9346 __isl_take isl_pw_multi_aff *pma2);
9348 If the input to a lexicographic optimization problem has
9349 multiple constraints with the same coefficients for the optimized
9350 variables, then, by default, this symmetry is exploited by
9351 replacing those constraints by a single constraint with
9352 an abstract bound, which is in turn bounded by the corresponding terms
9353 in the original constraints.
9354 Without this optimization, the solver would typically consider
9355 all possible orderings of those original bounds, resulting in a needless
9356 decomposition of the domain.
9357 However, the optimization can also result in slowdowns since
9358 an extra parameter is introduced that may get used in additional
9360 The following option determines whether symmetry detection is applied
9361 during lexicographic optimization.
9363 #include <isl/options.h>
9364 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9366 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9370 See also \autoref{s:offline}.
9374 =head2 Ternary Operations
9376 #include <isl/aff.h>
9377 __isl_give isl_pw_aff *isl_pw_aff_cond(
9378 __isl_take isl_pw_aff *cond,
9379 __isl_take isl_pw_aff *pwaff_true,
9380 __isl_take isl_pw_aff *pwaff_false);
9382 The function C<isl_pw_aff_cond> performs a conditional operator
9383 and returns an expression that is equal to C<pwaff_true>
9384 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9385 where C<cond> is zero.
9389 Lists are defined over several element types, including
9390 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9391 C<isl_union_pw_aff>,
9392 C<isl_union_pw_multi_aff>,
9393 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9395 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9396 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9397 Here we take lists of C<isl_set>s as an example.
9398 Lists can be created, copied, modified and freed using the following functions.
9400 #include <isl/set.h>
9401 __isl_give isl_set_list *isl_set_to_list(
9402 __isl_take isl_set *el);
9403 __isl_give isl_set_list *isl_set_list_from_set(
9404 __isl_take isl_set *el);
9405 __isl_give isl_set_list *isl_set_list_alloc(
9406 isl_ctx *ctx, int n);
9407 __isl_give isl_set_list *isl_set_list_copy(
9408 __isl_keep isl_set_list *list);
9409 __isl_give isl_set_list *isl_set_list_insert(
9410 __isl_take isl_set_list *list, unsigned pos,
9411 __isl_take isl_set *el);
9412 __isl_give isl_set_list *isl_set_list_add(
9413 __isl_take isl_set_list *list,
9414 __isl_take isl_set *el);
9415 __isl_give isl_set_list *isl_set_list_drop(
9416 __isl_take isl_set_list *list,
9417 unsigned first, unsigned n);
9418 __isl_give isl_set_list *isl_set_list_clear(
9419 __isl_take isl_set_list *list);
9420 __isl_give isl_set_list *isl_set_list_swap(
9421 __isl_take isl_set_list *list,
9422 unsigned pos1, unsigned pos2);
9423 __isl_give isl_set_list *isl_set_list_reverse(
9424 __isl_take isl_set_list *list);
9425 __isl_give isl_set_list *isl_set_list_set_set(
9426 __isl_take isl_set_list *list, int index,
9427 __isl_take isl_set *set);
9428 __isl_give isl_set_list *isl_set_list_concat(
9429 __isl_take isl_set_list *list1,
9430 __isl_take isl_set_list *list2);
9431 __isl_give isl_set_list *isl_set_list_map(
9432 __isl_take isl_set_list *list,
9433 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9436 __isl_give isl_set_list *isl_set_list_sort(
9437 __isl_take isl_set_list *list,
9438 int (*cmp)(__isl_keep isl_set *a,
9439 __isl_keep isl_set *b, void *user),
9441 __isl_null isl_set_list *isl_set_list_free(
9442 __isl_take isl_set_list *list);
9444 C<isl_set_list_alloc> creates an empty list with an initial capacity
9445 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9446 add elements to a list, increasing its capacity as needed.
9447 C<isl_set_to_list> creates a list with a single element.
9448 C<isl_set_list_from_set> performs the same operation.
9449 C<isl_set_list_clear> removes all elements from a list.
9450 C<isl_set_list_swap> swaps the elements at the specified locations.
9451 C<isl_set_list_reverse> reverses the elements in the list.
9453 Lists can be inspected using the following functions.
9455 #include <isl/set.h>
9456 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9457 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9458 __isl_give isl_set *isl_set_list_get_at(
9459 __isl_keep isl_set_list *list, int index);
9460 __isl_give isl_set *isl_set_list_get_set(
9461 __isl_keep isl_set_list *list, int index);
9462 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9463 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9465 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9466 isl_bool (*test)(__isl_take isl_set *el,
9469 isl_stat isl_set_list_foreach_scc(
9470 __isl_keep isl_set_list *list,
9471 isl_bool (*follows)(__isl_keep isl_set *a,
9472 __isl_keep isl_set *b, void *user),
9474 isl_stat (*fn)(__isl_take isl_set_list *scc,
9478 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9480 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9481 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9482 strongly connected components of the graph with as vertices the elements
9483 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9484 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9485 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9487 Lists can be printed using
9489 #include <isl/set.h>
9490 __isl_give isl_printer *isl_printer_print_set_list(
9491 __isl_take isl_printer *p,
9492 __isl_keep isl_set_list *list);
9494 Alternatively, a string representation can be obtained
9495 directly using the following function, which always prints
9498 #include <isl/set.h>
9499 __isl_give char *isl_set_list_to_str(
9500 __isl_keep isl_set_list *list);
9502 An C<isl_val_list>, C<isl_id_list>,
9503 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9504 C<isl_union_pw_aff_list>,
9505 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9506 can also be read from input using the following functions.
9508 #include <isl/val.h>
9509 __isl_give isl_val_list *isl_val_list_read_from_str(
9510 isl_ctx *ctx, const char *str);
9513 __isl_give isl_id_list *isl_id_list_read_from_str(
9514 isl_ctx *ctx, const char *str);
9516 #include <isl/aff.h>
9517 __isl_give isl_aff_list *
9518 isl_aff_list_read_from_str(isl_ctx *ctx,
9520 __isl_give isl_pw_aff_list *
9521 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9523 __isl_give isl_pw_multi_aff_list *
9524 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9526 __isl_give isl_union_pw_aff_list *
9527 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9530 #include <isl/set.h>
9531 __isl_give isl_set_list *isl_set_list_read_from_str(
9532 isl_ctx *ctx, const char *str);
9534 #include <isl/map.h>
9535 __isl_give isl_map_list *isl_map_list_read_from_str(
9536 isl_ctx *ctx, const char *str);
9538 #include <isl/union_set.h>
9539 __isl_give isl_union_set_list *
9540 isl_union_set_list_read_from_str(isl_ctx *ctx,
9543 =head2 Associative arrays
9545 Associative arrays map isl objects of a specific type to isl objects
9546 of some (other) specific type. They are defined for several pairs
9547 of types, including (C<isl_map>, C<isl_basic_set>),
9548 (C<isl_id>, C<isl_ast_expr>),
9549 (C<isl_id>, C<isl_id>) and
9550 (C<isl_id>, C<isl_pw_aff>).
9551 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9554 Associative arrays can be created, copied and freed using
9555 the following functions.
9557 #include <isl/id_to_ast_expr.h>
9558 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9559 isl_ctx *ctx, int min_size);
9560 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9561 __isl_keep isl_id_to_ast_expr *id2expr);
9562 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9563 __isl_take isl_id_to_ast_expr *id2expr);
9565 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9566 to specify the expected size of the associative array.
9567 The associative array will be grown automatically as needed.
9569 Associative arrays can be inspected using the following functions.
9571 #include <isl/id_to_ast_expr.h>
9572 __isl_give isl_maybe_isl_ast_expr
9573 isl_id_to_ast_expr_try_get(
9574 __isl_keep isl_id_to_ast_expr *id2expr,
9575 __isl_keep isl_id *key);
9576 isl_bool isl_id_to_ast_expr_has(
9577 __isl_keep isl_id_to_ast_expr *id2expr,
9578 __isl_keep isl_id *key);
9579 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9580 __isl_keep isl_id_to_ast_expr *id2expr,
9581 __isl_take isl_id *key);
9582 isl_stat isl_id_to_ast_expr_foreach(
9583 __isl_keep isl_id_to_ast_expr *id2expr,
9584 isl_stat (*fn)(__isl_take isl_id *key,
9585 __isl_take isl_ast_expr *val, void *user),
9588 The function C<isl_id_to_ast_expr_try_get> returns a structure
9589 containing two elements, C<valid> and C<value>.
9590 If there is a value associated to the key, then C<valid>
9591 is set to C<isl_bool_true> and C<value> contains a copy of
9592 the associated value. Otherwise C<value> is C<NULL> and
9593 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9594 on whether some error has occurred or there simply is no associated value.
9595 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9596 in the structure and
9597 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9599 Associative arrays can be modified using the following functions.
9601 #include <isl/id_to_ast_expr.h>
9602 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9603 __isl_take isl_id_to_ast_expr *id2expr,
9604 __isl_take isl_id *key,
9605 __isl_take isl_ast_expr *val);
9606 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9607 __isl_take isl_id_to_ast_expr *id2expr,
9608 __isl_take isl_id *key);
9610 Associative arrays can be printed using the following function.
9612 #include <isl/id_to_ast_expr.h>
9613 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9614 __isl_take isl_printer *p,
9615 __isl_keep isl_id_to_ast_expr *id2expr);
9619 Vectors can be created, copied and freed using the following functions.
9621 #include <isl/vec.h>
9622 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9624 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9626 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9627 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9629 Note that the elements of a vector created by C<isl_vec_alloc>
9630 may have arbitrary values.
9631 A vector created by C<isl_vec_zero> has elements with value zero.
9632 The elements can be changed and inspected using the following functions.
9634 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9635 __isl_give isl_val *isl_vec_get_element_val(
9636 __isl_keep isl_vec *vec, int pos);
9637 __isl_give isl_vec *isl_vec_set_element_si(
9638 __isl_take isl_vec *vec, int pos, int v);
9639 __isl_give isl_vec *isl_vec_set_element_val(
9640 __isl_take isl_vec *vec, int pos,
9641 __isl_take isl_val *v);
9642 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9644 __isl_give isl_vec *isl_vec_set_val(
9645 __isl_take isl_vec *vec, __isl_take isl_val *v);
9646 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9647 __isl_keep isl_vec *vec2, int pos);
9649 C<isl_vec_get_element> will return a negative value if anything went wrong.
9650 In that case, the value of C<*v> is undefined.
9652 The following function can be used to concatenate two vectors.
9654 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9655 __isl_take isl_vec *vec2);
9659 Matrices can be created, copied and freed using the following functions.
9661 #include <isl/mat.h>
9662 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9663 unsigned n_row, unsigned n_col);
9664 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9665 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9667 Note that the elements of a newly created matrix may have arbitrary values.
9668 The elements can be changed and inspected using the following functions.
9670 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9671 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9672 __isl_give isl_val *isl_mat_get_element_val(
9673 __isl_keep isl_mat *mat, int row, int col);
9674 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9675 int row, int col, int v);
9676 __isl_give isl_mat *isl_mat_set_element_val(
9677 __isl_take isl_mat *mat, int row, int col,
9678 __isl_take isl_val *v);
9680 The following function computes the rank of a matrix.
9681 The return value may be -1 if some error occurred.
9683 #include <isl/mat.h>
9684 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9686 The following function can be used to compute the (right) inverse
9687 of a matrix, i.e., a matrix such that the product of the original
9688 and the inverse (in that order) is a multiple of the identity matrix.
9689 The input matrix is assumed to be of full row-rank.
9691 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9693 The following function can be used to compute the (right) kernel
9694 (or null space) of a matrix, i.e., a matrix such that the product of
9695 the original and the kernel (in that order) is the zero matrix.
9697 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9699 The following function computes a basis for the space spanned
9700 by the rows of a matrix.
9702 __isl_give isl_mat *isl_mat_row_basis(
9703 __isl_take isl_mat *mat);
9705 The following function computes rows that extend a basis of C<mat1>
9706 to a basis that also covers C<mat2>.
9708 __isl_give isl_mat *isl_mat_row_basis_extension(
9709 __isl_take isl_mat *mat1,
9710 __isl_take isl_mat *mat2);
9712 The following function checks whether there is no linear dependence
9713 among the combined rows of "mat1" and "mat2" that is not already present
9714 in "mat1" or "mat2" individually.
9715 If "mat1" and "mat2" have linearly independent rows by themselves,
9716 then this means that there is no linear dependence among all rows together.
9718 isl_bool isl_mat_has_linearly_independent_rows(
9719 __isl_keep isl_mat *mat1,
9720 __isl_keep isl_mat *mat2);
9722 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9724 The following functions determine
9725 an upper or lower bound on a quasipolynomial over its domain.
9727 __isl_give isl_pw_qpolynomial_fold *
9728 isl_pw_qpolynomial_bound(
9729 __isl_take isl_pw_qpolynomial *pwqp,
9730 enum isl_fold type, isl_bool *tight);
9732 __isl_give isl_union_pw_qpolynomial_fold *
9733 isl_union_pw_qpolynomial_bound(
9734 __isl_take isl_union_pw_qpolynomial *upwqp,
9735 enum isl_fold type, isl_bool *tight);
9737 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9738 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9739 is the returned bound is known be tight, i.e., for each value
9740 of the parameters there is at least
9741 one element in the domain that reaches the bound.
9742 If the domain of C<pwqp> is not wrapping, then the bound is computed
9743 over all elements in that domain and the result has a purely parametric
9744 domain. If the domain of C<pwqp> is wrapping, then the bound is
9745 computed over the range of the wrapped relation. The domain of the
9746 wrapped relation becomes the domain of the result.
9748 =head2 Parametric Vertex Enumeration
9750 The parametric vertex enumeration described in this section
9751 is mainly intended to be used internally and by the C<barvinok>
9754 #include <isl/vertices.h>
9755 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9756 __isl_keep isl_basic_set *bset);
9758 The function C<isl_basic_set_compute_vertices> performs the
9759 actual computation of the parametric vertices and the chamber
9760 decomposition and stores the result in an C<isl_vertices> object.
9761 This information can be queried by either iterating over all
9762 the vertices or iterating over all the chambers or cells
9763 and then iterating over all vertices that are active on the chamber.
9765 isl_stat isl_vertices_foreach_vertex(
9766 __isl_keep isl_vertices *vertices,
9767 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9768 void *user), void *user);
9770 isl_stat isl_vertices_foreach_cell(
9771 __isl_keep isl_vertices *vertices,
9772 isl_stat (*fn)(__isl_take isl_cell *cell,
9773 void *user), void *user);
9774 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9775 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9776 void *user), void *user);
9778 Other operations that can be performed on an C<isl_vertices> object are
9781 isl_size isl_vertices_get_n_vertices(
9782 __isl_keep isl_vertices *vertices);
9783 __isl_null isl_vertices *isl_vertices_free(
9784 __isl_take isl_vertices *vertices);
9786 Vertices can be inspected and destroyed using the following functions.
9788 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9789 __isl_give isl_basic_set *isl_vertex_get_domain(
9790 __isl_keep isl_vertex *vertex);
9791 __isl_give isl_multi_aff *isl_vertex_get_expr(
9792 __isl_keep isl_vertex *vertex);
9793 __isl_null isl_vertex *isl_vertex_free(
9794 __isl_take isl_vertex *vertex);
9796 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9797 describing the vertex in terms of the parameters,
9798 while C<isl_vertex_get_domain> returns the activity domain
9801 Chambers can be inspected and destroyed using the following functions.
9803 __isl_give isl_basic_set *isl_cell_get_domain(
9804 __isl_keep isl_cell *cell);
9805 __isl_null isl_cell *isl_cell_free(
9806 __isl_take isl_cell *cell);
9808 =head1 Polyhedral Compilation Library
9810 This section collects functionality in C<isl> that has been specifically
9811 designed for use during polyhedral compilation.
9813 =head2 Schedule Trees
9815 A schedule tree is a structured representation of a schedule,
9816 assigning a relative order to a set of domain elements.
9817 The relative order expressed by the schedule tree is
9818 defined recursively. In particular, the order between
9819 two domain elements is determined by the node that is closest
9820 to the root that refers to both elements and that orders them apart.
9821 Each node in the tree is of one of several types.
9822 The root node is always of type C<isl_schedule_node_domain>
9823 (or C<isl_schedule_node_extension>)
9824 and it describes the (extra) domain elements to which the schedule applies.
9825 The other types of nodes are as follows.
9829 =item C<isl_schedule_node_band>
9831 A band of schedule dimensions. Each schedule dimension is represented
9832 by a union piecewise quasi-affine expression. If this expression
9833 assigns a different value to two domain elements, while all previous
9834 schedule dimensions in the same band assign them the same value,
9835 then the two domain elements are ordered according to these two
9837 Each expression is required to be total in the domain elements
9838 that reach the band node.
9840 =item C<isl_schedule_node_expansion>
9842 An expansion node maps each of the domain elements that reach the node
9843 to one or more domain elements. The image of this mapping forms
9844 the set of domain elements that reach the child of the expansion node.
9845 The function that maps each of the expanded domain elements
9846 to the original domain element from which it was expanded
9847 is called the contraction.
9849 =item C<isl_schedule_node_filter>
9851 A filter node does not impose any ordering, but rather intersects
9852 the set of domain elements that the current subtree refers to
9853 with a given union set. The subtree of the filter node only
9854 refers to domain elements in the intersection.
9855 A filter node is typically only used as a child of a sequence or
9858 =item C<isl_schedule_node_leaf>
9860 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9862 =item C<isl_schedule_node_mark>
9864 A mark node can be used to attach any kind of information to a subtree
9865 of the schedule tree.
9867 =item C<isl_schedule_node_sequence>
9869 A sequence node has one or more children, each of which is a filter node.
9870 The filters on these filter nodes form a partition of
9871 the domain elements that the current subtree refers to.
9872 If two domain elements appear in distinct filters then the sequence
9873 node orders them according to the child positions of the corresponding
9876 =item C<isl_schedule_node_set>
9878 A set node is similar to a sequence node, except that
9879 it expresses that domain elements appearing in distinct filters
9880 may have any order. The order of the children of a set node
9881 is therefore also immaterial.
9885 The following node types are only supported by the AST generator.
9889 =item C<isl_schedule_node_context>
9891 The context describes constraints on the parameters and
9892 the schedule dimensions of outer
9893 bands that the AST generator may assume to hold. It is also the only
9894 kind of node that may introduce additional parameters.
9895 The space of the context is that of the flat product of the outer
9896 band nodes. In particular, if there are no outer band nodes, then
9897 this space is the unnamed zero-dimensional space.
9898 Since a context node references the outer band nodes, any tree
9899 containing a context node is considered to be anchored.
9901 =item C<isl_schedule_node_extension>
9903 An extension node instructs the AST generator to add additional
9904 domain elements that need to be scheduled.
9905 The additional domain elements are described by the range of
9906 the extension map in terms of the outer schedule dimensions,
9907 i.e., the flat product of the outer band nodes.
9908 Note that domain elements are added whenever the AST generator
9909 reaches the extension node, meaning that there are still some
9910 active domain elements for which an AST needs to be generated.
9911 The conditions under which some domain elements are still active
9912 may however not be completely described by the outer AST nodes
9913 generated at that point.
9914 Since an extension node references the outer band nodes, any tree
9915 containing an extension node is considered to be anchored.
9917 An extension node may also appear as the root of a schedule tree,
9918 when it is intended to be inserted into another tree
9919 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
9920 In this case, the domain of the extension node should
9921 correspond to the flat product of the outer band nodes
9922 in this other schedule tree at the point where the extension tree
9925 =item C<isl_schedule_node_guard>
9927 The guard describes constraints on the parameters and
9928 the schedule dimensions of outer
9929 bands that need to be enforced by the outer nodes
9930 in the generated AST.
9931 That is, the part of the AST that is generated from descendants
9932 of the guard node can assume that these constraints are satisfied.
9933 The space of the guard is that of the flat product of the outer
9934 band nodes. In particular, if there are no outer band nodes, then
9935 this space is the unnamed zero-dimensional space.
9936 Since a guard node references the outer band nodes, any tree
9937 containing a guard node is considered to be anchored.
9941 Except for the C<isl_schedule_node_context> nodes,
9942 none of the nodes may introduce any parameters that were not
9943 already present in the root domain node.
9945 A schedule tree is encapsulated in an C<isl_schedule> object.
9946 The simplest such objects, those with a tree consisting of single domain node,
9947 can be created using the following functions with either an empty
9948 domain or a given domain.
9950 #include <isl/schedule.h>
9951 __isl_give isl_schedule *isl_schedule_empty(
9952 __isl_take isl_space *space);
9953 __isl_give isl_schedule *isl_schedule_from_domain(
9954 __isl_take isl_union_set *domain);
9956 The function C<isl_schedule_constraints_compute_schedule> described
9957 in L</"Scheduling"> can also be used to construct schedules.
9959 C<isl_schedule> objects may be copied and freed using the following functions.
9961 #include <isl/schedule.h>
9962 __isl_give isl_schedule *isl_schedule_copy(
9963 __isl_keep isl_schedule *sched);
9964 __isl_null isl_schedule *isl_schedule_free(
9965 __isl_take isl_schedule *sched);
9967 The following functions checks whether two C<isl_schedule> objects
9968 are obviously the same.
9970 #include <isl/schedule.h>
9971 isl_bool isl_schedule_plain_is_equal(
9972 __isl_keep isl_schedule *schedule1,
9973 __isl_keep isl_schedule *schedule2);
9975 The domain of the schedule, i.e., the domain described by the root node,
9976 can be obtained using the following function.
9978 #include <isl/schedule.h>
9979 __isl_give isl_union_set *isl_schedule_get_domain(
9980 __isl_keep isl_schedule *schedule);
9982 An extra top-level band node (right underneath the domain node) can
9983 be introduced into the schedule using the following function.
9984 The schedule tree is assumed not to have any anchored nodes.
9986 #include <isl/schedule.h>
9987 __isl_give isl_schedule *
9988 isl_schedule_insert_partial_schedule(
9989 __isl_take isl_schedule *schedule,
9990 __isl_take isl_multi_union_pw_aff *partial);
9992 A top-level context node (right underneath the domain node) can
9993 be introduced into the schedule using the following function.
9995 #include <isl/schedule.h>
9996 __isl_give isl_schedule *isl_schedule_insert_context(
9997 __isl_take isl_schedule *schedule,
9998 __isl_take isl_set *context)
10000 A top-level guard node (right underneath the domain node) can
10001 be introduced into the schedule using the following function.
10003 #include <isl/schedule.h>
10004 __isl_give isl_schedule *isl_schedule_insert_guard(
10005 __isl_take isl_schedule *schedule,
10006 __isl_take isl_set *guard)
10008 A schedule that combines two schedules either in the given
10009 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10010 or an C<isl_schedule_node_set> node,
10011 can be created using the following functions.
10013 #include <isl/schedule.h>
10014 __isl_give isl_schedule *isl_schedule_sequence(
10015 __isl_take isl_schedule *schedule1,
10016 __isl_take isl_schedule *schedule2);
10017 __isl_give isl_schedule *isl_schedule_set(
10018 __isl_take isl_schedule *schedule1,
10019 __isl_take isl_schedule *schedule2);
10021 The domains of the two input schedules need to be disjoint.
10023 The following function can be used to restrict the domain
10024 of a schedule with a domain node as root to be a subset of the given union set.
10025 This operation may remove nodes in the tree that have become
10028 #include <isl/schedule.h>
10029 __isl_give isl_schedule *isl_schedule_intersect_domain(
10030 __isl_take isl_schedule *schedule,
10031 __isl_take isl_union_set *domain);
10033 The following function can be used to simplify the domain
10034 of a schedule with a domain node as root with respect to the given
10037 #include <isl/schedule.h>
10038 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10039 __isl_take isl_schedule *schedule,
10040 __isl_take isl_set *context);
10042 The following function resets the user pointers on all parameter
10043 and tuple identifiers referenced by the nodes of the given schedule.
10045 #include <isl/schedule.h>
10046 __isl_give isl_schedule *isl_schedule_reset_user(
10047 __isl_take isl_schedule *schedule);
10049 The following function aligns the parameters of all nodes
10050 in the given schedule to the given space.
10052 #include <isl/schedule.h>
10053 __isl_give isl_schedule *isl_schedule_align_params(
10054 __isl_take isl_schedule *schedule,
10055 __isl_take isl_space *space);
10057 The following function allows the user to plug in a given function
10058 in the iteration domains. The input schedule is not allowed to contain
10059 any expansion nodes.
10061 #include <isl/schedule.h>
10062 __isl_give isl_schedule *
10063 isl_schedule_pullback_union_pw_multi_aff(
10064 __isl_take isl_schedule *schedule,
10065 __isl_take isl_union_pw_multi_aff *upma);
10067 The following function can be used to plug in the schedule C<expansion>
10068 in the leaves of C<schedule>, where C<contraction> describes how
10069 the domain elements of C<expansion> map to the domain elements
10070 at the original leaves of C<schedule>.
10071 The resulting schedule will contain expansion nodes, unless
10072 C<contraction> is an identity function.
10074 #include <isl/schedule.h>
10075 __isl_give isl_schedule *isl_schedule_expand(
10076 __isl_take isl_schedule *schedule,
10077 __isl_take isl_union_pw_multi_aff *contraction,
10078 __isl_take isl_schedule *expansion);
10080 An C<isl_union_map> representation of the schedule can be obtained
10081 from an C<isl_schedule> using the following function.
10083 #include <isl/schedule.h>
10084 __isl_give isl_union_map *isl_schedule_get_map(
10085 __isl_keep isl_schedule *sched);
10087 The resulting relation encodes the same relative ordering as
10088 the schedule by mapping the domain elements to a common schedule space.
10089 If the schedule_separate_components option is set, then the order
10090 of the children of a set node is explicitly encoded in the result.
10091 If the tree contains any expansion nodes, then the relation
10092 is formulated in terms of the expanded domain elements.
10094 Schedules can be read from input using the following functions.
10096 #include <isl/schedule.h>
10097 __isl_give isl_schedule *isl_schedule_read_from_file(
10098 isl_ctx *ctx, FILE *input);
10099 __isl_give isl_schedule *isl_schedule_read_from_str(
10100 isl_ctx *ctx, const char *str);
10102 A representation of the schedule can be printed using
10104 #include <isl/schedule.h>
10105 __isl_give isl_printer *isl_printer_print_schedule(
10106 __isl_take isl_printer *p,
10107 __isl_keep isl_schedule *schedule);
10108 __isl_give char *isl_schedule_to_str(
10109 __isl_keep isl_schedule *schedule);
10111 C<isl_schedule_to_str> prints the schedule in flow format.
10113 The schedule tree can be traversed through the use of
10114 C<isl_schedule_node> objects that point to a particular
10115 position in the schedule tree. Whenever a C<isl_schedule_node>
10116 is used to modify a node in the schedule tree, the original schedule
10117 tree is left untouched and the modifications are performed to a copy
10118 of the tree. The returned C<isl_schedule_node> then points to
10119 this modified copy of the tree.
10121 The root of the schedule tree can be obtained using the following function.
10123 #include <isl/schedule.h>
10124 __isl_give isl_schedule_node *isl_schedule_get_root(
10125 __isl_keep isl_schedule *schedule);
10127 A pointer to a newly created schedule tree with a single domain
10128 node can be created using the following functions.
10130 #include <isl/schedule_node.h>
10131 __isl_give isl_schedule_node *
10132 isl_schedule_node_from_domain(
10133 __isl_take isl_union_set *domain);
10134 __isl_give isl_schedule_node *
10135 isl_schedule_node_from_extension(
10136 __isl_take isl_union_map *extension);
10138 C<isl_schedule_node_from_extension> creates a tree with an extension
10141 Schedule nodes can be copied and freed using the following functions.
10143 #include <isl/schedule_node.h>
10144 __isl_give isl_schedule_node *isl_schedule_node_copy(
10145 __isl_keep isl_schedule_node *node);
10146 __isl_null isl_schedule_node *isl_schedule_node_free(
10147 __isl_take isl_schedule_node *node);
10149 The following functions can be used to check if two schedule
10150 nodes point to the same position in the same schedule.
10152 #include <isl/schedule_node.h>
10153 isl_bool isl_schedule_node_is_equal(
10154 __isl_keep isl_schedule_node *node1,
10155 __isl_keep isl_schedule_node *node2);
10157 The following properties can be obtained from a schedule node.
10159 #include <isl/schedule_node.h>
10160 enum isl_schedule_node_type isl_schedule_node_get_type(
10161 __isl_keep isl_schedule_node *node);
10162 enum isl_schedule_node_type
10163 isl_schedule_node_get_parent_type(
10164 __isl_keep isl_schedule_node *node);
10165 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10166 __isl_keep isl_schedule_node *node);
10168 The function C<isl_schedule_node_get_type> returns the type of
10169 the node, while C<isl_schedule_node_get_parent_type> returns
10170 type of the parent of the node, which is required to exist.
10171 The function C<isl_schedule_node_get_schedule> returns a copy
10172 to the schedule to which the node belongs.
10174 The following functions can be used to move the schedule node
10175 to a different position in the tree or to check if such a position
10178 #include <isl/schedule_node.h>
10179 isl_bool isl_schedule_node_has_parent(
10180 __isl_keep isl_schedule_node *node);
10181 __isl_give isl_schedule_node *isl_schedule_node_parent(
10182 __isl_take isl_schedule_node *node);
10183 __isl_give isl_schedule_node *
10184 isl_schedule_node_grandparent(
10185 __isl_take isl_schedule_node *node);
10186 __isl_give isl_schedule_node *isl_schedule_node_root(
10187 __isl_take isl_schedule_node *node);
10188 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10189 __isl_take isl_schedule_node *node,
10191 isl_size isl_schedule_node_n_children(
10192 __isl_keep isl_schedule_node *node);
10193 __isl_give isl_schedule_node *isl_schedule_node_child(
10194 __isl_take isl_schedule_node *node, int pos);
10195 isl_bool isl_schedule_node_has_children(
10196 __isl_keep isl_schedule_node *node);
10197 __isl_give isl_schedule_node *
10198 isl_schedule_node_grandchild(
10199 __isl_take isl_schedule_node *node,
10200 int pos1, int pos2);
10201 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10202 __isl_take isl_schedule_node *node);
10203 isl_bool isl_schedule_node_has_previous_sibling(
10204 __isl_keep isl_schedule_node *node);
10205 __isl_give isl_schedule_node *
10206 isl_schedule_node_previous_sibling(
10207 __isl_take isl_schedule_node *node);
10208 isl_bool isl_schedule_node_has_next_sibling(
10209 __isl_keep isl_schedule_node *node);
10210 __isl_give isl_schedule_node *
10211 isl_schedule_node_next_sibling(
10212 __isl_take isl_schedule_node *node);
10214 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10215 is the node itself, the ancestor of generation 1 is its parent and so on.
10217 It is also possible to query the number of ancestors of a node,
10218 the position of the current node
10219 within the children of its parent, the position of the subtree
10220 containing a node within the children of an ancestor
10221 or to obtain a copy of a given
10222 child without destroying the current node.
10223 Given two nodes that point to the same schedule, their closest
10224 shared ancestor can be obtained using
10225 C<isl_schedule_node_get_shared_ancestor>.
10227 #include <isl/schedule_node.h>
10228 isl_size isl_schedule_node_get_tree_depth(
10229 __isl_keep isl_schedule_node *node);
10230 isl_size isl_schedule_node_get_child_position(
10231 __isl_keep isl_schedule_node *node);
10232 isl_size isl_schedule_node_get_ancestor_child_position(
10233 __isl_keep isl_schedule_node *node,
10234 __isl_keep isl_schedule_node *ancestor);
10235 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10236 __isl_keep isl_schedule_node *node, int pos);
10237 __isl_give isl_schedule_node *
10238 isl_schedule_node_get_shared_ancestor(
10239 __isl_keep isl_schedule_node *node1,
10240 __isl_keep isl_schedule_node *node2);
10242 All nodes in a schedule tree or
10243 all descendants of a specific node (including the node) can be visited
10244 in depth-first pre-order using the following functions.
10246 #include <isl/schedule.h>
10247 isl_stat isl_schedule_foreach_schedule_node_top_down(
10248 __isl_keep isl_schedule *sched,
10249 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10250 void *user), void *user);
10252 #include <isl/schedule_node.h>
10253 isl_stat isl_schedule_node_foreach_descendant_top_down(
10254 __isl_keep isl_schedule_node *node,
10255 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10256 void *user), void *user);
10258 The callback function is slightly different from the usual
10259 callbacks in that it not only indicates success (non-negative result)
10260 or failure (negative result), but also indicates whether the children
10261 of the given node should be visited. In particular, if the callback
10262 returns a positive value, then the children are visited, but if
10263 the callback returns zero, then the children are not visited.
10265 The following functions checks whether
10266 all descendants of a specific node (including the node itself)
10267 satisfy a user-specified test.
10269 #include <isl/schedule_node.h>
10270 isl_bool isl_schedule_node_every_descendant(
10271 __isl_keep isl_schedule_node *node,
10272 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10273 void *user), void *user)
10275 The ancestors of a node in a schedule tree can be visited from
10276 the root down to and including the parent of the node using
10277 the following function.
10279 #include <isl/schedule_node.h>
10280 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10281 __isl_keep isl_schedule_node *node,
10282 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10283 void *user), void *user);
10285 The following functions allows for a depth-first post-order
10286 traversal of the nodes in a schedule tree or
10287 of the descendants of a specific node (including the node
10288 itself), where the user callback is allowed to modify the
10291 #include <isl/schedule.h>
10292 __isl_give isl_schedule *
10293 isl_schedule_map_schedule_node_bottom_up(
10294 __isl_take isl_schedule *schedule,
10295 __isl_give isl_schedule_node *(*fn)(
10296 __isl_take isl_schedule_node *node,
10297 void *user), void *user);
10299 #include <isl/schedule_node.h>
10300 __isl_give isl_schedule_node *
10301 isl_schedule_node_map_descendant_bottom_up(
10302 __isl_take isl_schedule_node *node,
10303 __isl_give isl_schedule_node *(*fn)(
10304 __isl_take isl_schedule_node *node,
10305 void *user), void *user);
10307 The traversal continues from the node returned by the callback function.
10308 It is the responsibility of the user to ensure that this does not
10309 lead to an infinite loop. It is safest to always return a pointer
10310 to the same position (same ancestors and child positions) as the input node.
10312 The following function removes a node (along with its descendants)
10313 from a schedule tree and returns a pointer to the leaf at the
10314 same position in the updated tree.
10315 It is not allowed to remove the root of a schedule tree or
10316 a child of a set or sequence node.
10318 #include <isl/schedule_node.h>
10319 __isl_give isl_schedule_node *isl_schedule_node_cut(
10320 __isl_take isl_schedule_node *node);
10322 The following function removes a single node
10323 from a schedule tree and returns a pointer to the child
10324 of the node, now located at the position of the original node
10325 or to a leaf node at that position if there was no child.
10326 It is not allowed to remove the root of a schedule tree,
10327 a set or sequence node, a child of a set or sequence node or
10328 a band node with an anchored subtree.
10330 #include <isl/schedule_node.h>
10331 __isl_give isl_schedule_node *isl_schedule_node_delete(
10332 __isl_take isl_schedule_node *node);
10334 Most nodes in a schedule tree only contain local information.
10335 In some cases, however, a node may also refer to the schedule dimensions
10336 of its outer band nodes.
10337 This means that the position of the node within the tree should
10338 not be changed, or at least that no changes are performed to the
10339 outer band nodes. The following function can be used to test
10340 whether the subtree rooted at a given node contains any such nodes.
10342 #include <isl/schedule_node.h>
10343 isl_bool isl_schedule_node_is_subtree_anchored(
10344 __isl_keep isl_schedule_node *node);
10346 The following function resets the user pointers on all parameter
10347 and tuple identifiers referenced by the given schedule node.
10349 #include <isl/schedule_node.h>
10350 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10351 __isl_take isl_schedule_node *node);
10353 The following function aligns the parameters of the given schedule
10354 node to the given space.
10356 #include <isl/schedule_node.h>
10357 __isl_give isl_schedule_node *
10358 isl_schedule_node_align_params(
10359 __isl_take isl_schedule_node *node,
10360 __isl_take isl_space *space);
10362 Several node types have their own functions for querying
10363 (and in some cases setting) some node type specific properties.
10365 #include <isl/schedule_node.h>
10366 __isl_give isl_space *isl_schedule_node_band_get_space(
10367 __isl_keep isl_schedule_node *node);
10368 __isl_give isl_multi_union_pw_aff *
10369 isl_schedule_node_band_get_partial_schedule(
10370 __isl_keep isl_schedule_node *node);
10371 __isl_give isl_union_map *
10372 isl_schedule_node_band_get_partial_schedule_union_map(
10373 __isl_keep isl_schedule_node *node);
10374 isl_size isl_schedule_node_band_n_member(
10375 __isl_keep isl_schedule_node *node);
10376 isl_bool isl_schedule_node_band_member_get_coincident(
10377 __isl_keep isl_schedule_node *node, int pos);
10378 __isl_give isl_schedule_node *
10379 isl_schedule_node_band_member_set_coincident(
10380 __isl_take isl_schedule_node *node, int pos,
10382 isl_bool isl_schedule_node_band_get_permutable(
10383 __isl_keep isl_schedule_node *node);
10384 __isl_give isl_schedule_node *
10385 isl_schedule_node_band_set_permutable(
10386 __isl_take isl_schedule_node *node, int permutable);
10387 enum isl_ast_loop_type
10388 isl_schedule_node_band_member_get_ast_loop_type(
10389 __isl_keep isl_schedule_node *node, int pos);
10390 __isl_give isl_schedule_node *
10391 isl_schedule_node_band_member_set_ast_loop_type(
10392 __isl_take isl_schedule_node *node, int pos,
10393 enum isl_ast_loop_type type);
10394 enum isl_ast_loop_type
10395 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10396 __isl_keep isl_schedule_node *node, int pos);
10397 __isl_give isl_schedule_node *
10398 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10399 __isl_take isl_schedule_node *node, int pos,
10400 enum isl_ast_loop_type type);
10401 __isl_give isl_union_set *
10402 isl_schedule_node_band_get_ast_build_options(
10403 __isl_keep isl_schedule_node *node);
10404 __isl_give isl_schedule_node *
10405 isl_schedule_node_band_set_ast_build_options(
10406 __isl_take isl_schedule_node *node,
10407 __isl_take isl_union_set *options);
10408 __isl_give isl_set *
10409 isl_schedule_node_band_get_ast_isolate_option(
10410 __isl_keep isl_schedule_node *node);
10412 The function C<isl_schedule_node_band_get_space> returns the space
10413 of the partial schedule of the band.
10414 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10415 returns a representation of the partial schedule of the band node
10416 in the form of an C<isl_union_map>.
10417 The coincident and permutable properties are set by
10418 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10420 A scheduling dimension is considered to be ``coincident''
10421 if it satisfies the coincidence constraints within its band.
10422 That is, if the dependence distances of the coincidence
10423 constraints are all zero in that direction (for fixed
10424 iterations of outer bands).
10425 A band is marked permutable if it was produced using the Pluto-like scheduler.
10426 Note that the scheduler may have to resort to a Feautrier style scheduling
10427 step even if the default scheduler is used.
10428 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10429 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10430 For the meaning of these loop AST generation types and the difference
10431 between the regular loop AST generation type and the isolate
10432 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10433 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10434 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10435 may return C<isl_ast_loop_error> if an error occurs.
10436 The AST build options govern how an AST is generated for
10437 the individual schedule dimensions during AST generation.
10438 See L</"AST Generation Options (Schedule Tree)">.
10439 The isolate option for the given node can be extracted from these
10440 AST build options using the function
10441 C<isl_schedule_node_band_get_ast_isolate_option>.
10443 #include <isl/schedule_node.h>
10444 __isl_give isl_set *
10445 isl_schedule_node_context_get_context(
10446 __isl_keep isl_schedule_node *node);
10448 #include <isl/schedule_node.h>
10449 __isl_give isl_union_set *
10450 isl_schedule_node_domain_get_domain(
10451 __isl_keep isl_schedule_node *node);
10453 #include <isl/schedule_node.h>
10454 __isl_give isl_union_map *
10455 isl_schedule_node_expansion_get_expansion(
10456 __isl_keep isl_schedule_node *node);
10457 __isl_give isl_union_pw_multi_aff *
10458 isl_schedule_node_expansion_get_contraction(
10459 __isl_keep isl_schedule_node *node);
10461 #include <isl/schedule_node.h>
10462 __isl_give isl_union_map *
10463 isl_schedule_node_extension_get_extension(
10464 __isl_keep isl_schedule_node *node);
10466 #include <isl/schedule_node.h>
10467 __isl_give isl_union_set *
10468 isl_schedule_node_filter_get_filter(
10469 __isl_keep isl_schedule_node *node);
10471 #include <isl/schedule_node.h>
10472 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10473 __isl_keep isl_schedule_node *node);
10475 #include <isl/schedule_node.h>
10476 __isl_give isl_id *isl_schedule_node_mark_get_id(
10477 __isl_keep isl_schedule_node *node);
10479 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10480 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10481 partial schedules related to the node.
10483 #include <isl/schedule_node.h>
10484 __isl_give isl_multi_union_pw_aff *
10485 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10486 __isl_keep isl_schedule_node *node);
10487 __isl_give isl_union_pw_multi_aff *
10488 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10489 __isl_keep isl_schedule_node *node);
10490 __isl_give isl_union_map *
10491 isl_schedule_node_get_prefix_schedule_union_map(
10492 __isl_keep isl_schedule_node *node);
10493 __isl_give isl_union_map *
10494 isl_schedule_node_get_prefix_schedule_relation(
10495 __isl_keep isl_schedule_node *node);
10496 __isl_give isl_union_map *
10497 isl_schedule_node_get_subtree_schedule_union_map(
10498 __isl_keep isl_schedule_node *node);
10500 In particular, the functions
10501 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10502 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10503 and C<isl_schedule_node_get_prefix_schedule_union_map>
10504 return a relative ordering on the domain elements that reach the given
10505 node determined by its ancestors.
10506 The function C<isl_schedule_node_get_prefix_schedule_relation>
10507 additionally includes the domain constraints in the result.
10508 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10509 returns a representation of the partial schedule defined by the
10510 subtree rooted at the given node.
10511 If the tree contains any expansion nodes, then the subtree schedule
10512 is formulated in terms of the expanded domain elements.
10513 The tree passed to functions returning a prefix schedule
10514 may only contain extension nodes if these would not affect
10515 the result of these functions. That is, if one of the ancestors
10516 is an extension node, then all of the domain elements that were
10517 added by the extension node need to have been filtered out
10518 by filter nodes between the extension node and the input node.
10519 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10520 may not contain in extension nodes in the selected subtree.
10522 The expansion/contraction defined by an entire subtree, combining
10523 the expansions/contractions
10524 on the expansion nodes in the subtree, can be obtained using
10525 the following functions.
10527 #include <isl/schedule_node.h>
10528 __isl_give isl_union_map *
10529 isl_schedule_node_get_subtree_expansion(
10530 __isl_keep isl_schedule_node *node);
10531 __isl_give isl_union_pw_multi_aff *
10532 isl_schedule_node_get_subtree_contraction(
10533 __isl_keep isl_schedule_node *node);
10535 The total number of outer band members of given node, i.e.,
10536 the shared output dimension of the maps in the result
10537 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10538 using the following function.
10540 #include <isl/schedule_node.h>
10541 isl_size isl_schedule_node_get_schedule_depth(
10542 __isl_keep isl_schedule_node *node);
10544 The following functions return the elements that reach the given node
10545 or the union of universes in the spaces that contain these elements.
10547 #include <isl/schedule_node.h>
10548 __isl_give isl_union_set *
10549 isl_schedule_node_get_domain(
10550 __isl_keep isl_schedule_node *node);
10551 __isl_give isl_union_set *
10552 isl_schedule_node_get_universe_domain(
10553 __isl_keep isl_schedule_node *node);
10555 The input tree of C<isl_schedule_node_get_domain>
10556 may only contain extension nodes if these would not affect
10557 the result of this function. That is, if one of the ancestors
10558 is an extension node, then all of the domain elements that were
10559 added by the extension node need to have been filtered out
10560 by filter nodes between the extension node and the input node.
10562 The following functions can be used to introduce additional nodes
10563 in the schedule tree. The new node is introduced at the point
10564 in the tree where the C<isl_schedule_node> points to and
10565 the results points to the new node.
10567 #include <isl/schedule_node.h>
10568 __isl_give isl_schedule_node *
10569 isl_schedule_node_insert_partial_schedule(
10570 __isl_take isl_schedule_node *node,
10571 __isl_take isl_multi_union_pw_aff *schedule);
10573 This function inserts a new band node with (the greatest integer
10574 part of) the given partial schedule.
10575 The subtree rooted at the given node is assumed not to have
10576 any anchored nodes.
10578 #include <isl/schedule_node.h>
10579 __isl_give isl_schedule_node *
10580 isl_schedule_node_insert_context(
10581 __isl_take isl_schedule_node *node,
10582 __isl_take isl_set *context);
10584 This function inserts a new context node with the given context constraints.
10586 #include <isl/schedule_node.h>
10587 __isl_give isl_schedule_node *
10588 isl_schedule_node_insert_filter(
10589 __isl_take isl_schedule_node *node,
10590 __isl_take isl_union_set *filter);
10592 This function inserts a new filter node with the given filter.
10593 If the original node already pointed to a filter node, then the
10594 two filter nodes are merged into one.
10596 #include <isl/schedule_node.h>
10597 __isl_give isl_schedule_node *
10598 isl_schedule_node_insert_guard(
10599 __isl_take isl_schedule_node *node,
10600 __isl_take isl_set *guard);
10602 This function inserts a new guard node with the given guard constraints.
10604 #include <isl/schedule_node.h>
10605 __isl_give isl_schedule_node *
10606 isl_schedule_node_insert_mark(
10607 __isl_take isl_schedule_node *node,
10608 __isl_take isl_id *mark);
10610 This function inserts a new mark node with the give mark identifier.
10612 #include <isl/schedule_node.h>
10613 __isl_give isl_schedule_node *
10614 isl_schedule_node_insert_sequence(
10615 __isl_take isl_schedule_node *node,
10616 __isl_take isl_union_set_list *filters);
10617 __isl_give isl_schedule_node *
10618 isl_schedule_node_insert_set(
10619 __isl_take isl_schedule_node *node,
10620 __isl_take isl_union_set_list *filters);
10622 These functions insert a new sequence or set node with the given
10623 filters as children.
10625 #include <isl/schedule_node.h>
10626 __isl_give isl_schedule_node *isl_schedule_node_group(
10627 __isl_take isl_schedule_node *node,
10628 __isl_take isl_id *group_id);
10630 This function introduces an expansion node in between the current
10631 node and its parent that expands instances of a space with tuple
10632 identifier C<group_id> to the original domain elements that reach
10633 the node. The group instances are identified by the prefix schedule
10634 of those domain elements. The ancestors of the node are adjusted
10635 to refer to the group instances instead of the original domain
10636 elements. The return value points to the same node in the updated
10637 schedule tree as the input node, i.e., to the child of the newly
10638 introduced expansion node. Grouping instances of different statements
10639 ensures that they will be treated as a single statement by the
10640 AST generator up to the point of the expansion node.
10642 The following function can be used to flatten a nested
10645 #include <isl/schedule_node.h>
10646 __isl_give isl_schedule_node *
10647 isl_schedule_node_sequence_splice_child(
10648 __isl_take isl_schedule_node *node, int pos);
10650 That is, given a sequence node C<node> that has another sequence node
10651 in its child at position C<pos> (in particular, the child of that filter
10652 node is a sequence node), attach the children of that other sequence
10653 node as children of C<node>, replacing the original child at position
10656 The partial schedule of a band node can be scaled (down) or reduced using
10657 the following functions.
10659 #include <isl/schedule_node.h>
10660 __isl_give isl_schedule_node *
10661 isl_schedule_node_band_scale(
10662 __isl_take isl_schedule_node *node,
10663 __isl_take isl_multi_val *mv);
10664 __isl_give isl_schedule_node *
10665 isl_schedule_node_band_scale_down(
10666 __isl_take isl_schedule_node *node,
10667 __isl_take isl_multi_val *mv);
10668 __isl_give isl_schedule_node *
10669 isl_schedule_node_band_mod(
10670 __isl_take isl_schedule_node *node,
10671 __isl_take isl_multi_val *mv);
10673 The spaces of the two arguments need to match.
10674 After scaling, the partial schedule is replaced by its greatest
10675 integer part to ensure that the schedule remains integral.
10677 The partial schedule of a band node can be shifted by an
10678 C<isl_multi_union_pw_aff> with a domain that is a superset
10679 of the domain of the partial schedule using
10680 the following function.
10682 #include <isl/schedule_node.h>
10683 __isl_give isl_schedule_node *
10684 isl_schedule_node_band_shift(
10685 __isl_take isl_schedule_node *node,
10686 __isl_take isl_multi_union_pw_aff *shift);
10688 A band node can be tiled using the following function.
10690 #include <isl/schedule_node.h>
10691 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10692 __isl_take isl_schedule_node *node,
10693 __isl_take isl_multi_val *sizes);
10695 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10697 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10698 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10700 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10702 The C<isl_schedule_node_band_tile> function tiles
10703 the band using the given tile sizes inside its schedule.
10704 A new child band node is created to represent the point loops and it is
10705 inserted between the modified band and its children.
10706 The subtree rooted at the given node is assumed not to have
10707 any anchored nodes.
10708 The C<tile_scale_tile_loops> option specifies whether the tile
10709 loops iterators should be scaled by the tile sizes.
10710 If the C<tile_shift_point_loops> option is set, then the point loops
10711 are shifted to start at zero.
10713 A band node can be split into two nested band nodes
10714 using the following function.
10716 #include <isl/schedule_node.h>
10717 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10718 __isl_take isl_schedule_node *node, int pos);
10720 The resulting outer band node contains the first C<pos> dimensions of
10721 the schedule of C<node> while the inner band contains the remaining dimensions.
10722 The schedules of the two band nodes live in anonymous spaces.
10723 The loop AST generation type options and the isolate option
10724 are split over the two band nodes.
10726 A band node can be moved down to the leaves of the subtree rooted
10727 at the band node using the following function.
10729 #include <isl/schedule_node.h>
10730 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10731 __isl_take isl_schedule_node *node);
10733 The subtree rooted at the given node is assumed not to have
10734 any anchored nodes.
10735 The result points to the node in the resulting tree that is in the same
10736 position as the node pointed to by C<node> in the original tree.
10738 #include <isl/schedule_node.h>
10739 __isl_give isl_schedule_node *
10740 isl_schedule_node_order_before(
10741 __isl_take isl_schedule_node *node,
10742 __isl_take isl_union_set *filter);
10743 __isl_give isl_schedule_node *
10744 isl_schedule_node_order_after(
10745 __isl_take isl_schedule_node *node,
10746 __isl_take isl_union_set *filter);
10748 These functions split the domain elements that reach C<node>
10749 into those that satisfy C<filter> and those that do not and
10750 arranges for the elements that do satisfy the filter to be
10751 executed before (in case of C<isl_schedule_node_order_before>)
10752 or after (in case of C<isl_schedule_node_order_after>)
10753 those that do not. The order is imposed by
10754 a sequence node, possibly reusing the grandparent of C<node>
10755 on two copies of the subtree attached to the original C<node>.
10756 Both copies are simplified with respect to their filter.
10758 Return a pointer to the copy of the subtree that does not
10759 satisfy C<filter>. If there is no such copy (because all
10760 reaching domain elements satisfy the filter), then return
10761 the original pointer.
10763 #include <isl/schedule_node.h>
10764 __isl_give isl_schedule_node *
10765 isl_schedule_node_graft_before(
10766 __isl_take isl_schedule_node *node,
10767 __isl_take isl_schedule_node *graft);
10768 __isl_give isl_schedule_node *
10769 isl_schedule_node_graft_after(
10770 __isl_take isl_schedule_node *node,
10771 __isl_take isl_schedule_node *graft);
10773 This function inserts the C<graft> tree into the tree containing C<node>
10774 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10775 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10776 The root node of C<graft>
10777 should be an extension node where the domain of the extension
10778 is the flat product of all outer band nodes of C<node>.
10779 The root node may also be a domain node.
10780 The elements of the domain or the range of the extension may not
10781 intersect with the domain elements that reach "node".
10782 The schedule tree of C<graft> may not be anchored.
10784 The schedule tree of C<node> is modified to include an extension node
10785 corresponding to the root node of C<graft> as a child of the original
10786 parent of C<node>. The original node that C<node> points to and the
10787 child of the root node of C<graft> are attached to this extension node
10788 through a sequence, with appropriate filters and with the child
10789 of C<graft> appearing before or after the original C<node>.
10791 If C<node> already appears inside a sequence that is the child of
10792 an extension node and if the spaces of the new domain elements
10793 do not overlap with those of the original domain elements,
10794 then that extension node is extended with the new extension
10795 rather than introducing a new segment of extension and sequence nodes.
10797 Return a pointer to the same node in the modified tree that
10798 C<node> pointed to in the original tree.
10800 A representation of the schedule node can be printed using
10802 #include <isl/schedule_node.h>
10803 __isl_give isl_printer *isl_printer_print_schedule_node(
10804 __isl_take isl_printer *p,
10805 __isl_keep isl_schedule_node *node);
10806 __isl_give char *isl_schedule_node_to_str(
10807 __isl_keep isl_schedule_node *node);
10809 C<isl_schedule_node_to_str> prints the schedule node in block format.
10811 =head2 Dependence Analysis
10813 C<isl> contains specialized functionality for performing
10814 array dataflow analysis. That is, given a I<sink> access relation,
10815 a collection of possible I<source> accesses and
10816 a collection of I<kill> accesses,
10817 C<isl> can compute relations that describe
10818 for each iteration of the sink access, which iterations
10819 of which of the source access relations may have
10820 accessed the same data element before the given iteration
10821 of the sink access without any intermediate kill of that data element.
10822 The resulting dependence relations map source iterations
10823 to either the corresponding sink iterations or
10824 pairs of corresponding sink iterations and accessed data elements.
10825 To compute standard flow dependences, the sink should be
10826 a read, while the sources should be writes.
10827 If no kills are specified,
10828 then memory based dependence analysis is performed.
10829 If, on the other hand, all sources are also kills,
10830 then value based dependence analysis is performed.
10831 If any of the source accesses are marked as being I<must>
10832 accesses, then they are also treated as kills.
10833 Furthermore, the specification of must-sources results
10834 in the computation of must-dependences.
10835 Only dependences originating in a must access not coscheduled
10836 with any other access to the same element and without
10837 any may accesses between the must access and the sink access
10838 are considered to be must dependences.
10840 =head3 High-level Interface
10842 A high-level interface to dependence analysis is provided
10843 by the following function.
10845 #include <isl/flow.h>
10846 __isl_give isl_union_flow *
10847 isl_union_access_info_compute_flow(
10848 __isl_take isl_union_access_info *access);
10850 The input C<isl_union_access_info> object describes the sink
10851 access relations, the source access relations and a schedule,
10852 while the output C<isl_union_flow> object describes
10853 the resulting dependence relations and the subsets of the
10854 sink relations for which no source was found.
10856 An C<isl_union_access_info> is created, modified, copied and freed using
10857 the following functions.
10859 #include <isl/flow.h>
10860 __isl_give isl_union_access_info *
10861 isl_union_access_info_from_sink(
10862 __isl_take isl_union_map *sink);
10863 __isl_give isl_union_access_info *
10864 isl_union_access_info_set_kill(
10865 __isl_take isl_union_access_info *access,
10866 __isl_take isl_union_map *kill);
10867 __isl_give isl_union_access_info *
10868 isl_union_access_info_set_may_source(
10869 __isl_take isl_union_access_info *access,
10870 __isl_take isl_union_map *may_source);
10871 __isl_give isl_union_access_info *
10872 isl_union_access_info_set_must_source(
10873 __isl_take isl_union_access_info *access,
10874 __isl_take isl_union_map *must_source);
10875 __isl_give isl_union_access_info *
10876 isl_union_access_info_set_schedule(
10877 __isl_take isl_union_access_info *access,
10878 __isl_take isl_schedule *schedule);
10879 __isl_give isl_union_access_info *
10880 isl_union_access_info_set_schedule_map(
10881 __isl_take isl_union_access_info *access,
10882 __isl_take isl_union_map *schedule_map);
10883 __isl_give isl_union_access_info *
10884 isl_union_access_info_copy(
10885 __isl_keep isl_union_access_info *access);
10886 __isl_null isl_union_access_info *
10887 isl_union_access_info_free(
10888 __isl_take isl_union_access_info *access);
10890 The may sources set by C<isl_union_access_info_set_may_source>
10891 do not need to include the must sources set by
10892 C<isl_union_access_info_set_must_source> as a subset.
10893 The kills set by C<isl_union_access_info_set_kill> may overlap
10894 with the may-sources and/or must-sources.
10895 The user is free not to call one (or more) of these functions,
10896 in which case the corresponding set is kept to its empty default.
10897 Similarly, the default schedule initialized by
10898 C<isl_union_access_info_from_sink> is empty.
10899 The current schedule is determined by the last call to either
10900 C<isl_union_access_info_set_schedule> or
10901 C<isl_union_access_info_set_schedule_map>.
10902 The domain of the schedule corresponds to the domains of
10903 the access relations. In particular, the domains of the access
10904 relations are effectively intersected with the domain of the schedule
10905 and only the resulting accesses are considered by the dependence analysis.
10907 An C<isl_union_access_info> object can be read from input
10908 using the following function.
10910 #include <isl/flow.h>
10911 __isl_give isl_union_access_info *
10912 isl_union_access_info_read_from_file(isl_ctx *ctx,
10915 A representation of the information contained in an object
10916 of type C<isl_union_access_info> can be obtained using
10918 #include <isl/flow.h>
10919 __isl_give isl_printer *
10920 isl_printer_print_union_access_info(
10921 __isl_take isl_printer *p,
10922 __isl_keep isl_union_access_info *access);
10923 __isl_give char *isl_union_access_info_to_str(
10924 __isl_keep isl_union_access_info *access);
10926 C<isl_union_access_info_to_str> prints the information in flow format.
10928 The output of C<isl_union_access_info_compute_flow> can be examined,
10929 copied, and freed using the following functions.
10931 #include <isl/flow.h>
10932 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
10933 __isl_keep isl_union_flow *flow);
10934 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
10935 __isl_keep isl_union_flow *flow);
10936 __isl_give isl_union_map *
10937 isl_union_flow_get_full_must_dependence(
10938 __isl_keep isl_union_flow *flow);
10939 __isl_give isl_union_map *
10940 isl_union_flow_get_full_may_dependence(
10941 __isl_keep isl_union_flow *flow);
10942 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
10943 __isl_keep isl_union_flow *flow);
10944 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
10945 __isl_keep isl_union_flow *flow);
10946 __isl_give isl_union_flow *isl_union_flow_copy(
10947 __isl_keep isl_union_flow *flow);
10948 __isl_null isl_union_flow *isl_union_flow_free(
10949 __isl_take isl_union_flow *flow);
10951 The relation returned by C<isl_union_flow_get_must_dependence>
10952 relates domain elements of must sources to domain elements of the sink.
10953 The relation returned by C<isl_union_flow_get_may_dependence>
10954 relates domain elements of must or may sources to domain elements of the sink
10955 and includes the previous relation as a subset.
10956 The relation returned by C<isl_union_flow_get_full_must_dependence>
10957 relates domain elements of must sources to pairs of domain elements of the sink
10958 and accessed data elements.
10959 The relation returned by C<isl_union_flow_get_full_may_dependence>
10960 relates domain elements of must or may sources to pairs of
10961 domain elements of the sink and accessed data elements.
10962 This relation includes the previous relation as a subset.
10963 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
10964 of the sink relation for which no dependences have been found.
10965 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
10966 of the sink relation for which no definite dependences have been found.
10967 That is, it contains those sink access that do not contribute to any
10968 of the elements in the relation returned
10969 by C<isl_union_flow_get_must_dependence>.
10971 A representation of the information contained in an object
10972 of type C<isl_union_flow> can be obtained using
10974 #include <isl/flow.h>
10975 __isl_give isl_printer *isl_printer_print_union_flow(
10976 __isl_take isl_printer *p,
10977 __isl_keep isl_union_flow *flow);
10978 __isl_give char *isl_union_flow_to_str(
10979 __isl_keep isl_union_flow *flow);
10981 C<isl_union_flow_to_str> prints the information in flow format.
10983 =head3 Low-level Interface
10985 A lower-level interface is provided by the following functions.
10987 #include <isl/flow.h>
10989 typedef int (*isl_access_level_before)(void *first, void *second);
10991 __isl_give isl_access_info *isl_access_info_alloc(
10992 __isl_take isl_map *sink,
10993 void *sink_user, isl_access_level_before fn,
10995 __isl_give isl_access_info *isl_access_info_add_source(
10996 __isl_take isl_access_info *acc,
10997 __isl_take isl_map *source, int must,
10998 void *source_user);
10999 __isl_null isl_access_info *isl_access_info_free(
11000 __isl_take isl_access_info *acc);
11002 __isl_give isl_flow *isl_access_info_compute_flow(
11003 __isl_take isl_access_info *acc);
11005 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11006 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11007 void *dep_user, void *user),
11009 __isl_give isl_map *isl_flow_get_no_source(
11010 __isl_keep isl_flow *deps, int must);
11011 __isl_null isl_flow *isl_flow_free(
11012 __isl_take isl_flow *deps);
11014 The function C<isl_access_info_compute_flow> performs the actual
11015 dependence analysis. The other functions are used to construct
11016 the input for this function or to read off the output.
11018 The input is collected in an C<isl_access_info>, which can
11019 be created through a call to C<isl_access_info_alloc>.
11020 The arguments to this functions are the sink access relation
11021 C<sink>, a token C<sink_user> used to identify the sink
11022 access to the user, a callback function for specifying the
11023 relative order of source and sink accesses, and the number
11024 of source access relations that will be added.
11026 The callback function has type C<int (*)(void *first, void *second)>.
11027 The function is called with two user supplied tokens identifying
11028 either a source or the sink and it should return the shared nesting
11029 level and the relative order of the two accesses.
11030 In particular, let I<n> be the number of loops shared by
11031 the two accesses. If C<first> precedes C<second> textually,
11032 then the function should return I<2 * n + 1>; otherwise,
11033 it should return I<2 * n>.
11034 The low-level interface assumes that no sources are coscheduled.
11035 If the information returned by the callback does not allow
11036 the relative order to be determined, then one of the sources
11037 is arbitrarily taken to be executed after the other(s).
11039 The sources can be added to the C<isl_access_info> object by performing
11040 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11041 C<must> indicates whether the source is a I<must> access
11042 or a I<may> access. Note that a multi-valued access relation
11043 should only be marked I<must> if every iteration in the domain
11044 of the relation accesses I<all> elements in its image.
11045 The C<source_user> token is again used to identify
11046 the source access. The range of the source access relation
11047 C<source> should have the same dimension as the range
11048 of the sink access relation.
11049 The C<isl_access_info_free> function should usually not be
11050 called explicitly, because it is already called implicitly by
11051 C<isl_access_info_compute_flow>.
11053 The result of the dependence analysis is collected in an
11054 C<isl_flow>. There may be elements of
11055 the sink access for which no preceding source access could be
11056 found or for which all preceding sources are I<may> accesses.
11057 The relations containing these elements can be obtained through
11058 calls to C<isl_flow_get_no_source>, the first with C<must> set
11059 and the second with C<must> unset.
11060 In the case of standard flow dependence analysis,
11061 with the sink a read and the sources I<must> writes,
11062 the first relation corresponds to the reads from uninitialized
11063 array elements and the second relation is empty.
11064 The actual flow dependences can be extracted using
11065 C<isl_flow_foreach>. This function will call the user-specified
11066 callback function C<fn> for each B<non-empty> dependence between
11067 a source and the sink. The callback function is called
11068 with four arguments, the actual flow dependence relation
11069 mapping source iterations to sink iterations, a boolean that
11070 indicates whether it is a I<must> or I<may> dependence, a token
11071 identifying the source and an additional C<void *> with value
11072 equal to the third argument of the C<isl_flow_foreach> call.
11073 A dependence is marked I<must> if it originates from a I<must>
11074 source and if it is not followed by any I<may> sources.
11076 After finishing with an C<isl_flow>, the user should call
11077 C<isl_flow_free> to free all associated memory.
11079 =head3 Interaction with the Low-level Interface
11081 During the dependence analysis, we frequently need to perform
11082 the following operation. Given a relation between sink iterations
11083 and potential source iterations from a particular source domain,
11084 what is the last potential source iteration corresponding to each
11085 sink iteration. It can sometimes be convenient to adjust
11086 the set of potential source iterations before or after each such operation.
11087 The prototypical example is fuzzy array dataflow analysis,
11088 where we need to analyze if, based on data-dependent constraints,
11089 the sink iteration can ever be executed without one or more of
11090 the corresponding potential source iterations being executed.
11091 If so, we can introduce extra parameters and select an unknown
11092 but fixed source iteration from the potential source iterations.
11093 To be able to perform such manipulations, C<isl> provides the following
11096 #include <isl/flow.h>
11098 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11099 __isl_keep isl_map *source_map,
11100 __isl_keep isl_set *sink, void *source_user,
11102 __isl_give isl_access_info *isl_access_info_set_restrict(
11103 __isl_take isl_access_info *acc,
11104 isl_access_restrict fn, void *user);
11106 The function C<isl_access_info_set_restrict> should be called
11107 before calling C<isl_access_info_compute_flow> and registers a callback function
11108 that will be called any time C<isl> is about to compute the last
11109 potential source. The first argument is the (reverse) proto-dependence,
11110 mapping sink iterations to potential source iterations.
11111 The second argument represents the sink iterations for which
11112 we want to compute the last source iteration.
11113 The third argument is the token corresponding to the source
11114 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11115 The callback is expected to return a restriction on either the input or
11116 the output of the operation computing the last potential source.
11117 If the input needs to be restricted then restrictions are needed
11118 for both the source and the sink iterations. The sink iterations
11119 and the potential source iterations will be intersected with these sets.
11120 If the output needs to be restricted then only a restriction on the source
11121 iterations is required.
11122 If any error occurs, the callback should return C<NULL>.
11123 An C<isl_restriction> object can be created, freed and inspected
11124 using the following functions.
11126 #include <isl/flow.h>
11128 __isl_give isl_restriction *isl_restriction_input(
11129 __isl_take isl_set *source_restr,
11130 __isl_take isl_set *sink_restr);
11131 __isl_give isl_restriction *isl_restriction_output(
11132 __isl_take isl_set *source_restr);
11133 __isl_give isl_restriction *isl_restriction_none(
11134 __isl_take isl_map *source_map);
11135 __isl_give isl_restriction *isl_restriction_empty(
11136 __isl_take isl_map *source_map);
11137 __isl_null isl_restriction *isl_restriction_free(
11138 __isl_take isl_restriction *restr);
11140 C<isl_restriction_none> and C<isl_restriction_empty> are special
11141 cases of C<isl_restriction_input>. C<isl_restriction_none>
11142 is essentially equivalent to
11144 isl_restriction_input(isl_set_universe(
11145 isl_space_range(isl_map_get_space(source_map))),
11147 isl_space_domain(isl_map_get_space(source_map))));
11149 whereas C<isl_restriction_empty> is essentially equivalent to
11151 isl_restriction_input(isl_set_empty(
11152 isl_space_range(isl_map_get_space(source_map))),
11154 isl_space_domain(isl_map_get_space(source_map))));
11158 #include <isl/schedule.h>
11159 __isl_give isl_schedule *
11160 isl_schedule_constraints_compute_schedule(
11161 __isl_take isl_schedule_constraints *sc);
11163 The function C<isl_schedule_constraints_compute_schedule> can be
11164 used to compute a schedule that satisfies the given schedule constraints.
11165 These schedule constraints include the iteration domain for which
11166 a schedule should be computed and dependences between pairs of
11167 iterations. In particular, these dependences include
11168 I<validity> dependences and I<proximity> dependences.
11169 By default, the algorithm used to construct the schedule is similar
11170 to that of C<Pluto>.
11171 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11173 The generated schedule respects all validity dependences.
11174 That is, all dependence distances over these dependences in the
11175 scheduled space are lexicographically positive.
11177 The default algorithm tries to ensure that the dependence distances
11178 over coincidence constraints are zero and to minimize the
11179 dependence distances over proximity dependences.
11180 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11181 for groups of domains where the dependence distances over validity
11182 dependences have only non-negative values.
11183 Note that when minimizing the maximal dependence distance
11184 over proximity dependences, a single affine expression in the parameters
11185 is constructed that bounds all dependence distances. If no such expression
11186 exists, then the algorithm will fail and resort to an alternative
11187 scheduling algorithm. In particular, this means that adding proximity
11188 dependences may eliminate valid solutions. A typical example where this
11189 phenomenon may occur is when some subset of the proximity dependences
11190 has no restriction on some parameter, forcing the coefficient of that
11191 parameter to be zero, while some other subset forces the dependence
11192 distance to depend on that parameter, requiring the same coefficient
11194 When using Feautrier's algorithm, the coincidence and proximity constraints
11195 are only taken into account during the extension to a
11196 full-dimensional schedule.
11198 An C<isl_schedule_constraints> object can be constructed
11199 and manipulated using the following functions.
11201 #include <isl/schedule.h>
11202 __isl_give isl_schedule_constraints *
11203 isl_schedule_constraints_copy(
11204 __isl_keep isl_schedule_constraints *sc);
11205 __isl_give isl_schedule_constraints *
11206 isl_schedule_constraints_on_domain(
11207 __isl_take isl_union_set *domain);
11208 __isl_give isl_schedule_constraints *
11209 isl_schedule_constraints_set_context(
11210 __isl_take isl_schedule_constraints *sc,
11211 __isl_take isl_set *context);
11212 __isl_give isl_schedule_constraints *
11213 isl_schedule_constraints_set_validity(
11214 __isl_take isl_schedule_constraints *sc,
11215 __isl_take isl_union_map *validity);
11216 __isl_give isl_schedule_constraints *
11217 isl_schedule_constraints_set_coincidence(
11218 __isl_take isl_schedule_constraints *sc,
11219 __isl_take isl_union_map *coincidence);
11220 __isl_give isl_schedule_constraints *
11221 isl_schedule_constraints_set_proximity(
11222 __isl_take isl_schedule_constraints *sc,
11223 __isl_take isl_union_map *proximity);
11224 __isl_give isl_schedule_constraints *
11225 isl_schedule_constraints_set_conditional_validity(
11226 __isl_take isl_schedule_constraints *sc,
11227 __isl_take isl_union_map *condition,
11228 __isl_take isl_union_map *validity);
11229 __isl_give isl_schedule_constraints *
11230 isl_schedule_constraints_apply(
11231 __isl_take isl_schedule_constraints *sc,
11232 __isl_take isl_union_map *umap);
11233 __isl_null isl_schedule_constraints *
11234 isl_schedule_constraints_free(
11235 __isl_take isl_schedule_constraints *sc);
11237 The initial C<isl_schedule_constraints> object created by
11238 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11239 That is, it has an empty set of dependences.
11240 The function C<isl_schedule_constraints_set_context> allows the user
11241 to specify additional constraints on the parameters that may
11242 be assumed to hold during the construction of the schedule.
11243 The function C<isl_schedule_constraints_set_validity> replaces the
11244 validity dependences, mapping domain elements I<i> to domain
11245 elements that should be scheduled after I<i>.
11246 The function C<isl_schedule_constraints_set_coincidence> replaces the
11247 coincidence dependences, mapping domain elements I<i> to domain
11248 elements that should be scheduled together with I<I>, if possible.
11249 The function C<isl_schedule_constraints_set_proximity> replaces the
11250 proximity dependences, mapping domain elements I<i> to domain
11251 elements that should be scheduled either before I<I>
11252 or as early as possible after I<i>.
11254 The function C<isl_schedule_constraints_set_conditional_validity>
11255 replaces the conditional validity constraints.
11256 A conditional validity constraint is only imposed when any of the corresponding
11257 conditions is satisfied, i.e., when any of them is non-zero.
11258 That is, the scheduler ensures that within each band if the dependence
11259 distances over the condition constraints are not all zero
11260 then all corresponding conditional validity constraints are respected.
11261 A conditional validity constraint corresponds to a condition
11262 if the two are adjacent, i.e., if the domain of one relation intersect
11263 the range of the other relation.
11264 The typical use case of conditional validity constraints is
11265 to allow order constraints between live ranges to be violated
11266 as long as the live ranges themselves are local to the band.
11267 To allow more fine-grained control over which conditions correspond
11268 to which conditional validity constraints, the domains and ranges
11269 of these relations may include I<tags>. That is, the domains and
11270 ranges of those relation may themselves be wrapped relations
11271 where the iteration domain appears in the domain of those wrapped relations
11272 and the range of the wrapped relations can be arbitrarily chosen
11273 by the user. Conditions and conditional validity constraints are only
11274 considered adjacent to each other if the entire wrapped relation matches.
11275 In particular, a relation with a tag will never be considered adjacent
11276 to a relation without a tag.
11278 The function C<isl_schedule_constraints_apply> takes
11279 schedule constraints that are defined on some set of domain elements
11280 and transforms them to schedule constraints on the elements
11281 to which these domain elements are mapped by the given transformation.
11283 An C<isl_schedule_constraints> object can be inspected
11284 using the following functions.
11286 #include <isl/schedule.h>
11287 __isl_give isl_union_set *
11288 isl_schedule_constraints_get_domain(
11289 __isl_keep isl_schedule_constraints *sc);
11290 __isl_give isl_set *isl_schedule_constraints_get_context(
11291 __isl_keep isl_schedule_constraints *sc);
11292 __isl_give isl_union_map *
11293 isl_schedule_constraints_get_validity(
11294 __isl_keep isl_schedule_constraints *sc);
11295 __isl_give isl_union_map *
11296 isl_schedule_constraints_get_coincidence(
11297 __isl_keep isl_schedule_constraints *sc);
11298 __isl_give isl_union_map *
11299 isl_schedule_constraints_get_proximity(
11300 __isl_keep isl_schedule_constraints *sc);
11301 __isl_give isl_union_map *
11302 isl_schedule_constraints_get_conditional_validity(
11303 __isl_keep isl_schedule_constraints *sc);
11304 __isl_give isl_union_map *
11305 isl_schedule_constraints_get_conditional_validity_condition(
11306 __isl_keep isl_schedule_constraints *sc);
11308 An C<isl_schedule_constraints> object can be read from input
11309 using the following functions.
11311 #include <isl/schedule.h>
11312 __isl_give isl_schedule_constraints *
11313 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11315 __isl_give isl_schedule_constraints *
11316 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11319 The contents of an C<isl_schedule_constraints> object can be printed
11320 using the following functions.
11322 #include <isl/schedule.h>
11323 __isl_give isl_printer *
11324 isl_printer_print_schedule_constraints(
11325 __isl_take isl_printer *p,
11326 __isl_keep isl_schedule_constraints *sc);
11327 __isl_give char *isl_schedule_constraints_to_str(
11328 __isl_keep isl_schedule_constraints *sc);
11330 The following function computes a schedule directly from
11331 an iteration domain and validity and proximity dependences
11332 and is implemented in terms of the functions described above.
11333 The use of C<isl_union_set_compute_schedule> is discouraged.
11335 #include <isl/schedule.h>
11336 __isl_give isl_schedule *isl_union_set_compute_schedule(
11337 __isl_take isl_union_set *domain,
11338 __isl_take isl_union_map *validity,
11339 __isl_take isl_union_map *proximity);
11341 The generated schedule represents a schedule tree.
11342 For more information on schedule trees, see
11343 L</"Schedule Trees">.
11347 #include <isl/schedule.h>
11348 isl_stat isl_options_set_schedule_max_coefficient(
11349 isl_ctx *ctx, int val);
11350 int isl_options_get_schedule_max_coefficient(
11352 isl_stat isl_options_set_schedule_max_constant_term(
11353 isl_ctx *ctx, int val);
11354 int isl_options_get_schedule_max_constant_term(
11356 isl_stat isl_options_set_schedule_serialize_sccs(
11357 isl_ctx *ctx, int val);
11358 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11359 isl_stat isl_options_set_schedule_whole_component(
11360 isl_ctx *ctx, int val);
11361 int isl_options_get_schedule_whole_component(
11363 isl_stat isl_options_set_schedule_maximize_band_depth(
11364 isl_ctx *ctx, int val);
11365 int isl_options_get_schedule_maximize_band_depth(
11367 isl_stat isl_options_set_schedule_maximize_coincidence(
11368 isl_ctx *ctx, int val);
11369 int isl_options_get_schedule_maximize_coincidence(
11371 isl_stat isl_options_set_schedule_outer_coincidence(
11372 isl_ctx *ctx, int val);
11373 int isl_options_get_schedule_outer_coincidence(
11375 isl_stat isl_options_set_schedule_split_scaled(
11376 isl_ctx *ctx, int val);
11377 int isl_options_get_schedule_split_scaled(
11379 isl_stat isl_options_set_schedule_treat_coalescing(
11380 isl_ctx *ctx, int val);
11381 int isl_options_get_schedule_treat_coalescing(
11383 isl_stat isl_options_set_schedule_algorithm(
11384 isl_ctx *ctx, int val);
11385 int isl_options_get_schedule_algorithm(
11387 isl_stat isl_options_set_schedule_carry_self_first(
11388 isl_ctx *ctx, int val);
11389 int isl_options_get_schedule_carry_self_first(
11391 isl_stat isl_options_set_schedule_separate_components(
11392 isl_ctx *ctx, int val);
11393 int isl_options_get_schedule_separate_components(
11398 =item * schedule_max_coefficient
11400 This option enforces that the coefficients for variable and parameter
11401 dimensions in the calculated schedule are not larger than the specified value.
11402 This option can significantly increase the speed of the scheduling calculation
11403 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11404 this option does not introduce bounds on the variable or parameter
11406 This option has no effect on the Feautrier style scheduler.
11408 =item * schedule_max_constant_term
11410 This option enforces that the constant coefficients in the calculated schedule
11411 are not larger than the maximal constant term. This option can significantly
11412 increase the speed of the scheduling calculation and may also prevent fusing of
11413 unrelated dimensions. A value of -1 means that this option does not introduce
11414 bounds on the constant coefficients.
11416 =item * schedule_serialize_sccs
11418 If this option is set, then all strongly connected components
11419 in the dependence graph are serialized as soon as they are detected.
11420 This means in particular that instances of statements will only
11421 appear in the same band node if these statements belong
11422 to the same strongly connected component at the point where
11423 the band node is constructed.
11425 =item * schedule_whole_component
11427 If this option is set, then entire (weakly) connected
11428 components in the dependence graph are scheduled together
11430 Otherwise, each strongly connected component within
11431 such a weakly connected component is first scheduled separately
11432 and then combined with other strongly connected components.
11433 This option has no effect if C<schedule_serialize_sccs> is set.
11435 =item * schedule_maximize_band_depth
11437 If this option is set, then the scheduler tries to maximize
11438 the width of the bands. Wider bands give more possibilities for tiling.
11439 In particular, if the C<schedule_whole_component> option is set,
11440 then bands are split if this might result in wider bands.
11441 Otherwise, the effect of this option is to only allow
11442 strongly connected components to be combined if this does
11443 not reduce the width of the bands.
11444 Note that if the C<schedule_serialize_sccs> options is set, then
11445 the C<schedule_maximize_band_depth> option therefore has no effect.
11447 =item * schedule_maximize_coincidence
11449 This option is only effective if the C<schedule_whole_component>
11450 option is turned off.
11451 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11452 strongly connected components are only combined with each other
11453 if this does not reduce the number of coincident band members.
11455 =item * schedule_outer_coincidence
11457 If this option is set, then we try to construct schedules
11458 where the outermost scheduling dimension in each band
11459 satisfies the coincidence constraints.
11461 =item * schedule_algorithm
11463 Selects the scheduling algorithm to be used.
11464 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11465 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11467 =item * schedule_split_scaled
11469 If this option is set, then we try to construct schedules in which the
11470 constant term is split off from the linear part if the linear parts of
11471 the scheduling rows for all nodes in the graph have a common non-trivial
11473 The constant term is then dropped and the linear
11475 This option is only effective when the Feautrier style scheduler is
11476 being used, either as the main scheduler or as a fallback for the
11477 Pluto-like scheduler.
11479 =item * schedule_treat_coalescing
11481 If this option is set, then the scheduler will try and avoid
11482 producing schedules that perform loop coalescing.
11483 In particular, for the Pluto-like scheduler, this option places
11484 bounds on the schedule coefficients based on the sizes of the instance sets.
11485 For the Feautrier style scheduler, this option detects potentially
11486 coalescing schedules and then tries to adjust the schedule to avoid
11489 =item * schedule_carry_self_first
11491 If this option is set, then the Feautrier style scheduler
11492 (when used as a fallback for the Pluto-like scheduler) will
11493 first try to only carry self-dependences.
11495 =item * schedule_separate_components
11497 If this option is set then the function C<isl_schedule_get_map>
11498 will treat set nodes in the same way as sequence nodes.
11502 =head2 AST Generation
11504 This section describes the C<isl> functionality for generating
11505 ASTs that visit all the elements
11506 in a domain in an order specified by a schedule tree or
11508 In case the schedule given as a C<isl_union_map>, an AST is generated
11509 that visits all the elements in the domain of the C<isl_union_map>
11510 according to the lexicographic order of the corresponding image
11511 element(s). If the range of the C<isl_union_map> consists of
11512 elements in more than one space, then each of these spaces is handled
11513 separately in an arbitrary order.
11514 It should be noted that the schedule tree or the image elements
11515 in a schedule map only specify the I<order>
11516 in which the corresponding domain elements should be visited.
11517 No direct relation between the partial schedule values
11518 or the image elements on the one hand and the loop iterators
11519 in the generated AST on the other hand should be assumed.
11521 Each AST is generated within a build. The initial build
11522 simply specifies the constraints on the parameters (if any)
11523 and can be created, inspected, copied and freed using the following functions.
11525 #include <isl/ast_build.h>
11526 __isl_give isl_ast_build *isl_ast_build_alloc(
11528 __isl_give isl_ast_build *isl_ast_build_from_context(
11529 __isl_take isl_set *set);
11530 __isl_give isl_ast_build *isl_ast_build_copy(
11531 __isl_keep isl_ast_build *build);
11532 __isl_null isl_ast_build *isl_ast_build_free(
11533 __isl_take isl_ast_build *build);
11535 The C<set> argument is usually a parameter set with zero or more parameters.
11536 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11537 this set is required to be a parameter set.
11538 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11539 specify any parameter constraints.
11540 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11541 and L</"Fine-grained Control over AST Generation">.
11542 Finally, the AST itself can be constructed using one of the following
11545 #include <isl/ast_build.h>
11546 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11547 __isl_keep isl_ast_build *build,
11548 __isl_take isl_schedule *schedule);
11549 __isl_give isl_ast_node *
11550 isl_ast_build_node_from_schedule_map(
11551 __isl_keep isl_ast_build *build,
11552 __isl_take isl_union_map *schedule);
11554 =head3 Inspecting the AST
11556 The basic properties of an AST node can be obtained as follows.
11558 #include <isl/ast.h>
11559 enum isl_ast_node_type isl_ast_node_get_type(
11560 __isl_keep isl_ast_node *node);
11562 The type of an AST node is one of
11563 C<isl_ast_node_for>,
11564 C<isl_ast_node_if>,
11565 C<isl_ast_node_block>,
11566 C<isl_ast_node_mark> or
11567 C<isl_ast_node_user>.
11568 An C<isl_ast_node_for> represents a for node.
11569 An C<isl_ast_node_if> represents an if node.
11570 An C<isl_ast_node_block> represents a compound node.
11571 An C<isl_ast_node_mark> introduces a mark in the AST.
11572 An C<isl_ast_node_user> represents an expression statement.
11573 An expression statement typically corresponds to a domain element, i.e.,
11574 one of the elements that is visited by the AST.
11576 Each type of node has its own additional properties.
11578 #include <isl/ast.h>
11579 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11580 __isl_keep isl_ast_node *node);
11581 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11582 __isl_keep isl_ast_node *node);
11583 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11584 __isl_keep isl_ast_node *node);
11585 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11586 __isl_keep isl_ast_node *node);
11587 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11588 __isl_keep isl_ast_node *node);
11589 isl_bool isl_ast_node_for_is_degenerate(
11590 __isl_keep isl_ast_node *node);
11592 An C<isl_ast_for> is considered degenerate if it is known to execute
11595 #include <isl/ast.h>
11596 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11597 __isl_keep isl_ast_node *node);
11598 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11599 __isl_keep isl_ast_node *node);
11600 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11601 __isl_keep isl_ast_node *node);
11602 isl_bool isl_ast_node_if_has_else_node(
11603 __isl_keep isl_ast_node *node);
11604 isl_bool isl_ast_node_if_has_else(
11605 __isl_keep isl_ast_node *node);
11606 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11607 __isl_keep isl_ast_node *node);
11608 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11609 __isl_keep isl_ast_node *node);
11611 C<isl_ast_node_if_get_then>,
11612 C<isl_ast_node_if_has_else> and
11613 C<isl_ast_node_if_get_else>
11614 are alternative names for
11615 C<isl_ast_node_if_get_then_node>,
11616 C<isl_ast_node_if_has_else_node> and
11617 C<isl_ast_node_if_get_else_node>, respectively.
11619 __isl_give isl_ast_node_list *
11620 isl_ast_node_block_get_children(
11621 __isl_keep isl_ast_node *node);
11623 __isl_give isl_id *isl_ast_node_mark_get_id(
11624 __isl_keep isl_ast_node *node);
11625 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11626 __isl_keep isl_ast_node *node);
11628 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11629 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11631 #include <isl/ast.h>
11632 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11633 __isl_keep isl_ast_node *node);
11635 All descendants of a specific node in the AST (including the node itself)
11637 in depth-first pre-order using the following function.
11639 #include <isl/ast.h>
11640 isl_stat isl_ast_node_foreach_descendant_top_down(
11641 __isl_keep isl_ast_node *node,
11642 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11643 void *user), void *user);
11645 The callback function should return C<isl_bool_true> if the children
11646 of the given node should be visited and C<isl_bool_false> if they should not.
11647 It should return C<isl_bool_error> in case of failure, in which case
11648 the entire traversal is aborted.
11650 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11651 the following functions.
11653 #include <isl/ast.h>
11654 enum isl_ast_expr_type isl_ast_expr_get_type(
11655 __isl_keep isl_ast_expr *expr);
11657 The type of an AST expression is one of
11658 C<isl_ast_expr_op>,
11659 C<isl_ast_expr_id> or
11660 C<isl_ast_expr_int>.
11661 An C<isl_ast_expr_op> represents the result of an operation.
11662 An C<isl_ast_expr_id> represents an identifier.
11663 An C<isl_ast_expr_int> represents an integer value.
11665 Each type of expression has its own additional properties.
11667 #include <isl/ast.h>
11668 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11669 __isl_keep isl_ast_expr *expr);
11670 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11671 __isl_keep isl_ast_expr *expr);
11672 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11673 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11674 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11675 __isl_keep isl_ast_expr *expr, int pos);
11676 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11677 __isl_keep isl_ast_expr *expr, int pos);
11678 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11679 __isl_keep isl_ast_expr *expr,
11680 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11681 void *user), void *user);
11682 isl_stat isl_ast_expr_foreach_ast_op_type(
11683 __isl_keep isl_ast_expr *expr,
11684 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11685 void *user), void *user);
11686 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11687 __isl_keep isl_ast_node *node,
11688 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11689 void *user), void *user);
11690 isl_stat isl_ast_node_foreach_ast_op_type(
11691 __isl_keep isl_ast_node *node,
11692 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11693 void *user), void *user);
11695 C<isl_ast_expr_op_get_type> returns the type of the operation
11696 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11697 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11699 C<isl_ast_expr_get_op_type> is an alternative name for
11700 C<isl_ast_expr_op_get_type>.
11702 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11703 C<isl_ast_expr_op_get_n_arg> and
11704 C<isl_ast_expr_get_op_arg> is an alternative name for
11705 C<isl_ast_expr_op_get_arg>.
11707 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11708 C<isl_ast_expr_op_type> that appears in C<expr>.
11709 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11710 C<isl_ast_expr_foreach_ast_expr_op_type>.
11711 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11712 C<isl_ast_expr_op_type> that appears in C<node>.
11713 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11714 C<isl_ast_node_foreach_ast_expr_op_type>.
11715 The operation type is one of the following.
11719 =item C<isl_ast_expr_op_and>
11721 Logical I<and> of two arguments.
11722 Both arguments can be evaluated.
11724 =item C<isl_ast_expr_op_and_then>
11726 Logical I<and> of two arguments.
11727 The second argument can only be evaluated if the first evaluates to true.
11729 =item C<isl_ast_expr_op_or>
11731 Logical I<or> of two arguments.
11732 Both arguments can be evaluated.
11734 =item C<isl_ast_expr_op_or_else>
11736 Logical I<or> of two arguments.
11737 The second argument can only be evaluated if the first evaluates to false.
11739 =item C<isl_ast_expr_op_max>
11741 Maximum of two or more arguments.
11743 =item C<isl_ast_expr_op_min>
11745 Minimum of two or more arguments.
11747 =item C<isl_ast_expr_op_minus>
11751 =item C<isl_ast_expr_op_add>
11753 Sum of two arguments.
11755 =item C<isl_ast_expr_op_sub>
11757 Difference of two arguments.
11759 =item C<isl_ast_expr_op_mul>
11761 Product of two arguments.
11763 =item C<isl_ast_expr_op_div>
11765 Exact division. That is, the result is known to be an integer.
11767 =item C<isl_ast_expr_op_fdiv_q>
11769 Result of integer division, rounded towards negative
11771 The divisor is known to be positive.
11773 =item C<isl_ast_expr_op_pdiv_q>
11775 Result of integer division, where dividend is known to be non-negative.
11776 The divisor is known to be positive.
11778 =item C<isl_ast_expr_op_pdiv_r>
11780 Remainder of integer division, where dividend is known to be non-negative.
11781 The divisor is known to be positive.
11783 =item C<isl_ast_expr_op_zdiv_r>
11785 Equal to zero iff the remainder on integer division is zero.
11786 The divisor is known to be positive.
11788 =item C<isl_ast_expr_op_cond>
11790 Conditional operator defined on three arguments.
11791 If the first argument evaluates to true, then the result
11792 is equal to the second argument. Otherwise, the result
11793 is equal to the third argument.
11794 The second and third argument may only be evaluated if
11795 the first argument evaluates to true and false, respectively.
11796 Corresponds to C<a ? b : c> in C.
11798 =item C<isl_ast_expr_op_select>
11800 Conditional operator defined on three arguments.
11801 If the first argument evaluates to true, then the result
11802 is equal to the second argument. Otherwise, the result
11803 is equal to the third argument.
11804 The second and third argument may be evaluated independently
11805 of the value of the first argument.
11806 Corresponds to C<a * b + (1 - a) * c> in C.
11808 =item C<isl_ast_expr_op_eq>
11812 =item C<isl_ast_expr_op_le>
11814 Less than or equal relation.
11816 =item C<isl_ast_expr_op_lt>
11818 Less than relation.
11820 =item C<isl_ast_expr_op_ge>
11822 Greater than or equal relation.
11824 =item C<isl_ast_expr_op_gt>
11826 Greater than relation.
11828 =item C<isl_ast_expr_op_call>
11831 The number of arguments of the C<isl_ast_expr> is one more than
11832 the number of arguments in the function call, the first argument
11833 representing the function being called.
11835 =item C<isl_ast_expr_op_access>
11838 The number of arguments of the C<isl_ast_expr> is one more than
11839 the number of index expressions in the array access, the first argument
11840 representing the array being accessed.
11842 =item C<isl_ast_expr_op_member>
11845 This operation has two arguments, a structure and the name of
11846 the member of the structure being accessed.
11850 #include <isl/ast.h>
11851 __isl_give isl_id *isl_ast_expr_id_get_id(
11852 __isl_keep isl_ast_expr *expr);
11853 __isl_give isl_id *isl_ast_expr_get_id(
11854 __isl_keep isl_ast_expr *expr);
11856 Return the identifier represented by the AST expression.
11857 C<isl_ast_expr_get_id> is an alternative name for
11858 C<isl_ast_expr_id_get_id>.
11860 #include <isl/ast.h>
11861 __isl_give isl_val *isl_ast_expr_int_get_val(
11862 __isl_keep isl_ast_expr *expr);
11863 __isl_give isl_val *isl_ast_expr_get_val(
11864 __isl_keep isl_ast_expr *expr);
11866 Return the integer represented by the AST expression.
11867 C<isl_ast_expr_get_val> is an alternative name for
11868 C<isl_ast_expr_int_get_val>.
11870 =head3 Properties of ASTs
11872 #include <isl/ast.h>
11873 isl_bool isl_ast_expr_is_equal(
11874 __isl_keep isl_ast_expr *expr1,
11875 __isl_keep isl_ast_expr *expr2);
11877 Check if two C<isl_ast_expr>s are equal to each other.
11879 =head3 Manipulating and printing the AST
11881 AST nodes can be copied and freed using the following functions.
11883 #include <isl/ast.h>
11884 __isl_give isl_ast_node *isl_ast_node_copy(
11885 __isl_keep isl_ast_node *node);
11886 __isl_null isl_ast_node *isl_ast_node_free(
11887 __isl_take isl_ast_node *node);
11889 AST expressions can be copied and freed using the following functions.
11891 #include <isl/ast.h>
11892 __isl_give isl_ast_expr *isl_ast_expr_copy(
11893 __isl_keep isl_ast_expr *expr);
11894 __isl_null isl_ast_expr *isl_ast_expr_free(
11895 __isl_take isl_ast_expr *expr);
11897 New AST expressions can be created either directly or within
11898 the context of an C<isl_ast_build>.
11900 #include <isl/ast.h>
11901 __isl_give isl_ast_expr *isl_ast_expr_from_val(
11902 __isl_take isl_val *v);
11903 __isl_give isl_ast_expr *isl_ast_expr_from_id(
11904 __isl_take isl_id *id);
11905 __isl_give isl_ast_expr *isl_ast_expr_neg(
11906 __isl_take isl_ast_expr *expr);
11907 __isl_give isl_ast_expr *isl_ast_expr_address_of(
11908 __isl_take isl_ast_expr *expr);
11909 __isl_give isl_ast_expr *isl_ast_expr_add(
11910 __isl_take isl_ast_expr *expr1,
11911 __isl_take isl_ast_expr *expr2);
11912 __isl_give isl_ast_expr *isl_ast_expr_sub(
11913 __isl_take isl_ast_expr *expr1,
11914 __isl_take isl_ast_expr *expr2);
11915 __isl_give isl_ast_expr *isl_ast_expr_mul(
11916 __isl_take isl_ast_expr *expr1,
11917 __isl_take isl_ast_expr *expr2);
11918 __isl_give isl_ast_expr *isl_ast_expr_div(
11919 __isl_take isl_ast_expr *expr1,
11920 __isl_take isl_ast_expr *expr2);
11921 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
11922 __isl_take isl_ast_expr *expr1,
11923 __isl_take isl_ast_expr *expr2);
11924 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
11925 __isl_take isl_ast_expr *expr1,
11926 __isl_take isl_ast_expr *expr2);
11927 __isl_give isl_ast_expr *isl_ast_expr_and(
11928 __isl_take isl_ast_expr *expr1,
11929 __isl_take isl_ast_expr *expr2)
11930 __isl_give isl_ast_expr *isl_ast_expr_and_then(
11931 __isl_take isl_ast_expr *expr1,
11932 __isl_take isl_ast_expr *expr2)
11933 __isl_give isl_ast_expr *isl_ast_expr_or(
11934 __isl_take isl_ast_expr *expr1,
11935 __isl_take isl_ast_expr *expr2)
11936 __isl_give isl_ast_expr *isl_ast_expr_or_else(
11937 __isl_take isl_ast_expr *expr1,
11938 __isl_take isl_ast_expr *expr2)
11939 __isl_give isl_ast_expr *isl_ast_expr_eq(
11940 __isl_take isl_ast_expr *expr1,
11941 __isl_take isl_ast_expr *expr2);
11942 __isl_give isl_ast_expr *isl_ast_expr_le(
11943 __isl_take isl_ast_expr *expr1,
11944 __isl_take isl_ast_expr *expr2);
11945 __isl_give isl_ast_expr *isl_ast_expr_lt(
11946 __isl_take isl_ast_expr *expr1,
11947 __isl_take isl_ast_expr *expr2);
11948 __isl_give isl_ast_expr *isl_ast_expr_ge(
11949 __isl_take isl_ast_expr *expr1,
11950 __isl_take isl_ast_expr *expr2);
11951 __isl_give isl_ast_expr *isl_ast_expr_gt(
11952 __isl_take isl_ast_expr *expr1,
11953 __isl_take isl_ast_expr *expr2);
11954 __isl_give isl_ast_expr *isl_ast_expr_access(
11955 __isl_take isl_ast_expr *array,
11956 __isl_take isl_ast_expr_list *indices);
11957 __isl_give isl_ast_expr *isl_ast_expr_call(
11958 __isl_take isl_ast_expr *function,
11959 __isl_take isl_ast_expr_list *arguments);
11961 The function C<isl_ast_expr_address_of> can be applied to an
11962 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
11963 to represent the address of the C<isl_ast_expr_access>.
11964 The second argument of the functions C<isl_ast_expr_pdiv_q> and
11965 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
11967 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
11968 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
11970 #include <isl/ast_build.h>
11971 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
11972 __isl_keep isl_ast_build *build,
11973 __isl_take isl_set *set);
11974 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
11975 __isl_keep isl_ast_build *build,
11976 __isl_take isl_pw_aff *pa);
11977 __isl_give isl_ast_expr *
11978 isl_ast_build_access_from_pw_multi_aff(
11979 __isl_keep isl_ast_build *build,
11980 __isl_take isl_pw_multi_aff *pma);
11981 __isl_give isl_ast_expr *
11982 isl_ast_build_access_from_multi_pw_aff(
11983 __isl_keep isl_ast_build *build,
11984 __isl_take isl_multi_pw_aff *mpa);
11985 __isl_give isl_ast_expr *
11986 isl_ast_build_call_from_pw_multi_aff(
11987 __isl_keep isl_ast_build *build,
11988 __isl_take isl_pw_multi_aff *pma);
11989 __isl_give isl_ast_expr *
11990 isl_ast_build_call_from_multi_pw_aff(
11991 __isl_keep isl_ast_build *build,
11992 __isl_take isl_multi_pw_aff *mpa);
11995 the domains of C<pa>, C<mpa> and C<pma> should correspond
11996 to the schedule space of C<build>.
11997 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
11998 the function being called.
11999 If the accessed space is a nested relation, then it is taken
12000 to represent an access of the member specified by the range
12001 of this nested relation of the structure specified by the domain
12002 of the nested relation.
12004 The following functions can be used to modify an C<isl_ast_expr>.
12006 #include <isl/ast.h>
12007 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12008 __isl_take isl_ast_expr *expr, int pos,
12009 __isl_take isl_ast_expr *arg);
12011 Replace the argument of C<expr> at position C<pos> by C<arg>.
12013 #include <isl/ast.h>
12014 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12015 __isl_take isl_ast_expr *expr,
12016 __isl_take isl_id_to_ast_expr *id2expr);
12018 The function C<isl_ast_expr_substitute_ids> replaces the
12019 subexpressions of C<expr> of type C<isl_ast_expr_id>
12020 by the corresponding expression in C<id2expr>, if there is any.
12023 User specified data can be attached to an C<isl_ast_node> and obtained
12024 from the same C<isl_ast_node> using the following functions.
12026 #include <isl/ast.h>
12027 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12028 __isl_take isl_ast_node *node,
12029 __isl_take isl_id *annotation);
12030 __isl_give isl_id *isl_ast_node_get_annotation(
12031 __isl_keep isl_ast_node *node);
12033 Basic printing can be performed using the following functions.
12035 #include <isl/ast.h>
12036 __isl_give isl_printer *isl_printer_print_ast_expr(
12037 __isl_take isl_printer *p,
12038 __isl_keep isl_ast_expr *expr);
12039 __isl_give isl_printer *isl_printer_print_ast_node(
12040 __isl_take isl_printer *p,
12041 __isl_keep isl_ast_node *node);
12042 __isl_give char *isl_ast_expr_to_str(
12043 __isl_keep isl_ast_expr *expr);
12044 __isl_give char *isl_ast_node_to_str(
12045 __isl_keep isl_ast_node *node);
12046 __isl_give char *isl_ast_expr_to_C_str(
12047 __isl_keep isl_ast_expr *expr);
12048 __isl_give char *isl_ast_node_to_C_str(
12049 __isl_keep isl_ast_node *node);
12051 The functions C<isl_ast_expr_to_C_str> and
12052 C<isl_ast_node_to_C_str> are convenience functions
12053 that return a string representation of the input in C format.
12055 More advanced printing can be performed using the following functions.
12057 #include <isl/ast.h>
12058 __isl_give isl_printer *
12059 isl_ast_expr_op_type_set_print_name(
12060 __isl_take isl_printer *p,
12061 enum isl_ast_expr_op_type type,
12062 __isl_keep const char *name);
12063 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12064 __isl_take isl_printer *p,
12065 enum isl_ast_expr_op_type type,
12066 __isl_keep const char *name);
12067 isl_stat isl_options_set_ast_print_macro_once(
12068 isl_ctx *ctx, int val);
12069 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12070 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12071 enum isl_ast_expr_op_type type,
12072 __isl_take isl_printer *p);
12073 __isl_give isl_printer *isl_ast_op_type_print_macro(
12074 enum isl_ast_expr_op_type type,
12075 __isl_take isl_printer *p);
12076 __isl_give isl_printer *isl_ast_expr_print_macros(
12077 __isl_keep isl_ast_expr *expr,
12078 __isl_take isl_printer *p);
12079 __isl_give isl_printer *isl_ast_node_print_macros(
12080 __isl_keep isl_ast_node *node,
12081 __isl_take isl_printer *p);
12082 __isl_give isl_printer *isl_ast_node_print(
12083 __isl_keep isl_ast_node *node,
12084 __isl_take isl_printer *p,
12085 __isl_take isl_ast_print_options *options);
12086 __isl_give isl_printer *isl_ast_node_for_print(
12087 __isl_keep isl_ast_node *node,
12088 __isl_take isl_printer *p,
12089 __isl_take isl_ast_print_options *options);
12090 __isl_give isl_printer *isl_ast_node_if_print(
12091 __isl_keep isl_ast_node *node,
12092 __isl_take isl_printer *p,
12093 __isl_take isl_ast_print_options *options);
12095 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12096 C<isl> may print out an AST that makes use of macros such
12097 as C<floord>, C<min> and C<max>.
12098 The names of these macros may be modified by a call
12099 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12100 names are associated to the printer object.
12101 C<isl_ast_op_type_set_print_name> is an alternative name for
12102 C<isl_ast_expr_op_type_set_print_name>.
12103 C<isl_ast_expr_op_type_print_macro> prints out the macro
12104 corresponding to a specific C<isl_ast_expr_op_type>.
12105 If the print-macro-once option is set, then a given macro definition
12106 is only printed once to any given printer object.
12107 C<isl_ast_op_type_print_macro> is an alternative name for
12108 C<isl_ast_expr_op_type_print_macro>.
12109 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12110 for subexpressions where these macros would be used and prints
12111 out the required macro definitions.
12112 Essentially, C<isl_ast_expr_print_macros> calls
12113 C<isl_ast_expr_foreach_ast_expr_op_type> with
12114 C<isl_ast_expr_op_type_print_macro>
12115 as function argument.
12116 C<isl_ast_node_print_macros> does the same
12117 for expressions in its C<isl_ast_node> argument.
12118 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12119 C<isl_ast_node_if_print> print an C<isl_ast_node>
12120 in C<ISL_FORMAT_C>, but allow for some extra control
12121 through an C<isl_ast_print_options> object.
12122 This object can be created using the following functions.
12124 #include <isl/ast.h>
12125 __isl_give isl_ast_print_options *
12126 isl_ast_print_options_alloc(isl_ctx *ctx);
12127 __isl_give isl_ast_print_options *
12128 isl_ast_print_options_copy(
12129 __isl_keep isl_ast_print_options *options);
12130 __isl_null isl_ast_print_options *
12131 isl_ast_print_options_free(
12132 __isl_take isl_ast_print_options *options);
12134 __isl_give isl_ast_print_options *
12135 isl_ast_print_options_set_print_user(
12136 __isl_take isl_ast_print_options *options,
12137 __isl_give isl_printer *(*print_user)(
12138 __isl_take isl_printer *p,
12139 __isl_take isl_ast_print_options *options,
12140 __isl_keep isl_ast_node *node, void *user),
12142 __isl_give isl_ast_print_options *
12143 isl_ast_print_options_set_print_for(
12144 __isl_take isl_ast_print_options *options,
12145 __isl_give isl_printer *(*print_for)(
12146 __isl_take isl_printer *p,
12147 __isl_take isl_ast_print_options *options,
12148 __isl_keep isl_ast_node *node, void *user),
12151 The callback set by C<isl_ast_print_options_set_print_user>
12152 is called whenever a node of type C<isl_ast_node_user> needs to
12154 The callback set by C<isl_ast_print_options_set_print_for>
12155 is called whenever a node of type C<isl_ast_node_for> needs to
12157 Note that C<isl_ast_node_for_print> will I<not> call the
12158 callback set by C<isl_ast_print_options_set_print_for> on the node
12159 on which C<isl_ast_node_for_print> is called, but only on nested
12160 nodes of type C<isl_ast_node_for>. It is therefore safe to
12161 call C<isl_ast_node_for_print> from within the callback set by
12162 C<isl_ast_print_options_set_print_for>.
12164 The following option determines the type to be used for iterators
12165 while printing the AST.
12167 isl_stat isl_options_set_ast_iterator_type(
12168 isl_ctx *ctx, const char *val);
12169 const char *isl_options_get_ast_iterator_type(
12172 The AST printer only prints body nodes of C<if> and C<for> nodes
12174 blocks cannot be safely omitted.
12175 For example, a C<for> node with one body node will not be
12176 surrounded with braces in C<ISL_FORMAT_C>.
12177 A block will always be printed by setting the following option.
12179 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12181 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12183 Explicit block nodes that appear inside the AST are always printed as blocks.
12184 If the block node appears as the outermost node,
12185 then it is only printed if the following option is set.
12187 isl_stat isl_options_set_ast_print_outermost_block(
12188 isl_ctx *ctx, int val);
12189 int isl_options_get_ast_print_outermost_block(
12194 #include <isl/ast_build.h>
12195 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12196 isl_ctx *ctx, int val);
12197 int isl_options_get_ast_build_atomic_upper_bound(
12199 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12201 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12202 isl_stat isl_options_set_ast_build_detect_min_max(
12203 isl_ctx *ctx, int val);
12204 int isl_options_get_ast_build_detect_min_max(
12206 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12207 isl_ctx *ctx, int val);
12208 int isl_options_get_ast_build_exploit_nested_bounds(
12210 isl_stat isl_options_set_ast_build_group_coscheduled(
12211 isl_ctx *ctx, int val);
12212 int isl_options_get_ast_build_group_coscheduled(
12214 isl_stat isl_options_set_ast_build_separation_bounds(
12215 isl_ctx *ctx, int val);
12216 int isl_options_get_ast_build_separation_bounds(
12218 isl_stat isl_options_set_ast_build_scale_strides(
12219 isl_ctx *ctx, int val);
12220 int isl_options_get_ast_build_scale_strides(
12222 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12224 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12225 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12227 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12231 =item * ast_build_atomic_upper_bound
12233 Generate loop upper bounds that consist of the current loop iterator,
12234 an operator and an expression not involving the iterator.
12235 If this option is not set, then the current loop iterator may appear
12236 several times in the upper bound.
12237 For example, when this option is turned off, AST generation
12240 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12244 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12247 When the option is turned on, the following AST is generated
12249 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12252 =item * ast_build_prefer_pdiv
12254 If this option is turned off, then the AST generation will
12255 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12256 operators, but no C<isl_ast_expr_op_pdiv_q> or
12257 C<isl_ast_expr_op_pdiv_r> operators.
12258 If this option is turned on, then C<isl> will try to convert
12259 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12260 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12262 =item * ast_build_detect_min_max
12264 If this option is turned on, then C<isl> will try and detect
12265 min or max-expressions when building AST expressions from
12266 piecewise affine expressions.
12268 =item * ast_build_exploit_nested_bounds
12270 Simplify conditions based on bounds of nested for loops.
12271 In particular, remove conditions that are implied by the fact
12272 that one or more nested loops have at least one iteration,
12273 meaning that the upper bound is at least as large as the lower bound.
12274 For example, when this option is turned off, AST generation
12277 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12283 for (int c0 = 0; c0 <= N; c0 += 1)
12284 for (int c1 = 0; c1 <= M; c1 += 1)
12287 When the option is turned on, the following AST is generated
12289 for (int c0 = 0; c0 <= N; c0 += 1)
12290 for (int c1 = 0; c1 <= M; c1 += 1)
12293 =item * ast_build_group_coscheduled
12295 If two domain elements are assigned the same schedule point, then
12296 they may be executed in any order and they may even appear in different
12297 loops. If this options is set, then the AST generator will make
12298 sure that coscheduled domain elements do not appear in separate parts
12299 of the AST. This is useful in case of nested AST generation
12300 if the outer AST generation is given only part of a schedule
12301 and the inner AST generation should handle the domains that are
12302 coscheduled by this initial part of the schedule together.
12303 For example if an AST is generated for a schedule
12305 { A[i] -> [0]; B[i] -> [0] }
12307 then the C<isl_ast_build_set_create_leaf> callback described
12308 below may get called twice, once for each domain.
12309 Setting this option ensures that the callback is only called once
12310 on both domains together.
12312 =item * ast_build_separation_bounds
12314 This option specifies which bounds to use during separation.
12315 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12316 then all (possibly implicit) bounds on the current dimension will
12317 be used during separation.
12318 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12319 then only those bounds that are explicitly available will
12320 be used during separation.
12322 =item * ast_build_scale_strides
12324 This option specifies whether the AST generator is allowed
12325 to scale down iterators of strided loops.
12327 =item * ast_build_allow_else
12329 This option specifies whether the AST generator is allowed
12330 to construct if statements with else branches.
12332 =item * ast_build_allow_or
12334 This option specifies whether the AST generator is allowed
12335 to construct if conditions with disjunctions.
12339 =head3 AST Generation Options (Schedule Tree)
12341 In case of AST construction from a schedule tree, the options
12342 that control how an AST is created from the individual schedule
12343 dimensions are stored in the band nodes of the tree
12344 (see L</"Schedule Trees">).
12346 In particular, a schedule dimension can be handled in four
12347 different ways, atomic, separate, unroll or the default.
12348 This loop AST generation type can be set using
12349 C<isl_schedule_node_band_member_set_ast_loop_type>.
12351 the first three can be selected by including a one-dimensional
12352 element with as value the position of the schedule dimension
12353 within the band and as name one of C<atomic>, C<separate>
12354 or C<unroll> in the options
12355 set by C<isl_schedule_node_band_set_ast_build_options>.
12356 Only one of these three may be specified for
12357 any given schedule dimension within a band node.
12358 If none of these is specified, then the default
12359 is used. The meaning of the options is as follows.
12365 When this option is specified, the AST generator will make
12366 sure that a given domain space only appears in a single
12367 loop at the specified level.
12369 For example, for the schedule tree
12371 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12373 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12374 options: "{ atomic[x] }"
12376 the following AST will be generated
12378 for (int c0 = 0; c0 <= 10; c0 += 1) {
12385 On the other hand, for the schedule tree
12387 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12389 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12390 options: "{ separate[x] }"
12392 the following AST will be generated
12396 for (int c0 = 1; c0 <= 9; c0 += 1) {
12403 If neither C<atomic> nor C<separate> is specified, then the AST generator
12404 may produce either of these two results or some intermediate form.
12408 When this option is specified, the AST generator will
12409 split the domain of the specified schedule dimension
12410 into pieces with a fixed set of statements for which
12411 instances need to be executed by the iterations in
12412 the schedule domain part. This option tends to avoid
12413 the generation of guards inside the corresponding loops.
12414 See also the C<atomic> option.
12418 When this option is specified, the AST generator will
12419 I<completely> unroll the corresponding schedule dimension.
12420 It is the responsibility of the user to ensure that such
12421 unrolling is possible.
12422 To obtain a partial unrolling, the user should apply an additional
12423 strip-mining to the schedule and fully unroll the inner schedule
12428 The C<isolate> option is a bit more involved. It allows the user
12429 to isolate a range of schedule dimension values from smaller and
12430 greater values. Additionally, the user may specify a different
12431 atomic/separate/unroll choice for the isolated part and the remaining
12432 parts. The typical use case of the C<isolate> option is to isolate
12433 full tiles from partial tiles.
12434 The part that needs to be isolated may depend on outer schedule dimensions.
12435 The option therefore needs to be able to reference those outer schedule
12436 dimensions. In particular, the space of the C<isolate> option is that
12437 of a wrapped map with as domain the flat product of all outer band nodes
12438 and as range the space of the current band node.
12439 The atomic/separate/unroll choice for the isolated part is determined
12440 by an option that lives in an unnamed wrapped space with as domain
12441 a zero-dimensional C<isolate> space and as range the regular
12442 C<atomic>, C<separate> or C<unroll> space.
12443 This option may also be set directly using
12444 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12445 The atomic/separate/unroll choice for the remaining part is determined
12446 by the regular C<atomic>, C<separate> or C<unroll> option.
12447 Since the C<isolate> option references outer schedule dimensions,
12448 its use in a band node causes any tree containing the node
12449 to be considered anchored.
12451 As an example, consider the isolation of full tiles from partial tiles
12452 in a tiling of a triangular domain. The original schedule is as follows.
12454 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12456 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12457 { A[i,j] -> [floor(j/10)] }, \
12458 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12462 for (int c0 = 0; c0 <= 10; c0 += 1)
12463 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12464 for (int c2 = 10 * c0;
12465 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12466 for (int c3 = 10 * c1;
12467 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12470 Isolating the full tiles, we have the following input
12472 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12474 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12475 { A[i,j] -> [floor(j/10)] }, \
12476 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12477 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12478 10a+9+10b+9 <= 100 }"
12483 for (int c0 = 0; c0 <= 8; c0 += 1) {
12484 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12485 for (int c2 = 10 * c0;
12486 c2 <= 10 * c0 + 9; c2 += 1)
12487 for (int c3 = 10 * c1;
12488 c3 <= 10 * c1 + 9; c3 += 1)
12490 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12491 for (int c2 = 10 * c0;
12492 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12493 for (int c3 = 10 * c1;
12494 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12497 for (int c0 = 9; c0 <= 10; c0 += 1)
12498 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12499 for (int c2 = 10 * c0;
12500 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12501 for (int c3 = 10 * c1;
12502 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12506 We may then additionally unroll the innermost loop of the isolated part
12508 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12510 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12511 { A[i,j] -> [floor(j/10)] }, \
12512 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12513 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12514 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12519 for (int c0 = 0; c0 <= 8; c0 += 1) {
12520 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12521 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12523 A(c2, 10 * c1 + 1);
12524 A(c2, 10 * c1 + 2);
12525 A(c2, 10 * c1 + 3);
12526 A(c2, 10 * c1 + 4);
12527 A(c2, 10 * c1 + 5);
12528 A(c2, 10 * c1 + 6);
12529 A(c2, 10 * c1 + 7);
12530 A(c2, 10 * c1 + 8);
12531 A(c2, 10 * c1 + 9);
12533 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12534 for (int c2 = 10 * c0;
12535 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12536 for (int c3 = 10 * c1;
12537 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12540 for (int c0 = 9; c0 <= 10; c0 += 1)
12541 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12542 for (int c2 = 10 * c0;
12543 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12544 for (int c3 = 10 * c1;
12545 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12550 =head3 AST Generation Options (Schedule Map)
12552 In case of AST construction using
12553 C<isl_ast_build_node_from_schedule_map>, the options
12554 that control how an AST is created from the individual schedule
12555 dimensions are stored in the C<isl_ast_build>.
12556 They can be set using the following function.
12558 #include <isl/ast_build.h>
12559 __isl_give isl_ast_build *
12560 isl_ast_build_set_options(
12561 __isl_take isl_ast_build *build,
12562 __isl_take isl_union_map *options);
12564 The options are encoded in an C<isl_union_map>.
12565 The domain of this union relation refers to the schedule domain,
12566 i.e., the range of the schedule passed
12567 to C<isl_ast_build_node_from_schedule_map>.
12568 In the case of nested AST generation (see L</"Nested AST Generation">),
12569 the domain of C<options> should refer to the extra piece of the schedule.
12570 That is, it should be equal to the range of the wrapped relation in the
12571 range of the schedule.
12572 The range of the options can consist of elements in one or more spaces,
12573 the names of which determine the effect of the option.
12574 The values of the range typically also refer to the schedule dimension
12575 to which the option applies, with value C<0> representing
12576 the outermost schedule dimension. In case of nested AST generation
12577 (see L</"Nested AST Generation">), these values refer to the position
12578 of the schedule dimension within the innermost AST generation.
12579 The constraints on the domain elements of
12580 the option should only refer to this dimension and earlier dimensions.
12581 We consider the following spaces.
12585 =item C<separation_class>
12587 B<This option has been deprecated. Use the isolate option on
12588 schedule trees instead.>
12590 This space is a wrapped relation between two one dimensional spaces.
12591 The input space represents the schedule dimension to which the option
12592 applies and the output space represents the separation class.
12593 While constructing a loop corresponding to the specified schedule
12594 dimension(s), the AST generator will try to generate separate loops
12595 for domain elements that are assigned different classes.
12596 If only some of the elements are assigned a class, then those elements
12597 that are not assigned any class will be treated as belonging to a class
12598 that is separate from the explicitly assigned classes.
12599 The typical use case for this option is to separate full tiles from
12601 The other options, described below, are applied after the separation
12604 As an example, consider the separation into full and partial tiles
12605 of a tiling of a triangular domain.
12606 Take, for example, the domain
12608 { A[i,j] : 0 <= i,j and i + j <= 100 }
12610 and a tiling into tiles of 10 by 10. The input to the AST generator
12611 is then the schedule
12613 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12616 Without any options, the following AST is generated
12618 for (int c0 = 0; c0 <= 10; c0 += 1)
12619 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12620 for (int c2 = 10 * c0;
12621 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12623 for (int c3 = 10 * c1;
12624 c3 <= min(10 * c1 + 9, -c2 + 100);
12628 Separation into full and partial tiles can be obtained by assigning
12629 a class, say C<0>, to the full tiles. The full tiles are represented by those
12630 values of the first and second schedule dimensions for which there are
12631 values of the third and fourth dimensions to cover an entire tile.
12632 That is, we need to specify the following option
12634 { [a,b,c,d] -> separation_class[[0]->[0]] :
12635 exists b': 0 <= 10a,10b' and
12636 10a+9+10b'+9 <= 100;
12637 [a,b,c,d] -> separation_class[[1]->[0]] :
12638 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12640 which simplifies to
12642 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12643 a >= 0 and b >= 0 and b <= 8 - a;
12644 [a, b, c, d] -> separation_class[[0] -> [0]] :
12645 a >= 0 and a <= 8 }
12647 With this option, the generated AST is as follows
12650 for (int c0 = 0; c0 <= 8; c0 += 1) {
12651 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12652 for (int c2 = 10 * c0;
12653 c2 <= 10 * c0 + 9; c2 += 1)
12654 for (int c3 = 10 * c1;
12655 c3 <= 10 * c1 + 9; c3 += 1)
12657 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12658 for (int c2 = 10 * c0;
12659 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12661 for (int c3 = 10 * c1;
12662 c3 <= min(-c2 + 100, 10 * c1 + 9);
12666 for (int c0 = 9; c0 <= 10; c0 += 1)
12667 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12668 for (int c2 = 10 * c0;
12669 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12671 for (int c3 = 10 * c1;
12672 c3 <= min(10 * c1 + 9, -c2 + 100);
12679 This is a single-dimensional space representing the schedule dimension(s)
12680 to which ``separation'' should be applied. Separation tries to split
12681 a loop into several pieces if this can avoid the generation of guards
12683 See also the C<atomic> option.
12687 This is a single-dimensional space representing the schedule dimension(s)
12688 for which the domains should be considered ``atomic''. That is, the
12689 AST generator will make sure that any given domain space will only appear
12690 in a single loop at the specified level.
12692 Consider the following schedule
12694 { a[i] -> [i] : 0 <= i < 10;
12695 b[i] -> [i+1] : 0 <= i < 10 }
12697 If the following option is specified
12699 { [i] -> separate[x] }
12701 then the following AST will be generated
12705 for (int c0 = 1; c0 <= 9; c0 += 1) {
12712 If, on the other hand, the following option is specified
12714 { [i] -> atomic[x] }
12716 then the following AST will be generated
12718 for (int c0 = 0; c0 <= 10; c0 += 1) {
12725 If neither C<atomic> nor C<separate> is specified, then the AST generator
12726 may produce either of these two results or some intermediate form.
12730 This is a single-dimensional space representing the schedule dimension(s)
12731 that should be I<completely> unrolled.
12732 To obtain a partial unrolling, the user should apply an additional
12733 strip-mining to the schedule and fully unroll the inner loop.
12737 =head3 Fine-grained Control over AST Generation
12739 Besides specifying the constraints on the parameters,
12740 an C<isl_ast_build> object can be used to control
12741 various aspects of the AST generation process.
12742 In case of AST construction using
12743 C<isl_ast_build_node_from_schedule_map>,
12744 the most prominent way of control is through ``options'',
12745 as explained above.
12747 Additional control is available through the following functions.
12749 #include <isl/ast_build.h>
12750 __isl_give isl_ast_build *
12751 isl_ast_build_set_iterators(
12752 __isl_take isl_ast_build *build,
12753 __isl_take isl_id_list *iterators);
12755 The function C<isl_ast_build_set_iterators> allows the user to
12756 specify a list of iterator C<isl_id>s to be used as iterators.
12757 If the input schedule is injective, then
12758 the number of elements in this list should be as large as the dimension
12759 of the schedule space, but no direct correspondence should be assumed
12760 between dimensions and elements.
12761 If the input schedule is not injective, then an additional number
12762 of C<isl_id>s equal to the largest dimension of the input domains
12764 If the number of provided C<isl_id>s is insufficient, then additional
12765 names are automatically generated.
12767 #include <isl/ast_build.h>
12768 __isl_give isl_ast_build *
12769 isl_ast_build_set_create_leaf(
12770 __isl_take isl_ast_build *build,
12771 __isl_give isl_ast_node *(*fn)(
12772 __isl_take isl_ast_build *build,
12773 void *user), void *user);
12776 C<isl_ast_build_set_create_leaf> function allows for the
12777 specification of a callback that should be called whenever the AST
12778 generator arrives at an element of the schedule domain.
12779 The callback should return an AST node that should be inserted
12780 at the corresponding position of the AST. The default action (when
12781 the callback is not set) is to continue generating parts of the AST to scan
12782 all the domain elements associated to the schedule domain element
12783 and to insert user nodes, ``calling'' the domain element, for each of them.
12784 The C<build> argument contains the current state of the C<isl_ast_build>.
12785 To ease nested AST generation (see L</"Nested AST Generation">),
12786 all control information that is
12787 specific to the current AST generation such as the options and
12788 the callbacks has been removed from this C<isl_ast_build>.
12789 The callback would typically return the result of a nested
12790 AST generation or a
12791 user defined node created using the following function.
12793 #include <isl/ast.h>
12794 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12795 __isl_take isl_ast_expr *expr);
12797 #include <isl/ast_build.h>
12798 __isl_give isl_ast_build *
12799 isl_ast_build_set_at_each_domain(
12800 __isl_take isl_ast_build *build,
12801 __isl_give isl_ast_node *(*fn)(
12802 __isl_take isl_ast_node *node,
12803 __isl_keep isl_ast_build *build,
12804 void *user), void *user);
12805 __isl_give isl_ast_build *
12806 isl_ast_build_set_before_each_for(
12807 __isl_take isl_ast_build *build,
12808 __isl_give isl_id *(*fn)(
12809 __isl_keep isl_ast_build *build,
12810 void *user), void *user);
12811 __isl_give isl_ast_build *
12812 isl_ast_build_set_after_each_for(
12813 __isl_take isl_ast_build *build,
12814 __isl_give isl_ast_node *(*fn)(
12815 __isl_take isl_ast_node *node,
12816 __isl_keep isl_ast_build *build,
12817 void *user), void *user);
12818 __isl_give isl_ast_build *
12819 isl_ast_build_set_before_each_mark(
12820 __isl_take isl_ast_build *build,
12821 isl_stat (*fn)(__isl_keep isl_id *mark,
12822 __isl_keep isl_ast_build *build,
12823 void *user), void *user);
12824 __isl_give isl_ast_build *
12825 isl_ast_build_set_after_each_mark(
12826 __isl_take isl_ast_build *build,
12827 __isl_give isl_ast_node *(*fn)(
12828 __isl_take isl_ast_node *node,
12829 __isl_keep isl_ast_build *build,
12830 void *user), void *user);
12832 The callback set by C<isl_ast_build_set_at_each_domain> will
12833 be called for each domain AST node.
12834 The callbacks set by C<isl_ast_build_set_before_each_for>
12835 and C<isl_ast_build_set_after_each_for> will be called
12836 for each for AST node. The first will be called in depth-first
12837 pre-order, while the second will be called in depth-first post-order.
12838 Since C<isl_ast_build_set_before_each_for> is called before the for
12839 node is actually constructed, it is only passed an C<isl_ast_build>.
12840 The returned C<isl_id> will be added as an annotation (using
12841 C<isl_ast_node_set_annotation>) to the constructed for node.
12842 In particular, if the user has also specified an C<after_each_for>
12843 callback, then the annotation can be retrieved from the node passed to
12844 that callback using C<isl_ast_node_get_annotation>.
12845 The callbacks set by C<isl_ast_build_set_before_each_mark>
12846 and C<isl_ast_build_set_after_each_mark> will be called for each
12847 mark AST node that is created, i.e., for each mark schedule node
12848 in the input schedule tree. The first will be called in depth-first
12849 pre-order, while the second will be called in depth-first post-order.
12850 Since the callback set by C<isl_ast_build_set_before_each_mark>
12851 is called before the mark AST node is actually constructed, it is passed
12852 the identifier of the mark node.
12853 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12854 The given C<isl_ast_build> can be used to create new
12855 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12856 or C<isl_ast_build_call_from_pw_multi_aff>.
12858 =head3 Nested AST Generation
12860 C<isl> allows the user to create an AST within the context
12861 of another AST. These nested ASTs are created using the
12862 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12863 the outer AST. The C<build> argument should be an C<isl_ast_build>
12864 passed to a callback set by
12865 C<isl_ast_build_set_create_leaf>.
12866 The space of the range of the C<schedule> argument should refer
12867 to this build. In particular, the space should be a wrapped
12868 relation and the domain of this wrapped relation should be the
12869 same as that of the range of the schedule returned by
12870 C<isl_ast_build_get_schedule> below.
12871 In practice, the new schedule is typically
12872 created by calling C<isl_union_map_range_product> on the old schedule
12873 and some extra piece of the schedule.
12874 The space of the schedule domain is also available from
12875 the C<isl_ast_build>.
12877 #include <isl/ast_build.h>
12878 __isl_give isl_union_map *isl_ast_build_get_schedule(
12879 __isl_keep isl_ast_build *build);
12880 __isl_give isl_space *isl_ast_build_get_schedule_space(
12881 __isl_keep isl_ast_build *build);
12882 __isl_give isl_ast_build *isl_ast_build_restrict(
12883 __isl_take isl_ast_build *build,
12884 __isl_take isl_set *set);
12886 The C<isl_ast_build_get_schedule> function returns a (partial)
12887 schedule for the domains elements for which part of the AST still needs to
12888 be generated in the current build.
12889 In particular, the domain elements are mapped to those iterations of the loops
12890 enclosing the current point of the AST generation inside which
12891 the domain elements are executed.
12892 No direct correspondence between
12893 the input schedule and this schedule should be assumed.
12894 The space obtained from C<isl_ast_build_get_schedule_space> can be used
12895 to create a set for C<isl_ast_build_restrict> to intersect
12896 with the current build. In particular, the set passed to
12897 C<isl_ast_build_restrict> can have additional parameters.
12898 The ids of the set dimensions in the space returned by
12899 C<isl_ast_build_get_schedule_space> correspond to the
12900 iterators of the already generated loops.
12901 The user should not rely on the ids of the output dimensions
12902 of the relations in the union relation returned by
12903 C<isl_ast_build_get_schedule> having any particular value.
12905 =head1 Applications
12907 Although C<isl> is mainly meant to be used as a library,
12908 it also contains some basic applications that use some
12909 of the functionality of C<isl>.
12910 For applications that take one or more polytopes or polyhedra
12911 as input, this input may be specified in either the L<isl format>
12912 or the L<PolyLib format>.
12914 =head2 C<isl_polyhedron_sample>
12916 C<isl_polyhedron_sample> takes a polyhedron as input and prints
12917 an integer element of the polyhedron, if there is any.
12918 The first column in the output is the denominator and is always
12919 equal to 1. If the polyhedron contains no integer points,
12920 then a vector of length zero is printed.
12924 C<isl_pip> takes the same input as the C<example> program
12925 from the C<piplib> distribution, i.e., a set of constraints
12926 on the parameters, a line containing only -1 and finally a set
12927 of constraints on a parametric polyhedron.
12928 The coefficients of the parameters appear in the last columns
12929 (but before the final constant column).
12930 The output is the lexicographic minimum of the parametric polyhedron.
12931 As C<isl> currently does not have its own output format, the output
12932 is just a dump of the internal state.
12934 =head2 C<isl_polyhedron_minimize>
12936 C<isl_polyhedron_minimize> computes the minimum of some linear
12937 or affine objective function over the integer points in a polyhedron.
12938 If an affine objective function
12939 is given, then the constant should appear in the last column.
12941 =head2 C<isl_polytope_scan>
12943 Given a polytope, C<isl_polytope_scan> prints
12944 all integer points in the polytope.
12948 Given an C<isl_union_access_info> object as input,
12949 C<isl_flow> prints out the corresponding dependences,
12950 as computed by C<isl_union_access_info_compute_flow>.
12952 =head2 C<isl_codegen>
12954 Given either a schedule tree or a sequence consisting of
12955 a schedule map, a context set and an options relation,
12956 C<isl_codegen> prints out an AST that scans the domain elements
12957 of the schedule in the order of their image(s) taking into account
12958 the constraints in the context set.
12960 =head2 C<isl_schedule>
12962 Given an C<isl_schedule_constraints> object as input,
12963 C<isl_schedule> prints out a schedule that satisfies the given