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 (16.0),
473 although any release since 3.5 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>.
711 Similarly, the function C<isl_stat_non_error_bool> converts an C<isl_bool>
712 to an C<isl_stat>, returning C<isl_stat_ok> if the C<isl_bool>
713 represents a valid result and C<isl_stat_error> if it is C<isl_bool_error>.
716 isl_stat isl_stat_non_null(void *obj);
717 isl_stat isl_stat_non_error_bool(isl_bool b);
719 See L</"Error Handling"> for more information on
720 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
724 An C<isl_val> represents an integer value, a rational value
725 or one of three special values, infinity, negative infinity and NaN.
726 Some predefined values can be created using the following functions.
729 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
730 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
731 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
732 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
733 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
734 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
736 Specific integer values can be created using the following functions.
739 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
741 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
743 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
744 size_t n, size_t size, const void *chunks);
746 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
747 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
748 The least significant digit is assumed to be stored first.
750 Value objects can be copied and freed using the following functions.
753 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
754 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
756 They can be inspected using the following functions.
759 long isl_val_get_num_si(__isl_keep isl_val *v);
760 long isl_val_get_den_si(__isl_keep isl_val *v);
761 __isl_give isl_val *isl_val_get_den_val(
762 __isl_keep isl_val *v);
763 double isl_val_get_d(__isl_keep isl_val *v);
764 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
766 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
767 size_t size, void *chunks);
769 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
770 of C<size> bytes needed to store the absolute value of the
772 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
773 which is assumed to have been preallocated by the caller.
774 The least significant digit is stored first.
775 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
776 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
777 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
779 An C<isl_val> can be modified using the following function.
782 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
785 The following unary properties are defined on C<isl_val>s.
788 int isl_val_sgn(__isl_keep isl_val *v);
789 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
790 isl_bool isl_val_is_one(__isl_keep isl_val *v);
791 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
792 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
793 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
794 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
795 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
796 isl_bool isl_val_is_int(__isl_keep isl_val *v);
797 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
798 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
799 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
800 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
802 Note that the sign of NaN is undefined.
804 The following binary properties are defined on pairs of C<isl_val>s.
807 isl_bool isl_val_lt(__isl_keep isl_val *v1,
808 __isl_keep isl_val *v2);
809 isl_bool isl_val_le(__isl_keep isl_val *v1,
810 __isl_keep isl_val *v2);
811 isl_bool isl_val_gt(__isl_keep isl_val *v1,
812 __isl_keep isl_val *v2);
813 isl_bool isl_val_ge(__isl_keep isl_val *v1,
814 __isl_keep isl_val *v2);
815 isl_bool isl_val_eq(__isl_keep isl_val *v1,
816 __isl_keep isl_val *v2);
817 isl_bool isl_val_ne(__isl_keep isl_val *v1,
818 __isl_keep isl_val *v2);
819 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
820 __isl_keep isl_val *v2);
822 Comparisons to NaN always return false.
823 That is, a NaN is not considered to hold any relative position
824 with respect to any value. In particular, a NaN
825 is neither considered to be equal to nor to be different from
826 any value (including another NaN).
827 The function C<isl_val_abs_eq> checks whether its two arguments
828 are equal in absolute value.
830 For integer C<isl_val>s we additionally have the following binary property.
833 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
834 __isl_keep isl_val *v2);
836 An C<isl_val> can also be compared to an integer using the following
837 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
840 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
841 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
842 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
844 The following unary operations are available on C<isl_val>s.
847 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
848 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
849 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
850 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
851 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
852 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
854 The following binary operations are available on C<isl_val>s.
857 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
858 __isl_take isl_val *v2);
859 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
860 __isl_take isl_val *v2);
861 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
862 __isl_take isl_val *v2);
863 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
865 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
866 __isl_take isl_val *v2);
867 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
869 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
870 __isl_take isl_val *v2);
871 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
873 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
874 __isl_take isl_val *v2);
875 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
878 On integer values, we additionally have the following operations.
881 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
882 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
883 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
884 __isl_take isl_val *v2);
885 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
886 __isl_take isl_val *v2);
887 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
888 __isl_take isl_val *v2, __isl_give isl_val **x,
889 __isl_give isl_val **y);
891 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
892 The function C<isl_val_gcdext> returns the greatest common divisor g
893 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
894 that C<*x> * C<v1> + C<*y> * C<v2> = g.
896 =head3 GMP specific functions
898 These functions are only available if C<isl> has been compiled with C<GMP>
901 Specific integer and rational values can be created from C<GMP> values using
902 the following functions.
904 #include <isl/val_gmp.h>
905 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
907 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
908 const mpz_t n, const mpz_t d);
910 The numerator and denominator of a rational value can be extracted as
911 C<GMP> values using the following functions.
913 #include <isl/val_gmp.h>
914 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
915 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
917 =head2 Sets and Relations
919 C<isl> uses six types of objects for representing sets and relations,
920 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
921 C<isl_union_set> and C<isl_union_map>.
922 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
923 can be described as a conjunction of affine constraints, while
924 C<isl_set> and C<isl_map> represent unions of
925 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
926 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
927 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
928 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
929 where spaces are considered different if they have a different number
930 of dimensions and/or different names (see L<"Spaces">).
931 The difference between sets and relations (maps) is that sets have
932 one set of variables, while relations have two sets of variables,
933 input variables and output variables.
935 =head2 Error Handling
937 C<isl> supports different ways to react in case a runtime error is triggered.
938 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
939 with two maps that have incompatible spaces. There are three possible ways
940 to react on error: to warn, to continue or to abort.
942 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
943 the last error in the corresponding C<isl_ctx> and the function in which the
944 error was triggered returns a value indicating that some error has
945 occurred. In case of functions returning a pointer, this value is
946 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
947 C<isl_stat>, this value is C<isl_size_error>,
948 C<isl_bool_error> or C<isl_stat_error>.
949 An error does not corrupt internal state,
950 such that isl can continue to be used. C<isl> also provides functions to
951 read the last error, including the specific error message,
952 the isl source file where the error occurred and the line number,
953 and to reset all information about the last error. The
954 last error is only stored for information purposes. Its presence does not
955 change the behavior of C<isl>. Hence, resetting an error is not required to
956 continue to use isl, but only to observe new errors.
959 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
960 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
961 const char *isl_ctx_last_error_file(isl_ctx *ctx);
962 int isl_ctx_last_error_line(isl_ctx *ctx);
963 void isl_ctx_reset_error(isl_ctx *ctx);
965 If no error has occurred since the last call to C<isl_ctx_reset_error>,
966 then the functions C<isl_ctx_last_error_msg> and
967 C<isl_ctx_last_error_file> return C<NULL>.
969 Another option is to continue on error. This is similar to warn on error mode,
970 except that C<isl> does not print any warning. This allows a program to
971 implement its own error reporting.
973 The last option is to directly abort the execution of the program from within
974 the isl library. This makes it obviously impossible to recover from an error,
975 but it allows to directly spot the error location. By aborting on error,
976 debuggers break at the location the error occurred and can provide a stack
977 trace. Other tools that automatically provide stack traces on abort or that do
978 not want to continue execution after an error was triggered may also prefer to
981 The on error behavior of isl can be specified by calling
982 C<isl_options_set_on_error> or by setting the command line option
983 C<--isl-on-error>. Valid arguments for the function call are
984 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
985 choices for the command line option are C<warn>, C<continue> and C<abort>.
986 It is also possible to query the current error mode.
988 #include <isl/options.h>
989 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
990 int isl_options_get_on_error(isl_ctx *ctx);
994 Identifiers are used to identify both individual dimensions
995 and tuples of dimensions. They consist of an optional name and an optional
996 user pointer. The name and the user pointer cannot both be C<NULL>, however.
997 Identifiers with the same name but different pointer values
998 are considered to be distinct.
999 Similarly, identifiers with different names but the same pointer value
1000 are also considered to be distinct.
1001 Equal identifiers are represented using the same object.
1002 Pairs of identifiers can therefore be tested for equality using the
1004 Identifiers can be constructed, copied, freed, inspected and printed
1005 using the following functions.
1008 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
1009 __isl_keep const char *name, void *user);
1010 __isl_give isl_id *isl_id_set_free_user(
1011 __isl_take isl_id *id,
1012 void (*free_user)(void *user));
1013 void (*isl_id_get_free_user(__isl_keep isl_id *id))
1015 __isl_give isl_id *isl_id_copy(isl_id *id);
1016 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
1018 void *isl_id_get_user(__isl_keep isl_id *id);
1019 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
1021 __isl_give isl_printer *isl_printer_print_id(
1022 __isl_take isl_printer *p, __isl_keep isl_id *id);
1024 The callback set by C<isl_id_set_free_user> is called on the user
1025 pointer when the last reference to the C<isl_id> is freed.
1026 This callback can be retrieved using C<isl_id_get_free_user>.
1027 Note that C<isl_id_get_name> returns a pointer to some internal
1028 data structure, so the result can only be used while the
1029 corresponding C<isl_id> is alive.
1033 Whenever a new set, relation or similar object is created from scratch,
1034 the space in which it lives needs to be specified using an C<isl_space>.
1035 Each space involves zero or more parameters and zero, one or two
1036 tuples of set or input/output dimensions. The parameters and dimensions
1037 are identified by an C<isl_dim_type> and a position.
1038 The type C<isl_dim_param> refers to parameters,
1039 the type C<isl_dim_set> refers to set dimensions (for spaces
1040 with a single tuple of dimensions) and the types C<isl_dim_in>
1041 and C<isl_dim_out> refer to input and output dimensions
1042 (for spaces with two tuples of dimensions).
1043 Local spaces (see L</"Local Spaces">) also contain dimensions
1044 of type C<isl_dim_div>.
1045 Note that parameters are only identified by their position within
1046 a given object. Across different objects, parameters are (usually)
1047 identified by their names or identifiers. Only unnamed parameters
1048 are identified by their positions across objects. The use of unnamed
1049 parameters is discouraged.
1051 #include <isl/space.h>
1052 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1053 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1054 unsigned nparam, unsigned n_in, unsigned n_out);
1055 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1057 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1058 unsigned nparam, unsigned dim);
1059 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1060 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1062 The space used for creating a parameter domain
1063 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1064 For other sets, the space
1065 needs to be created using C<isl_space_set_alloc>, while
1066 for a relation, the space
1067 needs to be created using C<isl_space_alloc>.
1068 The use of C<isl_space_params_alloc>,
1069 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1070 for the introduction of unnamed parameters.
1072 To check whether a given space is that of a set or a map
1073 or whether it is a parameter space, use these functions:
1075 #include <isl/space.h>
1076 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1077 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1078 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1080 Spaces can be compared using the following functions:
1082 #include <isl/space.h>
1083 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1084 __isl_keep isl_space *space2);
1085 isl_bool isl_space_has_equal_params(
1086 __isl_keep isl_space *space1,
1087 __isl_keep isl_space *space2);
1088 isl_bool isl_space_has_equal_tuples(
1089 __isl_keep isl_space *space1,
1090 __isl_keep isl_space *space2);
1091 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1092 __isl_keep isl_space *space2);
1093 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1094 __isl_keep isl_space *space2);
1095 isl_bool isl_space_tuple_is_equal(
1096 __isl_keep isl_space *space1,
1097 enum isl_dim_type type1,
1098 __isl_keep isl_space *space2,
1099 enum isl_dim_type type2);
1101 C<isl_space_is_domain> checks whether the first argument is equal
1102 to the domain of the second argument. This requires in particular that
1103 the first argument is a set space and that the second argument
1104 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1105 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1106 spaces are the same. That is, it checks if they have the same
1107 identifier (if any), the same dimension and the same internal structure
1110 C<isl_space_has_equal_params> checks whether two spaces
1111 have the same parameters in the same order.
1112 C<isl_space_has_equal_tuples> check whether two spaces have
1113 the same tuples. In contrast to C<isl_space_is_equal> below,
1114 it does not check the
1115 parameters. This is useful because many C<isl> functions align the
1116 parameters before they perform their operations, such that equivalence
1118 C<isl_space_is_equal> checks whether two spaces are identical,
1119 meaning that they have the same parameters and the same tuples.
1120 That is, it checks whether both C<isl_space_has_equal_params> and
1121 C<isl_space_has_equal_tuples> hold.
1123 It is often useful to create objects that live in the
1124 same space as some other object. This can be accomplished
1125 by creating the new objects
1126 (see L</"Creating New Sets and Relations"> or
1127 L</"Functions">) based on the space
1128 of the original object.
1130 #include <isl/set.h>
1131 __isl_give isl_space *isl_basic_set_get_space(
1132 __isl_keep isl_basic_set *bset);
1133 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1135 #include <isl/union_set.h>
1136 __isl_give isl_space *isl_union_set_get_space(
1137 __isl_keep isl_union_set *uset);
1139 #include <isl/map.h>
1140 __isl_give isl_space *isl_basic_map_get_space(
1141 __isl_keep isl_basic_map *bmap);
1142 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1144 #include <isl/union_map.h>
1145 __isl_give isl_space *isl_union_map_get_space(
1146 __isl_keep isl_union_map *umap);
1148 #include <isl/constraint.h>
1149 __isl_give isl_space *isl_constraint_get_space(
1150 __isl_keep isl_constraint *constraint);
1152 #include <isl/polynomial.h>
1153 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1154 __isl_keep isl_qpolynomial *qp);
1155 __isl_give isl_space *isl_qpolynomial_get_space(
1156 __isl_keep isl_qpolynomial *qp);
1157 __isl_give isl_space *
1158 isl_qpolynomial_fold_get_domain_space(
1159 __isl_keep isl_qpolynomial_fold *fold);
1160 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1161 __isl_keep isl_qpolynomial_fold *fold);
1162 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1163 __isl_keep isl_pw_qpolynomial *pwqp);
1164 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1165 __isl_keep isl_pw_qpolynomial *pwqp);
1166 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1167 __isl_keep isl_pw_qpolynomial_fold *pwf);
1168 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1169 __isl_keep isl_pw_qpolynomial_fold *pwf);
1170 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1171 __isl_keep isl_union_pw_qpolynomial *upwqp);
1172 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1173 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1176 __isl_give isl_space *isl_multi_id_get_space(
1177 __isl_keep isl_multi_id *mi);
1179 #include <isl/val.h>
1180 __isl_give isl_space *isl_multi_val_get_space(
1181 __isl_keep isl_multi_val *mv);
1183 #include <isl/aff.h>
1184 __isl_give isl_space *isl_aff_get_domain_space(
1185 __isl_keep isl_aff *aff);
1186 __isl_give isl_space *isl_aff_get_space(
1187 __isl_keep isl_aff *aff);
1188 __isl_give isl_space *isl_pw_aff_get_domain_space(
1189 __isl_keep isl_pw_aff *pwaff);
1190 __isl_give isl_space *isl_pw_aff_get_space(
1191 __isl_keep isl_pw_aff *pwaff);
1192 __isl_give isl_space *isl_multi_aff_get_domain_space(
1193 __isl_keep isl_multi_aff *maff);
1194 __isl_give isl_space *isl_multi_aff_get_space(
1195 __isl_keep isl_multi_aff *maff);
1196 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1197 __isl_keep isl_pw_multi_aff *pma);
1198 __isl_give isl_space *isl_pw_multi_aff_get_space(
1199 __isl_keep isl_pw_multi_aff *pma);
1200 __isl_give isl_space *isl_union_pw_aff_get_space(
1201 __isl_keep isl_union_pw_aff *upa);
1202 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1203 __isl_keep isl_union_pw_multi_aff *upma);
1204 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1205 __isl_keep isl_multi_pw_aff *mpa);
1206 __isl_give isl_space *isl_multi_pw_aff_get_space(
1207 __isl_keep isl_multi_pw_aff *mpa);
1208 __isl_give isl_space *
1209 isl_multi_union_pw_aff_get_domain_space(
1210 __isl_keep isl_multi_union_pw_aff *mupa);
1211 __isl_give isl_space *
1212 isl_multi_union_pw_aff_get_space(
1213 __isl_keep isl_multi_union_pw_aff *mupa);
1215 #include <isl/point.h>
1216 __isl_give isl_space *isl_point_get_space(
1217 __isl_keep isl_point *pnt);
1219 #include <isl/fixed_box.h>
1220 __isl_give isl_space *isl_fixed_box_get_space(
1221 __isl_keep isl_fixed_box *box);
1223 The number of dimensions of a given type of space
1224 may be read off from a space or an object that lives
1225 in a space using the following functions.
1226 In case of C<isl_space_dim>, type may be
1227 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1228 C<isl_dim_out> (only for relations), C<isl_dim_set>
1229 (only for sets) or C<isl_dim_all>.
1231 #include <isl/space.h>
1232 isl_size isl_space_dim(__isl_keep isl_space *space,
1233 enum isl_dim_type type);
1235 #include <isl/local_space.h>
1236 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1237 enum isl_dim_type type);
1239 #include <isl/set.h>
1240 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1241 enum isl_dim_type type);
1242 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1243 isl_size isl_set_dim(__isl_keep isl_set *set,
1244 enum isl_dim_type type);
1246 #include <isl/union_set.h>
1247 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1248 enum isl_dim_type type);
1250 #include <isl/map.h>
1251 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1252 enum isl_dim_type type);
1253 isl_size isl_map_domain_tuple_dim(
1254 __isl_keep isl_map *map);
1255 isl_size isl_map_range_tuple_dim(
1256 __isl_keep isl_map *map);
1257 isl_size isl_map_dim(__isl_keep isl_map *map,
1258 enum isl_dim_type type);
1260 #include <isl/union_map.h>
1261 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1262 enum isl_dim_type type);
1264 #include <isl/val.h>
1265 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1266 enum isl_dim_type type);
1268 #include <isl/aff.h>
1269 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1270 enum isl_dim_type type);
1271 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1272 enum isl_dim_type type);
1273 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1274 enum isl_dim_type type);
1275 isl_size isl_pw_multi_aff_dim(
1276 __isl_keep isl_pw_multi_aff *pma,
1277 enum isl_dim_type type);
1278 isl_size isl_multi_pw_aff_dim(
1279 __isl_keep isl_multi_pw_aff *mpa,
1280 enum isl_dim_type type);
1281 isl_size isl_union_pw_aff_dim(
1282 __isl_keep isl_union_pw_aff *upa,
1283 enum isl_dim_type type);
1284 isl_size isl_union_pw_multi_aff_dim(
1285 __isl_keep isl_union_pw_multi_aff *upma,
1286 enum isl_dim_type type);
1287 isl_size isl_multi_union_pw_aff_dim(
1288 __isl_keep isl_multi_union_pw_aff *mupa,
1289 enum isl_dim_type type);
1291 #include <isl/polynomial.h>
1292 isl_size isl_union_pw_qpolynomial_dim(
1293 __isl_keep isl_union_pw_qpolynomial *upwqp,
1294 enum isl_dim_type type);
1295 isl_size isl_union_pw_qpolynomial_fold_dim(
1296 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1297 enum isl_dim_type type);
1299 Note that an C<isl_union_set>, an C<isl_union_map>,
1300 an C<isl_union_pw_multi_aff>,
1301 an C<isl_union_pw_qpolynomial> and
1302 an C<isl_union_pw_qpolynomial_fold>
1303 only have parameters.
1305 Additional parameters can be added to a space using the following function.
1307 #include <isl/space.h>
1308 __isl_give isl_space *isl_space_add_param_id(
1309 __isl_take isl_space *space,
1310 __isl_take isl_id *id);
1312 If a parameter with the given identifier already appears in the space,
1313 then it is not added again.
1315 Conversely, all parameters can be removed from a space
1316 using the following function.
1318 #include <isl/space.h>
1319 __isl_give isl_space *isl_space_drop_all_params(
1320 __isl_take isl_space *space);
1322 The identifiers or names of the individual dimensions of spaces
1323 may be set or read off using the following functions on spaces
1324 or objects that live in spaces.
1325 These functions are mostly useful to obtain the identifiers, positions
1326 or names of the parameters. Identifiers of individual dimensions are
1327 essentially only useful for printing. They are ignored by all other
1328 operations and may not be preserved across those operations.
1329 To keep track of a space along with names/identifiers of
1330 the set dimensions, use an C<isl_multi_id> as described in
1333 #include <isl/space.h>
1334 __isl_give isl_space *isl_space_set_dim_id(
1335 __isl_take isl_space *space,
1336 enum isl_dim_type type, unsigned pos,
1337 __isl_take isl_id *id);
1338 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_id *isl_space_get_dim_id(
1341 __isl_keep isl_space *space,
1342 enum isl_dim_type type, unsigned pos);
1343 __isl_give isl_space *isl_space_set_dim_name(
1344 __isl_take isl_space *space,
1345 enum isl_dim_type type, unsigned pos,
1346 __isl_keep const char *name);
1347 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1348 enum isl_dim_type type, unsigned pos);
1349 __isl_keep const char *isl_space_get_dim_name(
1350 __isl_keep isl_space *space,
1351 enum isl_dim_type type, unsigned pos);
1353 #include <isl/local_space.h>
1354 __isl_give isl_local_space *isl_local_space_set_dim_id(
1355 __isl_take isl_local_space *ls,
1356 enum isl_dim_type type, unsigned pos,
1357 __isl_take isl_id *id);
1358 isl_bool isl_local_space_has_dim_id(
1359 __isl_keep isl_local_space *ls,
1360 enum isl_dim_type type, unsigned pos);
1361 __isl_give isl_id *isl_local_space_get_dim_id(
1362 __isl_keep isl_local_space *ls,
1363 enum isl_dim_type type, unsigned pos);
1364 __isl_give isl_local_space *isl_local_space_set_dim_name(
1365 __isl_take isl_local_space *ls,
1366 enum isl_dim_type type, unsigned pos, const char *s);
1367 isl_bool isl_local_space_has_dim_name(
1368 __isl_keep isl_local_space *ls,
1369 enum isl_dim_type type, unsigned pos)
1370 const char *isl_local_space_get_dim_name(
1371 __isl_keep isl_local_space *ls,
1372 enum isl_dim_type type, unsigned pos);
1374 #include <isl/constraint.h>
1375 const char *isl_constraint_get_dim_name(
1376 __isl_keep isl_constraint *constraint,
1377 enum isl_dim_type type, unsigned pos);
1379 #include <isl/set.h>
1380 __isl_give isl_id *isl_basic_set_get_dim_id(
1381 __isl_keep isl_basic_set *bset,
1382 enum isl_dim_type type, unsigned pos);
1383 __isl_give isl_set *isl_set_set_dim_id(
1384 __isl_take isl_set *set, enum isl_dim_type type,
1385 unsigned pos, __isl_take isl_id *id);
1386 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1387 enum isl_dim_type type, unsigned pos);
1388 __isl_give isl_id *isl_set_get_dim_id(
1389 __isl_keep isl_set *set, enum isl_dim_type type,
1391 const char *isl_basic_set_get_dim_name(
1392 __isl_keep isl_basic_set *bset,
1393 enum isl_dim_type type, unsigned pos);
1394 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1395 enum isl_dim_type type, unsigned pos);
1396 const char *isl_set_get_dim_name(
1397 __isl_keep isl_set *set,
1398 enum isl_dim_type type, unsigned pos);
1400 #include <isl/map.h>
1401 __isl_give isl_map *isl_map_set_dim_id(
1402 __isl_take isl_map *map, enum isl_dim_type type,
1403 unsigned pos, __isl_take isl_id *id);
1404 isl_bool isl_basic_map_has_dim_id(
1405 __isl_keep isl_basic_map *bmap,
1406 enum isl_dim_type type, unsigned pos);
1407 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1408 enum isl_dim_type type, unsigned pos);
1409 __isl_give isl_id *isl_map_get_dim_id(
1410 __isl_keep isl_map *map, enum isl_dim_type type,
1412 __isl_give isl_id *isl_union_map_get_dim_id(
1413 __isl_keep isl_union_map *umap,
1414 enum isl_dim_type type, unsigned pos);
1415 const char *isl_basic_map_get_dim_name(
1416 __isl_keep isl_basic_map *bmap,
1417 enum isl_dim_type type, unsigned pos);
1418 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1419 enum isl_dim_type type, unsigned pos);
1420 const char *isl_map_get_dim_name(
1421 __isl_keep isl_map *map,
1422 enum isl_dim_type type, unsigned pos);
1424 #include <isl/val.h>
1425 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1426 __isl_take isl_multi_val *mv,
1427 enum isl_dim_type type, unsigned pos,
1428 __isl_take isl_id *id);
1429 __isl_give isl_id *isl_multi_val_get_dim_id(
1430 __isl_keep isl_multi_val *mv,
1431 enum isl_dim_type type, unsigned pos);
1432 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1433 __isl_take isl_multi_val *mv,
1434 enum isl_dim_type type, unsigned pos, const char *s);
1436 #include <isl/aff.h>
1437 __isl_give isl_aff *isl_aff_set_dim_id(
1438 __isl_take isl_aff *aff, enum isl_dim_type type,
1439 unsigned pos, __isl_take isl_id *id);
1440 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1441 __isl_take isl_multi_aff *maff,
1442 enum isl_dim_type type, unsigned pos,
1443 __isl_take isl_id *id);
1444 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1445 __isl_take isl_pw_aff *pma,
1446 enum isl_dim_type type, unsigned pos,
1447 __isl_take isl_id *id);
1448 __isl_give isl_multi_pw_aff *
1449 isl_multi_pw_aff_set_dim_id(
1450 __isl_take isl_multi_pw_aff *mpa,
1451 enum isl_dim_type type, unsigned pos,
1452 __isl_take isl_id *id);
1453 __isl_give isl_multi_union_pw_aff *
1454 isl_multi_union_pw_aff_set_dim_id(
1455 __isl_take isl_multi_union_pw_aff *mupa,
1456 enum isl_dim_type type, unsigned pos,
1457 __isl_take isl_id *id);
1458 __isl_give isl_id *isl_multi_aff_get_dim_id(
1459 __isl_keep isl_multi_aff *ma,
1460 enum isl_dim_type type, unsigned pos);
1461 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1462 enum isl_dim_type type, unsigned pos);
1463 __isl_give isl_id *isl_pw_aff_get_dim_id(
1464 __isl_keep isl_pw_aff *pa,
1465 enum isl_dim_type type, unsigned pos);
1466 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1467 __isl_keep isl_pw_multi_aff *pma,
1468 enum isl_dim_type type, unsigned pos);
1469 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1470 __isl_keep isl_multi_pw_aff *mpa,
1471 enum isl_dim_type type, unsigned pos);
1472 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1473 __isl_keep isl_multi_union_pw_aff *mupa,
1474 enum isl_dim_type type, unsigned pos);
1475 __isl_give isl_aff *isl_aff_set_dim_name(
1476 __isl_take isl_aff *aff, enum isl_dim_type type,
1477 unsigned pos, const char *s);
1478 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1479 __isl_take isl_multi_aff *maff,
1480 enum isl_dim_type type, unsigned pos, const char *s);
1481 __isl_give isl_multi_pw_aff *
1482 isl_multi_pw_aff_set_dim_name(
1483 __isl_take isl_multi_pw_aff *mpa,
1484 enum isl_dim_type type, unsigned pos, const char *s);
1485 __isl_give isl_union_pw_aff *
1486 isl_union_pw_aff_set_dim_name(
1487 __isl_take isl_union_pw_aff *upa,
1488 enum isl_dim_type type, unsigned pos,
1490 __isl_give isl_union_pw_multi_aff *
1491 isl_union_pw_multi_aff_set_dim_name(
1492 __isl_take isl_union_pw_multi_aff *upma,
1493 enum isl_dim_type type, unsigned pos,
1495 __isl_give isl_multi_union_pw_aff *
1496 isl_multi_union_pw_aff_set_dim_name(
1497 __isl_take isl_multi_union_pw_aff *mupa,
1498 enum isl_dim_type type, unsigned pos,
1500 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1501 enum isl_dim_type type, unsigned pos);
1502 const char *isl_pw_aff_get_dim_name(
1503 __isl_keep isl_pw_aff *pa,
1504 enum isl_dim_type type, unsigned pos);
1505 const char *isl_pw_multi_aff_get_dim_name(
1506 __isl_keep isl_pw_multi_aff *pma,
1507 enum isl_dim_type type, unsigned pos);
1509 #include <isl/polynomial.h>
1510 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1511 __isl_take isl_qpolynomial *qp,
1512 enum isl_dim_type type, unsigned pos,
1514 __isl_give isl_pw_qpolynomial *
1515 isl_pw_qpolynomial_set_dim_name(
1516 __isl_take isl_pw_qpolynomial *pwqp,
1517 enum isl_dim_type type, unsigned pos,
1519 __isl_give isl_pw_qpolynomial_fold *
1520 isl_pw_qpolynomial_fold_set_dim_name(
1521 __isl_take isl_pw_qpolynomial_fold *pwf,
1522 enum isl_dim_type type, unsigned pos,
1524 __isl_give isl_union_pw_qpolynomial *
1525 isl_union_pw_qpolynomial_set_dim_name(
1526 __isl_take isl_union_pw_qpolynomial *upwqp,
1527 enum isl_dim_type type, unsigned pos,
1529 __isl_give isl_union_pw_qpolynomial_fold *
1530 isl_union_pw_qpolynomial_fold_set_dim_name(
1531 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1532 enum isl_dim_type type, unsigned pos,
1535 Note that C<isl_space_get_name> returns a pointer to some internal
1536 data structure, so the result can only be used while the
1537 corresponding C<isl_space> is alive.
1538 Also note that every function that operates on two sets or relations
1539 requires that both arguments have the same parameters. This also
1540 means that if one of the arguments has named parameters, then the
1541 other needs to have named parameters too and the names need to match.
1542 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1543 arguments may have different parameters (as long as they are named),
1544 in which case the result will have as parameters the union of the parameters of
1547 Given the identifier or name of a dimension (typically a parameter),
1548 its position can be obtained from the following functions.
1550 #include <isl/space.h>
1551 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1552 enum isl_dim_type type, __isl_keep isl_id *id);
1553 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1554 enum isl_dim_type type, const char *name);
1556 #include <isl/local_space.h>
1557 int isl_local_space_find_dim_by_name(
1558 __isl_keep isl_local_space *ls,
1559 enum isl_dim_type type, const char *name);
1561 #include <isl/val.h>
1562 int isl_multi_val_find_dim_by_id(
1563 __isl_keep isl_multi_val *mv,
1564 enum isl_dim_type type, __isl_keep isl_id *id);
1565 int isl_multi_val_find_dim_by_name(
1566 __isl_keep isl_multi_val *mv,
1567 enum isl_dim_type type, const char *name);
1569 #include <isl/set.h>
1570 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1571 enum isl_dim_type type, __isl_keep isl_id *id);
1572 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1573 enum isl_dim_type type, const char *name);
1575 #include <isl/map.h>
1576 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1577 enum isl_dim_type type, __isl_keep isl_id *id);
1578 int isl_basic_map_find_dim_by_name(
1579 __isl_keep isl_basic_map *bmap,
1580 enum isl_dim_type type, const char *name);
1581 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1582 enum isl_dim_type type, const char *name);
1583 int isl_union_map_find_dim_by_name(
1584 __isl_keep isl_union_map *umap,
1585 enum isl_dim_type type, const char *name);
1587 #include <isl/aff.h>
1588 int isl_multi_aff_find_dim_by_id(
1589 __isl_keep isl_multi_aff *ma,
1590 enum isl_dim_type type, __isl_keep isl_id *id);
1591 int isl_multi_pw_aff_find_dim_by_id(
1592 __isl_keep isl_multi_pw_aff *mpa,
1593 enum isl_dim_type type, __isl_keep isl_id *id);
1594 int isl_multi_union_pw_aff_find_dim_by_id(
1595 __isl_keep isl_multi_union_pw_aff *mupa,
1596 enum isl_dim_type type, __isl_keep isl_id *id);
1597 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1598 enum isl_dim_type type, const char *name);
1599 int isl_multi_aff_find_dim_by_name(
1600 __isl_keep isl_multi_aff *ma,
1601 enum isl_dim_type type, const char *name);
1602 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1603 enum isl_dim_type type, const char *name);
1604 int isl_multi_pw_aff_find_dim_by_name(
1605 __isl_keep isl_multi_pw_aff *mpa,
1606 enum isl_dim_type type, const char *name);
1607 int isl_pw_multi_aff_find_dim_by_name(
1608 __isl_keep isl_pw_multi_aff *pma,
1609 enum isl_dim_type type, const char *name);
1610 int isl_union_pw_aff_find_dim_by_name(
1611 __isl_keep isl_union_pw_aff *upa,
1612 enum isl_dim_type type, const char *name);
1613 int isl_union_pw_multi_aff_find_dim_by_name(
1614 __isl_keep isl_union_pw_multi_aff *upma,
1615 enum isl_dim_type type, const char *name);
1616 int isl_multi_union_pw_aff_find_dim_by_name(
1617 __isl_keep isl_multi_union_pw_aff *mupa,
1618 enum isl_dim_type type, const char *name);
1620 #include <isl/polynomial.h>
1621 int isl_pw_qpolynomial_find_dim_by_name(
1622 __isl_keep isl_pw_qpolynomial *pwqp,
1623 enum isl_dim_type type, const char *name);
1624 int isl_pw_qpolynomial_fold_find_dim_by_name(
1625 __isl_keep isl_pw_qpolynomial_fold *pwf,
1626 enum isl_dim_type type, const char *name);
1627 int isl_union_pw_qpolynomial_find_dim_by_name(
1628 __isl_keep isl_union_pw_qpolynomial *upwqp,
1629 enum isl_dim_type type, const char *name);
1630 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1631 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1632 enum isl_dim_type type, const char *name);
1634 The identifiers or names of entire spaces may be set or read off
1635 using the following functions.
1637 #include <isl/space.h>
1638 __isl_give isl_space *isl_space_set_domain_tuple_id(
1639 __isl_take isl_space *space,
1640 __isl_take isl_id *id);
1641 __isl_give isl_space *isl_space_set_range_tuple_id(
1642 __isl_take isl_space *space,
1643 __isl_take isl_id *id);
1644 __isl_give isl_space *isl_space_set_tuple_id(
1645 __isl_take isl_space *space,
1646 enum isl_dim_type type, __isl_take isl_id *id);
1647 __isl_give isl_space *isl_space_reset_tuple_id(
1648 __isl_take isl_space *space, enum isl_dim_type type);
1649 isl_bool isl_space_has_domain_tuple_id(
1650 __isl_keep isl_space *space);
1651 isl_bool isl_space_has_range_tuple_id(
1652 __isl_keep isl_space *space);
1653 isl_bool isl_space_has_tuple_id(
1654 __isl_keep isl_space *space,
1655 enum isl_dim_type type);
1656 __isl_give isl_id *isl_space_get_domain_tuple_id(
1657 __isl_keep isl_space *space);
1658 __isl_give isl_id *isl_space_get_range_tuple_id(
1659 __isl_keep isl_space *space);
1660 __isl_give isl_id *isl_space_get_tuple_id(
1661 __isl_keep isl_space *space, enum isl_dim_type type);
1662 __isl_give isl_space *isl_space_set_tuple_name(
1663 __isl_take isl_space *space,
1664 enum isl_dim_type type, const char *s);
1665 isl_bool isl_space_has_tuple_name(
1666 __isl_keep isl_space *space,
1667 enum isl_dim_type type);
1668 __isl_keep const char *isl_space_get_tuple_name(
1669 __isl_keep isl_space *space,
1670 enum isl_dim_type type);
1672 #include <isl/local_space.h>
1673 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1674 __isl_take isl_local_space *ls,
1675 enum isl_dim_type type, __isl_take isl_id *id);
1677 #include <isl/set.h>
1678 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1679 __isl_take isl_basic_set *bset,
1680 __isl_take isl_id *id);
1681 __isl_give isl_set *isl_set_set_tuple_id(
1682 __isl_take isl_set *set, __isl_take isl_id *id);
1683 __isl_give isl_set *isl_set_reset_tuple_id(
1684 __isl_take isl_set *set);
1685 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1686 __isl_give isl_id *isl_set_get_tuple_id(
1687 __isl_keep isl_set *set);
1688 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1689 __isl_take isl_basic_set *set, const char *s);
1690 __isl_give isl_set *isl_set_set_tuple_name(
1691 __isl_take isl_set *set, const char *s);
1692 const char *isl_basic_set_get_tuple_name(
1693 __isl_keep isl_basic_set *bset);
1694 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1695 const char *isl_set_get_tuple_name(
1696 __isl_keep isl_set *set);
1698 #include <isl/map.h>
1699 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1700 __isl_take isl_basic_map *bmap,
1701 enum isl_dim_type type, __isl_take isl_id *id);
1702 __isl_give isl_map *isl_map_set_domain_tuple_id(
1703 __isl_take isl_map *map, __isl_take isl_id *id);
1704 __isl_give isl_map *isl_map_set_range_tuple_id(
1705 __isl_take isl_map *map, __isl_take isl_id *id);
1706 __isl_give isl_map *isl_map_set_tuple_id(
1707 __isl_take isl_map *map, enum isl_dim_type type,
1708 __isl_take isl_id *id);
1709 __isl_give isl_map *isl_map_reset_tuple_id(
1710 __isl_take isl_map *map, enum isl_dim_type type);
1711 isl_bool isl_map_has_domain_tuple_id(
1712 __isl_keep isl_map *map);
1713 isl_bool isl_map_has_range_tuple_id(
1714 __isl_keep isl_map *map);
1715 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1716 enum isl_dim_type type);
1717 __isl_give isl_id *isl_map_get_domain_tuple_id(
1718 __isl_keep isl_map *map);
1719 __isl_give isl_id *isl_map_get_range_tuple_id(
1720 __isl_keep isl_map *map);
1721 __isl_give isl_id *isl_map_get_tuple_id(
1722 __isl_keep isl_map *map, enum isl_dim_type type);
1723 __isl_give isl_map *isl_map_set_tuple_name(
1724 __isl_take isl_map *map,
1725 enum isl_dim_type type, const char *s);
1726 const char *isl_basic_map_get_tuple_name(
1727 __isl_keep isl_basic_map *bmap,
1728 enum isl_dim_type type);
1729 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1730 __isl_take isl_basic_map *bmap,
1731 enum isl_dim_type type, const char *s);
1732 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1733 enum isl_dim_type type);
1734 const char *isl_map_get_tuple_name(
1735 __isl_keep isl_map *map,
1736 enum isl_dim_type type);
1738 #include <isl/val.h>
1739 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1740 __isl_take isl_multi_val *mv,
1741 __isl_take isl_id *id);
1742 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1743 __isl_take isl_multi_val *mv,
1744 enum isl_dim_type type, __isl_take isl_id *id);
1745 __isl_give isl_multi_val *
1746 isl_multi_val_reset_range_tuple_id(
1747 __isl_take isl_multi_val *mv);
1748 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1749 __isl_take isl_multi_val *mv,
1750 enum isl_dim_type type);
1751 isl_bool isl_multi_val_has_range_tuple_id(
1752 __isl_keep isl_multi_val *mv);
1753 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1754 __isl_keep isl_multi_val *mv);
1755 isl_bool isl_multi_val_has_tuple_id(
1756 __isl_keep isl_multi_val *mv,
1757 enum isl_dim_type type);
1758 __isl_give isl_id *isl_multi_val_get_tuple_id(
1759 __isl_keep isl_multi_val *mv,
1760 enum isl_dim_type type);
1761 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1762 __isl_take isl_multi_val *mv,
1763 enum isl_dim_type type, const char *s);
1764 const char *isl_multi_val_get_tuple_name(
1765 __isl_keep isl_multi_val *mv,
1766 enum isl_dim_type type);
1768 #include <isl/aff.h>
1769 __isl_give isl_aff *isl_aff_set_tuple_id(
1770 __isl_take isl_aff *aff,
1771 enum isl_dim_type type, __isl_take isl_id *id);
1772 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1773 __isl_take isl_multi_aff *ma,
1774 __isl_take isl_id *id);
1775 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1776 __isl_take isl_multi_aff *maff,
1777 enum isl_dim_type type, __isl_take isl_id *id);
1778 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1779 __isl_take isl_pw_aff *pwaff,
1780 enum isl_dim_type type, __isl_take isl_id *id);
1781 __isl_give isl_pw_multi_aff *
1782 isl_pw_multi_aff_set_range_tuple_id(
1783 __isl_take isl_pw_multi_aff *pma,
1784 __isl_take isl_id *id);
1785 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1786 __isl_take isl_pw_multi_aff *pma,
1787 enum isl_dim_type type, __isl_take isl_id *id);
1788 __isl_give isl_multi_pw_aff *
1789 isl_multi_pw_aff_set_range_tuple_id(
1790 __isl_take isl_multi_pw_aff *mpa,
1791 __isl_take isl_id *id);
1792 __isl_give isl_multi_union_pw_aff *
1793 isl_multi_union_pw_aff_set_range_tuple_id(
1794 __isl_take isl_multi_union_pw_aff *mupa,
1795 __isl_take isl_id *id);
1796 __isl_give isl_multi_union_pw_aff *
1797 isl_multi_union_pw_aff_set_tuple_id(
1798 __isl_take isl_multi_union_pw_aff *mupa,
1799 enum isl_dim_type type, __isl_take isl_id *id);
1800 __isl_give isl_multi_aff *
1801 isl_multi_aff_reset_range_tuple_id(
1802 __isl_take isl_multi_aff *ma);
1803 __isl_give isl_multi_pw_aff *
1804 isl_multi_pw_aff_reset_range_tuple_id(
1805 __isl_take isl_multi_pw_aff *mpa);
1806 __isl_give isl_multi_union_pw_aff *
1807 isl_multi_union_pw_aff_reset_range_tuple_id(
1808 __isl_take isl_multi_union_pw_aff *mupa);
1809 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1810 __isl_take isl_multi_aff *ma,
1811 enum isl_dim_type type);
1812 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1813 __isl_take isl_pw_aff *pa,
1814 enum isl_dim_type type);
1815 __isl_give isl_multi_pw_aff *
1816 isl_multi_pw_aff_reset_tuple_id(
1817 __isl_take isl_multi_pw_aff *mpa,
1818 enum isl_dim_type type);
1819 __isl_give isl_pw_multi_aff *
1820 isl_pw_multi_aff_reset_tuple_id(
1821 __isl_take isl_pw_multi_aff *pma,
1822 enum isl_dim_type type);
1823 __isl_give isl_multi_union_pw_aff *
1824 isl_multi_union_pw_aff_reset_tuple_id(
1825 __isl_take isl_multi_union_pw_aff *mupa,
1826 enum isl_dim_type type);
1827 isl_bool isl_multi_aff_has_range_tuple_id(
1828 __isl_keep isl_multi_aff *ma);
1829 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1830 __isl_keep isl_multi_aff *ma);
1831 isl_bool isl_multi_aff_has_tuple_id(
1832 __isl_keep isl_multi_aff *ma,
1833 enum isl_dim_type type);
1834 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1835 __isl_keep isl_multi_aff *ma,
1836 enum isl_dim_type type);
1837 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1838 enum isl_dim_type type);
1839 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1840 __isl_keep isl_pw_aff *pa,
1841 enum isl_dim_type type);
1842 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1843 __isl_keep isl_pw_multi_aff *pma);
1844 isl_bool isl_pw_multi_aff_has_tuple_id(
1845 __isl_keep isl_pw_multi_aff *pma,
1846 enum isl_dim_type type);
1847 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1848 __isl_keep isl_pw_multi_aff *pma);
1849 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1850 __isl_keep isl_pw_multi_aff *pma,
1851 enum isl_dim_type type);
1852 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1853 __isl_keep isl_multi_pw_aff *mpa);
1854 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1855 __isl_keep isl_multi_pw_aff *mpa);
1856 isl_bool isl_multi_pw_aff_has_tuple_id(
1857 __isl_keep isl_multi_pw_aff *mpa,
1858 enum isl_dim_type type);
1859 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1860 __isl_keep isl_multi_pw_aff *mpa,
1861 enum isl_dim_type type);
1862 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1863 __isl_keep isl_multi_union_pw_aff *mupa);
1865 isl_multi_union_pw_aff_get_range_tuple_id(
1866 __isl_keep isl_multi_union_pw_aff *mupa);
1867 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1868 __isl_keep isl_multi_union_pw_aff *mupa,
1869 enum isl_dim_type type);
1870 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1871 __isl_keep isl_multi_union_pw_aff *mupa,
1872 enum isl_dim_type type);
1873 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1874 __isl_take isl_multi_aff *maff,
1875 enum isl_dim_type type, const char *s);
1876 __isl_give isl_multi_pw_aff *
1877 isl_multi_pw_aff_set_tuple_name(
1878 __isl_take isl_multi_pw_aff *mpa,
1879 enum isl_dim_type type, const char *s);
1880 __isl_give isl_multi_union_pw_aff *
1881 isl_multi_union_pw_aff_set_tuple_name(
1882 __isl_take isl_multi_union_pw_aff *mupa,
1883 enum isl_dim_type type, const char *s);
1884 const char *isl_multi_aff_get_tuple_name(
1885 __isl_keep isl_multi_aff *multi,
1886 enum isl_dim_type type);
1887 isl_bool isl_pw_multi_aff_has_tuple_name(
1888 __isl_keep isl_pw_multi_aff *pma,
1889 enum isl_dim_type type);
1890 const char *isl_pw_multi_aff_get_tuple_name(
1891 __isl_keep isl_pw_multi_aff *pma,
1892 enum isl_dim_type type);
1893 const char *isl_multi_union_pw_aff_get_tuple_name(
1894 __isl_keep isl_multi_union_pw_aff *mupa,
1895 enum isl_dim_type type);
1897 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1898 or C<isl_dim_set>. As with C<isl_space_get_name>,
1899 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1901 Binary operations require the corresponding spaces of their arguments
1902 to have the same name.
1904 To keep the names of all parameters and tuples, but reset the user pointers
1905 of all the corresponding identifiers, use the following function.
1907 #include <isl/space.h>
1908 __isl_give isl_space *isl_space_reset_user(
1909 __isl_take isl_space *space);
1911 #include <isl/set.h>
1912 __isl_give isl_set *isl_set_reset_user(
1913 __isl_take isl_set *set);
1915 #include <isl/map.h>
1916 __isl_give isl_map *isl_map_reset_user(
1917 __isl_take isl_map *map);
1919 #include <isl/union_set.h>
1920 __isl_give isl_union_set *isl_union_set_reset_user(
1921 __isl_take isl_union_set *uset);
1923 #include <isl/union_map.h>
1924 __isl_give isl_union_map *isl_union_map_reset_user(
1925 __isl_take isl_union_map *umap);
1928 __isl_give isl_multi_id *isl_multi_id_reset_user(
1929 __isl_take isl_multi_id *mi);
1931 #include <isl/val.h>
1932 __isl_give isl_multi_val *isl_multi_val_reset_user(
1933 __isl_take isl_multi_val *mv);
1935 #include <isl/aff.h>
1936 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1937 __isl_take isl_multi_aff *ma);
1938 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1939 __isl_take isl_pw_aff *pa);
1940 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1941 __isl_take isl_multi_pw_aff *mpa);
1942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1943 __isl_take isl_pw_multi_aff *pma);
1944 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1945 __isl_take isl_union_pw_aff *upa);
1946 __isl_give isl_multi_union_pw_aff *
1947 isl_multi_union_pw_aff_reset_user(
1948 __isl_take isl_multi_union_pw_aff *mupa);
1949 __isl_give isl_union_pw_multi_aff *
1950 isl_union_pw_multi_aff_reset_user(
1951 __isl_take isl_union_pw_multi_aff *upma);
1953 #include <isl/polynomial.h>
1954 __isl_give isl_pw_qpolynomial *
1955 isl_pw_qpolynomial_reset_user(
1956 __isl_take isl_pw_qpolynomial *pwqp);
1957 __isl_give isl_union_pw_qpolynomial *
1958 isl_union_pw_qpolynomial_reset_user(
1959 __isl_take isl_union_pw_qpolynomial *upwqp);
1960 __isl_give isl_pw_qpolynomial_fold *
1961 isl_pw_qpolynomial_fold_reset_user(
1962 __isl_take isl_pw_qpolynomial_fold *pwf);
1963 __isl_give isl_union_pw_qpolynomial_fold *
1964 isl_union_pw_qpolynomial_fold_reset_user(
1965 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1967 Spaces can be nested. In particular, the domain of a set or
1968 the domain or range of a relation can be a nested relation.
1969 This process is also called I<wrapping>.
1970 The functions for detecting, constructing and deconstructing
1971 such nested spaces can be found in the wrapping properties
1972 of L</"Unary Properties">, the wrapping operations
1973 of L</"Unary Operations"> and the Cartesian product operations
1974 of L</"Basic Operations">.
1976 Spaces can be created from other spaces
1977 using the functions described in L</"Unary Operations">
1978 and L</"Binary Operations">.
1982 A local space is essentially a space with
1983 zero or more existentially quantified variables.
1984 The local space of various objects can be obtained
1985 using the following functions.
1987 #include <isl/constraint.h>
1988 __isl_give isl_local_space *isl_constraint_get_local_space(
1989 __isl_keep isl_constraint *constraint);
1991 #include <isl/set.h>
1992 __isl_give isl_local_space *isl_basic_set_get_local_space(
1993 __isl_keep isl_basic_set *bset);
1995 #include <isl/map.h>
1996 __isl_give isl_local_space *isl_basic_map_get_local_space(
1997 __isl_keep isl_basic_map *bmap);
1999 #include <isl/aff.h>
2000 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2001 __isl_keep isl_aff *aff);
2002 __isl_give isl_local_space *isl_aff_get_local_space(
2003 __isl_keep isl_aff *aff);
2005 A new local space can be created from a space using
2007 #include <isl/local_space.h>
2008 __isl_give isl_local_space *isl_local_space_from_space(
2009 __isl_take isl_space *space);
2011 They can be inspected, modified, copied and freed using the following functions.
2013 #include <isl/local_space.h>
2014 isl_bool isl_local_space_is_params(
2015 __isl_keep isl_local_space *ls);
2016 isl_bool isl_local_space_is_set(
2017 __isl_keep isl_local_space *ls);
2018 __isl_give isl_space *isl_local_space_get_space(
2019 __isl_keep isl_local_space *ls);
2020 __isl_give isl_aff *isl_local_space_get_div(
2021 __isl_keep isl_local_space *ls, int pos);
2022 __isl_give isl_local_space *isl_local_space_copy(
2023 __isl_keep isl_local_space *ls);
2024 __isl_null isl_local_space *isl_local_space_free(
2025 __isl_take isl_local_space *ls);
2027 Note that C<isl_local_space_get_div> can only be used on local spaces
2030 Two local spaces can be compared using
2032 isl_bool isl_local_space_is_equal(
2033 __isl_keep isl_local_space *ls1,
2034 __isl_keep isl_local_space *ls2);
2036 Local spaces can be created from other local spaces
2037 using the functions described in L</"Unary Operations">
2038 and L</"Binary Operations">.
2040 =head2 Creating New Sets and Relations
2042 C<isl> has functions for creating some standard sets and relations.
2046 =item * Empty sets and relations
2048 __isl_give isl_basic_set *isl_basic_set_empty(
2049 __isl_take isl_space *space);
2050 __isl_give isl_basic_map *isl_basic_map_empty(
2051 __isl_take isl_space *space);
2052 __isl_give isl_set *isl_set_empty(
2053 __isl_take isl_space *space);
2054 __isl_give isl_map *isl_map_empty(
2055 __isl_take isl_space *space);
2056 __isl_give isl_union_set *isl_union_set_empty_ctx(
2058 __isl_give isl_union_set *isl_union_set_empty_space(
2059 __isl_take isl_space *space);
2060 __isl_give isl_union_set *isl_union_set_empty(
2061 __isl_take isl_space *space);
2062 __isl_give isl_union_map *isl_union_map_empty_ctx(
2064 __isl_give isl_union_map *isl_union_map_empty_space(
2065 __isl_take isl_space *space);
2066 __isl_give isl_union_map *isl_union_map_empty(
2067 __isl_take isl_space *space);
2069 For C<isl_union_set>s and C<isl_union_map>s, the space
2070 is only used to specify the parameters.
2071 C<isl_union_set_empty> is an alternative name for
2072 C<isl_union_set_empty_space>.
2073 Similarly for the other pair of functions.
2075 =item * Universe sets and relations
2077 #include <isl/set.h>
2078 __isl_give isl_basic_set *isl_basic_set_universe(
2079 __isl_take isl_space *space);
2080 __isl_give isl_set *isl_set_universe(
2081 __isl_take isl_space *space);
2082 __isl_give isl_set *isl_space_universe_set(
2083 __isl_take isl_space *space);
2085 #include <isl/map.h>
2086 __isl_give isl_basic_map *isl_basic_map_universe(
2087 __isl_take isl_space *space);
2088 __isl_give isl_map *isl_map_universe(
2089 __isl_take isl_space *space);
2090 __isl_give isl_map *isl_space_universe_map(
2091 __isl_take isl_space *space);
2093 #include <isl/union_set.h>
2094 __isl_give isl_union_set *isl_union_set_universe(
2095 __isl_take isl_union_set *uset);
2097 #include <isl/union_map.h>
2098 __isl_give isl_union_map *isl_union_map_universe(
2099 __isl_take isl_union_map *umap);
2101 C<isl_set_universe> and C<isl_space_universe_set>
2102 perform the same operation.
2104 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2106 The sets and relations constructed by the functions above
2107 contain all integer values, while those constructed by the
2108 functions below only contain non-negative values.
2110 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2111 __isl_take isl_space *space);
2112 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2113 __isl_take isl_space *space);
2114 __isl_give isl_set *isl_set_nat_universe(
2115 __isl_take isl_space *space);
2116 __isl_give isl_map *isl_map_nat_universe(
2117 __isl_take isl_space *space);
2119 =item * Identity relations
2121 __isl_give isl_basic_map *isl_basic_map_identity(
2122 __isl_take isl_space *space);
2123 __isl_give isl_map *isl_map_identity(
2124 __isl_take isl_space *space);
2126 The number of input and output dimensions in C<space> needs
2129 =item * Lexicographic order
2131 __isl_give isl_map *isl_map_lex_lt(
2132 __isl_take isl_space *set_space);
2133 __isl_give isl_map *isl_map_lex_le(
2134 __isl_take isl_space *set_space);
2135 __isl_give isl_map *isl_map_lex_gt(
2136 __isl_take isl_space *set_space);
2137 __isl_give isl_map *isl_map_lex_ge(
2138 __isl_take isl_space *set_space);
2139 __isl_give isl_map *isl_map_lex_lt_first(
2140 __isl_take isl_space *space, unsigned n);
2141 __isl_give isl_map *isl_map_lex_le_first(
2142 __isl_take isl_space *space, unsigned n);
2143 __isl_give isl_map *isl_map_lex_gt_first(
2144 __isl_take isl_space *space, unsigned n);
2145 __isl_give isl_map *isl_map_lex_ge_first(
2146 __isl_take isl_space *space, unsigned n);
2148 The first four functions take a space for a B<set>
2149 and return relations that express that the elements in the domain
2150 are lexicographically less
2151 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2152 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2153 than the elements in the range.
2154 The last four functions take a space for a map
2155 and return relations that express that the first C<n> dimensions
2156 in the domain are lexicographically less
2157 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2158 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2159 than the first C<n> dimensions in the range.
2163 A basic set or relation can be converted to a set or relation
2164 using the following functions.
2166 __isl_give isl_set *isl_basic_set_to_set(
2167 __isl_take isl_basic_set *bset);
2168 __isl_give isl_set *isl_set_from_basic_set(
2169 __isl_take isl_basic_set *bset);
2170 __isl_give isl_map *isl_map_from_basic_map(
2171 __isl_take isl_basic_map *bmap);
2173 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2176 Sets and relations can be converted to union sets and relations
2177 using the following functions.
2179 __isl_give isl_union_set *isl_union_set_from_basic_set(
2180 __isl_take isl_basic_set *bset);
2181 __isl_give isl_union_map *isl_union_map_from_basic_map(
2182 __isl_take isl_basic_map *bmap);
2183 __isl_give isl_union_set *isl_set_to_union_set(
2184 __isl_take isl_set *set);
2185 __isl_give isl_union_set *isl_union_set_from_set(
2186 __isl_take isl_set *set);
2187 __isl_give isl_union_map *isl_map_to_union_map(
2188 __isl_take isl_map *map);
2189 __isl_give isl_union_map *isl_union_map_from_map(
2190 __isl_take isl_map *map);
2192 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2194 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2196 The inverse conversions below can only be used if the input
2197 union set or relation is known to contain elements in exactly one
2200 #include <isl/union_set.h>
2201 isl_bool isl_union_set_isa_set(
2202 __isl_keep isl_union_set *uset);
2203 __isl_give isl_set *isl_union_set_as_set(
2204 __isl_take isl_union_set *uset);
2205 __isl_give isl_set *isl_set_from_union_set(
2206 __isl_take isl_union_set *uset);
2208 #include <isl/union_map.h>
2209 isl_bool isl_union_map_isa_map(
2210 __isl_keep isl_union_map *umap);
2211 __isl_give isl_map *isl_union_map_as_map(
2212 __isl_take isl_union_map *umap);
2213 __isl_give isl_map *isl_map_from_union_map(
2214 __isl_take isl_union_map *umap);
2216 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2218 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2220 Sets and relations can be copied and freed again using the following
2223 __isl_give isl_basic_set *isl_basic_set_copy(
2224 __isl_keep isl_basic_set *bset);
2225 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2226 __isl_give isl_union_set *isl_union_set_copy(
2227 __isl_keep isl_union_set *uset);
2228 __isl_give isl_basic_map *isl_basic_map_copy(
2229 __isl_keep isl_basic_map *bmap);
2230 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2231 __isl_give isl_union_map *isl_union_map_copy(
2232 __isl_keep isl_union_map *umap);
2233 __isl_null isl_basic_set *isl_basic_set_free(
2234 __isl_take isl_basic_set *bset);
2235 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2236 __isl_null isl_union_set *isl_union_set_free(
2237 __isl_take isl_union_set *uset);
2238 __isl_null isl_basic_map *isl_basic_map_free(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2241 __isl_null isl_union_map *isl_union_map_free(
2242 __isl_take isl_union_map *umap);
2244 Other sets and relations can be constructed by starting
2245 from a universe set or relation, adding equality and/or
2246 inequality constraints and then projecting out the
2247 existentially quantified variables, if any.
2248 Constraints can be constructed, manipulated and
2249 added to (or removed from) (basic) sets and relations
2250 using the following functions.
2252 #include <isl/constraint.h>
2253 __isl_give isl_constraint *isl_constraint_alloc_equality(
2254 __isl_take isl_local_space *ls);
2255 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2256 __isl_take isl_local_space *ls);
2257 __isl_give isl_constraint *isl_constraint_set_constant_si(
2258 __isl_take isl_constraint *constraint, int v);
2259 __isl_give isl_constraint *isl_constraint_set_constant_val(
2260 __isl_take isl_constraint *constraint,
2261 __isl_take isl_val *v);
2262 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2263 __isl_take isl_constraint *constraint,
2264 enum isl_dim_type type, int pos, int v);
2265 __isl_give isl_constraint *
2266 isl_constraint_set_coefficient_val(
2267 __isl_take isl_constraint *constraint,
2268 enum isl_dim_type type, int pos,
2269 __isl_take isl_val *v);
2270 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2271 __isl_take isl_basic_map *bmap,
2272 __isl_take isl_constraint *constraint);
2273 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2274 __isl_take isl_basic_set *bset,
2275 __isl_take isl_constraint *constraint);
2276 __isl_give isl_map *isl_map_add_constraint(
2277 __isl_take isl_map *map,
2278 __isl_take isl_constraint *constraint);
2279 __isl_give isl_set *isl_set_add_constraint(
2280 __isl_take isl_set *set,
2281 __isl_take isl_constraint *constraint);
2283 For example, to create a set containing the even integers
2284 between 10 and 42, you could use the following code.
2287 isl_local_space *ls;
2289 isl_basic_set *bset;
2291 space = isl_space_set_alloc(ctx, 0, 2);
2292 bset = isl_basic_set_universe(isl_space_copy(space));
2293 ls = isl_local_space_from_space(space);
2295 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2296 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2297 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2298 bset = isl_basic_set_add_constraint(bset, c);
2300 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2301 c = isl_constraint_set_constant_si(c, -10);
2302 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2303 bset = isl_basic_set_add_constraint(bset, c);
2305 c = isl_constraint_alloc_inequality(ls);
2306 c = isl_constraint_set_constant_si(c, 42);
2307 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2308 bset = isl_basic_set_add_constraint(bset, c);
2310 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2312 However, this is considered to be a fairly low-level approach.
2313 It is more appropriate to construct a (basic) set by means
2314 of affine expressions (defined below in L</"Functions">).
2315 For example, the same set could be constructed as follows.
2321 isl_basic_set *bset;
2323 space = isl_space_unit(ctx);
2324 space = isl_space_add_unnamed_tuple_ui(space, 1);
2325 ma = isl_multi_aff_identity_on_domain_space(
2326 isl_space_copy(space));
2327 var = isl_multi_aff_get_at(ma, 0);
2328 v = isl_val_int_from_si(ctx, 10);
2329 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2330 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2332 v = isl_val_int_from_si(ctx, 42);
2333 cst = isl_aff_val_on_domain_space(space, v);
2334 bset = isl_basic_set_intersect(bset,
2335 isl_aff_le_basic_set(var, cst));
2337 two = isl_val_int_from_si(ctx, 2);
2338 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2339 bset = isl_basic_set_preimage_multi_aff(bset,
2340 isl_multi_aff_copy(ma));
2341 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2342 ma = isl_multi_aff_scale_down_val(ma, two);
2343 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2345 Alternatively, the set can be parsed from a string representation.
2347 isl_basic_set *bset;
2348 bset = isl_basic_set_read_from_str(ctx,
2349 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2351 A basic set or relation can also be constructed from two matrices
2352 describing the equalities and the inequalities.
2354 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2355 __isl_take isl_space *space,
2356 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2357 enum isl_dim_type c1,
2358 enum isl_dim_type c2, enum isl_dim_type c3,
2359 enum isl_dim_type c4);
2360 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2361 __isl_take isl_space *space,
2362 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2363 enum isl_dim_type c1,
2364 enum isl_dim_type c2, enum isl_dim_type c3,
2365 enum isl_dim_type c4, enum isl_dim_type c5);
2367 The C<isl_dim_type> arguments indicate the order in which
2368 different kinds of variables appear in the input matrices
2369 and should be a permutation of C<isl_dim_cst> (the constant term),
2370 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2371 of C<isl_dim_cst>, C<isl_dim_param>,
2372 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2374 A (basic or union) set or relation can also be constructed from a
2375 (union) (piecewise) (multiple) affine expression
2376 or a list of affine expressions
2377 (See L</"Functions">), provided these affine expressions do not
2380 #include <isl/set.h>
2381 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2382 __isl_take isl_multi_aff *ma);
2383 __isl_give isl_set *isl_multi_aff_as_set(
2384 __isl_take isl_multi_aff *ma);
2385 __isl_give isl_set *isl_set_from_multi_aff(
2386 __isl_take isl_multi_aff *ma);
2388 #include <isl/map.h>
2389 __isl_give isl_basic_map *isl_basic_map_from_aff(
2390 __isl_take isl_aff *aff);
2391 __isl_give isl_map *isl_map_from_aff(
2392 __isl_take isl_aff *aff);
2393 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2394 __isl_take isl_space *domain_space,
2395 __isl_take isl_aff_list *list);
2396 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2397 __isl_take isl_multi_aff *maff)
2398 __isl_give isl_map *isl_multi_aff_as_map(
2399 __isl_take isl_multi_aff *ma);
2400 __isl_give isl_map *isl_map_from_multi_aff(
2401 __isl_take isl_multi_aff *maff)
2403 #include <isl/aff.h>
2404 __isl_give isl_set *isl_set_from_pw_aff(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_map *isl_pw_aff_as_map(
2407 __isl_take isl_pw_aff *pa);
2408 __isl_give isl_map *isl_map_from_pw_aff(
2409 __isl_take isl_pw_aff *pwaff);
2410 __isl_give isl_set *isl_pw_multi_aff_as_set(
2411 __isl_take isl_pw_multi_aff *pma);
2412 __isl_give isl_set *isl_set_from_pw_multi_aff(
2413 __isl_take isl_pw_multi_aff *pma);
2414 __isl_give isl_map *isl_pw_multi_aff_as_map(
2415 __isl_take isl_pw_multi_aff *pma);
2416 __isl_give isl_map *isl_map_from_pw_multi_aff(
2417 __isl_take isl_pw_multi_aff *pma);
2418 __isl_give isl_set *isl_multi_pw_aff_as_set(
2419 __isl_take isl_multi_pw_aff *mpa);
2420 __isl_give isl_set *isl_set_from_multi_pw_aff(
2421 __isl_take isl_multi_pw_aff *mpa);
2422 __isl_give isl_map *isl_multi_pw_aff_as_map(
2423 __isl_take isl_multi_pw_aff *mpa);
2424 __isl_give isl_map *isl_map_from_multi_pw_aff(
2425 __isl_take isl_multi_pw_aff *mpa);
2426 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2427 __isl_take isl_union_pw_aff *upa);
2428 __isl_give isl_union_map *
2429 isl_union_pw_multi_aff_as_union_map(
2430 __isl_take isl_union_pw_multi_aff *upma);
2431 __isl_give isl_union_map *
2432 isl_union_map_from_union_pw_multi_aff(
2433 __isl_take isl_union_pw_multi_aff *upma);
2434 __isl_give isl_union_map *
2435 isl_union_map_from_multi_union_pw_aff(
2436 __isl_take isl_multi_union_pw_aff *mupa);
2438 The C<domain_space> argument describes the domain of the resulting
2439 basic relation. It is required because the C<list> may consist
2440 of zero affine expressions.
2441 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2442 is not allowed to be zero-dimensional. The domain of the result
2443 is the shared domain of the union piecewise affine elements.
2444 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2446 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2447 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2448 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2449 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2450 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2451 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2453 C<isl_union_pw_multi_aff_as_union_map> and
2454 C<isl_union_map_from_union_pw_multi_aff>.
2456 =head2 Inspecting Sets and Relations
2458 Usually, the user should not have to care about the actual constraints
2459 of the sets and maps, but should instead apply the abstract operations
2460 explained in the following sections.
2461 Occasionally, however, it may be required to inspect the individual
2462 coefficients of the constraints. This section explains how to do so.
2463 In these cases, it may also be useful to have C<isl> compute
2464 an explicit representation of the existentially quantified variables.
2466 __isl_give isl_set *isl_set_compute_divs(
2467 __isl_take isl_set *set);
2468 __isl_give isl_map *isl_map_compute_divs(
2469 __isl_take isl_map *map);
2470 __isl_give isl_union_set *isl_union_set_compute_divs(
2471 __isl_take isl_union_set *uset);
2472 __isl_give isl_union_map *isl_union_map_compute_divs(
2473 __isl_take isl_union_map *umap);
2475 This explicit representation defines the existentially quantified
2476 variables as integer divisions of the other variables, possibly
2477 including earlier existentially quantified variables.
2478 An explicitly represented existentially quantified variable therefore
2479 has a unique value when the values of the other variables are known.
2481 Alternatively, the existentially quantified variables can be removed
2482 using the following functions, which compute an overapproximation.
2484 #include <isl/set.h>
2485 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2486 __isl_take isl_basic_set *bset);
2487 __isl_give isl_set *isl_set_remove_divs(
2488 __isl_take isl_set *set);
2490 #include <isl/map.h>
2491 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2492 __isl_take isl_basic_map *bmap);
2493 __isl_give isl_map *isl_map_remove_divs(
2494 __isl_take isl_map *map);
2496 #include <isl/union_set.h>
2497 __isl_give isl_union_set *isl_union_set_remove_divs(
2498 __isl_take isl_union_set *bset);
2500 #include <isl/union_map.h>
2501 __isl_give isl_union_map *isl_union_map_remove_divs(
2502 __isl_take isl_union_map *bmap);
2504 It is also possible to only remove those divs that are defined
2505 in terms of a given range of dimensions or only those for which
2506 no explicit representation is known.
2508 __isl_give isl_basic_set *
2509 isl_basic_set_remove_divs_involving_dims(
2510 __isl_take isl_basic_set *bset,
2511 enum isl_dim_type type,
2512 unsigned first, unsigned n);
2513 __isl_give isl_basic_map *
2514 isl_basic_map_remove_divs_involving_dims(
2515 __isl_take isl_basic_map *bmap,
2516 enum isl_dim_type type,
2517 unsigned first, unsigned n);
2518 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2519 __isl_take isl_set *set, enum isl_dim_type type,
2520 unsigned first, unsigned n);
2521 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2522 __isl_take isl_map *map, enum isl_dim_type type,
2523 unsigned first, unsigned n);
2525 __isl_give isl_basic_set *
2526 isl_basic_set_remove_unknown_divs(
2527 __isl_take isl_basic_set *bset);
2528 __isl_give isl_set *isl_set_remove_unknown_divs(
2529 __isl_take isl_set *set);
2530 __isl_give isl_map *isl_map_remove_unknown_divs(
2531 __isl_take isl_map *map);
2533 To iterate over all the sets or maps in a union set or map, use
2535 #include <isl/union_set.h>
2536 isl_stat isl_union_set_foreach_set(
2537 __isl_keep isl_union_set *uset,
2538 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2540 isl_bool isl_union_set_every_set(
2541 __isl_keep isl_union_set *uset,
2542 isl_bool (*test)(__isl_keep isl_set *set,
2546 #include <isl/union_map.h>
2547 isl_stat isl_union_map_foreach_map(
2548 __isl_keep isl_union_map *umap,
2549 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2551 isl_bool isl_union_map_every_map(
2552 __isl_keep isl_union_map *umap,
2553 isl_bool (*test)(__isl_keep isl_map *map,
2557 These functions call the callback function once for each
2558 (pair of) space(s) for which there are elements in the input.
2559 The argument to the callback contains all elements in the input
2560 with that (pair of) space(s).
2561 The C<isl_union_set_every_set> and
2562 C<isl_union_map_every_map> variants check whether each
2563 call to the callback returns true and stops checking as soon as one
2564 of these calls returns false.
2566 The number of sets or maps in a union set or map can be obtained
2569 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2570 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2572 To extract the set or map in a given space from a union, use
2574 __isl_give isl_set *isl_union_set_extract_set(
2575 __isl_keep isl_union_set *uset,
2576 __isl_take isl_space *space);
2577 __isl_give isl_map *isl_union_map_extract_map(
2578 __isl_keep isl_union_map *umap,
2579 __isl_take isl_space *space);
2581 To iterate over all the basic sets or maps in a set or map, use
2583 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2584 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2587 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2588 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2592 The callback function C<fn> should return C<isl_stat_ok> if successful and
2593 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2594 occurs, the above functions will return C<isl_stat_error>.
2596 It should be noted that C<isl> does not guarantee that
2597 the basic sets or maps passed to C<fn> are disjoint.
2598 If this is required, then the user should call one of
2599 the following functions first.
2601 __isl_give isl_set *isl_set_make_disjoint(
2602 __isl_take isl_set *set);
2603 __isl_give isl_map *isl_map_make_disjoint(
2604 __isl_take isl_map *map);
2606 The number of basic sets in a set can be obtained
2607 or the number of basic maps in a map can be obtained
2610 #include <isl/set.h>
2611 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2613 #include <isl/map.h>
2614 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2616 It is also possible to obtain a list of (basic) sets from a set
2617 or union set, a list of basic maps from a map and a list of maps from a union
2620 #include <isl/set.h>
2621 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2622 __isl_keep isl_set *set);
2624 #include <isl/union_set.h>
2625 __isl_give isl_basic_set_list *
2626 isl_union_set_get_basic_set_list(
2627 __isl_keep isl_union_set *uset);
2628 __isl_give isl_set_list *isl_union_set_get_set_list(
2629 __isl_keep isl_union_set *uset);
2631 #include <isl/map.h>
2632 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2633 __isl_keep isl_map *map);
2635 #include <isl/union_map.h>
2636 __isl_give isl_map_list *isl_union_map_get_map_list(
2637 __isl_keep isl_union_map *umap);
2639 The returned list can be manipulated using the functions in L<"Lists">.
2641 To iterate over the constraints of a basic set or map, use
2643 #include <isl/constraint.h>
2645 isl_size isl_basic_set_n_constraint(
2646 __isl_keep isl_basic_set *bset);
2647 isl_stat isl_basic_set_foreach_constraint(
2648 __isl_keep isl_basic_set *bset,
2649 isl_stat (*fn)(__isl_take isl_constraint *c,
2652 isl_size isl_basic_map_n_constraint(
2653 __isl_keep isl_basic_map *bmap);
2654 isl_stat isl_basic_map_foreach_constraint(
2655 __isl_keep isl_basic_map *bmap,
2656 isl_stat (*fn)(__isl_take isl_constraint *c,
2659 __isl_null isl_constraint *isl_constraint_free(
2660 __isl_take isl_constraint *c);
2662 Again, the callback function C<fn> should return C<isl_stat_ok>
2664 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2665 occurs, the above functions will return C<isl_stat_error>.
2666 The constraint C<c> represents either an equality or an inequality.
2667 Use the following function to find out whether a constraint
2668 represents an equality. If not, it represents an inequality.
2670 isl_bool isl_constraint_is_equality(
2671 __isl_keep isl_constraint *constraint);
2673 It is also possible to obtain a list of constraints from a basic
2676 #include <isl/constraint.h>
2677 __isl_give isl_constraint_list *
2678 isl_basic_map_get_constraint_list(
2679 __isl_keep isl_basic_map *bmap);
2680 __isl_give isl_constraint_list *
2681 isl_basic_set_get_constraint_list(
2682 __isl_keep isl_basic_set *bset);
2684 These functions require that all existentially quantified variables
2685 have an explicit representation.
2686 The returned list can be manipulated using the functions in L<"Lists">.
2688 The coefficients of the constraints can be inspected using
2689 the following functions.
2691 isl_bool isl_constraint_is_lower_bound(
2692 __isl_keep isl_constraint *constraint,
2693 enum isl_dim_type type, unsigned pos);
2694 isl_bool isl_constraint_is_upper_bound(
2695 __isl_keep isl_constraint *constraint,
2696 enum isl_dim_type type, unsigned pos);
2697 __isl_give isl_val *isl_constraint_get_constant_val(
2698 __isl_keep isl_constraint *constraint);
2699 __isl_give isl_val *isl_constraint_get_coefficient_val(
2700 __isl_keep isl_constraint *constraint,
2701 enum isl_dim_type type, int pos);
2703 The explicit representations of the existentially quantified
2704 variables can be inspected using the following function.
2705 Note that the user is only allowed to use this function
2706 if the inspected set or map is the result of a call
2707 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2708 The existentially quantified variable is equal to the floor
2709 of the returned affine expression. The affine expression
2710 itself can be inspected using the functions in
2713 __isl_give isl_aff *isl_constraint_get_div(
2714 __isl_keep isl_constraint *constraint, int pos);
2716 To obtain the constraints of a basic set or map in matrix
2717 form, use the following functions.
2719 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
2724 __isl_keep isl_basic_set *bset,
2725 enum isl_dim_type c1, enum isl_dim_type c2,
2726 enum isl_dim_type c3, enum isl_dim_type c4);
2727 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2728 __isl_keep isl_basic_map *bmap,
2729 enum isl_dim_type c1,
2730 enum isl_dim_type c2, enum isl_dim_type c3,
2731 enum isl_dim_type c4, enum isl_dim_type c5);
2732 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2733 __isl_keep isl_basic_map *bmap,
2734 enum isl_dim_type c1,
2735 enum isl_dim_type c2, enum isl_dim_type c3,
2736 enum isl_dim_type c4, enum isl_dim_type c5);
2738 The C<isl_dim_type> arguments dictate the order in which
2739 different kinds of variables appear in the resulting matrix.
2740 For set inputs, they should be a permutation of
2741 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2743 For map inputs, they should be a permutation of
2744 C<isl_dim_cst>, C<isl_dim_param>,
2745 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2749 Points are elements of a set. They can be used to construct
2750 simple sets (boxes) or they can be used to represent the
2751 individual elements of a set.
2752 The zero point (the origin) can be created using
2754 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2756 The coordinates of a point can be inspected, set and changed
2759 #include <isl/point.h>
2760 __isl_give isl_multi_val *isl_point_get_multi_val(
2761 __isl_keep isl_point *pnt);
2762 __isl_give isl_val *isl_point_get_coordinate_val(
2763 __isl_keep isl_point *pnt,
2764 enum isl_dim_type type, int pos);
2765 __isl_give isl_point *isl_point_set_coordinate_val(
2766 __isl_take isl_point *pnt,
2767 enum isl_dim_type type, int pos,
2768 __isl_take isl_val *v);
2770 __isl_give isl_point *isl_point_add_ui(
2771 __isl_take isl_point *pnt,
2772 enum isl_dim_type type, int pos, unsigned val);
2773 __isl_give isl_point *isl_point_sub_ui(
2774 __isl_take isl_point *pnt,
2775 enum isl_dim_type type, int pos, unsigned val);
2777 Points can be copied or freed using
2779 __isl_give isl_point *isl_point_copy(
2780 __isl_keep isl_point *pnt);
2781 __isl_null isl_point *isl_point_free(
2782 __isl_take isl_point *pnt);
2784 A singleton set can be created from a point using the following functions.
2786 __isl_give isl_basic_set *isl_basic_set_from_point(
2787 __isl_take isl_point *pnt);
2788 __isl_give isl_set *isl_point_to_set(
2789 __isl_take isl_point *pnt);
2790 __isl_give isl_set *isl_set_from_point(
2791 __isl_take isl_point *pnt);
2792 __isl_give isl_union_set *isl_union_set_from_point(
2793 __isl_take isl_point *pnt);
2795 C<isl_point_to_set> and C<isl_set_from_point> perform
2798 A box can be created from two opposite extremal points using
2800 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2801 __isl_take isl_point *pnt1,
2802 __isl_take isl_point *pnt2);
2803 __isl_give isl_set *isl_set_box_from_points(
2804 __isl_take isl_point *pnt1,
2805 __isl_take isl_point *pnt2);
2807 All elements of a B<bounded> (union) set can be enumerated using
2808 the following functions.
2810 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2811 isl_stat (*fn)(__isl_take isl_point *pnt,
2814 isl_stat isl_union_set_foreach_point(
2815 __isl_keep isl_union_set *uset,
2816 isl_stat (*fn)(__isl_take isl_point *pnt,
2820 The function C<fn> is called for each integer point in
2821 C<set> with as second argument the last argument of
2822 the C<isl_set_foreach_point> call. The function C<fn>
2823 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2824 In the latter case, C<isl_set_foreach_point> will stop
2825 enumerating and return C<isl_stat_error> as well.
2826 If the enumeration is performed successfully and to completion,
2827 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2829 To obtain a single point of a (basic or union) set, use
2831 __isl_give isl_point *isl_basic_set_sample_point(
2832 __isl_take isl_basic_set *bset);
2833 __isl_give isl_point *isl_set_sample_point(
2834 __isl_take isl_set *set);
2835 __isl_give isl_point *isl_union_set_sample_point(
2836 __isl_take isl_union_set *uset);
2838 If C<set> does not contain any (integer) points, then the
2839 resulting point will be ``void'', a property that can be
2842 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2846 Besides sets and relation, C<isl> also supports various types of functions.
2847 Each of these types is derived from the value type (see L</"Values">)
2848 or from one of two primitive function types
2849 through the application of zero or more type constructors.
2850 As a special case, a multiple expression can also be derived
2851 from an identifier (see L</"Identifiers">) although the result
2852 is not really a function.
2853 We first describe the primitive type and then we describe
2854 the types derived from these primitive types.
2856 =head3 Primitive Functions
2858 C<isl> support two primitive function types, quasi-affine
2859 expressions and quasipolynomials.
2860 A quasi-affine expression is defined either over a parameter
2861 space or over a set and is composed of integer constants,
2862 parameters and set variables, addition, subtraction and
2863 integer division by an integer constant.
2864 For example, the quasi-affine expression
2866 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2868 maps C<x> to C<2*floor((4 n + x)/9>.
2869 A quasipolynomial is a polynomial expression in quasi-affine
2870 expression. That is, it additionally allows for multiplication.
2871 Note, though, that it is not allowed to construct an integer
2872 division of an expression involving multiplications.
2873 Here is an example of a quasipolynomial that is not
2874 quasi-affine expression
2876 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2878 Note that the external representations of quasi-affine expressions
2879 and quasipolynomials are different. Quasi-affine expressions
2880 use a notation with square brackets just like binary relations,
2881 while quasipolynomials do not. This might change at some point.
2883 If a primitive function is defined over a parameter space,
2884 then the space of the function itself is that of a set.
2885 If it is defined over a set, then the space of the function
2886 is that of a relation. In both cases, the set space (or
2887 the output space) is single-dimensional, anonymous and unstructured.
2888 To create functions with multiple dimensions or with other kinds
2889 of set or output spaces, use multiple expressions
2890 (see L</"Multiple Expressions">).
2894 =item * Quasi-affine Expressions
2896 Besides the expressions described above, a quasi-affine
2897 expression can also be set to NaN. Such expressions
2898 typically represent a failure to represent a result
2899 as a quasi-affine expression.
2901 The zero quasi affine expression or the quasi affine expression
2902 that is equal to a given value, parameter or
2903 a specified dimension on a given domain can be created using
2905 #include <isl/aff.h>
2906 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2907 __isl_take isl_space *space);
2908 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2909 __isl_take isl_space *space);
2910 __isl_give isl_aff *isl_aff_zero_on_domain(
2911 __isl_take isl_local_space *ls);
2912 __isl_give isl_aff *isl_aff_val_on_domain_space(
2913 __isl_take isl_space *space,
2914 __isl_take isl_val *val);
2915 __isl_give isl_aff *isl_aff_val_on_domain(
2916 __isl_take isl_local_space *ls,
2917 __isl_take isl_val *val);
2918 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2919 __isl_take isl_space *space,
2920 __isl_take isl_id *id);
2921 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2922 __isl_take isl_space *space,
2923 __isl_take isl_id *id);
2924 __isl_give isl_aff *isl_aff_var_on_domain(
2925 __isl_take isl_local_space *ls,
2926 enum isl_dim_type type, unsigned pos);
2927 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2928 __isl_take isl_space *space);
2929 __isl_give isl_aff *isl_aff_nan_on_domain(
2930 __isl_take isl_local_space *ls);
2932 The space passed to C<isl_aff_param_on_domain_space_id>
2933 is required to have a parameter with the given identifier.
2934 C<isl_aff_param_on_domain_space_id> and
2935 C<isl_space_param_aff_on_domain_id> perform the same operation.
2937 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2938 perform the same operation.
2940 Quasi affine expressions can be copied and freed using
2942 #include <isl/aff.h>
2943 __isl_give isl_aff *isl_aff_copy(
2944 __isl_keep isl_aff *aff);
2945 __isl_null isl_aff *isl_aff_free(
2946 __isl_take isl_aff *aff);
2948 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2949 using the following function. The constraint is required to have
2950 a non-zero coefficient for the specified dimension.
2952 #include <isl/constraint.h>
2953 __isl_give isl_aff *isl_constraint_get_bound(
2954 __isl_keep isl_constraint *constraint,
2955 enum isl_dim_type type, int pos);
2957 The entire affine expression of the constraint can also be extracted
2958 using the following function.
2960 #include <isl/constraint.h>
2961 __isl_give isl_aff *isl_constraint_get_aff(
2962 __isl_keep isl_constraint *constraint);
2964 Conversely, an equality constraint equating
2965 the affine expression to zero or an inequality constraint enforcing
2966 the affine expression to be non-negative, can be constructed using
2968 __isl_give isl_constraint *isl_equality_from_aff(
2969 __isl_take isl_aff *aff);
2970 __isl_give isl_constraint *isl_inequality_from_aff(
2971 __isl_take isl_aff *aff);
2973 The coefficients and the integer divisions of an affine expression
2974 can be inspected using the following functions.
2976 #include <isl/aff.h>
2977 __isl_give isl_val *isl_aff_get_constant_val(
2978 __isl_keep isl_aff *aff);
2979 __isl_give isl_val *isl_aff_get_coefficient_val(
2980 __isl_keep isl_aff *aff,
2981 enum isl_dim_type type, int pos);
2982 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2983 enum isl_dim_type type, int pos);
2984 __isl_give isl_val *isl_aff_get_denominator_val(
2985 __isl_keep isl_aff *aff);
2986 __isl_give isl_aff *isl_aff_get_div(
2987 __isl_keep isl_aff *aff, int pos);
2989 They can be modified using the following functions.
2991 #include <isl/aff.h>
2992 __isl_give isl_aff *isl_aff_set_constant_si(
2993 __isl_take isl_aff *aff, int v);
2994 __isl_give isl_aff *isl_aff_set_constant_val(
2995 __isl_take isl_aff *aff, __isl_take isl_val *v);
2996 __isl_give isl_aff *isl_aff_set_coefficient_si(
2997 __isl_take isl_aff *aff,
2998 enum isl_dim_type type, int pos, int v);
2999 __isl_give isl_aff *isl_aff_set_coefficient_val(
3000 __isl_take isl_aff *aff,
3001 enum isl_dim_type type, int pos,
3002 __isl_take isl_val *v);
3004 __isl_give isl_aff *isl_aff_add_constant_si(
3005 __isl_take isl_aff *aff, int v);
3006 __isl_give isl_aff *isl_aff_add_constant_val(
3007 __isl_take isl_aff *aff, __isl_take isl_val *v);
3008 __isl_give isl_aff *isl_aff_add_constant_num_si(
3009 __isl_take isl_aff *aff, int v);
3010 __isl_give isl_aff *isl_aff_add_coefficient_si(
3011 __isl_take isl_aff *aff,
3012 enum isl_dim_type type, int pos, int v);
3013 __isl_give isl_aff *isl_aff_add_coefficient_val(
3014 __isl_take isl_aff *aff,
3015 enum isl_dim_type type, int pos,
3016 __isl_take isl_val *v);
3018 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3019 set the I<numerator> of the constant or coefficient, while
3020 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3021 the constant or coefficient as a whole.
3022 The C<add_constant> and C<add_coefficient> functions add an integer
3023 or rational value to
3024 the possibly rational constant or coefficient.
3025 The C<add_constant_num> functions add an integer value to
3028 =item * Quasipolynomials
3030 Some simple quasipolynomials can be created using the following functions.
3032 #include <isl/polynomial.h>
3033 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3034 __isl_take isl_space *domain);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3036 __isl_take isl_space *domain);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3038 __isl_take isl_space *domain);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3040 __isl_take isl_space *domain);
3041 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3042 __isl_take isl_space *domain);
3043 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3044 __isl_take isl_space *domain,
3045 __isl_take isl_val *val);
3046 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3047 __isl_take isl_space *domain,
3048 enum isl_dim_type type, unsigned pos);
3049 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3050 __isl_take isl_aff *aff);
3052 Recall that the space in which a quasipolynomial lives is a map space
3053 with a one-dimensional range. The C<domain> argument in some of
3054 the functions above corresponds to the domain of this map space.
3056 A quasi-polynomial that can also be represented as a quasi-affine expression
3057 can be converted using the function below.
3059 #include <isl/polynomial.h>
3060 isl_bool isl_qpolynomial_isa_aff(
3061 __isl_keep isl_qpolynomial *qp);
3062 __isl_give isl_aff *isl_qpolynomial_as_aff(
3063 __isl_take isl_qpolynomial *qp);
3065 Quasipolynomials can be copied and freed again using the following
3068 #include <isl/polynomial.h>
3069 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3070 __isl_keep isl_qpolynomial *qp);
3071 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3072 __isl_take isl_qpolynomial *qp);
3074 The constant term of a quasipolynomial can be extracted using
3076 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3077 __isl_keep isl_qpolynomial *qp);
3079 To iterate over all terms in a quasipolynomial,
3082 isl_stat isl_qpolynomial_foreach_term(
3083 __isl_keep isl_qpolynomial *qp,
3084 isl_stat (*fn)(__isl_take isl_term *term,
3085 void *user), void *user);
3087 The terms themselves can be inspected and freed using
3090 isl_size isl_term_dim(__isl_keep isl_term *term,
3091 enum isl_dim_type type);
3092 __isl_give isl_val *isl_term_get_coefficient_val(
3093 __isl_keep isl_term *term);
3094 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3095 enum isl_dim_type type, unsigned pos);
3096 __isl_give isl_aff *isl_term_get_div(
3097 __isl_keep isl_term *term, unsigned pos);
3098 __isl_null isl_term *isl_term_free(
3099 __isl_take isl_term *term);
3101 Each term is a product of parameters, set variables and
3102 integer divisions. The function C<isl_term_get_exp>
3103 returns the exponent of a given dimensions in the given term.
3109 A reduction represents a maximum or a minimum of its
3111 The only reduction type defined by C<isl> is
3112 C<isl_qpolynomial_fold>.
3114 There are currently no functions to directly create such
3115 objects, but they do appear in the piecewise quasipolynomial
3116 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3118 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3120 Reductions can be copied and freed using
3121 the following functions.
3123 #include <isl/polynomial.h>
3124 __isl_give isl_qpolynomial_fold *
3125 isl_qpolynomial_fold_copy(
3126 __isl_keep isl_qpolynomial_fold *fold);
3127 __isl_null isl_qpolynomial_fold *
3128 isl_qpolynomial_fold_free(
3129 __isl_take isl_qpolynomial_fold *fold);
3131 The type of a (union piecewise) reduction
3132 can be obtained using the following functions.
3134 #include <isl/polynomial.h>
3135 enum isl_fold isl_qpolynomial_fold_get_type(
3136 __isl_keep isl_qpolynomial_fold *fold);
3137 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3138 __isl_keep isl_pw_qpolynomial_fold *pwf);
3139 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3140 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3142 The type may be either C<isl_fold_min> or C<isl_fold_max>
3143 (or C<isl_fold_error> in case of error).
3145 To iterate over all quasipolynomials in a reduction, use
3147 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3148 __isl_keep isl_qpolynomial_fold *fold,
3149 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3150 void *user), void *user);
3152 =head3 Multiple Expressions
3154 A multiple expression represents a sequence of zero or
3155 more base expressions, all defined on the same domain space.
3156 The domain space of the multiple expression is the same
3157 as that of the base expressions, but the range space
3158 can be any space. In case the base expressions have
3159 a set space, the corresponding multiple expression
3160 also has a set space.
3161 Objects of the value or identifier type do not have an associated space.
3162 The space of a multiple value or
3163 multiple identifier is therefore always a set space.
3164 Similarly, the space of a multiple union piecewise
3165 affine expression is always a set space.
3166 If the base expressions are not total, then
3167 a corresponding zero-dimensional multiple expression may
3168 have an explicit domain that keeps track of the domain
3169 outside of any base expressions.
3171 The multiple expression types defined by C<isl>
3172 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3173 C<isl_multi_union_pw_aff>.
3175 A multiple expression with the value zero for
3176 each output (or set) dimension can be created
3177 using the following functions.
3179 #include <isl/val.h>
3180 __isl_give isl_multi_val *isl_multi_val_zero(
3181 __isl_take isl_space *space);
3182 __isl_give isl_multi_val *isl_space_zero_multi_val(
3183 __isl_take isl_space *space);
3185 #include <isl/aff.h>
3186 __isl_give isl_multi_aff *isl_multi_aff_zero(
3187 __isl_take isl_space *space);
3188 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3189 __isl_take isl_space *space);
3190 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3191 __isl_take isl_space *space);
3192 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3193 __isl_take isl_space *space);
3194 __isl_give isl_multi_union_pw_aff *
3195 isl_multi_union_pw_aff_zero(
3196 __isl_take isl_space *space);
3197 __isl_give isl_multi_union_pw_aff *
3198 isl_space_zero_multi_union_pw_aff(
3199 __isl_take isl_space *space);
3201 Since there is no canonical way of representing a zero
3202 value of type C<isl_union_pw_aff>, the space passed
3203 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3204 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3205 perform the same operation.
3207 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3208 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3209 for the pair C<isl_multi_union_pw_aff_zero> and
3210 C<isl_space_zero_multi_union_pw_aff>.
3213 An identity function can be created using the following
3215 For the first group of functions, the space needs to be that of a set.
3216 For the second group,
3217 the space needs to be that of a relation
3218 with the same number of input and output dimensions.
3219 For the third group, the input function needs to live in a space
3220 with the same number of input and output dimensions and
3221 the identity function is created in that space.
3223 #include <isl/aff.h>
3224 __isl_give isl_multi_aff *
3225 isl_multi_aff_identity_on_domain_space(
3226 __isl_take isl_space *space);
3227 __isl_give isl_multi_aff *
3228 isl_space_identity_multi_aff_on_domain(
3229 __isl_take isl_space *space);
3230 __isl_give isl_multi_pw_aff *
3231 isl_multi_pw_aff_identity_on_domain_space(
3232 __isl_take isl_space *space);
3233 __isl_give isl_multi_pw_aff *
3234 isl_space_identity_multi_pw_aff_on_domain(
3235 __isl_take isl_space *space);
3236 __isl_give isl_multi_aff *isl_multi_aff_identity(
3237 __isl_take isl_space *space);
3238 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3239 __isl_take isl_space *space);
3240 __isl_give isl_multi_aff *
3241 isl_multi_aff_identity_multi_aff(
3242 __isl_take isl_multi_aff *ma);
3243 __isl_give isl_multi_pw_aff *
3244 isl_multi_pw_aff_identity_multi_pw_aff(
3245 __isl_take isl_multi_pw_aff *mpa);
3247 C<isl_multi_aff_identity_on_domain_space> and
3248 C<isl_space_identity_multi_aff_on_domain>
3249 perform the same operation.
3251 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3252 C<isl_space_identity_multi_pw_aff_on_domain>.
3254 A function that performs a projection on a universe
3255 relation or set can be created using the following functions.
3256 See also the corresponding
3257 projection operations in L</"Unary Operations">.
3259 #include <isl/aff.h>
3260 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3261 __isl_take isl_space *space);
3262 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3263 __isl_take isl_space *space);
3264 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3265 __isl_take isl_space *space);
3266 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3267 __isl_take isl_space *space);
3268 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3269 __isl_take isl_space *space,
3270 enum isl_dim_type type,
3271 unsigned first, unsigned n);
3273 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3276 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3278 A multiple expression can be created from a single
3279 base expression using the following functions.
3280 The space of the created multiple expression is the same
3281 as that of the base expression, except for
3282 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3283 lives in a parameter space and the output lives
3284 in a single-dimensional set space.
3286 #include <isl/aff.h>
3287 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3288 __isl_take isl_aff *aff);
3289 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3290 __isl_take isl_pw_aff *pa);
3291 __isl_give isl_multi_union_pw_aff *
3292 isl_multi_union_pw_aff_from_union_pw_aff(
3293 __isl_take isl_union_pw_aff *upa);
3295 A multiple expression can be created from a list
3296 of base expression in a specified space.
3297 The domain of this space needs to be the same
3298 as the domains of the base expressions in the list.
3299 If the base expressions have a set space (or no associated space),
3300 then this space also needs to be a set space.
3303 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3304 __isl_take isl_space *space,
3305 __isl_take isl_id_list *list);
3306 __isl_give isl_multi_id *isl_space_multi_id(
3307 __isl_take isl_space *space,
3308 __isl_take isl_id_list *list);
3310 #include <isl/val.h>
3311 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3312 __isl_take isl_space *space,
3313 __isl_take isl_val_list *list);
3314 __isl_give isl_multi_val *isl_space_multi_val(
3315 __isl_take isl_space *space,
3316 __isl_take isl_val_list *list);
3318 #include <isl/aff.h>
3319 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3320 __isl_take isl_space *space,
3321 __isl_take isl_aff_list *list);
3322 __isl_give isl_multi_aff *isl_space_multi_aff(
3323 __isl_take isl_space *space,
3324 __isl_take isl_aff_list *list);
3325 __isl_give isl_multi_pw_aff *
3326 isl_multi_pw_aff_from_pw_aff_list(
3327 __isl_take isl_space *space,
3328 __isl_take isl_pw_aff_list *list);
3329 __isl_give isl_multi_pw_aff *
3330 isl_space_multi_pw_aff(
3331 __isl_take isl_space *space,
3332 __isl_take isl_pw_aff_list *list);
3333 __isl_give isl_multi_union_pw_aff *
3334 isl_multi_union_pw_aff_from_union_pw_aff_list(
3335 __isl_take isl_space *space,
3336 __isl_take isl_union_pw_aff_list *list);
3337 __isl_give isl_multi_union_pw_aff *
3338 isl_space_multi_union_pw_aff(
3339 __isl_take isl_space *space,
3340 __isl_take isl_union_pw_aff_list *list);
3342 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3344 Similarly for the pair C<isl_multi_val_from_val_list> and
3345 C<isl_space_multi_val>,
3346 for the pair C<isl_multi_aff_from_aff_list> and
3347 C<isl_space_multi_aff>,
3348 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3349 C<isl_space_multi_pw_aff> and
3350 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3351 C<isl_space_multi_union_pw_aff>.
3353 As a convenience, a multiple piecewise expression can
3354 also be created from a multiple expression,
3355 or even directly from a single base expression.
3356 Each piecewise expression in the result has a single
3359 #include <isl/aff.h>
3360 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3361 __isl_take isl_aff *aff);
3362 __isl_give isl_multi_pw_aff *
3363 isl_multi_aff_to_multi_pw_aff(
3364 __isl_take isl_multi_aff *ma);
3365 __isl_give isl_multi_pw_aff *
3366 isl_multi_pw_aff_from_multi_aff(
3367 __isl_take isl_multi_aff *ma);
3369 C<isl_multi_aff_to_multi_pw_aff> and
3370 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3372 Similarly, a multiple union expression can be
3373 created from a multiple expression.
3375 #include <isl/aff.h>
3376 __isl_give isl_multi_union_pw_aff *
3377 isl_multi_union_pw_aff_from_multi_aff(
3378 __isl_take isl_multi_aff *ma);
3379 __isl_give isl_multi_union_pw_aff *
3380 isl_multi_aff_to_multi_union_pw_aff(
3381 __isl_take isl_multi_aff *ma);
3382 __isl_give isl_multi_union_pw_aff *
3383 isl_multi_union_pw_aff_from_multi_pw_aff(
3384 __isl_take isl_multi_pw_aff *mpa);
3386 C<isl_multi_aff_to_multi_union_pw_aff> and
3387 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3389 A multiple quasi-affine expression can be created from
3390 a multiple value with a given domain space using the following
3393 #include <isl/aff.h>
3394 __isl_give isl_multi_aff *
3395 isl_multi_aff_multi_val_on_domain_space(
3396 __isl_take isl_space *space,
3397 __isl_take isl_multi_val *mv);
3398 __isl_give isl_multi_aff *
3399 isl_space_multi_aff_on_domain_multi_val(
3400 __isl_take isl_space *space,
3401 __isl_take isl_multi_val *mv);
3402 __isl_give isl_multi_aff *
3403 isl_multi_aff_multi_val_on_space(
3404 __isl_take isl_space *space,
3405 __isl_take isl_multi_val *mv);
3407 C<isl_space_multi_aff_on_domain_multi_val> and
3408 C<isl_multi_aff_multi_val_on_space> are alternative names
3409 for C<isl_multi_aff_multi_val_on_domain_space>.
3412 a multiple union piecewise affine expression can be created from
3413 a multiple value with a given domain or
3414 a (piecewise) multiple affine expression with a given domain
3415 using the following functions.
3417 #include <isl/aff.h>
3418 __isl_give isl_multi_union_pw_aff *
3419 isl_multi_union_pw_aff_multi_val_on_domain(
3420 __isl_take isl_union_set *domain,
3421 __isl_take isl_multi_val *mv);
3422 __isl_give isl_multi_union_pw_aff *
3423 isl_multi_union_pw_aff_multi_aff_on_domain(
3424 __isl_take isl_union_set *domain,
3425 __isl_take isl_multi_aff *ma);
3426 __isl_give isl_multi_union_pw_aff *
3427 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3428 __isl_take isl_union_set *domain,
3429 __isl_take isl_pw_multi_aff *pma);
3431 Multiple expressions can be copied and freed using
3432 the following functions.
3435 __isl_give isl_multi_id *isl_multi_id_copy(
3436 __isl_keep isl_multi_id *mi);
3437 __isl_null isl_multi_id *isl_multi_id_free(
3438 __isl_take isl_multi_id *mi);
3440 #include <isl/val.h>
3441 __isl_give isl_multi_val *isl_multi_val_copy(
3442 __isl_keep isl_multi_val *mv);
3443 __isl_null isl_multi_val *isl_multi_val_free(
3444 __isl_take isl_multi_val *mv);
3446 #include <isl/aff.h>
3447 __isl_give isl_multi_aff *isl_multi_aff_copy(
3448 __isl_keep isl_multi_aff *maff);
3449 __isl_null isl_multi_aff *isl_multi_aff_free(
3450 __isl_take isl_multi_aff *maff);
3451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3452 __isl_keep isl_multi_pw_aff *mpa);
3453 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3454 __isl_take isl_multi_pw_aff *mpa);
3455 __isl_give isl_multi_union_pw_aff *
3456 isl_multi_union_pw_aff_copy(
3457 __isl_keep isl_multi_union_pw_aff *mupa);
3458 __isl_null isl_multi_union_pw_aff *
3459 isl_multi_union_pw_aff_free(
3460 __isl_take isl_multi_union_pw_aff *mupa);
3462 The number of base expressions in a multiple
3463 expression can be obtained using the following functions.
3466 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3468 #include <isl/val.h>
3469 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3471 #include <isl/aff.h>
3472 isl_size isl_multi_aff_size(
3473 __isl_keep isl_multi_aff *multi);
3474 isl_size isl_multi_pw_aff_size(
3475 __isl_keep isl_multi_pw_aff *mpa);
3476 isl_size isl_multi_union_pw_aff_size(
3477 __isl_keep isl_multi_union_pw_aff *mupa);
3479 The base expression at a given position of a multiple
3480 expression can be extracted using the following functions.
3483 __isl_give isl_id *isl_multi_id_get_at(
3484 __isl_keep isl_multi_id *mi, int pos);
3485 __isl_give isl_id *isl_multi_id_get_id(
3486 __isl_keep isl_multi_id *mi, int pos);
3488 #include <isl/val.h>
3489 __isl_give isl_val *isl_multi_val_get_at(
3490 __isl_keep isl_multi_val *mv, int pos);
3491 __isl_give isl_val *isl_multi_val_get_val(
3492 __isl_keep isl_multi_val *mv, int pos);
3494 #include <isl/aff.h>
3495 __isl_give isl_aff *isl_multi_aff_get_at(
3496 __isl_keep isl_multi_aff *ma, int pos);
3497 __isl_give isl_aff *isl_multi_aff_get_aff(
3498 __isl_keep isl_multi_aff *multi, int pos);
3499 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3500 __isl_keep isl_multi_pw_aff *mpa, int pos);
3501 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3502 __isl_keep isl_multi_pw_aff *mpa, int pos);
3503 __isl_give isl_union_pw_aff *
3504 isl_multi_union_pw_aff_get_at(
3505 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3506 __isl_give isl_union_pw_aff *
3507 isl_multi_union_pw_aff_get_union_pw_aff(
3508 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3510 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3511 Similarly for the other pairs of functions.
3513 The base expression can be replaced using the following functions.
3516 __isl_give isl_multi_id *isl_multi_id_set_at(
3517 __isl_take isl_multi_id *mi, int pos,
3518 __isl_take isl_id *id);
3519 __isl_give isl_multi_id *isl_multi_id_set_id(
3520 __isl_take isl_multi_id *mi, int pos,
3521 __isl_take isl_id *id);
3523 #include <isl/val.h>
3524 __isl_give isl_multi_val *isl_multi_val_set_at(
3525 __isl_take isl_multi_val *mv, int pos,
3526 __isl_take isl_val *val);
3527 __isl_give isl_multi_val *isl_multi_val_set_val(
3528 __isl_take isl_multi_val *mv, int pos,
3529 __isl_take isl_val *val);
3531 #include <isl/aff.h>
3532 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3533 __isl_take isl_multi_aff *ma, int pos,
3534 __isl_take isl_aff *aff);
3535 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3536 __isl_take isl_multi_aff *multi, int pos,
3537 __isl_take isl_aff *aff);
3538 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3539 __isl_take isl_multi_pw_aff *mpa, int pos,
3540 __isl_take isl_pw_aff *pa);
3541 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3542 __isl_take isl_multi_pw_aff *mpa, int pos,
3543 __isl_take isl_pw_aff *pa);
3544 __isl_give isl_multi_union_pw_aff *
3545 isl_multi_union_pw_aff_set_at(
3546 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3547 __isl_take isl_union_pw_aff *upa);
3548 __isl_give isl_multi_union_pw_aff *
3549 isl_multi_union_pw_aff_set_union_pw_aff(
3550 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3551 __isl_take isl_union_pw_aff *upa);
3553 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3554 Similarly for the other pairs of functions.
3556 A list of all base expressions of a multiple
3557 expression can be extracted using the following functions.
3560 __isl_give isl_id_list *isl_multi_id_get_list(
3561 __isl_keep isl_multi_id *mi);
3563 #include <isl/val.h>
3564 __isl_give isl_val_list *isl_multi_val_get_list(
3565 __isl_keep isl_multi_val *mv);
3567 #include <isl/aff.h>
3568 __isl_give isl_aff_list *isl_multi_aff_get_list(
3569 __isl_keep isl_multi_aff *multi);
3570 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3571 __isl_keep isl_multi_pw_aff *mpa);
3572 __isl_give isl_union_pw_aff_list *
3573 isl_multi_union_pw_aff_list(
3574 __isl_keep isl_multi_union_pw_aff *mupa);
3576 The constant terms of the base expressions can be obtained using
3577 the following function.
3579 #include <isl/aff.h>
3580 __isl_give isl_multi_val *
3581 isl_multi_aff_get_constant_multi_val(
3582 __isl_keep isl_multi_aff *ma);
3584 As a convenience, a sequence of base expressions that have
3585 their domains in a given space can be extracted from a sequence
3586 of union expressions using the following function.
3588 #include <isl/aff.h>
3589 __isl_give isl_multi_pw_aff *
3590 isl_multi_union_pw_aff_extract_multi_pw_aff(
3591 __isl_keep isl_multi_union_pw_aff *mupa,
3592 __isl_take isl_space *space);
3594 Note that there is a difference between C<isl_multi_union_pw_aff>
3595 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3596 of unions of piecewise expressions, while the second is a union
3597 of piecewise sequences. In particular, multiple affine expressions
3598 in an C<isl_union_pw_multi_aff> may live in different spaces,
3599 while there is only a single multiple expression in
3600 an C<isl_multi_union_pw_aff>, which can therefore only live
3601 in a single space. This means that not every
3602 C<isl_union_pw_multi_aff> can be converted to
3603 an C<isl_multi_union_pw_aff>. Conversely, the elements
3604 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3605 while each multiple expression inside an C<isl_union_pw_multi_aff>
3606 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3607 of dimension greater than one may therefore not be exact.
3608 The following functions can
3609 be used to perform these conversions when they are possible.
3611 #include <isl/aff.h>
3612 __isl_give isl_multi_union_pw_aff *
3613 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3614 __isl_take isl_union_pw_multi_aff *upma);
3615 __isl_give isl_multi_union_pw_aff *
3616 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3617 __isl_take isl_union_pw_multi_aff *upma);
3618 __isl_give isl_union_pw_multi_aff *
3619 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3620 __isl_take isl_multi_union_pw_aff *mupa);
3622 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3623 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3624 perform the same operation.
3626 =head3 Piecewise Expressions
3628 A piecewise expression is an expression that is described
3629 using zero or more base expression defined over the same
3630 number of cells in the domain space of the base expressions.
3631 All base expressions are defined over the same
3632 domain space and the cells are disjoint.
3633 The space of a piecewise expression is the same as
3634 that of the base expressions.
3635 If the union of the cells is a strict subset of the domain
3636 space, then the value of the piecewise expression outside
3637 this union is different for types derived from quasi-affine
3638 expressions and those derived from quasipolynomials.
3639 Piecewise expressions derived from quasi-affine expressions
3640 are considered to be undefined outside the union of their cells.
3641 Piecewise expressions derived from quasipolynomials
3642 are considered to be zero outside the union of their cells.
3644 Piecewise quasipolynomials are mainly used by the C<barvinok>
3645 library for representing the number of elements in a parametric set or map.
3646 For example, the piecewise quasipolynomial
3648 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3650 represents the number of points in the map
3652 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3654 The piecewise expression types defined by C<isl>
3655 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3656 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3658 A piecewise expression with no cells can be created using
3659 the following functions.
3661 #include <isl/aff.h>
3662 __isl_give isl_pw_aff *isl_pw_aff_empty(
3663 __isl_take isl_space *space);
3664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3665 __isl_take isl_space *space);
3667 A piecewise expression with a single universe cell can be
3668 created using the following functions.
3670 #include <isl/aff.h>
3671 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3672 __isl_take isl_aff *aff);
3673 __isl_give isl_pw_multi_aff *
3674 isl_multi_aff_to_pw_multi_aff(
3675 __isl_take isl_multi_aff *ma);
3676 __isl_give isl_pw_multi_aff *
3677 isl_pw_multi_aff_from_multi_aff(
3678 __isl_take isl_multi_aff *ma);
3680 #include <isl/polynomial.h>
3681 __isl_give isl_pw_qpolynomial *
3682 isl_pw_qpolynomial_from_qpolynomial(
3683 __isl_take isl_qpolynomial *qp);
3684 __isl_give isl_pw_qpolynomial_fold *
3685 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3686 __isl_take isl_qpolynomial_fold *fold);
3688 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3691 The inverse conversions below can only be used if the input
3692 expression is known to be defined over a single universe domain.
3694 #include <isl/aff.h>
3695 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3696 __isl_give isl_aff *isl_pw_aff_as_aff(
3697 __isl_take isl_pw_aff *pa);
3698 isl_bool isl_multi_pw_aff_isa_multi_aff(
3699 __isl_keep isl_multi_pw_aff *mpa);
3700 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3701 __isl_take isl_multi_pw_aff *mpa);
3702 isl_bool isl_pw_multi_aff_isa_multi_aff(
3703 __isl_keep isl_pw_multi_aff *pma);
3704 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3705 __isl_take isl_pw_multi_aff *pma);
3707 #include <isl/polynomial.h>
3708 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3709 __isl_keep isl_pw_qpolynomial *pwqp);
3710 __isl_give isl_qpolynomial *
3711 isl_pw_qpolynomial_as_qpolynomial(
3712 __isl_take isl_pw_qpolynomial *pwqp);
3713 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3714 __isl_keep isl_pw_qpolynomial_fold *pwf);
3715 __isl_give isl_qpolynomial_fold *
3716 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3717 __isl_take isl_pw_qpolynomial_fold *pwf);
3719 A piecewise expression with a single specified cell can be
3720 created using the following functions.
3722 #include <isl/aff.h>
3723 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3724 __isl_take isl_set *set, __isl_take isl_aff *aff);
3725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3726 __isl_take isl_set *set,
3727 __isl_take isl_multi_aff *maff);
3729 #include <isl/polynomial.h>
3730 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3731 __isl_take isl_set *set,
3732 __isl_take isl_qpolynomial *qp);
3734 The following convenience functions first create a base expression and
3735 then create a piecewise expression over a universe domain.
3737 #include <isl/aff.h>
3738 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3739 __isl_take isl_local_space *ls);
3740 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3741 __isl_take isl_local_space *ls,
3742 enum isl_dim_type type, unsigned pos);
3743 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3744 __isl_take isl_space *space);
3745 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3746 __isl_take isl_local_space *ls);
3747 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3748 __isl_take isl_space *space);
3749 __isl_give isl_pw_multi_aff *
3750 isl_pw_multi_aff_identity_on_domain_space(
3751 __isl_take isl_space *space)
3752 __isl_give isl_pw_multi_aff *
3753 isl_space_identity_pw_multi_aff_on_domain(
3754 __isl_take isl_space *space)
3755 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3756 __isl_take isl_space *space);
3757 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3758 __isl_take isl_space *space);
3759 __isl_give isl_pw_multi_aff *
3760 isl_space_domain_map_pw_multi_aff(
3761 __isl_take isl_space *space);
3762 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3763 __isl_take isl_space *space);
3764 __isl_give isl_pw_multi_aff *
3765 isl_space_range_map_pw_multi_aff(
3766 __isl_take isl_space *space);
3767 __isl_give isl_pw_multi_aff *
3768 isl_pw_multi_aff_project_out_map(
3769 __isl_take isl_space *space,
3770 enum isl_dim_type type,
3771 unsigned first, unsigned n);
3773 #include <isl/polynomial.h>
3774 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3775 __isl_take isl_space *space);
3777 C<isl_pw_multi_aff_identity_on_domain_space> and
3778 C<isl_space_identity_pw_multi_aff_on_domain>
3779 perform the same operation.
3781 for the pair C<isl_pw_multi_aff_domain_map> and
3782 C<isl_space_domain_map_pw_multi_aff> and
3783 for the pair C<isl_pw_multi_aff_range_map> and
3784 C<isl_space_range_map_pw_multi_aff>.
3786 The following convenience functions first create a base expression and
3787 then create a piecewise expression over a given domain.
3789 #include <isl/aff.h>
3790 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3791 __isl_take isl_set *domain,
3792 __isl_take isl_val *v);
3793 __isl_give isl_pw_aff *isl_set_pw_aff_on_domain_val(
3794 __isl_take isl_set *domain,
3795 __isl_take isl_val *v);
3796 __isl_give isl_pw_multi_aff *
3797 isl_pw_multi_aff_multi_val_on_domain(
3798 __isl_take isl_set *domain,
3799 __isl_take isl_multi_val *mv);
3800 __isl_give isl_pw_multi_aff *
3801 isl_set_pw_multi_aff_on_domain_multi_val(
3802 __isl_take isl_set *domain,
3803 __isl_take isl_multi_val *mv);
3804 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3805 __isl_take isl_set *domain,
3806 __isl_take isl_id *id);
3807 __isl_give isl_pw_aff *isl_set_param_pw_aff_on_domain_id(
3808 __isl_take isl_set *domain,
3809 __isl_take isl_id *id);
3811 C<isl_set_pw_aff_on_domain_val> is an alternative name
3812 for C<isl_pw_aff_val_on_domain>.
3813 Similarly for the pair
3814 C<isl_set_pw_multi_aff_on_domain_multi_val> and
3815 C<isl_pw_multi_aff_multi_val_on_domain> and
3816 for the pair C<isl_set_param_pw_aff_on_domain_id> and
3817 C<isl_pw_aff_param_on_domain_id>.
3819 As a convenience, a piecewise multiple expression can
3820 also be created from a piecewise expression.
3821 Each multiple expression in the result is derived
3822 from the corresponding base expression.
3824 #include <isl/aff.h>
3825 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3826 __isl_take isl_pw_aff *pa);
3828 Similarly, a piecewise quasipolynomial can be
3829 created from a piecewise quasi-affine expression using
3830 the following function.
3832 #include <isl/polynomial.h>
3833 __isl_give isl_pw_qpolynomial *
3834 isl_pw_qpolynomial_from_pw_aff(
3835 __isl_take isl_pw_aff *pwaff);
3837 Piecewise expressions can be copied and freed using the following functions.
3839 #include <isl/aff.h>
3840 __isl_give isl_pw_aff *isl_pw_aff_copy(
3841 __isl_keep isl_pw_aff *pwaff);
3842 __isl_null isl_pw_aff *isl_pw_aff_free(
3843 __isl_take isl_pw_aff *pwaff);
3844 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3845 __isl_keep isl_pw_multi_aff *pma);
3846 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3847 __isl_take isl_pw_multi_aff *pma);
3849 #include <isl/polynomial.h>
3850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3851 __isl_keep isl_pw_qpolynomial *pwqp);
3852 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3853 __isl_take isl_pw_qpolynomial *pwqp);
3854 __isl_give isl_pw_qpolynomial_fold *
3855 isl_pw_qpolynomial_fold_copy(
3856 __isl_keep isl_pw_qpolynomial_fold *pwf);
3857 __isl_null isl_pw_qpolynomial_fold *
3858 isl_pw_qpolynomial_fold_free(
3859 __isl_take isl_pw_qpolynomial_fold *pwf);
3861 To iterate over the different cells of a piecewise expression,
3862 use the following functions.
3864 #include <isl/aff.h>
3865 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3866 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3867 isl_stat isl_pw_aff_foreach_piece(
3868 __isl_keep isl_pw_aff *pwaff,
3869 isl_stat (*fn)(__isl_take isl_set *set,
3870 __isl_take isl_aff *aff,
3871 void *user), void *user);
3872 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3873 isl_bool (*test)(__isl_keep isl_set *set,
3874 __isl_keep isl_aff *aff, void *user),
3876 isl_size isl_pw_multi_aff_n_piece(
3877 __isl_keep isl_pw_multi_aff *pma);
3878 isl_stat isl_pw_multi_aff_foreach_piece(
3879 __isl_keep isl_pw_multi_aff *pma,
3880 isl_stat (*fn)(__isl_take isl_set *set,
3881 __isl_take isl_multi_aff *maff,
3882 void *user), void *user);
3883 isl_bool isl_pw_multi_aff_every_piece(
3884 __isl_keep isl_pw_multi_aff *pma,
3885 isl_bool (*test)(__isl_keep isl_set *set,
3886 __isl_keep isl_multi_aff *ma, void *user),
3889 #include <isl/polynomial.h>
3890 isl_size isl_pw_qpolynomial_n_piece(
3891 __isl_keep isl_pw_qpolynomial *pwqp);
3892 isl_stat isl_pw_qpolynomial_foreach_piece(
3893 __isl_keep isl_pw_qpolynomial *pwqp,
3894 isl_stat (*fn)(__isl_take isl_set *set,
3895 __isl_take isl_qpolynomial *qp,
3896 void *user), void *user);
3897 isl_bool isl_pw_qpolynomial_every_piece(
3898 __isl_keep isl_pw_qpolynomial *pwqp,
3899 isl_bool (*test)(__isl_keep isl_set *set,
3900 __isl_keep isl_qpolynomial *qp,
3901 void *user), void *user);
3902 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3903 __isl_keep isl_pw_qpolynomial *pwqp,
3904 isl_stat (*fn)(__isl_take isl_set *set,
3905 __isl_take isl_qpolynomial *qp,
3906 void *user), void *user);
3907 isl_size isl_pw_qpolynomial_fold_n_piece(
3908 __isl_keep isl_pw_qpolynomial_fold *pwf);
3909 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3910 __isl_keep isl_pw_qpolynomial_fold *pwf,
3911 isl_stat (*fn)(__isl_take isl_set *set,
3912 __isl_take isl_qpolynomial_fold *fold,
3913 void *user), void *user);
3914 isl_bool isl_pw_qpolynomial_fold_every_piece(
3915 __isl_keep isl_pw_qpolynomial_fold *pwf,
3916 isl_bool (*test)(__isl_keep isl_set *set,
3917 __isl_keep isl_qpolynomial_fold *fold,
3918 void *user), void *user);
3919 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3920 __isl_keep isl_pw_qpolynomial_fold *pwf,
3921 isl_stat (*fn)(__isl_take isl_set *set,
3922 __isl_take isl_qpolynomial_fold *fold,
3923 void *user), void *user);
3925 As usual, the function C<fn> should return C<isl_stat_ok> on success
3926 and C<isl_stat_error> on failure. The difference between
3927 C<isl_pw_qpolynomial_foreach_piece> and
3928 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3929 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3930 compute unique representations for all existentially quantified
3931 variables and then turn these existentially quantified variables
3932 into extra set variables, adapting the associated quasipolynomial
3933 accordingly. This means that the C<set> passed to C<fn>
3934 will not have any existentially quantified variables, but that
3935 the dimensions of the sets may be different for different
3936 invocations of C<fn>.
3937 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3938 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3939 The function C<isl_pw_aff_every_piece> and its variants
3940 check whether each call to the callback returns true and
3941 stop checking as soon as one of these calls returns false (or error).
3943 A piecewise expression consisting of the expressions at a given
3944 position of a piecewise multiple expression can be extracted
3945 using the following function.
3947 #include <isl/aff.h>
3948 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3949 __isl_keep isl_pw_multi_aff *pma, int pos);
3950 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3951 __isl_keep isl_pw_multi_aff *pma, int pos);
3953 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3954 C<isl_pw_multi_aff_get_at>.
3956 These expressions can be replaced using the following function.
3958 #include <isl/aff.h>
3959 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3960 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3961 __isl_take isl_pw_aff *pa);
3963 Note that there is a difference between C<isl_multi_pw_aff> and
3964 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3965 affine expressions, while the second is a piecewise sequence
3966 of affine expressions. In particular, each of the piecewise
3967 affine expressions in an C<isl_multi_pw_aff> may have a different
3968 domain, while all multiple expressions associated to a cell
3969 in an C<isl_pw_multi_aff> have the same domain.
3970 It is possible to convert between the two, but when converting
3971 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3972 of the result is the intersection of the domains of the input.
3973 The reverse conversion is exact.
3975 #include <isl/aff.h>
3976 __isl_give isl_pw_multi_aff *
3977 isl_pw_multi_aff_from_multi_pw_aff(
3978 __isl_take isl_multi_pw_aff *mpa);
3979 __isl_give isl_multi_pw_aff *
3980 isl_pw_multi_aff_to_multi_pw_aff(
3981 __isl_take isl_pw_multi_aff *pma);
3982 __isl_give isl_multi_pw_aff *
3983 isl_multi_pw_aff_from_pw_multi_aff(
3984 __isl_take isl_pw_multi_aff *pma);
3986 C<isl_pw_multi_aff_to_multi_pw_aff> and
3987 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3989 =head3 Union Expressions
3991 A union expression collects base expressions defined
3992 over different domains. The space of a union expression
3993 is that of the shared parameter space.
3995 The union expression types defined by C<isl>
3996 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3997 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3999 C<isl_union_pw_aff>,
4000 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
4001 there can be at most one base expression for a given domain space.
4003 C<isl_union_pw_multi_aff>,
4004 there can be multiple such expressions for a given domain space,
4005 but the domains of these expressions need to be disjoint.
4007 An empty union expression can be created using the following functions.
4009 #include <isl/aff.h>
4010 __isl_give isl_union_pw_aff *
4011 isl_union_pw_aff_empty_ctx(
4013 __isl_give isl_union_pw_aff *
4014 isl_union_pw_aff_empty_space(
4015 __isl_take isl_space *space);
4016 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
4017 __isl_take isl_space *space);
4018 __isl_give isl_union_pw_multi_aff *
4019 isl_union_pw_multi_aff_empty_ctx(
4021 __isl_give isl_union_pw_multi_aff *
4022 isl_union_pw_multi_aff_empty_space(
4023 __isl_take isl_space *space);
4024 __isl_give isl_union_pw_multi_aff *
4025 isl_union_pw_multi_aff_empty(
4026 __isl_take isl_space *space);
4028 #include <isl/polynomial.h>
4029 __isl_give isl_union_pw_qpolynomial *
4030 isl_union_pw_qpolynomial_zero_ctx(
4032 __isl_give isl_union_pw_qpolynomial *
4033 isl_union_pw_qpolynomial_zero_space(
4034 __isl_take isl_space *space);
4035 __isl_give isl_union_pw_qpolynomial *
4036 isl_union_pw_qpolynomial_zero(
4037 __isl_take isl_space *space);
4039 C<isl_union_pw_aff_empty> is an alternative name for
4040 C<isl_union_pw_aff_empty_space>.
4041 Similarly for the other pairs of functions.
4043 A union expression containing a single base expression
4044 can be created using the following functions.
4046 #include <isl/aff.h>
4047 __isl_give isl_union_pw_aff *
4048 isl_pw_aff_to_union_pw_aff(
4049 __isl_take isl_pw_aff *pa);
4050 __isl_give isl_union_pw_aff *
4051 isl_union_pw_aff_from_pw_aff(
4052 __isl_take isl_pw_aff *pa);
4053 __isl_give isl_union_pw_multi_aff *
4054 isl_union_pw_multi_aff_from_aff(
4055 __isl_take isl_aff *aff);
4056 __isl_give isl_union_pw_multi_aff *
4057 isl_pw_multi_aff_to_union_pw_multi_aff(
4058 __isl_take isl_pw_multi_aff *pma);
4059 __isl_give isl_union_pw_multi_aff *
4060 isl_union_pw_multi_aff_from_pw_multi_aff(
4061 __isl_take isl_pw_multi_aff *pma);
4063 #include <isl/polynomial.h>
4064 __isl_give isl_union_pw_qpolynomial *
4065 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4066 __isl_take isl_pw_qpolynomial *pwqp);
4067 __isl_give isl_union_pw_qpolynomial *
4068 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4069 __isl_take isl_pw_qpolynomial *pwqp);
4070 __isl_give isl_union_pw_qpolynomial_fold *
4071 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4072 __isl_take isl_pw_qpolynomial_fold *pwf);
4073 __isl_give isl_union_pw_qpolynomial_fold *
4074 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4075 __isl_take isl_pw_qpolynomial_fold *pwf);
4077 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4079 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4080 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4082 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4083 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4085 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4086 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4088 The inverse conversions below can only be used if the input
4089 expression is known to live in exactly one space.
4091 #include <isl/aff.h>
4092 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4093 __isl_keep isl_union_pw_multi_aff *upma);
4094 __isl_give isl_pw_multi_aff *
4095 isl_union_pw_multi_aff_as_pw_multi_aff(
4096 __isl_take isl_union_pw_multi_aff *upma);
4098 A union piecewise expression containing a single base expression
4099 on a universe domain can also be created directly from
4100 a base expression using the following functions.
4102 #include <isl/aff.h>
4103 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4104 __isl_take isl_aff *aff);
4105 __isl_give isl_union_pw_multi_aff *
4106 isl_union_pw_multi_aff_from_multi_aff(
4107 __isl_take isl_multi_aff *ma);
4109 The following functions create a base expression on each
4110 of the sets in the union set and collect the results.
4112 #include <isl/aff.h>
4113 __isl_give isl_union_pw_multi_aff *
4114 isl_union_pw_multi_aff_from_union_pw_aff(
4115 __isl_take isl_union_pw_aff *upa);
4116 __isl_give isl_union_pw_aff *
4117 isl_union_pw_multi_aff_get_union_pw_aff(
4118 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4119 __isl_give isl_union_pw_aff *
4120 isl_union_pw_aff_val_on_domain(
4121 __isl_take isl_union_set *domain,
4122 __isl_take isl_val *v);
4123 __isl_give isl_union_pw_multi_aff *
4124 isl_union_pw_multi_aff_multi_val_on_domain(
4125 __isl_take isl_union_set *domain,
4126 __isl_take isl_multi_val *mv);
4127 __isl_give isl_union_pw_aff *
4128 isl_union_pw_aff_param_on_domain_id(
4129 __isl_take isl_union_set *domain,
4130 __isl_take isl_id *id);
4132 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4133 is the identifier of a parameter that may or may not already
4134 be present in C<domain>.
4136 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4138 expression on a given domain can be created using the following
4141 #include <isl/aff.h>
4142 __isl_give isl_union_pw_aff *
4143 isl_union_pw_aff_aff_on_domain(
4144 __isl_take isl_union_set *domain,
4145 __isl_take isl_aff *aff);
4146 __isl_give isl_union_pw_aff *
4147 isl_union_pw_aff_pw_aff_on_domain(
4148 __isl_take isl_union_set *domain,
4149 __isl_take isl_pw_aff *pa);
4151 A base expression can be added to a union expression using
4152 the following functions.
4154 #include <isl/aff.h>
4155 __isl_give isl_union_pw_aff *
4156 isl_union_pw_aff_add_pw_aff(
4157 __isl_take isl_union_pw_aff *upa,
4158 __isl_take isl_pw_aff *pa);
4159 __isl_give isl_union_pw_multi_aff *
4160 isl_union_pw_multi_aff_add_pw_multi_aff(
4161 __isl_take isl_union_pw_multi_aff *upma,
4162 __isl_take isl_pw_multi_aff *pma);
4164 #include <isl/polynomial.h>
4165 __isl_give isl_union_pw_qpolynomial *
4166 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4167 __isl_take isl_union_pw_qpolynomial *upwqp,
4168 __isl_take isl_pw_qpolynomial *pwqp);
4170 Union expressions can be copied and freed using
4171 the following functions.
4173 #include <isl/aff.h>
4174 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4175 __isl_keep isl_union_pw_aff *upa);
4176 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4177 __isl_take isl_union_pw_aff *upa);
4178 __isl_give isl_union_pw_multi_aff *
4179 isl_union_pw_multi_aff_copy(
4180 __isl_keep isl_union_pw_multi_aff *upma);
4181 __isl_null isl_union_pw_multi_aff *
4182 isl_union_pw_multi_aff_free(
4183 __isl_take isl_union_pw_multi_aff *upma);
4185 #include <isl/polynomial.h>
4186 __isl_give isl_union_pw_qpolynomial *
4187 isl_union_pw_qpolynomial_copy(
4188 __isl_keep isl_union_pw_qpolynomial *upwqp);
4189 __isl_null isl_union_pw_qpolynomial *
4190 isl_union_pw_qpolynomial_free(
4191 __isl_take isl_union_pw_qpolynomial *upwqp);
4192 __isl_give isl_union_pw_qpolynomial_fold *
4193 isl_union_pw_qpolynomial_fold_copy(
4194 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4195 __isl_null isl_union_pw_qpolynomial_fold *
4196 isl_union_pw_qpolynomial_fold_free(
4197 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4199 To iterate over the base expressions in a union expression,
4200 use the following functions.
4202 #include <isl/aff.h>
4203 isl_size isl_union_pw_aff_n_pw_aff(
4204 __isl_keep isl_union_pw_aff *upa);
4205 isl_stat isl_union_pw_aff_foreach_pw_aff(
4206 __isl_keep isl_union_pw_aff *upa,
4207 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4208 void *user), void *user);
4209 isl_bool isl_union_pw_aff_every_pw_aff(
4210 __isl_keep isl_union_pw_aff *upa,
4211 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4212 void *user), void *user);
4213 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4214 __isl_keep isl_union_pw_multi_aff *upma);
4215 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4216 __isl_keep isl_union_pw_multi_aff *upma,
4217 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4218 void *user), void *user);
4219 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4220 __isl_keep isl_union_pw_multi_aff *upma,
4222 __isl_keep isl_pw_multi_aff *pma,
4223 void *user), void *user);
4225 #include <isl/polynomial.h>
4226 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4227 __isl_keep isl_union_pw_qpolynomial *upwqp);
4228 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4229 __isl_keep isl_union_pw_qpolynomial *upwqp,
4230 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4231 void *user), void *user);
4232 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4233 __isl_keep isl_union_pw_qpolynomial *upwqp,
4235 __isl_keep isl_pw_qpolynomial *pwqp,
4236 void *user), void *user);
4237 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4238 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4239 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4240 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4241 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4242 void *user), void *user);
4244 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4245 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4247 __isl_keep isl_pw_qpolynomial_fold *pwf,
4248 void *user), void *user);
4250 To extract the base expression in a given space from a union, use
4251 the following functions.
4253 #include <isl/aff.h>
4254 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4255 __isl_keep isl_union_pw_aff *upa,
4256 __isl_take isl_space *space);
4257 __isl_give isl_pw_multi_aff *
4258 isl_union_pw_multi_aff_extract_pw_multi_aff(
4259 __isl_keep isl_union_pw_multi_aff *upma,
4260 __isl_take isl_space *space);
4262 #include <isl/polynomial.h>
4263 __isl_give isl_pw_qpolynomial *
4264 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4265 __isl_keep isl_union_pw_qpolynomial *upwqp,
4266 __isl_take isl_space *space);
4268 It is also possible to obtain a list of the base expressions using
4269 the following functions.
4271 #include <isl/aff.h>
4272 __isl_give isl_pw_aff_list *
4273 isl_union_pw_aff_get_pw_aff_list(
4274 __isl_keep isl_union_pw_aff *upa);
4275 __isl_give isl_pw_multi_aff_list *
4276 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4277 __isl_keep isl_union_pw_multi_aff *upma);
4279 #include <isl/polynomial.h>
4280 __isl_give isl_pw_qpolynomial_list *
4281 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4282 __isl_keep isl_union_pw_qpolynomial *upwqp);
4283 __isl_give isl_pw_qpolynomial_fold_list *
4284 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4285 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4287 The returned list can be manipulated using the functions in L<"Lists">.
4289 =head2 Input and Output
4291 For set and relation,
4292 C<isl> supports its own input/output format, which is similar
4293 to the C<Omega> format, but also supports the C<PolyLib> format
4295 For other object types, typically only an C<isl> format is supported.
4297 =head3 C<isl> format
4299 The C<isl> format is similar to that of C<Omega>, but has a different
4300 syntax for describing the parameters and allows for the definition
4301 of an existentially quantified variable as the integer division
4302 of an affine expression.
4303 For example, the set of integers C<i> between C<0> and C<n>
4304 such that C<i % 10 <= 6> can be described as
4306 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4309 A set or relation can have several disjuncts, separated
4310 by the keyword C<or>. Each disjunct is either a conjunction
4311 of constraints or a projection (C<exists>) of a conjunction
4312 of constraints. The constraints are separated by the keyword
4315 =head3 C<PolyLib> format
4317 If the represented set is a union, then the first line
4318 contains a single number representing the number of disjuncts.
4319 Otherwise, a line containing the number C<1> is optional.
4321 Each disjunct is represented by a matrix of constraints.
4322 The first line contains two numbers representing
4323 the number of rows and columns,
4324 where the number of rows is equal to the number of constraints
4325 and the number of columns is equal to two plus the number of variables.
4326 The following lines contain the actual rows of the constraint matrix.
4327 In each row, the first column indicates whether the constraint
4328 is an equality (C<0>) or inequality (C<1>). The final column
4329 corresponds to the constant term.
4331 If the set is parametric, then the coefficients of the parameters
4332 appear in the last columns before the constant column.
4333 The coefficients of any existentially quantified variables appear
4334 between those of the set variables and those of the parameters.
4336 =head3 Extended C<PolyLib> format
4338 The extended C<PolyLib> format is nearly identical to the
4339 C<PolyLib> format. The only difference is that the line
4340 containing the number of rows and columns of a constraint matrix
4341 also contains four additional numbers:
4342 the number of output dimensions, the number of input dimensions,
4343 the number of local dimensions (i.e., the number of existentially
4344 quantified variables) and the number of parameters.
4345 For sets, the number of ``output'' dimensions is equal
4346 to the number of set dimensions, while the number of ``input''
4351 Objects can be read from input using the following functions.
4354 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4356 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4357 isl_ctx *ctx, const char *str);
4359 #include <isl/val.h>
4360 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4362 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4363 isl_ctx *ctx, const char *str);
4365 #include <isl/space.h>
4366 __isl_give isl_space *isl_space_read_from_str(
4367 isl_ctx *ctx, const char *str);
4369 #include <isl/set.h>
4370 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4371 isl_ctx *ctx, FILE *input);
4372 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4373 isl_ctx *ctx, const char *str);
4374 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4376 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4379 #include <isl/map.h>
4380 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4381 isl_ctx *ctx, FILE *input);
4382 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4383 isl_ctx *ctx, const char *str);
4384 __isl_give isl_map *isl_map_read_from_file(
4385 isl_ctx *ctx, FILE *input);
4386 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4389 #include <isl/union_set.h>
4390 __isl_give isl_union_set *isl_union_set_read_from_file(
4391 isl_ctx *ctx, FILE *input);
4392 __isl_give isl_union_set *isl_union_set_read_from_str(
4393 isl_ctx *ctx, const char *str);
4395 #include <isl/union_map.h>
4396 __isl_give isl_union_map *isl_union_map_read_from_file(
4397 isl_ctx *ctx, FILE *input);
4398 __isl_give isl_union_map *isl_union_map_read_from_str(
4399 isl_ctx *ctx, const char *str);
4401 #include <isl/aff.h>
4402 __isl_give isl_aff *isl_aff_read_from_str(
4403 isl_ctx *ctx, const char *str);
4404 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4405 isl_ctx *ctx, const char *str);
4406 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4407 isl_ctx *ctx, const char *str);
4408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4409 isl_ctx *ctx, const char *str);
4410 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4411 isl_ctx *ctx, const char *str);
4412 __isl_give isl_union_pw_aff *
4413 isl_union_pw_aff_read_from_str(
4414 isl_ctx *ctx, const char *str);
4415 __isl_give isl_union_pw_multi_aff *
4416 isl_union_pw_multi_aff_read_from_str(
4417 isl_ctx *ctx, const char *str);
4418 __isl_give isl_multi_union_pw_aff *
4419 isl_multi_union_pw_aff_read_from_str(
4420 isl_ctx *ctx, const char *str);
4422 #include <isl/polynomial.h>
4423 __isl_give isl_union_pw_qpolynomial *
4424 isl_union_pw_qpolynomial_read_from_str(
4425 isl_ctx *ctx, const char *str);
4427 __isl_give isl_pw_qpolynomial_fold *
4428 isl_pw_qpolynomial_fold_read_from_str(
4429 isl_ctx *ctx, const char *str);
4431 For sets and relations,
4432 the input format is autodetected and may be either the C<PolyLib> format
4433 or the C<isl> format.
4437 Before anything can be printed, an C<isl_printer> needs to
4440 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4442 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4443 __isl_null isl_printer *isl_printer_free(
4444 __isl_take isl_printer *printer);
4446 C<isl_printer_to_file> prints to the given file, while
4447 C<isl_printer_to_str> prints to a string that can be extracted
4448 using the following function.
4450 #include <isl/printer.h>
4451 __isl_give char *isl_printer_get_str(
4452 __isl_keep isl_printer *printer);
4454 The printer can be inspected using the following functions.
4456 FILE *isl_printer_get_file(
4457 __isl_keep isl_printer *printer);
4458 int isl_printer_get_output_format(
4459 __isl_keep isl_printer *p);
4460 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4462 The behavior of the printer can be modified in various ways
4464 __isl_give isl_printer *isl_printer_set_output_format(
4465 __isl_take isl_printer *p, int output_format);
4466 __isl_give isl_printer *isl_printer_set_indent(
4467 __isl_take isl_printer *p, int indent);
4468 __isl_give isl_printer *isl_printer_set_indent_prefix(
4469 __isl_take isl_printer *p, const char *prefix);
4470 __isl_give isl_printer *isl_printer_indent(
4471 __isl_take isl_printer *p, int indent);
4472 __isl_give isl_printer *isl_printer_set_prefix(
4473 __isl_take isl_printer *p, const char *prefix);
4474 __isl_give isl_printer *isl_printer_set_suffix(
4475 __isl_take isl_printer *p, const char *suffix);
4476 __isl_give isl_printer *isl_printer_set_yaml_style(
4477 __isl_take isl_printer *p, int yaml_style);
4479 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4480 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4481 and defaults to C<ISL_FORMAT_ISL>.
4482 Each line in the output is prefixed by C<indent_prefix>,
4483 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4484 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4485 In the C<PolyLib> format output,
4486 the coefficients of the existentially quantified variables
4487 appear between those of the set variables and those
4489 The function C<isl_printer_indent> increases the indentation
4490 by the specified amount (which may be negative).
4491 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4492 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4495 To actually print something, use
4497 #include <isl/printer.h>
4498 __isl_give isl_printer *isl_printer_print_double(
4499 __isl_take isl_printer *p, double d);
4501 #include <isl/val.h>
4502 __isl_give isl_printer *isl_printer_print_val(
4503 __isl_take isl_printer *p, __isl_keep isl_val *v);
4504 __isl_give isl_printer *isl_printer_print_multi_val(
4505 __isl_take isl_printer *p,
4506 __isl_keep isl_multi_val *mv);
4508 #include <isl/set.h>
4509 __isl_give isl_printer *isl_printer_print_basic_set(
4510 __isl_take isl_printer *printer,
4511 __isl_keep isl_basic_set *bset);
4512 __isl_give isl_printer *isl_printer_print_set(
4513 __isl_take isl_printer *printer,
4514 __isl_keep isl_set *set);
4516 #include <isl/map.h>
4517 __isl_give isl_printer *isl_printer_print_basic_map(
4518 __isl_take isl_printer *printer,
4519 __isl_keep isl_basic_map *bmap);
4520 __isl_give isl_printer *isl_printer_print_map(
4521 __isl_take isl_printer *printer,
4522 __isl_keep isl_map *map);
4524 #include <isl/union_set.h>
4525 __isl_give isl_printer *isl_printer_print_union_set(
4526 __isl_take isl_printer *p,
4527 __isl_keep isl_union_set *uset);
4529 #include <isl/union_map.h>
4530 __isl_give isl_printer *isl_printer_print_union_map(
4531 __isl_take isl_printer *p,
4532 __isl_keep isl_union_map *umap);
4535 __isl_give isl_printer *isl_printer_print_multi_id(
4536 __isl_take isl_printer *p,
4537 __isl_keep isl_multi_id *mi);
4539 #include <isl/aff.h>
4540 __isl_give isl_printer *isl_printer_print_aff(
4541 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4542 __isl_give isl_printer *isl_printer_print_multi_aff(
4543 __isl_take isl_printer *p,
4544 __isl_keep isl_multi_aff *maff);
4545 __isl_give isl_printer *isl_printer_print_pw_aff(
4546 __isl_take isl_printer *p,
4547 __isl_keep isl_pw_aff *pwaff);
4548 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4549 __isl_take isl_printer *p,
4550 __isl_keep isl_pw_multi_aff *pma);
4551 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4552 __isl_take isl_printer *p,
4553 __isl_keep isl_multi_pw_aff *mpa);
4554 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4555 __isl_take isl_printer *p,
4556 __isl_keep isl_union_pw_aff *upa);
4557 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_union_pw_multi_aff *upma);
4560 __isl_give isl_printer *
4561 isl_printer_print_multi_union_pw_aff(
4562 __isl_take isl_printer *p,
4563 __isl_keep isl_multi_union_pw_aff *mupa);
4565 #include <isl/polynomial.h>
4566 __isl_give isl_printer *isl_printer_print_qpolynomial(
4567 __isl_take isl_printer *p,
4568 __isl_keep isl_qpolynomial *qp);
4569 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4570 __isl_take isl_printer *p,
4571 __isl_keep isl_pw_qpolynomial *pwqp);
4572 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4573 __isl_take isl_printer *p,
4574 __isl_keep isl_union_pw_qpolynomial *upwqp);
4576 __isl_give isl_printer *
4577 isl_printer_print_pw_qpolynomial_fold(
4578 __isl_take isl_printer *p,
4579 __isl_keep isl_pw_qpolynomial_fold *pwf);
4580 __isl_give isl_printer *
4581 isl_printer_print_union_pw_qpolynomial_fold(
4582 __isl_take isl_printer *p,
4583 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4585 For C<isl_printer_print_qpolynomial>,
4586 C<isl_printer_print_pw_qpolynomial> and
4587 C<isl_printer_print_pw_qpolynomial_fold>,
4588 the output format of the printer
4589 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4590 For C<isl_printer_print_union_pw_qpolynomial> and
4591 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4593 In case of printing in C<ISL_FORMAT_C>, the user may want
4594 to set the names of all dimensions first.
4596 C<isl> also provides limited support for printing YAML documents,
4597 just enough for the internal use for printing such documents.
4599 #include <isl/printer.h>
4600 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4601 __isl_take isl_printer *p);
4602 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4603 __isl_take isl_printer *p);
4604 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4605 __isl_take isl_printer *p);
4606 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4607 __isl_take isl_printer *p);
4608 __isl_give isl_printer *isl_printer_yaml_next(
4609 __isl_take isl_printer *p);
4611 A document is started by a call to either
4612 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4613 Anything printed to the printer after such a call belong to the
4614 first key of the mapping or the first element in the sequence.
4615 The function C<isl_printer_yaml_next> moves to the value if
4616 we are currently printing a mapping key, the next key if we
4617 are printing a value or the next element if we are printing
4618 an element in a sequence.
4619 Nested mappings and sequences are initiated by the same
4620 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4621 Each call to these functions needs to have a corresponding call to
4622 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4624 When called on a file printer, the following function flushes
4625 the file. When called on a string printer, the buffer is cleared.
4627 __isl_give isl_printer *isl_printer_flush(
4628 __isl_take isl_printer *p);
4630 The following functions allow the user to attach
4631 notes to a printer in order to keep track of additional state.
4633 #include <isl/printer.h>
4634 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4635 __isl_keep isl_id *id);
4636 __isl_give isl_id *isl_printer_get_note(
4637 __isl_keep isl_printer *p, __isl_take isl_id *id);
4638 __isl_give isl_printer *isl_printer_set_note(
4639 __isl_take isl_printer *p,
4640 __isl_take isl_id *id, __isl_take isl_id *note);
4642 C<isl_printer_set_note> associates the given note to the given
4643 identifier in the printer.
4644 C<isl_printer_get_note> retrieves a note associated to an
4646 C<isl_printer_has_note> checks if there is such a note.
4647 C<isl_printer_get_note> fails if the requested note does not exist.
4649 Alternatively, a string representation can be obtained
4650 directly using the following functions, which always print
4654 __isl_give char *isl_id_to_str(
4655 __isl_keep isl_id *id);
4656 __isl_give char *isl_multi_id_to_str(
4657 __isl_keep isl_multi_id *mi);
4659 #include <isl/space.h>
4660 __isl_give char *isl_space_to_str(
4661 __isl_keep isl_space *space);
4663 #include <isl/val.h>
4664 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4665 __isl_give char *isl_multi_val_to_str(
4666 __isl_keep isl_multi_val *mv);
4668 #include <isl/set.h>
4669 __isl_give char *isl_basic_set_to_str(
4670 __isl_keep isl_basic_set *bset);
4671 __isl_give char *isl_set_to_str(
4672 __isl_keep isl_set *set);
4674 #include <isl/union_set.h>
4675 __isl_give char *isl_union_set_to_str(
4676 __isl_keep isl_union_set *uset);
4678 #include <isl/map.h>
4679 __isl_give char *isl_basic_map_to_str(
4680 __isl_keep isl_basic_map *bmap);
4681 __isl_give char *isl_map_to_str(
4682 __isl_keep isl_map *map);
4684 #include <isl/union_map.h>
4685 __isl_give char *isl_union_map_to_str(
4686 __isl_keep isl_union_map *umap);
4688 #include <isl/aff.h>
4689 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4690 __isl_give char *isl_pw_aff_to_str(
4691 __isl_keep isl_pw_aff *pa);
4692 __isl_give char *isl_multi_aff_to_str(
4693 __isl_keep isl_multi_aff *ma);
4694 __isl_give char *isl_pw_multi_aff_to_str(
4695 __isl_keep isl_pw_multi_aff *pma);
4696 __isl_give char *isl_multi_pw_aff_to_str(
4697 __isl_keep isl_multi_pw_aff *mpa);
4698 __isl_give char *isl_union_pw_aff_to_str(
4699 __isl_keep isl_union_pw_aff *upa);
4700 __isl_give char *isl_union_pw_multi_aff_to_str(
4701 __isl_keep isl_union_pw_multi_aff *upma);
4702 __isl_give char *isl_multi_union_pw_aff_to_str(
4703 __isl_keep isl_multi_union_pw_aff *mupa);
4705 #include <isl/point.h>
4706 __isl_give char *isl_point_to_str(
4707 __isl_keep isl_point *pnt);
4709 #include <isl/polynomial.h>
4710 __isl_give char *isl_pw_qpolynomial_to_str(
4711 __isl_keep isl_pw_qpolynomial *pwqp);
4712 __isl_give char *isl_union_pw_qpolynomial_to_str(
4713 __isl_keep isl_union_pw_qpolynomial *upwqp);
4717 =head3 Unary Properties
4723 The following functions test whether the given set or relation
4724 contains any integer points. The ``plain'' variants do not perform
4725 any computations, but simply check if the given set or relation
4726 is already known to be empty.
4728 #include <isl/set.h>
4729 isl_bool isl_basic_set_plain_is_empty(
4730 __isl_keep isl_basic_set *bset);
4731 isl_bool isl_basic_set_is_empty(
4732 __isl_keep isl_basic_set *bset);
4733 isl_bool isl_set_plain_is_empty(
4734 __isl_keep isl_set *set);
4735 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4737 #include <isl/union_set.h>
4738 isl_bool isl_union_set_is_empty(
4739 __isl_keep isl_union_set *uset);
4741 #include <isl/map.h>
4742 isl_bool isl_basic_map_plain_is_empty(
4743 __isl_keep isl_basic_map *bmap);
4744 isl_bool isl_basic_map_is_empty(
4745 __isl_keep isl_basic_map *bmap);
4746 isl_bool isl_map_plain_is_empty(
4747 __isl_keep isl_map *map);
4748 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4750 #include <isl/union_map.h>
4751 isl_bool isl_union_map_plain_is_empty(
4752 __isl_keep isl_union_map *umap);
4753 isl_bool isl_union_map_is_empty(
4754 __isl_keep isl_union_map *umap);
4756 #include <isl/aff.h>
4757 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4758 __isl_keep isl_union_pw_multi_aff *upma);
4760 =item * Universality
4762 isl_bool isl_basic_set_plain_is_universe(
4763 __isl_keep isl_basic_set *bset);
4764 isl_bool isl_basic_set_is_universe(
4765 __isl_keep isl_basic_set *bset);
4766 isl_bool isl_basic_map_plain_is_universe(
4767 __isl_keep isl_basic_map *bmap);
4768 isl_bool isl_basic_map_is_universe(
4769 __isl_keep isl_basic_map *bmap);
4770 isl_bool isl_set_plain_is_universe(
4771 __isl_keep isl_set *set);
4772 isl_bool isl_map_plain_is_universe(
4773 __isl_keep isl_map *map);
4775 =item * Single-valuedness
4777 #include <isl/set.h>
4778 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4780 #include <isl/map.h>
4781 isl_bool isl_basic_map_is_single_valued(
4782 __isl_keep isl_basic_map *bmap);
4783 isl_bool isl_map_plain_is_single_valued(
4784 __isl_keep isl_map *map);
4785 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4787 #include <isl/union_map.h>
4788 isl_bool isl_union_map_is_single_valued(
4789 __isl_keep isl_union_map *umap);
4793 isl_bool isl_map_plain_is_injective(
4794 __isl_keep isl_map *map);
4795 isl_bool isl_map_is_injective(
4796 __isl_keep isl_map *map);
4797 isl_bool isl_union_map_plain_is_injective(
4798 __isl_keep isl_union_map *umap);
4799 isl_bool isl_union_map_is_injective(
4800 __isl_keep isl_union_map *umap);
4804 isl_bool isl_map_is_bijective(
4805 __isl_keep isl_map *map);
4806 isl_bool isl_union_map_is_bijective(
4807 __isl_keep isl_union_map *umap);
4811 The following functions test whether the given relation
4812 only maps elements to themselves.
4814 #include <isl/map.h>
4815 isl_bool isl_map_is_identity(
4816 __isl_keep isl_map *map);
4818 #include <isl/union_map.h>
4819 isl_bool isl_union_map_is_identity(
4820 __isl_keep isl_union_map *umap);
4824 __isl_give isl_val *
4825 isl_basic_map_plain_get_val_if_fixed(
4826 __isl_keep isl_basic_map *bmap,
4827 enum isl_dim_type type, unsigned pos);
4828 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4829 __isl_keep isl_set *set,
4830 enum isl_dim_type type, unsigned pos);
4831 __isl_give isl_multi_val *
4832 isl_set_get_plain_multi_val_if_fixed(
4833 __isl_keep isl_set *set);
4834 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4835 __isl_keep isl_map *map,
4836 enum isl_dim_type type, unsigned pos);
4838 If the set or relation obviously lies on a hyperplane where the given dimension
4839 has a fixed value, then return that value.
4840 Otherwise return NaN.
4841 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4846 Stride detection is based on heuristics.
4847 The strides returned by the functions below are always valid,
4848 but there may be larger valid strides that are not detected.
4850 isl_stat isl_set_dim_residue_class_val(
4851 __isl_keep isl_set *set,
4852 int pos, __isl_give isl_val **modulo,
4853 __isl_give isl_val **residue);
4855 Check if the values of the given set dimension are equal to a fixed
4856 value modulo some integer value. If so, assign the modulo to C<*modulo>
4857 and the fixed value to C<*residue>. If the given dimension attains only
4858 a single value, then assign C<0> to C<*modulo> and the fixed value to
4860 If the dimension does not attain only a single value and if no modulo
4861 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4863 #include <isl/set.h>
4864 __isl_give isl_stride_info *isl_set_get_stride_info(
4865 __isl_keep isl_set *set, int pos);
4866 __isl_give isl_val *isl_set_get_stride(
4867 __isl_keep isl_set *set, int pos);
4868 __isl_give isl_fixed_box *isl_set_get_lattice_tile(
4869 __isl_keep isl_set *set);
4871 #include <isl/map.h>
4872 __isl_give isl_stride_info *
4873 isl_map_get_range_stride_info(
4874 __isl_keep isl_map *map, int pos);
4875 __isl_give isl_fixed_box *
4876 isl_map_get_range_lattice_tile(
4877 __isl_keep isl_map *map);
4879 Check if the values of the given set dimension are equal to
4880 some affine expression of the other dimensions (the offset)
4881 modulo some integer stride or
4882 check if the values of the given output dimensions are equal to
4883 some affine expression of the input dimensions (the offset)
4884 modulo some integer stride.
4885 If no more specific information can be found, then the stride
4886 is taken to be one and the offset is taken to be the zero expression.
4887 The function C<isl_set_get_stride> performs the same
4888 computation as C<isl_set_get_stride_info> but only returns the stride.
4889 The function C<isl_map_get_range_lattice_tile> collects the stride
4890 information over all output dimensions.
4891 In particular, it returns a tile of a rectangular lattice
4892 (possibly of size 1 in all directions)
4893 containing the output in terms of the parameters and the input dimensions.
4894 The size and the offset of this tile correspond to
4895 the strides and the offsets of the stride information and
4896 can be extracted from the returned
4897 C<isl_fixed_box> using the functions described under "Box hull" in
4898 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4899 C<isl_map_get_range_lattice_tile> is always valid.
4900 The function C<isl_set_get_lattice_tile> collects the same stride
4901 information over all set dimensions.
4902 For the other functions,
4903 the stride and offset can be extracted from the returned object
4904 using the following functions.
4906 #include <isl/stride_info.h>
4907 __isl_give isl_val *isl_stride_info_get_stride(
4908 __isl_keep isl_stride_info *si);
4909 __isl_give isl_aff *isl_stride_info_get_offset(
4910 __isl_keep isl_stride_info *si);
4912 The stride info object can be copied and released using the following
4915 #include <isl/stride_info.h>
4916 __isl_give isl_stride_info *isl_stride_info_copy(
4917 __isl_keep isl_stride_info *si);
4918 __isl_null isl_stride_info *isl_stride_info_free(
4919 __isl_take isl_stride_info *si);
4923 To check whether a function involves any local variables,
4924 i.e., integer divisions,
4925 the following functions can be used.
4927 #include <isl/set.h>
4928 isl_bool isl_set_involves_locals(
4929 __isl_keep isl_set *set);
4931 #include <isl/aff.h>
4932 isl_bool isl_aff_involves_locals(
4933 __isl_keep isl_aff *aff);
4934 isl_bool isl_multi_aff_involves_locals(
4935 __isl_keep isl_multi_aff *ma);
4936 isl_bool isl_pw_multi_aff_involves_locals(
4937 __isl_keep isl_pw_multi_aff *pma);
4938 isl_bool isl_union_pw_multi_aff_involves_locals(
4939 __isl_keep isl_union_pw_multi_aff *upma);
4941 To check whether the description of a set, relation or function depends
4942 on a parameter or one or more given dimensions,
4943 the following functions can be used.
4945 #include <isl/constraint.h>
4946 isl_bool isl_constraint_involves_dims(
4947 __isl_keep isl_constraint *constraint,
4948 enum isl_dim_type type, unsigned first, unsigned n);
4950 #include <isl/set.h>
4951 isl_bool isl_basic_set_involves_dims(
4952 __isl_keep isl_basic_set *bset,
4953 enum isl_dim_type type, unsigned first, unsigned n);
4954 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4955 enum isl_dim_type type, unsigned first, unsigned n);
4957 #include <isl/map.h>
4958 isl_bool isl_basic_map_involves_dims(
4959 __isl_keep isl_basic_map *bmap,
4960 enum isl_dim_type type, unsigned first, unsigned n);
4961 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4962 enum isl_dim_type type, unsigned first, unsigned n);
4964 #include <isl/union_map.h>
4965 isl_bool isl_union_map_involves_dims(
4966 __isl_keep isl_union_map *umap,
4967 enum isl_dim_type type, unsigned first, unsigned n);
4969 #include <isl/aff.h>
4970 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4971 enum isl_dim_type type, unsigned first, unsigned n);
4972 isl_bool isl_pw_aff_involves_param_id(
4973 __isl_keep isl_pw_aff *pa,
4974 __isl_keep isl_id *id);
4975 isl_bool isl_pw_aff_involves_dims(
4976 __isl_keep isl_pw_aff *pwaff,
4977 enum isl_dim_type type, unsigned first, unsigned n);
4978 isl_bool isl_multi_aff_involves_dims(
4979 __isl_keep isl_multi_aff *ma,
4980 enum isl_dim_type type, unsigned first, unsigned n);
4981 isl_bool isl_pw_multi_aff_involves_param_id(
4982 __isl_keep isl_pw_multi_aff *pma,
4983 __isl_keep isl_id *id);
4984 isl_bool isl_pw_multi_aff_involves_dims(
4985 __isl_keep isl_pw_multi_aff *pma,
4986 enum isl_dim_type type, unsigned first, unsigned n);
4987 isl_bool isl_multi_pw_aff_involves_dims(
4988 __isl_keep isl_multi_pw_aff *mpa,
4989 enum isl_dim_type type, unsigned first, unsigned n);
4990 isl_bool isl_multi_pw_aff_involves_param_id(
4991 __isl_keep isl_multi_pw_aff *mpa,
4992 __isl_keep isl_id *id);
4993 isl_bool isl_multi_pw_aff_involves_param_id_list(
4994 __isl_keep isl_multi_pw_aff *mpa,
4995 __isl_keep isl_id_list *list);
4997 #include <isl/polynomial.h>
4998 isl_bool isl_qpolynomial_involves_dims(
4999 __isl_keep isl_qpolynomial *qp,
5000 enum isl_dim_type type, unsigned first, unsigned n);
5001 isl_bool isl_pw_qpolynomial_involves_param_id(
5002 __isl_keep isl_pw_qpolynomial *pwqp,
5003 __isl_keep isl_id *id);
5004 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
5005 __isl_keep isl_pw_qpolynomial_fold *pwf,
5006 __isl_keep isl_id *id);
5008 Similarly, the following functions can be used to check whether
5009 a given dimension is involved in any lower or upper bound.
5011 #include <isl/set.h>
5012 isl_bool isl_set_dim_has_any_lower_bound(
5013 __isl_keep isl_set *set,
5014 enum isl_dim_type type, unsigned pos);
5015 isl_bool isl_set_dim_has_any_upper_bound(
5016 __isl_keep isl_set *set,
5017 enum isl_dim_type type, unsigned pos);
5019 Note that these functions return true even if there is a bound on
5020 the dimension on only some of the basic sets of C<set>.
5021 To check if they have a bound for all of the basic sets in C<set>,
5022 use the following functions instead.
5024 #include <isl/set.h>
5025 isl_bool isl_set_dim_has_lower_bound(
5026 __isl_keep isl_set *set,
5027 enum isl_dim_type type, unsigned pos);
5028 isl_bool isl_set_dim_has_upper_bound(
5029 __isl_keep isl_set *set,
5030 enum isl_dim_type type, unsigned pos);
5034 To check whether a set is a parameter domain, use this function:
5036 isl_bool isl_set_is_params(__isl_keep isl_set *set);
5037 isl_bool isl_union_set_is_params(
5038 __isl_keep isl_union_set *uset);
5042 The following functions check whether the space of the given
5043 (basic) set or relation domain and/or range is a wrapped relation.
5045 #include <isl/space.h>
5046 isl_bool isl_space_is_wrapping(
5047 __isl_keep isl_space *space);
5048 isl_bool isl_space_domain_is_wrapping(
5049 __isl_keep isl_space *space);
5050 isl_bool isl_space_range_is_wrapping(
5051 __isl_keep isl_space *space);
5052 isl_bool isl_space_is_product(
5053 __isl_keep isl_space *space);
5055 #include <isl/set.h>
5056 isl_bool isl_basic_set_is_wrapping(
5057 __isl_keep isl_basic_set *bset);
5058 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
5060 #include <isl/map.h>
5061 isl_bool isl_map_domain_is_wrapping(
5062 __isl_keep isl_map *map);
5063 isl_bool isl_map_range_is_wrapping(
5064 __isl_keep isl_map *map);
5065 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5068 isl_bool isl_multi_id_range_is_wrapping(
5069 __isl_keep isl_multi_id *mi);
5071 #include <isl/val.h>
5072 isl_bool isl_multi_val_range_is_wrapping(
5073 __isl_keep isl_multi_val *mv);
5075 #include <isl/aff.h>
5076 isl_bool isl_multi_aff_range_is_wrapping(
5077 __isl_keep isl_multi_aff *ma);
5078 isl_bool isl_multi_pw_aff_range_is_wrapping(
5079 __isl_keep isl_multi_pw_aff *mpa);
5080 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5081 __isl_keep isl_multi_union_pw_aff *mupa);
5083 The input to C<isl_space_is_wrapping> should
5084 be the space of a set, while that of
5085 C<isl_space_domain_is_wrapping> and
5086 C<isl_space_range_is_wrapping> should be the space of a relation.
5087 The input to C<isl_space_is_product> can be either the space
5088 of a set or that of a binary relation.
5089 In case the input is the space of a binary relation, it checks
5090 whether both domain and range are wrapping.
5092 =item * Internal Product
5094 isl_bool isl_basic_map_can_zip(
5095 __isl_keep isl_basic_map *bmap);
5096 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5098 Check whether the product of domain and range of the given relation
5100 i.e., whether both domain and range are nested relations.
5104 #include <isl/space.h>
5105 isl_bool isl_space_can_curry(
5106 __isl_keep isl_space *space);
5108 #include <isl/map.h>
5109 isl_bool isl_basic_map_can_curry(
5110 __isl_keep isl_basic_map *bmap);
5111 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5113 Check whether the domain of the (basic) relation is a wrapped relation.
5115 #include <isl/space.h>
5116 isl_bool isl_space_can_uncurry(
5117 __isl_keep isl_space *space);
5119 #include <isl/map.h>
5120 isl_bool isl_basic_map_can_uncurry(
5121 __isl_keep isl_basic_map *bmap);
5122 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5124 Check whether the range of the (basic) relation is a wrapped relation.
5126 #include <isl/space.h>
5127 isl_bool isl_space_can_range_curry(
5128 __isl_keep isl_space *space);
5130 #include <isl/map.h>
5131 isl_bool isl_map_can_range_curry(
5132 __isl_keep isl_map *map);
5134 Check whether the domain of the relation wrapped in the range of
5135 the input is itself a wrapped relation.
5137 =item * Special Values
5139 #include <isl/aff.h>
5140 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5141 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5142 isl_bool isl_multi_pw_aff_is_cst(
5143 __isl_keep isl_multi_pw_aff *mpa);
5145 Check whether the given expression is a constant.
5147 #include <isl/val.h>
5148 isl_bool isl_multi_val_involves_nan(
5149 __isl_keep isl_multi_val *mv);
5151 #include <isl/aff.h>
5152 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5153 isl_bool isl_multi_aff_involves_nan(
5154 __isl_keep isl_multi_aff *ma);
5155 isl_bool isl_pw_aff_involves_nan(
5156 __isl_keep isl_pw_aff *pa);
5157 isl_bool isl_pw_multi_aff_involves_nan(
5158 __isl_keep isl_pw_multi_aff *pma);
5159 isl_bool isl_multi_pw_aff_involves_nan(
5160 __isl_keep isl_multi_pw_aff *mpa);
5161 isl_bool isl_union_pw_aff_involves_nan(
5162 __isl_keep isl_union_pw_aff *upa);
5163 isl_bool isl_union_pw_multi_aff_involves_nan(
5164 __isl_keep isl_union_pw_multi_aff *upma);
5165 isl_bool isl_multi_union_pw_aff_involves_nan(
5166 __isl_keep isl_multi_union_pw_aff *mupa);
5168 #include <isl/polynomial.h>
5169 isl_bool isl_qpolynomial_is_nan(
5170 __isl_keep isl_qpolynomial *qp);
5171 isl_bool isl_qpolynomial_fold_is_nan(
5172 __isl_keep isl_qpolynomial_fold *fold);
5173 isl_bool isl_pw_qpolynomial_involves_nan(
5174 __isl_keep isl_pw_qpolynomial *pwqp);
5175 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5176 __isl_keep isl_pw_qpolynomial_fold *pwf);
5177 isl_bool isl_union_pw_qpolynomial_involves_nan(
5178 __isl_keep isl_union_pw_qpolynomial *upwqp);
5179 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5180 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5182 Check whether the given expression is equal to or involves NaN.
5184 #include <isl/val.h>
5185 isl_bool isl_multi_val_is_zero(
5186 __isl_keep isl_multi_val *mv);
5188 Check whether the multiple value is zero.
5190 #include <isl/aff.h>
5191 isl_bool isl_aff_plain_is_zero(
5192 __isl_keep isl_aff *aff);
5194 Check whether the affine expression is obviously zero.
5198 =head3 Binary Properties
5204 The following functions check whether two objects
5205 represent the same set, relation or function.
5206 The C<plain> variants only return true if the objects
5207 are obviously the same. That is, they may return false
5208 even if the objects are the same, but they will never
5209 return true if the objects are not the same.
5211 #include <isl/set.h>
5212 isl_bool isl_basic_set_plain_is_equal(
5213 __isl_keep isl_basic_set *bset1,
5214 __isl_keep isl_basic_set *bset2);
5215 isl_bool isl_basic_set_is_equal(
5216 __isl_keep isl_basic_set *bset1,
5217 __isl_keep isl_basic_set *bset2);
5218 isl_bool isl_set_plain_is_equal(
5219 __isl_keep isl_set *set1,
5220 __isl_keep isl_set *set2);
5221 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5222 __isl_keep isl_set *set2);
5224 #include <isl/map.h>
5225 isl_bool isl_basic_map_is_equal(
5226 __isl_keep isl_basic_map *bmap1,
5227 __isl_keep isl_basic_map *bmap2);
5228 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5229 __isl_keep isl_map *map2);
5230 isl_bool isl_map_plain_is_equal(
5231 __isl_keep isl_map *map1,
5232 __isl_keep isl_map *map2);
5234 #include <isl/union_set.h>
5235 isl_bool isl_union_set_is_equal(
5236 __isl_keep isl_union_set *uset1,
5237 __isl_keep isl_union_set *uset2);
5239 #include <isl/union_map.h>
5240 isl_bool isl_union_map_is_equal(
5241 __isl_keep isl_union_map *umap1,
5242 __isl_keep isl_union_map *umap2);
5245 isl_bool isl_multi_id_plain_is_equal(
5246 __isl_keep isl_multi_id *mi1,
5247 __isl_keep isl_multi_id *mi2);
5249 #include <isl/val.h>
5250 isl_bool isl_multi_val_plain_is_equal(
5251 __isl_keep isl_multi_val *mv1,
5252 __isl_keep isl_multi_val *mv2);
5254 #include <isl/aff.h>
5255 isl_bool isl_aff_plain_is_equal(
5256 __isl_keep isl_aff *aff1,
5257 __isl_keep isl_aff *aff2);
5258 isl_bool isl_multi_aff_plain_is_equal(
5259 __isl_keep isl_multi_aff *maff1,
5260 __isl_keep isl_multi_aff *maff2);
5261 isl_bool isl_pw_aff_plain_is_equal(
5262 __isl_keep isl_pw_aff *pwaff1,
5263 __isl_keep isl_pw_aff *pwaff2);
5264 isl_bool isl_pw_aff_is_equal(
5265 __isl_keep isl_pw_aff *pa1,
5266 __isl_keep isl_pw_aff *pa2);
5267 isl_bool isl_pw_multi_aff_plain_is_equal(
5268 __isl_keep isl_pw_multi_aff *pma1,
5269 __isl_keep isl_pw_multi_aff *pma2);
5270 isl_bool isl_pw_multi_aff_is_equal(
5271 __isl_keep isl_pw_multi_aff *pma1,
5272 __isl_keep isl_pw_multi_aff *pma2);
5273 isl_bool isl_multi_pw_aff_plain_is_equal(
5274 __isl_keep isl_multi_pw_aff *mpa1,
5275 __isl_keep isl_multi_pw_aff *mpa2);
5276 isl_bool isl_multi_pw_aff_is_equal(
5277 __isl_keep isl_multi_pw_aff *mpa1,
5278 __isl_keep isl_multi_pw_aff *mpa2);
5279 isl_bool isl_union_pw_aff_plain_is_equal(
5280 __isl_keep isl_union_pw_aff *upa1,
5281 __isl_keep isl_union_pw_aff *upa2);
5282 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5283 __isl_keep isl_union_pw_multi_aff *upma1,
5284 __isl_keep isl_union_pw_multi_aff *upma2);
5285 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5286 __isl_keep isl_multi_union_pw_aff *mupa1,
5287 __isl_keep isl_multi_union_pw_aff *mupa2);
5289 #include <isl/polynomial.h>
5290 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5291 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5292 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5293 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5294 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5295 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5297 =item * Disjointness
5299 #include <isl/set.h>
5300 isl_bool isl_basic_set_is_disjoint(
5301 __isl_keep isl_basic_set *bset1,
5302 __isl_keep isl_basic_set *bset2);
5303 isl_bool isl_set_plain_is_disjoint(
5304 __isl_keep isl_set *set1,
5305 __isl_keep isl_set *set2);
5306 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5307 __isl_keep isl_set *set2);
5309 #include <isl/map.h>
5310 isl_bool isl_basic_map_is_disjoint(
5311 __isl_keep isl_basic_map *bmap1,
5312 __isl_keep isl_basic_map *bmap2);
5313 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5314 __isl_keep isl_map *map2);
5316 #include <isl/union_set.h>
5317 isl_bool isl_union_set_is_disjoint(
5318 __isl_keep isl_union_set *uset1,
5319 __isl_keep isl_union_set *uset2);
5321 #include <isl/union_map.h>
5322 isl_bool isl_union_map_is_disjoint(
5323 __isl_keep isl_union_map *umap1,
5324 __isl_keep isl_union_map *umap2);
5328 isl_bool isl_basic_set_is_subset(
5329 __isl_keep isl_basic_set *bset1,
5330 __isl_keep isl_basic_set *bset2);
5331 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5332 __isl_keep isl_set *set2);
5333 isl_bool isl_set_is_strict_subset(
5334 __isl_keep isl_set *set1,
5335 __isl_keep isl_set *set2);
5336 isl_bool isl_union_set_is_subset(
5337 __isl_keep isl_union_set *uset1,
5338 __isl_keep isl_union_set *uset2);
5339 isl_bool isl_union_set_is_strict_subset(
5340 __isl_keep isl_union_set *uset1,
5341 __isl_keep isl_union_set *uset2);
5342 isl_bool isl_basic_map_is_subset(
5343 __isl_keep isl_basic_map *bmap1,
5344 __isl_keep isl_basic_map *bmap2);
5345 isl_bool isl_basic_map_is_strict_subset(
5346 __isl_keep isl_basic_map *bmap1,
5347 __isl_keep isl_basic_map *bmap2);
5348 isl_bool isl_map_is_subset(
5349 __isl_keep isl_map *map1,
5350 __isl_keep isl_map *map2);
5351 isl_bool isl_map_is_strict_subset(
5352 __isl_keep isl_map *map1,
5353 __isl_keep isl_map *map2);
5354 isl_bool isl_union_map_is_subset(
5355 __isl_keep isl_union_map *umap1,
5356 __isl_keep isl_union_map *umap2);
5357 isl_bool isl_union_map_is_strict_subset(
5358 __isl_keep isl_union_map *umap1,
5359 __isl_keep isl_union_map *umap2);
5361 Check whether the first argument is a (strict) subset of the
5366 Every comparison function returns a negative value if the first
5367 argument is considered smaller than the second, a positive value
5368 if the first argument is considered greater and zero if the two
5369 constraints are considered the same by the comparison criterion.
5371 #include <isl/constraint.h>
5372 int isl_constraint_plain_cmp(
5373 __isl_keep isl_constraint *c1,
5374 __isl_keep isl_constraint *c2);
5376 This function is useful for sorting C<isl_constraint>s.
5377 The order depends on the internal representation of the inputs.
5378 The order is fixed over different calls to the function (assuming
5379 the internal representation of the inputs has not changed), but may
5380 change over different versions of C<isl>.
5382 #include <isl/constraint.h>
5383 int isl_constraint_cmp_last_non_zero(
5384 __isl_keep isl_constraint *c1,
5385 __isl_keep isl_constraint *c2);
5387 This function can be used to sort constraints that live in the same
5388 local space. Constraints that involve ``earlier'' dimensions or
5389 that have a smaller coefficient for the shared latest dimension
5390 are considered smaller than other constraints.
5391 This function only defines a B<partial> order.
5393 #include <isl/set.h>
5394 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5395 __isl_keep isl_set *set2);
5397 This function is useful for sorting C<isl_set>s.
5398 The order depends on the internal representation of the inputs.
5399 The order is fixed over different calls to the function (assuming
5400 the internal representation of the inputs has not changed), but may
5401 change over different versions of C<isl>.
5403 #include <isl/aff.h>
5404 int isl_multi_aff_plain_cmp(
5405 __isl_keep isl_multi_aff *ma1,
5406 __isl_keep isl_multi_aff *ma2);
5407 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5408 __isl_keep isl_pw_aff *pa2);
5410 The functions C<isl_multi_aff_plain_cmp> and
5411 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5412 C<isl_pw_aff>s. The order is not strictly defined.
5413 The current order sorts expressions that only involve
5414 earlier dimensions before those that involve later dimensions.
5418 =head2 Unary Operations
5424 __isl_give isl_set *isl_set_complement(
5425 __isl_take isl_set *set);
5426 __isl_give isl_map *isl_map_complement(
5427 __isl_take isl_map *map);
5431 #include <isl/space.h>
5432 __isl_give isl_space *isl_space_reverse(
5433 __isl_take isl_space *space);
5434 __isl_give isl_space *isl_space_wrapped_reverse(
5435 __isl_take isl_space *space);
5436 __isl_give isl_space *isl_space_domain_reverse(
5437 __isl_take isl_space *space);
5438 __isl_give isl_space *isl_space_range_reverse(
5439 __isl_take isl_space *space);
5441 #include <isl/aff.h>
5442 __isl_give isl_aff *isl_aff_domain_reverse(
5443 __isl_take isl_aff *aff);
5444 __isl_give isl_multi_aff *
5445 isl_multi_aff_domain_reverse(
5446 __isl_take isl_multi_aff *ma);
5447 __isl_give isl_pw_aff *isl_pw_aff_domain_reverse(
5448 __isl_take isl_pw_aff *pa);
5449 __isl_give isl_pw_multi_aff *
5450 isl_pw_multi_aff_domain_reverse(
5451 __isl_take isl_pw_multi_aff *pma);
5452 __isl_give isl_multi_pw_aff *
5453 isl_multi_pw_aff_domain_reverse(
5454 __isl_take isl_multi_pw_aff *mpa);
5456 #include <isl/set.h>
5457 __isl_give isl_set *isl_set_wrapped_reverse(
5458 __isl_take isl_set *set);
5460 #include <isl/map.h>
5461 __isl_give isl_basic_map *isl_basic_map_reverse(
5462 __isl_take isl_basic_map *bmap);
5463 __isl_give isl_map *isl_map_reverse(
5464 __isl_take isl_map *map);
5465 __isl_give isl_map *isl_map_domain_reverse(
5466 __isl_take isl_map *map);
5467 __isl_give isl_map *isl_map_range_reverse(
5468 __isl_take isl_map *map);
5470 #include <isl/union_map.h>
5471 __isl_give isl_union_map *isl_union_map_reverse(
5472 __isl_take isl_union_map *umap);
5473 __isl_give isl_union_map *isl_union_map_domain_reverse(
5474 __isl_take isl_union_map *umap);
5475 __isl_give isl_union_map *isl_union_map_range_reverse(
5476 __isl_take isl_union_map *umap);
5478 #include <isl/polynomial.h>
5479 __isl_give isl_qpolynomial *
5480 isl_qpolynomial_domain_reverse(
5481 __isl_take isl_qpolynomial *qp);
5482 __isl_give isl_pw_qpolynomial *
5483 isl_pw_qpolynomial_domain_reverse(
5484 __isl_take isl_pw_qpolynomial *pwqp);
5485 __isl_give isl_union_pw_qpolynomial *
5486 isl_union_pw_qpolynomial_domain_reverse(
5487 __isl_take isl_union_pw_qpolynomial *upwqp);
5489 The function C<isl_space_range_reverse> reverses the relation
5490 that is embedded in the range of the input map space.
5491 The identifier of the range, if any, is only preserved
5492 if this embedded relation has identical input and output tuples.
5493 Similarly for C<isl_space_domain_reverse>.
5494 Along the same lines, C<isl_space_wrapped_reverse> reverses
5495 the relation that is embedded in a set space.
5497 =item * Tuple binding
5499 The following function binds
5500 a tuple to a sequence of parameter identifiers, equating
5501 the tuple dimensions to the parameters with those identifiers and
5502 subsequently projecting out the tuple.
5503 If the original object did not reference any such parameters,
5504 then this means that the tuple dimensions are reinterpreted
5506 The space of C<tuple> needs to match that of the bound tuple.
5508 #include <isl/set.h>
5509 __isl_give isl_set *isl_set_bind(
5510 __isl_take isl_set *set,
5511 __isl_take isl_multi_id *tuple);
5513 #include <isl/map.h>
5514 __isl_give isl_set *isl_map_bind_domain(
5515 __isl_take isl_map *map,
5516 __isl_take isl_multi_id *tuple);
5517 __isl_give isl_set *isl_map_bind_range(
5518 __isl_take isl_map *map,
5519 __isl_take isl_multi_id *tuple);
5521 #include <isl/union_map.h>
5522 __isl_give isl_union_set *isl_union_map_bind_range(
5523 __isl_take isl_union_map *umap,
5524 __isl_take isl_multi_id *tuple);
5526 #include <isl/aff.h>
5527 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5528 __isl_take isl_pw_aff *pa,
5529 __isl_take isl_multi_id *tuple);
5530 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5531 __isl_take isl_multi_aff *ma,
5532 __isl_take isl_multi_id *tuple);
5533 __isl_give isl_pw_multi_aff *
5534 isl_pw_multi_aff_bind_domain(
5535 __isl_take isl_pw_multi_aff *pma,
5536 __isl_take isl_multi_id *tuple);
5537 __isl_give isl_multi_pw_aff *
5538 isl_multi_pw_aff_bind_domain(
5539 __isl_take isl_multi_pw_aff *mpa,
5540 __isl_take isl_multi_id *tuple);
5541 __isl_give isl_pw_aff *
5542 isl_pw_aff_bind_domain_wrapped_domain(
5543 __isl_take isl_pw_aff *pa,
5544 __isl_take isl_multi_id *tuple);
5545 __isl_give isl_multi_aff *
5546 isl_multi_aff_bind_domain_wrapped_domain(
5547 __isl_take isl_multi_aff *ma,
5548 __isl_take isl_multi_id *tuple);
5549 __isl_give isl_pw_multi_aff *
5550 isl_pw_multi_aff_bind_domain_wrapped_domain(
5551 __isl_take isl_pw_multi_aff *pma,
5552 __isl_take isl_multi_id *tuple);
5553 __isl_give isl_multi_pw_aff *
5554 isl_multi_pw_aff_bind_domain_wrapped_domain(
5555 __isl_take isl_multi_pw_aff *mpa,
5556 __isl_take isl_multi_id *tuple);
5557 __isl_give isl_basic_set *isl_aff_bind_id(
5558 __isl_take isl_aff *aff,
5559 __isl_take isl_id *id);
5560 __isl_give isl_set *isl_pw_aff_bind_id(
5561 __isl_take isl_pw_aff *pa,
5562 __isl_take isl_id *id);
5563 __isl_give isl_basic_set *isl_multi_aff_bind(
5564 __isl_take isl_multi_aff *ma,
5565 __isl_take isl_multi_id *tuple);
5566 __isl_give isl_set *isl_multi_pw_aff_bind(
5567 __isl_take isl_multi_pw_aff *mpa,
5568 __isl_take isl_multi_id *tuple);
5569 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5570 __isl_take isl_union_pw_aff *upa,
5571 __isl_take isl_id *id);
5572 __isl_give isl_union_set *
5573 isl_multi_union_pw_aff_bind(
5574 __isl_take isl_multi_union_pw_aff *mupa,
5575 __isl_take isl_multi_id *tuple);
5577 Projecting out the domain of the wrapped relation in the domain
5578 of a function leaves the range of that wrapped relation
5579 in the domain of the resulting function.
5580 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5581 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5582 C<isl_union_pw_aff_bind_id> and
5583 C<isl_multi_union_pw_aff_bind>, the parameters
5584 are bound to the function values and the result lives
5585 in the domain of the input function.
5589 #include <isl/space.h>
5590 __isl_give isl_space *isl_space_domain(
5591 __isl_take isl_space *space);
5592 __isl_give isl_space *isl_space_range(
5593 __isl_take isl_space *space);
5594 __isl_give isl_space *isl_space_params(
5595 __isl_take isl_space *space);
5596 __isl_give isl_space *
5597 isl_space_domain_wrapped_domain(
5598 __isl_take isl_space *space);
5599 __isl_give isl_space *
5600 isl_space_domain_wrapped_range(
5601 __isl_take isl_space *space);
5602 __isl_give isl_space *
5603 isl_space_range_wrapped_domain(
5604 __isl_take isl_space *space);
5605 __isl_give isl_space *
5606 isl_space_range_wrapped_range(
5607 __isl_take isl_space *space);
5609 #include <isl/local_space.h>
5610 __isl_give isl_local_space *isl_local_space_domain(
5611 __isl_take isl_local_space *ls);
5612 __isl_give isl_local_space *isl_local_space_range(
5613 __isl_take isl_local_space *ls);
5615 #include <isl/set.h>
5616 __isl_give isl_basic_set *isl_basic_set_project_out(
5617 __isl_take isl_basic_set *bset,
5618 enum isl_dim_type type, unsigned first, unsigned n);
5619 __isl_give isl_set *isl_set_project_out_param_id(
5620 __isl_take isl_set *set,
5621 __isl_take isl_id *id);
5622 __isl_give isl_set *
5623 isl_set_project_out_param_id_list(
5624 __isl_take isl_set *set,
5625 __isl_take isl_id_list *list);
5626 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5627 enum isl_dim_type type, unsigned first, unsigned n);
5628 __isl_give isl_set *isl_set_project_out_all_params(
5629 __isl_take isl_set *set);
5630 __isl_give isl_map *isl_set_project_onto_map(
5631 __isl_take isl_set *set,
5632 enum isl_dim_type type, unsigned first,
5634 __isl_give isl_basic_set *isl_basic_set_params(
5635 __isl_take isl_basic_set *bset);
5636 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5638 The function C<isl_space_domain_wrapped_domain> returns the domain
5639 of the binary relation wrapped inside the domain of the input.
5640 The function C<isl_set_project_onto_map> returns a relation
5641 that projects the input set onto the given set dimensions.
5643 #include <isl/map.h>
5644 __isl_give isl_basic_map *isl_basic_map_project_out(
5645 __isl_take isl_basic_map *bmap,
5646 enum isl_dim_type type, unsigned first, unsigned n);
5647 __isl_give isl_map *isl_map_project_out_param_id(
5648 __isl_take isl_map *map,
5649 __isl_take isl_id *id);
5650 __isl_give isl_map *isl_map_project_out_param_id_list(
5651 __isl_take isl_map *map,
5652 __isl_take isl_id_list *list);
5653 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5654 enum isl_dim_type type, unsigned first, unsigned n);
5655 __isl_give isl_map *isl_map_project_out_all_params(
5656 __isl_take isl_map *map);
5657 __isl_give isl_basic_set *isl_basic_map_domain(
5658 __isl_take isl_basic_map *bmap);
5659 __isl_give isl_basic_set *isl_basic_map_range(
5660 __isl_take isl_basic_map *bmap);
5661 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5662 __isl_give isl_set *isl_map_domain(
5663 __isl_take isl_map *bmap);
5664 __isl_give isl_set *isl_map_range(
5665 __isl_take isl_map *map);
5667 #include <isl/union_set.h>
5668 __isl_give isl_union_set *isl_union_set_project_out(
5669 __isl_take isl_union_set *uset,
5670 enum isl_dim_type type,
5671 unsigned first, unsigned n);
5672 __isl_give isl_union_set *
5673 isl_union_set_project_out_all_params(
5674 __isl_take isl_union_set *uset);
5675 __isl_give isl_set *isl_union_set_params(
5676 __isl_take isl_union_set *uset);
5678 The function C<isl_union_set_project_out> can only project out
5681 #include <isl/union_map.h>
5682 __isl_give isl_union_map *
5683 isl_union_map_project_out_param_id(
5684 __isl_take isl_union_map *umap,
5685 __isl_take isl_id *id);
5686 __isl_give isl_union_map *
5687 isl_union_map_project_out_param_id_list(
5688 __isl_take isl_union_map *umap,
5689 __isl_take isl_id_list *list);
5690 __isl_give isl_union_map *isl_union_map_project_out(
5691 __isl_take isl_union_map *umap,
5692 enum isl_dim_type type, unsigned first, unsigned n);
5693 __isl_give isl_union_map *
5694 isl_union_map_project_out_all_params(
5695 __isl_take isl_union_map *umap);
5696 __isl_give isl_set *isl_union_map_params(
5697 __isl_take isl_union_map *umap);
5698 __isl_give isl_union_set *isl_union_map_domain(
5699 __isl_take isl_union_map *umap);
5700 __isl_give isl_union_set *isl_union_map_range(
5701 __isl_take isl_union_map *umap);
5703 The function C<isl_union_map_project_out> can only project out
5706 #include <isl/aff.h>
5707 __isl_give isl_aff *isl_aff_project_domain_on_params(
5708 __isl_take isl_aff *aff);
5709 __isl_give isl_multi_aff *
5710 isl_multi_aff_project_domain_on_params(
5711 __isl_take isl_multi_aff *ma);
5712 __isl_give isl_pw_aff *
5713 isl_pw_aff_project_domain_on_params(
5714 __isl_take isl_pw_aff *pa);
5715 __isl_give isl_multi_pw_aff *
5716 isl_multi_pw_aff_project_domain_on_params(
5717 __isl_take isl_multi_pw_aff *mpa);
5718 __isl_give isl_pw_multi_aff *
5719 isl_pw_multi_aff_project_domain_on_params(
5720 __isl_take isl_pw_multi_aff *pma);
5721 __isl_give isl_set *isl_pw_aff_domain(
5722 __isl_take isl_pw_aff *pwaff);
5723 __isl_give isl_set *isl_pw_multi_aff_domain(
5724 __isl_take isl_pw_multi_aff *pma);
5725 __isl_give isl_set *isl_multi_pw_aff_domain(
5726 __isl_take isl_multi_pw_aff *mpa);
5727 __isl_give isl_union_set *isl_union_pw_aff_domain(
5728 __isl_take isl_union_pw_aff *upa);
5729 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5730 __isl_take isl_union_pw_multi_aff *upma);
5731 __isl_give isl_union_set *
5732 isl_multi_union_pw_aff_domain(
5733 __isl_take isl_multi_union_pw_aff *mupa);
5734 __isl_give isl_set *isl_pw_aff_params(
5735 __isl_take isl_pw_aff *pwa);
5737 If no explicit domain was set on a zero-dimensional input to
5738 C<isl_multi_union_pw_aff_domain>, then this function will
5739 return a parameter set.
5741 #include <isl/polynomial.h>
5742 __isl_give isl_qpolynomial *
5743 isl_qpolynomial_project_domain_on_params(
5744 __isl_take isl_qpolynomial *qp);
5745 __isl_give isl_pw_qpolynomial *
5746 isl_pw_qpolynomial_project_domain_on_params(
5747 __isl_take isl_pw_qpolynomial *pwqp);
5748 __isl_give isl_pw_qpolynomial_fold *
5749 isl_pw_qpolynomial_fold_project_domain_on_params(
5750 __isl_take isl_pw_qpolynomial_fold *pwf);
5751 __isl_give isl_set *isl_pw_qpolynomial_domain(
5752 __isl_take isl_pw_qpolynomial *pwqp);
5753 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5754 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5755 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5756 __isl_take isl_union_pw_qpolynomial *upwqp);
5758 #include <isl/space.h>
5759 __isl_give isl_space *isl_space_domain_map(
5760 __isl_take isl_space *space);
5761 __isl_give isl_space *isl_space_range_map(
5762 __isl_take isl_space *space);
5764 #include <isl/map.h>
5765 __isl_give isl_map *isl_set_wrapped_domain_map(
5766 __isl_take isl_set *set);
5767 __isl_give isl_basic_map *isl_basic_map_domain_map(
5768 __isl_take isl_basic_map *bmap);
5769 __isl_give isl_basic_map *isl_basic_map_range_map(
5770 __isl_take isl_basic_map *bmap);
5771 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5772 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5774 #include <isl/union_map.h>
5775 __isl_give isl_union_map *isl_union_map_domain_map(
5776 __isl_take isl_union_map *umap);
5777 __isl_give isl_union_pw_multi_aff *
5778 isl_union_map_domain_map_union_pw_multi_aff(
5779 __isl_take isl_union_map *umap);
5780 __isl_give isl_union_map *isl_union_map_range_map(
5781 __isl_take isl_union_map *umap);
5782 __isl_give isl_union_map *
5783 isl_union_set_wrapped_domain_map(
5784 __isl_take isl_union_set *uset);
5786 The functions above construct a (basic, regular or union) relation
5787 that maps (a wrapped version of) the input relation to its domain or range.
5788 C<isl_set_wrapped_domain_map> maps the input set to the domain
5789 of its wrapped relation.
5793 __isl_give isl_basic_set *isl_basic_set_eliminate(
5794 __isl_take isl_basic_set *bset,
5795 enum isl_dim_type type,
5796 unsigned first, unsigned n);
5797 __isl_give isl_set *isl_set_eliminate(
5798 __isl_take isl_set *set, enum isl_dim_type type,
5799 unsigned first, unsigned n);
5800 __isl_give isl_basic_map *isl_basic_map_eliminate(
5801 __isl_take isl_basic_map *bmap,
5802 enum isl_dim_type type,
5803 unsigned first, unsigned n);
5804 __isl_give isl_map *isl_map_eliminate(
5805 __isl_take isl_map *map, enum isl_dim_type type,
5806 unsigned first, unsigned n);
5808 Eliminate the coefficients for the given dimensions from the constraints,
5809 without removing the dimensions.
5811 =item * Constructing a set from a parameter domain
5813 A set space of a given dimension and with an optional name
5814 can be created from a parameter space using the following functions.
5816 #include <isl/space.h>
5817 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5818 __isl_take isl_space *space, unsigned dim);
5819 __isl_give isl_space *
5820 isl_space_add_named_tuple_id_ui(
5821 __isl_take isl_space *space,
5822 __isl_take isl_id *tuple_id, unsigned dim);
5824 A set with a given tuple can be created from a parameter domain
5825 using the following function.
5827 #include <isl/set.h>
5828 __isl_give isl_set *isl_set_unbind_params(
5829 __isl_take isl_set *set,
5830 __isl_take isl_multi_id *tuple);
5832 Any parameters with identifiers in C<tuple> are reinterpreted
5833 as the corresponding set dimensions.
5835 A zero-dimensional (local) space or (basic) set can be constructed
5836 on a given parameter domain using the following functions.
5838 #include <isl/space.h>
5839 __isl_give isl_space *isl_space_set_from_params(
5840 __isl_take isl_space *space);
5842 #include <isl/local_space.h>
5843 __isl_give isl_local_space *
5844 isl_local_space_set_from_params(
5845 __isl_take isl_local_space *ls);
5847 #include <isl/set.h>
5848 __isl_give isl_basic_set *isl_basic_set_from_params(
5849 __isl_take isl_basic_set *bset);
5850 __isl_give isl_set *isl_set_from_params(
5851 __isl_take isl_set *set);
5853 =item * Constructing a relation from one or two sets
5855 A map space with a range of a given dimension and with an optional name
5856 can be created from a domain space using the functions
5857 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5860 A relation with a given domain tuple can be created from a set
5861 that will become the range of the relation
5862 using the following function.
5864 #include <isl/set.h>
5865 __isl_give isl_map *
5866 isl_set_unbind_params_insert_domain(
5867 __isl_take isl_set *set,
5868 __isl_take isl_multi_id *domain);
5870 Any parameters with identifiers in C<domain> are reinterpreted
5871 as the corresponding input dimensions.
5873 Similarly, a function defined over a parameter domain can
5874 be converted into one defined over a set domain
5875 using the following functions.
5877 #include <isl/aff.h>
5878 __isl_give isl_aff *
5879 isl_aff_unbind_params_insert_domain(
5880 __isl_take isl_aff *aff,
5881 __isl_take isl_multi_id *domain);
5882 __isl_give isl_multi_aff *
5883 isl_multi_aff_unbind_params_insert_domain(
5884 __isl_take isl_multi_aff *ma,
5885 __isl_take isl_multi_id *domain);
5886 __isl_give isl_multi_pw_aff *
5887 isl_multi_pw_aff_unbind_params_insert_domain(
5888 __isl_take isl_multi_pw_aff *mpa,
5889 __isl_take isl_multi_id *domain);
5892 any parameters with identifiers in C<domain> are reinterpreted
5893 as the corresponding input dimensions.
5895 Create a relation with the given set(s) as domain and/or range.
5896 If only the domain or the range is specified, then
5897 the range or domain of the created relation is a zero-dimensional
5898 flat anonymous space.
5899 If the case of C<isl_space_map_from_set>, the input space
5900 specifies both the domain and the range of the result.
5902 #include <isl/space.h>
5903 __isl_give isl_space *isl_space_from_domain(
5904 __isl_take isl_space *space);
5905 __isl_give isl_space *isl_space_from_range(
5906 __isl_take isl_space *space);
5907 __isl_give isl_space *isl_space_map_from_set(
5908 __isl_take isl_space *space);
5909 __isl_give isl_space *isl_space_map_from_domain_and_range(
5910 __isl_take isl_space *domain,
5911 __isl_take isl_space *range);
5913 #include <isl/local_space.h>
5914 __isl_give isl_local_space *isl_local_space_from_domain(
5915 __isl_take isl_local_space *ls);
5917 #include <isl/map.h>
5918 __isl_give isl_map *isl_set_insert_domain(
5919 __isl_take isl_set *set,
5920 __isl_take isl_space *domain);
5921 __isl_give isl_map *isl_map_from_domain(
5922 __isl_take isl_set *set);
5923 __isl_give isl_map *isl_map_from_range(
5924 __isl_take isl_set *set);
5926 #include <isl/union_map.h>
5927 __isl_give isl_union_map *isl_union_map_from_domain(
5928 __isl_take isl_union_set *uset);
5929 __isl_give isl_union_map *isl_union_map_from_range(
5930 __isl_take isl_union_set *uset);
5931 __isl_give isl_union_map *
5932 isl_union_map_from_domain_and_range(
5933 __isl_take isl_union_set *domain,
5934 __isl_take isl_union_set *range);
5937 __isl_give isl_multi_id *isl_multi_id_from_range(
5938 __isl_take isl_multi_id *mi);
5940 #include <isl/val.h>
5941 __isl_give isl_multi_val *isl_multi_val_from_range(
5942 __isl_take isl_multi_val *mv);
5944 #include <isl/aff.h>
5945 __isl_give isl_multi_aff *
5946 isl_multi_aff_insert_domain(
5947 __isl_take isl_multi_aff *ma,
5948 __isl_take isl_space *domain);
5949 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5950 __isl_take isl_pw_aff *pa,
5951 __isl_take isl_space *domain);
5952 __isl_give isl_pw_multi_aff *
5953 isl_pw_multi_aff_insert_domain(
5954 __isl_take isl_pw_multi_aff *pma,
5955 __isl_take isl_space *domain);
5956 __isl_give isl_multi_pw_aff *
5957 isl_multi_pw_aff_insert_domain(
5958 __isl_take isl_multi_pw_aff *mpa,
5959 __isl_take isl_space *domain);
5960 __isl_give isl_aff *isl_aff_from_range(
5961 __isl_take isl_aff *aff);
5962 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5963 __isl_take isl_multi_aff *ma);
5964 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5965 __isl_take isl_pw_aff *pwa);
5966 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5967 __isl_take isl_multi_pw_aff *mpa);
5968 __isl_give isl_multi_union_pw_aff *
5969 isl_multi_union_pw_aff_from_range(
5970 __isl_take isl_multi_union_pw_aff *mupa);
5971 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5972 __isl_take isl_set *set);
5973 __isl_give isl_union_pw_multi_aff *
5974 isl_union_pw_multi_aff_from_domain(
5975 __isl_take isl_union_set *uset);
5977 #include <isl/polynomial.h>
5978 __isl_give isl_pw_qpolynomial *
5979 isl_pw_qpolynomial_from_range(
5980 __isl_take isl_pw_qpolynomial *pwqp);
5981 __isl_give isl_pw_qpolynomial_fold *
5982 isl_pw_qpolynomial_fold_from_range(
5983 __isl_take isl_pw_qpolynomial_fold *pwf);
5987 #include <isl/set.h>
5988 __isl_give isl_basic_set *isl_basic_set_fix_si(
5989 __isl_take isl_basic_set *bset,
5990 enum isl_dim_type type, unsigned pos, int value);
5991 __isl_give isl_basic_set *isl_basic_set_fix_val(
5992 __isl_take isl_basic_set *bset,
5993 enum isl_dim_type type, unsigned pos,
5994 __isl_take isl_val *v);
5995 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5996 enum isl_dim_type type, unsigned pos, int value);
5997 __isl_give isl_set *isl_set_fix_val(
5998 __isl_take isl_set *set,
5999 enum isl_dim_type type, unsigned pos,
6000 __isl_take isl_val *v);
6002 #include <isl/map.h>
6003 __isl_give isl_basic_map *isl_basic_map_fix_si(
6004 __isl_take isl_basic_map *bmap,
6005 enum isl_dim_type type, unsigned pos, int value);
6006 __isl_give isl_basic_map *isl_basic_map_fix_val(
6007 __isl_take isl_basic_map *bmap,
6008 enum isl_dim_type type, unsigned pos,
6009 __isl_take isl_val *v);
6010 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
6011 enum isl_dim_type type, unsigned pos, int value);
6012 __isl_give isl_map *isl_map_fix_val(
6013 __isl_take isl_map *map,
6014 enum isl_dim_type type, unsigned pos,
6015 __isl_take isl_val *v);
6017 #include <isl/aff.h>
6018 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
6019 __isl_take isl_pw_multi_aff *pma,
6020 enum isl_dim_type type, unsigned pos, int value);
6022 #include <isl/polynomial.h>
6023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
6024 __isl_take isl_pw_qpolynomial *pwqp,
6025 enum isl_dim_type type, unsigned n,
6026 __isl_take isl_val *v);
6027 __isl_give isl_pw_qpolynomial_fold *
6028 isl_pw_qpolynomial_fold_fix_val(
6029 __isl_take isl_pw_qpolynomial_fold *pwf,
6030 enum isl_dim_type type, unsigned n,
6031 __isl_take isl_val *v);
6033 Intersect the set, relation or function domain
6034 with the hyperplane where the given
6035 dimension has the fixed given value.
6037 #include <isl/set.h>
6038 __isl_give isl_basic_set *
6039 isl_basic_set_lower_bound_val(
6040 __isl_take isl_basic_set *bset,
6041 enum isl_dim_type type, unsigned pos,
6042 __isl_take isl_val *value);
6043 __isl_give isl_basic_set *
6044 isl_basic_set_upper_bound_val(
6045 __isl_take isl_basic_set *bset,
6046 enum isl_dim_type type, unsigned pos,
6047 __isl_take isl_val *value);
6048 __isl_give isl_set *isl_set_lower_bound_si(
6049 __isl_take isl_set *set,
6050 enum isl_dim_type type, unsigned pos, int value);
6051 __isl_give isl_set *isl_set_lower_bound_val(
6052 __isl_take isl_set *set,
6053 enum isl_dim_type type, unsigned pos,
6054 __isl_take isl_val *value);
6055 __isl_give isl_set *isl_set_upper_bound_si(
6056 __isl_take isl_set *set,
6057 enum isl_dim_type type, unsigned pos, int value);
6058 __isl_give isl_set *isl_set_upper_bound_val(
6059 __isl_take isl_set *set,
6060 enum isl_dim_type type, unsigned pos,
6061 __isl_take isl_val *value);
6062 __isl_give isl_set *isl_set_lower_bound_multi_val(
6063 __isl_take isl_set *set,
6064 __isl_take isl_multi_val *lower);
6065 __isl_give isl_set *isl_set_upper_bound_multi_val(
6066 __isl_take isl_set *set,
6067 __isl_take isl_multi_val *upper);
6068 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6069 __isl_take isl_set *set,
6070 __isl_take isl_multi_pw_aff *lower);
6071 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6072 __isl_take isl_set *set,
6073 __isl_take isl_multi_pw_aff *upper);
6075 #include <isl/map.h>
6076 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6077 __isl_take isl_basic_map *bmap,
6078 enum isl_dim_type type, unsigned pos, int value);
6079 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6080 __isl_take isl_basic_map *bmap,
6081 enum isl_dim_type type, unsigned pos, int value);
6082 __isl_give isl_map *isl_map_lower_bound_si(
6083 __isl_take isl_map *map,
6084 enum isl_dim_type type, unsigned pos, int value);
6085 __isl_give isl_map *isl_map_upper_bound_si(
6086 __isl_take isl_map *map,
6087 enum isl_dim_type type, unsigned pos, int value);
6088 __isl_give isl_map *isl_map_lower_bound_val(
6089 __isl_take isl_map *map,
6090 enum isl_dim_type type, unsigned pos,
6091 __isl_take isl_val *value);
6092 __isl_give isl_map *isl_map_upper_bound_val(
6093 __isl_take isl_map *map,
6094 enum isl_dim_type type, unsigned pos,
6095 __isl_take isl_val *value);
6096 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6097 __isl_take isl_map *map,
6098 __isl_take isl_multi_pw_aff *lower);
6099 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6100 __isl_take isl_map *map,
6101 __isl_take isl_multi_pw_aff *upper);
6103 Intersect the set or relation with the half-space where the given
6104 dimension has a value bounded by the given fixed integer value or
6105 symbolic constant expression.
6106 For functions taking a multi expression,
6107 this applies to all set dimensions.
6108 Those that bound a map, bound the range of that map.
6109 If the multi expression is zero-dimensional but has an explicit domain,
6110 then the (parameter) domain of the set or map is intersected
6111 with this explicit domain.
6113 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6114 enum isl_dim_type type1, int pos1,
6115 enum isl_dim_type type2, int pos2);
6116 __isl_give isl_basic_map *isl_basic_map_equate(
6117 __isl_take isl_basic_map *bmap,
6118 enum isl_dim_type type1, int pos1,
6119 enum isl_dim_type type2, int pos2);
6120 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6121 enum isl_dim_type type1, int pos1,
6122 enum isl_dim_type type2, int pos2);
6124 Intersect the set or relation with the hyperplane where the given
6125 dimensions are equal to each other.
6127 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6128 enum isl_dim_type type1, int pos1,
6129 enum isl_dim_type type2, int pos2);
6131 Intersect the relation with the hyperplane where the given
6132 dimensions have opposite values.
6134 __isl_give isl_map *isl_map_order_le(
6135 __isl_take isl_map *map,
6136 enum isl_dim_type type1, int pos1,
6137 enum isl_dim_type type2, int pos2);
6138 __isl_give isl_basic_map *isl_basic_map_order_ge(
6139 __isl_take isl_basic_map *bmap,
6140 enum isl_dim_type type1, int pos1,
6141 enum isl_dim_type type2, int pos2);
6142 __isl_give isl_map *isl_map_order_ge(
6143 __isl_take isl_map *map,
6144 enum isl_dim_type type1, int pos1,
6145 enum isl_dim_type type2, int pos2);
6146 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6147 enum isl_dim_type type1, int pos1,
6148 enum isl_dim_type type2, int pos2);
6149 __isl_give isl_basic_map *isl_basic_map_order_gt(
6150 __isl_take isl_basic_map *bmap,
6151 enum isl_dim_type type1, int pos1,
6152 enum isl_dim_type type2, int pos2);
6153 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6154 enum isl_dim_type type1, int pos1,
6155 enum isl_dim_type type2, int pos2);
6157 Intersect the relation with the half-space where the given
6158 dimensions satisfy the given ordering.
6160 #include <isl/union_set.h>
6161 __isl_give isl_union_map *isl_union_map_remove_map_if(
6162 __isl_take isl_union_map *umap,
6163 isl_bool (*fn)(__isl_keep isl_map *map,
6164 void *user), void *user);
6166 This function calls the callback function once for each
6167 pair of spaces for which there are elements in the input.
6168 If the callback returns C<isl_bool_true>, then all those elements
6169 are removed from the result. The only remaining elements in the output
6170 are then those for which the callback returns C<isl_bool_false>.
6174 #include <isl/aff.h>
6175 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6176 __isl_take isl_aff *aff);
6177 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6178 __isl_take isl_aff *aff);
6179 __isl_give isl_set *isl_pw_aff_pos_set(
6180 __isl_take isl_pw_aff *pa);
6181 __isl_give isl_set *isl_pw_aff_nonneg_set(
6182 __isl_take isl_pw_aff *pwaff);
6183 __isl_give isl_set *isl_pw_aff_zero_set(
6184 __isl_take isl_pw_aff *pwaff);
6185 __isl_give isl_set *isl_pw_aff_non_zero_set(
6186 __isl_take isl_pw_aff *pwaff);
6187 __isl_give isl_union_set *
6188 isl_union_pw_aff_zero_union_set(
6189 __isl_take isl_union_pw_aff *upa);
6190 __isl_give isl_union_set *
6191 isl_multi_union_pw_aff_zero_union_set(
6192 __isl_take isl_multi_union_pw_aff *mupa);
6194 The function C<isl_aff_neg_basic_set> returns a basic set
6195 containing those elements in the domain space
6196 of C<aff> where C<aff> is negative.
6197 The function C<isl_pw_aff_nonneg_set> returns a set
6198 containing those elements in the domain
6199 of C<pwaff> where C<pwaff> is non-negative.
6200 The function C<isl_multi_union_pw_aff_zero_union_set>
6201 returns a union set containing those elements
6202 in the domains of its elements where they are all zero.
6206 __isl_give isl_map *isl_set_identity(
6207 __isl_take isl_set *set);
6208 __isl_give isl_union_map *isl_union_set_identity(
6209 __isl_take isl_union_set *uset);
6210 __isl_give isl_union_pw_multi_aff *
6211 isl_union_set_identity_union_pw_multi_aff(
6212 __isl_take isl_union_set *uset);
6214 Construct an identity relation on the given (union) set.
6216 =item * Function Extraction
6218 A piecewise quasi affine expression that is equal to 1 on a set
6219 and 0 outside the set can be created using the following function.
6221 #include <isl/aff.h>
6222 __isl_give isl_pw_aff *isl_set_indicator_function(
6223 __isl_take isl_set *set);
6225 A piecewise multiple quasi affine expression can be extracted
6226 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6227 and the C<isl_map> is single-valued.
6228 In case of a conversion from an C<isl_union_map>
6229 to an C<isl_union_pw_multi_aff>, these properties need to hold
6230 in each domain space.
6231 A conversion to a C<isl_multi_union_pw_aff> additionally
6232 requires that the input is non-empty and involves only a single
6235 #include <isl/aff.h>
6236 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6237 __isl_take isl_set *set);
6238 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6239 __isl_take isl_set *set);
6240 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6241 __isl_take isl_map *map);
6242 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6243 __isl_take isl_map *map);
6245 __isl_give isl_union_pw_multi_aff *
6246 isl_union_pw_multi_aff_from_union_set(
6247 __isl_take isl_union_set *uset);
6248 __isl_give isl_union_pw_multi_aff *
6249 isl_union_map_as_union_pw_multi_aff(
6250 __isl_take isl_union_map *umap);
6251 __isl_give isl_union_pw_multi_aff *
6252 isl_union_pw_multi_aff_from_union_map(
6253 __isl_take isl_union_map *umap);
6255 __isl_give isl_multi_union_pw_aff *
6256 isl_union_map_as_multi_union_pw_aff(
6257 __isl_take isl_union_map *umap);
6258 __isl_give isl_multi_union_pw_aff *
6259 isl_multi_union_pw_aff_from_union_map(
6260 __isl_take isl_union_map *umap);
6262 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6264 Similarly for C<isl_set_as_pw_multi_aff> and
6265 C<isl_pw_multi_aff_from_set>,
6266 for C<isl_union_map_as_union_pw_multi_aff> and
6267 C<isl_union_pw_multi_aff_from_union_map> and
6268 for C<isl_union_map_as_multi_union_pw_aff> and
6269 C<isl_multi_union_pw_aff_from_union_map>.
6273 __isl_give isl_basic_set *isl_basic_map_deltas(
6274 __isl_take isl_basic_map *bmap);
6275 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6276 __isl_give isl_union_set *isl_union_map_deltas(
6277 __isl_take isl_union_map *umap);
6279 These functions return a (basic) set containing the differences
6280 between image elements and corresponding domain elements in the input.
6282 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6283 __isl_take isl_basic_map *bmap);
6284 __isl_give isl_map *isl_map_deltas_map(
6285 __isl_take isl_map *map);
6286 __isl_give isl_union_map *isl_union_map_deltas_map(
6287 __isl_take isl_union_map *umap);
6289 The functions above construct a (basic, regular or union) relation
6290 that maps (a wrapped version of) the input relation to its delta set.
6294 #include <isl/map.h>
6295 __isl_give isl_map *isl_set_translation(
6296 __isl_take isl_set *deltas);
6298 This function performs essentially the opposite operation
6299 of C<isl_map_deltas>. In particular, it returns pairs
6300 of elements in the same space that have a difference in C<deltas>.
6304 Simplify the representation of a set, relation or functions by trying
6305 to combine pairs of basic sets or relations into a single
6306 basic set or relation.
6308 #include <isl/set.h>
6309 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6311 #include <isl/map.h>
6312 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6314 #include <isl/union_set.h>
6315 __isl_give isl_union_set *isl_union_set_coalesce(
6316 __isl_take isl_union_set *uset);
6318 #include <isl/union_map.h>
6319 __isl_give isl_union_map *isl_union_map_coalesce(
6320 __isl_take isl_union_map *umap);
6322 #include <isl/aff.h>
6323 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6324 __isl_take isl_pw_aff *pa);
6325 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6326 __isl_take isl_pw_multi_aff *pma);
6327 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6328 __isl_take isl_multi_pw_aff *mpa);
6329 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6330 __isl_take isl_union_pw_aff *upa);
6331 __isl_give isl_union_pw_multi_aff *
6332 isl_union_pw_multi_aff_coalesce(
6333 __isl_take isl_union_pw_multi_aff *upma);
6334 __isl_give isl_multi_union_pw_aff *
6335 isl_multi_union_pw_aff_coalesce(
6336 __isl_take isl_multi_union_pw_aff *mupa);
6338 #include <isl/polynomial.h>
6339 __isl_give isl_pw_qpolynomial_fold *
6340 isl_pw_qpolynomial_fold_coalesce(
6341 __isl_take isl_pw_qpolynomial_fold *pwf);
6342 __isl_give isl_union_pw_qpolynomial *
6343 isl_union_pw_qpolynomial_coalesce(
6344 __isl_take isl_union_pw_qpolynomial *upwqp);
6345 __isl_give isl_union_pw_qpolynomial_fold *
6346 isl_union_pw_qpolynomial_fold_coalesce(
6347 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6349 One of the methods for combining pairs of basic sets or relations
6350 can result in coefficients that are much larger than those that appear
6351 in the constraints of the input. By default, the coefficients are
6352 not allowed to grow larger, but this can be changed by unsetting
6353 the following option.
6355 isl_stat isl_options_set_coalesce_bounded_wrapping(
6356 isl_ctx *ctx, int val);
6357 int isl_options_get_coalesce_bounded_wrapping(
6360 One of the other methods tries to combine pairs of basic sets
6361 with different local variables, treating them as existentially
6362 quantified variables even if they have known (but different)
6363 integer division expressions. The result may then also have
6364 existentially quantified variables. Turning on the following
6365 option prevents this from happening.
6367 isl_stat isl_options_set_coalesce_preserve_locals(
6368 isl_ctx *ctx, int val);
6369 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6371 =item * Detecting equalities
6373 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6374 __isl_take isl_basic_set *bset);
6375 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6376 __isl_take isl_basic_map *bmap);
6377 __isl_give isl_set *isl_set_detect_equalities(
6378 __isl_take isl_set *set);
6379 __isl_give isl_map *isl_map_detect_equalities(
6380 __isl_take isl_map *map);
6381 __isl_give isl_union_set *isl_union_set_detect_equalities(
6382 __isl_take isl_union_set *uset);
6383 __isl_give isl_union_map *isl_union_map_detect_equalities(
6384 __isl_take isl_union_map *umap);
6386 Simplify the representation of a set or relation by detecting implicit
6389 =item * Removing redundant constraints
6391 #include <isl/set.h>
6392 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6393 __isl_take isl_basic_set *bset);
6394 __isl_give isl_set *isl_set_remove_redundancies(
6395 __isl_take isl_set *set);
6397 #include <isl/union_set.h>
6398 __isl_give isl_union_set *
6399 isl_union_set_remove_redundancies(
6400 __isl_take isl_union_set *uset);
6402 #include <isl/map.h>
6403 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6404 __isl_take isl_basic_map *bmap);
6405 __isl_give isl_map *isl_map_remove_redundancies(
6406 __isl_take isl_map *map);
6408 #include <isl/union_map.h>
6409 __isl_give isl_union_map *
6410 isl_union_map_remove_redundancies(
6411 __isl_take isl_union_map *umap);
6415 __isl_give isl_basic_set *isl_set_convex_hull(
6416 __isl_take isl_set *set);
6417 __isl_give isl_basic_map *isl_map_convex_hull(
6418 __isl_take isl_map *map);
6420 If the input set or relation has any existentially quantified
6421 variables, then the result of these operations is currently undefined.
6425 #include <isl/set.h>
6426 __isl_give isl_basic_set *
6427 isl_set_unshifted_simple_hull(
6428 __isl_take isl_set *set);
6429 __isl_give isl_basic_set *isl_set_simple_hull(
6430 __isl_take isl_set *set);
6431 __isl_give isl_basic_set *
6432 isl_set_plain_unshifted_simple_hull(
6433 __isl_take isl_set *set);
6434 __isl_give isl_basic_set *
6435 isl_set_unshifted_simple_hull_from_set_list(
6436 __isl_take isl_set *set,
6437 __isl_take isl_set_list *list);
6439 #include <isl/map.h>
6440 __isl_give isl_basic_map *
6441 isl_map_unshifted_simple_hull(
6442 __isl_take isl_map *map);
6443 __isl_give isl_basic_map *isl_map_simple_hull(
6444 __isl_take isl_map *map);
6445 __isl_give isl_basic_map *
6446 isl_map_plain_unshifted_simple_hull(
6447 __isl_take isl_map *map);
6448 __isl_give isl_basic_map *
6449 isl_map_unshifted_simple_hull_from_map_list(
6450 __isl_take isl_map *map,
6451 __isl_take isl_map_list *list);
6453 #include <isl/union_map.h>
6454 __isl_give isl_union_map *isl_union_map_simple_hull(
6455 __isl_take isl_union_map *umap);
6457 These functions compute a single basic set or relation
6458 that contains the whole input set or relation.
6459 In particular, the output is described by translates
6460 of the constraints describing the basic sets or relations in the input.
6461 In case of C<isl_set_unshifted_simple_hull>, only the original
6462 constraints are used, without any translation.
6463 In case of C<isl_set_plain_unshifted_simple_hull> and
6464 C<isl_map_plain_unshifted_simple_hull>, the result is described
6465 by original constraints that are obviously satisfied
6466 by the entire input set or relation.
6467 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6468 C<isl_map_unshifted_simple_hull_from_map_list>, the
6469 constraints are taken from the elements of the second argument.
6473 (See \autoref{s:simple hull}.)
6479 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6480 __isl_take isl_basic_set *bset);
6481 __isl_give isl_basic_set *isl_set_affine_hull(
6482 __isl_take isl_set *set);
6483 __isl_give isl_union_set *isl_union_set_affine_hull(
6484 __isl_take isl_union_set *uset);
6485 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6486 __isl_take isl_basic_map *bmap);
6487 __isl_give isl_basic_map *isl_map_affine_hull(
6488 __isl_take isl_map *map);
6489 __isl_give isl_union_map *isl_union_map_affine_hull(
6490 __isl_take isl_union_map *umap);
6492 In case of union sets and relations, the affine hull is computed
6495 =item * Polyhedral hull
6497 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6498 __isl_take isl_set *set);
6499 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6500 __isl_take isl_map *map);
6501 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6502 __isl_take isl_union_set *uset);
6503 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6504 __isl_take isl_union_map *umap);
6506 These functions compute a single basic set or relation
6507 not involving any existentially quantified variables
6508 that contains the whole input set or relation.
6509 In case of union sets and relations, the polyhedral hull is computed
6514 #include <isl/set.h>
6515 __isl_give isl_fixed_box *
6516 isl_set_get_simple_fixed_box_hull(
6517 __isl_keep isl_set *set)
6519 #include <isl/map.h>
6520 __isl_give isl_fixed_box *
6521 isl_map_get_range_simple_fixed_box_hull(
6522 __isl_keep isl_map *map);
6524 These functions try to approximate the set or
6525 the range of the map by a box of fixed size.
6526 The box is described in terms of an offset living in the same space as
6527 the input and a size living in the set or range space. For any element
6528 in the input map, the range value is greater than or equal to
6529 the offset applied to the domain value and the difference with
6530 this offset is strictly smaller than the size.
6531 The same holds for the elements of the input set, where
6532 the offset is a parametric constant value.
6533 If no fixed-size approximation can be found,
6534 an I<invalid> box is returned, i.e., one for which
6535 C<isl_fixed_box_is_valid> below returns false.
6537 The validity, the offset and the size of the box can be obtained using
6538 the following functions.
6540 #include <isl/fixed_box.h>
6541 isl_bool isl_fixed_box_is_valid(
6542 __isl_keep isl_fixed_box *box);
6543 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6544 __isl_keep isl_fixed_box *box);
6545 __isl_give isl_multi_val *isl_fixed_box_get_size(
6546 __isl_keep isl_fixed_box *box);
6548 The box can be copied and freed using the following functions.
6550 #include <isl/fixed_box.h>
6551 __isl_give isl_fixed_box *isl_fixed_box_copy(
6552 __isl_keep isl_fixed_box *box);
6553 __isl_null isl_fixed_box *isl_fixed_box_free(
6554 __isl_take isl_fixed_box *box);
6556 An object of type C<isl_fixed_box> can be read from input
6557 using the following function.
6559 #include <isl/fixed_box.h>
6560 __isl_give isl_fixed_box *
6561 isl_fixed_box_read_from_str(isl_ctx *ctx,
6564 A representation of the information contained in an object
6565 of type C<isl_fixed_box> can be obtained using
6567 #include <isl/fixed_box.h>
6568 __isl_give isl_printer *isl_printer_print_fixed_box(
6569 __isl_take isl_printer *p,
6570 __isl_keep isl_fixed_box *box);
6571 __isl_give char *isl_fixed_box_to_str(
6572 __isl_keep isl_fixed_box *box);
6574 C<isl_fixed_box_to_str> prints the information in flow format.
6576 =item * Other approximations
6578 #include <isl/set.h>
6579 __isl_give isl_basic_set *
6580 isl_basic_set_drop_constraints_involving_dims(
6581 __isl_take isl_basic_set *bset,
6582 enum isl_dim_type type,
6583 unsigned first, unsigned n);
6584 __isl_give isl_basic_set *
6585 isl_basic_set_drop_constraints_not_involving_dims(
6586 __isl_take isl_basic_set *bset,
6587 enum isl_dim_type type,
6588 unsigned first, unsigned n);
6589 __isl_give isl_set *
6590 isl_set_drop_constraints_involving_dims(
6591 __isl_take isl_set *set,
6592 enum isl_dim_type type,
6593 unsigned first, unsigned n);
6594 __isl_give isl_set *
6595 isl_set_drop_constraints_not_involving_dims(
6596 __isl_take isl_set *set,
6597 enum isl_dim_type type,
6598 unsigned first, unsigned n);
6600 #include <isl/map.h>
6601 __isl_give isl_basic_map *
6602 isl_basic_map_drop_constraints_involving_dims(
6603 __isl_take isl_basic_map *bmap,
6604 enum isl_dim_type type,
6605 unsigned first, unsigned n);
6606 __isl_give isl_basic_map *
6607 isl_basic_map_drop_constraints_not_involving_dims(
6608 __isl_take isl_basic_map *bmap,
6609 enum isl_dim_type type,
6610 unsigned first, unsigned n);
6611 __isl_give isl_map *
6612 isl_map_drop_constraints_involving_dims(
6613 __isl_take isl_map *map,
6614 enum isl_dim_type type,
6615 unsigned first, unsigned n);
6616 __isl_give isl_map *
6617 isl_map_drop_constraints_not_involving_dims(
6618 __isl_take isl_map *map,
6619 enum isl_dim_type type,
6620 unsigned first, unsigned n);
6622 These functions drop any constraints (not) involving the specified dimensions.
6623 Note that the result depends on the representation of the input.
6625 #include <isl/polynomial.h>
6626 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6627 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6628 __isl_give isl_union_pw_qpolynomial *
6629 isl_union_pw_qpolynomial_to_polynomial(
6630 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6632 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6633 the polynomial will be an overapproximation. If C<sign> is negative,
6634 it will be an underapproximation. If C<sign> is zero, the approximation
6635 will lie somewhere in between.
6639 __isl_give isl_basic_set *isl_basic_set_sample(
6640 __isl_take isl_basic_set *bset);
6641 __isl_give isl_basic_set *isl_set_sample(
6642 __isl_take isl_set *set);
6643 __isl_give isl_basic_map *isl_basic_map_sample(
6644 __isl_take isl_basic_map *bmap);
6645 __isl_give isl_basic_map *isl_map_sample(
6646 __isl_take isl_map *map);
6648 If the input (basic) set or relation is non-empty, then return
6649 a singleton subset of the input. Otherwise, return an empty set.
6651 =item * Optimization
6653 #include <isl/ilp.h>
6654 __isl_give isl_val *isl_basic_set_max_val(
6655 __isl_keep isl_basic_set *bset,
6656 __isl_keep isl_aff *obj);
6657 __isl_give isl_val *isl_set_min_val(
6658 __isl_keep isl_set *set,
6659 __isl_keep isl_aff *obj);
6660 __isl_give isl_val *isl_set_max_val(
6661 __isl_keep isl_set *set,
6662 __isl_keep isl_aff *obj);
6663 __isl_give isl_multi_val *
6664 isl_union_set_min_multi_union_pw_aff(
6665 __isl_keep isl_union_set *uset,
6666 __isl_keep isl_multi_union_pw_aff *obj);
6668 Compute the minimum or maximum of the integer affine expression C<obj>
6669 over the points in C<set>.
6670 The result is C<NULL> in case of an error, the optimal value in case
6671 there is one, negative infinity or infinity if the problem is unbounded and
6672 NaN if the problem is empty.
6674 #include <isl/ilp.h>
6675 __isl_give isl_val *isl_pw_aff_min_val(
6676 __isl_take isl_pw_aff *pa);
6677 __isl_give isl_val *isl_pw_aff_max_val(
6678 __isl_take isl_pw_aff *pa);
6679 __isl_give isl_multi_val *
6680 isl_pw_multi_aff_min_multi_val(
6681 __isl_take isl_pw_multi_aff *pma);
6682 __isl_give isl_multi_val *
6683 isl_pw_multi_aff_max_multi_val(
6684 __isl_take isl_pw_multi_aff *pma);
6685 __isl_give isl_multi_val *
6686 isl_multi_pw_aff_min_multi_val(
6687 __isl_take isl_multi_pw_aff *mpa);
6688 __isl_give isl_multi_val *
6689 isl_multi_pw_aff_max_multi_val(
6690 __isl_take isl_multi_pw_aff *mpa);
6691 __isl_give isl_val *isl_union_pw_aff_min_val(
6692 __isl_take isl_union_pw_aff *upa);
6693 __isl_give isl_val *isl_union_pw_aff_max_val(
6694 __isl_take isl_union_pw_aff *upa);
6695 __isl_give isl_multi_val *
6696 isl_multi_union_pw_aff_min_multi_val(
6697 __isl_take isl_multi_union_pw_aff *mupa);
6698 __isl_give isl_multi_val *
6699 isl_multi_union_pw_aff_max_multi_val(
6700 __isl_take isl_multi_union_pw_aff *mupa);
6702 Compute the minimum or maximum of the integer affine expression
6703 over its definition domain.
6704 The result is C<NULL> in case of an error, the optimal value in case
6705 there is one, negative infinity or infinity if the problem is unbounded and
6706 NaN if the problem is empty.
6708 #include <isl/ilp.h>
6709 __isl_give isl_val *isl_basic_set_dim_max_val(
6710 __isl_take isl_basic_set *bset, int pos);
6711 __isl_give isl_val *isl_set_dim_min_val(
6712 __isl_take isl_set *set, int pos);
6713 __isl_give isl_val *isl_set_dim_max_val(
6714 __isl_take isl_set *set, int pos);
6716 Return the minimal or maximal value attained by the given set dimension,
6717 independently of the parameter values and of any other dimensions.
6718 The result is C<NULL> in case of an error, the optimal value in case
6719 there is one, (negative) infinity if the problem is unbounded and
6720 NaN if the input is empty.
6722 =item * Parametric optimization
6724 __isl_give isl_pw_aff *isl_set_dim_min(
6725 __isl_take isl_set *set, int pos);
6726 __isl_give isl_pw_aff *isl_set_dim_max(
6727 __isl_take isl_set *set, int pos);
6728 __isl_give isl_pw_aff *isl_map_dim_min(
6729 __isl_take isl_map *map, int pos);
6730 __isl_give isl_pw_aff *isl_map_dim_max(
6731 __isl_take isl_map *map, int pos);
6732 __isl_give isl_multi_pw_aff *
6733 isl_set_min_multi_pw_aff(
6734 __isl_take isl_set *set);
6735 __isl_give isl_multi_pw_aff *
6736 isl_set_max_multi_pw_aff(
6737 __isl_take isl_set *set);
6738 __isl_give isl_multi_pw_aff *
6739 isl_map_min_multi_pw_aff(
6740 __isl_take isl_map *map);
6741 __isl_give isl_multi_pw_aff *
6742 isl_map_max_multi_pw_aff(
6743 __isl_take isl_map *map);
6745 Compute the minimum or maximum of the (given) set or output dimension(s)
6746 as a function of the parameters (and input dimensions), but independently
6747 of the other set or output dimensions.
6748 For lexicographic optimization, see L<"Lexicographic Optimization">.
6752 The following functions compute either the set of (rational) coefficient
6753 values of valid constraints for the given set or the set of (rational)
6754 values satisfying the constraints with coefficients from the given set.
6755 Internally, these two sets of functions perform essentially the
6756 same operations, except that the set of coefficients is assumed to
6757 be a cone, while the set of values may be any polyhedron.
6758 The current implementation is based on the Farkas lemma and
6759 Fourier-Motzkin elimination, but this may change or be made optional
6760 in future. In particular, future implementations may use different
6761 dualization algorithms or skip the elimination step.
6763 #include <isl/set.h>
6764 __isl_give isl_basic_set *isl_basic_set_coefficients(
6765 __isl_take isl_basic_set *bset);
6766 __isl_give isl_basic_set_list *
6767 isl_basic_set_list_coefficients(
6768 __isl_take isl_basic_set_list *list);
6769 __isl_give isl_basic_set *isl_set_coefficients(
6770 __isl_take isl_set *set);
6771 __isl_give isl_union_set *isl_union_set_coefficients(
6772 __isl_take isl_union_set *bset);
6773 __isl_give isl_basic_set *isl_basic_set_solutions(
6774 __isl_take isl_basic_set *bset);
6775 __isl_give isl_basic_set *isl_set_solutions(
6776 __isl_take isl_set *set);
6777 __isl_give isl_union_set *isl_union_set_solutions(
6778 __isl_take isl_union_set *bset);
6782 __isl_give isl_map *isl_map_fixed_power_val(
6783 __isl_take isl_map *map,
6784 __isl_take isl_val *exp);
6785 __isl_give isl_union_map *
6786 isl_union_map_fixed_power_val(
6787 __isl_take isl_union_map *umap,
6788 __isl_take isl_val *exp);
6790 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6791 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6792 of C<map> is computed.
6794 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6796 __isl_give isl_union_map *isl_union_map_power(
6797 __isl_take isl_union_map *umap, isl_bool *exact);
6799 Compute a parametric representation for all positive powers I<k> of C<map>.
6800 The result maps I<k> to a nested relation corresponding to the
6801 I<k>th power of C<map>.
6802 The result may be an overapproximation. If the result is known to be exact,
6803 then C<*exact> is set to C<1>.
6805 =item * Transitive closure
6807 __isl_give isl_map *isl_map_transitive_closure(
6808 __isl_take isl_map *map, isl_bool *exact);
6809 __isl_give isl_union_map *isl_union_map_transitive_closure(
6810 __isl_take isl_union_map *umap, isl_bool *exact);
6812 Compute the transitive closure of C<map>.
6813 The result may be an overapproximation. If the result is known to be exact,
6814 then C<*exact> is set to C<1>.
6816 =item * Reaching path lengths
6818 __isl_give isl_map *isl_map_reaching_path_lengths(
6819 __isl_take isl_map *map, isl_bool *exact);
6821 Compute a relation that maps each element in the range of C<map>
6822 to the lengths of all paths composed of edges in C<map> that
6823 end up in the given element.
6824 The result may be an overapproximation. If the result is known to be exact,
6825 then C<*exact> is set to C<1>.
6826 To compute the I<maximal> path length, the resulting relation
6827 should be postprocessed by C<isl_map_lexmax>.
6828 In particular, if the input relation is a dependence relation
6829 (mapping sources to sinks), then the maximal path length corresponds
6830 to the free schedule.
6831 Note, however, that C<isl_map_lexmax> expects the maximum to be
6832 finite, so if the path lengths are unbounded (possibly due to
6833 the overapproximation), then you will get an error message.
6837 #include <isl/space.h>
6838 __isl_give isl_space *isl_space_wrap(
6839 __isl_take isl_space *space);
6840 __isl_give isl_space *isl_space_unwrap(
6841 __isl_take isl_space *space);
6843 #include <isl/local_space.h>
6844 __isl_give isl_local_space *isl_local_space_wrap(
6845 __isl_take isl_local_space *ls);
6847 #include <isl/set.h>
6848 __isl_give isl_basic_map *isl_basic_set_unwrap(
6849 __isl_take isl_basic_set *bset);
6850 __isl_give isl_map *isl_set_unwrap(
6851 __isl_take isl_set *set);
6853 #include <isl/map.h>
6854 __isl_give isl_basic_set *isl_basic_map_wrap(
6855 __isl_take isl_basic_map *bmap);
6856 __isl_give isl_set *isl_map_wrap(
6857 __isl_take isl_map *map);
6859 #include <isl/union_set.h>
6860 __isl_give isl_union_map *isl_union_set_unwrap(
6861 __isl_take isl_union_set *uset);
6863 #include <isl/union_map.h>
6864 __isl_give isl_union_set *isl_union_map_wrap(
6865 __isl_take isl_union_map *umap);
6867 The input to C<isl_space_unwrap> should
6868 be the space of a set, while that of
6869 C<isl_space_wrap> should be the space of a relation.
6870 Conversely, the output of C<isl_space_unwrap> is the space
6871 of a relation, while that of C<isl_space_wrap> is the space of a set.
6875 Remove any internal structure of domain (and range) of the given
6876 set or relation. If there is any such internal structure in the input,
6877 then the name of the space is also removed.
6879 #include <isl/space.h>
6880 __isl_give isl_space *isl_space_flatten_domain(
6881 __isl_take isl_space *space);
6882 __isl_give isl_space *isl_space_flatten_range(
6883 __isl_take isl_space *space);
6885 #include <isl/local_space.h>
6886 __isl_give isl_local_space *
6887 isl_local_space_flatten_domain(
6888 __isl_take isl_local_space *ls);
6889 __isl_give isl_local_space *
6890 isl_local_space_flatten_range(
6891 __isl_take isl_local_space *ls);
6893 #include <isl/set.h>
6894 __isl_give isl_basic_set *isl_basic_set_flatten(
6895 __isl_take isl_basic_set *bset);
6896 __isl_give isl_set *isl_set_flatten(
6897 __isl_take isl_set *set);
6899 #include <isl/map.h>
6900 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6901 __isl_take isl_basic_map *bmap);
6902 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6903 __isl_take isl_basic_map *bmap);
6904 __isl_give isl_map *isl_map_flatten_range(
6905 __isl_take isl_map *map);
6906 __isl_give isl_map *isl_map_flatten_domain(
6907 __isl_take isl_map *map);
6908 __isl_give isl_basic_map *isl_basic_map_flatten(
6909 __isl_take isl_basic_map *bmap);
6910 __isl_give isl_map *isl_map_flatten(
6911 __isl_take isl_map *map);
6914 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6915 __isl_take isl_multi_id *mi);
6917 #include <isl/val.h>
6918 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6919 __isl_take isl_multi_val *mv);
6921 #include <isl/aff.h>
6922 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6923 __isl_take isl_multi_aff *ma);
6924 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6925 __isl_take isl_multi_aff *ma);
6926 __isl_give isl_multi_pw_aff *
6927 isl_multi_pw_aff_flatten_range(
6928 __isl_take isl_multi_pw_aff *mpa);
6929 __isl_give isl_multi_union_pw_aff *
6930 isl_multi_union_pw_aff_flatten_range(
6931 __isl_take isl_multi_union_pw_aff *mupa);
6933 #include <isl/map.h>
6934 __isl_give isl_map *isl_set_flatten_map(
6935 __isl_take isl_set *set);
6937 The function above constructs a relation
6938 that maps the input set to a flattened version of the set.
6942 Lift the input set to a space with extra dimensions corresponding
6943 to the existentially quantified variables in the input.
6944 In particular, the result lives in a wrapped map where the domain
6945 is the original space and the range corresponds to the original
6946 existentially quantified variables.
6948 #include <isl/set.h>
6949 __isl_give isl_basic_set *isl_basic_set_lift(
6950 __isl_take isl_basic_set *bset);
6951 __isl_give isl_set *isl_set_lift(
6952 __isl_take isl_set *set);
6953 __isl_give isl_union_set *isl_union_set_lift(
6954 __isl_take isl_union_set *uset);
6956 Given a local space that contains the existentially quantified
6957 variables of a set, a basic relation that, when applied to
6958 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6959 can be constructed using the following function.
6961 #include <isl/local_space.h>
6962 __isl_give isl_basic_map *isl_local_space_lifting(
6963 __isl_take isl_local_space *ls);
6965 #include <isl/aff.h>
6966 __isl_give isl_multi_aff *isl_multi_aff_lift(
6967 __isl_take isl_multi_aff *maff,
6968 __isl_give isl_local_space **ls);
6970 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6971 then it is assigned the local space that lies at the basis of
6972 the lifting applied.
6974 =item * Internal Product
6976 #include <isl/space.h>
6977 __isl_give isl_space *isl_space_zip(
6978 __isl_take isl_space *space);
6980 #include <isl/map.h>
6981 __isl_give isl_basic_map *isl_basic_map_zip(
6982 __isl_take isl_basic_map *bmap);
6983 __isl_give isl_map *isl_map_zip(
6984 __isl_take isl_map *map);
6986 #include <isl/union_map.h>
6987 __isl_give isl_union_map *isl_union_map_zip(
6988 __isl_take isl_union_map *umap);
6990 Given a relation with nested relations for domain and range,
6991 interchange the range of the domain with the domain of the range.
6995 #include <isl/space.h>
6996 __isl_give isl_space *isl_space_curry(
6997 __isl_take isl_space *space);
6998 __isl_give isl_space *isl_space_uncurry(
6999 __isl_take isl_space *space);
7001 #include <isl/map.h>
7002 __isl_give isl_basic_map *isl_basic_map_curry(
7003 __isl_take isl_basic_map *bmap);
7004 __isl_give isl_basic_map *isl_basic_map_uncurry(
7005 __isl_take isl_basic_map *bmap);
7006 __isl_give isl_map *isl_map_curry(
7007 __isl_take isl_map *map);
7008 __isl_give isl_map *isl_map_uncurry(
7009 __isl_take isl_map *map);
7011 #include <isl/union_map.h>
7012 __isl_give isl_union_map *isl_union_map_curry(
7013 __isl_take isl_union_map *umap);
7014 __isl_give isl_union_map *isl_union_map_uncurry(
7015 __isl_take isl_union_map *umap);
7017 Given a relation with a nested relation for domain,
7018 the C<curry> functions
7019 move the range of the nested relation out of the domain
7020 and use it as the domain of a nested relation in the range,
7021 with the original range as range of this nested relation.
7022 The C<uncurry> functions perform the inverse operation.
7024 #include <isl/space.h>
7025 __isl_give isl_space *isl_space_range_curry(
7026 __isl_take isl_space *space);
7028 #include <isl/map.h>
7029 __isl_give isl_map *isl_map_range_curry(
7030 __isl_take isl_map *map);
7032 #include <isl/union_map.h>
7033 __isl_give isl_union_map *isl_union_map_range_curry(
7034 __isl_take isl_union_map *umap);
7036 These functions apply the currying to the relation that
7037 is nested inside the range of the input.
7039 =item * Aligning parameters
7041 Change the order of the parameters of the given set, relation
7043 such that the first parameters match those of C<model>.
7044 This may involve the introduction of extra parameters.
7045 All parameters need to be named.
7047 #include <isl/space.h>
7048 __isl_give isl_space *isl_space_align_params(
7049 __isl_take isl_space *space1,
7050 __isl_take isl_space *space2)
7052 #include <isl/set.h>
7053 __isl_give isl_basic_set *isl_basic_set_align_params(
7054 __isl_take isl_basic_set *bset,
7055 __isl_take isl_space *model);
7056 __isl_give isl_set *isl_set_align_params(
7057 __isl_take isl_set *set,
7058 __isl_take isl_space *model);
7060 #include <isl/map.h>
7061 __isl_give isl_basic_map *isl_basic_map_align_params(
7062 __isl_take isl_basic_map *bmap,
7063 __isl_take isl_space *model);
7064 __isl_give isl_map *isl_map_align_params(
7065 __isl_take isl_map *map,
7066 __isl_take isl_space *model);
7069 __isl_give isl_multi_id *isl_multi_id_align_params(
7070 __isl_take isl_multi_id *mi,
7071 __isl_take isl_space *model);
7073 #include <isl/val.h>
7074 __isl_give isl_multi_val *isl_multi_val_align_params(
7075 __isl_take isl_multi_val *mv,
7076 __isl_take isl_space *model);
7078 #include <isl/aff.h>
7079 __isl_give isl_aff *isl_aff_align_params(
7080 __isl_take isl_aff *aff,
7081 __isl_take isl_space *model);
7082 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7083 __isl_take isl_multi_aff *multi,
7084 __isl_take isl_space *model);
7085 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7086 __isl_take isl_pw_aff *pwaff,
7087 __isl_take isl_space *model);
7088 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7089 __isl_take isl_pw_multi_aff *pma,
7090 __isl_take isl_space *model);
7091 __isl_give isl_union_pw_aff *
7092 isl_union_pw_aff_align_params(
7093 __isl_take isl_union_pw_aff *upa,
7094 __isl_take isl_space *model);
7095 __isl_give isl_union_pw_multi_aff *
7096 isl_union_pw_multi_aff_align_params(
7097 __isl_take isl_union_pw_multi_aff *upma,
7098 __isl_take isl_space *model);
7099 __isl_give isl_multi_union_pw_aff *
7100 isl_multi_union_pw_aff_align_params(
7101 __isl_take isl_multi_union_pw_aff *mupa,
7102 __isl_take isl_space *model);
7104 #include <isl/polynomial.h>
7105 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7106 __isl_take isl_qpolynomial *qp,
7107 __isl_take isl_space *model);
7109 =item * Drop unused parameters
7111 Drop parameters that are not referenced by the isl object.
7112 All parameters need to be named.
7114 #include <isl/set.h>
7115 __isl_give isl_basic_set *
7116 isl_basic_set_drop_unused_params(
7117 __isl_take isl_basic_set *bset);
7118 __isl_give isl_set *isl_set_drop_unused_params(
7119 __isl_take isl_set *set);
7121 #include <isl/map.h>
7122 __isl_give isl_basic_map *
7123 isl_basic_map_drop_unused_params(
7124 __isl_take isl_basic_map *bmap);
7125 __isl_give isl_map *isl_map_drop_unused_params(
7126 __isl_take isl_map *map);
7128 #include <isl/union_set.h>
7129 __isl_give isl_union_set *
7130 isl_union_set_drop_unused_params(
7131 __isl_take isl_union_set *uset);
7133 #include <isl/union_map.h>
7134 __isl_give isl_union_map *
7135 isl_union_map_drop_unused_params(
7136 __isl_take isl_union_map *umap);
7138 #include <isl/aff.h>
7139 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7140 __isl_take isl_pw_aff *pa);
7141 __isl_give isl_pw_multi_aff *
7142 isl_pw_multi_aff_drop_unused_params(
7143 __isl_take isl_pw_multi_aff *pma);
7144 __isl_give isl_union_pw_aff *
7145 isl_union_pw_aff_drop_unused_params(
7146 __isl_take isl_union_pw_aff *upa);
7147 __isl_give isl_union_pw_multi_aff *
7148 isl_union_pw_multi_aff_drop_unused_params(
7149 __isl_take isl_union_pw_multi_aff *upma);
7151 #include <isl/polynomial.h>
7152 __isl_give isl_pw_qpolynomial *
7153 isl_pw_qpolynomial_drop_unused_params(
7154 __isl_take isl_pw_qpolynomial *pwqp);
7155 __isl_give isl_pw_qpolynomial_fold *
7156 isl_pw_qpolynomial_fold_drop_unused_params(
7157 __isl_take isl_pw_qpolynomial_fold *pwf);
7158 __isl_give isl_union_pw_qpolynomial *
7159 isl_union_pw_qpolynomial_drop_unused_params(
7160 __isl_take isl_union_pw_qpolynomial *upwqp);
7161 __isl_give isl_union_pw_qpolynomial_fold *
7162 isl_union_pw_qpolynomial_fold_drop_unused_params(
7163 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7165 =item * Unary Arithmetic Operations
7167 #include <isl/set.h>
7168 __isl_give isl_set *isl_set_neg(
7169 __isl_take isl_set *set);
7170 #include <isl/map.h>
7171 __isl_give isl_map *isl_map_neg(
7172 __isl_take isl_map *map);
7174 C<isl_set_neg> constructs a set containing the opposites of
7175 the elements in its argument.
7176 The domain of the result of C<isl_map_neg> is the same
7177 as the domain of its argument. The corresponding range
7178 elements are the opposites of the corresponding range
7179 elements in the argument.
7181 #include <isl/val.h>
7182 __isl_give isl_multi_val *isl_multi_val_neg(
7183 __isl_take isl_multi_val *mv);
7185 #include <isl/aff.h>
7186 __isl_give isl_aff *isl_aff_neg(
7187 __isl_take isl_aff *aff);
7188 __isl_give isl_multi_aff *isl_multi_aff_neg(
7189 __isl_take isl_multi_aff *ma);
7190 __isl_give isl_pw_aff *isl_pw_aff_neg(
7191 __isl_take isl_pw_aff *pwaff);
7192 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7193 __isl_take isl_pw_multi_aff *pma);
7194 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7195 __isl_take isl_multi_pw_aff *mpa);
7196 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7197 __isl_take isl_union_pw_aff *upa);
7198 __isl_give isl_union_pw_multi_aff *
7199 isl_union_pw_multi_aff_neg(
7200 __isl_take isl_union_pw_multi_aff *upma);
7201 __isl_give isl_multi_union_pw_aff *
7202 isl_multi_union_pw_aff_neg(
7203 __isl_take isl_multi_union_pw_aff *mupa);
7204 __isl_give isl_aff *isl_aff_ceil(
7205 __isl_take isl_aff *aff);
7206 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7207 __isl_take isl_pw_aff *pwaff);
7208 __isl_give isl_aff *isl_aff_floor(
7209 __isl_take isl_aff *aff);
7210 __isl_give isl_multi_aff *isl_multi_aff_floor(
7211 __isl_take isl_multi_aff *ma);
7212 __isl_give isl_pw_aff *isl_pw_aff_floor(
7213 __isl_take isl_pw_aff *pwaff);
7214 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7215 __isl_take isl_union_pw_aff *upa);
7216 __isl_give isl_multi_union_pw_aff *
7217 isl_multi_union_pw_aff_floor(
7218 __isl_take isl_multi_union_pw_aff *mupa);
7220 #include <isl/aff.h>
7221 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7222 __isl_take isl_pw_aff_list *list);
7223 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7224 __isl_take isl_pw_aff_list *list);
7226 #include <isl/polynomial.h>
7227 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7228 __isl_take isl_qpolynomial *qp);
7229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7230 __isl_take isl_pw_qpolynomial *pwqp);
7231 __isl_give isl_union_pw_qpolynomial *
7232 isl_union_pw_qpolynomial_neg(
7233 __isl_take isl_union_pw_qpolynomial *upwqp);
7234 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7235 __isl_take isl_qpolynomial *qp,
7237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7238 __isl_take isl_pw_qpolynomial *pwqp,
7243 The following functions evaluate a function in a point.
7245 #include <isl/aff.h>
7246 __isl_give isl_val *isl_aff_eval(
7247 __isl_take isl_aff *aff,
7248 __isl_take isl_point *pnt);
7249 __isl_give isl_val *isl_pw_aff_eval(
7250 __isl_take isl_pw_aff *pa,
7251 __isl_take isl_point *pnt);
7253 #include <isl/polynomial.h>
7254 __isl_give isl_val *isl_pw_qpolynomial_eval(
7255 __isl_take isl_pw_qpolynomial *pwqp,
7256 __isl_take isl_point *pnt);
7257 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7258 __isl_take isl_pw_qpolynomial_fold *pwf,
7259 __isl_take isl_point *pnt);
7260 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7261 __isl_take isl_union_pw_qpolynomial *upwqp,
7262 __isl_take isl_point *pnt);
7263 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7264 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7265 __isl_take isl_point *pnt);
7267 These functions return NaN when evaluated at a void point.
7268 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7269 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7270 when the function is evaluated outside its explicit domain.
7272 =item * Dimension manipulation
7274 It is usually not advisable to directly change the (input or output)
7275 space of a set or a relation as this removes the name and the internal
7276 structure of the space. However, the functions below can be useful
7277 to add new parameters, assuming
7278 C<isl_set_align_params> and C<isl_map_align_params>
7281 #include <isl/space.h>
7282 __isl_give isl_space *isl_space_add_dims(
7283 __isl_take isl_space *space,
7284 enum isl_dim_type type, unsigned n);
7285 __isl_give isl_space *isl_space_insert_dims(
7286 __isl_take isl_space *space,
7287 enum isl_dim_type type, unsigned pos, unsigned n);
7288 __isl_give isl_space *isl_space_drop_dims(
7289 __isl_take isl_space *space,
7290 enum isl_dim_type type, unsigned first, unsigned n);
7291 __isl_give isl_space *isl_space_move_dims(
7292 __isl_take isl_space *space,
7293 enum isl_dim_type dst_type, unsigned dst_pos,
7294 enum isl_dim_type src_type, unsigned src_pos,
7297 #include <isl/local_space.h>
7298 __isl_give isl_local_space *isl_local_space_add_dims(
7299 __isl_take isl_local_space *ls,
7300 enum isl_dim_type type, unsigned n);
7301 __isl_give isl_local_space *isl_local_space_insert_dims(
7302 __isl_take isl_local_space *ls,
7303 enum isl_dim_type type, unsigned first, unsigned n);
7304 __isl_give isl_local_space *isl_local_space_drop_dims(
7305 __isl_take isl_local_space *ls,
7306 enum isl_dim_type type, unsigned first, unsigned n);
7308 #include <isl/set.h>
7309 __isl_give isl_basic_set *isl_basic_set_add_dims(
7310 __isl_take isl_basic_set *bset,
7311 enum isl_dim_type type, unsigned n);
7312 __isl_give isl_set *isl_set_add_dims(
7313 __isl_take isl_set *set,
7314 enum isl_dim_type type, unsigned n);
7315 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7316 __isl_take isl_basic_set *bset,
7317 enum isl_dim_type type, unsigned pos,
7319 __isl_give isl_set *isl_set_insert_dims(
7320 __isl_take isl_set *set,
7321 enum isl_dim_type type, unsigned pos, unsigned n);
7322 __isl_give isl_basic_set *isl_basic_set_move_dims(
7323 __isl_take isl_basic_set *bset,
7324 enum isl_dim_type dst_type, unsigned dst_pos,
7325 enum isl_dim_type src_type, unsigned src_pos,
7327 __isl_give isl_set *isl_set_move_dims(
7328 __isl_take isl_set *set,
7329 enum isl_dim_type dst_type, unsigned dst_pos,
7330 enum isl_dim_type src_type, unsigned src_pos,
7333 #include <isl/map.h>
7334 __isl_give isl_basic_map *isl_basic_map_add_dims(
7335 __isl_take isl_basic_map *bmap,
7336 enum isl_dim_type type, unsigned n);
7337 __isl_give isl_map *isl_map_add_dims(
7338 __isl_take isl_map *map,
7339 enum isl_dim_type type, unsigned n);
7340 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7341 __isl_take isl_basic_map *bmap,
7342 enum isl_dim_type type, unsigned pos,
7344 __isl_give isl_map *isl_map_insert_dims(
7345 __isl_take isl_map *map,
7346 enum isl_dim_type type, unsigned pos, unsigned n);
7347 __isl_give isl_basic_map *isl_basic_map_move_dims(
7348 __isl_take isl_basic_map *bmap,
7349 enum isl_dim_type dst_type, unsigned dst_pos,
7350 enum isl_dim_type src_type, unsigned src_pos,
7352 __isl_give isl_map *isl_map_move_dims(
7353 __isl_take isl_map *map,
7354 enum isl_dim_type dst_type, unsigned dst_pos,
7355 enum isl_dim_type src_type, unsigned src_pos,
7358 #include <isl/val.h>
7359 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7360 __isl_take isl_multi_val *mv,
7361 enum isl_dim_type type, unsigned first, unsigned n);
7362 __isl_give isl_multi_val *isl_multi_val_add_dims(
7363 __isl_take isl_multi_val *mv,
7364 enum isl_dim_type type, unsigned n);
7365 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7366 __isl_take isl_multi_val *mv,
7367 enum isl_dim_type type, unsigned first, unsigned n);
7369 #include <isl/aff.h>
7370 __isl_give isl_aff *isl_aff_insert_dims(
7371 __isl_take isl_aff *aff,
7372 enum isl_dim_type type, unsigned first, unsigned n);
7373 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7374 __isl_take isl_multi_aff *ma,
7375 enum isl_dim_type type, unsigned first, unsigned n);
7376 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7377 __isl_take isl_pw_aff *pwaff,
7378 enum isl_dim_type type, unsigned first, unsigned n);
7379 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7380 __isl_take isl_multi_pw_aff *mpa,
7381 enum isl_dim_type type, unsigned first, unsigned n);
7382 __isl_give isl_aff *isl_aff_add_dims(
7383 __isl_take isl_aff *aff,
7384 enum isl_dim_type type, unsigned n);
7385 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7386 __isl_take isl_multi_aff *ma,
7387 enum isl_dim_type type, unsigned n);
7388 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7389 __isl_take isl_pw_aff *pwaff,
7390 enum isl_dim_type type, unsigned n);
7391 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7392 __isl_take isl_multi_pw_aff *mpa,
7393 enum isl_dim_type type, unsigned n);
7394 __isl_give isl_aff *isl_aff_drop_dims(
7395 __isl_take isl_aff *aff,
7396 enum isl_dim_type type, unsigned first, unsigned n);
7397 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7398 __isl_take isl_multi_aff *maff,
7399 enum isl_dim_type type, unsigned first, unsigned n);
7400 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7401 __isl_take isl_pw_aff *pwaff,
7402 enum isl_dim_type type, unsigned first, unsigned n);
7403 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7404 __isl_take isl_pw_multi_aff *pma,
7405 enum isl_dim_type type, unsigned first, unsigned n);
7406 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7407 __isl_take isl_union_pw_aff *upa,
7408 enum isl_dim_type type, unsigned first, unsigned n);
7409 __isl_give isl_union_pw_multi_aff *
7410 isl_union_pw_multi_aff_drop_dims(
7411 __isl_take isl_union_pw_multi_aff *upma,
7412 enum isl_dim_type type,
7413 unsigned first, unsigned n);
7414 __isl_give isl_multi_union_pw_aff *
7415 isl_multi_union_pw_aff_drop_dims(
7416 __isl_take isl_multi_union_pw_aff *mupa,
7417 enum isl_dim_type type, unsigned first,
7419 __isl_give isl_aff *isl_aff_move_dims(
7420 __isl_take isl_aff *aff,
7421 enum isl_dim_type dst_type, unsigned dst_pos,
7422 enum isl_dim_type src_type, unsigned src_pos,
7424 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7425 __isl_take isl_multi_aff *ma,
7426 enum isl_dim_type dst_type, unsigned dst_pos,
7427 enum isl_dim_type src_type, unsigned src_pos,
7429 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7430 __isl_take isl_pw_aff *pa,
7431 enum isl_dim_type dst_type, unsigned dst_pos,
7432 enum isl_dim_type src_type, unsigned src_pos,
7434 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7435 __isl_take isl_multi_pw_aff *pma,
7436 enum isl_dim_type dst_type, unsigned dst_pos,
7437 enum isl_dim_type src_type, unsigned src_pos,
7440 #include <isl/polynomial.h>
7441 __isl_give isl_union_pw_qpolynomial *
7442 isl_union_pw_qpolynomial_drop_dims(
7443 __isl_take isl_union_pw_qpolynomial *upwqp,
7444 enum isl_dim_type type,
7445 unsigned first, unsigned n);
7446 __isl_give isl_union_pw_qpolynomial_fold *
7447 isl_union_pw_qpolynomial_fold_drop_dims(
7448 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7449 enum isl_dim_type type,
7450 unsigned first, unsigned n);
7452 The operations on union expressions can only manipulate parameters.
7456 =head2 Binary Operations
7458 The two arguments of a binary operation not only need to live
7459 in the same C<isl_ctx>, they currently also need to have
7460 the same (number of) parameters.
7462 =head3 Basic Operations
7466 =item * Intersection
7468 #include <isl/local_space.h>
7469 __isl_give isl_local_space *isl_local_space_intersect(
7470 __isl_take isl_local_space *ls1,
7471 __isl_take isl_local_space *ls2);
7473 #include <isl/set.h>
7474 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7475 __isl_take isl_basic_set *bset1,
7476 __isl_take isl_basic_set *bset2);
7477 __isl_give isl_basic_set *isl_basic_set_intersect(
7478 __isl_take isl_basic_set *bset1,
7479 __isl_take isl_basic_set *bset2);
7480 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7481 __isl_take struct isl_basic_set_list *list);
7482 __isl_give isl_set *isl_set_intersect_params(
7483 __isl_take isl_set *set,
7484 __isl_take isl_set *params);
7485 __isl_give isl_set *isl_set_intersect(
7486 __isl_take isl_set *set1,
7487 __isl_take isl_set *set2);
7488 __isl_give isl_set *isl_set_intersect_factor_domain(
7489 __isl_take isl_set *set,
7490 __isl_take isl_set *domain);
7491 __isl_give isl_set *isl_set_intersect_factor_range(
7492 __isl_take isl_set *set,
7493 __isl_take isl_set *range);
7495 #include <isl/map.h>
7496 __isl_give isl_basic_map *isl_basic_map_intersect_params(
7497 __isl_take isl_basic_map *bmap,
7498 __isl_take isl_basic_set *bset);
7499 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7500 __isl_take isl_basic_map *bmap,
7501 __isl_take isl_basic_set *bset);
7502 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7503 __isl_take isl_basic_map *bmap,
7504 __isl_take isl_basic_set *bset);
7505 __isl_give isl_basic_map *isl_basic_map_intersect(
7506 __isl_take isl_basic_map *bmap1,
7507 __isl_take isl_basic_map *bmap2);
7508 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7509 __isl_take isl_basic_map_list *list);
7510 __isl_give isl_map *isl_map_intersect_params(
7511 __isl_take isl_map *map,
7512 __isl_take isl_set *params);
7513 __isl_give isl_map *isl_map_intersect_domain(
7514 __isl_take isl_map *map,
7515 __isl_take isl_set *set);
7516 __isl_give isl_map *isl_map_intersect_range(
7517 __isl_take isl_map *map,
7518 __isl_take isl_set *set);
7519 __isl_give isl_map *isl_map_intersect(
7520 __isl_take isl_map *map1,
7521 __isl_take isl_map *map2);
7522 __isl_give isl_map *
7523 isl_map_intersect_domain_factor_domain(
7524 __isl_take isl_map *map,
7525 __isl_take isl_map *factor);
7526 __isl_give isl_map *
7527 isl_map_intersect_domain_factor_range(
7528 __isl_take isl_map *map,
7529 __isl_take isl_map *factor);
7530 __isl_give isl_map *
7531 isl_map_intersect_range_factor_domain(
7532 __isl_take isl_map *map,
7533 __isl_take isl_map *factor);
7534 __isl_give isl_map *
7535 isl_map_intersect_range_factor_range(
7536 __isl_take isl_map *map,
7537 __isl_take isl_map *factor);
7538 __isl_give isl_map *
7539 isl_map_intersect_domain_wrapped_domain(
7540 __isl_take isl_map *map,
7541 __isl_take isl_set *domain);
7542 __isl_give isl_map *
7543 isl_map_intersect_range_wrapped_domain(
7544 __isl_take isl_map *map,
7545 __isl_take isl_set *domain);
7547 #include <isl/union_set.h>
7548 __isl_give isl_union_set *isl_union_set_intersect_params(
7549 __isl_take isl_union_set *uset,
7550 __isl_take isl_set *set);
7551 __isl_give isl_union_set *isl_union_set_intersect(
7552 __isl_take isl_union_set *uset1,
7553 __isl_take isl_union_set *uset2);
7555 #include <isl/union_map.h>
7556 __isl_give isl_union_map *isl_union_map_intersect_params(
7557 __isl_take isl_union_map *umap,
7558 __isl_take isl_set *set);
7559 __isl_give isl_union_map *
7560 isl_union_map_intersect_domain_union_set(
7561 __isl_take isl_union_map *umap,
7562 __isl_take isl_union_set *uset);
7563 __isl_give isl_union_map *
7564 isl_union_map_intersect_domain_space(
7565 __isl_take isl_union_map *umap,
7566 __isl_take isl_space *space);
7567 __isl_give isl_union_map *isl_union_map_intersect_domain(
7568 __isl_take isl_union_map *umap,
7569 __isl_take isl_union_set *uset);
7570 __isl_give isl_union_map *
7571 isl_union_map_intersect_range_union_set(
7572 __isl_take isl_union_map *umap,
7573 __isl_take isl_union_set *uset);
7574 __isl_give isl_union_map *
7575 isl_union_map_intersect_range_space(
7576 __isl_take isl_union_map *umap,
7577 __isl_take isl_space *space);
7578 __isl_give isl_union_map *isl_union_map_intersect_range(
7579 __isl_take isl_union_map *umap,
7580 __isl_take isl_union_set *uset);
7581 __isl_give isl_union_map *isl_union_map_intersect(
7582 __isl_take isl_union_map *umap1,
7583 __isl_take isl_union_map *umap2);
7584 __isl_give isl_union_map *
7585 isl_union_map_intersect_domain_factor_domain(
7586 __isl_take isl_union_map *umap,
7587 __isl_take isl_union_map *factor);
7588 __isl_give isl_union_map *
7589 isl_union_map_intersect_domain_factor_range(
7590 __isl_take isl_union_map *umap,
7591 __isl_take isl_union_map *factor);
7592 __isl_give isl_union_map *
7593 isl_union_map_intersect_range_factor_domain(
7594 __isl_take isl_union_map *umap,
7595 __isl_take isl_union_map *factor);
7596 __isl_give isl_union_map *
7597 isl_union_map_intersect_range_factor_range(
7598 __isl_take isl_union_map *umap,
7599 __isl_take isl_union_map *factor);
7600 __isl_give isl_union_map *
7601 isl_union_map_intersect_domain_wrapped_domain_union_set(
7602 __isl_take isl_union_map *umap,
7603 __isl_take isl_union_set *domain);
7604 __isl_give isl_union_map *
7605 isl_union_map_intersect_range_wrapped_domain_union_set(
7606 __isl_take isl_union_map *umap,
7607 __isl_take isl_union_set *domain);
7609 #include <isl/aff.h>
7610 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7611 __isl_take isl_pw_aff *pa,
7612 __isl_take isl_set *set);
7613 __isl_give isl_multi_pw_aff *
7614 isl_multi_pw_aff_intersect_domain(
7615 __isl_take isl_multi_pw_aff *mpa,
7616 __isl_take isl_set *domain);
7617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7618 __isl_take isl_pw_multi_aff *pma,
7619 __isl_take isl_set *set);
7620 __isl_give isl_union_pw_aff *
7621 isl_union_pw_aff_intersect_domain_space(
7622 __isl_take isl_union_pw_aff *upa,
7623 __isl_take isl_space *space);
7624 __isl_give isl_union_pw_aff *
7625 isl_union_pw_aff_intersect_domain_union_set(
7626 __isl_take isl_union_pw_aff *upa,
7627 __isl_take isl_union_set *uset);
7628 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7629 __isl_take isl_union_pw_aff *upa,
7630 __isl_take isl_union_set *uset);
7631 __isl_give isl_union_pw_multi_aff *
7632 isl_union_pw_multi_aff_intersect_domain_space(
7633 __isl_take isl_union_pw_multi_aff *upma,
7634 __isl_take isl_space *space);
7635 __isl_give isl_union_pw_multi_aff *
7636 isl_union_pw_multi_aff_intersect_domain_union_set(
7637 __isl_take isl_union_pw_multi_aff *upma,
7638 __isl_take isl_union_set *uset);
7639 __isl_give isl_union_pw_multi_aff *
7640 isl_union_pw_multi_aff_intersect_domain(
7641 __isl_take isl_union_pw_multi_aff *upma,
7642 __isl_take isl_union_set *uset);
7643 __isl_give isl_multi_union_pw_aff *
7644 isl_multi_union_pw_aff_intersect_domain(
7645 __isl_take isl_multi_union_pw_aff *mupa,
7646 __isl_take isl_union_set *uset);
7647 __isl_give isl_pw_aff *
7648 isl_pw_aff_intersect_domain_wrapped_domain(
7649 __isl_take isl_pw_aff *pa,
7650 __isl_take isl_set *set);
7651 __isl_give isl_pw_multi_aff *
7652 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7653 __isl_take isl_pw_multi_aff *pma,
7654 __isl_take isl_set *set);
7655 __isl_give isl_union_pw_aff *
7656 isl_union_pw_aff_intersect_domain_wrapped_domain(
7657 __isl_take isl_union_pw_aff *upa,
7658 __isl_take isl_union_set *uset);
7659 __isl_give isl_union_pw_multi_aff *
7660 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7661 __isl_take isl_union_pw_multi_aff *upma,
7662 __isl_take isl_union_set *uset);
7663 __isl_give isl_pw_aff *
7664 isl_pw_aff_intersect_domain_wrapped_range(
7665 __isl_take isl_pw_aff *pa,
7666 __isl_take isl_set *set);
7667 __isl_give isl_pw_multi_aff *
7668 isl_pw_multi_aff_intersect_domain_wrapped_range(
7669 __isl_take isl_pw_multi_aff *pma,
7670 __isl_take isl_set *set);
7671 __isl_give isl_union_pw_multi_aff *
7672 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7673 __isl_take isl_union_pw_multi_aff *upma,
7674 __isl_take isl_union_set *uset);
7675 __isl_give isl_union_pw_aff *
7676 isl_union_pw_aff_intersect_domain_wrapped_range(
7677 __isl_take isl_union_pw_aff *upa,
7678 __isl_take isl_union_set *uset);
7679 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7680 __isl_take isl_pw_aff *pa,
7681 __isl_take isl_set *set);
7682 __isl_give isl_multi_pw_aff *
7683 isl_multi_pw_aff_intersect_params(
7684 __isl_take isl_multi_pw_aff *mpa,
7685 __isl_take isl_set *set);
7686 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7687 __isl_take isl_pw_multi_aff *pma,
7688 __isl_take isl_set *set);
7689 __isl_give isl_union_pw_aff *
7690 isl_union_pw_aff_intersect_params(
7691 __isl_take isl_union_pw_aff *upa,
7692 __isl_take isl_set *set);
7693 __isl_give isl_union_pw_multi_aff *
7694 isl_union_pw_multi_aff_intersect_params(
7695 __isl_take isl_union_pw_multi_aff *upma,
7696 __isl_take isl_set *set);
7697 __isl_give isl_multi_union_pw_aff *
7698 isl_multi_union_pw_aff_intersect_params(
7699 __isl_take isl_multi_union_pw_aff *mupa,
7700 __isl_take isl_set *params);
7701 __isl_give isl_multi_union_pw_aff *
7702 isl_multi_union_pw_aff_intersect_range(
7703 __isl_take isl_multi_union_pw_aff *mupa,
7704 __isl_take isl_set *set);
7706 #include <isl/polynomial.h>
7707 __isl_give isl_pw_qpolynomial *
7708 isl_pw_qpolynomial_intersect_domain(
7709 __isl_take isl_pw_qpolynomial *pwpq,
7710 __isl_take isl_set *set);
7711 __isl_give isl_union_pw_qpolynomial *
7712 isl_union_pw_qpolynomial_intersect_domain_space(
7713 __isl_take isl_union_pw_qpolynomial *upwpq,
7714 __isl_take isl_space *space);
7715 __isl_give isl_union_pw_qpolynomial *
7716 isl_union_pw_qpolynomial_intersect_domain_union_set(
7717 __isl_take isl_union_pw_qpolynomial *upwpq,
7718 __isl_take isl_union_set *uset);
7719 __isl_give isl_union_pw_qpolynomial *
7720 isl_union_pw_qpolynomial_intersect_domain(
7721 __isl_take isl_union_pw_qpolynomial *upwpq,
7722 __isl_take isl_union_set *uset);
7723 __isl_give isl_union_pw_qpolynomial_fold *
7724 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7725 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7726 __isl_take isl_space *space);
7727 __isl_give isl_union_pw_qpolynomial_fold *
7728 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7729 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7730 __isl_take isl_union_set *uset);
7731 __isl_give isl_union_pw_qpolynomial_fold *
7732 isl_union_pw_qpolynomial_fold_intersect_domain(
7733 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7734 __isl_take isl_union_set *uset);
7735 __isl_give isl_pw_qpolynomial *
7736 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7737 __isl_take isl_pw_qpolynomial *pwpq,
7738 __isl_take isl_set *set);
7739 __isl_give isl_pw_qpolynomial_fold *
7740 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7741 __isl_take isl_pw_qpolynomial_fold *pwf,
7742 __isl_take isl_set *set);
7743 __isl_give isl_union_pw_qpolynomial *
7744 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7745 __isl_take isl_union_pw_qpolynomial *upwpq,
7746 __isl_take isl_union_set *uset);
7747 __isl_give isl_union_pw_qpolynomial_fold *
7748 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7749 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7750 __isl_take isl_union_set *uset);
7751 __isl_give isl_pw_qpolynomial *
7752 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7753 __isl_take isl_pw_qpolynomial *pwpq,
7754 __isl_take isl_set *set);
7755 __isl_give isl_pw_qpolynomial_fold *
7756 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7757 __isl_take isl_pw_qpolynomial_fold *pwf,
7758 __isl_take isl_set *set);
7759 __isl_give isl_union_pw_qpolynomial *
7760 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7761 __isl_take isl_union_pw_qpolynomial *upwpq,
7762 __isl_take isl_union_set *uset);
7763 __isl_give isl_union_pw_qpolynomial_fold *
7764 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7765 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7766 __isl_take isl_union_set *uset);
7767 __isl_give isl_pw_qpolynomial *
7768 isl_pw_qpolynomial_intersect_params(
7769 __isl_take isl_pw_qpolynomial *pwpq,
7770 __isl_take isl_set *set);
7771 __isl_give isl_pw_qpolynomial_fold *
7772 isl_pw_qpolynomial_fold_intersect_params(
7773 __isl_take isl_pw_qpolynomial_fold *pwf,
7774 __isl_take isl_set *set);
7775 __isl_give isl_union_pw_qpolynomial *
7776 isl_union_pw_qpolynomial_intersect_params(
7777 __isl_take isl_union_pw_qpolynomial *upwpq,
7778 __isl_take isl_set *set);
7779 __isl_give isl_union_pw_qpolynomial_fold *
7780 isl_union_pw_qpolynomial_fold_intersect_params(
7781 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7782 __isl_take isl_set *set);
7784 The second argument to the C<_params> functions needs to be
7785 a parametric (basic) set. For the other functions, a parametric set
7786 for either argument is only allowed if the other argument is
7787 a parametric set as well.
7788 The list passed to C<isl_basic_set_list_intersect> needs to have
7789 at least one element and all elements need to live in the same space.
7790 The function C<isl_multi_union_pw_aff_intersect_range>
7791 restricts the input function to those shared domain elements
7792 that map to the specified range.
7793 C<isl_union_map_intersect_domain> is an alternative name for
7794 C<isl_union_map_intersect_domain_union_set>.
7795 Similarly for the other pairs of functions.
7799 #include <isl/set.h>
7800 __isl_give isl_set *isl_basic_set_union(
7801 __isl_take isl_basic_set *bset1,
7802 __isl_take isl_basic_set *bset2);
7803 __isl_give isl_set *isl_set_union(
7804 __isl_take isl_set *set1,
7805 __isl_take isl_set *set2);
7806 __isl_give isl_set *isl_set_list_union(
7807 __isl_take isl_set_list *list);
7809 #include <isl/map.h>
7810 __isl_give isl_map *isl_basic_map_union(
7811 __isl_take isl_basic_map *bmap1,
7812 __isl_take isl_basic_map *bmap2);
7813 __isl_give isl_map *isl_map_union(
7814 __isl_take isl_map *map1,
7815 __isl_take isl_map *map2);
7817 #include <isl/union_set.h>
7818 __isl_give isl_union_set *isl_union_set_union(
7819 __isl_take isl_union_set *uset1,
7820 __isl_take isl_union_set *uset2);
7821 __isl_give isl_union_set *isl_union_set_list_union(
7822 __isl_take isl_union_set_list *list);
7824 #include <isl/union_map.h>
7825 __isl_give isl_union_map *isl_union_map_union(
7826 __isl_take isl_union_map *umap1,
7827 __isl_take isl_union_map *umap2);
7829 The list passed to C<isl_set_list_union> needs to have
7830 at least one element and all elements need to live in the same space.
7832 =item * Set difference
7834 #include <isl/set.h>
7835 __isl_give isl_set *isl_set_subtract(
7836 __isl_take isl_set *set1,
7837 __isl_take isl_set *set2);
7839 #include <isl/map.h>
7840 __isl_give isl_map *isl_map_subtract(
7841 __isl_take isl_map *map1,
7842 __isl_take isl_map *map2);
7843 __isl_give isl_map *isl_map_subtract_domain(
7844 __isl_take isl_map *map,
7845 __isl_take isl_set *dom);
7846 __isl_give isl_map *isl_map_subtract_range(
7847 __isl_take isl_map *map,
7848 __isl_take isl_set *dom);
7850 #include <isl/union_set.h>
7851 __isl_give isl_union_set *isl_union_set_subtract(
7852 __isl_take isl_union_set *uset1,
7853 __isl_take isl_union_set *uset2);
7855 #include <isl/union_map.h>
7856 __isl_give isl_union_map *isl_union_map_subtract(
7857 __isl_take isl_union_map *umap1,
7858 __isl_take isl_union_map *umap2);
7859 __isl_give isl_union_map *isl_union_map_subtract_domain(
7860 __isl_take isl_union_map *umap,
7861 __isl_take isl_union_set *dom);
7862 __isl_give isl_union_map *isl_union_map_subtract_range(
7863 __isl_take isl_union_map *umap,
7864 __isl_take isl_union_set *dom);
7866 #include <isl/aff.h>
7867 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7868 __isl_take isl_pw_aff *pa,
7869 __isl_take isl_set *set);
7870 __isl_give isl_pw_multi_aff *
7871 isl_pw_multi_aff_subtract_domain(
7872 __isl_take isl_pw_multi_aff *pma,
7873 __isl_take isl_set *set);
7874 __isl_give isl_union_pw_aff *
7875 isl_union_pw_aff_subtract_domain_union_set(
7876 __isl_take isl_union_pw_aff *upa,
7877 __isl_take isl_union_set *uset);
7878 __isl_give isl_union_pw_aff *
7879 isl_union_pw_aff_subtract_domain_space(
7880 __isl_take isl_union_pw_aff *upa,
7881 __isl_take isl_space *space);
7882 __isl_give isl_union_pw_aff *
7883 isl_union_pw_aff_subtract_domain(
7884 __isl_take isl_union_pw_aff *upa,
7885 __isl_take isl_union_set *uset);
7886 __isl_give isl_union_pw_multi_aff *
7887 isl_union_pw_multi_aff_subtract_domain_union_set(
7888 __isl_take isl_union_pw_multi_aff *upma,
7889 __isl_take isl_set *set);
7890 __isl_give isl_union_pw_multi_aff *
7891 isl_union_pw_multi_aff_subtract_domain_space(
7892 __isl_take isl_union_pw_multi_aff *upma,
7893 __isl_take isl_space *space);
7894 __isl_give isl_union_pw_multi_aff *
7895 isl_union_pw_multi_aff_subtract_domain(
7896 __isl_take isl_union_pw_multi_aff *upma,
7897 __isl_take isl_union_set *uset);
7899 #include <isl/polynomial.h>
7900 __isl_give isl_pw_qpolynomial *
7901 isl_pw_qpolynomial_subtract_domain(
7902 __isl_take isl_pw_qpolynomial *pwpq,
7903 __isl_take isl_set *set);
7904 __isl_give isl_pw_qpolynomial_fold *
7905 isl_pw_qpolynomial_fold_subtract_domain(
7906 __isl_take isl_pw_qpolynomial_fold *pwf,
7907 __isl_take isl_set *set);
7908 __isl_give isl_union_pw_qpolynomial *
7909 isl_union_pw_qpolynomial_subtract_domain_union_set(
7910 __isl_take isl_union_pw_qpolynomial *upwpq,
7911 __isl_take isl_union_set *uset);
7912 __isl_give isl_union_pw_qpolynomial *
7913 isl_union_pw_qpolynomial_subtract_domain_space(
7914 __isl_take isl_union_pw_qpolynomial *upwpq,
7915 __isl_take isl_space *space);
7916 __isl_give isl_union_pw_qpolynomial *
7917 isl_union_pw_qpolynomial_subtract_domain(
7918 __isl_take isl_union_pw_qpolynomial *upwpq,
7919 __isl_take isl_union_set *uset);
7920 __isl_give isl_union_pw_qpolynomial_fold *
7921 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7922 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7923 __isl_take isl_union_set *uset);
7924 __isl_give isl_union_pw_qpolynomial_fold *
7925 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7926 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7927 __isl_take isl_space *space);
7928 __isl_give isl_union_pw_qpolynomial_fold *
7929 isl_union_pw_qpolynomial_fold_subtract_domain(
7930 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7931 __isl_take isl_union_set *uset);
7933 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7934 C<isl_union_pw_aff_subtract_domain_union_set>.
7935 Similarly for the other pairs of functions.
7939 #include <isl/space.h>
7940 __isl_give isl_space *isl_space_join(
7941 __isl_take isl_space *left,
7942 __isl_take isl_space *right);
7944 #include <isl/set.h>
7945 __isl_give isl_basic_set *isl_basic_set_apply(
7946 __isl_take isl_basic_set *bset,
7947 __isl_take isl_basic_map *bmap);
7948 __isl_give isl_set *isl_set_apply(
7949 __isl_take isl_set *set,
7950 __isl_take isl_map *map);
7952 #include <isl/union_set.h>
7953 __isl_give isl_union_set *isl_union_set_apply(
7954 __isl_take isl_union_set *uset,
7955 __isl_take isl_union_map *umap);
7957 #include <isl/map.h>
7958 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7959 __isl_take isl_basic_map *bmap1,
7960 __isl_take isl_basic_map *bmap2);
7961 __isl_give isl_basic_map *isl_basic_map_apply_range(
7962 __isl_take isl_basic_map *bmap1,
7963 __isl_take isl_basic_map *bmap2);
7964 __isl_give isl_map *isl_map_apply_domain(
7965 __isl_take isl_map *map1,
7966 __isl_take isl_map *map2);
7967 __isl_give isl_map *isl_map_apply_range(
7968 __isl_take isl_map *map1,
7969 __isl_take isl_map *map2);
7971 #include <isl/union_map.h>
7972 __isl_give isl_union_map *isl_union_map_apply_domain(
7973 __isl_take isl_union_map *umap1,
7974 __isl_take isl_union_map *umap2);
7975 __isl_give isl_union_map *isl_union_map_apply_range(
7976 __isl_take isl_union_map *umap1,
7977 __isl_take isl_union_map *umap2);
7979 #include <isl/aff.h>
7980 __isl_give isl_union_pw_multi_aff *
7981 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7982 __isl_take isl_union_pw_multi_aff *upma1,
7983 __isl_take isl_union_pw_multi_aff *upma2);
7984 __isl_give isl_union_pw_aff *
7985 isl_multi_union_pw_aff_apply_aff(
7986 __isl_take isl_multi_union_pw_aff *mupa,
7987 __isl_take isl_aff *aff);
7988 __isl_give isl_union_pw_aff *
7989 isl_multi_union_pw_aff_apply_pw_aff(
7990 __isl_take isl_multi_union_pw_aff *mupa,
7991 __isl_take isl_pw_aff *pa);
7992 __isl_give isl_multi_union_pw_aff *
7993 isl_multi_union_pw_aff_apply_multi_aff(
7994 __isl_take isl_multi_union_pw_aff *mupa,
7995 __isl_take isl_multi_aff *ma);
7996 __isl_give isl_multi_union_pw_aff *
7997 isl_multi_union_pw_aff_apply_pw_multi_aff(
7998 __isl_take isl_multi_union_pw_aff *mupa,
7999 __isl_take isl_pw_multi_aff *pma);
8001 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
8002 over the shared domain of the elements of the input. The dimension is
8003 required to be greater than zero.
8004 The C<isl_multi_union_pw_aff> argument of
8005 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
8006 but only if the range of the C<isl_multi_aff> argument
8007 is also zero-dimensional.
8008 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
8010 #include <isl/polynomial.h>
8011 __isl_give isl_pw_qpolynomial_fold *
8012 isl_set_apply_pw_qpolynomial_fold(
8013 __isl_take isl_set *set,
8014 __isl_take isl_pw_qpolynomial_fold *pwf,
8016 __isl_give isl_pw_qpolynomial_fold *
8017 isl_map_apply_pw_qpolynomial_fold(
8018 __isl_take isl_map *map,
8019 __isl_take isl_pw_qpolynomial_fold *pwf,
8021 __isl_give isl_union_pw_qpolynomial_fold *
8022 isl_union_set_apply_union_pw_qpolynomial_fold(
8023 __isl_take isl_union_set *uset,
8024 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8026 __isl_give isl_union_pw_qpolynomial_fold *
8027 isl_union_map_apply_union_pw_qpolynomial_fold(
8028 __isl_take isl_union_map *umap,
8029 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8032 The functions taking a map
8033 compose the given map with the given piecewise quasipolynomial reduction.
8034 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
8035 over all elements in the intersection of the range of the map
8036 and the domain of the piecewise quasipolynomial reduction
8037 as a function of an element in the domain of the map.
8038 The functions taking a set compute a bound over all elements in the
8039 intersection of the set and the domain of the
8040 piecewise quasipolynomial reduction.
8044 #include <isl/set.h>
8045 __isl_give isl_basic_set *
8046 isl_basic_set_preimage_multi_aff(
8047 __isl_take isl_basic_set *bset,
8048 __isl_take isl_multi_aff *ma);
8049 __isl_give isl_set *isl_set_preimage_multi_aff(
8050 __isl_take isl_set *set,
8051 __isl_take isl_multi_aff *ma);
8052 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8053 __isl_take isl_set *set,
8054 __isl_take isl_pw_multi_aff *pma);
8055 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8056 __isl_take isl_set *set,
8057 __isl_take isl_multi_pw_aff *mpa);
8059 #include <isl/union_set.h>
8060 __isl_give isl_union_set *
8061 isl_union_set_preimage_multi_aff(
8062 __isl_take isl_union_set *uset,
8063 __isl_take isl_multi_aff *ma);
8064 __isl_give isl_union_set *
8065 isl_union_set_preimage_pw_multi_aff(
8066 __isl_take isl_union_set *uset,
8067 __isl_take isl_pw_multi_aff *pma);
8068 __isl_give isl_union_set *
8069 isl_union_set_preimage_union_pw_multi_aff(
8070 __isl_take isl_union_set *uset,
8071 __isl_take isl_union_pw_multi_aff *upma);
8073 #include <isl/map.h>
8074 __isl_give isl_basic_map *
8075 isl_basic_map_preimage_domain_multi_aff(
8076 __isl_take isl_basic_map *bmap,
8077 __isl_take isl_multi_aff *ma);
8078 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8079 __isl_take isl_map *map,
8080 __isl_take isl_multi_aff *ma);
8081 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8082 __isl_take isl_map *map,
8083 __isl_take isl_multi_aff *ma);
8084 __isl_give isl_map *
8085 isl_map_preimage_domain_pw_multi_aff(
8086 __isl_take isl_map *map,
8087 __isl_take isl_pw_multi_aff *pma);
8088 __isl_give isl_map *
8089 isl_map_preimage_range_pw_multi_aff(
8090 __isl_take isl_map *map,
8091 __isl_take isl_pw_multi_aff *pma);
8092 __isl_give isl_map *
8093 isl_map_preimage_domain_multi_pw_aff(
8094 __isl_take isl_map *map,
8095 __isl_take isl_multi_pw_aff *mpa);
8096 __isl_give isl_basic_map *
8097 isl_basic_map_preimage_range_multi_aff(
8098 __isl_take isl_basic_map *bmap,
8099 __isl_take isl_multi_aff *ma);
8101 #include <isl/union_map.h>
8102 __isl_give isl_union_map *
8103 isl_union_map_preimage_domain_multi_aff(
8104 __isl_take isl_union_map *umap,
8105 __isl_take isl_multi_aff *ma);
8106 __isl_give isl_union_map *
8107 isl_union_map_preimage_range_multi_aff(
8108 __isl_take isl_union_map *umap,
8109 __isl_take isl_multi_aff *ma);
8110 __isl_give isl_union_map *
8111 isl_union_map_preimage_domain_pw_multi_aff(
8112 __isl_take isl_union_map *umap,
8113 __isl_take isl_pw_multi_aff *pma);
8114 __isl_give isl_union_map *
8115 isl_union_map_preimage_range_pw_multi_aff(
8116 __isl_take isl_union_map *umap,
8117 __isl_take isl_pw_multi_aff *pma);
8118 __isl_give isl_union_map *
8119 isl_union_map_preimage_domain_union_pw_multi_aff(
8120 __isl_take isl_union_map *umap,
8121 __isl_take isl_union_pw_multi_aff *upma);
8122 __isl_give isl_union_map *
8123 isl_union_map_preimage_range_union_pw_multi_aff(
8124 __isl_take isl_union_map *umap,
8125 __isl_take isl_union_pw_multi_aff *upma);
8127 #include <isl/aff.h>
8128 __isl_give isl_pw_multi_aff *
8129 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8130 __isl_take isl_pw_multi_aff *pma1,
8131 __isl_take isl_pw_multi_aff *pma2);
8132 __isl_give isl_union_pw_multi_aff *
8133 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8134 __isl_take isl_union_pw_multi_aff *upma1,
8135 __isl_take isl_union_pw_multi_aff *upma2);
8137 These functions compute the preimage of the given set or map domain/range under
8138 the given function. In other words, the expression is plugged
8139 into the set description or into the domain/range of the map or function.
8143 #include <isl/aff.h>
8144 __isl_give isl_aff *isl_aff_pullback_aff(
8145 __isl_take isl_aff *aff1,
8146 __isl_take isl_aff *aff2);
8147 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8148 __isl_take isl_aff *aff,
8149 __isl_take isl_multi_aff *ma);
8150 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8151 __isl_take isl_pw_aff *pa,
8152 __isl_take isl_multi_aff *ma);
8153 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8154 __isl_take isl_pw_aff *pa,
8155 __isl_take isl_pw_multi_aff *pma);
8156 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8157 __isl_take isl_pw_aff *pa,
8158 __isl_take isl_multi_pw_aff *mpa);
8159 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8160 __isl_take isl_multi_aff *ma1,
8161 __isl_take isl_multi_aff *ma2);
8162 __isl_give isl_pw_multi_aff *
8163 isl_pw_multi_aff_pullback_multi_aff(
8164 __isl_take isl_pw_multi_aff *pma,
8165 __isl_take isl_multi_aff *ma);
8166 __isl_give isl_multi_pw_aff *
8167 isl_multi_pw_aff_pullback_multi_aff(
8168 __isl_take isl_multi_pw_aff *mpa,
8169 __isl_take isl_multi_aff *ma);
8170 __isl_give isl_pw_multi_aff *
8171 isl_pw_multi_aff_pullback_pw_multi_aff(
8172 __isl_take isl_pw_multi_aff *pma1,
8173 __isl_take isl_pw_multi_aff *pma2);
8174 __isl_give isl_multi_pw_aff *
8175 isl_multi_pw_aff_pullback_pw_multi_aff(
8176 __isl_take isl_multi_pw_aff *mpa,
8177 __isl_take isl_pw_multi_aff *pma);
8178 __isl_give isl_multi_pw_aff *
8179 isl_multi_pw_aff_pullback_multi_pw_aff(
8180 __isl_take isl_multi_pw_aff *mpa1,
8181 __isl_take isl_multi_pw_aff *mpa2);
8182 __isl_give isl_union_pw_aff *
8183 isl_union_pw_aff_pullback_union_pw_multi_aff(
8184 __isl_take isl_union_pw_aff *upa,
8185 __isl_take isl_union_pw_multi_aff *upma);
8186 __isl_give isl_union_pw_multi_aff *
8187 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8188 __isl_take isl_union_pw_multi_aff *upma1,
8189 __isl_take isl_union_pw_multi_aff *upma2);
8190 __isl_give isl_multi_union_pw_aff *
8191 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8192 __isl_take isl_multi_union_pw_aff *mupa,
8193 __isl_take isl_union_pw_multi_aff *upma);
8195 These functions precompose the first expression by the second function.
8196 In other words, the second function is plugged
8197 into the first expression.
8201 #include <isl/aff.h>
8202 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8203 __isl_take isl_aff *aff1,
8204 __isl_take isl_aff *aff2);
8205 __isl_give isl_set *isl_aff_eq_set(
8206 __isl_take isl_aff *aff1,
8207 __isl_take isl_aff *aff2);
8208 __isl_give isl_set *isl_aff_ne_set(
8209 __isl_take isl_aff *aff1,
8210 __isl_take isl_aff *aff2);
8211 __isl_give isl_basic_set *isl_aff_le_basic_set(
8212 __isl_take isl_aff *aff1,
8213 __isl_take isl_aff *aff2);
8214 __isl_give isl_set *isl_aff_le_set(
8215 __isl_take isl_aff *aff1,
8216 __isl_take isl_aff *aff2);
8217 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8218 __isl_take isl_aff *aff1,
8219 __isl_take isl_aff *aff2);
8220 __isl_give isl_set *isl_aff_lt_set(
8221 __isl_take isl_aff *aff1,
8222 __isl_take isl_aff *aff2);
8223 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8224 __isl_take isl_aff *aff1,
8225 __isl_take isl_aff *aff2);
8226 __isl_give isl_set *isl_aff_ge_set(
8227 __isl_take isl_aff *aff1,
8228 __isl_take isl_aff *aff2);
8229 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8230 __isl_take isl_aff *aff1,
8231 __isl_take isl_aff *aff2);
8232 __isl_give isl_set *isl_aff_gt_set(
8233 __isl_take isl_aff *aff1,
8234 __isl_take isl_aff *aff2);
8235 __isl_give isl_set *isl_pw_aff_eq_set(
8236 __isl_take isl_pw_aff *pwaff1,
8237 __isl_take isl_pw_aff *pwaff2);
8238 __isl_give isl_set *isl_pw_aff_ne_set(
8239 __isl_take isl_pw_aff *pwaff1,
8240 __isl_take isl_pw_aff *pwaff2);
8241 __isl_give isl_set *isl_pw_aff_le_set(
8242 __isl_take isl_pw_aff *pwaff1,
8243 __isl_take isl_pw_aff *pwaff2);
8244 __isl_give isl_set *isl_pw_aff_lt_set(
8245 __isl_take isl_pw_aff *pwaff1,
8246 __isl_take isl_pw_aff *pwaff2);
8247 __isl_give isl_set *isl_pw_aff_ge_set(
8248 __isl_take isl_pw_aff *pwaff1,
8249 __isl_take isl_pw_aff *pwaff2);
8250 __isl_give isl_set *isl_pw_aff_gt_set(
8251 __isl_take isl_pw_aff *pwaff1,
8252 __isl_take isl_pw_aff *pwaff2);
8254 __isl_give isl_set *isl_multi_aff_lex_le_set(
8255 __isl_take isl_multi_aff *ma1,
8256 __isl_take isl_multi_aff *ma2);
8257 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8258 __isl_take isl_multi_aff *ma1,
8259 __isl_take isl_multi_aff *ma2);
8260 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8261 __isl_take isl_multi_aff *ma1,
8262 __isl_take isl_multi_aff *ma2);
8263 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8264 __isl_take isl_multi_aff *ma1,
8265 __isl_take isl_multi_aff *ma2);
8267 __isl_give isl_set *isl_pw_aff_list_eq_set(
8268 __isl_take isl_pw_aff_list *list1,
8269 __isl_take isl_pw_aff_list *list2);
8270 __isl_give isl_set *isl_pw_aff_list_ne_set(
8271 __isl_take isl_pw_aff_list *list1,
8272 __isl_take isl_pw_aff_list *list2);
8273 __isl_give isl_set *isl_pw_aff_list_le_set(
8274 __isl_take isl_pw_aff_list *list1,
8275 __isl_take isl_pw_aff_list *list2);
8276 __isl_give isl_set *isl_pw_aff_list_lt_set(
8277 __isl_take isl_pw_aff_list *list1,
8278 __isl_take isl_pw_aff_list *list2);
8279 __isl_give isl_set *isl_pw_aff_list_ge_set(
8280 __isl_take isl_pw_aff_list *list1,
8281 __isl_take isl_pw_aff_list *list2);
8282 __isl_give isl_set *isl_pw_aff_list_gt_set(
8283 __isl_take isl_pw_aff_list *list1,
8284 __isl_take isl_pw_aff_list *list2);
8286 The function C<isl_aff_ge_basic_set> returns a basic set
8287 containing those elements in the shared space
8288 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8289 The function C<isl_pw_aff_ge_set> returns a set
8290 containing those elements in the shared domain
8291 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8292 greater than or equal to C<pwaff2>.
8293 The function C<isl_multi_aff_lex_le_set> returns a set
8294 containing those elements in the shared domain space
8295 where C<ma1> is lexicographically smaller than or
8297 The functions operating on C<isl_pw_aff_list> apply the corresponding
8298 C<isl_pw_aff> function to each pair of elements in the two lists.
8300 #include <isl/aff.h>
8301 __isl_give isl_map *isl_pw_aff_eq_map(
8302 __isl_take isl_pw_aff *pa1,
8303 __isl_take isl_pw_aff *pa2);
8304 __isl_give isl_map *isl_pw_aff_le_map(
8305 __isl_take isl_pw_aff *pa1,
8306 __isl_take isl_pw_aff *pa2);
8307 __isl_give isl_map *isl_pw_aff_lt_map(
8308 __isl_take isl_pw_aff *pa1,
8309 __isl_take isl_pw_aff *pa2);
8310 __isl_give isl_map *isl_pw_aff_ge_map(
8311 __isl_take isl_pw_aff *pa1,
8312 __isl_take isl_pw_aff *pa2);
8313 __isl_give isl_map *isl_pw_aff_gt_map(
8314 __isl_take isl_pw_aff *pa1,
8315 __isl_take isl_pw_aff *pa2);
8317 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8318 __isl_take isl_multi_pw_aff *mpa1,
8319 __isl_take isl_multi_pw_aff *mpa2);
8320 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8321 __isl_take isl_multi_pw_aff *mpa1,
8322 __isl_take isl_multi_pw_aff *mpa2);
8323 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8324 __isl_take isl_multi_pw_aff *mpa1,
8325 __isl_take isl_multi_pw_aff *mpa2);
8326 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8327 __isl_take isl_multi_pw_aff *mpa1,
8328 __isl_take isl_multi_pw_aff *mpa2);
8329 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8330 __isl_take isl_multi_pw_aff *mpa1,
8331 __isl_take isl_multi_pw_aff *mpa2);
8333 These functions return a map between domain elements of the arguments
8334 where the function values satisfy the given relation.
8336 #include <isl/map.h>
8337 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8338 __isl_take isl_map *map,
8339 __isl_take isl_multi_pw_aff *mpa);
8340 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8341 __isl_take isl_map *map,
8342 __isl_take isl_multi_pw_aff *mpa);
8343 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8344 __isl_take isl_map *map,
8345 __isl_take isl_multi_pw_aff *mpa);
8346 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8347 __isl_take isl_map *map,
8348 __isl_take isl_multi_pw_aff *mpa);
8349 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8350 __isl_take isl_map *map,
8351 __isl_take isl_multi_pw_aff *mpa);
8353 #include <isl/union_map.h>
8354 __isl_give isl_union_map *
8355 isl_union_map_eq_at_multi_union_pw_aff(
8356 __isl_take isl_union_map *umap,
8357 __isl_take isl_multi_union_pw_aff *mupa);
8358 __isl_give isl_union_map *
8359 isl_union_map_lex_lt_at_multi_union_pw_aff(
8360 __isl_take isl_union_map *umap,
8361 __isl_take isl_multi_union_pw_aff *mupa);
8362 __isl_give isl_union_map *
8363 isl_union_map_lex_le_at_multi_union_pw_aff(
8364 __isl_take isl_union_map *umap,
8365 __isl_take isl_multi_union_pw_aff *mupa);
8366 __isl_give isl_union_map *
8367 isl_union_map_lex_gt_at_multi_union_pw_aff(
8368 __isl_take isl_union_map *umap,
8369 __isl_take isl_multi_union_pw_aff *mupa);
8370 __isl_give isl_union_map *
8371 isl_union_map_lex_ge_at_multi_union_pw_aff(
8372 __isl_take isl_union_map *umap,
8373 __isl_take isl_multi_union_pw_aff *mupa);
8375 These functions select the subset of elements in the union map
8376 that have an equal or lexicographically smaller or greater function value.
8378 =item * Cartesian Product
8380 #include <isl/space.h>
8381 __isl_give isl_space *isl_space_product(
8382 __isl_take isl_space *space1,
8383 __isl_take isl_space *space2);
8384 __isl_give isl_space *isl_space_domain_product(
8385 __isl_take isl_space *space1,
8386 __isl_take isl_space *space2);
8387 __isl_give isl_space *isl_space_range_product(
8388 __isl_take isl_space *space1,
8389 __isl_take isl_space *space2);
8392 C<isl_space_product>, C<isl_space_domain_product>
8393 and C<isl_space_range_product> take pairs or relation spaces and
8394 produce a single relations space, where either the domain, the range
8395 or both domain and range are wrapped spaces of relations between
8396 the domains and/or ranges of the input spaces.
8397 If the product is only constructed over the domain or the range
8398 then the ranges or the domains of the inputs should be the same.
8399 The function C<isl_space_product> also accepts a pair of set spaces,
8400 in which case it returns a wrapped space of a relation between the
8403 #include <isl/set.h>
8404 __isl_give isl_set *isl_set_product(
8405 __isl_take isl_set *set1,
8406 __isl_take isl_set *set2);
8408 #include <isl/map.h>
8409 __isl_give isl_basic_map *isl_basic_map_domain_product(
8410 __isl_take isl_basic_map *bmap1,
8411 __isl_take isl_basic_map *bmap2);
8412 __isl_give isl_basic_map *isl_basic_map_range_product(
8413 __isl_take isl_basic_map *bmap1,
8414 __isl_take isl_basic_map *bmap2);
8415 __isl_give isl_basic_map *isl_basic_map_product(
8416 __isl_take isl_basic_map *bmap1,
8417 __isl_take isl_basic_map *bmap2);
8418 __isl_give isl_map *isl_map_domain_product(
8419 __isl_take isl_map *map1,
8420 __isl_take isl_map *map2);
8421 __isl_give isl_map *isl_map_range_product(
8422 __isl_take isl_map *map1,
8423 __isl_take isl_map *map2);
8424 __isl_give isl_map *isl_map_product(
8425 __isl_take isl_map *map1,
8426 __isl_take isl_map *map2);
8428 #include <isl/union_set.h>
8429 __isl_give isl_union_set *isl_union_set_product(
8430 __isl_take isl_union_set *uset1,
8431 __isl_take isl_union_set *uset2);
8433 #include <isl/union_map.h>
8434 __isl_give isl_union_map *isl_union_map_domain_product(
8435 __isl_take isl_union_map *umap1,
8436 __isl_take isl_union_map *umap2);
8437 __isl_give isl_union_map *isl_union_map_range_product(
8438 __isl_take isl_union_map *umap1,
8439 __isl_take isl_union_map *umap2);
8440 __isl_give isl_union_map *isl_union_map_product(
8441 __isl_take isl_union_map *umap1,
8442 __isl_take isl_union_map *umap2);
8445 __isl_give isl_multi_id *isl_multi_id_range_product(
8446 __isl_take isl_multi_id *mi1,
8447 __isl_take isl_multi_id *mi2);
8449 #include <isl/val.h>
8450 __isl_give isl_multi_val *isl_multi_val_range_product(
8451 __isl_take isl_multi_val *mv1,
8452 __isl_take isl_multi_val *mv2);
8453 __isl_give isl_multi_val *isl_multi_val_product(
8454 __isl_take isl_multi_val *mv1,
8455 __isl_take isl_multi_val *mv2);
8457 #include <isl/aff.h>
8458 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8459 __isl_take isl_multi_aff *ma1,
8460 __isl_take isl_multi_aff *ma2);
8461 __isl_give isl_multi_aff *isl_multi_aff_product(
8462 __isl_take isl_multi_aff *ma1,
8463 __isl_take isl_multi_aff *ma2);
8464 __isl_give isl_multi_pw_aff *
8465 isl_multi_pw_aff_range_product(
8466 __isl_take isl_multi_pw_aff *mpa1,
8467 __isl_take isl_multi_pw_aff *mpa2);
8468 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8469 __isl_take isl_multi_pw_aff *mpa1,
8470 __isl_take isl_multi_pw_aff *mpa2);
8471 __isl_give isl_pw_multi_aff *
8472 isl_pw_multi_aff_range_product(
8473 __isl_take isl_pw_multi_aff *pma1,
8474 __isl_take isl_pw_multi_aff *pma2);
8475 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8476 __isl_take isl_pw_multi_aff *pma1,
8477 __isl_take isl_pw_multi_aff *pma2);
8478 __isl_give isl_union_pw_multi_aff *
8479 isl_union_pw_multi_aff_range_product(
8480 __isl_take isl_union_pw_multi_aff *upma1,
8481 __isl_take isl_union_pw_multi_aff *upma2);
8482 __isl_give isl_multi_union_pw_aff *
8483 isl_multi_union_pw_aff_range_product(
8484 __isl_take isl_multi_union_pw_aff *mupa1,
8485 __isl_take isl_multi_union_pw_aff *mupa2);
8487 The above functions compute the cross product of the given
8488 sets, relations or functions. The domains and ranges of the results
8489 are wrapped maps between domains and ranges of the inputs.
8490 To obtain a ``flat'' product, use the following functions
8493 #include <isl/set.h>
8494 __isl_give isl_basic_set *isl_basic_set_flat_product(
8495 __isl_take isl_basic_set *bset1,
8496 __isl_take isl_basic_set *bset2);
8497 __isl_give isl_set *isl_set_flat_product(
8498 __isl_take isl_set *set1,
8499 __isl_take isl_set *set2);
8501 #include <isl/map.h>
8502 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8503 __isl_take isl_basic_map *bmap1,
8504 __isl_take isl_basic_map *bmap2);
8505 __isl_give isl_map *isl_map_flat_domain_product(
8506 __isl_take isl_map *map1,
8507 __isl_take isl_map *map2);
8508 __isl_give isl_map *isl_map_flat_range_product(
8509 __isl_take isl_map *map1,
8510 __isl_take isl_map *map2);
8511 __isl_give isl_basic_map *isl_basic_map_flat_product(
8512 __isl_take isl_basic_map *bmap1,
8513 __isl_take isl_basic_map *bmap2);
8514 __isl_give isl_map *isl_map_flat_product(
8515 __isl_take isl_map *map1,
8516 __isl_take isl_map *map2);
8518 #include <isl/union_map.h>
8519 __isl_give isl_union_map *
8520 isl_union_map_flat_domain_product(
8521 __isl_take isl_union_map *umap1,
8522 __isl_take isl_union_map *umap2);
8523 __isl_give isl_union_map *
8524 isl_union_map_flat_range_product(
8525 __isl_take isl_union_map *umap1,
8526 __isl_take isl_union_map *umap2);
8529 __isl_give isl_multi_id *
8530 isl_multi_id_flat_range_product(
8531 __isl_take isl_multi_id *mi1,
8532 __isl_take isl_multi_id *mi2);
8534 #include <isl/val.h>
8535 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8536 __isl_take isl_multi_val *mv1,
8537 __isl_take isl_multi_val *mv2);
8539 #include <isl/aff.h>
8540 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8541 __isl_take isl_multi_aff *ma1,
8542 __isl_take isl_multi_aff *ma2);
8543 __isl_give isl_pw_multi_aff *
8544 isl_pw_multi_aff_flat_range_product(
8545 __isl_take isl_pw_multi_aff *pma1,
8546 __isl_take isl_pw_multi_aff *pma2);
8547 __isl_give isl_multi_pw_aff *
8548 isl_multi_pw_aff_flat_range_product(
8549 __isl_take isl_multi_pw_aff *mpa1,
8550 __isl_take isl_multi_pw_aff *mpa2);
8551 __isl_give isl_union_pw_multi_aff *
8552 isl_union_pw_multi_aff_flat_range_product(
8553 __isl_take isl_union_pw_multi_aff *upma1,
8554 __isl_take isl_union_pw_multi_aff *upma2);
8555 __isl_give isl_multi_union_pw_aff *
8556 isl_multi_union_pw_aff_flat_range_product(
8557 __isl_take isl_multi_union_pw_aff *mupa1,
8558 __isl_take isl_multi_union_pw_aff *mupa2);
8560 #include <isl/space.h>
8561 __isl_give isl_space *isl_space_factor_domain(
8562 __isl_take isl_space *space);
8563 __isl_give isl_space *isl_space_factor_range(
8564 __isl_take isl_space *space);
8565 __isl_give isl_space *isl_space_domain_factor_domain(
8566 __isl_take isl_space *space);
8567 __isl_give isl_space *isl_space_domain_factor_range(
8568 __isl_take isl_space *space);
8569 __isl_give isl_space *isl_space_range_factor_domain(
8570 __isl_take isl_space *space);
8571 __isl_give isl_space *isl_space_range_factor_range(
8572 __isl_take isl_space *space);
8574 The functions C<isl_space_range_factor_domain> and
8575 C<isl_space_range_factor_range> extract the two arguments from
8576 the result of a call to C<isl_space_range_product>.
8578 The arguments of a call to a product can be extracted
8579 from the result using the following functions.
8581 #include <isl/map.h>
8582 __isl_give isl_map *isl_map_factor_domain(
8583 __isl_take isl_map *map);
8584 __isl_give isl_map *isl_map_factor_range(
8585 __isl_take isl_map *map);
8586 __isl_give isl_map *isl_map_domain_factor_domain(
8587 __isl_take isl_map *map);
8588 __isl_give isl_map *isl_map_domain_factor_range(
8589 __isl_take isl_map *map);
8590 __isl_give isl_map *isl_map_range_factor_domain(
8591 __isl_take isl_map *map);
8592 __isl_give isl_map *isl_map_range_factor_range(
8593 __isl_take isl_map *map);
8595 #include <isl/union_map.h>
8596 __isl_give isl_union_map *isl_union_map_factor_domain(
8597 __isl_take isl_union_map *umap);
8598 __isl_give isl_union_map *isl_union_map_factor_range(
8599 __isl_take isl_union_map *umap);
8600 __isl_give isl_union_map *
8601 isl_union_map_domain_factor_domain(
8602 __isl_take isl_union_map *umap);
8603 __isl_give isl_union_map *
8604 isl_union_map_domain_factor_range(
8605 __isl_take isl_union_map *umap);
8606 __isl_give isl_union_map *
8607 isl_union_map_range_factor_domain(
8608 __isl_take isl_union_map *umap);
8609 __isl_give isl_union_map *
8610 isl_union_map_range_factor_range(
8611 __isl_take isl_union_map *umap);
8614 __isl_give isl_multi_id *isl_multi_id_factor_range(
8615 __isl_take isl_multi_id *mi);
8616 __isl_give isl_multi_id *
8617 isl_multi_id_range_factor_domain(
8618 __isl_take isl_multi_id *mi);
8619 __isl_give isl_multi_id *
8620 isl_multi_id_range_factor_range(
8621 __isl_take isl_multi_id *mi);
8623 #include <isl/val.h>
8624 __isl_give isl_multi_val *isl_multi_val_factor_range(
8625 __isl_take isl_multi_val *mv);
8626 __isl_give isl_multi_val *
8627 isl_multi_val_range_factor_domain(
8628 __isl_take isl_multi_val *mv);
8629 __isl_give isl_multi_val *
8630 isl_multi_val_range_factor_range(
8631 __isl_take isl_multi_val *mv);
8633 #include <isl/aff.h>
8634 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8635 __isl_take isl_multi_aff *ma);
8636 __isl_give isl_multi_aff *
8637 isl_multi_aff_range_factor_domain(
8638 __isl_take isl_multi_aff *ma);
8639 __isl_give isl_multi_aff *
8640 isl_multi_aff_range_factor_range(
8641 __isl_take isl_multi_aff *ma);
8642 __isl_give isl_multi_pw_aff *
8643 isl_multi_pw_aff_factor_range(
8644 __isl_take isl_multi_pw_aff *mpa);
8645 __isl_give isl_multi_pw_aff *
8646 isl_multi_pw_aff_range_factor_domain(
8647 __isl_take isl_multi_pw_aff *mpa);
8648 __isl_give isl_multi_pw_aff *
8649 isl_multi_pw_aff_range_factor_range(
8650 __isl_take isl_multi_pw_aff *mpa);
8651 __isl_give isl_pw_multi_aff *
8652 isl_pw_multi_aff_range_factor_domain(
8653 __isl_take isl_pw_multi_aff *pma);
8654 __isl_give isl_pw_multi_aff *
8655 isl_pw_multi_aff_range_factor_range(
8656 __isl_take isl_pw_multi_aff *pma);
8657 __isl_give isl_union_pw_multi_aff *
8658 isl_union_pw_multi_aff_range_factor_domain(
8659 __isl_take isl_union_pw_multi_aff *upma);
8660 __isl_give isl_union_pw_multi_aff *
8661 isl_union_pw_multi_aff_range_factor_range(
8662 __isl_take isl_union_pw_multi_aff *upma);
8663 __isl_give isl_multi_union_pw_aff *
8664 isl_multi_union_pw_aff_factor_range(
8665 __isl_take isl_multi_union_pw_aff *mupa);
8666 __isl_give isl_multi_union_pw_aff *
8667 isl_multi_union_pw_aff_range_factor_domain(
8668 __isl_take isl_multi_union_pw_aff *mupa);
8669 __isl_give isl_multi_union_pw_aff *
8670 isl_multi_union_pw_aff_range_factor_range(
8671 __isl_take isl_multi_union_pw_aff *mupa);
8673 The splice functions are a generalization of the flat product functions,
8674 where the second argument may be inserted at any position inside
8675 the first argument rather than being placed at the end.
8676 The functions C<isl_multi_val_factor_range>,
8677 C<isl_multi_aff_factor_range>,
8678 C<isl_multi_pw_aff_factor_range> and
8679 C<isl_multi_union_pw_aff_factor_range>
8680 take functions that live in a set space.
8683 __isl_give isl_multi_id *isl_multi_id_range_splice(
8684 __isl_take isl_multi_id *mi1, unsigned pos,
8685 __isl_take isl_multi_id *mi2);
8687 #include <isl/val.h>
8688 __isl_give isl_multi_val *isl_multi_val_range_splice(
8689 __isl_take isl_multi_val *mv1, unsigned pos,
8690 __isl_take isl_multi_val *mv2);
8692 #include <isl/aff.h>
8693 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8694 __isl_take isl_multi_aff *ma1, unsigned pos,
8695 __isl_take isl_multi_aff *ma2);
8696 __isl_give isl_multi_aff *isl_multi_aff_splice(
8697 __isl_take isl_multi_aff *ma1,
8698 unsigned in_pos, unsigned out_pos,
8699 __isl_take isl_multi_aff *ma2);
8700 __isl_give isl_multi_pw_aff *
8701 isl_multi_pw_aff_range_splice(
8702 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8703 __isl_take isl_multi_pw_aff *mpa2);
8704 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8705 __isl_take isl_multi_pw_aff *mpa1,
8706 unsigned in_pos, unsigned out_pos,
8707 __isl_take isl_multi_pw_aff *mpa2);
8708 __isl_give isl_multi_union_pw_aff *
8709 isl_multi_union_pw_aff_range_splice(
8710 __isl_take isl_multi_union_pw_aff *mupa1,
8712 __isl_take isl_multi_union_pw_aff *mupa2);
8714 =item * Simplification
8716 When applied to a set or relation,
8717 the gist operation returns a set or relation that has the
8718 same intersection with the context as the input set or relation.
8719 Any implicit equality in the intersection is made explicit in the result,
8720 while all inequalities that are redundant with respect to the intersection
8722 In case of union sets and relations, the gist operation is performed
8725 When applied to a function,
8726 the gist operation applies the set gist operation to each of
8727 the cells in the domain of the input piecewise expression.
8728 The context is also exploited
8729 to simplify the expression associated to each cell.
8731 #include <isl/set.h>
8732 __isl_give isl_basic_set *isl_basic_set_gist(
8733 __isl_take isl_basic_set *bset,
8734 __isl_take isl_basic_set *context);
8735 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8736 __isl_take isl_set *context);
8737 __isl_give isl_set *isl_set_gist_params(
8738 __isl_take isl_set *set,
8739 __isl_take isl_set *context);
8741 #include <isl/map.h>
8742 __isl_give isl_basic_map *isl_basic_map_gist(
8743 __isl_take isl_basic_map *bmap,
8744 __isl_take isl_basic_map *context);
8745 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8746 __isl_take isl_basic_map *bmap,
8747 __isl_take isl_basic_set *context);
8748 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8749 __isl_take isl_map *context);
8750 __isl_give isl_map *isl_map_gist_params(
8751 __isl_take isl_map *map,
8752 __isl_take isl_set *context);
8753 __isl_give isl_map *isl_map_gist_domain(
8754 __isl_take isl_map *map,
8755 __isl_take isl_set *context);
8756 __isl_give isl_map *isl_map_gist_range(
8757 __isl_take isl_map *map,
8758 __isl_take isl_set *context);
8760 #include <isl/union_set.h>
8761 __isl_give isl_union_set *isl_union_set_gist(
8762 __isl_take isl_union_set *uset,
8763 __isl_take isl_union_set *context);
8764 __isl_give isl_union_set *isl_union_set_gist_params(
8765 __isl_take isl_union_set *uset,
8766 __isl_take isl_set *set);
8768 #include <isl/union_map.h>
8769 __isl_give isl_union_map *isl_union_map_gist(
8770 __isl_take isl_union_map *umap,
8771 __isl_take isl_union_map *context);
8772 __isl_give isl_union_map *isl_union_map_gist_params(
8773 __isl_take isl_union_map *umap,
8774 __isl_take isl_set *set);
8775 __isl_give isl_union_map *isl_union_map_gist_domain(
8776 __isl_take isl_union_map *umap,
8777 __isl_take isl_union_set *uset);
8778 __isl_give isl_union_map *isl_union_map_gist_range(
8779 __isl_take isl_union_map *umap,
8780 __isl_take isl_union_set *uset);
8782 #include <isl/aff.h>
8783 __isl_give isl_aff *isl_aff_gist_params(
8784 __isl_take isl_aff *aff,
8785 __isl_take isl_set *context);
8786 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8787 __isl_take isl_set *context);
8788 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8789 __isl_take isl_multi_aff *maff,
8790 __isl_take isl_set *context);
8791 __isl_give isl_multi_aff *isl_multi_aff_gist(
8792 __isl_take isl_multi_aff *maff,
8793 __isl_take isl_set *context);
8794 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8795 __isl_take isl_pw_aff *pwaff,
8796 __isl_take isl_set *context);
8797 __isl_give isl_pw_aff *isl_pw_aff_gist(
8798 __isl_take isl_pw_aff *pwaff,
8799 __isl_take isl_set *context);
8800 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8801 __isl_take isl_pw_multi_aff *pma,
8802 __isl_take isl_set *set);
8803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8804 __isl_take isl_pw_multi_aff *pma,
8805 __isl_take isl_set *set);
8806 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8807 __isl_take isl_multi_pw_aff *mpa,
8808 __isl_take isl_set *set);
8809 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8810 __isl_take isl_multi_pw_aff *mpa,
8811 __isl_take isl_set *set);
8812 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8813 __isl_take isl_union_pw_aff *upa,
8814 __isl_take isl_union_set *context);
8815 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8816 __isl_take isl_union_pw_aff *upa,
8817 __isl_take isl_set *context);
8818 __isl_give isl_union_pw_multi_aff *
8819 isl_union_pw_multi_aff_gist_params(
8820 __isl_take isl_union_pw_multi_aff *upma,
8821 __isl_take isl_set *context);
8822 __isl_give isl_union_pw_multi_aff *
8823 isl_union_pw_multi_aff_gist(
8824 __isl_take isl_union_pw_multi_aff *upma,
8825 __isl_take isl_union_set *context);
8826 __isl_give isl_multi_union_pw_aff *
8827 isl_multi_union_pw_aff_gist_params(
8828 __isl_take isl_multi_union_pw_aff *mupa,
8829 __isl_take isl_set *context);
8830 __isl_give isl_multi_union_pw_aff *
8831 isl_multi_union_pw_aff_gist(
8832 __isl_take isl_multi_union_pw_aff *mupa,
8833 __isl_take isl_union_set *context);
8835 #include <isl/polynomial.h>
8836 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8837 __isl_take isl_qpolynomial *qp,
8838 __isl_take isl_set *context);
8839 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8840 __isl_take isl_qpolynomial *qp,
8841 __isl_take isl_set *context);
8842 __isl_give isl_qpolynomial_fold *
8843 isl_qpolynomial_fold_gist_params(
8844 __isl_take isl_qpolynomial_fold *fold,
8845 __isl_take isl_set *context);
8846 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8847 __isl_take isl_qpolynomial_fold *fold,
8848 __isl_take isl_set *context);
8849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8850 __isl_take isl_pw_qpolynomial *pwqp,
8851 __isl_take isl_set *context);
8852 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8853 __isl_take isl_pw_qpolynomial *pwqp,
8854 __isl_take isl_set *context);
8855 __isl_give isl_pw_qpolynomial_fold *
8856 isl_pw_qpolynomial_fold_gist(
8857 __isl_take isl_pw_qpolynomial_fold *pwf,
8858 __isl_take isl_set *context);
8859 __isl_give isl_pw_qpolynomial_fold *
8860 isl_pw_qpolynomial_fold_gist_params(
8861 __isl_take isl_pw_qpolynomial_fold *pwf,
8862 __isl_take isl_set *context);
8863 __isl_give isl_union_pw_qpolynomial *
8864 isl_union_pw_qpolynomial_gist_params(
8865 __isl_take isl_union_pw_qpolynomial *upwqp,
8866 __isl_take isl_set *context);
8867 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8868 __isl_take isl_union_pw_qpolynomial *upwqp,
8869 __isl_take isl_union_set *context);
8870 __isl_give isl_union_pw_qpolynomial_fold *
8871 isl_union_pw_qpolynomial_fold_gist(
8872 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8873 __isl_take isl_union_set *context);
8874 __isl_give isl_union_pw_qpolynomial_fold *
8875 isl_union_pw_qpolynomial_fold_gist_params(
8876 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8877 __isl_take isl_set *context);
8879 =item * Binary Arithmetic Operations
8881 #include <isl/set.h>
8882 __isl_give isl_set *isl_set_sum(
8883 __isl_take isl_set *set1,
8884 __isl_take isl_set *set2);
8885 #include <isl/map.h>
8886 __isl_give isl_map *isl_map_sum(
8887 __isl_take isl_map *map1,
8888 __isl_take isl_map *map2);
8890 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8891 i.e., the set containing the sums of pairs of elements from
8892 C<set1> and C<set2>.
8893 The domain of the result of C<isl_map_sum> is the intersection
8894 of the domains of its two arguments. The corresponding range
8895 elements are the sums of the corresponding range elements
8896 in the two arguments.
8898 #include <isl/val.h>
8899 __isl_give isl_multi_val *isl_multi_val_add(
8900 __isl_take isl_multi_val *mv1,
8901 __isl_take isl_multi_val *mv2);
8902 __isl_give isl_multi_val *isl_multi_val_sub(
8903 __isl_take isl_multi_val *mv1,
8904 __isl_take isl_multi_val *mv2);
8905 __isl_give isl_multi_val *isl_multi_val_min(
8906 __isl_take isl_multi_val *mv1,
8907 __isl_take isl_multi_val *mv2);
8908 __isl_give isl_multi_val *isl_multi_val_max(
8909 __isl_take isl_multi_val *mv1,
8910 __isl_take isl_multi_val *mv2);
8912 #include <isl/aff.h>
8913 __isl_give isl_aff *isl_aff_add(
8914 __isl_take isl_aff *aff1,
8915 __isl_take isl_aff *aff2);
8916 __isl_give isl_multi_aff *isl_multi_aff_add(
8917 __isl_take isl_multi_aff *maff1,
8918 __isl_take isl_multi_aff *maff2);
8919 __isl_give isl_pw_aff *isl_pw_aff_add(
8920 __isl_take isl_pw_aff *pwaff1,
8921 __isl_take isl_pw_aff *pwaff2);
8922 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8923 __isl_take isl_multi_pw_aff *mpa1,
8924 __isl_take isl_multi_pw_aff *mpa2);
8925 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8926 __isl_take isl_pw_multi_aff *pma1,
8927 __isl_take isl_pw_multi_aff *pma2);
8928 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8929 __isl_take isl_union_pw_aff *upa1,
8930 __isl_take isl_union_pw_aff *upa2);
8931 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8932 __isl_take isl_union_pw_multi_aff *upma1,
8933 __isl_take isl_union_pw_multi_aff *upma2);
8934 __isl_give isl_multi_union_pw_aff *
8935 isl_multi_union_pw_aff_add(
8936 __isl_take isl_multi_union_pw_aff *mupa1,
8937 __isl_take isl_multi_union_pw_aff *mupa2);
8938 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8939 __isl_take isl_pw_aff *pa,
8940 __isl_take isl_val *v);
8941 __isl_give isl_multi_aff *
8942 isl_multi_aff_add_constant_val(
8943 __isl_take isl_multi_aff *pa,
8944 __isl_take isl_val *v);
8945 __isl_give isl_pw_multi_aff *
8946 isl_pw_multi_aff_add_constant_val(
8947 __isl_take isl_pw_multi_aff *pma,
8948 __isl_take isl_val *v);
8949 __isl_give isl_pw_multi_aff *
8950 isl_pw_multi_aff_add_constant_multi_val(
8951 __isl_take isl_pw_multi_aff *pma,
8952 __isl_take isl_multi_val *mv);
8953 __isl_give isl_multi_pw_aff *
8954 isl_multi_pw_aff_add_constant_val(
8955 __isl_take isl_multi_pw_aff *mpa,
8956 __isl_take isl_val *v);
8957 __isl_give isl_multi_aff *
8958 isl_multi_aff_add_constant_multi_val(
8959 __isl_take isl_multi_aff *pa,
8960 __isl_take isl_multi_val *mv);
8961 __isl_give isl_multi_pw_aff *
8962 isl_multi_pw_aff_add_constant_multi_val(
8963 __isl_take isl_multi_pw_aff *mpa,
8964 __isl_take isl_multi_val *mv);
8965 __isl_give isl_pw_aff *isl_pw_aff_min(
8966 __isl_take isl_pw_aff *pwaff1,
8967 __isl_take isl_pw_aff *pwaff2);
8968 __isl_give isl_pw_aff *isl_pw_aff_max(
8969 __isl_take isl_pw_aff *pwaff1,
8970 __isl_take isl_pw_aff *pwaff2);
8971 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8972 __isl_take isl_multi_pw_aff *mpa1,
8973 __isl_take isl_multi_pw_aff *mpa2);
8974 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8975 __isl_take isl_multi_pw_aff *mpa1,
8976 __isl_take isl_multi_pw_aff *mpa2);
8977 __isl_give isl_aff *isl_aff_sub(
8978 __isl_take isl_aff *aff1,
8979 __isl_take isl_aff *aff2);
8980 __isl_give isl_multi_aff *isl_multi_aff_sub(
8981 __isl_take isl_multi_aff *ma1,
8982 __isl_take isl_multi_aff *ma2);
8983 __isl_give isl_pw_aff *isl_pw_aff_sub(
8984 __isl_take isl_pw_aff *pwaff1,
8985 __isl_take isl_pw_aff *pwaff2);
8986 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8987 __isl_take isl_multi_pw_aff *mpa1,
8988 __isl_take isl_multi_pw_aff *mpa2);
8989 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8990 __isl_take isl_pw_multi_aff *pma1,
8991 __isl_take isl_pw_multi_aff *pma2);
8992 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8993 __isl_take isl_union_pw_aff *upa1,
8994 __isl_take isl_union_pw_aff *upa2);
8995 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8996 __isl_take isl_union_pw_multi_aff *upma1,
8997 __isl_take isl_union_pw_multi_aff *upma2);
8998 __isl_give isl_multi_union_pw_aff *
8999 isl_multi_union_pw_aff_sub(
9000 __isl_take isl_multi_union_pw_aff *mupa1,
9001 __isl_take isl_multi_union_pw_aff *mupa2);
9003 C<isl_aff_sub> subtracts the second argument from the first.
9005 #include <isl/polynomial.h>
9006 __isl_give isl_qpolynomial *isl_qpolynomial_add(
9007 __isl_take isl_qpolynomial *qp1,
9008 __isl_take isl_qpolynomial *qp2);
9009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
9010 __isl_take isl_pw_qpolynomial *pwqp1,
9011 __isl_take isl_pw_qpolynomial *pwqp2);
9012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
9013 __isl_take isl_pw_qpolynomial *pwqp1,
9014 __isl_take isl_pw_qpolynomial *pwqp2);
9015 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
9016 __isl_take isl_pw_qpolynomial_fold *pwf1,
9017 __isl_take isl_pw_qpolynomial_fold *pwf2);
9018 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
9019 __isl_take isl_union_pw_qpolynomial *upwqp1,
9020 __isl_take isl_union_pw_qpolynomial *upwqp2);
9021 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
9022 __isl_take isl_qpolynomial *qp1,
9023 __isl_take isl_qpolynomial *qp2);
9024 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
9025 __isl_take isl_pw_qpolynomial *pwqp1,
9026 __isl_take isl_pw_qpolynomial *pwqp2);
9027 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
9028 __isl_take isl_union_pw_qpolynomial *upwqp1,
9029 __isl_take isl_union_pw_qpolynomial *upwqp2);
9030 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
9031 __isl_take isl_pw_qpolynomial_fold *pwf1,
9032 __isl_take isl_pw_qpolynomial_fold *pwf2);
9033 __isl_give isl_union_pw_qpolynomial_fold *
9034 isl_union_pw_qpolynomial_fold_fold(
9035 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
9036 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
9038 #include <isl/aff.h>
9039 __isl_give isl_pw_aff *isl_pw_aff_union_add(
9040 __isl_take isl_pw_aff *pwaff1,
9041 __isl_take isl_pw_aff *pwaff2);
9042 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
9043 __isl_take isl_multi_pw_aff *mpa1,
9044 __isl_take isl_multi_pw_aff *mpa2);
9045 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9046 __isl_take isl_pw_multi_aff *pma1,
9047 __isl_take isl_pw_multi_aff *pma2);
9048 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9049 __isl_take isl_union_pw_aff *upa1,
9050 __isl_take isl_union_pw_aff *upa2);
9051 __isl_give isl_union_pw_multi_aff *
9052 isl_union_pw_multi_aff_union_add(
9053 __isl_take isl_union_pw_multi_aff *upma1,
9054 __isl_take isl_union_pw_multi_aff *upma2);
9055 __isl_give isl_multi_union_pw_aff *
9056 isl_multi_union_pw_aff_union_add(
9057 __isl_take isl_multi_union_pw_aff *mupa1,
9058 __isl_take isl_multi_union_pw_aff *mupa2);
9059 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9060 __isl_take isl_pw_aff *pwaff1,
9061 __isl_take isl_pw_aff *pwaff2);
9062 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9063 __isl_take isl_pw_aff *pwaff1,
9064 __isl_take isl_pw_aff *pwaff2);
9066 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9067 expression with a domain that is the union of those of C<pwaff1> and
9068 C<pwaff2> and such that on each cell, the quasi-affine expression is
9069 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9070 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9071 associated expression is the defined one.
9072 This in contrast to the C<isl_pw_aff_max> function, which is
9073 only defined on the shared definition domain of the arguments.
9075 #include <isl/val.h>
9076 __isl_give isl_multi_val *isl_multi_val_add_val(
9077 __isl_take isl_multi_val *mv,
9078 __isl_take isl_val *v);
9079 __isl_give isl_multi_val *isl_multi_val_mod_val(
9080 __isl_take isl_multi_val *mv,
9081 __isl_take isl_val *v);
9082 __isl_give isl_multi_val *isl_multi_val_scale_val(
9083 __isl_take isl_multi_val *mv,
9084 __isl_take isl_val *v);
9085 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9086 __isl_take isl_multi_val *mv,
9087 __isl_take isl_val *v);
9089 #include <isl/aff.h>
9090 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9091 __isl_take isl_val *mod);
9092 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9093 __isl_take isl_pw_aff *pa,
9094 __isl_take isl_val *mod);
9095 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9096 __isl_take isl_union_pw_aff *upa,
9097 __isl_take isl_val *f);
9098 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9099 __isl_take isl_val *v);
9100 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9101 __isl_take isl_multi_aff *ma,
9102 __isl_take isl_val *v);
9103 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9104 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9105 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9106 __isl_take isl_multi_pw_aff *mpa,
9107 __isl_take isl_val *v);
9108 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9109 __isl_take isl_pw_multi_aff *pma,
9110 __isl_take isl_val *v);
9111 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9112 __isl_take isl_union_pw_aff *upa,
9113 __isl_take isl_val *f);
9114 __isl_give isl_union_pw_multi_aff *
9115 isl_union_pw_multi_aff_scale_val(
9116 __isl_take isl_union_pw_multi_aff *upma,
9117 __isl_take isl_val *val);
9118 __isl_give isl_multi_union_pw_aff *
9119 isl_multi_union_pw_aff_scale_val(
9120 __isl_take isl_multi_union_pw_aff *mupa,
9121 __isl_take isl_val *v);
9122 __isl_give isl_aff *isl_aff_scale_down_ui(
9123 __isl_take isl_aff *aff, unsigned f);
9124 __isl_give isl_aff *isl_aff_scale_down_val(
9125 __isl_take isl_aff *aff, __isl_take isl_val *v);
9126 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9127 __isl_take isl_multi_aff *ma,
9128 __isl_take isl_val *v);
9129 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9130 __isl_take isl_pw_aff *pa,
9131 __isl_take isl_val *f);
9132 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9133 __isl_take isl_multi_pw_aff *mpa,
9134 __isl_take isl_val *v);
9135 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9136 __isl_take isl_pw_multi_aff *pma,
9137 __isl_take isl_val *v);
9138 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9139 __isl_take isl_union_pw_aff *upa,
9140 __isl_take isl_val *v);
9141 __isl_give isl_union_pw_multi_aff *
9142 isl_union_pw_multi_aff_scale_down_val(
9143 __isl_take isl_union_pw_multi_aff *upma,
9144 __isl_take isl_val *val);
9145 __isl_give isl_multi_union_pw_aff *
9146 isl_multi_union_pw_aff_scale_down_val(
9147 __isl_take isl_multi_union_pw_aff *mupa,
9148 __isl_take isl_val *v);
9150 #include <isl/polynomial.h>
9151 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9152 __isl_take isl_qpolynomial *qp,
9153 __isl_take isl_val *v);
9154 __isl_give isl_qpolynomial_fold *
9155 isl_qpolynomial_fold_scale_val(
9156 __isl_take isl_qpolynomial_fold *fold,
9157 __isl_take isl_val *v);
9158 __isl_give isl_pw_qpolynomial *
9159 isl_pw_qpolynomial_scale_val(
9160 __isl_take isl_pw_qpolynomial *pwqp,
9161 __isl_take isl_val *v);
9162 __isl_give isl_pw_qpolynomial_fold *
9163 isl_pw_qpolynomial_fold_scale_val(
9164 __isl_take isl_pw_qpolynomial_fold *pwf,
9165 __isl_take isl_val *v);
9166 __isl_give isl_union_pw_qpolynomial *
9167 isl_union_pw_qpolynomial_scale_val(
9168 __isl_take isl_union_pw_qpolynomial *upwqp,
9169 __isl_take isl_val *v);
9170 __isl_give isl_union_pw_qpolynomial_fold *
9171 isl_union_pw_qpolynomial_fold_scale_val(
9172 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9173 __isl_take isl_val *v);
9174 __isl_give isl_qpolynomial *
9175 isl_qpolynomial_scale_down_val(
9176 __isl_take isl_qpolynomial *qp,
9177 __isl_take isl_val *v);
9178 __isl_give isl_qpolynomial_fold *
9179 isl_qpolynomial_fold_scale_down_val(
9180 __isl_take isl_qpolynomial_fold *fold,
9181 __isl_take isl_val *v);
9182 __isl_give isl_pw_qpolynomial *
9183 isl_pw_qpolynomial_scale_down_val(
9184 __isl_take isl_pw_qpolynomial *pwqp,
9185 __isl_take isl_val *v);
9186 __isl_give isl_pw_qpolynomial_fold *
9187 isl_pw_qpolynomial_fold_scale_down_val(
9188 __isl_take isl_pw_qpolynomial_fold *pwf,
9189 __isl_take isl_val *v);
9190 __isl_give isl_union_pw_qpolynomial *
9191 isl_union_pw_qpolynomial_scale_down_val(
9192 __isl_take isl_union_pw_qpolynomial *upwqp,
9193 __isl_take isl_val *v);
9194 __isl_give isl_union_pw_qpolynomial_fold *
9195 isl_union_pw_qpolynomial_fold_scale_down_val(
9196 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9197 __isl_take isl_val *v);
9199 #include <isl/val.h>
9200 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9201 __isl_take isl_multi_val *mv1,
9202 __isl_take isl_multi_val *mv2);
9203 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9204 __isl_take isl_multi_val *mv1,
9205 __isl_take isl_multi_val *mv2);
9206 __isl_give isl_multi_val *
9207 isl_multi_val_scale_down_multi_val(
9208 __isl_take isl_multi_val *mv1,
9209 __isl_take isl_multi_val *mv2);
9211 #include <isl/aff.h>
9212 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9213 __isl_take isl_multi_aff *ma,
9214 __isl_take isl_multi_val *mv);
9215 __isl_give isl_multi_union_pw_aff *
9216 isl_multi_union_pw_aff_mod_multi_val(
9217 __isl_take isl_multi_union_pw_aff *upma,
9218 __isl_take isl_multi_val *mv);
9219 __isl_give isl_multi_pw_aff *
9220 isl_multi_pw_aff_mod_multi_val(
9221 __isl_take isl_multi_pw_aff *mpa,
9222 __isl_take isl_multi_val *mv);
9223 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9224 __isl_take isl_multi_aff *ma,
9225 __isl_take isl_multi_val *mv);
9226 __isl_give isl_pw_multi_aff *
9227 isl_pw_multi_aff_scale_multi_val(
9228 __isl_take isl_pw_multi_aff *pma,
9229 __isl_take isl_multi_val *mv);
9230 __isl_give isl_multi_pw_aff *
9231 isl_multi_pw_aff_scale_multi_val(
9232 __isl_take isl_multi_pw_aff *mpa,
9233 __isl_take isl_multi_val *mv);
9234 __isl_give isl_multi_union_pw_aff *
9235 isl_multi_union_pw_aff_scale_multi_val(
9236 __isl_take isl_multi_union_pw_aff *mupa,
9237 __isl_take isl_multi_val *mv);
9238 __isl_give isl_union_pw_multi_aff *
9239 isl_union_pw_multi_aff_scale_multi_val(
9240 __isl_take isl_union_pw_multi_aff *upma,
9241 __isl_take isl_multi_val *mv);
9242 __isl_give isl_multi_aff *
9243 isl_multi_aff_scale_down_multi_val(
9244 __isl_take isl_multi_aff *ma,
9245 __isl_take isl_multi_val *mv);
9246 __isl_give isl_pw_multi_aff *
9247 isl_pw_multi_aff_scale_down_multi_val(
9248 __isl_take isl_pw_multi_aff *pma,
9249 __isl_take isl_multi_val *mv);
9250 __isl_give isl_multi_pw_aff *
9251 isl_multi_pw_aff_scale_down_multi_val(
9252 __isl_take isl_multi_pw_aff *mpa,
9253 __isl_take isl_multi_val *mv);
9254 __isl_give isl_multi_union_pw_aff *
9255 isl_multi_union_pw_aff_scale_down_multi_val(
9256 __isl_take isl_multi_union_pw_aff *mupa,
9257 __isl_take isl_multi_val *mv);
9259 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9260 by the corresponding elements of C<mv>.
9262 #include <isl/aff.h>
9263 __isl_give isl_aff *isl_aff_mul(
9264 __isl_take isl_aff *aff1,
9265 __isl_take isl_aff *aff2);
9266 __isl_give isl_aff *isl_aff_div(
9267 __isl_take isl_aff *aff1,
9268 __isl_take isl_aff *aff2);
9269 __isl_give isl_pw_aff *isl_pw_aff_mul(
9270 __isl_take isl_pw_aff *pwaff1,
9271 __isl_take isl_pw_aff *pwaff2);
9272 __isl_give isl_pw_aff *isl_pw_aff_div(
9273 __isl_take isl_pw_aff *pa1,
9274 __isl_take isl_pw_aff *pa2);
9275 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9276 __isl_take isl_pw_aff *pa1,
9277 __isl_take isl_pw_aff *pa2);
9278 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9279 __isl_take isl_pw_aff *pa1,
9280 __isl_take isl_pw_aff *pa2);
9282 When multiplying two affine expressions, at least one of the two needs
9283 to be a constant. Similarly, when dividing an affine expression by another,
9284 the second expression needs to be a constant.
9285 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9286 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9289 #include <isl/polynomial.h>
9290 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9291 __isl_take isl_qpolynomial *qp1,
9292 __isl_take isl_qpolynomial *qp2);
9293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9294 __isl_take isl_pw_qpolynomial *pwqp1,
9295 __isl_take isl_pw_qpolynomial *pwqp2);
9296 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9297 __isl_take isl_union_pw_qpolynomial *upwqp1,
9298 __isl_take isl_union_pw_qpolynomial *upwqp2);
9302 =head3 Lexicographic Optimization
9304 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9305 the following functions
9306 compute a set that contains the lexicographic minimum or maximum
9307 of the elements in C<set> (or C<bset>) for those values of the parameters
9308 that satisfy C<dom>.
9309 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9310 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9312 In other words, the union of the parameter values
9313 for which the result is non-empty and of C<*empty>
9316 #include <isl/set.h>
9317 __isl_give isl_set *isl_basic_set_partial_lexmin(
9318 __isl_take isl_basic_set *bset,
9319 __isl_take isl_basic_set *dom,
9320 __isl_give isl_set **empty);
9321 __isl_give isl_set *isl_basic_set_partial_lexmax(
9322 __isl_take isl_basic_set *bset,
9323 __isl_take isl_basic_set *dom,
9324 __isl_give isl_set **empty);
9325 __isl_give isl_set *isl_set_partial_lexmin(
9326 __isl_take isl_set *set, __isl_take isl_set *dom,
9327 __isl_give isl_set **empty);
9328 __isl_give isl_set *isl_set_partial_lexmax(
9329 __isl_take isl_set *set, __isl_take isl_set *dom,
9330 __isl_give isl_set **empty);
9332 Given a (basic) set C<set> (or C<bset>), the following functions simply
9333 return a set containing the lexicographic minimum or maximum
9334 of the elements in C<set> (or C<bset>).
9335 In case of union sets, the optimum is computed per space.
9337 #include <isl/set.h>
9338 __isl_give isl_set *isl_basic_set_lexmin(
9339 __isl_take isl_basic_set *bset);
9340 __isl_give isl_set *isl_basic_set_lexmax(
9341 __isl_take isl_basic_set *bset);
9342 __isl_give isl_set *isl_set_lexmin(
9343 __isl_take isl_set *set);
9344 __isl_give isl_set *isl_set_lexmax(
9345 __isl_take isl_set *set);
9346 __isl_give isl_union_set *isl_union_set_lexmin(
9347 __isl_take isl_union_set *uset);
9348 __isl_give isl_union_set *isl_union_set_lexmax(
9349 __isl_take isl_union_set *uset);
9351 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9352 the following functions
9353 compute a relation that maps each element of C<dom>
9354 to the single lexicographic minimum or maximum
9355 of the elements that are associated to that same
9356 element in C<map> (or C<bmap>).
9357 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9358 that contains the elements in C<dom> that do not map
9359 to any elements in C<map> (or C<bmap>).
9360 In other words, the union of the domain of the result and of C<*empty>
9363 #include <isl/map.h>
9364 __isl_give isl_map *isl_basic_map_partial_lexmax(
9365 __isl_take isl_basic_map *bmap,
9366 __isl_take isl_basic_set *dom,
9367 __isl_give isl_set **empty);
9368 __isl_give isl_map *isl_basic_map_partial_lexmin(
9369 __isl_take isl_basic_map *bmap,
9370 __isl_take isl_basic_set *dom,
9371 __isl_give isl_set **empty);
9372 __isl_give isl_map *isl_map_partial_lexmax(
9373 __isl_take isl_map *map, __isl_take isl_set *dom,
9374 __isl_give isl_set **empty);
9375 __isl_give isl_map *isl_map_partial_lexmin(
9376 __isl_take isl_map *map, __isl_take isl_set *dom,
9377 __isl_give isl_set **empty);
9379 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9380 return a map mapping each element in the domain of
9381 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9382 of all elements associated to that element.
9383 In case of union relations, the optimum is computed per space.
9385 #include <isl/map.h>
9386 __isl_give isl_map *isl_basic_map_lexmin(
9387 __isl_take isl_basic_map *bmap);
9388 __isl_give isl_map *isl_basic_map_lexmax(
9389 __isl_take isl_basic_map *bmap);
9390 __isl_give isl_map *isl_map_lexmin(
9391 __isl_take isl_map *map);
9392 __isl_give isl_map *isl_map_lexmax(
9393 __isl_take isl_map *map);
9394 __isl_give isl_union_map *isl_union_map_lexmin(
9395 __isl_take isl_union_map *umap);
9396 __isl_give isl_union_map *isl_union_map_lexmax(
9397 __isl_take isl_union_map *umap);
9399 The following functions return their result in the form of
9400 a piecewise multi-affine expression,
9401 but are otherwise equivalent to the corresponding functions
9402 returning a basic set or relation.
9404 #include <isl/set.h>
9405 __isl_give isl_pw_multi_aff *
9406 isl_basic_set_partial_lexmin_pw_multi_aff(
9407 __isl_take isl_basic_set *bset,
9408 __isl_take isl_basic_set *dom,
9409 __isl_give isl_set **empty);
9410 __isl_give isl_pw_multi_aff *
9411 isl_basic_set_partial_lexmax_pw_multi_aff(
9412 __isl_take isl_basic_set *bset,
9413 __isl_take isl_basic_set *dom,
9414 __isl_give isl_set **empty);
9415 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9416 __isl_take isl_set *set);
9417 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9418 __isl_take isl_set *set);
9420 #include <isl/map.h>
9421 __isl_give isl_pw_multi_aff *
9422 isl_basic_map_lexmin_pw_multi_aff(
9423 __isl_take isl_basic_map *bmap);
9424 __isl_give isl_pw_multi_aff *
9425 isl_basic_map_partial_lexmin_pw_multi_aff(
9426 __isl_take isl_basic_map *bmap,
9427 __isl_take isl_basic_set *dom,
9428 __isl_give isl_set **empty);
9429 __isl_give isl_pw_multi_aff *
9430 isl_basic_map_partial_lexmax_pw_multi_aff(
9431 __isl_take isl_basic_map *bmap,
9432 __isl_take isl_basic_set *dom,
9433 __isl_give isl_set **empty);
9434 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9435 __isl_take isl_map *map);
9436 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9437 __isl_take isl_map *map);
9439 The following functions return the lexicographic minimum or maximum
9440 on the shared domain of the inputs and the single defined function
9441 on those parts of the domain where only a single function is defined.
9443 #include <isl/aff.h>
9444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9445 __isl_take isl_pw_multi_aff *pma1,
9446 __isl_take isl_pw_multi_aff *pma2);
9447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9448 __isl_take isl_pw_multi_aff *pma1,
9449 __isl_take isl_pw_multi_aff *pma2);
9451 If the input to a lexicographic optimization problem has
9452 multiple constraints with the same coefficients for the optimized
9453 variables, then, by default, this symmetry is exploited by
9454 replacing those constraints by a single constraint with
9455 an abstract bound, which is in turn bounded by the corresponding terms
9456 in the original constraints.
9457 Without this optimization, the solver would typically consider
9458 all possible orderings of those original bounds, resulting in a needless
9459 decomposition of the domain.
9460 However, the optimization can also result in slowdowns since
9461 an extra parameter is introduced that may get used in additional
9463 The following option determines whether symmetry detection is applied
9464 during lexicographic optimization.
9466 #include <isl/options.h>
9467 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9469 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9473 See also \autoref{s:offline}.
9477 =head2 Ternary Operations
9479 #include <isl/aff.h>
9480 __isl_give isl_pw_aff *isl_pw_aff_cond(
9481 __isl_take isl_pw_aff *cond,
9482 __isl_take isl_pw_aff *pwaff_true,
9483 __isl_take isl_pw_aff *pwaff_false);
9485 The function C<isl_pw_aff_cond> performs a conditional operator
9486 and returns an expression that is equal to C<pwaff_true>
9487 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9488 where C<cond> is zero.
9492 Lists are defined over several element types, including
9493 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9494 C<isl_union_pw_aff>,
9495 C<isl_union_pw_multi_aff>,
9496 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9498 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9499 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9500 Here we take lists of C<isl_set>s as an example.
9501 Lists can be created, copied, modified and freed using the following functions.
9503 #include <isl/set.h>
9504 __isl_give isl_set_list *isl_set_to_list(
9505 __isl_take isl_set *el);
9506 __isl_give isl_set_list *isl_set_list_from_set(
9507 __isl_take isl_set *el);
9508 __isl_give isl_set_list *isl_set_list_alloc(
9509 isl_ctx *ctx, int n);
9510 __isl_give isl_set_list *isl_set_list_copy(
9511 __isl_keep isl_set_list *list);
9512 __isl_give isl_set_list *isl_set_list_insert(
9513 __isl_take isl_set_list *list, unsigned pos,
9514 __isl_take isl_set *el);
9515 __isl_give isl_set_list *isl_set_list_add(
9516 __isl_take isl_set_list *list,
9517 __isl_take isl_set *el);
9518 __isl_give isl_set_list *isl_set_list_drop(
9519 __isl_take isl_set_list *list,
9520 unsigned first, unsigned n);
9521 __isl_give isl_set_list *isl_set_list_clear(
9522 __isl_take isl_set_list *list);
9523 __isl_give isl_set_list *isl_set_list_swap(
9524 __isl_take isl_set_list *list,
9525 unsigned pos1, unsigned pos2);
9526 __isl_give isl_set_list *isl_set_list_reverse(
9527 __isl_take isl_set_list *list);
9528 __isl_give isl_set_list *isl_set_list_set_at(
9529 __isl_take isl_set_list *list, int index,
9530 __isl_take isl_set *set);
9531 __isl_give isl_set_list *isl_set_list_set_set(
9532 __isl_take isl_set_list *list, int index,
9533 __isl_take isl_set *set);
9534 __isl_give isl_set_list *isl_set_list_concat(
9535 __isl_take isl_set_list *list1,
9536 __isl_take isl_set_list *list2);
9537 __isl_give isl_set_list *isl_set_list_map(
9538 __isl_take isl_set_list *list,
9539 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9542 __isl_give isl_set_list *isl_set_list_sort(
9543 __isl_take isl_set_list *list,
9544 int (*cmp)(__isl_keep isl_set *a,
9545 __isl_keep isl_set *b, void *user),
9547 __isl_null isl_set_list *isl_set_list_free(
9548 __isl_take isl_set_list *list);
9550 C<isl_set_list_alloc> creates an empty list with an initial capacity
9551 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9552 add elements to a list, increasing its capacity as needed.
9553 C<isl_set_to_list> creates a list with a single element.
9554 C<isl_set_list_from_set> performs the same operation.
9555 C<isl_set_list_clear> removes all elements from a list.
9556 C<isl_set_list_swap> swaps the elements at the specified locations.
9557 C<isl_set_list_reverse> reverses the elements in the list.
9558 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9560 Lists can be inspected using the following functions.
9562 #include <isl/set.h>
9563 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9564 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9565 __isl_give isl_set *isl_set_list_get_at(
9566 __isl_keep isl_set_list *list, int index);
9567 __isl_give isl_set *isl_set_list_get_set(
9568 __isl_keep isl_set_list *list, int index);
9569 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9570 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9572 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9573 isl_bool (*test)(__isl_take isl_set *el,
9576 isl_stat isl_set_list_foreach_scc(
9577 __isl_keep isl_set_list *list,
9578 isl_bool (*follows)(__isl_keep isl_set *a,
9579 __isl_keep isl_set *b, void *user),
9581 isl_stat (*fn)(__isl_take isl_set_list *scc,
9585 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9587 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9588 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9589 strongly connected components of the graph with as vertices the elements
9590 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9591 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9592 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9594 Lists can be printed using
9596 #include <isl/set.h>
9597 __isl_give isl_printer *isl_printer_print_set_list(
9598 __isl_take isl_printer *p,
9599 __isl_keep isl_set_list *list);
9601 Alternatively, a string representation can be obtained
9602 directly using the following function, which always prints
9605 #include <isl/set.h>
9606 __isl_give char *isl_set_list_to_str(
9607 __isl_keep isl_set_list *list);
9609 An C<isl_val_list>, C<isl_id_list>,
9610 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9611 C<isl_union_pw_aff_list>,
9612 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9613 can also be read from input using the following functions.
9615 #include <isl/val.h>
9616 __isl_give isl_val_list *isl_val_list_read_from_str(
9617 isl_ctx *ctx, const char *str);
9620 __isl_give isl_id_list *isl_id_list_read_from_str(
9621 isl_ctx *ctx, const char *str);
9623 #include <isl/aff.h>
9624 __isl_give isl_aff_list *
9625 isl_aff_list_read_from_str(isl_ctx *ctx,
9627 __isl_give isl_pw_aff_list *
9628 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9630 __isl_give isl_pw_multi_aff_list *
9631 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9633 __isl_give isl_union_pw_aff_list *
9634 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9637 #include <isl/set.h>
9638 __isl_give isl_set_list *isl_set_list_read_from_str(
9639 isl_ctx *ctx, const char *str);
9641 #include <isl/map.h>
9642 __isl_give isl_map_list *isl_map_list_read_from_str(
9643 isl_ctx *ctx, const char *str);
9645 #include <isl/union_set.h>
9646 __isl_give isl_union_set_list *
9647 isl_union_set_list_read_from_str(isl_ctx *ctx,
9650 =head2 Associative arrays
9652 Associative arrays map isl objects of a specific type to isl objects
9653 of some (other) specific type. They are defined for several pairs
9654 of types, including (C<isl_map>, C<isl_basic_set>),
9655 (C<isl_id>, C<isl_ast_expr>),
9656 (C<isl_id>, C<isl_id>) and
9657 (C<isl_id>, C<isl_pw_aff>).
9658 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9661 Associative arrays can be created, copied and freed using
9662 the following functions.
9664 #include <isl/id_to_ast_expr.h>
9665 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9666 isl_ctx *ctx, int min_size);
9667 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9668 __isl_keep isl_id_to_ast_expr *id2expr);
9669 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9670 __isl_take isl_id_to_ast_expr *id2expr);
9672 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9673 to specify the expected size of the associative array.
9674 The associative array will be grown automatically as needed.
9676 Associative arrays can be inspected using the following functions.
9678 #include <isl/id_to_ast_expr.h>
9679 __isl_give isl_maybe_isl_ast_expr
9680 isl_id_to_ast_expr_try_get(
9681 __isl_keep isl_id_to_ast_expr *id2expr,
9682 __isl_keep isl_id *key);
9683 isl_bool isl_id_to_ast_expr_has(
9684 __isl_keep isl_id_to_ast_expr *id2expr,
9685 __isl_keep isl_id *key);
9686 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9687 __isl_keep isl_id_to_ast_expr *id2expr,
9688 __isl_take isl_id *key);
9689 isl_stat isl_id_to_ast_expr_foreach(
9690 __isl_keep isl_id_to_ast_expr *id2expr,
9691 isl_stat (*fn)(__isl_take isl_id *key,
9692 __isl_take isl_ast_expr *val, void *user),
9694 isl_bool isl_id_to_ast_expr_every(
9695 __isl_keep isl_id_to_ast_expr *id2expr,
9696 isl_bool (*test)(__isl_keep isl_id *key,
9697 __isl_keep isl_ast_expr *val, void *user),
9700 The function C<isl_id_to_ast_expr_try_get> returns a structure
9701 containing two elements, C<valid> and C<value>.
9702 If there is a value associated to the key, then C<valid>
9703 is set to C<isl_bool_true> and C<value> contains a copy of
9704 the associated value. Otherwise C<value> is C<NULL> and
9705 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9706 on whether some error has occurred or there simply is no associated value.
9707 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9708 in the structure and
9709 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9711 Associative arrays can be modified using the following functions.
9713 #include <isl/id_to_ast_expr.h>
9714 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9715 __isl_take isl_id_to_ast_expr *id2expr,
9716 __isl_take isl_id *key,
9717 __isl_take isl_ast_expr *val);
9718 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9719 __isl_take isl_id_to_ast_expr *id2expr,
9720 __isl_take isl_id *key);
9722 Associative arrays can be checked for (obvious) equality
9723 using the following function.
9725 #include <isl/id_to_ast_expr.h>
9726 isl_bool isl_id_to_ast_expr_is_equal(
9727 __isl_take isl_id_to_ast_expr *id2expr1,
9728 __isl_take isl_id_to_ast_expr *id2expr2);
9730 Note that depending on how the keys and values are being compared,
9731 for other types of keys and/or values, this function may be called
9732 C<plain_is_equal> rather than C<is_equal>.
9734 Associative arrays can be printed using the following functions.
9736 #include <isl/id_to_ast_expr.h>
9737 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9738 __isl_take isl_printer *p,
9739 __isl_keep isl_id_to_ast_expr *id2expr);
9740 __isl_give char *isl_id_to_ast_expr_to_str(
9741 __isl_keep isl_id_to_ast_expr *id2expr);
9743 They can be read from input using the following function.
9745 #include <isl/id_to_ast_expr.h>
9746 __isl_give isl_id_to_ast_expr *
9747 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9752 Vectors can be created, copied and freed using the following functions.
9754 #include <isl/vec.h>
9755 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9757 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9759 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9760 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9762 Note that the elements of a vector created by C<isl_vec_alloc>
9763 may have arbitrary values.
9764 A vector created by C<isl_vec_zero> has elements with value zero.
9765 The elements can be changed and inspected using the following functions.
9767 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9768 __isl_give isl_val *isl_vec_get_element_val(
9769 __isl_keep isl_vec *vec, int pos);
9770 __isl_give isl_vec *isl_vec_set_element_si(
9771 __isl_take isl_vec *vec, int pos, int v);
9772 __isl_give isl_vec *isl_vec_set_element_val(
9773 __isl_take isl_vec *vec, int pos,
9774 __isl_take isl_val *v);
9775 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9777 __isl_give isl_vec *isl_vec_set_val(
9778 __isl_take isl_vec *vec, __isl_take isl_val *v);
9779 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9780 __isl_keep isl_vec *vec2, int pos);
9782 C<isl_vec_get_element> will return a negative value if anything went wrong.
9783 In that case, the value of C<*v> is undefined.
9785 The following function can be used to concatenate two vectors.
9787 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9788 __isl_take isl_vec *vec2);
9792 Matrices can be created, copied and freed using the following functions.
9794 #include <isl/mat.h>
9795 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9796 unsigned n_row, unsigned n_col);
9797 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9798 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9800 Note that the elements of a newly created matrix may have arbitrary values.
9801 The elements can be changed and inspected using the following functions.
9803 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9804 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9805 __isl_give isl_val *isl_mat_get_element_val(
9806 __isl_keep isl_mat *mat, int row, int col);
9807 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9808 int row, int col, int v);
9809 __isl_give isl_mat *isl_mat_set_element_val(
9810 __isl_take isl_mat *mat, int row, int col,
9811 __isl_take isl_val *v);
9813 The following function computes the rank of a matrix.
9814 The return value may be -1 if some error occurred.
9816 #include <isl/mat.h>
9817 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9819 The following function can be used to compute the (right) inverse
9820 of a matrix, i.e., a matrix such that the product of the original
9821 and the inverse (in that order) is a multiple of the identity matrix.
9822 The input matrix is assumed to be of full row-rank.
9824 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9826 The following function can be used to compute the (right) kernel
9827 (or null space) of a matrix, i.e., a matrix such that the product of
9828 the original and the kernel (in that order) is the zero matrix.
9830 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9832 The following function computes a basis for the space spanned
9833 by the rows of a matrix.
9835 __isl_give isl_mat *isl_mat_row_basis(
9836 __isl_take isl_mat *mat);
9838 The following function computes rows that extend a basis of C<mat1>
9839 to a basis that also covers C<mat2>.
9841 __isl_give isl_mat *isl_mat_row_basis_extension(
9842 __isl_take isl_mat *mat1,
9843 __isl_take isl_mat *mat2);
9845 The following function checks whether there is no linear dependence
9846 among the combined rows of "mat1" and "mat2" that is not already present
9847 in "mat1" or "mat2" individually.
9848 If "mat1" and "mat2" have linearly independent rows by themselves,
9849 then this means that there is no linear dependence among all rows together.
9851 isl_bool isl_mat_has_linearly_independent_rows(
9852 __isl_keep isl_mat *mat1,
9853 __isl_keep isl_mat *mat2);
9855 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9857 The following functions determine
9858 an upper or lower bound on a quasipolynomial over its domain.
9860 __isl_give isl_pw_qpolynomial_fold *
9861 isl_pw_qpolynomial_bound(
9862 __isl_take isl_pw_qpolynomial *pwqp,
9863 enum isl_fold type, isl_bool *tight);
9865 __isl_give isl_union_pw_qpolynomial_fold *
9866 isl_union_pw_qpolynomial_bound(
9867 __isl_take isl_union_pw_qpolynomial *upwqp,
9868 enum isl_fold type, isl_bool *tight);
9870 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9871 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9872 is the returned bound is known be tight, i.e., for each value
9873 of the parameters there is at least
9874 one element in the domain that reaches the bound.
9875 If the domain of C<pwqp> is not wrapping, then the bound is computed
9876 over all elements in that domain and the result has a purely parametric
9877 domain. If the domain of C<pwqp> is wrapping, then the bound is
9878 computed over the range of the wrapped relation. The domain of the
9879 wrapped relation becomes the domain of the result.
9881 =head2 Parametric Vertex Enumeration
9883 The parametric vertex enumeration described in this section
9884 is mainly intended to be used internally and by the C<barvinok>
9887 #include <isl/vertices.h>
9888 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9889 __isl_keep isl_basic_set *bset);
9891 The function C<isl_basic_set_compute_vertices> performs the
9892 actual computation of the parametric vertices and the chamber
9893 decomposition and stores the result in an C<isl_vertices> object.
9894 This information can be queried by either iterating over all
9895 the vertices or iterating over all the chambers or cells
9896 and then iterating over all vertices that are active on the chamber.
9898 isl_stat isl_vertices_foreach_vertex(
9899 __isl_keep isl_vertices *vertices,
9900 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9901 void *user), void *user);
9903 isl_stat isl_vertices_foreach_cell(
9904 __isl_keep isl_vertices *vertices,
9905 isl_stat (*fn)(__isl_take isl_cell *cell,
9906 void *user), void *user);
9907 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9908 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9909 void *user), void *user);
9911 Other operations that can be performed on an C<isl_vertices> object are
9914 isl_size isl_vertices_get_n_vertices(
9915 __isl_keep isl_vertices *vertices);
9916 __isl_null isl_vertices *isl_vertices_free(
9917 __isl_take isl_vertices *vertices);
9919 Vertices can be inspected and destroyed using the following functions.
9921 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9922 __isl_give isl_basic_set *isl_vertex_get_domain(
9923 __isl_keep isl_vertex *vertex);
9924 __isl_give isl_multi_aff *isl_vertex_get_expr(
9925 __isl_keep isl_vertex *vertex);
9926 __isl_null isl_vertex *isl_vertex_free(
9927 __isl_take isl_vertex *vertex);
9929 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9930 describing the vertex in terms of the parameters,
9931 while C<isl_vertex_get_domain> returns the activity domain
9934 Chambers can be inspected and destroyed using the following functions.
9936 __isl_give isl_basic_set *isl_cell_get_domain(
9937 __isl_keep isl_cell *cell);
9938 __isl_null isl_cell *isl_cell_free(
9939 __isl_take isl_cell *cell);
9941 =head1 Polyhedral Compilation Library
9943 This section collects functionality in C<isl> that has been specifically
9944 designed for use during polyhedral compilation.
9946 =head2 Schedule Trees
9948 A schedule tree is a structured representation of a schedule,
9949 assigning a relative order to a set of domain elements.
9950 The relative order expressed by the schedule tree is
9951 defined recursively. In particular, the order between
9952 two domain elements is determined by the node that is closest
9953 to the root that refers to both elements and that orders them apart.
9954 Each node in the tree is of one of several types.
9955 The root node is always of type C<isl_schedule_node_domain>
9956 (or C<isl_schedule_node_extension>)
9957 and it describes the (extra) domain elements to which the schedule applies.
9958 The other types of nodes are as follows.
9962 =item C<isl_schedule_node_band>
9964 A band of schedule dimensions. Each schedule dimension is represented
9965 by a union piecewise quasi-affine expression. If this expression
9966 assigns a different value to two domain elements, while all previous
9967 schedule dimensions in the same band assign them the same value,
9968 then the two domain elements are ordered according to these two
9970 Each expression is required to be total in the domain elements
9971 that reach the band node.
9973 =item C<isl_schedule_node_expansion>
9975 An expansion node maps each of the domain elements that reach the node
9976 to one or more domain elements. The image of this mapping forms
9977 the set of domain elements that reach the child of the expansion node.
9978 The function that maps each of the expanded domain elements
9979 to the original domain element from which it was expanded
9980 is called the contraction.
9982 =item C<isl_schedule_node_filter>
9984 A filter node does not impose any ordering, but rather intersects
9985 the set of domain elements that the current subtree refers to
9986 with a given union set. The subtree of the filter node only
9987 refers to domain elements in the intersection.
9988 A filter node is typically only used as a child of a sequence or
9991 =item C<isl_schedule_node_leaf>
9993 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9995 =item C<isl_schedule_node_mark>
9997 A mark node can be used to attach any kind of information to a subtree
9998 of the schedule tree.
10000 =item C<isl_schedule_node_sequence>
10002 A sequence node has one or more children, each of which is a filter node.
10003 The filters on these filter nodes form a partition of
10004 the domain elements that the current subtree refers to.
10005 If two domain elements appear in distinct filters then the sequence
10006 node orders them according to the child positions of the corresponding
10009 =item C<isl_schedule_node_set>
10011 A set node is similar to a sequence node, except that
10012 it expresses that domain elements appearing in distinct filters
10013 may have any order. The order of the children of a set node
10014 is therefore also immaterial.
10018 The following node types are only supported by the AST generator.
10022 =item C<isl_schedule_node_context>
10024 The context describes constraints on the parameters and
10025 the schedule dimensions of outer
10026 bands that the AST generator may assume to hold. It is also the only
10027 kind of node that may introduce additional parameters.
10028 The space of the context is that of the flat product of the outer
10029 band nodes. In particular, if there are no outer band nodes, then
10030 this space is the unnamed zero-dimensional space.
10031 Since a context node references the outer band nodes, any tree
10032 containing a context node is considered to be anchored.
10034 =item C<isl_schedule_node_extension>
10036 An extension node instructs the AST generator to add additional
10037 domain elements that need to be scheduled.
10038 The additional domain elements are described by the range of
10039 the extension map in terms of the outer schedule dimensions,
10040 i.e., the flat product of the outer band nodes.
10041 Note that domain elements are added whenever the AST generator
10042 reaches the extension node, meaning that there are still some
10043 active domain elements for which an AST needs to be generated.
10044 The conditions under which some domain elements are still active
10045 may however not be completely described by the outer AST nodes
10046 generated at that point.
10047 Since an extension node references the outer band nodes, any tree
10048 containing an extension node is considered to be anchored.
10050 An extension node may also appear as the root of a schedule tree,
10051 when it is intended to be inserted into another tree
10052 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10053 In this case, the domain of the extension node should
10054 correspond to the flat product of the outer band nodes
10055 in this other schedule tree at the point where the extension tree
10058 =item C<isl_schedule_node_guard>
10060 The guard describes constraints on the parameters and
10061 the schedule dimensions of outer
10062 bands that need to be enforced by the outer nodes
10063 in the generated AST.
10064 That is, the part of the AST that is generated from descendants
10065 of the guard node can assume that these constraints are satisfied.
10066 The space of the guard is that of the flat product of the outer
10067 band nodes. In particular, if there are no outer band nodes, then
10068 this space is the unnamed zero-dimensional space.
10069 Since a guard node references the outer band nodes, any tree
10070 containing a guard node is considered to be anchored.
10074 Except for the C<isl_schedule_node_context> nodes,
10075 none of the nodes may introduce any parameters that were not
10076 already present in the root domain node.
10078 A schedule tree is encapsulated in an C<isl_schedule> object.
10079 The simplest such objects, those with a tree consisting of single domain node,
10080 can be created using the following functions with either an empty
10081 domain or a given domain.
10083 #include <isl/schedule.h>
10084 __isl_give isl_schedule *isl_schedule_empty(
10085 __isl_take isl_space *space);
10086 __isl_give isl_schedule *isl_schedule_from_domain(
10087 __isl_take isl_union_set *domain);
10089 The function C<isl_schedule_constraints_compute_schedule> described
10090 in L</"Scheduling"> can also be used to construct schedules.
10092 C<isl_schedule> objects may be copied and freed using the following functions.
10094 #include <isl/schedule.h>
10095 __isl_give isl_schedule *isl_schedule_copy(
10096 __isl_keep isl_schedule *sched);
10097 __isl_null isl_schedule *isl_schedule_free(
10098 __isl_take isl_schedule *sched);
10100 The following functions checks whether two C<isl_schedule> objects
10101 are obviously the same.
10103 #include <isl/schedule.h>
10104 isl_bool isl_schedule_plain_is_equal(
10105 __isl_keep isl_schedule *schedule1,
10106 __isl_keep isl_schedule *schedule2);
10108 The domain of the schedule, i.e., the domain described by the root node,
10109 can be obtained using the following function.
10111 #include <isl/schedule.h>
10112 __isl_give isl_union_set *isl_schedule_get_domain(
10113 __isl_keep isl_schedule *schedule);
10115 An extra top-level band node (right underneath the domain node) can
10116 be introduced into the schedule using the following function.
10117 The schedule tree is assumed not to have any anchored nodes.
10119 #include <isl/schedule.h>
10120 __isl_give isl_schedule *
10121 isl_schedule_insert_partial_schedule(
10122 __isl_take isl_schedule *schedule,
10123 __isl_take isl_multi_union_pw_aff *partial);
10125 A top-level context node (right underneath the domain node) can
10126 be introduced into the schedule using the following function.
10128 #include <isl/schedule.h>
10129 __isl_give isl_schedule *isl_schedule_insert_context(
10130 __isl_take isl_schedule *schedule,
10131 __isl_take isl_set *context)
10133 A top-level guard node (right underneath the domain node) can
10134 be introduced into the schedule using the following function.
10136 #include <isl/schedule.h>
10137 __isl_give isl_schedule *isl_schedule_insert_guard(
10138 __isl_take isl_schedule *schedule,
10139 __isl_take isl_set *guard)
10141 A schedule that combines two schedules either in the given
10142 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10143 or an C<isl_schedule_node_set> node,
10144 can be created using the following functions.
10146 #include <isl/schedule.h>
10147 __isl_give isl_schedule *isl_schedule_sequence(
10148 __isl_take isl_schedule *schedule1,
10149 __isl_take isl_schedule *schedule2);
10150 __isl_give isl_schedule *isl_schedule_set(
10151 __isl_take isl_schedule *schedule1,
10152 __isl_take isl_schedule *schedule2);
10154 The domains of the two input schedules need to be disjoint.
10156 The following function can be used to restrict the domain
10157 of a schedule with a domain node as root to be a subset of the given union set.
10158 This operation may remove nodes in the tree that have become
10161 #include <isl/schedule.h>
10162 __isl_give isl_schedule *isl_schedule_intersect_domain(
10163 __isl_take isl_schedule *schedule,
10164 __isl_take isl_union_set *domain);
10166 The following function can be used to simplify the domain
10167 of a schedule with a domain node as root with respect to the given
10170 #include <isl/schedule.h>
10171 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10172 __isl_take isl_schedule *schedule,
10173 __isl_take isl_set *context);
10175 The following function resets the user pointers on all parameter
10176 and tuple identifiers referenced by the nodes of the given schedule.
10178 #include <isl/schedule.h>
10179 __isl_give isl_schedule *isl_schedule_reset_user(
10180 __isl_take isl_schedule *schedule);
10182 The following function aligns the parameters of all nodes
10183 in the given schedule to the given space.
10185 #include <isl/schedule.h>
10186 __isl_give isl_schedule *isl_schedule_align_params(
10187 __isl_take isl_schedule *schedule,
10188 __isl_take isl_space *space);
10190 The following function allows the user to plug in a given function
10191 in the iteration domains. The input schedule is not allowed to contain
10192 any expansion nodes.
10194 #include <isl/schedule.h>
10195 __isl_give isl_schedule *
10196 isl_schedule_pullback_union_pw_multi_aff(
10197 __isl_take isl_schedule *schedule,
10198 __isl_take isl_union_pw_multi_aff *upma);
10200 The following function can be used to plug in the schedule C<expansion>
10201 in the leaves of C<schedule>, where C<contraction> describes how
10202 the domain elements of C<expansion> map to the domain elements
10203 at the original leaves of C<schedule>.
10204 The resulting schedule will contain expansion nodes, unless
10205 C<contraction> is an identity function.
10207 #include <isl/schedule.h>
10208 __isl_give isl_schedule *isl_schedule_expand(
10209 __isl_take isl_schedule *schedule,
10210 __isl_take isl_union_pw_multi_aff *contraction,
10211 __isl_take isl_schedule *expansion);
10213 An C<isl_union_map> representation of the schedule can be obtained
10214 from an C<isl_schedule> using the following function.
10216 #include <isl/schedule.h>
10217 __isl_give isl_union_map *isl_schedule_get_map(
10218 __isl_keep isl_schedule *sched);
10220 The resulting relation encodes the same relative ordering as
10221 the schedule by mapping the domain elements to a common schedule space.
10222 If the schedule_separate_components option is set, then the order
10223 of the children of a set node is explicitly encoded in the result.
10224 If the tree contains any expansion nodes, then the relation
10225 is formulated in terms of the expanded domain elements.
10227 Schedules can be read from input using the following functions.
10229 #include <isl/schedule.h>
10230 __isl_give isl_schedule *isl_schedule_read_from_file(
10231 isl_ctx *ctx, FILE *input);
10232 __isl_give isl_schedule *isl_schedule_read_from_str(
10233 isl_ctx *ctx, const char *str);
10235 A representation of the schedule can be printed using
10237 #include <isl/schedule.h>
10238 __isl_give isl_printer *isl_printer_print_schedule(
10239 __isl_take isl_printer *p,
10240 __isl_keep isl_schedule *schedule);
10241 __isl_give char *isl_schedule_to_str(
10242 __isl_keep isl_schedule *schedule);
10244 C<isl_schedule_to_str> prints the schedule in flow format.
10246 The schedule tree can be traversed through the use of
10247 C<isl_schedule_node> objects that point to a particular
10248 position in the schedule tree. Whenever a C<isl_schedule_node>
10249 is used to modify a node in the schedule tree, the original schedule
10250 tree is left untouched and the modifications are performed to a copy
10251 of the tree. The returned C<isl_schedule_node> then points to
10252 this modified copy of the tree.
10254 The root of the schedule tree can be obtained using the following function.
10256 #include <isl/schedule.h>
10257 __isl_give isl_schedule_node *isl_schedule_get_root(
10258 __isl_keep isl_schedule *schedule);
10260 A pointer to a newly created schedule tree with a single domain
10261 node can be created using the following functions.
10263 #include <isl/schedule_node.h>
10264 __isl_give isl_schedule_node *
10265 isl_schedule_node_from_domain(
10266 __isl_take isl_union_set *domain);
10267 __isl_give isl_schedule_node *
10268 isl_schedule_node_from_extension(
10269 __isl_take isl_union_map *extension);
10271 C<isl_schedule_node_from_extension> creates a tree with an extension
10274 Schedule nodes can be copied and freed using the following functions.
10276 #include <isl/schedule_node.h>
10277 __isl_give isl_schedule_node *isl_schedule_node_copy(
10278 __isl_keep isl_schedule_node *node);
10279 __isl_null isl_schedule_node *isl_schedule_node_free(
10280 __isl_take isl_schedule_node *node);
10282 The following functions can be used to check if two schedule
10283 nodes point to the same position in the same schedule.
10285 #include <isl/schedule_node.h>
10286 isl_bool isl_schedule_node_is_equal(
10287 __isl_keep isl_schedule_node *node1,
10288 __isl_keep isl_schedule_node *node2);
10290 The following properties can be obtained from a schedule node.
10292 #include <isl/schedule_node.h>
10293 enum isl_schedule_node_type isl_schedule_node_get_type(
10294 __isl_keep isl_schedule_node *node);
10295 enum isl_schedule_node_type
10296 isl_schedule_node_get_parent_type(
10297 __isl_keep isl_schedule_node *node);
10298 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10299 __isl_keep isl_schedule_node *node);
10301 The function C<isl_schedule_node_get_type> returns the type of
10302 the node, while C<isl_schedule_node_get_parent_type> returns
10303 type of the parent of the node, which is required to exist.
10304 The function C<isl_schedule_node_get_schedule> returns a copy
10305 to the schedule to which the node belongs.
10307 The following functions can be used to move the schedule node
10308 to a different position in the tree or to check if such a position
10311 #include <isl/schedule_node.h>
10312 isl_bool isl_schedule_node_has_parent(
10313 __isl_keep isl_schedule_node *node);
10314 __isl_give isl_schedule_node *isl_schedule_node_parent(
10315 __isl_take isl_schedule_node *node);
10316 __isl_give isl_schedule_node *
10317 isl_schedule_node_grandparent(
10318 __isl_take isl_schedule_node *node);
10319 __isl_give isl_schedule_node *isl_schedule_node_root(
10320 __isl_take isl_schedule_node *node);
10321 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10322 __isl_take isl_schedule_node *node,
10324 isl_size isl_schedule_node_n_children(
10325 __isl_keep isl_schedule_node *node);
10326 __isl_give isl_schedule_node *isl_schedule_node_child(
10327 __isl_take isl_schedule_node *node, int pos);
10328 isl_bool isl_schedule_node_has_children(
10329 __isl_keep isl_schedule_node *node);
10330 __isl_give isl_schedule_node *
10331 isl_schedule_node_grandchild(
10332 __isl_take isl_schedule_node *node,
10333 int pos1, int pos2);
10334 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10335 __isl_take isl_schedule_node *node);
10336 isl_bool isl_schedule_node_has_previous_sibling(
10337 __isl_keep isl_schedule_node *node);
10338 __isl_give isl_schedule_node *
10339 isl_schedule_node_previous_sibling(
10340 __isl_take isl_schedule_node *node);
10341 isl_bool isl_schedule_node_has_next_sibling(
10342 __isl_keep isl_schedule_node *node);
10343 __isl_give isl_schedule_node *
10344 isl_schedule_node_next_sibling(
10345 __isl_take isl_schedule_node *node);
10347 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10348 is the node itself, the ancestor of generation 1 is its parent and so on.
10350 It is also possible to query the number of ancestors of a node,
10351 the position of the current node
10352 within the children of its parent, the position of the subtree
10353 containing a node within the children of an ancestor
10354 or to obtain a copy of a given
10355 child without destroying the current node.
10356 Given two nodes that point to the same schedule, their closest
10357 shared ancestor can be obtained using
10358 C<isl_schedule_node_get_shared_ancestor>.
10360 #include <isl/schedule_node.h>
10361 isl_size isl_schedule_node_get_tree_depth(
10362 __isl_keep isl_schedule_node *node);
10363 isl_size isl_schedule_node_get_child_position(
10364 __isl_keep isl_schedule_node *node);
10365 isl_size isl_schedule_node_get_ancestor_child_position(
10366 __isl_keep isl_schedule_node *node,
10367 __isl_keep isl_schedule_node *ancestor);
10368 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10369 __isl_keep isl_schedule_node *node, int pos);
10370 __isl_give isl_schedule_node *
10371 isl_schedule_node_get_shared_ancestor(
10372 __isl_keep isl_schedule_node *node1,
10373 __isl_keep isl_schedule_node *node2);
10375 All nodes in a schedule tree or
10376 all descendants of a specific node (including the node) can be visited
10377 in depth-first pre-order using the following functions.
10379 #include <isl/schedule.h>
10380 isl_stat isl_schedule_foreach_schedule_node_top_down(
10381 __isl_keep isl_schedule *sched,
10382 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10383 void *user), void *user);
10385 #include <isl/schedule_node.h>
10386 isl_stat isl_schedule_node_foreach_descendant_top_down(
10387 __isl_keep isl_schedule_node *node,
10388 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10389 void *user), void *user);
10391 The callback function is slightly different from the usual
10392 callbacks in that it not only indicates success (non-negative result)
10393 or failure (negative result), but also indicates whether the children
10394 of the given node should be visited. In particular, if the callback
10395 returns a positive value, then the children are visited, but if
10396 the callback returns zero, then the children are not visited.
10398 The following functions checks whether
10399 all descendants of a specific node (including the node itself)
10400 satisfy a user-specified test.
10402 #include <isl/schedule_node.h>
10403 isl_bool isl_schedule_node_every_descendant(
10404 __isl_keep isl_schedule_node *node,
10405 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10406 void *user), void *user)
10408 The ancestors of a node in a schedule tree can be visited from
10409 the root down to and including the parent of the node using
10410 the following function.
10412 #include <isl/schedule_node.h>
10413 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10414 __isl_keep isl_schedule_node *node,
10415 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10416 void *user), void *user);
10418 The following functions allows for a depth-first post-order
10419 traversal of the nodes in a schedule tree or
10420 of the descendants of a specific node (including the node
10421 itself), where the user callback is allowed to modify the
10424 #include <isl/schedule.h>
10425 __isl_give isl_schedule *
10426 isl_schedule_map_schedule_node_bottom_up(
10427 __isl_take isl_schedule *schedule,
10428 __isl_give isl_schedule_node *(*fn)(
10429 __isl_take isl_schedule_node *node,
10430 void *user), void *user);
10432 #include <isl/schedule_node.h>
10433 __isl_give isl_schedule_node *
10434 isl_schedule_node_map_descendant_bottom_up(
10435 __isl_take isl_schedule_node *node,
10436 __isl_give isl_schedule_node *(*fn)(
10437 __isl_take isl_schedule_node *node,
10438 void *user), void *user);
10440 The traversal continues from the node returned by the callback function.
10441 It is the responsibility of the user to ensure that this does not
10442 lead to an infinite loop. It is safest to always return a pointer
10443 to the same position (same ancestors and child positions) as the input node.
10445 The following function removes a node (along with its descendants)
10446 from a schedule tree and returns a pointer to the leaf at the
10447 same position in the updated tree.
10448 It is not allowed to remove the root of a schedule tree or
10449 a child of a set or sequence node.
10451 #include <isl/schedule_node.h>
10452 __isl_give isl_schedule_node *isl_schedule_node_cut(
10453 __isl_take isl_schedule_node *node);
10455 The following function removes a single node
10456 from a schedule tree and returns a pointer to the child
10457 of the node, now located at the position of the original node
10458 or to a leaf node at that position if there was no child.
10459 It is not allowed to remove the root of a schedule tree,
10460 a set or sequence node, a child of a set or sequence node or
10461 a band node with an anchored subtree.
10463 #include <isl/schedule_node.h>
10464 __isl_give isl_schedule_node *isl_schedule_node_delete(
10465 __isl_take isl_schedule_node *node);
10467 Most nodes in a schedule tree only contain local information.
10468 In some cases, however, a node may also refer to the schedule dimensions
10469 of its outer band nodes.
10470 This means that the position of the node within the tree should
10471 not be changed, or at least that no changes are performed to the
10472 outer band nodes. The following function can be used to test
10473 whether the subtree rooted at a given node contains any such nodes.
10475 #include <isl/schedule_node.h>
10476 isl_bool isl_schedule_node_is_subtree_anchored(
10477 __isl_keep isl_schedule_node *node);
10479 The following function resets the user pointers on all parameter
10480 and tuple identifiers referenced by the given schedule node.
10482 #include <isl/schedule_node.h>
10483 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10484 __isl_take isl_schedule_node *node);
10486 The following function aligns the parameters of the given schedule
10487 node to the given space.
10489 #include <isl/schedule_node.h>
10490 __isl_give isl_schedule_node *
10491 isl_schedule_node_align_params(
10492 __isl_take isl_schedule_node *node,
10493 __isl_take isl_space *space);
10495 Several node types have their own functions for querying
10496 (and in some cases setting) some node type specific properties.
10498 #include <isl/schedule_node.h>
10499 __isl_give isl_space *isl_schedule_node_band_get_space(
10500 __isl_keep isl_schedule_node *node);
10501 __isl_give isl_multi_union_pw_aff *
10502 isl_schedule_node_band_get_partial_schedule(
10503 __isl_keep isl_schedule_node *node);
10504 __isl_give isl_union_map *
10505 isl_schedule_node_band_get_partial_schedule_union_map(
10506 __isl_keep isl_schedule_node *node);
10507 isl_size isl_schedule_node_band_n_member(
10508 __isl_keep isl_schedule_node *node);
10509 isl_bool isl_schedule_node_band_member_get_coincident(
10510 __isl_keep isl_schedule_node *node, int pos);
10511 __isl_give isl_schedule_node *
10512 isl_schedule_node_band_member_set_coincident(
10513 __isl_take isl_schedule_node *node, int pos,
10515 isl_bool isl_schedule_node_band_get_permutable(
10516 __isl_keep isl_schedule_node *node);
10517 __isl_give isl_schedule_node *
10518 isl_schedule_node_band_set_permutable(
10519 __isl_take isl_schedule_node *node, int permutable);
10520 enum isl_ast_loop_type
10521 isl_schedule_node_band_member_get_ast_loop_type(
10522 __isl_keep isl_schedule_node *node, int pos);
10523 __isl_give isl_schedule_node *
10524 isl_schedule_node_band_member_set_ast_loop_type(
10525 __isl_take isl_schedule_node *node, int pos,
10526 enum isl_ast_loop_type type);
10527 enum isl_ast_loop_type
10528 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10529 __isl_keep isl_schedule_node *node, int pos);
10530 __isl_give isl_schedule_node *
10531 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10532 __isl_take isl_schedule_node *node, int pos,
10533 enum isl_ast_loop_type type);
10534 __isl_give isl_union_set *
10535 isl_schedule_node_band_get_ast_build_options(
10536 __isl_keep isl_schedule_node *node);
10537 __isl_give isl_schedule_node *
10538 isl_schedule_node_band_set_ast_build_options(
10539 __isl_take isl_schedule_node *node,
10540 __isl_take isl_union_set *options);
10541 __isl_give isl_set *
10542 isl_schedule_node_band_get_ast_isolate_option(
10543 __isl_keep isl_schedule_node *node);
10545 The function C<isl_schedule_node_band_get_space> returns the space
10546 of the partial schedule of the band.
10547 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10548 returns a representation of the partial schedule of the band node
10549 in the form of an C<isl_union_map>.
10550 The coincident and permutable properties are set by
10551 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10553 A scheduling dimension is considered to be ``coincident''
10554 if it satisfies the coincidence constraints within its band.
10555 That is, if the dependence distances of the coincidence
10556 constraints are all zero in that direction (for fixed
10557 iterations of outer bands).
10558 A band is marked permutable if it was produced using the Pluto-like scheduler.
10559 Note that the scheduler may have to resort to a Feautrier style scheduling
10560 step even if the default scheduler is used.
10561 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10562 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10563 For the meaning of these loop AST generation types and the difference
10564 between the regular loop AST generation type and the isolate
10565 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10566 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10567 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10568 may return C<isl_ast_loop_error> if an error occurs.
10569 The AST build options govern how an AST is generated for
10570 the individual schedule dimensions during AST generation.
10571 See L</"AST Generation Options (Schedule Tree)">.
10572 The isolate option for the given node can be extracted from these
10573 AST build options using the function
10574 C<isl_schedule_node_band_get_ast_isolate_option>.
10576 #include <isl/schedule_node.h>
10577 __isl_give isl_set *
10578 isl_schedule_node_context_get_context(
10579 __isl_keep isl_schedule_node *node);
10581 #include <isl/schedule_node.h>
10582 __isl_give isl_union_set *
10583 isl_schedule_node_domain_get_domain(
10584 __isl_keep isl_schedule_node *node);
10586 #include <isl/schedule_node.h>
10587 __isl_give isl_union_map *
10588 isl_schedule_node_expansion_get_expansion(
10589 __isl_keep isl_schedule_node *node);
10590 __isl_give isl_union_pw_multi_aff *
10591 isl_schedule_node_expansion_get_contraction(
10592 __isl_keep isl_schedule_node *node);
10594 #include <isl/schedule_node.h>
10595 __isl_give isl_union_map *
10596 isl_schedule_node_extension_get_extension(
10597 __isl_keep isl_schedule_node *node);
10599 #include <isl/schedule_node.h>
10600 __isl_give isl_union_set *
10601 isl_schedule_node_filter_get_filter(
10602 __isl_keep isl_schedule_node *node);
10604 #include <isl/schedule_node.h>
10605 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10606 __isl_keep isl_schedule_node *node);
10608 #include <isl/schedule_node.h>
10609 __isl_give isl_id *isl_schedule_node_mark_get_id(
10610 __isl_keep isl_schedule_node *node);
10612 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10613 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10614 partial schedules related to the node.
10616 #include <isl/schedule_node.h>
10617 __isl_give isl_multi_union_pw_aff *
10618 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10619 __isl_keep isl_schedule_node *node);
10620 __isl_give isl_union_pw_multi_aff *
10621 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10622 __isl_keep isl_schedule_node *node);
10623 __isl_give isl_union_map *
10624 isl_schedule_node_get_prefix_schedule_union_map(
10625 __isl_keep isl_schedule_node *node);
10626 __isl_give isl_union_map *
10627 isl_schedule_node_get_prefix_schedule_relation(
10628 __isl_keep isl_schedule_node *node);
10629 __isl_give isl_union_map *
10630 isl_schedule_node_get_subtree_schedule_union_map(
10631 __isl_keep isl_schedule_node *node);
10633 In particular, the functions
10634 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10635 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10636 and C<isl_schedule_node_get_prefix_schedule_union_map>
10637 return a relative ordering on the domain elements that reach the given
10638 node determined by its ancestors.
10639 The function C<isl_schedule_node_get_prefix_schedule_relation>
10640 additionally includes the domain constraints in the result.
10641 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10642 returns a representation of the partial schedule defined by the
10643 subtree rooted at the given node.
10644 If the tree contains any expansion nodes, then the subtree schedule
10645 is formulated in terms of the expanded domain elements.
10646 The tree passed to functions returning a prefix schedule
10647 may only contain extension nodes if these would not affect
10648 the result of these functions. That is, if one of the ancestors
10649 is an extension node, then all of the domain elements that were
10650 added by the extension node need to have been filtered out
10651 by filter nodes between the extension node and the input node.
10652 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10653 may not contain in extension nodes in the selected subtree.
10655 The expansion/contraction defined by an entire subtree, combining
10656 the expansions/contractions
10657 on the expansion nodes in the subtree, can be obtained using
10658 the following functions.
10660 #include <isl/schedule_node.h>
10661 __isl_give isl_union_map *
10662 isl_schedule_node_get_subtree_expansion(
10663 __isl_keep isl_schedule_node *node);
10664 __isl_give isl_union_pw_multi_aff *
10665 isl_schedule_node_get_subtree_contraction(
10666 __isl_keep isl_schedule_node *node);
10668 The total number of outer band members of given node, i.e.,
10669 the shared output dimension of the maps in the result
10670 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10671 using the following function.
10673 #include <isl/schedule_node.h>
10674 isl_size isl_schedule_node_get_schedule_depth(
10675 __isl_keep isl_schedule_node *node);
10677 The following functions return the elements that reach the given node
10678 or the union of universes in the spaces that contain these elements.
10680 #include <isl/schedule_node.h>
10681 __isl_give isl_union_set *
10682 isl_schedule_node_get_domain(
10683 __isl_keep isl_schedule_node *node);
10684 __isl_give isl_union_set *
10685 isl_schedule_node_get_universe_domain(
10686 __isl_keep isl_schedule_node *node);
10688 The input tree of C<isl_schedule_node_get_domain>
10689 may only contain extension nodes if these would not affect
10690 the result of this function. That is, if one of the ancestors
10691 is an extension node, then all of the domain elements that were
10692 added by the extension node need to have been filtered out
10693 by filter nodes between the extension node and the input node.
10695 The following functions can be used to introduce additional nodes
10696 in the schedule tree. The new node is introduced at the point
10697 in the tree where the C<isl_schedule_node> points to and
10698 the results points to the new node.
10700 #include <isl/schedule_node.h>
10701 __isl_give isl_schedule_node *
10702 isl_schedule_node_insert_partial_schedule(
10703 __isl_take isl_schedule_node *node,
10704 __isl_take isl_multi_union_pw_aff *schedule);
10706 This function inserts a new band node with (the greatest integer
10707 part of) the given partial schedule.
10708 The subtree rooted at the given node is assumed not to have
10709 any anchored nodes.
10711 #include <isl/schedule_node.h>
10712 __isl_give isl_schedule_node *
10713 isl_schedule_node_insert_context(
10714 __isl_take isl_schedule_node *node,
10715 __isl_take isl_set *context);
10717 This function inserts a new context node with the given context constraints.
10719 #include <isl/schedule_node.h>
10720 __isl_give isl_schedule_node *
10721 isl_schedule_node_insert_filter(
10722 __isl_take isl_schedule_node *node,
10723 __isl_take isl_union_set *filter);
10725 This function inserts a new filter node with the given filter.
10726 If the original node already pointed to a filter node, then the
10727 two filter nodes are merged into one.
10729 #include <isl/schedule_node.h>
10730 __isl_give isl_schedule_node *
10731 isl_schedule_node_insert_guard(
10732 __isl_take isl_schedule_node *node,
10733 __isl_take isl_set *guard);
10735 This function inserts a new guard node with the given guard constraints.
10737 #include <isl/schedule_node.h>
10738 __isl_give isl_schedule_node *
10739 isl_schedule_node_insert_mark(
10740 __isl_take isl_schedule_node *node,
10741 __isl_take isl_id *mark);
10743 This function inserts a new mark node with the give mark identifier.
10745 #include <isl/schedule_node.h>
10746 __isl_give isl_schedule_node *
10747 isl_schedule_node_insert_sequence(
10748 __isl_take isl_schedule_node *node,
10749 __isl_take isl_union_set_list *filters);
10750 __isl_give isl_schedule_node *
10751 isl_schedule_node_insert_set(
10752 __isl_take isl_schedule_node *node,
10753 __isl_take isl_union_set_list *filters);
10755 These functions insert a new sequence or set node with the given
10756 filters as children.
10758 #include <isl/schedule_node.h>
10759 __isl_give isl_schedule_node *isl_schedule_node_group(
10760 __isl_take isl_schedule_node *node,
10761 __isl_take isl_id *group_id);
10763 This function introduces an expansion node in between the current
10764 node and its parent that expands instances of a space with tuple
10765 identifier C<group_id> to the original domain elements that reach
10766 the node. The group instances are identified by the prefix schedule
10767 of those domain elements. The ancestors of the node are adjusted
10768 to refer to the group instances instead of the original domain
10769 elements. The return value points to the same node in the updated
10770 schedule tree as the input node, i.e., to the child of the newly
10771 introduced expansion node. Grouping instances of different statements
10772 ensures that they will be treated as a single statement by the
10773 AST generator up to the point of the expansion node.
10775 The following functions can be used to flatten a nested
10778 #include <isl/schedule_node.h>
10779 __isl_give isl_schedule_node *
10780 isl_schedule_node_sequence_splice_child(
10781 __isl_take isl_schedule_node *node, int pos);
10782 __isl_give isl_schedule_node *
10783 isl_schedule_node_sequence_splice_children(
10784 __isl_take isl_schedule_node *node);
10786 That is, given a sequence node C<node> that has another sequence node
10787 in its child at position C<pos> (in particular, the child of that filter
10788 node is a sequence node), the function
10789 C<isl_schedule_node_sequence_splice_child>
10790 attaches the children of that other sequence
10791 node as children of C<node>, replacing the original child at position
10793 C<isl_schedule_node_sequence_splice_children> does this for all
10796 The partial schedule of a band node can be scaled (down) or reduced using
10797 the following functions.
10799 #include <isl/schedule_node.h>
10800 __isl_give isl_schedule_node *
10801 isl_schedule_node_band_scale(
10802 __isl_take isl_schedule_node *node,
10803 __isl_take isl_multi_val *mv);
10804 __isl_give isl_schedule_node *
10805 isl_schedule_node_band_scale_down(
10806 __isl_take isl_schedule_node *node,
10807 __isl_take isl_multi_val *mv);
10808 __isl_give isl_schedule_node *
10809 isl_schedule_node_band_mod(
10810 __isl_take isl_schedule_node *node,
10811 __isl_take isl_multi_val *mv);
10813 The spaces of the two arguments need to match.
10814 After scaling, the partial schedule is replaced by its greatest
10815 integer part to ensure that the schedule remains integral.
10817 The partial schedule of a band node can be shifted by an
10818 C<isl_multi_union_pw_aff> with a domain that is a superset
10819 of the domain of the partial schedule using
10820 the following function.
10822 #include <isl/schedule_node.h>
10823 __isl_give isl_schedule_node *
10824 isl_schedule_node_band_shift(
10825 __isl_take isl_schedule_node *node,
10826 __isl_take isl_multi_union_pw_aff *shift);
10828 A band node can be tiled using the following function.
10830 #include <isl/schedule_node.h>
10831 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10832 __isl_take isl_schedule_node *node,
10833 __isl_take isl_multi_val *sizes);
10835 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10837 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10838 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10840 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10842 The C<isl_schedule_node_band_tile> function tiles
10843 the band using the given tile sizes inside its schedule.
10844 A new child band node is created to represent the point loops and it is
10845 inserted between the modified band and its children.
10846 The subtree rooted at the given node is assumed not to have
10847 any anchored nodes.
10848 The C<tile_scale_tile_loops> option specifies whether the tile
10849 loops iterators should be scaled by the tile sizes.
10850 If the C<tile_shift_point_loops> option is set, then the point loops
10851 are shifted to start at zero.
10853 A band node can be split into two nested band nodes
10854 using the following function.
10856 #include <isl/schedule_node.h>
10857 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10858 __isl_take isl_schedule_node *node, int pos);
10860 The resulting outer band node contains the first C<pos> dimensions of
10861 the schedule of C<node> while the inner band contains the remaining dimensions.
10862 The schedules of the two band nodes live in anonymous spaces.
10863 The loop AST generation type options and the isolate option
10864 are split over the two band nodes.
10866 A band node can be moved down to the leaves of the subtree rooted
10867 at the band node using the following function.
10869 #include <isl/schedule_node.h>
10870 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10871 __isl_take isl_schedule_node *node);
10873 The subtree rooted at the given node is assumed not to have
10874 any anchored nodes.
10875 The result points to the node in the resulting tree that is in the same
10876 position as the node pointed to by C<node> in the original tree.
10878 #include <isl/schedule_node.h>
10879 __isl_give isl_schedule_node *
10880 isl_schedule_node_order_before(
10881 __isl_take isl_schedule_node *node,
10882 __isl_take isl_union_set *filter);
10883 __isl_give isl_schedule_node *
10884 isl_schedule_node_order_after(
10885 __isl_take isl_schedule_node *node,
10886 __isl_take isl_union_set *filter);
10888 These functions split the domain elements that reach C<node>
10889 into those that satisfy C<filter> and those that do not and
10890 arranges for the elements that do satisfy the filter to be
10891 executed before (in case of C<isl_schedule_node_order_before>)
10892 or after (in case of C<isl_schedule_node_order_after>)
10893 those that do not. The order is imposed by
10894 a sequence node, possibly reusing the grandparent of C<node>
10895 on two copies of the subtree attached to the original C<node>.
10896 Both copies are simplified with respect to their filter.
10898 Return a pointer to the copy of the subtree that does not
10899 satisfy C<filter>. If there is no such copy (because all
10900 reaching domain elements satisfy the filter), then return
10901 the original pointer.
10903 #include <isl/schedule_node.h>
10904 __isl_give isl_schedule_node *
10905 isl_schedule_node_graft_before(
10906 __isl_take isl_schedule_node *node,
10907 __isl_take isl_schedule_node *graft);
10908 __isl_give isl_schedule_node *
10909 isl_schedule_node_graft_after(
10910 __isl_take isl_schedule_node *node,
10911 __isl_take isl_schedule_node *graft);
10913 This function inserts the C<graft> tree into the tree containing C<node>
10914 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10915 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10916 The root node of C<graft>
10917 should be an extension node where the domain of the extension
10918 is the flat product of all outer band nodes of C<node>.
10919 The root node may also be a domain node.
10920 The elements of the domain or the range of the extension may not
10921 intersect with the domain elements that reach "node".
10922 The schedule tree of C<graft> may not be anchored.
10924 The schedule tree of C<node> is modified to include an extension node
10925 corresponding to the root node of C<graft> as a child of the original
10926 parent of C<node>. The original node that C<node> points to and the
10927 child of the root node of C<graft> are attached to this extension node
10928 through a sequence, with appropriate filters and with the child
10929 of C<graft> appearing before or after the original C<node>.
10931 If C<node> already appears inside a sequence that is the child of
10932 an extension node and if the spaces of the new domain elements
10933 do not overlap with those of the original domain elements,
10934 then that extension node is extended with the new extension
10935 rather than introducing a new segment of extension and sequence nodes.
10937 Return a pointer to the same node in the modified tree that
10938 C<node> pointed to in the original tree.
10940 A representation of the schedule node can be printed using
10942 #include <isl/schedule_node.h>
10943 __isl_give isl_printer *isl_printer_print_schedule_node(
10944 __isl_take isl_printer *p,
10945 __isl_keep isl_schedule_node *node);
10946 __isl_give char *isl_schedule_node_to_str(
10947 __isl_keep isl_schedule_node *node);
10949 C<isl_schedule_node_to_str> prints the schedule node in block format.
10951 =head2 Dependence Analysis
10953 C<isl> contains specialized functionality for performing
10954 array dataflow analysis. That is, given a I<sink> access relation,
10955 a collection of possible I<source> accesses and
10956 a collection of I<kill> accesses,
10957 C<isl> can compute relations that describe
10958 for each iteration of the sink access, which iterations
10959 of which of the source access relations may have
10960 accessed the same data element before the given iteration
10961 of the sink access without any intermediate kill of that data element.
10962 The resulting dependence relations map source iterations
10963 to either the corresponding sink iterations or
10964 pairs of corresponding sink iterations and accessed data elements.
10965 To compute standard flow dependences, the sink should be
10966 a read, while the sources should be writes.
10967 If no kills are specified,
10968 then memory based dependence analysis is performed.
10969 If, on the other hand, all sources are also kills,
10970 then value based dependence analysis is performed.
10971 If any of the source accesses are marked as being I<must>
10972 accesses, then they are also treated as kills.
10973 Furthermore, the specification of must-sources results
10974 in the computation of must-dependences.
10975 Only dependences originating in a must access not coscheduled
10976 with any other access to the same element and without
10977 any may accesses between the must access and the sink access
10978 are considered to be must dependences.
10980 =head3 High-level Interface
10982 A high-level interface to dependence analysis is provided
10983 by the following function.
10985 #include <isl/flow.h>
10986 __isl_give isl_union_flow *
10987 isl_union_access_info_compute_flow(
10988 __isl_take isl_union_access_info *access);
10990 The input C<isl_union_access_info> object describes the sink
10991 access relations, the source access relations and a schedule,
10992 while the output C<isl_union_flow> object describes
10993 the resulting dependence relations and the subsets of the
10994 sink relations for which no source was found.
10996 An C<isl_union_access_info> is created, modified, copied and freed using
10997 the following functions.
10999 #include <isl/flow.h>
11000 __isl_give isl_union_access_info *
11001 isl_union_access_info_from_sink(
11002 __isl_take isl_union_map *sink);
11003 __isl_give isl_union_access_info *
11004 isl_union_access_info_set_kill(
11005 __isl_take isl_union_access_info *access,
11006 __isl_take isl_union_map *kill);
11007 __isl_give isl_union_access_info *
11008 isl_union_access_info_set_may_source(
11009 __isl_take isl_union_access_info *access,
11010 __isl_take isl_union_map *may_source);
11011 __isl_give isl_union_access_info *
11012 isl_union_access_info_set_must_source(
11013 __isl_take isl_union_access_info *access,
11014 __isl_take isl_union_map *must_source);
11015 __isl_give isl_union_access_info *
11016 isl_union_access_info_set_schedule(
11017 __isl_take isl_union_access_info *access,
11018 __isl_take isl_schedule *schedule);
11019 __isl_give isl_union_access_info *
11020 isl_union_access_info_set_schedule_map(
11021 __isl_take isl_union_access_info *access,
11022 __isl_take isl_union_map *schedule_map);
11023 __isl_give isl_union_access_info *
11024 isl_union_access_info_copy(
11025 __isl_keep isl_union_access_info *access);
11026 __isl_null isl_union_access_info *
11027 isl_union_access_info_free(
11028 __isl_take isl_union_access_info *access);
11030 The may sources set by C<isl_union_access_info_set_may_source>
11031 do not need to include the must sources set by
11032 C<isl_union_access_info_set_must_source> as a subset.
11033 The kills set by C<isl_union_access_info_set_kill> may overlap
11034 with the may-sources and/or must-sources.
11035 The user is free not to call one (or more) of these functions,
11036 in which case the corresponding set is kept to its empty default.
11037 Similarly, the default schedule initialized by
11038 C<isl_union_access_info_from_sink> is empty.
11039 The current schedule is determined by the last call to either
11040 C<isl_union_access_info_set_schedule> or
11041 C<isl_union_access_info_set_schedule_map>.
11042 The domain of the schedule corresponds to the domains of
11043 the access relations. In particular, the domains of the access
11044 relations are effectively intersected with the domain of the schedule
11045 and only the resulting accesses are considered by the dependence analysis.
11047 An C<isl_union_access_info> object can be read from input
11048 using the following function.
11050 #include <isl/flow.h>
11051 __isl_give isl_union_access_info *
11052 isl_union_access_info_read_from_file(isl_ctx *ctx,
11055 A representation of the information contained in an object
11056 of type C<isl_union_access_info> can be obtained using
11058 #include <isl/flow.h>
11059 __isl_give isl_printer *
11060 isl_printer_print_union_access_info(
11061 __isl_take isl_printer *p,
11062 __isl_keep isl_union_access_info *access);
11063 __isl_give char *isl_union_access_info_to_str(
11064 __isl_keep isl_union_access_info *access);
11066 C<isl_union_access_info_to_str> prints the information in flow format.
11068 The output of C<isl_union_access_info_compute_flow> can be examined,
11069 copied, and freed using the following functions.
11071 #include <isl/flow.h>
11072 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11073 __isl_keep isl_union_flow *flow);
11074 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11075 __isl_keep isl_union_flow *flow);
11076 __isl_give isl_union_map *
11077 isl_union_flow_get_full_must_dependence(
11078 __isl_keep isl_union_flow *flow);
11079 __isl_give isl_union_map *
11080 isl_union_flow_get_full_may_dependence(
11081 __isl_keep isl_union_flow *flow);
11082 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11083 __isl_keep isl_union_flow *flow);
11084 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11085 __isl_keep isl_union_flow *flow);
11086 __isl_give isl_union_flow *isl_union_flow_copy(
11087 __isl_keep isl_union_flow *flow);
11088 __isl_null isl_union_flow *isl_union_flow_free(
11089 __isl_take isl_union_flow *flow);
11091 The relation returned by C<isl_union_flow_get_must_dependence>
11092 relates domain elements of must sources to domain elements of the sink.
11093 The relation returned by C<isl_union_flow_get_may_dependence>
11094 relates domain elements of must or may sources to domain elements of the sink
11095 and includes the previous relation as a subset.
11096 The relation returned by C<isl_union_flow_get_full_must_dependence>
11097 relates domain elements of must sources to pairs of domain elements of the sink
11098 and accessed data elements.
11099 The relation returned by C<isl_union_flow_get_full_may_dependence>
11100 relates domain elements of must or may sources to pairs of
11101 domain elements of the sink and accessed data elements.
11102 This relation includes the previous relation as a subset.
11103 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11104 of the sink relation for which no dependences have been found.
11105 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11106 of the sink relation for which no definite dependences have been found.
11107 That is, it contains those sink access that do not contribute to any
11108 of the elements in the relation returned
11109 by C<isl_union_flow_get_must_dependence>.
11111 A representation of the information contained in an object
11112 of type C<isl_union_flow> can be obtained using
11114 #include <isl/flow.h>
11115 __isl_give isl_printer *isl_printer_print_union_flow(
11116 __isl_take isl_printer *p,
11117 __isl_keep isl_union_flow *flow);
11118 __isl_give char *isl_union_flow_to_str(
11119 __isl_keep isl_union_flow *flow);
11121 C<isl_union_flow_to_str> prints the information in flow format.
11123 =head3 Low-level Interface
11125 A lower-level interface is provided by the following functions.
11127 #include <isl/flow.h>
11129 typedef int (*isl_access_level_before)(void *first, void *second);
11131 __isl_give isl_access_info *isl_access_info_alloc(
11132 __isl_take isl_map *sink,
11133 void *sink_user, isl_access_level_before fn,
11135 __isl_give isl_access_info *isl_access_info_add_source(
11136 __isl_take isl_access_info *acc,
11137 __isl_take isl_map *source, int must,
11138 void *source_user);
11139 __isl_null isl_access_info *isl_access_info_free(
11140 __isl_take isl_access_info *acc);
11142 __isl_give isl_flow *isl_access_info_compute_flow(
11143 __isl_take isl_access_info *acc);
11145 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11146 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11147 void *dep_user, void *user),
11149 __isl_give isl_map *isl_flow_get_no_source(
11150 __isl_keep isl_flow *deps, int must);
11151 __isl_null isl_flow *isl_flow_free(
11152 __isl_take isl_flow *deps);
11154 The function C<isl_access_info_compute_flow> performs the actual
11155 dependence analysis. The other functions are used to construct
11156 the input for this function or to read off the output.
11158 The input is collected in an C<isl_access_info>, which can
11159 be created through a call to C<isl_access_info_alloc>.
11160 The arguments to this functions are the sink access relation
11161 C<sink>, a token C<sink_user> used to identify the sink
11162 access to the user, a callback function for specifying the
11163 relative order of source and sink accesses, and the number
11164 of source access relations that will be added.
11166 The callback function has type C<int (*)(void *first, void *second)>.
11167 The function is called with two user supplied tokens identifying
11168 either a source or the sink and it should return the shared nesting
11169 level and the relative order of the two accesses.
11170 In particular, let I<n> be the number of loops shared by
11171 the two accesses. If C<first> precedes C<second> textually,
11172 then the function should return I<2 * n + 1>; otherwise,
11173 it should return I<2 * n>.
11174 The low-level interface assumes that no sources are coscheduled.
11175 If the information returned by the callback does not allow
11176 the relative order to be determined, then one of the sources
11177 is arbitrarily taken to be executed after the other(s).
11179 The sources can be added to the C<isl_access_info> object by performing
11180 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11181 C<must> indicates whether the source is a I<must> access
11182 or a I<may> access. Note that a multi-valued access relation
11183 should only be marked I<must> if every iteration in the domain
11184 of the relation accesses I<all> elements in its image.
11185 The C<source_user> token is again used to identify
11186 the source access. The range of the source access relation
11187 C<source> should have the same dimension as the range
11188 of the sink access relation.
11189 The C<isl_access_info_free> function should usually not be
11190 called explicitly, because it is already called implicitly by
11191 C<isl_access_info_compute_flow>.
11193 The result of the dependence analysis is collected in an
11194 C<isl_flow>. There may be elements of
11195 the sink access for which no preceding source access could be
11196 found or for which all preceding sources are I<may> accesses.
11197 The relations containing these elements can be obtained through
11198 calls to C<isl_flow_get_no_source>, the first with C<must> set
11199 and the second with C<must> unset.
11200 In the case of standard flow dependence analysis,
11201 with the sink a read and the sources I<must> writes,
11202 the first relation corresponds to the reads from uninitialized
11203 array elements and the second relation is empty.
11204 The actual flow dependences can be extracted using
11205 C<isl_flow_foreach>. This function will call the user-specified
11206 callback function C<fn> for each B<non-empty> dependence between
11207 a source and the sink. The callback function is called
11208 with four arguments, the actual flow dependence relation
11209 mapping source iterations to sink iterations, a boolean that
11210 indicates whether it is a I<must> or I<may> dependence, a token
11211 identifying the source and an additional C<void *> with value
11212 equal to the third argument of the C<isl_flow_foreach> call.
11213 A dependence is marked I<must> if it originates from a I<must>
11214 source and if it is not followed by any I<may> sources.
11216 After finishing with an C<isl_flow>, the user should call
11217 C<isl_flow_free> to free all associated memory.
11219 =head3 Interaction with the Low-level Interface
11221 During the dependence analysis, we frequently need to perform
11222 the following operation. Given a relation between sink iterations
11223 and potential source iterations from a particular source domain,
11224 what is the last potential source iteration corresponding to each
11225 sink iteration. It can sometimes be convenient to adjust
11226 the set of potential source iterations before or after each such operation.
11227 The prototypical example is fuzzy array dataflow analysis,
11228 where we need to analyze if, based on data-dependent constraints,
11229 the sink iteration can ever be executed without one or more of
11230 the corresponding potential source iterations being executed.
11231 If so, we can introduce extra parameters and select an unknown
11232 but fixed source iteration from the potential source iterations.
11233 To be able to perform such manipulations, C<isl> provides the following
11236 #include <isl/flow.h>
11238 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11239 __isl_keep isl_map *source_map,
11240 __isl_keep isl_set *sink, void *source_user,
11242 __isl_give isl_access_info *isl_access_info_set_restrict(
11243 __isl_take isl_access_info *acc,
11244 isl_access_restrict fn, void *user);
11246 The function C<isl_access_info_set_restrict> should be called
11247 before calling C<isl_access_info_compute_flow> and registers a callback function
11248 that will be called any time C<isl> is about to compute the last
11249 potential source. The first argument is the (reverse) proto-dependence,
11250 mapping sink iterations to potential source iterations.
11251 The second argument represents the sink iterations for which
11252 we want to compute the last source iteration.
11253 The third argument is the token corresponding to the source
11254 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11255 The callback is expected to return a restriction on either the input or
11256 the output of the operation computing the last potential source.
11257 If the input needs to be restricted then restrictions are needed
11258 for both the source and the sink iterations. The sink iterations
11259 and the potential source iterations will be intersected with these sets.
11260 If the output needs to be restricted then only a restriction on the source
11261 iterations is required.
11262 If any error occurs, the callback should return C<NULL>.
11263 An C<isl_restriction> object can be created, freed and inspected
11264 using the following functions.
11266 #include <isl/flow.h>
11268 __isl_give isl_restriction *isl_restriction_input(
11269 __isl_take isl_set *source_restr,
11270 __isl_take isl_set *sink_restr);
11271 __isl_give isl_restriction *isl_restriction_output(
11272 __isl_take isl_set *source_restr);
11273 __isl_give isl_restriction *isl_restriction_none(
11274 __isl_take isl_map *source_map);
11275 __isl_give isl_restriction *isl_restriction_empty(
11276 __isl_take isl_map *source_map);
11277 __isl_null isl_restriction *isl_restriction_free(
11278 __isl_take isl_restriction *restr);
11280 C<isl_restriction_none> and C<isl_restriction_empty> are special
11281 cases of C<isl_restriction_input>. C<isl_restriction_none>
11282 is essentially equivalent to
11284 isl_restriction_input(isl_set_universe(
11285 isl_space_range(isl_map_get_space(source_map))),
11287 isl_space_domain(isl_map_get_space(source_map))));
11289 whereas C<isl_restriction_empty> is essentially equivalent to
11291 isl_restriction_input(isl_set_empty(
11292 isl_space_range(isl_map_get_space(source_map))),
11294 isl_space_domain(isl_map_get_space(source_map))));
11298 #include <isl/schedule.h>
11299 __isl_give isl_schedule *
11300 isl_schedule_constraints_compute_schedule(
11301 __isl_take isl_schedule_constraints *sc);
11303 The function C<isl_schedule_constraints_compute_schedule> can be
11304 used to compute a schedule that satisfies the given schedule constraints.
11305 These schedule constraints include the iteration domain for which
11306 a schedule should be computed and dependences between pairs of
11307 iterations. In particular, these dependences include
11308 I<validity> dependences and I<proximity> dependences.
11309 By default, the algorithm used to construct the schedule is similar
11310 to that of C<Pluto>.
11311 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11313 The generated schedule respects all validity dependences.
11314 That is, all dependence distances over these dependences in the
11315 scheduled space are lexicographically positive.
11317 The default algorithm tries to ensure that the dependence distances
11318 over coincidence constraints are zero and to minimize the
11319 dependence distances over proximity dependences.
11320 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11321 for groups of domains where the dependence distances over validity
11322 dependences have only non-negative values.
11323 Note that when minimizing the maximal dependence distance
11324 over proximity dependences, a single affine expression in the parameters
11325 is constructed that bounds all dependence distances. If no such expression
11326 exists, then the algorithm will fail and resort to an alternative
11327 scheduling algorithm. In particular, this means that adding proximity
11328 dependences may eliminate valid solutions. A typical example where this
11329 phenomenon may occur is when some subset of the proximity dependences
11330 has no restriction on some parameter, forcing the coefficient of that
11331 parameter to be zero, while some other subset forces the dependence
11332 distance to depend on that parameter, requiring the same coefficient
11334 When using Feautrier's algorithm, the coincidence and proximity constraints
11335 are only taken into account during the extension to a
11336 full-dimensional schedule.
11338 An C<isl_schedule_constraints> object can be constructed
11339 and manipulated using the following functions.
11341 #include <isl/schedule.h>
11342 __isl_give isl_schedule_constraints *
11343 isl_schedule_constraints_copy(
11344 __isl_keep isl_schedule_constraints *sc);
11345 __isl_give isl_schedule_constraints *
11346 isl_schedule_constraints_on_domain(
11347 __isl_take isl_union_set *domain);
11348 __isl_give isl_schedule_constraints *
11349 isl_schedule_constraints_set_context(
11350 __isl_take isl_schedule_constraints *sc,
11351 __isl_take isl_set *context);
11352 __isl_give isl_schedule_constraints *
11353 isl_schedule_constraints_set_validity(
11354 __isl_take isl_schedule_constraints *sc,
11355 __isl_take isl_union_map *validity);
11356 __isl_give isl_schedule_constraints *
11357 isl_schedule_constraints_set_coincidence(
11358 __isl_take isl_schedule_constraints *sc,
11359 __isl_take isl_union_map *coincidence);
11360 __isl_give isl_schedule_constraints *
11361 isl_schedule_constraints_set_proximity(
11362 __isl_take isl_schedule_constraints *sc,
11363 __isl_take isl_union_map *proximity);
11364 __isl_give isl_schedule_constraints *
11365 isl_schedule_constraints_set_conditional_validity(
11366 __isl_take isl_schedule_constraints *sc,
11367 __isl_take isl_union_map *condition,
11368 __isl_take isl_union_map *validity);
11369 __isl_give isl_schedule_constraints *
11370 isl_schedule_constraints_apply(
11371 __isl_take isl_schedule_constraints *sc,
11372 __isl_take isl_union_map *umap);
11373 __isl_null isl_schedule_constraints *
11374 isl_schedule_constraints_free(
11375 __isl_take isl_schedule_constraints *sc);
11377 The initial C<isl_schedule_constraints> object created by
11378 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11379 That is, it has an empty set of dependences.
11380 The function C<isl_schedule_constraints_set_context> allows the user
11381 to specify additional constraints on the parameters that may
11382 be assumed to hold during the construction of the schedule.
11383 The function C<isl_schedule_constraints_set_validity> replaces the
11384 validity dependences, mapping domain elements I<i> to domain
11385 elements that should be scheduled after I<i>.
11386 The function C<isl_schedule_constraints_set_coincidence> replaces the
11387 coincidence dependences, mapping domain elements I<i> to domain
11388 elements that should be scheduled together with I<I>, if possible.
11389 The function C<isl_schedule_constraints_set_proximity> replaces the
11390 proximity dependences, mapping domain elements I<i> to domain
11391 elements that should be scheduled either before I<I>
11392 or as early as possible after I<i>.
11394 The function C<isl_schedule_constraints_set_conditional_validity>
11395 replaces the conditional validity constraints.
11396 A conditional validity constraint is only imposed when any of the corresponding
11397 conditions is satisfied, i.e., when any of them is non-zero.
11398 That is, the scheduler ensures that within each band if the dependence
11399 distances over the condition constraints are not all zero
11400 then all corresponding conditional validity constraints are respected.
11401 A conditional validity constraint corresponds to a condition
11402 if the two are adjacent, i.e., if the domain of one relation intersect
11403 the range of the other relation.
11404 The typical use case of conditional validity constraints is
11405 to allow order constraints between live ranges to be violated
11406 as long as the live ranges themselves are local to the band.
11407 To allow more fine-grained control over which conditions correspond
11408 to which conditional validity constraints, the domains and ranges
11409 of these relations may include I<tags>. That is, the domains and
11410 ranges of those relation may themselves be wrapped relations
11411 where the iteration domain appears in the domain of those wrapped relations
11412 and the range of the wrapped relations can be arbitrarily chosen
11413 by the user. Conditions and conditional validity constraints are only
11414 considered adjacent to each other if the entire wrapped relation matches.
11415 In particular, a relation with a tag will never be considered adjacent
11416 to a relation without a tag.
11418 The function C<isl_schedule_constraints_apply> takes
11419 schedule constraints that are defined on some set of domain elements
11420 and transforms them to schedule constraints on the elements
11421 to which these domain elements are mapped by the given transformation.
11423 An C<isl_schedule_constraints> object can be inspected
11424 using the following functions.
11426 #include <isl/schedule.h>
11427 __isl_give isl_union_set *
11428 isl_schedule_constraints_get_domain(
11429 __isl_keep isl_schedule_constraints *sc);
11430 __isl_give isl_set *isl_schedule_constraints_get_context(
11431 __isl_keep isl_schedule_constraints *sc);
11432 __isl_give isl_union_map *
11433 isl_schedule_constraints_get_validity(
11434 __isl_keep isl_schedule_constraints *sc);
11435 __isl_give isl_union_map *
11436 isl_schedule_constraints_get_coincidence(
11437 __isl_keep isl_schedule_constraints *sc);
11438 __isl_give isl_union_map *
11439 isl_schedule_constraints_get_proximity(
11440 __isl_keep isl_schedule_constraints *sc);
11441 __isl_give isl_union_map *
11442 isl_schedule_constraints_get_conditional_validity(
11443 __isl_keep isl_schedule_constraints *sc);
11444 __isl_give isl_union_map *
11445 isl_schedule_constraints_get_conditional_validity_condition(
11446 __isl_keep isl_schedule_constraints *sc);
11448 An C<isl_schedule_constraints> object can be read from input
11449 using the following functions.
11451 #include <isl/schedule.h>
11452 __isl_give isl_schedule_constraints *
11453 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11455 __isl_give isl_schedule_constraints *
11456 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11459 The contents of an C<isl_schedule_constraints> object can be printed
11460 using the following functions.
11462 #include <isl/schedule.h>
11463 __isl_give isl_printer *
11464 isl_printer_print_schedule_constraints(
11465 __isl_take isl_printer *p,
11466 __isl_keep isl_schedule_constraints *sc);
11467 __isl_give char *isl_schedule_constraints_to_str(
11468 __isl_keep isl_schedule_constraints *sc);
11470 The following function computes a schedule directly from
11471 an iteration domain and validity and proximity dependences
11472 and is implemented in terms of the functions described above.
11473 The use of C<isl_union_set_compute_schedule> is discouraged.
11475 #include <isl/schedule.h>
11476 __isl_give isl_schedule *isl_union_set_compute_schedule(
11477 __isl_take isl_union_set *domain,
11478 __isl_take isl_union_map *validity,
11479 __isl_take isl_union_map *proximity);
11481 The generated schedule represents a schedule tree.
11482 For more information on schedule trees, see
11483 L</"Schedule Trees">.
11487 #include <isl/schedule.h>
11488 isl_stat isl_options_set_schedule_max_coefficient(
11489 isl_ctx *ctx, int val);
11490 int isl_options_get_schedule_max_coefficient(
11492 isl_stat isl_options_set_schedule_max_constant_term(
11493 isl_ctx *ctx, int val);
11494 int isl_options_get_schedule_max_constant_term(
11496 isl_stat isl_options_set_schedule_serialize_sccs(
11497 isl_ctx *ctx, int val);
11498 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11499 isl_stat isl_options_set_schedule_whole_component(
11500 isl_ctx *ctx, int val);
11501 int isl_options_get_schedule_whole_component(
11503 isl_stat isl_options_set_schedule_maximize_band_depth(
11504 isl_ctx *ctx, int val);
11505 int isl_options_get_schedule_maximize_band_depth(
11507 isl_stat isl_options_set_schedule_maximize_coincidence(
11508 isl_ctx *ctx, int val);
11509 int isl_options_get_schedule_maximize_coincidence(
11511 isl_stat isl_options_set_schedule_outer_coincidence(
11512 isl_ctx *ctx, int val);
11513 int isl_options_get_schedule_outer_coincidence(
11515 isl_stat isl_options_set_schedule_split_scaled(
11516 isl_ctx *ctx, int val);
11517 int isl_options_get_schedule_split_scaled(
11519 isl_stat isl_options_set_schedule_treat_coalescing(
11520 isl_ctx *ctx, int val);
11521 int isl_options_get_schedule_treat_coalescing(
11523 isl_stat isl_options_set_schedule_algorithm(
11524 isl_ctx *ctx, int val);
11525 int isl_options_get_schedule_algorithm(
11527 isl_stat isl_options_set_schedule_carry_self_first(
11528 isl_ctx *ctx, int val);
11529 int isl_options_get_schedule_carry_self_first(
11531 isl_stat isl_options_set_schedule_separate_components(
11532 isl_ctx *ctx, int val);
11533 int isl_options_get_schedule_separate_components(
11538 =item * schedule_max_coefficient
11540 This option enforces that the coefficients for variable and parameter
11541 dimensions in the calculated schedule are not larger than the specified value.
11542 This option can significantly increase the speed of the scheduling calculation
11543 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11544 this option does not introduce bounds on the variable or parameter
11546 This option has no effect on the Feautrier style scheduler.
11548 =item * schedule_max_constant_term
11550 This option enforces that the constant coefficients in the calculated schedule
11551 are not larger than the maximal constant term. This option can significantly
11552 increase the speed of the scheduling calculation and may also prevent fusing of
11553 unrelated dimensions. A value of -1 means that this option does not introduce
11554 bounds on the constant coefficients.
11556 =item * schedule_serialize_sccs
11558 If this option is set, then all strongly connected components
11559 in the dependence graph are serialized as soon as they are detected.
11560 This means in particular that instances of statements will only
11561 appear in the same band node if these statements belong
11562 to the same strongly connected component at the point where
11563 the band node is constructed.
11565 =item * schedule_whole_component
11567 If this option is set, then entire (weakly) connected
11568 components in the dependence graph are scheduled together
11570 Otherwise, each strongly connected component within
11571 such a weakly connected component is first scheduled separately
11572 and then combined with other strongly connected components.
11573 This option has no effect if C<schedule_serialize_sccs> is set.
11575 =item * schedule_maximize_band_depth
11577 If this option is set, then the scheduler tries to maximize
11578 the width of the bands. Wider bands give more possibilities for tiling.
11579 In particular, if the C<schedule_whole_component> option is set,
11580 then bands are split if this might result in wider bands.
11581 Otherwise, the effect of this option is to only allow
11582 strongly connected components to be combined if this does
11583 not reduce the width of the bands.
11584 Note that if the C<schedule_serialize_sccs> options is set, then
11585 the C<schedule_maximize_band_depth> option therefore has no effect.
11587 =item * schedule_maximize_coincidence
11589 This option is only effective if the C<schedule_whole_component>
11590 option is turned off.
11591 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11592 strongly connected components are only combined with each other
11593 if this does not reduce the number of coincident band members.
11595 =item * schedule_outer_coincidence
11597 If this option is set, then we try to construct schedules
11598 where the outermost scheduling dimension in each band
11599 satisfies the coincidence constraints.
11601 =item * schedule_algorithm
11603 Selects the scheduling algorithm to be used.
11604 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11605 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11607 =item * schedule_split_scaled
11609 If this option is set, then we try to construct schedules in which the
11610 constant term is split off from the linear part if the linear parts of
11611 the scheduling rows for all nodes in the graph have a common non-trivial
11613 The constant term is then dropped and the linear
11615 This option is only effective when the Feautrier style scheduler is
11616 being used, either as the main scheduler or as a fallback for the
11617 Pluto-like scheduler.
11619 =item * schedule_treat_coalescing
11621 If this option is set, then the scheduler will try and avoid
11622 producing schedules that perform loop coalescing.
11623 In particular, for the Pluto-like scheduler, this option places
11624 bounds on the schedule coefficients based on the sizes of the instance sets.
11625 For the Feautrier style scheduler, this option detects potentially
11626 coalescing schedules and then tries to adjust the schedule to avoid
11629 =item * schedule_carry_self_first
11631 If this option is set, then the Feautrier style scheduler
11632 (when used as a fallback for the Pluto-like scheduler) will
11633 first try to only carry self-dependences.
11635 =item * schedule_separate_components
11637 If this option is set then the function C<isl_schedule_get_map>
11638 will treat set nodes in the same way as sequence nodes.
11642 =head2 AST Generation
11644 This section describes the C<isl> functionality for generating
11645 ASTs that visit all the elements
11646 in a domain in an order specified by a schedule tree or
11648 In case the schedule given as a C<isl_union_map>, an AST is generated
11649 that visits all the elements in the domain of the C<isl_union_map>
11650 according to the lexicographic order of the corresponding image
11651 element(s). If the range of the C<isl_union_map> consists of
11652 elements in more than one space, then each of these spaces is handled
11653 separately in an arbitrary order.
11654 It should be noted that the schedule tree or the image elements
11655 in a schedule map only specify the I<order>
11656 in which the corresponding domain elements should be visited.
11657 No direct relation between the partial schedule values
11658 or the image elements on the one hand and the loop iterators
11659 in the generated AST on the other hand should be assumed.
11661 Each AST is generated within a build. The initial build
11662 simply specifies the constraints on the parameters (if any)
11663 and can be created, inspected, copied and freed using the following functions.
11665 #include <isl/ast_build.h>
11666 __isl_give isl_ast_build *isl_ast_build_alloc(
11668 __isl_give isl_ast_build *isl_ast_build_from_context(
11669 __isl_take isl_set *set);
11670 __isl_give isl_ast_build *isl_ast_build_copy(
11671 __isl_keep isl_ast_build *build);
11672 __isl_null isl_ast_build *isl_ast_build_free(
11673 __isl_take isl_ast_build *build);
11675 The C<set> argument is usually a parameter set with zero or more parameters.
11676 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11677 this set is required to be a parameter set.
11678 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11679 specify any parameter constraints.
11680 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11681 and L</"Fine-grained Control over AST Generation">.
11682 Finally, the AST itself can be constructed using one of the following
11685 #include <isl/ast_build.h>
11686 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11687 __isl_keep isl_ast_build *build,
11688 __isl_take isl_schedule *schedule);
11689 __isl_give isl_ast_node *
11690 isl_ast_build_node_from_schedule_map(
11691 __isl_keep isl_ast_build *build,
11692 __isl_take isl_union_map *schedule);
11694 =head3 Inspecting the AST
11696 The basic properties of an AST node can be obtained as follows.
11698 #include <isl/ast.h>
11699 enum isl_ast_node_type isl_ast_node_get_type(
11700 __isl_keep isl_ast_node *node);
11702 The type of an AST node is one of
11703 C<isl_ast_node_for>,
11704 C<isl_ast_node_if>,
11705 C<isl_ast_node_block>,
11706 C<isl_ast_node_mark> or
11707 C<isl_ast_node_user>.
11708 An C<isl_ast_node_for> represents a for node.
11709 An C<isl_ast_node_if> represents an if node.
11710 An C<isl_ast_node_block> represents a compound node.
11711 An C<isl_ast_node_mark> introduces a mark in the AST.
11712 An C<isl_ast_node_user> represents an expression statement.
11713 An expression statement typically corresponds to a domain element, i.e.,
11714 one of the elements that is visited by the AST.
11716 Each type of node has its own additional properties.
11718 #include <isl/ast.h>
11719 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11720 __isl_keep isl_ast_node *node);
11721 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11722 __isl_keep isl_ast_node *node);
11723 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11724 __isl_keep isl_ast_node *node);
11725 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11726 __isl_keep isl_ast_node *node);
11727 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11728 __isl_keep isl_ast_node *node);
11729 isl_bool isl_ast_node_for_is_degenerate(
11730 __isl_keep isl_ast_node *node);
11732 An C<isl_ast_for> is considered degenerate if it is known to execute
11735 #include <isl/ast.h>
11736 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11737 __isl_keep isl_ast_node *node);
11738 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11739 __isl_keep isl_ast_node *node);
11740 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11741 __isl_keep isl_ast_node *node);
11742 isl_bool isl_ast_node_if_has_else_node(
11743 __isl_keep isl_ast_node *node);
11744 isl_bool isl_ast_node_if_has_else(
11745 __isl_keep isl_ast_node *node);
11746 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11747 __isl_keep isl_ast_node *node);
11748 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11749 __isl_keep isl_ast_node *node);
11751 C<isl_ast_node_if_get_then>,
11752 C<isl_ast_node_if_has_else> and
11753 C<isl_ast_node_if_get_else>
11754 are alternative names for
11755 C<isl_ast_node_if_get_then_node>,
11756 C<isl_ast_node_if_has_else_node> and
11757 C<isl_ast_node_if_get_else_node>, respectively.
11759 __isl_give isl_ast_node_list *
11760 isl_ast_node_block_get_children(
11761 __isl_keep isl_ast_node *node);
11763 __isl_give isl_id *isl_ast_node_mark_get_id(
11764 __isl_keep isl_ast_node *node);
11765 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11766 __isl_keep isl_ast_node *node);
11768 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11769 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11771 #include <isl/ast.h>
11772 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11773 __isl_keep isl_ast_node *node);
11775 All descendants of a specific node in the AST (including the node itself)
11777 in depth-first pre-order using the following function.
11779 #include <isl/ast.h>
11780 isl_stat isl_ast_node_foreach_descendant_top_down(
11781 __isl_keep isl_ast_node *node,
11782 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11783 void *user), void *user);
11785 The callback function should return C<isl_bool_true> if the children
11786 of the given node should be visited and C<isl_bool_false> if they should not.
11787 It should return C<isl_bool_error> in case of failure, in which case
11788 the entire traversal is aborted.
11790 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11791 the following functions.
11793 #include <isl/ast.h>
11794 enum isl_ast_expr_type isl_ast_expr_get_type(
11795 __isl_keep isl_ast_expr *expr);
11797 The type of an AST expression is one of
11798 C<isl_ast_expr_op>,
11799 C<isl_ast_expr_id> or
11800 C<isl_ast_expr_int>.
11801 An C<isl_ast_expr_op> represents the result of an operation.
11802 An C<isl_ast_expr_id> represents an identifier.
11803 An C<isl_ast_expr_int> represents an integer value.
11805 Each type of expression has its own additional properties.
11807 #include <isl/ast.h>
11808 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11809 __isl_keep isl_ast_expr *expr);
11810 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11811 __isl_keep isl_ast_expr *expr);
11812 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11813 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11814 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11815 __isl_keep isl_ast_expr *expr, int pos);
11816 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11817 __isl_keep isl_ast_expr *expr, int pos);
11818 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11819 __isl_keep isl_ast_expr *expr,
11820 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11821 void *user), void *user);
11822 isl_stat isl_ast_expr_foreach_ast_op_type(
11823 __isl_keep isl_ast_expr *expr,
11824 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11825 void *user), void *user);
11826 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11827 __isl_keep isl_ast_node *node,
11828 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11829 void *user), void *user);
11830 isl_stat isl_ast_node_foreach_ast_op_type(
11831 __isl_keep isl_ast_node *node,
11832 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11833 void *user), void *user);
11835 C<isl_ast_expr_op_get_type> returns the type of the operation
11836 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11837 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11839 C<isl_ast_expr_get_op_type> is an alternative name for
11840 C<isl_ast_expr_op_get_type>.
11842 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11843 C<isl_ast_expr_op_get_n_arg> and
11844 C<isl_ast_expr_get_op_arg> is an alternative name for
11845 C<isl_ast_expr_op_get_arg>.
11847 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11848 C<isl_ast_expr_op_type> that appears in C<expr>.
11849 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11850 C<isl_ast_expr_foreach_ast_expr_op_type>.
11851 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11852 C<isl_ast_expr_op_type> that appears in C<node>.
11853 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11854 C<isl_ast_node_foreach_ast_expr_op_type>.
11855 The operation type is one of the following.
11859 =item C<isl_ast_expr_op_and>
11861 Logical I<and> of two arguments.
11862 Both arguments can be evaluated.
11864 =item C<isl_ast_expr_op_and_then>
11866 Logical I<and> of two arguments.
11867 The second argument can only be evaluated if the first evaluates to true.
11869 =item C<isl_ast_expr_op_or>
11871 Logical I<or> of two arguments.
11872 Both arguments can be evaluated.
11874 =item C<isl_ast_expr_op_or_else>
11876 Logical I<or> of two arguments.
11877 The second argument can only be evaluated if the first evaluates to false.
11879 =item C<isl_ast_expr_op_max>
11881 Maximum of two or more arguments.
11883 =item C<isl_ast_expr_op_min>
11885 Minimum of two or more arguments.
11887 =item C<isl_ast_expr_op_minus>
11891 =item C<isl_ast_expr_op_add>
11893 Sum of two arguments.
11895 =item C<isl_ast_expr_op_sub>
11897 Difference of two arguments.
11899 =item C<isl_ast_expr_op_mul>
11901 Product of two arguments.
11903 =item C<isl_ast_expr_op_div>
11905 Exact division. That is, the result is known to be an integer.
11907 =item C<isl_ast_expr_op_fdiv_q>
11909 Result of integer division, rounded towards negative
11911 The divisor is known to be positive.
11913 =item C<isl_ast_expr_op_pdiv_q>
11915 Result of integer division, where dividend is known to be non-negative.
11916 The divisor is known to be positive.
11918 =item C<isl_ast_expr_op_pdiv_r>
11920 Remainder of integer division, where dividend is known to be non-negative.
11921 The divisor is known to be positive.
11923 =item C<isl_ast_expr_op_zdiv_r>
11925 Equal to zero iff the remainder on integer division is zero.
11926 The divisor is known to be positive.
11928 =item C<isl_ast_expr_op_cond>
11930 Conditional operator defined on three arguments.
11931 If the first argument evaluates to true, then the result
11932 is equal to the second argument. Otherwise, the result
11933 is equal to the third argument.
11934 The second and third argument may only be evaluated if
11935 the first argument evaluates to true and false, respectively.
11936 Corresponds to C<a ? b : c> in C.
11938 =item C<isl_ast_expr_op_select>
11940 Conditional operator defined on three arguments.
11941 If the first argument evaluates to true, then the result
11942 is equal to the second argument. Otherwise, the result
11943 is equal to the third argument.
11944 The second and third argument may be evaluated independently
11945 of the value of the first argument.
11946 Corresponds to C<a * b + (1 - a) * c> in C.
11948 =item C<isl_ast_expr_op_eq>
11952 =item C<isl_ast_expr_op_le>
11954 Less than or equal relation.
11956 =item C<isl_ast_expr_op_lt>
11958 Less than relation.
11960 =item C<isl_ast_expr_op_ge>
11962 Greater than or equal relation.
11964 =item C<isl_ast_expr_op_gt>
11966 Greater than relation.
11968 =item C<isl_ast_expr_op_call>
11971 The number of arguments of the C<isl_ast_expr> is one more than
11972 the number of arguments in the function call, the first argument
11973 representing the function being called.
11975 =item C<isl_ast_expr_op_access>
11978 The number of arguments of the C<isl_ast_expr> is one more than
11979 the number of index expressions in the array access, the first argument
11980 representing the array being accessed.
11982 =item C<isl_ast_expr_op_member>
11985 This operation has two arguments, a structure and the name of
11986 the member of the structure being accessed.
11988 =item C<isl_ast_expr_op_address_of>
11990 The address of its single argument, which is always an array access.
11994 #include <isl/ast.h>
11995 __isl_give isl_id *isl_ast_expr_id_get_id(
11996 __isl_keep isl_ast_expr *expr);
11997 __isl_give isl_id *isl_ast_expr_get_id(
11998 __isl_keep isl_ast_expr *expr);
12000 Return the identifier represented by the AST expression.
12001 C<isl_ast_expr_get_id> is an alternative name for
12002 C<isl_ast_expr_id_get_id>.
12004 #include <isl/ast.h>
12005 __isl_give isl_val *isl_ast_expr_int_get_val(
12006 __isl_keep isl_ast_expr *expr);
12007 __isl_give isl_val *isl_ast_expr_get_val(
12008 __isl_keep isl_ast_expr *expr);
12010 Return the integer represented by the AST expression.
12011 C<isl_ast_expr_get_val> is an alternative name for
12012 C<isl_ast_expr_int_get_val>.
12014 =head3 Properties of ASTs
12016 #include <isl/ast.h>
12017 isl_bool isl_ast_expr_is_equal(
12018 __isl_keep isl_ast_expr *expr1,
12019 __isl_keep isl_ast_expr *expr2);
12021 Check if two C<isl_ast_expr>s are equal to each other.
12023 =head3 Manipulating and printing the AST
12025 AST nodes can be copied and freed using the following functions.
12027 #include <isl/ast.h>
12028 __isl_give isl_ast_node *isl_ast_node_copy(
12029 __isl_keep isl_ast_node *node);
12030 __isl_null isl_ast_node *isl_ast_node_free(
12031 __isl_take isl_ast_node *node);
12033 AST expressions can be copied and freed using the following functions.
12035 #include <isl/ast.h>
12036 __isl_give isl_ast_expr *isl_ast_expr_copy(
12037 __isl_keep isl_ast_expr *expr);
12038 __isl_null isl_ast_expr *isl_ast_expr_free(
12039 __isl_take isl_ast_expr *expr);
12041 New AST expressions can be created either directly or within
12042 the context of an C<isl_ast_build>.
12044 #include <isl/ast.h>
12045 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12046 __isl_take isl_val *v);
12047 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12048 __isl_take isl_id *id);
12049 __isl_give isl_ast_expr *isl_ast_expr_neg(
12050 __isl_take isl_ast_expr *expr);
12051 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12052 __isl_take isl_ast_expr *expr);
12053 __isl_give isl_ast_expr *isl_ast_expr_add(
12054 __isl_take isl_ast_expr *expr1,
12055 __isl_take isl_ast_expr *expr2);
12056 __isl_give isl_ast_expr *isl_ast_expr_sub(
12057 __isl_take isl_ast_expr *expr1,
12058 __isl_take isl_ast_expr *expr2);
12059 __isl_give isl_ast_expr *isl_ast_expr_mul(
12060 __isl_take isl_ast_expr *expr1,
12061 __isl_take isl_ast_expr *expr2);
12062 __isl_give isl_ast_expr *isl_ast_expr_div(
12063 __isl_take isl_ast_expr *expr1,
12064 __isl_take isl_ast_expr *expr2);
12065 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12066 __isl_take isl_ast_expr *expr1,
12067 __isl_take isl_ast_expr *expr2);
12068 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12069 __isl_take isl_ast_expr *expr1,
12070 __isl_take isl_ast_expr *expr2);
12071 __isl_give isl_ast_expr *isl_ast_expr_and(
12072 __isl_take isl_ast_expr *expr1,
12073 __isl_take isl_ast_expr *expr2)
12074 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12075 __isl_take isl_ast_expr *expr1,
12076 __isl_take isl_ast_expr *expr2)
12077 __isl_give isl_ast_expr *isl_ast_expr_or(
12078 __isl_take isl_ast_expr *expr1,
12079 __isl_take isl_ast_expr *expr2)
12080 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12081 __isl_take isl_ast_expr *expr1,
12082 __isl_take isl_ast_expr *expr2)
12083 __isl_give isl_ast_expr *isl_ast_expr_eq(
12084 __isl_take isl_ast_expr *expr1,
12085 __isl_take isl_ast_expr *expr2);
12086 __isl_give isl_ast_expr *isl_ast_expr_le(
12087 __isl_take isl_ast_expr *expr1,
12088 __isl_take isl_ast_expr *expr2);
12089 __isl_give isl_ast_expr *isl_ast_expr_lt(
12090 __isl_take isl_ast_expr *expr1,
12091 __isl_take isl_ast_expr *expr2);
12092 __isl_give isl_ast_expr *isl_ast_expr_ge(
12093 __isl_take isl_ast_expr *expr1,
12094 __isl_take isl_ast_expr *expr2);
12095 __isl_give isl_ast_expr *isl_ast_expr_gt(
12096 __isl_take isl_ast_expr *expr1,
12097 __isl_take isl_ast_expr *expr2);
12098 __isl_give isl_ast_expr *isl_ast_expr_access(
12099 __isl_take isl_ast_expr *array,
12100 __isl_take isl_ast_expr_list *indices);
12101 __isl_give isl_ast_expr *isl_ast_expr_call(
12102 __isl_take isl_ast_expr *function,
12103 __isl_take isl_ast_expr_list *arguments);
12105 The function C<isl_ast_expr_address_of> can be applied to an
12106 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12107 to represent the address of the C<isl_ast_expr_access>.
12108 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12109 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12111 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12112 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12114 #include <isl/ast_build.h>
12115 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12116 __isl_keep isl_ast_build *build,
12117 __isl_take isl_set *set);
12118 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12119 __isl_keep isl_ast_build *build,
12120 __isl_take isl_pw_aff *pa);
12121 __isl_give isl_ast_expr *
12122 isl_ast_build_access_from_pw_multi_aff(
12123 __isl_keep isl_ast_build *build,
12124 __isl_take isl_pw_multi_aff *pma);
12125 __isl_give isl_ast_expr *
12126 isl_ast_build_access_from_multi_pw_aff(
12127 __isl_keep isl_ast_build *build,
12128 __isl_take isl_multi_pw_aff *mpa);
12129 __isl_give isl_ast_expr *
12130 isl_ast_build_call_from_pw_multi_aff(
12131 __isl_keep isl_ast_build *build,
12132 __isl_take isl_pw_multi_aff *pma);
12133 __isl_give isl_ast_expr *
12134 isl_ast_build_call_from_multi_pw_aff(
12135 __isl_keep isl_ast_build *build,
12136 __isl_take isl_multi_pw_aff *mpa);
12139 the domains of C<pa>, C<mpa> and C<pma> should correspond
12140 to the schedule space of C<build>.
12141 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12142 the function being called.
12143 If the accessed space is a nested relation, then it is taken
12144 to represent an access of the member specified by the range
12145 of this nested relation of the structure specified by the domain
12146 of the nested relation.
12148 The following functions can be used to modify an C<isl_ast_expr>.
12150 #include <isl/ast.h>
12151 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12152 __isl_take isl_ast_expr *expr, int pos,
12153 __isl_take isl_ast_expr *arg);
12155 Replace the argument of C<expr> at position C<pos> by C<arg>.
12157 #include <isl/ast.h>
12158 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12159 __isl_take isl_ast_expr *expr,
12160 __isl_take isl_id_to_ast_expr *id2expr);
12162 The function C<isl_ast_expr_substitute_ids> replaces the
12163 subexpressions of C<expr> of type C<isl_ast_expr_id>
12164 by the corresponding expression in C<id2expr>, if there is any.
12167 The following function can be used to modify the descendants
12168 of a specific node in an AST using a depth-first post-order
12169 traversal of those descendants (including the node itself).
12171 #include <isl/ast.h>
12172 __isl_give isl_ast_node *
12173 isl_ast_node_map_descendant_bottom_up(
12174 __isl_take isl_ast_node *node,
12175 __isl_give isl_ast_node *(*fn)(
12176 __isl_take isl_ast_node *node,
12177 void *user), void *user);
12179 User specified data can be attached to an C<isl_ast_node> and obtained
12180 from the same C<isl_ast_node> using the following functions.
12182 #include <isl/ast.h>
12183 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12184 __isl_take isl_ast_node *node,
12185 __isl_take isl_id *annotation);
12186 __isl_give isl_id *isl_ast_node_get_annotation(
12187 __isl_keep isl_ast_node *node);
12189 Basic printing can be performed using the following functions.
12191 #include <isl/ast.h>
12192 __isl_give isl_printer *isl_printer_print_ast_expr(
12193 __isl_take isl_printer *p,
12194 __isl_keep isl_ast_expr *expr);
12195 __isl_give isl_printer *isl_printer_print_ast_node(
12196 __isl_take isl_printer *p,
12197 __isl_keep isl_ast_node *node);
12198 __isl_give char *isl_ast_expr_to_str(
12199 __isl_keep isl_ast_expr *expr);
12200 __isl_give char *isl_ast_node_to_str(
12201 __isl_keep isl_ast_node *node);
12202 __isl_give char *isl_ast_expr_to_C_str(
12203 __isl_keep isl_ast_expr *expr);
12204 __isl_give char *isl_ast_node_to_C_str(
12205 __isl_keep isl_ast_node *node);
12207 The functions C<isl_ast_expr_to_C_str> and
12208 C<isl_ast_node_to_C_str> are convenience functions
12209 that return a string representation of the input in C format.
12211 More advanced printing can be performed using the following functions.
12213 #include <isl/ast.h>
12214 __isl_give isl_printer *
12215 isl_ast_expr_op_type_set_print_name(
12216 __isl_take isl_printer *p,
12217 enum isl_ast_expr_op_type type,
12218 __isl_keep const char *name);
12219 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12220 __isl_take isl_printer *p,
12221 enum isl_ast_expr_op_type type,
12222 __isl_keep const char *name);
12223 isl_stat isl_options_set_ast_print_macro_once(
12224 isl_ctx *ctx, int val);
12225 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12226 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12227 enum isl_ast_expr_op_type type,
12228 __isl_take isl_printer *p);
12229 __isl_give isl_printer *isl_ast_op_type_print_macro(
12230 enum isl_ast_expr_op_type type,
12231 __isl_take isl_printer *p);
12232 __isl_give isl_printer *isl_ast_expr_print_macros(
12233 __isl_keep isl_ast_expr *expr,
12234 __isl_take isl_printer *p);
12235 __isl_give isl_printer *isl_ast_node_print_macros(
12236 __isl_keep isl_ast_node *node,
12237 __isl_take isl_printer *p);
12238 __isl_give isl_printer *isl_ast_node_print(
12239 __isl_keep isl_ast_node *node,
12240 __isl_take isl_printer *p,
12241 __isl_take isl_ast_print_options *options);
12242 __isl_give isl_printer *isl_ast_node_for_print(
12243 __isl_keep isl_ast_node *node,
12244 __isl_take isl_printer *p,
12245 __isl_take isl_ast_print_options *options);
12246 __isl_give isl_printer *isl_ast_node_if_print(
12247 __isl_keep isl_ast_node *node,
12248 __isl_take isl_printer *p,
12249 __isl_take isl_ast_print_options *options);
12251 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12252 C<isl> may print out an AST that makes use of macros such
12253 as C<floord>, C<min> and C<max>.
12254 The names of these macros may be modified by a call
12255 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12256 names are associated to the printer object.
12257 C<isl_ast_op_type_set_print_name> is an alternative name for
12258 C<isl_ast_expr_op_type_set_print_name>.
12259 C<isl_ast_expr_op_type_print_macro> prints out the macro
12260 corresponding to a specific C<isl_ast_expr_op_type>.
12261 If the print-macro-once option is set, then a given macro definition
12262 is only printed once to any given printer object.
12263 C<isl_ast_op_type_print_macro> is an alternative name for
12264 C<isl_ast_expr_op_type_print_macro>.
12265 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12266 for subexpressions where these macros would be used and prints
12267 out the required macro definitions.
12268 Essentially, C<isl_ast_expr_print_macros> calls
12269 C<isl_ast_expr_foreach_ast_expr_op_type> with
12270 C<isl_ast_expr_op_type_print_macro>
12271 as function argument.
12272 C<isl_ast_node_print_macros> does the same
12273 for expressions in its C<isl_ast_node> argument.
12274 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12275 C<isl_ast_node_if_print> print an C<isl_ast_node>
12276 in C<ISL_FORMAT_C>, but allow for some extra control
12277 through an C<isl_ast_print_options> object.
12278 This object can be created using the following functions.
12280 #include <isl/ast.h>
12281 __isl_give isl_ast_print_options *
12282 isl_ast_print_options_alloc(isl_ctx *ctx);
12283 __isl_give isl_ast_print_options *
12284 isl_ast_print_options_copy(
12285 __isl_keep isl_ast_print_options *options);
12286 __isl_null isl_ast_print_options *
12287 isl_ast_print_options_free(
12288 __isl_take isl_ast_print_options *options);
12290 __isl_give isl_ast_print_options *
12291 isl_ast_print_options_set_print_user(
12292 __isl_take isl_ast_print_options *options,
12293 __isl_give isl_printer *(*print_user)(
12294 __isl_take isl_printer *p,
12295 __isl_take isl_ast_print_options *options,
12296 __isl_keep isl_ast_node *node, void *user),
12298 __isl_give isl_ast_print_options *
12299 isl_ast_print_options_set_print_for(
12300 __isl_take isl_ast_print_options *options,
12301 __isl_give isl_printer *(*print_for)(
12302 __isl_take isl_printer *p,
12303 __isl_take isl_ast_print_options *options,
12304 __isl_keep isl_ast_node *node, void *user),
12307 The callback set by C<isl_ast_print_options_set_print_user>
12308 is called whenever a node of type C<isl_ast_node_user> needs to
12310 The callback set by C<isl_ast_print_options_set_print_for>
12311 is called whenever a node of type C<isl_ast_node_for> needs to
12313 Note that C<isl_ast_node_for_print> will I<not> call the
12314 callback set by C<isl_ast_print_options_set_print_for> on the node
12315 on which C<isl_ast_node_for_print> is called, but only on nested
12316 nodes of type C<isl_ast_node_for>. It is therefore safe to
12317 call C<isl_ast_node_for_print> from within the callback set by
12318 C<isl_ast_print_options_set_print_for>.
12320 The following option determines the type to be used for iterators
12321 while printing the AST.
12323 isl_stat isl_options_set_ast_iterator_type(
12324 isl_ctx *ctx, const char *val);
12325 const char *isl_options_get_ast_iterator_type(
12328 The AST printer only prints body nodes of C<if> and C<for> nodes
12330 blocks cannot be safely omitted.
12331 For example, a C<for> node with one body node will not be
12332 surrounded with braces in C<ISL_FORMAT_C>.
12333 A block will always be printed by setting the following option.
12335 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12337 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12339 Explicit block nodes that appear inside the AST are always printed as blocks.
12340 If the block node appears as the outermost node,
12341 then it is only printed if the following option is set.
12343 isl_stat isl_options_set_ast_print_outermost_block(
12344 isl_ctx *ctx, int val);
12345 int isl_options_get_ast_print_outermost_block(
12350 #include <isl/ast_build.h>
12351 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12352 isl_ctx *ctx, int val);
12353 int isl_options_get_ast_build_atomic_upper_bound(
12355 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12357 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12358 isl_stat isl_options_set_ast_build_detect_min_max(
12359 isl_ctx *ctx, int val);
12360 int isl_options_get_ast_build_detect_min_max(
12362 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12363 isl_ctx *ctx, int val);
12364 int isl_options_get_ast_build_exploit_nested_bounds(
12366 isl_stat isl_options_set_ast_build_group_coscheduled(
12367 isl_ctx *ctx, int val);
12368 int isl_options_get_ast_build_group_coscheduled(
12370 isl_stat isl_options_set_ast_build_separation_bounds(
12371 isl_ctx *ctx, int val);
12372 int isl_options_get_ast_build_separation_bounds(
12374 isl_stat isl_options_set_ast_build_scale_strides(
12375 isl_ctx *ctx, int val);
12376 int isl_options_get_ast_build_scale_strides(
12378 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12380 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12381 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12383 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12387 =item * ast_build_atomic_upper_bound
12389 Generate loop upper bounds that consist of the current loop iterator,
12390 an operator and an expression not involving the iterator.
12391 If this option is not set, then the current loop iterator may appear
12392 several times in the upper bound.
12393 For example, when this option is turned off, AST generation
12396 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12400 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12403 When the option is turned on, the following AST is generated
12405 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12408 =item * ast_build_prefer_pdiv
12410 If this option is turned off, then the AST generation will
12411 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12412 operators, but no C<isl_ast_expr_op_pdiv_q> or
12413 C<isl_ast_expr_op_pdiv_r> operators.
12414 If this option is turned on, then C<isl> will try to convert
12415 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12416 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12418 =item * ast_build_detect_min_max
12420 If this option is turned on, then C<isl> will try and detect
12421 min or max-expressions when building AST expressions from
12422 piecewise affine expressions.
12424 =item * ast_build_exploit_nested_bounds
12426 Simplify conditions based on bounds of nested for loops.
12427 In particular, remove conditions that are implied by the fact
12428 that one or more nested loops have at least one iteration,
12429 meaning that the upper bound is at least as large as the lower bound.
12430 For example, when this option is turned off, AST generation
12433 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12439 for (int c0 = 0; c0 <= N; c0 += 1)
12440 for (int c1 = 0; c1 <= M; c1 += 1)
12443 When the option is turned on, the following AST is generated
12445 for (int c0 = 0; c0 <= N; c0 += 1)
12446 for (int c1 = 0; c1 <= M; c1 += 1)
12449 =item * ast_build_group_coscheduled
12451 If two domain elements are assigned the same schedule point, then
12452 they may be executed in any order and they may even appear in different
12453 loops. If this options is set, then the AST generator will make
12454 sure that coscheduled domain elements do not appear in separate parts
12455 of the AST. This is useful in case of nested AST generation
12456 if the outer AST generation is given only part of a schedule
12457 and the inner AST generation should handle the domains that are
12458 coscheduled by this initial part of the schedule together.
12459 For example if an AST is generated for a schedule
12461 { A[i] -> [0]; B[i] -> [0] }
12463 then the C<isl_ast_build_set_create_leaf> callback described
12464 below may get called twice, once for each domain.
12465 Setting this option ensures that the callback is only called once
12466 on both domains together.
12468 =item * ast_build_separation_bounds
12470 This option specifies which bounds to use during separation.
12471 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12472 then all (possibly implicit) bounds on the current dimension will
12473 be used during separation.
12474 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12475 then only those bounds that are explicitly available will
12476 be used during separation.
12478 =item * ast_build_scale_strides
12480 This option specifies whether the AST generator is allowed
12481 to scale down iterators of strided loops.
12483 =item * ast_build_allow_else
12485 This option specifies whether the AST generator is allowed
12486 to construct if statements with else branches.
12488 =item * ast_build_allow_or
12490 This option specifies whether the AST generator is allowed
12491 to construct if conditions with disjunctions.
12495 =head3 AST Generation Options (Schedule Tree)
12497 In case of AST construction from a schedule tree, the options
12498 that control how an AST is created from the individual schedule
12499 dimensions are stored in the band nodes of the tree
12500 (see L</"Schedule Trees">).
12502 In particular, a schedule dimension can be handled in four
12503 different ways, atomic, separate, unroll or the default.
12504 This loop AST generation type can be set using
12505 C<isl_schedule_node_band_member_set_ast_loop_type>.
12507 the first three can be selected by including a one-dimensional
12508 element with as value the position of the schedule dimension
12509 within the band and as name one of C<atomic>, C<separate>
12510 or C<unroll> in the options
12511 set by C<isl_schedule_node_band_set_ast_build_options>.
12512 Only one of these three may be specified for
12513 any given schedule dimension within a band node.
12514 If none of these is specified, then the default
12515 is used. The meaning of the options is as follows.
12521 When this option is specified, the AST generator will make
12522 sure that a given domain space only appears in a single
12523 loop at the specified level.
12525 For example, for the schedule tree
12527 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12529 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12530 options: "{ atomic[x] }"
12532 the following AST will be generated
12534 for (int c0 = 0; c0 <= 10; c0 += 1) {
12541 On the other hand, for the schedule tree
12543 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12545 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12546 options: "{ separate[x] }"
12548 the following AST will be generated
12552 for (int c0 = 1; c0 <= 9; c0 += 1) {
12559 If neither C<atomic> nor C<separate> is specified, then the AST generator
12560 may produce either of these two results or some intermediate form.
12564 When this option is specified, the AST generator will
12565 split the domain of the specified schedule dimension
12566 into pieces with a fixed set of statements for which
12567 instances need to be executed by the iterations in
12568 the schedule domain part. This option tends to avoid
12569 the generation of guards inside the corresponding loops.
12570 See also the C<atomic> option.
12574 When this option is specified, the AST generator will
12575 I<completely> unroll the corresponding schedule dimension.
12576 It is the responsibility of the user to ensure that such
12577 unrolling is possible.
12578 To obtain a partial unrolling, the user should apply an additional
12579 strip-mining to the schedule and fully unroll the inner schedule
12584 The C<isolate> option is a bit more involved. It allows the user
12585 to isolate a range of schedule dimension values from smaller and
12586 greater values. Additionally, the user may specify a different
12587 atomic/separate/unroll choice for the isolated part and the remaining
12588 parts. The typical use case of the C<isolate> option is to isolate
12589 full tiles from partial tiles.
12590 The part that needs to be isolated may depend on outer schedule dimensions.
12591 The option therefore needs to be able to reference those outer schedule
12592 dimensions. In particular, the space of the C<isolate> option is that
12593 of a wrapped map with as domain the flat product of all outer band nodes
12594 and as range the space of the current band node.
12595 The atomic/separate/unroll choice for the isolated part is determined
12596 by an option that lives in an unnamed wrapped space with as domain
12597 a zero-dimensional C<isolate> space and as range the regular
12598 C<atomic>, C<separate> or C<unroll> space.
12599 This option may also be set directly using
12600 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12601 The atomic/separate/unroll choice for the remaining part is determined
12602 by the regular C<atomic>, C<separate> or C<unroll> option.
12603 Since the C<isolate> option references outer schedule dimensions,
12604 its use in a band node causes any tree containing the node
12605 to be considered anchored.
12607 As an example, consider the isolation of full tiles from partial tiles
12608 in a tiling of a triangular domain. The original schedule is as follows.
12610 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12612 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12613 { A[i,j] -> [floor(j/10)] }, \
12614 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
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 * c0 + 9, -10 * c1 + 100); c2 += 1)
12622 for (int c3 = 10 * c1;
12623 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12626 Isolating the full tiles, we have the following input
12628 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12630 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12631 { A[i,j] -> [floor(j/10)] }, \
12632 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12633 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12634 10a+9+10b+9 <= 100 }"
12639 for (int c0 = 0; c0 <= 8; c0 += 1) {
12640 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12641 for (int c2 = 10 * c0;
12642 c2 <= 10 * c0 + 9; c2 += 1)
12643 for (int c3 = 10 * c1;
12644 c3 <= 10 * c1 + 9; c3 += 1)
12646 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12647 for (int c2 = 10 * c0;
12648 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12649 for (int c3 = 10 * c1;
12650 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12653 for (int c0 = 9; c0 <= 10; c0 += 1)
12654 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12655 for (int c2 = 10 * c0;
12656 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12657 for (int c3 = 10 * c1;
12658 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12662 We may then additionally unroll the innermost loop of the isolated part
12664 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12666 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12667 { A[i,j] -> [floor(j/10)] }, \
12668 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12669 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12670 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12675 for (int c0 = 0; c0 <= 8; c0 += 1) {
12676 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12677 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12679 A(c2, 10 * c1 + 1);
12680 A(c2, 10 * c1 + 2);
12681 A(c2, 10 * c1 + 3);
12682 A(c2, 10 * c1 + 4);
12683 A(c2, 10 * c1 + 5);
12684 A(c2, 10 * c1 + 6);
12685 A(c2, 10 * c1 + 7);
12686 A(c2, 10 * c1 + 8);
12687 A(c2, 10 * c1 + 9);
12689 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12690 for (int c2 = 10 * c0;
12691 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12692 for (int c3 = 10 * c1;
12693 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12696 for (int c0 = 9; c0 <= 10; c0 += 1)
12697 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12698 for (int c2 = 10 * c0;
12699 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12700 for (int c3 = 10 * c1;
12701 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12706 =head3 AST Generation Options (Schedule Map)
12708 In case of AST construction using
12709 C<isl_ast_build_node_from_schedule_map>, the options
12710 that control how an AST is created from the individual schedule
12711 dimensions are stored in the C<isl_ast_build>.
12712 They can be set using the following function.
12714 #include <isl/ast_build.h>
12715 __isl_give isl_ast_build *
12716 isl_ast_build_set_options(
12717 __isl_take isl_ast_build *build,
12718 __isl_take isl_union_map *options);
12720 The options are encoded in an C<isl_union_map>.
12721 The domain of this union relation refers to the schedule domain,
12722 i.e., the range of the schedule passed
12723 to C<isl_ast_build_node_from_schedule_map>.
12724 In the case of nested AST generation (see L</"Nested AST Generation">),
12725 the domain of C<options> should refer to the extra piece of the schedule.
12726 That is, it should be equal to the range of the wrapped relation in the
12727 range of the schedule.
12728 The range of the options can consist of elements in one or more spaces,
12729 the names of which determine the effect of the option.
12730 The values of the range typically also refer to the schedule dimension
12731 to which the option applies, with value C<0> representing
12732 the outermost schedule dimension. In case of nested AST generation
12733 (see L</"Nested AST Generation">), these values refer to the position
12734 of the schedule dimension within the innermost AST generation.
12735 The constraints on the domain elements of
12736 the option should only refer to this dimension and earlier dimensions.
12737 We consider the following spaces.
12741 =item C<separation_class>
12743 B<This option has been deprecated. Use the isolate option on
12744 schedule trees instead.>
12746 This space is a wrapped relation between two one dimensional spaces.
12747 The input space represents the schedule dimension to which the option
12748 applies and the output space represents the separation class.
12749 While constructing a loop corresponding to the specified schedule
12750 dimension(s), the AST generator will try to generate separate loops
12751 for domain elements that are assigned different classes.
12752 If only some of the elements are assigned a class, then those elements
12753 that are not assigned any class will be treated as belonging to a class
12754 that is separate from the explicitly assigned classes.
12755 The typical use case for this option is to separate full tiles from
12757 The other options, described below, are applied after the separation
12760 As an example, consider the separation into full and partial tiles
12761 of a tiling of a triangular domain.
12762 Take, for example, the domain
12764 { A[i,j] : 0 <= i,j and i + j <= 100 }
12766 and a tiling into tiles of 10 by 10. The input to the AST generator
12767 is then the schedule
12769 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12772 Without any options, the following AST is generated
12774 for (int c0 = 0; c0 <= 10; c0 += 1)
12775 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12776 for (int c2 = 10 * c0;
12777 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12779 for (int c3 = 10 * c1;
12780 c3 <= min(10 * c1 + 9, -c2 + 100);
12784 Separation into full and partial tiles can be obtained by assigning
12785 a class, say C<0>, to the full tiles. The full tiles are represented by those
12786 values of the first and second schedule dimensions for which there are
12787 values of the third and fourth dimensions to cover an entire tile.
12788 That is, we need to specify the following option
12790 { [a,b,c,d] -> separation_class[[0]->[0]] :
12791 exists b': 0 <= 10a,10b' and
12792 10a+9+10b'+9 <= 100;
12793 [a,b,c,d] -> separation_class[[1]->[0]] :
12794 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12796 which simplifies to
12798 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12799 a >= 0 and b >= 0 and b <= 8 - a;
12800 [a, b, c, d] -> separation_class[[0] -> [0]] :
12801 a >= 0 and a <= 8 }
12803 With this option, the generated AST is as follows
12806 for (int c0 = 0; c0 <= 8; c0 += 1) {
12807 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12808 for (int c2 = 10 * c0;
12809 c2 <= 10 * c0 + 9; c2 += 1)
12810 for (int c3 = 10 * c1;
12811 c3 <= 10 * c1 + 9; c3 += 1)
12813 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12814 for (int c2 = 10 * c0;
12815 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12817 for (int c3 = 10 * c1;
12818 c3 <= min(-c2 + 100, 10 * c1 + 9);
12822 for (int c0 = 9; c0 <= 10; c0 += 1)
12823 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12824 for (int c2 = 10 * c0;
12825 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12827 for (int c3 = 10 * c1;
12828 c3 <= min(10 * c1 + 9, -c2 + 100);
12835 This is a single-dimensional space representing the schedule dimension(s)
12836 to which ``separation'' should be applied. Separation tries to split
12837 a loop into several pieces if this can avoid the generation of guards
12839 See also the C<atomic> option.
12843 This is a single-dimensional space representing the schedule dimension(s)
12844 for which the domains should be considered ``atomic''. That is, the
12845 AST generator will make sure that any given domain space will only appear
12846 in a single loop at the specified level.
12848 Consider the following schedule
12850 { a[i] -> [i] : 0 <= i < 10;
12851 b[i] -> [i+1] : 0 <= i < 10 }
12853 If the following option is specified
12855 { [i] -> separate[x] }
12857 then the following AST will be generated
12861 for (int c0 = 1; c0 <= 9; c0 += 1) {
12868 If, on the other hand, the following option is specified
12870 { [i] -> atomic[x] }
12872 then the following AST will be generated
12874 for (int c0 = 0; c0 <= 10; c0 += 1) {
12881 If neither C<atomic> nor C<separate> is specified, then the AST generator
12882 may produce either of these two results or some intermediate form.
12886 This is a single-dimensional space representing the schedule dimension(s)
12887 that should be I<completely> unrolled.
12888 To obtain a partial unrolling, the user should apply an additional
12889 strip-mining to the schedule and fully unroll the inner loop.
12893 =head3 Fine-grained Control over AST Generation
12895 Besides specifying the constraints on the parameters,
12896 an C<isl_ast_build> object can be used to control
12897 various aspects of the AST generation process.
12898 In case of AST construction using
12899 C<isl_ast_build_node_from_schedule_map>,
12900 the most prominent way of control is through ``options'',
12901 as explained above.
12903 Additional control is available through the following functions.
12905 #include <isl/ast_build.h>
12906 __isl_give isl_ast_build *
12907 isl_ast_build_set_iterators(
12908 __isl_take isl_ast_build *build,
12909 __isl_take isl_id_list *iterators);
12911 The function C<isl_ast_build_set_iterators> allows the user to
12912 specify a list of iterator C<isl_id>s to be used as iterators.
12913 If the input schedule is injective, then
12914 the number of elements in this list should be as large as the dimension
12915 of the schedule space, but no direct correspondence should be assumed
12916 between dimensions and elements.
12917 If the input schedule is not injective, then an additional number
12918 of C<isl_id>s equal to the largest dimension of the input domains
12920 If the number of provided C<isl_id>s is insufficient, then additional
12921 names are automatically generated.
12923 #include <isl/ast_build.h>
12924 __isl_give isl_ast_build *
12925 isl_ast_build_set_create_leaf(
12926 __isl_take isl_ast_build *build,
12927 __isl_give isl_ast_node *(*fn)(
12928 __isl_take isl_ast_build *build,
12929 void *user), void *user);
12932 C<isl_ast_build_set_create_leaf> function allows for the
12933 specification of a callback that should be called whenever the AST
12934 generator arrives at an element of the schedule domain.
12935 The callback should return an AST node that should be inserted
12936 at the corresponding position of the AST. The default action (when
12937 the callback is not set) is to continue generating parts of the AST to scan
12938 all the domain elements associated to the schedule domain element
12939 and to insert user nodes, ``calling'' the domain element, for each of them.
12940 The C<build> argument contains the current state of the C<isl_ast_build>.
12941 To ease nested AST generation (see L</"Nested AST Generation">),
12942 all control information that is
12943 specific to the current AST generation such as the options and
12944 the callbacks has been removed from this C<isl_ast_build>.
12945 The callback would typically return the result of a nested
12946 AST generation or a
12947 user defined node created using the following function.
12949 #include <isl/ast.h>
12950 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12951 __isl_take isl_ast_expr *expr);
12952 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12953 __isl_take isl_ast_expr *expr);
12955 C<isl_ast_node_alloc_user> is an alternative name for
12956 C<isl_ast_node_user_from_expr>.
12958 In some cases, a single user defined node is not enough,
12959 in which case the following function can be used
12960 to create a block node from multiple AST nodes.
12962 #include <isl/ast.h>
12963 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12964 __isl_take isl_ast_node_list *list);
12966 #include <isl/ast_build.h>
12967 __isl_give isl_ast_build *
12968 isl_ast_build_set_at_each_domain(
12969 __isl_take isl_ast_build *build,
12970 __isl_give isl_ast_node *(*fn)(
12971 __isl_take isl_ast_node *node,
12972 __isl_keep isl_ast_build *build,
12973 void *user), void *user);
12974 __isl_give isl_ast_build *
12975 isl_ast_build_set_before_each_for(
12976 __isl_take isl_ast_build *build,
12977 __isl_give isl_id *(*fn)(
12978 __isl_keep isl_ast_build *build,
12979 void *user), void *user);
12980 __isl_give isl_ast_build *
12981 isl_ast_build_set_after_each_for(
12982 __isl_take isl_ast_build *build,
12983 __isl_give isl_ast_node *(*fn)(
12984 __isl_take isl_ast_node *node,
12985 __isl_keep isl_ast_build *build,
12986 void *user), void *user);
12987 __isl_give isl_ast_build *
12988 isl_ast_build_set_before_each_mark(
12989 __isl_take isl_ast_build *build,
12990 isl_stat (*fn)(__isl_keep isl_id *mark,
12991 __isl_keep isl_ast_build *build,
12992 void *user), void *user);
12993 __isl_give isl_ast_build *
12994 isl_ast_build_set_after_each_mark(
12995 __isl_take isl_ast_build *build,
12996 __isl_give isl_ast_node *(*fn)(
12997 __isl_take isl_ast_node *node,
12998 __isl_keep isl_ast_build *build,
12999 void *user), void *user);
13001 The callback set by C<isl_ast_build_set_at_each_domain> will
13002 be called for each domain AST node.
13003 The callbacks set by C<isl_ast_build_set_before_each_for>
13004 and C<isl_ast_build_set_after_each_for> will be called
13005 for each for AST node. The first will be called in depth-first
13006 pre-order, while the second will be called in depth-first post-order.
13007 Since C<isl_ast_build_set_before_each_for> is called before the for
13008 node is actually constructed, it is only passed an C<isl_ast_build>.
13009 The returned C<isl_id> will be added as an annotation (using
13010 C<isl_ast_node_set_annotation>) to the constructed for node.
13011 In particular, if the user has also specified an C<after_each_for>
13012 callback, then the annotation can be retrieved from the node passed to
13013 that callback using C<isl_ast_node_get_annotation>.
13014 The callbacks set by C<isl_ast_build_set_before_each_mark>
13015 and C<isl_ast_build_set_after_each_mark> will be called for each
13016 mark AST node that is created, i.e., for each mark schedule node
13017 in the input schedule tree. The first will be called in depth-first
13018 pre-order, while the second will be called in depth-first post-order.
13019 Since the callback set by C<isl_ast_build_set_before_each_mark>
13020 is called before the mark AST node is actually constructed, it is passed
13021 the identifier of the mark node.
13022 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
13023 The given C<isl_ast_build> can be used to create new
13024 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
13025 or C<isl_ast_build_call_from_pw_multi_aff>.
13027 =head3 Nested AST Generation
13029 C<isl> allows the user to create an AST within the context
13030 of another AST. These nested ASTs are created using the
13031 same C<isl_ast_build_node_from_schedule_map> function that is used to create
13032 the outer AST. The C<build> argument should be an C<isl_ast_build>
13033 passed to a callback set by
13034 C<isl_ast_build_set_create_leaf>.
13035 The space of the range of the C<schedule> argument should refer
13036 to this build. In particular, the space should be a wrapped
13037 relation and the domain of this wrapped relation should be the
13038 same as that of the range of the schedule returned by
13039 C<isl_ast_build_get_schedule> below.
13040 In practice, the new schedule is typically
13041 created by calling C<isl_union_map_range_product> on the old schedule
13042 and some extra piece of the schedule.
13043 The space of the schedule domain is also available from
13044 the C<isl_ast_build>.
13046 #include <isl/ast_build.h>
13047 __isl_give isl_union_map *isl_ast_build_get_schedule(
13048 __isl_keep isl_ast_build *build);
13049 __isl_give isl_space *isl_ast_build_get_schedule_space(
13050 __isl_keep isl_ast_build *build);
13051 __isl_give isl_ast_build *isl_ast_build_restrict(
13052 __isl_take isl_ast_build *build,
13053 __isl_take isl_set *set);
13055 The C<isl_ast_build_get_schedule> function returns a (partial)
13056 schedule for the domains elements for which part of the AST still needs to
13057 be generated in the current build.
13058 In particular, the domain elements are mapped to those iterations of the loops
13059 enclosing the current point of the AST generation inside which
13060 the domain elements are executed.
13061 No direct correspondence between
13062 the input schedule and this schedule should be assumed.
13063 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13064 to create a set for C<isl_ast_build_restrict> to intersect
13065 with the current build. In particular, the set passed to
13066 C<isl_ast_build_restrict> can have additional parameters.
13067 The ids of the set dimensions in the space returned by
13068 C<isl_ast_build_get_schedule_space> correspond to the
13069 iterators of the already generated loops.
13070 The user should not rely on the ids of the output dimensions
13071 of the relations in the union relation returned by
13072 C<isl_ast_build_get_schedule> having any particular value.
13074 =head1 Applications
13076 Although C<isl> is mainly meant to be used as a library,
13077 it also contains some basic applications that use some
13078 of the functionality of C<isl>.
13079 For applications that take one or more polytopes or polyhedra
13080 as input, this input may be specified in either the L<isl format>
13081 or the L<PolyLib format>.
13083 =head2 C<isl_polyhedron_sample>
13085 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13086 an integer element of the polyhedron, if there is any.
13087 The first column in the output is the denominator and is always
13088 equal to 1. If the polyhedron contains no integer points,
13089 then a vector of length zero is printed.
13093 C<isl_pip> takes the same input as the C<example> program
13094 from the C<piplib> distribution, i.e., a set of constraints
13095 on the parameters, a line containing only -1 and finally a set
13096 of constraints on a parametric polyhedron.
13097 The coefficients of the parameters appear in the last columns
13098 (but before the final constant column).
13099 The output is the lexicographic minimum of the parametric polyhedron.
13100 As C<isl> currently does not have its own output format, the output
13101 is just a dump of the internal state.
13103 =head2 C<isl_polyhedron_minimize>
13105 C<isl_polyhedron_minimize> computes the minimum of some linear
13106 or affine objective function over the integer points in a polyhedron.
13107 If an affine objective function
13108 is given, then the constant should appear in the last column.
13110 =head2 C<isl_polytope_scan>
13112 Given a polytope, C<isl_polytope_scan> prints
13113 all integer points in the polytope.
13117 Given an C<isl_union_access_info> object as input,
13118 C<isl_flow> prints out the corresponding dependences,
13119 as computed by C<isl_union_access_info_compute_flow>.
13121 =head2 C<isl_codegen>
13123 Given either a schedule tree or a sequence consisting of
13124 a schedule map, a context set and an options relation,
13125 C<isl_codegen> prints out an AST that scans the domain elements
13126 of the schedule in the order of their image(s) taking into account
13127 the constraints in the context set.
13129 =head2 C<isl_schedule>
13131 Given an C<isl_schedule_constraints> object as input,
13132 C<isl_schedule> prints out a schedule that satisfies the given