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>.
713 isl_stat isl_stat_non_null(void *obj);
715 See L</"Error Handling"> for more information on
716 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
720 An C<isl_val> represents an integer value, a rational value
721 or one of three special values, infinity, negative infinity and NaN.
722 Some predefined values can be created using the following functions.
725 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
726 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
727 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
728 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
729 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
730 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
732 Specific integer values can be created using the following functions.
735 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
737 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
739 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
740 size_t n, size_t size, const void *chunks);
742 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
743 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
744 The least significant digit is assumed to be stored first.
746 Value objects can be copied and freed using the following functions.
749 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
750 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
752 They can be inspected using the following functions.
755 long isl_val_get_num_si(__isl_keep isl_val *v);
756 long isl_val_get_den_si(__isl_keep isl_val *v);
757 __isl_give isl_val *isl_val_get_den_val(
758 __isl_keep isl_val *v);
759 double isl_val_get_d(__isl_keep isl_val *v);
760 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
762 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
763 size_t size, void *chunks);
765 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
766 of C<size> bytes needed to store the absolute value of the
768 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
769 which is assumed to have been preallocated by the caller.
770 The least significant digit is stored first.
771 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
772 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
773 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
775 An C<isl_val> can be modified using the following function.
778 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
781 The following unary properties are defined on C<isl_val>s.
784 int isl_val_sgn(__isl_keep isl_val *v);
785 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
786 isl_bool isl_val_is_one(__isl_keep isl_val *v);
787 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
788 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
789 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
790 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
791 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
792 isl_bool isl_val_is_int(__isl_keep isl_val *v);
793 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
794 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
795 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
796 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
798 Note that the sign of NaN is undefined.
800 The following binary properties are defined on pairs of C<isl_val>s.
803 isl_bool isl_val_lt(__isl_keep isl_val *v1,
804 __isl_keep isl_val *v2);
805 isl_bool isl_val_le(__isl_keep isl_val *v1,
806 __isl_keep isl_val *v2);
807 isl_bool isl_val_gt(__isl_keep isl_val *v1,
808 __isl_keep isl_val *v2);
809 isl_bool isl_val_ge(__isl_keep isl_val *v1,
810 __isl_keep isl_val *v2);
811 isl_bool isl_val_eq(__isl_keep isl_val *v1,
812 __isl_keep isl_val *v2);
813 isl_bool isl_val_ne(__isl_keep isl_val *v1,
814 __isl_keep isl_val *v2);
815 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
816 __isl_keep isl_val *v2);
818 Comparisons to NaN always return false.
819 That is, a NaN is not considered to hold any relative position
820 with respect to any value. In particular, a NaN
821 is neither considered to be equal to nor to be different from
822 any value (including another NaN).
823 The function C<isl_val_abs_eq> checks whether its two arguments
824 are equal in absolute value.
826 For integer C<isl_val>s we additionally have the following binary property.
829 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
830 __isl_keep isl_val *v2);
832 An C<isl_val> can also be compared to an integer using the following
833 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
836 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
837 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
838 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
840 The following unary operations are available on C<isl_val>s.
843 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
844 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
845 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
846 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
847 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
848 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
850 The following binary operations are available on C<isl_val>s.
853 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
854 __isl_take isl_val *v2);
855 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
856 __isl_take isl_val *v2);
857 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
858 __isl_take isl_val *v2);
859 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
861 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
862 __isl_take isl_val *v2);
863 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
865 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
866 __isl_take isl_val *v2);
867 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
869 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
870 __isl_take isl_val *v2);
871 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
874 On integer values, we additionally have the following operations.
877 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
878 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
879 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
880 __isl_take isl_val *v2);
881 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
882 __isl_take isl_val *v2);
883 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
884 __isl_take isl_val *v2, __isl_give isl_val **x,
885 __isl_give isl_val **y);
887 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
888 The function C<isl_val_gcdext> returns the greatest common divisor g
889 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
890 that C<*x> * C<v1> + C<*y> * C<v2> = g.
892 =head3 GMP specific functions
894 These functions are only available if C<isl> has been compiled with C<GMP>
897 Specific integer and rational values can be created from C<GMP> values using
898 the following functions.
900 #include <isl/val_gmp.h>
901 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
903 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
904 const mpz_t n, const mpz_t d);
906 The numerator and denominator of a rational value can be extracted as
907 C<GMP> values using the following functions.
909 #include <isl/val_gmp.h>
910 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
911 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
913 =head2 Sets and Relations
915 C<isl> uses six types of objects for representing sets and relations,
916 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
917 C<isl_union_set> and C<isl_union_map>.
918 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
919 can be described as a conjunction of affine constraints, while
920 C<isl_set> and C<isl_map> represent unions of
921 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
922 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
923 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
924 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
925 where spaces are considered different if they have a different number
926 of dimensions and/or different names (see L<"Spaces">).
927 The difference between sets and relations (maps) is that sets have
928 one set of variables, while relations have two sets of variables,
929 input variables and output variables.
931 =head2 Error Handling
933 C<isl> supports different ways to react in case a runtime error is triggered.
934 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
935 with two maps that have incompatible spaces. There are three possible ways
936 to react on error: to warn, to continue or to abort.
938 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
939 the last error in the corresponding C<isl_ctx> and the function in which the
940 error was triggered returns a value indicating that some error has
941 occurred. In case of functions returning a pointer, this value is
942 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
943 C<isl_stat>, this value is C<isl_size_error>,
944 C<isl_bool_error> or C<isl_stat_error>.
945 An error does not corrupt internal state,
946 such that isl can continue to be used. C<isl> also provides functions to
947 read the last error, including the specific error message,
948 the isl source file where the error occurred and the line number,
949 and to reset all information about the last error. The
950 last error is only stored for information purposes. Its presence does not
951 change the behavior of C<isl>. Hence, resetting an error is not required to
952 continue to use isl, but only to observe new errors.
955 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
956 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
957 const char *isl_ctx_last_error_file(isl_ctx *ctx);
958 int isl_ctx_last_error_line(isl_ctx *ctx);
959 void isl_ctx_reset_error(isl_ctx *ctx);
961 If no error has occurred since the last call to C<isl_ctx_reset_error>,
962 then the functions C<isl_ctx_last_error_msg> and
963 C<isl_ctx_last_error_file> return C<NULL>.
965 Another option is to continue on error. This is similar to warn on error mode,
966 except that C<isl> does not print any warning. This allows a program to
967 implement its own error reporting.
969 The last option is to directly abort the execution of the program from within
970 the isl library. This makes it obviously impossible to recover from an error,
971 but it allows to directly spot the error location. By aborting on error,
972 debuggers break at the location the error occurred and can provide a stack
973 trace. Other tools that automatically provide stack traces on abort or that do
974 not want to continue execution after an error was triggered may also prefer to
977 The on error behavior of isl can be specified by calling
978 C<isl_options_set_on_error> or by setting the command line option
979 C<--isl-on-error>. Valid arguments for the function call are
980 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
981 choices for the command line option are C<warn>, C<continue> and C<abort>.
982 It is also possible to query the current error mode.
984 #include <isl/options.h>
985 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
986 int isl_options_get_on_error(isl_ctx *ctx);
990 Identifiers are used to identify both individual dimensions
991 and tuples of dimensions. They consist of an optional name and an optional
992 user pointer. The name and the user pointer cannot both be C<NULL>, however.
993 Identifiers with the same name but different pointer values
994 are considered to be distinct.
995 Similarly, identifiers with different names but the same pointer value
996 are also considered to be distinct.
997 Equal identifiers are represented using the same object.
998 Pairs of identifiers can therefore be tested for equality using the
1000 Identifiers can be constructed, copied, freed, inspected and printed
1001 using the following functions.
1004 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
1005 __isl_keep const char *name, void *user);
1006 __isl_give isl_id *isl_id_set_free_user(
1007 __isl_take isl_id *id,
1008 void (*free_user)(void *user));
1009 void (*isl_id_get_free_user(__isl_keep isl_id *id))
1011 __isl_give isl_id *isl_id_copy(isl_id *id);
1012 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
1014 void *isl_id_get_user(__isl_keep isl_id *id);
1015 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
1017 __isl_give isl_printer *isl_printer_print_id(
1018 __isl_take isl_printer *p, __isl_keep isl_id *id);
1020 The callback set by C<isl_id_set_free_user> is called on the user
1021 pointer when the last reference to the C<isl_id> is freed.
1022 This callback can be retrieved using C<isl_id_get_free_user>.
1023 Note that C<isl_id_get_name> returns a pointer to some internal
1024 data structure, so the result can only be used while the
1025 corresponding C<isl_id> is alive.
1029 Whenever a new set, relation or similar object is created from scratch,
1030 the space in which it lives needs to be specified using an C<isl_space>.
1031 Each space involves zero or more parameters and zero, one or two
1032 tuples of set or input/output dimensions. The parameters and dimensions
1033 are identified by an C<isl_dim_type> and a position.
1034 The type C<isl_dim_param> refers to parameters,
1035 the type C<isl_dim_set> refers to set dimensions (for spaces
1036 with a single tuple of dimensions) and the types C<isl_dim_in>
1037 and C<isl_dim_out> refer to input and output dimensions
1038 (for spaces with two tuples of dimensions).
1039 Local spaces (see L</"Local Spaces">) also contain dimensions
1040 of type C<isl_dim_div>.
1041 Note that parameters are only identified by their position within
1042 a given object. Across different objects, parameters are (usually)
1043 identified by their names or identifiers. Only unnamed parameters
1044 are identified by their positions across objects. The use of unnamed
1045 parameters is discouraged.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1049 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1050 unsigned nparam, unsigned n_in, unsigned n_out);
1051 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1053 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1054 unsigned nparam, unsigned dim);
1055 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1056 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1058 The space used for creating a parameter domain
1059 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1060 For other sets, the space
1061 needs to be created using C<isl_space_set_alloc>, while
1062 for a relation, the space
1063 needs to be created using C<isl_space_alloc>.
1064 The use of C<isl_space_params_alloc>,
1065 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1066 for the introduction of unnamed parameters.
1068 To check whether a given space is that of a set or a map
1069 or whether it is a parameter space, use these functions:
1071 #include <isl/space.h>
1072 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1073 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1074 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1076 Spaces can be compared using the following functions:
1078 #include <isl/space.h>
1079 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1080 __isl_keep isl_space *space2);
1081 isl_bool isl_space_has_equal_params(
1082 __isl_keep isl_space *space1,
1083 __isl_keep isl_space *space2);
1084 isl_bool isl_space_has_equal_tuples(
1085 __isl_keep isl_space *space1,
1086 __isl_keep isl_space *space2);
1087 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1088 __isl_keep isl_space *space2);
1089 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1090 __isl_keep isl_space *space2);
1091 isl_bool isl_space_tuple_is_equal(
1092 __isl_keep isl_space *space1,
1093 enum isl_dim_type type1,
1094 __isl_keep isl_space *space2,
1095 enum isl_dim_type type2);
1097 C<isl_space_is_domain> checks whether the first argument is equal
1098 to the domain of the second argument. This requires in particular that
1099 the first argument is a set space and that the second argument
1100 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1101 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1102 spaces are the same. That is, it checks if they have the same
1103 identifier (if any), the same dimension and the same internal structure
1106 C<isl_space_has_equal_params> checks whether two spaces
1107 have the same parameters in the same order.
1108 C<isl_space_has_equal_tuples> check whether two spaces have
1109 the same tuples. In contrast to C<isl_space_is_equal> below,
1110 it does not check the
1111 parameters. This is useful because many C<isl> functions align the
1112 parameters before they perform their operations, such that equivalence
1114 C<isl_space_is_equal> checks whether two spaces are identical,
1115 meaning that they have the same parameters and the same tuples.
1116 That is, it checks whether both C<isl_space_has_equal_params> and
1117 C<isl_space_has_equal_tuples> hold.
1119 It is often useful to create objects that live in the
1120 same space as some other object. This can be accomplished
1121 by creating the new objects
1122 (see L</"Creating New Sets and Relations"> or
1123 L</"Functions">) based on the space
1124 of the original object.
1126 #include <isl/set.h>
1127 __isl_give isl_space *isl_basic_set_get_space(
1128 __isl_keep isl_basic_set *bset);
1129 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1131 #include <isl/union_set.h>
1132 __isl_give isl_space *isl_union_set_get_space(
1133 __isl_keep isl_union_set *uset);
1135 #include <isl/map.h>
1136 __isl_give isl_space *isl_basic_map_get_space(
1137 __isl_keep isl_basic_map *bmap);
1138 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1140 #include <isl/union_map.h>
1141 __isl_give isl_space *isl_union_map_get_space(
1142 __isl_keep isl_union_map *umap);
1144 #include <isl/constraint.h>
1145 __isl_give isl_space *isl_constraint_get_space(
1146 __isl_keep isl_constraint *constraint);
1148 #include <isl/polynomial.h>
1149 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1150 __isl_keep isl_qpolynomial *qp);
1151 __isl_give isl_space *isl_qpolynomial_get_space(
1152 __isl_keep isl_qpolynomial *qp);
1153 __isl_give isl_space *
1154 isl_qpolynomial_fold_get_domain_space(
1155 __isl_keep isl_qpolynomial_fold *fold);
1156 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1157 __isl_keep isl_qpolynomial_fold *fold);
1158 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1159 __isl_keep isl_pw_qpolynomial *pwqp);
1160 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1161 __isl_keep isl_pw_qpolynomial *pwqp);
1162 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1163 __isl_keep isl_pw_qpolynomial_fold *pwf);
1164 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1165 __isl_keep isl_pw_qpolynomial_fold *pwf);
1166 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1167 __isl_keep isl_union_pw_qpolynomial *upwqp);
1168 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1169 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1172 __isl_give isl_space *isl_multi_id_get_space(
1173 __isl_keep isl_multi_id *mi);
1175 #include <isl/val.h>
1176 __isl_give isl_space *isl_multi_val_get_space(
1177 __isl_keep isl_multi_val *mv);
1179 #include <isl/aff.h>
1180 __isl_give isl_space *isl_aff_get_domain_space(
1181 __isl_keep isl_aff *aff);
1182 __isl_give isl_space *isl_aff_get_space(
1183 __isl_keep isl_aff *aff);
1184 __isl_give isl_space *isl_pw_aff_get_domain_space(
1185 __isl_keep isl_pw_aff *pwaff);
1186 __isl_give isl_space *isl_pw_aff_get_space(
1187 __isl_keep isl_pw_aff *pwaff);
1188 __isl_give isl_space *isl_multi_aff_get_domain_space(
1189 __isl_keep isl_multi_aff *maff);
1190 __isl_give isl_space *isl_multi_aff_get_space(
1191 __isl_keep isl_multi_aff *maff);
1192 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1193 __isl_keep isl_pw_multi_aff *pma);
1194 __isl_give isl_space *isl_pw_multi_aff_get_space(
1195 __isl_keep isl_pw_multi_aff *pma);
1196 __isl_give isl_space *isl_union_pw_aff_get_space(
1197 __isl_keep isl_union_pw_aff *upa);
1198 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1199 __isl_keep isl_union_pw_multi_aff *upma);
1200 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1201 __isl_keep isl_multi_pw_aff *mpa);
1202 __isl_give isl_space *isl_multi_pw_aff_get_space(
1203 __isl_keep isl_multi_pw_aff *mpa);
1204 __isl_give isl_space *
1205 isl_multi_union_pw_aff_get_domain_space(
1206 __isl_keep isl_multi_union_pw_aff *mupa);
1207 __isl_give isl_space *
1208 isl_multi_union_pw_aff_get_space(
1209 __isl_keep isl_multi_union_pw_aff *mupa);
1211 #include <isl/point.h>
1212 __isl_give isl_space *isl_point_get_space(
1213 __isl_keep isl_point *pnt);
1215 #include <isl/fixed_box.h>
1216 __isl_give isl_space *isl_fixed_box_get_space(
1217 __isl_keep isl_fixed_box *box);
1219 The number of dimensions of a given type of space
1220 may be read off from a space or an object that lives
1221 in a space using the following functions.
1222 In case of C<isl_space_dim>, type may be
1223 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1224 C<isl_dim_out> (only for relations), C<isl_dim_set>
1225 (only for sets) or C<isl_dim_all>.
1227 #include <isl/space.h>
1228 isl_size isl_space_dim(__isl_keep isl_space *space,
1229 enum isl_dim_type type);
1231 #include <isl/local_space.h>
1232 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1233 enum isl_dim_type type);
1235 #include <isl/set.h>
1236 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1237 enum isl_dim_type type);
1238 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1239 isl_size isl_set_dim(__isl_keep isl_set *set,
1240 enum isl_dim_type type);
1242 #include <isl/union_set.h>
1243 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1244 enum isl_dim_type type);
1246 #include <isl/map.h>
1247 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type);
1249 isl_size isl_map_domain_tuple_dim(
1250 __isl_keep isl_map *map);
1251 isl_size isl_map_range_tuple_dim(
1252 __isl_keep isl_map *map);
1253 isl_size isl_map_dim(__isl_keep isl_map *map,
1254 enum isl_dim_type type);
1256 #include <isl/union_map.h>
1257 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1258 enum isl_dim_type type);
1260 #include <isl/val.h>
1261 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1262 enum isl_dim_type type);
1264 #include <isl/aff.h>
1265 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1266 enum isl_dim_type type);
1267 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1268 enum isl_dim_type type);
1269 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1270 enum isl_dim_type type);
1271 isl_size isl_pw_multi_aff_dim(
1272 __isl_keep isl_pw_multi_aff *pma,
1273 enum isl_dim_type type);
1274 isl_size isl_multi_pw_aff_dim(
1275 __isl_keep isl_multi_pw_aff *mpa,
1276 enum isl_dim_type type);
1277 isl_size isl_union_pw_aff_dim(
1278 __isl_keep isl_union_pw_aff *upa,
1279 enum isl_dim_type type);
1280 isl_size isl_union_pw_multi_aff_dim(
1281 __isl_keep isl_union_pw_multi_aff *upma,
1282 enum isl_dim_type type);
1283 isl_size isl_multi_union_pw_aff_dim(
1284 __isl_keep isl_multi_union_pw_aff *mupa,
1285 enum isl_dim_type type);
1287 #include <isl/polynomial.h>
1288 isl_size isl_union_pw_qpolynomial_dim(
1289 __isl_keep isl_union_pw_qpolynomial *upwqp,
1290 enum isl_dim_type type);
1291 isl_size isl_union_pw_qpolynomial_fold_dim(
1292 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1293 enum isl_dim_type type);
1295 Note that an C<isl_union_set>, an C<isl_union_map>,
1296 an C<isl_union_pw_multi_aff>,
1297 an C<isl_union_pw_qpolynomial> and
1298 an C<isl_union_pw_qpolynomial_fold>
1299 only have parameters.
1301 Additional parameters can be added to a space using the following function.
1303 #include <isl/space.h>
1304 __isl_give isl_space *isl_space_add_param_id(
1305 __isl_take isl_space *space,
1306 __isl_take isl_id *id);
1308 If a parameter with the given identifier already appears in the space,
1309 then it is not added again.
1311 Conversely, all parameters can be removed from a space
1312 using the following function.
1314 #include <isl/space.h>
1315 __isl_give isl_space *isl_space_drop_all_params(
1316 __isl_take isl_space *space);
1318 The identifiers or names of the individual dimensions of spaces
1319 may be set or read off using the following functions on spaces
1320 or objects that live in spaces.
1321 These functions are mostly useful to obtain the identifiers, positions
1322 or names of the parameters. Identifiers of individual dimensions are
1323 essentially only useful for printing. They are ignored by all other
1324 operations and may not be preserved across those operations.
1325 To keep track of a space along with names/identifiers of
1326 the set dimensions, use an C<isl_multi_id> as described in
1329 #include <isl/space.h>
1330 __isl_give isl_space *isl_space_set_dim_id(
1331 __isl_take isl_space *space,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1335 enum isl_dim_type type, unsigned pos);
1336 __isl_give isl_id *isl_space_get_dim_id(
1337 __isl_keep isl_space *space,
1338 enum isl_dim_type type, unsigned pos);
1339 __isl_give isl_space *isl_space_set_dim_name(
1340 __isl_take isl_space *space,
1341 enum isl_dim_type type, unsigned pos,
1342 __isl_keep const char *name);
1343 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1344 enum isl_dim_type type, unsigned pos);
1345 __isl_keep const char *isl_space_get_dim_name(
1346 __isl_keep isl_space *space,
1347 enum isl_dim_type type, unsigned pos);
1349 #include <isl/local_space.h>
1350 __isl_give isl_local_space *isl_local_space_set_dim_id(
1351 __isl_take isl_local_space *ls,
1352 enum isl_dim_type type, unsigned pos,
1353 __isl_take isl_id *id);
1354 isl_bool isl_local_space_has_dim_id(
1355 __isl_keep isl_local_space *ls,
1356 enum isl_dim_type type, unsigned pos);
1357 __isl_give isl_id *isl_local_space_get_dim_id(
1358 __isl_keep isl_local_space *ls,
1359 enum isl_dim_type type, unsigned pos);
1360 __isl_give isl_local_space *isl_local_space_set_dim_name(
1361 __isl_take isl_local_space *ls,
1362 enum isl_dim_type type, unsigned pos, const char *s);
1363 isl_bool isl_local_space_has_dim_name(
1364 __isl_keep isl_local_space *ls,
1365 enum isl_dim_type type, unsigned pos)
1366 const char *isl_local_space_get_dim_name(
1367 __isl_keep isl_local_space *ls,
1368 enum isl_dim_type type, unsigned pos);
1370 #include <isl/constraint.h>
1371 const char *isl_constraint_get_dim_name(
1372 __isl_keep isl_constraint *constraint,
1373 enum isl_dim_type type, unsigned pos);
1375 #include <isl/set.h>
1376 __isl_give isl_id *isl_basic_set_get_dim_id(
1377 __isl_keep isl_basic_set *bset,
1378 enum isl_dim_type type, unsigned pos);
1379 __isl_give isl_set *isl_set_set_dim_id(
1380 __isl_take isl_set *set, enum isl_dim_type type,
1381 unsigned pos, __isl_take isl_id *id);
1382 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_id *isl_set_get_dim_id(
1385 __isl_keep isl_set *set, enum isl_dim_type type,
1387 const char *isl_basic_set_get_dim_name(
1388 __isl_keep isl_basic_set *bset,
1389 enum isl_dim_type type, unsigned pos);
1390 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1391 enum isl_dim_type type, unsigned pos);
1392 const char *isl_set_get_dim_name(
1393 __isl_keep isl_set *set,
1394 enum isl_dim_type type, unsigned pos);
1396 #include <isl/map.h>
1397 __isl_give isl_map *isl_map_set_dim_id(
1398 __isl_take isl_map *map, enum isl_dim_type type,
1399 unsigned pos, __isl_take isl_id *id);
1400 isl_bool isl_basic_map_has_dim_id(
1401 __isl_keep isl_basic_map *bmap,
1402 enum isl_dim_type type, unsigned pos);
1403 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1404 enum isl_dim_type type, unsigned pos);
1405 __isl_give isl_id *isl_map_get_dim_id(
1406 __isl_keep isl_map *map, enum isl_dim_type type,
1408 __isl_give isl_id *isl_union_map_get_dim_id(
1409 __isl_keep isl_union_map *umap,
1410 enum isl_dim_type type, unsigned pos);
1411 const char *isl_basic_map_get_dim_name(
1412 __isl_keep isl_basic_map *bmap,
1413 enum isl_dim_type type, unsigned pos);
1414 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1415 enum isl_dim_type type, unsigned pos);
1416 const char *isl_map_get_dim_name(
1417 __isl_keep isl_map *map,
1418 enum isl_dim_type type, unsigned pos);
1420 #include <isl/val.h>
1421 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1422 __isl_take isl_multi_val *mv,
1423 enum isl_dim_type type, unsigned pos,
1424 __isl_take isl_id *id);
1425 __isl_give isl_id *isl_multi_val_get_dim_id(
1426 __isl_keep isl_multi_val *mv,
1427 enum isl_dim_type type, unsigned pos);
1428 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1429 __isl_take isl_multi_val *mv,
1430 enum isl_dim_type type, unsigned pos, const char *s);
1432 #include <isl/aff.h>
1433 __isl_give isl_aff *isl_aff_set_dim_id(
1434 __isl_take isl_aff *aff, enum isl_dim_type type,
1435 unsigned pos, __isl_take isl_id *id);
1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1437 __isl_take isl_multi_aff *maff,
1438 enum isl_dim_type type, unsigned pos,
1439 __isl_take isl_id *id);
1440 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1441 __isl_take isl_pw_aff *pma,
1442 enum isl_dim_type type, unsigned pos,
1443 __isl_take isl_id *id);
1444 __isl_give isl_multi_pw_aff *
1445 isl_multi_pw_aff_set_dim_id(
1446 __isl_take isl_multi_pw_aff *mpa,
1447 enum isl_dim_type type, unsigned pos,
1448 __isl_take isl_id *id);
1449 __isl_give isl_multi_union_pw_aff *
1450 isl_multi_union_pw_aff_set_dim_id(
1451 __isl_take isl_multi_union_pw_aff *mupa,
1452 enum isl_dim_type type, unsigned pos,
1453 __isl_take isl_id *id);
1454 __isl_give isl_id *isl_multi_aff_get_dim_id(
1455 __isl_keep isl_multi_aff *ma,
1456 enum isl_dim_type type, unsigned pos);
1457 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1458 enum isl_dim_type type, unsigned pos);
1459 __isl_give isl_id *isl_pw_aff_get_dim_id(
1460 __isl_keep isl_pw_aff *pa,
1461 enum isl_dim_type type, unsigned pos);
1462 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type, unsigned pos);
1465 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1466 __isl_keep isl_multi_pw_aff *mpa,
1467 enum isl_dim_type type, unsigned pos);
1468 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1469 __isl_keep isl_multi_union_pw_aff *mupa,
1470 enum isl_dim_type type, unsigned pos);
1471 __isl_give isl_aff *isl_aff_set_dim_name(
1472 __isl_take isl_aff *aff, enum isl_dim_type type,
1473 unsigned pos, const char *s);
1474 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1475 __isl_take isl_multi_aff *maff,
1476 enum isl_dim_type type, unsigned pos, const char *s);
1477 __isl_give isl_multi_pw_aff *
1478 isl_multi_pw_aff_set_dim_name(
1479 __isl_take isl_multi_pw_aff *mpa,
1480 enum isl_dim_type type, unsigned pos, const char *s);
1481 __isl_give isl_union_pw_aff *
1482 isl_union_pw_aff_set_dim_name(
1483 __isl_take isl_union_pw_aff *upa,
1484 enum isl_dim_type type, unsigned pos,
1486 __isl_give isl_union_pw_multi_aff *
1487 isl_union_pw_multi_aff_set_dim_name(
1488 __isl_take isl_union_pw_multi_aff *upma,
1489 enum isl_dim_type type, unsigned pos,
1491 __isl_give isl_multi_union_pw_aff *
1492 isl_multi_union_pw_aff_set_dim_name(
1493 __isl_take isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, unsigned pos,
1496 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_pw_aff_get_dim_name(
1499 __isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_pw_multi_aff_get_dim_name(
1502 __isl_keep isl_pw_multi_aff *pma,
1503 enum isl_dim_type type, unsigned pos);
1505 #include <isl/polynomial.h>
1506 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1507 __isl_take isl_qpolynomial *qp,
1508 enum isl_dim_type type, unsigned pos,
1510 __isl_give isl_pw_qpolynomial *
1511 isl_pw_qpolynomial_set_dim_name(
1512 __isl_take isl_pw_qpolynomial *pwqp,
1513 enum isl_dim_type type, unsigned pos,
1515 __isl_give isl_pw_qpolynomial_fold *
1516 isl_pw_qpolynomial_fold_set_dim_name(
1517 __isl_take isl_pw_qpolynomial_fold *pwf,
1518 enum isl_dim_type type, unsigned pos,
1520 __isl_give isl_union_pw_qpolynomial *
1521 isl_union_pw_qpolynomial_set_dim_name(
1522 __isl_take isl_union_pw_qpolynomial *upwqp,
1523 enum isl_dim_type type, unsigned pos,
1525 __isl_give isl_union_pw_qpolynomial_fold *
1526 isl_union_pw_qpolynomial_fold_set_dim_name(
1527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1528 enum isl_dim_type type, unsigned pos,
1531 Note that C<isl_space_get_name> returns a pointer to some internal
1532 data structure, so the result can only be used while the
1533 corresponding C<isl_space> is alive.
1534 Also note that every function that operates on two sets or relations
1535 requires that both arguments have the same parameters. This also
1536 means that if one of the arguments has named parameters, then the
1537 other needs to have named parameters too and the names need to match.
1538 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1539 arguments may have different parameters (as long as they are named),
1540 in which case the result will have as parameters the union of the parameters of
1543 Given the identifier or name of a dimension (typically a parameter),
1544 its position can be obtained from the following functions.
1546 #include <isl/space.h>
1547 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1550 enum isl_dim_type type, const char *name);
1552 #include <isl/local_space.h>
1553 int isl_local_space_find_dim_by_name(
1554 __isl_keep isl_local_space *ls,
1555 enum isl_dim_type type, const char *name);
1557 #include <isl/val.h>
1558 int isl_multi_val_find_dim_by_id(
1559 __isl_keep isl_multi_val *mv,
1560 enum isl_dim_type type, __isl_keep isl_id *id);
1561 int isl_multi_val_find_dim_by_name(
1562 __isl_keep isl_multi_val *mv,
1563 enum isl_dim_type type, const char *name);
1565 #include <isl/set.h>
1566 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1567 enum isl_dim_type type, __isl_keep isl_id *id);
1568 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1569 enum isl_dim_type type, const char *name);
1571 #include <isl/map.h>
1572 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1573 enum isl_dim_type type, __isl_keep isl_id *id);
1574 int isl_basic_map_find_dim_by_name(
1575 __isl_keep isl_basic_map *bmap,
1576 enum isl_dim_type type, const char *name);
1577 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1578 enum isl_dim_type type, const char *name);
1579 int isl_union_map_find_dim_by_name(
1580 __isl_keep isl_union_map *umap,
1581 enum isl_dim_type type, const char *name);
1583 #include <isl/aff.h>
1584 int isl_multi_aff_find_dim_by_id(
1585 __isl_keep isl_multi_aff *ma,
1586 enum isl_dim_type type, __isl_keep isl_id *id);
1587 int isl_multi_pw_aff_find_dim_by_id(
1588 __isl_keep isl_multi_pw_aff *mpa,
1589 enum isl_dim_type type, __isl_keep isl_id *id);
1590 int isl_multi_union_pw_aff_find_dim_by_id(
1591 __isl_keep isl_multi_union_pw_aff *mupa,
1592 enum isl_dim_type type, __isl_keep isl_id *id);
1593 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1594 enum isl_dim_type type, const char *name);
1595 int isl_multi_aff_find_dim_by_name(
1596 __isl_keep isl_multi_aff *ma,
1597 enum isl_dim_type type, const char *name);
1598 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1599 enum isl_dim_type type, const char *name);
1600 int isl_multi_pw_aff_find_dim_by_name(
1601 __isl_keep isl_multi_pw_aff *mpa,
1602 enum isl_dim_type type, const char *name);
1603 int isl_pw_multi_aff_find_dim_by_name(
1604 __isl_keep isl_pw_multi_aff *pma,
1605 enum isl_dim_type type, const char *name);
1606 int isl_union_pw_aff_find_dim_by_name(
1607 __isl_keep isl_union_pw_aff *upa,
1608 enum isl_dim_type type, const char *name);
1609 int isl_union_pw_multi_aff_find_dim_by_name(
1610 __isl_keep isl_union_pw_multi_aff *upma,
1611 enum isl_dim_type type, const char *name);
1612 int isl_multi_union_pw_aff_find_dim_by_name(
1613 __isl_keep isl_multi_union_pw_aff *mupa,
1614 enum isl_dim_type type, const char *name);
1616 #include <isl/polynomial.h>
1617 int isl_pw_qpolynomial_find_dim_by_name(
1618 __isl_keep isl_pw_qpolynomial *pwqp,
1619 enum isl_dim_type type, const char *name);
1620 int isl_pw_qpolynomial_fold_find_dim_by_name(
1621 __isl_keep isl_pw_qpolynomial_fold *pwf,
1622 enum isl_dim_type type, const char *name);
1623 int isl_union_pw_qpolynomial_find_dim_by_name(
1624 __isl_keep isl_union_pw_qpolynomial *upwqp,
1625 enum isl_dim_type type, const char *name);
1626 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1627 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1628 enum isl_dim_type type, const char *name);
1630 The identifiers or names of entire spaces may be set or read off
1631 using the following functions.
1633 #include <isl/space.h>
1634 __isl_give isl_space *isl_space_set_domain_tuple_id(
1635 __isl_take isl_space *space,
1636 __isl_take isl_id *id);
1637 __isl_give isl_space *isl_space_set_range_tuple_id(
1638 __isl_take isl_space *space,
1639 __isl_take isl_id *id);
1640 __isl_give isl_space *isl_space_set_tuple_id(
1641 __isl_take isl_space *space,
1642 enum isl_dim_type type, __isl_take isl_id *id);
1643 __isl_give isl_space *isl_space_reset_tuple_id(
1644 __isl_take isl_space *space, enum isl_dim_type type);
1645 isl_bool isl_space_has_domain_tuple_id(
1646 __isl_keep isl_space *space);
1647 isl_bool isl_space_has_range_tuple_id(
1648 __isl_keep isl_space *space);
1649 isl_bool isl_space_has_tuple_id(
1650 __isl_keep isl_space *space,
1651 enum isl_dim_type type);
1652 __isl_give isl_id *isl_space_get_domain_tuple_id(
1653 __isl_keep isl_space *space);
1654 __isl_give isl_id *isl_space_get_range_tuple_id(
1655 __isl_keep isl_space *space);
1656 __isl_give isl_id *isl_space_get_tuple_id(
1657 __isl_keep isl_space *space, enum isl_dim_type type);
1658 __isl_give isl_space *isl_space_set_tuple_name(
1659 __isl_take isl_space *space,
1660 enum isl_dim_type type, const char *s);
1661 isl_bool isl_space_has_tuple_name(
1662 __isl_keep isl_space *space,
1663 enum isl_dim_type type);
1664 __isl_keep const char *isl_space_get_tuple_name(
1665 __isl_keep isl_space *space,
1666 enum isl_dim_type type);
1668 #include <isl/local_space.h>
1669 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1670 __isl_take isl_local_space *ls,
1671 enum isl_dim_type type, __isl_take isl_id *id);
1673 #include <isl/set.h>
1674 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1675 __isl_take isl_basic_set *bset,
1676 __isl_take isl_id *id);
1677 __isl_give isl_set *isl_set_set_tuple_id(
1678 __isl_take isl_set *set, __isl_take isl_id *id);
1679 __isl_give isl_set *isl_set_reset_tuple_id(
1680 __isl_take isl_set *set);
1681 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1682 __isl_give isl_id *isl_set_get_tuple_id(
1683 __isl_keep isl_set *set);
1684 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1685 __isl_take isl_basic_set *set, const char *s);
1686 __isl_give isl_set *isl_set_set_tuple_name(
1687 __isl_take isl_set *set, const char *s);
1688 const char *isl_basic_set_get_tuple_name(
1689 __isl_keep isl_basic_set *bset);
1690 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1691 const char *isl_set_get_tuple_name(
1692 __isl_keep isl_set *set);
1694 #include <isl/map.h>
1695 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, __isl_take isl_id *id);
1698 __isl_give isl_map *isl_map_set_domain_tuple_id(
1699 __isl_take isl_map *map, __isl_take isl_id *id);
1700 __isl_give isl_map *isl_map_set_range_tuple_id(
1701 __isl_take isl_map *map, __isl_take isl_id *id);
1702 __isl_give isl_map *isl_map_set_tuple_id(
1703 __isl_take isl_map *map, enum isl_dim_type type,
1704 __isl_take isl_id *id);
1705 __isl_give isl_map *isl_map_reset_tuple_id(
1706 __isl_take isl_map *map, enum isl_dim_type type);
1707 isl_bool isl_map_has_domain_tuple_id(
1708 __isl_keep isl_map *map);
1709 isl_bool isl_map_has_range_tuple_id(
1710 __isl_keep isl_map *map);
1711 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1712 enum isl_dim_type type);
1713 __isl_give isl_id *isl_map_get_domain_tuple_id(
1714 __isl_keep isl_map *map);
1715 __isl_give isl_id *isl_map_get_range_tuple_id(
1716 __isl_keep isl_map *map);
1717 __isl_give isl_id *isl_map_get_tuple_id(
1718 __isl_keep isl_map *map, enum isl_dim_type type);
1719 __isl_give isl_map *isl_map_set_tuple_name(
1720 __isl_take isl_map *map,
1721 enum isl_dim_type type, const char *s);
1722 const char *isl_basic_map_get_tuple_name(
1723 __isl_keep isl_basic_map *bmap,
1724 enum isl_dim_type type);
1725 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1726 __isl_take isl_basic_map *bmap,
1727 enum isl_dim_type type, const char *s);
1728 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1729 enum isl_dim_type type);
1730 const char *isl_map_get_tuple_name(
1731 __isl_keep isl_map *map,
1732 enum isl_dim_type type);
1734 #include <isl/val.h>
1735 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1736 __isl_take isl_multi_val *mv,
1737 __isl_take isl_id *id);
1738 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1739 __isl_take isl_multi_val *mv,
1740 enum isl_dim_type type, __isl_take isl_id *id);
1741 __isl_give isl_multi_val *
1742 isl_multi_val_reset_range_tuple_id(
1743 __isl_take isl_multi_val *mv);
1744 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1745 __isl_take isl_multi_val *mv,
1746 enum isl_dim_type type);
1747 isl_bool isl_multi_val_has_range_tuple_id(
1748 __isl_keep isl_multi_val *mv);
1749 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1750 __isl_keep isl_multi_val *mv);
1751 isl_bool isl_multi_val_has_tuple_id(
1752 __isl_keep isl_multi_val *mv,
1753 enum isl_dim_type type);
1754 __isl_give isl_id *isl_multi_val_get_tuple_id(
1755 __isl_keep isl_multi_val *mv,
1756 enum isl_dim_type type);
1757 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1758 __isl_take isl_multi_val *mv,
1759 enum isl_dim_type type, const char *s);
1760 const char *isl_multi_val_get_tuple_name(
1761 __isl_keep isl_multi_val *mv,
1762 enum isl_dim_type type);
1764 #include <isl/aff.h>
1765 __isl_give isl_aff *isl_aff_set_tuple_id(
1766 __isl_take isl_aff *aff,
1767 enum isl_dim_type type, __isl_take isl_id *id);
1768 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1769 __isl_take isl_multi_aff *ma,
1770 __isl_take isl_id *id);
1771 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1772 __isl_take isl_multi_aff *maff,
1773 enum isl_dim_type type, __isl_take isl_id *id);
1774 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1775 __isl_take isl_pw_aff *pwaff,
1776 enum isl_dim_type type, __isl_take isl_id *id);
1777 __isl_give isl_pw_multi_aff *
1778 isl_pw_multi_aff_set_range_tuple_id(
1779 __isl_take isl_pw_multi_aff *pma,
1780 __isl_take isl_id *id);
1781 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1782 __isl_take isl_pw_multi_aff *pma,
1783 enum isl_dim_type type, __isl_take isl_id *id);
1784 __isl_give isl_multi_pw_aff *
1785 isl_multi_pw_aff_set_range_tuple_id(
1786 __isl_take isl_multi_pw_aff *mpa,
1787 __isl_take isl_id *id);
1788 __isl_give isl_multi_union_pw_aff *
1789 isl_multi_union_pw_aff_set_range_tuple_id(
1790 __isl_take isl_multi_union_pw_aff *mupa,
1791 __isl_take isl_id *id);
1792 __isl_give isl_multi_union_pw_aff *
1793 isl_multi_union_pw_aff_set_tuple_id(
1794 __isl_take isl_multi_union_pw_aff *mupa,
1795 enum isl_dim_type type, __isl_take isl_id *id);
1796 __isl_give isl_multi_aff *
1797 isl_multi_aff_reset_range_tuple_id(
1798 __isl_take isl_multi_aff *ma);
1799 __isl_give isl_multi_pw_aff *
1800 isl_multi_pw_aff_reset_range_tuple_id(
1801 __isl_take isl_multi_pw_aff *mpa);
1802 __isl_give isl_multi_union_pw_aff *
1803 isl_multi_union_pw_aff_reset_range_tuple_id(
1804 __isl_take isl_multi_union_pw_aff *mupa);
1805 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1806 __isl_take isl_multi_aff *ma,
1807 enum isl_dim_type type);
1808 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1809 __isl_take isl_pw_aff *pa,
1810 enum isl_dim_type type);
1811 __isl_give isl_multi_pw_aff *
1812 isl_multi_pw_aff_reset_tuple_id(
1813 __isl_take isl_multi_pw_aff *mpa,
1814 enum isl_dim_type type);
1815 __isl_give isl_pw_multi_aff *
1816 isl_pw_multi_aff_reset_tuple_id(
1817 __isl_take isl_pw_multi_aff *pma,
1818 enum isl_dim_type type);
1819 __isl_give isl_multi_union_pw_aff *
1820 isl_multi_union_pw_aff_reset_tuple_id(
1821 __isl_take isl_multi_union_pw_aff *mupa,
1822 enum isl_dim_type type);
1823 isl_bool isl_multi_aff_has_range_tuple_id(
1824 __isl_keep isl_multi_aff *ma);
1825 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1826 __isl_keep isl_multi_aff *ma);
1827 isl_bool isl_multi_aff_has_tuple_id(
1828 __isl_keep isl_multi_aff *ma,
1829 enum isl_dim_type type);
1830 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1831 __isl_keep isl_multi_aff *ma,
1832 enum isl_dim_type type);
1833 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1834 enum isl_dim_type type);
1835 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1836 __isl_keep isl_pw_aff *pa,
1837 enum isl_dim_type type);
1838 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1839 __isl_keep isl_pw_multi_aff *pma);
1840 isl_bool isl_pw_multi_aff_has_tuple_id(
1841 __isl_keep isl_pw_multi_aff *pma,
1842 enum isl_dim_type type);
1843 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1844 __isl_keep isl_pw_multi_aff *pma);
1845 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1846 __isl_keep isl_pw_multi_aff *pma,
1847 enum isl_dim_type type);
1848 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1849 __isl_keep isl_multi_pw_aff *mpa);
1850 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1851 __isl_keep isl_multi_pw_aff *mpa);
1852 isl_bool isl_multi_pw_aff_has_tuple_id(
1853 __isl_keep isl_multi_pw_aff *mpa,
1854 enum isl_dim_type type);
1855 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1856 __isl_keep isl_multi_pw_aff *mpa,
1857 enum isl_dim_type type);
1858 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1859 __isl_keep isl_multi_union_pw_aff *mupa);
1861 isl_multi_union_pw_aff_get_range_tuple_id(
1862 __isl_keep isl_multi_union_pw_aff *mupa);
1863 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1864 __isl_keep isl_multi_union_pw_aff *mupa,
1865 enum isl_dim_type type);
1866 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1867 __isl_keep isl_multi_union_pw_aff *mupa,
1868 enum isl_dim_type type);
1869 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1870 __isl_take isl_multi_aff *maff,
1871 enum isl_dim_type type, const char *s);
1872 __isl_give isl_multi_pw_aff *
1873 isl_multi_pw_aff_set_tuple_name(
1874 __isl_take isl_multi_pw_aff *mpa,
1875 enum isl_dim_type type, const char *s);
1876 __isl_give isl_multi_union_pw_aff *
1877 isl_multi_union_pw_aff_set_tuple_name(
1878 __isl_take isl_multi_union_pw_aff *mupa,
1879 enum isl_dim_type type, const char *s);
1880 const char *isl_multi_aff_get_tuple_name(
1881 __isl_keep isl_multi_aff *multi,
1882 enum isl_dim_type type);
1883 isl_bool isl_pw_multi_aff_has_tuple_name(
1884 __isl_keep isl_pw_multi_aff *pma,
1885 enum isl_dim_type type);
1886 const char *isl_pw_multi_aff_get_tuple_name(
1887 __isl_keep isl_pw_multi_aff *pma,
1888 enum isl_dim_type type);
1889 const char *isl_multi_union_pw_aff_get_tuple_name(
1890 __isl_keep isl_multi_union_pw_aff *mupa,
1891 enum isl_dim_type type);
1893 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1894 or C<isl_dim_set>. As with C<isl_space_get_name>,
1895 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1897 Binary operations require the corresponding spaces of their arguments
1898 to have the same name.
1900 To keep the names of all parameters and tuples, but reset the user pointers
1901 of all the corresponding identifiers, use the following function.
1903 #include <isl/space.h>
1904 __isl_give isl_space *isl_space_reset_user(
1905 __isl_take isl_space *space);
1907 #include <isl/set.h>
1908 __isl_give isl_set *isl_set_reset_user(
1909 __isl_take isl_set *set);
1911 #include <isl/map.h>
1912 __isl_give isl_map *isl_map_reset_user(
1913 __isl_take isl_map *map);
1915 #include <isl/union_set.h>
1916 __isl_give isl_union_set *isl_union_set_reset_user(
1917 __isl_take isl_union_set *uset);
1919 #include <isl/union_map.h>
1920 __isl_give isl_union_map *isl_union_map_reset_user(
1921 __isl_take isl_union_map *umap);
1924 __isl_give isl_multi_id *isl_multi_id_reset_user(
1925 __isl_take isl_multi_id *mi);
1927 #include <isl/val.h>
1928 __isl_give isl_multi_val *isl_multi_val_reset_user(
1929 __isl_take isl_multi_val *mv);
1931 #include <isl/aff.h>
1932 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1933 __isl_take isl_multi_aff *ma);
1934 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1935 __isl_take isl_pw_aff *pa);
1936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1937 __isl_take isl_multi_pw_aff *mpa);
1938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1939 __isl_take isl_pw_multi_aff *pma);
1940 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1941 __isl_take isl_union_pw_aff *upa);
1942 __isl_give isl_multi_union_pw_aff *
1943 isl_multi_union_pw_aff_reset_user(
1944 __isl_take isl_multi_union_pw_aff *mupa);
1945 __isl_give isl_union_pw_multi_aff *
1946 isl_union_pw_multi_aff_reset_user(
1947 __isl_take isl_union_pw_multi_aff *upma);
1949 #include <isl/polynomial.h>
1950 __isl_give isl_pw_qpolynomial *
1951 isl_pw_qpolynomial_reset_user(
1952 __isl_take isl_pw_qpolynomial *pwqp);
1953 __isl_give isl_union_pw_qpolynomial *
1954 isl_union_pw_qpolynomial_reset_user(
1955 __isl_take isl_union_pw_qpolynomial *upwqp);
1956 __isl_give isl_pw_qpolynomial_fold *
1957 isl_pw_qpolynomial_fold_reset_user(
1958 __isl_take isl_pw_qpolynomial_fold *pwf);
1959 __isl_give isl_union_pw_qpolynomial_fold *
1960 isl_union_pw_qpolynomial_fold_reset_user(
1961 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1963 Spaces can be nested. In particular, the domain of a set or
1964 the domain or range of a relation can be a nested relation.
1965 This process is also called I<wrapping>.
1966 The functions for detecting, constructing and deconstructing
1967 such nested spaces can be found in the wrapping properties
1968 of L</"Unary Properties">, the wrapping operations
1969 of L</"Unary Operations"> and the Cartesian product operations
1970 of L</"Basic Operations">.
1972 Spaces can be created from other spaces
1973 using the functions described in L</"Unary Operations">
1974 and L</"Binary Operations">.
1978 A local space is essentially a space with
1979 zero or more existentially quantified variables.
1980 The local space of various objects can be obtained
1981 using the following functions.
1983 #include <isl/constraint.h>
1984 __isl_give isl_local_space *isl_constraint_get_local_space(
1985 __isl_keep isl_constraint *constraint);
1987 #include <isl/set.h>
1988 __isl_give isl_local_space *isl_basic_set_get_local_space(
1989 __isl_keep isl_basic_set *bset);
1991 #include <isl/map.h>
1992 __isl_give isl_local_space *isl_basic_map_get_local_space(
1993 __isl_keep isl_basic_map *bmap);
1995 #include <isl/aff.h>
1996 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1997 __isl_keep isl_aff *aff);
1998 __isl_give isl_local_space *isl_aff_get_local_space(
1999 __isl_keep isl_aff *aff);
2001 A new local space can be created from a space using
2003 #include <isl/local_space.h>
2004 __isl_give isl_local_space *isl_local_space_from_space(
2005 __isl_take isl_space *space);
2007 They can be inspected, modified, copied and freed using the following functions.
2009 #include <isl/local_space.h>
2010 isl_bool isl_local_space_is_params(
2011 __isl_keep isl_local_space *ls);
2012 isl_bool isl_local_space_is_set(
2013 __isl_keep isl_local_space *ls);
2014 __isl_give isl_space *isl_local_space_get_space(
2015 __isl_keep isl_local_space *ls);
2016 __isl_give isl_aff *isl_local_space_get_div(
2017 __isl_keep isl_local_space *ls, int pos);
2018 __isl_give isl_local_space *isl_local_space_copy(
2019 __isl_keep isl_local_space *ls);
2020 __isl_null isl_local_space *isl_local_space_free(
2021 __isl_take isl_local_space *ls);
2023 Note that C<isl_local_space_get_div> can only be used on local spaces
2026 Two local spaces can be compared using
2028 isl_bool isl_local_space_is_equal(
2029 __isl_keep isl_local_space *ls1,
2030 __isl_keep isl_local_space *ls2);
2032 Local spaces can be created from other local spaces
2033 using the functions described in L</"Unary Operations">
2034 and L</"Binary Operations">.
2036 =head2 Creating New Sets and Relations
2038 C<isl> has functions for creating some standard sets and relations.
2042 =item * Empty sets and relations
2044 __isl_give isl_basic_set *isl_basic_set_empty(
2045 __isl_take isl_space *space);
2046 __isl_give isl_basic_map *isl_basic_map_empty(
2047 __isl_take isl_space *space);
2048 __isl_give isl_set *isl_set_empty(
2049 __isl_take isl_space *space);
2050 __isl_give isl_map *isl_map_empty(
2051 __isl_take isl_space *space);
2052 __isl_give isl_union_set *isl_union_set_empty_ctx(
2054 __isl_give isl_union_set *isl_union_set_empty_space(
2055 __isl_take isl_space *space);
2056 __isl_give isl_union_set *isl_union_set_empty(
2057 __isl_take isl_space *space);
2058 __isl_give isl_union_map *isl_union_map_empty_ctx(
2060 __isl_give isl_union_map *isl_union_map_empty_space(
2061 __isl_take isl_space *space);
2062 __isl_give isl_union_map *isl_union_map_empty(
2063 __isl_take isl_space *space);
2065 For C<isl_union_set>s and C<isl_union_map>s, the space
2066 is only used to specify the parameters.
2067 C<isl_union_set_empty> is an alternative name for
2068 C<isl_union_set_empty_space>.
2069 Similarly for the other pair of functions.
2071 =item * Universe sets and relations
2073 #include <isl/set.h>
2074 __isl_give isl_basic_set *isl_basic_set_universe(
2075 __isl_take isl_space *space);
2076 __isl_give isl_set *isl_set_universe(
2077 __isl_take isl_space *space);
2078 __isl_give isl_set *isl_space_universe_set(
2079 __isl_take isl_space *space);
2081 #include <isl/map.h>
2082 __isl_give isl_basic_map *isl_basic_map_universe(
2083 __isl_take isl_space *space);
2084 __isl_give isl_map *isl_map_universe(
2085 __isl_take isl_space *space);
2086 __isl_give isl_map *isl_space_universe_map(
2087 __isl_take isl_space *space);
2089 #include <isl/union_set.h>
2090 __isl_give isl_union_set *isl_union_set_universe(
2091 __isl_take isl_union_set *uset);
2093 #include <isl/union_map.h>
2094 __isl_give isl_union_map *isl_union_map_universe(
2095 __isl_take isl_union_map *umap);
2097 C<isl_set_universe> and C<isl_space_universe_set>
2098 perform the same operation.
2100 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2102 The sets and relations constructed by the functions above
2103 contain all integer values, while those constructed by the
2104 functions below only contain non-negative values.
2106 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2107 __isl_take isl_space *space);
2108 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2109 __isl_take isl_space *space);
2110 __isl_give isl_set *isl_set_nat_universe(
2111 __isl_take isl_space *space);
2112 __isl_give isl_map *isl_map_nat_universe(
2113 __isl_take isl_space *space);
2115 =item * Identity relations
2117 __isl_give isl_basic_map *isl_basic_map_identity(
2118 __isl_take isl_space *space);
2119 __isl_give isl_map *isl_map_identity(
2120 __isl_take isl_space *space);
2122 The number of input and output dimensions in C<space> needs
2125 =item * Lexicographic order
2127 __isl_give isl_map *isl_map_lex_lt(
2128 __isl_take isl_space *set_space);
2129 __isl_give isl_map *isl_map_lex_le(
2130 __isl_take isl_space *set_space);
2131 __isl_give isl_map *isl_map_lex_gt(
2132 __isl_take isl_space *set_space);
2133 __isl_give isl_map *isl_map_lex_ge(
2134 __isl_take isl_space *set_space);
2135 __isl_give isl_map *isl_map_lex_lt_first(
2136 __isl_take isl_space *space, unsigned n);
2137 __isl_give isl_map *isl_map_lex_le_first(
2138 __isl_take isl_space *space, unsigned n);
2139 __isl_give isl_map *isl_map_lex_gt_first(
2140 __isl_take isl_space *space, unsigned n);
2141 __isl_give isl_map *isl_map_lex_ge_first(
2142 __isl_take isl_space *space, unsigned n);
2144 The first four functions take a space for a B<set>
2145 and return relations that express that the elements in the domain
2146 are lexicographically less
2147 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2148 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2149 than the elements in the range.
2150 The last four functions take a space for a map
2151 and return relations that express that the first C<n> dimensions
2152 in the domain are lexicographically less
2153 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2154 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2155 than the first C<n> dimensions in the range.
2159 A basic set or relation can be converted to a set or relation
2160 using the following functions.
2162 __isl_give isl_set *isl_basic_set_to_set(
2163 __isl_take isl_basic_set *bset);
2164 __isl_give isl_set *isl_set_from_basic_set(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_map *isl_map_from_basic_map(
2167 __isl_take isl_basic_map *bmap);
2169 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2172 Sets and relations can be converted to union sets and relations
2173 using the following functions.
2175 __isl_give isl_union_set *isl_union_set_from_basic_set(
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_union_map *isl_union_map_from_basic_map(
2178 __isl_take isl_basic_map *bmap);
2179 __isl_give isl_union_set *isl_set_to_union_set(
2180 __isl_take isl_set *set);
2181 __isl_give isl_union_set *isl_union_set_from_set(
2182 __isl_take isl_set *set);
2183 __isl_give isl_union_map *isl_map_to_union_map(
2184 __isl_take isl_map *map);
2185 __isl_give isl_union_map *isl_union_map_from_map(
2186 __isl_take isl_map *map);
2188 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2190 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2192 The inverse conversions below can only be used if the input
2193 union set or relation is known to contain elements in exactly one
2196 #include <isl/union_set.h>
2197 isl_bool isl_union_set_isa_set(
2198 __isl_keep isl_union_set *uset);
2199 __isl_give isl_set *isl_union_set_as_set(
2200 __isl_take isl_union_set *uset);
2201 __isl_give isl_set *isl_set_from_union_set(
2202 __isl_take isl_union_set *uset);
2204 #include <isl/union_map.h>
2205 isl_bool isl_union_map_isa_map(
2206 __isl_keep isl_union_map *umap);
2207 __isl_give isl_map *isl_union_map_as_map(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_map *isl_map_from_union_map(
2210 __isl_take isl_union_map *umap);
2212 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2214 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2216 Sets and relations can be copied and freed again using the following
2219 __isl_give isl_basic_set *isl_basic_set_copy(
2220 __isl_keep isl_basic_set *bset);
2221 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2222 __isl_give isl_union_set *isl_union_set_copy(
2223 __isl_keep isl_union_set *uset);
2224 __isl_give isl_basic_map *isl_basic_map_copy(
2225 __isl_keep isl_basic_map *bmap);
2226 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2227 __isl_give isl_union_map *isl_union_map_copy(
2228 __isl_keep isl_union_map *umap);
2229 __isl_null isl_basic_set *isl_basic_set_free(
2230 __isl_take isl_basic_set *bset);
2231 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2232 __isl_null isl_union_set *isl_union_set_free(
2233 __isl_take isl_union_set *uset);
2234 __isl_null isl_basic_map *isl_basic_map_free(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2237 __isl_null isl_union_map *isl_union_map_free(
2238 __isl_take isl_union_map *umap);
2240 Other sets and relations can be constructed by starting
2241 from a universe set or relation, adding equality and/or
2242 inequality constraints and then projecting out the
2243 existentially quantified variables, if any.
2244 Constraints can be constructed, manipulated and
2245 added to (or removed from) (basic) sets and relations
2246 using the following functions.
2248 #include <isl/constraint.h>
2249 __isl_give isl_constraint *isl_constraint_alloc_equality(
2250 __isl_take isl_local_space *ls);
2251 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2252 __isl_take isl_local_space *ls);
2253 __isl_give isl_constraint *isl_constraint_set_constant_si(
2254 __isl_take isl_constraint *constraint, int v);
2255 __isl_give isl_constraint *isl_constraint_set_constant_val(
2256 __isl_take isl_constraint *constraint,
2257 __isl_take isl_val *v);
2258 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2259 __isl_take isl_constraint *constraint,
2260 enum isl_dim_type type, int pos, int v);
2261 __isl_give isl_constraint *
2262 isl_constraint_set_coefficient_val(
2263 __isl_take isl_constraint *constraint,
2264 enum isl_dim_type type, int pos,
2265 __isl_take isl_val *v);
2266 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2267 __isl_take isl_basic_map *bmap,
2268 __isl_take isl_constraint *constraint);
2269 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2270 __isl_take isl_basic_set *bset,
2271 __isl_take isl_constraint *constraint);
2272 __isl_give isl_map *isl_map_add_constraint(
2273 __isl_take isl_map *map,
2274 __isl_take isl_constraint *constraint);
2275 __isl_give isl_set *isl_set_add_constraint(
2276 __isl_take isl_set *set,
2277 __isl_take isl_constraint *constraint);
2279 For example, to create a set containing the even integers
2280 between 10 and 42, you could use the following code.
2283 isl_local_space *ls;
2285 isl_basic_set *bset;
2287 space = isl_space_set_alloc(ctx, 0, 2);
2288 bset = isl_basic_set_universe(isl_space_copy(space));
2289 ls = isl_local_space_from_space(space);
2291 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2293 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2294 bset = isl_basic_set_add_constraint(bset, c);
2296 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2297 c = isl_constraint_set_constant_si(c, -10);
2298 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2299 bset = isl_basic_set_add_constraint(bset, c);
2301 c = isl_constraint_alloc_inequality(ls);
2302 c = isl_constraint_set_constant_si(c, 42);
2303 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2304 bset = isl_basic_set_add_constraint(bset, c);
2306 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2308 However, this is considered to be a fairly low-level approach.
2309 It is more appropriate to construct a (basic) set by means
2310 of affine expressions (defined below in L</"Functions">).
2311 For example, the same set could be constructed as follows.
2317 isl_basic_set *bset;
2319 space = isl_space_unit(ctx);
2320 space = isl_space_add_unnamed_tuple_ui(space, 1);
2321 ma = isl_multi_aff_identity_on_domain_space(
2322 isl_space_copy(space));
2323 var = isl_multi_aff_get_at(ma, 0);
2324 v = isl_val_int_from_si(ctx, 10);
2325 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2326 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2328 v = isl_val_int_from_si(ctx, 42);
2329 cst = isl_aff_val_on_domain_space(space, v);
2330 bset = isl_basic_set_intersect(bset,
2331 isl_aff_le_basic_set(var, cst));
2333 two = isl_val_int_from_si(ctx, 2);
2334 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2335 bset = isl_basic_set_preimage_multi_aff(bset,
2336 isl_multi_aff_copy(ma));
2337 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2338 ma = isl_multi_aff_scale_down_val(ma, two);
2339 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2341 Alternatively, the set can be parsed from a string representation.
2343 isl_basic_set *bset;
2344 bset = isl_basic_set_read_from_str(ctx,
2345 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2347 A basic set or relation can also be constructed from two matrices
2348 describing the equalities and the inequalities.
2350 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2351 __isl_take isl_space *space,
2352 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2353 enum isl_dim_type c1,
2354 enum isl_dim_type c2, enum isl_dim_type c3,
2355 enum isl_dim_type c4);
2356 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2357 __isl_take isl_space *space,
2358 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2359 enum isl_dim_type c1,
2360 enum isl_dim_type c2, enum isl_dim_type c3,
2361 enum isl_dim_type c4, enum isl_dim_type c5);
2363 The C<isl_dim_type> arguments indicate the order in which
2364 different kinds of variables appear in the input matrices
2365 and should be a permutation of C<isl_dim_cst> (the constant term),
2366 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2367 of C<isl_dim_cst>, C<isl_dim_param>,
2368 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2370 A (basic or union) set or relation can also be constructed from a
2371 (union) (piecewise) (multiple) affine expression
2372 or a list of affine expressions
2373 (See L</"Functions">), provided these affine expressions do not
2376 #include <isl/set.h>
2377 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2378 __isl_take isl_multi_aff *ma);
2379 __isl_give isl_set *isl_multi_aff_as_set(
2380 __isl_take isl_multi_aff *ma);
2381 __isl_give isl_set *isl_set_from_multi_aff(
2382 __isl_take isl_multi_aff *ma);
2384 #include <isl/map.h>
2385 __isl_give isl_basic_map *isl_basic_map_from_aff(
2386 __isl_take isl_aff *aff);
2387 __isl_give isl_map *isl_map_from_aff(
2388 __isl_take isl_aff *aff);
2389 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2390 __isl_take isl_space *domain_space,
2391 __isl_take isl_aff_list *list);
2392 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2393 __isl_take isl_multi_aff *maff)
2394 __isl_give isl_map *isl_multi_aff_as_map(
2395 __isl_take isl_multi_aff *ma);
2396 __isl_give isl_map *isl_map_from_multi_aff(
2397 __isl_take isl_multi_aff *maff)
2399 #include <isl/aff.h>
2400 __isl_give isl_set *isl_set_from_pw_aff(
2401 __isl_take isl_pw_aff *pwaff);
2402 __isl_give isl_map *isl_pw_aff_as_map(
2403 __isl_take isl_pw_aff *pa);
2404 __isl_give isl_map *isl_map_from_pw_aff(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_set *isl_pw_multi_aff_as_set(
2407 __isl_take isl_pw_multi_aff *pma);
2408 __isl_give isl_set *isl_set_from_pw_multi_aff(
2409 __isl_take isl_pw_multi_aff *pma);
2410 __isl_give isl_map *isl_pw_multi_aff_as_map(
2411 __isl_take isl_pw_multi_aff *pma);
2412 __isl_give isl_map *isl_map_from_pw_multi_aff(
2413 __isl_take isl_pw_multi_aff *pma);
2414 __isl_give isl_set *isl_multi_pw_aff_as_set(
2415 __isl_take isl_multi_pw_aff *mpa);
2416 __isl_give isl_set *isl_set_from_multi_pw_aff(
2417 __isl_take isl_multi_pw_aff *mpa);
2418 __isl_give isl_map *isl_multi_pw_aff_as_map(
2419 __isl_take isl_multi_pw_aff *mpa);
2420 __isl_give isl_map *isl_map_from_multi_pw_aff(
2421 __isl_take isl_multi_pw_aff *mpa);
2422 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2423 __isl_take isl_union_pw_aff *upa);
2424 __isl_give isl_union_map *
2425 isl_union_pw_multi_aff_as_union_map(
2426 __isl_take isl_union_pw_multi_aff *upma);
2427 __isl_give isl_union_map *
2428 isl_union_map_from_union_pw_multi_aff(
2429 __isl_take isl_union_pw_multi_aff *upma);
2430 __isl_give isl_union_map *
2431 isl_union_map_from_multi_union_pw_aff(
2432 __isl_take isl_multi_union_pw_aff *mupa);
2434 The C<domain_space> argument describes the domain of the resulting
2435 basic relation. It is required because the C<list> may consist
2436 of zero affine expressions.
2437 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2438 is not allowed to be zero-dimensional. The domain of the result
2439 is the shared domain of the union piecewise affine elements.
2440 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2442 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2443 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2444 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2445 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2446 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2447 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2449 C<isl_union_pw_multi_aff_as_union_map> and
2450 C<isl_union_map_from_union_pw_multi_aff>.
2452 =head2 Inspecting Sets and Relations
2454 Usually, the user should not have to care about the actual constraints
2455 of the sets and maps, but should instead apply the abstract operations
2456 explained in the following sections.
2457 Occasionally, however, it may be required to inspect the individual
2458 coefficients of the constraints. This section explains how to do so.
2459 In these cases, it may also be useful to have C<isl> compute
2460 an explicit representation of the existentially quantified variables.
2462 __isl_give isl_set *isl_set_compute_divs(
2463 __isl_take isl_set *set);
2464 __isl_give isl_map *isl_map_compute_divs(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_set *isl_union_set_compute_divs(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_union_map *isl_union_map_compute_divs(
2469 __isl_take isl_union_map *umap);
2471 This explicit representation defines the existentially quantified
2472 variables as integer divisions of the other variables, possibly
2473 including earlier existentially quantified variables.
2474 An explicitly represented existentially quantified variable therefore
2475 has a unique value when the values of the other variables are known.
2477 Alternatively, the existentially quantified variables can be removed
2478 using the following functions, which compute an overapproximation.
2480 #include <isl/set.h>
2481 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2482 __isl_take isl_basic_set *bset);
2483 __isl_give isl_set *isl_set_remove_divs(
2484 __isl_take isl_set *set);
2486 #include <isl/map.h>
2487 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2488 __isl_take isl_basic_map *bmap);
2489 __isl_give isl_map *isl_map_remove_divs(
2490 __isl_take isl_map *map);
2492 #include <isl/union_set.h>
2493 __isl_give isl_union_set *isl_union_set_remove_divs(
2494 __isl_take isl_union_set *bset);
2496 #include <isl/union_map.h>
2497 __isl_give isl_union_map *isl_union_map_remove_divs(
2498 __isl_take isl_union_map *bmap);
2500 It is also possible to only remove those divs that are defined
2501 in terms of a given range of dimensions or only those for which
2502 no explicit representation is known.
2504 __isl_give isl_basic_set *
2505 isl_basic_set_remove_divs_involving_dims(
2506 __isl_take isl_basic_set *bset,
2507 enum isl_dim_type type,
2508 unsigned first, unsigned n);
2509 __isl_give isl_basic_map *
2510 isl_basic_map_remove_divs_involving_dims(
2511 __isl_take isl_basic_map *bmap,
2512 enum isl_dim_type type,
2513 unsigned first, unsigned n);
2514 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2515 __isl_take isl_set *set, enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2518 __isl_take isl_map *map, enum isl_dim_type type,
2519 unsigned first, unsigned n);
2521 __isl_give isl_basic_set *
2522 isl_basic_set_remove_unknown_divs(
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_set *isl_set_remove_unknown_divs(
2525 __isl_take isl_set *set);
2526 __isl_give isl_map *isl_map_remove_unknown_divs(
2527 __isl_take isl_map *map);
2529 To iterate over all the sets or maps in a union set or map, use
2531 #include <isl/union_set.h>
2532 isl_stat isl_union_set_foreach_set(
2533 __isl_keep isl_union_set *uset,
2534 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2536 isl_bool isl_union_set_every_set(
2537 __isl_keep isl_union_set *uset,
2538 isl_bool (*test)(__isl_keep isl_set *set,
2542 #include <isl/union_map.h>
2543 isl_stat isl_union_map_foreach_map(
2544 __isl_keep isl_union_map *umap,
2545 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2547 isl_bool isl_union_map_every_map(
2548 __isl_keep isl_union_map *umap,
2549 isl_bool (*test)(__isl_keep isl_map *map,
2553 These functions call the callback function once for each
2554 (pair of) space(s) for which there are elements in the input.
2555 The argument to the callback contains all elements in the input
2556 with that (pair of) space(s).
2557 The C<isl_union_set_every_set> and
2558 C<isl_union_map_every_map> variants check whether each
2559 call to the callback returns true and stops checking as soon as one
2560 of these calls returns false.
2562 The number of sets or maps in a union set or map can be obtained
2565 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2566 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2568 To extract the set or map in a given space from a union, use
2570 __isl_give isl_set *isl_union_set_extract_set(
2571 __isl_keep isl_union_set *uset,
2572 __isl_take isl_space *space);
2573 __isl_give isl_map *isl_union_map_extract_map(
2574 __isl_keep isl_union_map *umap,
2575 __isl_take isl_space *space);
2577 To iterate over all the basic sets or maps in a set or map, use
2579 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2580 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2583 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2584 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2588 The callback function C<fn> should return C<isl_stat_ok> if successful and
2589 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2590 occurs, the above functions will return C<isl_stat_error>.
2592 It should be noted that C<isl> does not guarantee that
2593 the basic sets or maps passed to C<fn> are disjoint.
2594 If this is required, then the user should call one of
2595 the following functions first.
2597 __isl_give isl_set *isl_set_make_disjoint(
2598 __isl_take isl_set *set);
2599 __isl_give isl_map *isl_map_make_disjoint(
2600 __isl_take isl_map *map);
2602 The number of basic sets in a set can be obtained
2603 or the number of basic maps in a map can be obtained
2606 #include <isl/set.h>
2607 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2609 #include <isl/map.h>
2610 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2612 It is also possible to obtain a list of (basic) sets from a set
2613 or union set, a list of basic maps from a map and a list of maps from a union
2616 #include <isl/set.h>
2617 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2618 __isl_keep isl_set *set);
2620 #include <isl/union_set.h>
2621 __isl_give isl_basic_set_list *
2622 isl_union_set_get_basic_set_list(
2623 __isl_keep isl_union_set *uset);
2624 __isl_give isl_set_list *isl_union_set_get_set_list(
2625 __isl_keep isl_union_set *uset);
2627 #include <isl/map.h>
2628 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2629 __isl_keep isl_map *map);
2631 #include <isl/union_map.h>
2632 __isl_give isl_map_list *isl_union_map_get_map_list(
2633 __isl_keep isl_union_map *umap);
2635 The returned list can be manipulated using the functions in L<"Lists">.
2637 To iterate over the constraints of a basic set or map, use
2639 #include <isl/constraint.h>
2641 isl_size isl_basic_set_n_constraint(
2642 __isl_keep isl_basic_set *bset);
2643 isl_stat isl_basic_set_foreach_constraint(
2644 __isl_keep isl_basic_set *bset,
2645 isl_stat (*fn)(__isl_take isl_constraint *c,
2648 isl_size isl_basic_map_n_constraint(
2649 __isl_keep isl_basic_map *bmap);
2650 isl_stat isl_basic_map_foreach_constraint(
2651 __isl_keep isl_basic_map *bmap,
2652 isl_stat (*fn)(__isl_take isl_constraint *c,
2655 __isl_null isl_constraint *isl_constraint_free(
2656 __isl_take isl_constraint *c);
2658 Again, the callback function C<fn> should return C<isl_stat_ok>
2660 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2661 occurs, the above functions will return C<isl_stat_error>.
2662 The constraint C<c> represents either an equality or an inequality.
2663 Use the following function to find out whether a constraint
2664 represents an equality. If not, it represents an inequality.
2666 isl_bool isl_constraint_is_equality(
2667 __isl_keep isl_constraint *constraint);
2669 It is also possible to obtain a list of constraints from a basic
2672 #include <isl/constraint.h>
2673 __isl_give isl_constraint_list *
2674 isl_basic_map_get_constraint_list(
2675 __isl_keep isl_basic_map *bmap);
2676 __isl_give isl_constraint_list *
2677 isl_basic_set_get_constraint_list(
2678 __isl_keep isl_basic_set *bset);
2680 These functions require that all existentially quantified variables
2681 have an explicit representation.
2682 The returned list can be manipulated using the functions in L<"Lists">.
2684 The coefficients of the constraints can be inspected using
2685 the following functions.
2687 isl_bool isl_constraint_is_lower_bound(
2688 __isl_keep isl_constraint *constraint,
2689 enum isl_dim_type type, unsigned pos);
2690 isl_bool isl_constraint_is_upper_bound(
2691 __isl_keep isl_constraint *constraint,
2692 enum isl_dim_type type, unsigned pos);
2693 __isl_give isl_val *isl_constraint_get_constant_val(
2694 __isl_keep isl_constraint *constraint);
2695 __isl_give isl_val *isl_constraint_get_coefficient_val(
2696 __isl_keep isl_constraint *constraint,
2697 enum isl_dim_type type, int pos);
2699 The explicit representations of the existentially quantified
2700 variables can be inspected using the following function.
2701 Note that the user is only allowed to use this function
2702 if the inspected set or map is the result of a call
2703 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2704 The existentially quantified variable is equal to the floor
2705 of the returned affine expression. The affine expression
2706 itself can be inspected using the functions in
2709 __isl_give isl_aff *isl_constraint_get_div(
2710 __isl_keep isl_constraint *constraint, int pos);
2712 To obtain the constraints of a basic set or map in matrix
2713 form, use the following functions.
2715 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2716 __isl_keep isl_basic_set *bset,
2717 enum isl_dim_type c1, enum isl_dim_type c2,
2718 enum isl_dim_type c3, enum isl_dim_type c4);
2719 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2720 __isl_keep isl_basic_set *bset,
2721 enum isl_dim_type c1, enum isl_dim_type c2,
2722 enum isl_dim_type c3, enum isl_dim_type c4);
2723 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2724 __isl_keep isl_basic_map *bmap,
2725 enum isl_dim_type c1,
2726 enum isl_dim_type c2, enum isl_dim_type c3,
2727 enum isl_dim_type c4, enum isl_dim_type c5);
2728 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2729 __isl_keep isl_basic_map *bmap,
2730 enum isl_dim_type c1,
2731 enum isl_dim_type c2, enum isl_dim_type c3,
2732 enum isl_dim_type c4, enum isl_dim_type c5);
2734 The C<isl_dim_type> arguments dictate the order in which
2735 different kinds of variables appear in the resulting matrix.
2736 For set inputs, they should be a permutation of
2737 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2739 For map inputs, they should be a permutation of
2740 C<isl_dim_cst>, C<isl_dim_param>,
2741 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2745 Points are elements of a set. They can be used to construct
2746 simple sets (boxes) or they can be used to represent the
2747 individual elements of a set.
2748 The zero point (the origin) can be created using
2750 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2752 The coordinates of a point can be inspected, set and changed
2755 #include <isl/point.h>
2756 __isl_give isl_multi_val *isl_point_get_multi_val(
2757 __isl_keep isl_point *pnt);
2758 __isl_give isl_val *isl_point_get_coordinate_val(
2759 __isl_keep isl_point *pnt,
2760 enum isl_dim_type type, int pos);
2761 __isl_give isl_point *isl_point_set_coordinate_val(
2762 __isl_take isl_point *pnt,
2763 enum isl_dim_type type, int pos,
2764 __isl_take isl_val *v);
2766 __isl_give isl_point *isl_point_add_ui(
2767 __isl_take isl_point *pnt,
2768 enum isl_dim_type type, int pos, unsigned val);
2769 __isl_give isl_point *isl_point_sub_ui(
2770 __isl_take isl_point *pnt,
2771 enum isl_dim_type type, int pos, unsigned val);
2773 Points can be copied or freed using
2775 __isl_give isl_point *isl_point_copy(
2776 __isl_keep isl_point *pnt);
2777 __isl_null isl_point *isl_point_free(
2778 __isl_take isl_point *pnt);
2780 A singleton set can be created from a point using the following functions.
2782 __isl_give isl_basic_set *isl_basic_set_from_point(
2783 __isl_take isl_point *pnt);
2784 __isl_give isl_set *isl_point_to_set(
2785 __isl_take isl_point *pnt);
2786 __isl_give isl_set *isl_set_from_point(
2787 __isl_take isl_point *pnt);
2788 __isl_give isl_union_set *isl_union_set_from_point(
2789 __isl_take isl_point *pnt);
2791 C<isl_point_to_set> and C<isl_set_from_point> perform
2794 A box can be created from two opposite extremal points using
2796 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2797 __isl_take isl_point *pnt1,
2798 __isl_take isl_point *pnt2);
2799 __isl_give isl_set *isl_set_box_from_points(
2800 __isl_take isl_point *pnt1,
2801 __isl_take isl_point *pnt2);
2803 All elements of a B<bounded> (union) set can be enumerated using
2804 the following functions.
2806 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2807 isl_stat (*fn)(__isl_take isl_point *pnt,
2810 isl_stat isl_union_set_foreach_point(
2811 __isl_keep isl_union_set *uset,
2812 isl_stat (*fn)(__isl_take isl_point *pnt,
2816 The function C<fn> is called for each integer point in
2817 C<set> with as second argument the last argument of
2818 the C<isl_set_foreach_point> call. The function C<fn>
2819 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2820 In the latter case, C<isl_set_foreach_point> will stop
2821 enumerating and return C<isl_stat_error> as well.
2822 If the enumeration is performed successfully and to completion,
2823 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2825 To obtain a single point of a (basic or union) set, use
2827 __isl_give isl_point *isl_basic_set_sample_point(
2828 __isl_take isl_basic_set *bset);
2829 __isl_give isl_point *isl_set_sample_point(
2830 __isl_take isl_set *set);
2831 __isl_give isl_point *isl_union_set_sample_point(
2832 __isl_take isl_union_set *uset);
2834 If C<set> does not contain any (integer) points, then the
2835 resulting point will be ``void'', a property that can be
2838 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2842 Besides sets and relation, C<isl> also supports various types of functions.
2843 Each of these types is derived from the value type (see L</"Values">)
2844 or from one of two primitive function types
2845 through the application of zero or more type constructors.
2846 As a special case, a multiple expression can also be derived
2847 from an identifier (see L</"Identifiers">) although the result
2848 is not really a function.
2849 We first describe the primitive type and then we describe
2850 the types derived from these primitive types.
2852 =head3 Primitive Functions
2854 C<isl> support two primitive function types, quasi-affine
2855 expressions and quasipolynomials.
2856 A quasi-affine expression is defined either over a parameter
2857 space or over a set and is composed of integer constants,
2858 parameters and set variables, addition, subtraction and
2859 integer division by an integer constant.
2860 For example, the quasi-affine expression
2862 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2864 maps C<x> to C<2*floor((4 n + x)/9>.
2865 A quasipolynomial is a polynomial expression in quasi-affine
2866 expression. That is, it additionally allows for multiplication.
2867 Note, though, that it is not allowed to construct an integer
2868 division of an expression involving multiplications.
2869 Here is an example of a quasipolynomial that is not
2870 quasi-affine expression
2872 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2874 Note that the external representations of quasi-affine expressions
2875 and quasipolynomials are different. Quasi-affine expressions
2876 use a notation with square brackets just like binary relations,
2877 while quasipolynomials do not. This might change at some point.
2879 If a primitive function is defined over a parameter space,
2880 then the space of the function itself is that of a set.
2881 If it is defined over a set, then the space of the function
2882 is that of a relation. In both cases, the set space (or
2883 the output space) is single-dimensional, anonymous and unstructured.
2884 To create functions with multiple dimensions or with other kinds
2885 of set or output spaces, use multiple expressions
2886 (see L</"Multiple Expressions">).
2890 =item * Quasi-affine Expressions
2892 Besides the expressions described above, a quasi-affine
2893 expression can also be set to NaN. Such expressions
2894 typically represent a failure to represent a result
2895 as a quasi-affine expression.
2897 The zero quasi affine expression or the quasi affine expression
2898 that is equal to a given value, parameter or
2899 a specified dimension on a given domain can be created using
2901 #include <isl/aff.h>
2902 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2903 __isl_take isl_space *space);
2904 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2905 __isl_take isl_space *space);
2906 __isl_give isl_aff *isl_aff_zero_on_domain(
2907 __isl_take isl_local_space *ls);
2908 __isl_give isl_aff *isl_aff_val_on_domain_space(
2909 __isl_take isl_space *space,
2910 __isl_take isl_val *val);
2911 __isl_give isl_aff *isl_aff_val_on_domain(
2912 __isl_take isl_local_space *ls,
2913 __isl_take isl_val *val);
2914 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2915 __isl_take isl_space *space,
2916 __isl_take isl_id *id);
2917 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2918 __isl_take isl_space *space,
2919 __isl_take isl_id *id);
2920 __isl_give isl_aff *isl_aff_var_on_domain(
2921 __isl_take isl_local_space *ls,
2922 enum isl_dim_type type, unsigned pos);
2923 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2924 __isl_take isl_space *space);
2925 __isl_give isl_aff *isl_aff_nan_on_domain(
2926 __isl_take isl_local_space *ls);
2928 The space passed to C<isl_aff_param_on_domain_space_id>
2929 is required to have a parameter with the given identifier.
2930 C<isl_aff_param_on_domain_space_id> and
2931 C<isl_space_param_aff_on_domain_id> perform the same operation.
2933 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2934 perform the same operation.
2936 Quasi affine expressions can be copied and freed using
2938 #include <isl/aff.h>
2939 __isl_give isl_aff *isl_aff_copy(
2940 __isl_keep isl_aff *aff);
2941 __isl_null isl_aff *isl_aff_free(
2942 __isl_take isl_aff *aff);
2944 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2945 using the following function. The constraint is required to have
2946 a non-zero coefficient for the specified dimension.
2948 #include <isl/constraint.h>
2949 __isl_give isl_aff *isl_constraint_get_bound(
2950 __isl_keep isl_constraint *constraint,
2951 enum isl_dim_type type, int pos);
2953 The entire affine expression of the constraint can also be extracted
2954 using the following function.
2956 #include <isl/constraint.h>
2957 __isl_give isl_aff *isl_constraint_get_aff(
2958 __isl_keep isl_constraint *constraint);
2960 Conversely, an equality constraint equating
2961 the affine expression to zero or an inequality constraint enforcing
2962 the affine expression to be non-negative, can be constructed using
2964 __isl_give isl_constraint *isl_equality_from_aff(
2965 __isl_take isl_aff *aff);
2966 __isl_give isl_constraint *isl_inequality_from_aff(
2967 __isl_take isl_aff *aff);
2969 The coefficients and the integer divisions of an affine expression
2970 can be inspected using the following functions.
2972 #include <isl/aff.h>
2973 __isl_give isl_val *isl_aff_get_constant_val(
2974 __isl_keep isl_aff *aff);
2975 __isl_give isl_val *isl_aff_get_coefficient_val(
2976 __isl_keep isl_aff *aff,
2977 enum isl_dim_type type, int pos);
2978 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2979 enum isl_dim_type type, int pos);
2980 __isl_give isl_val *isl_aff_get_denominator_val(
2981 __isl_keep isl_aff *aff);
2982 __isl_give isl_aff *isl_aff_get_div(
2983 __isl_keep isl_aff *aff, int pos);
2985 They can be modified using the following functions.
2987 #include <isl/aff.h>
2988 __isl_give isl_aff *isl_aff_set_constant_si(
2989 __isl_take isl_aff *aff, int v);
2990 __isl_give isl_aff *isl_aff_set_constant_val(
2991 __isl_take isl_aff *aff, __isl_take isl_val *v);
2992 __isl_give isl_aff *isl_aff_set_coefficient_si(
2993 __isl_take isl_aff *aff,
2994 enum isl_dim_type type, int pos, int v);
2995 __isl_give isl_aff *isl_aff_set_coefficient_val(
2996 __isl_take isl_aff *aff,
2997 enum isl_dim_type type, int pos,
2998 __isl_take isl_val *v);
3000 __isl_give isl_aff *isl_aff_add_constant_si(
3001 __isl_take isl_aff *aff, int v);
3002 __isl_give isl_aff *isl_aff_add_constant_val(
3003 __isl_take isl_aff *aff, __isl_take isl_val *v);
3004 __isl_give isl_aff *isl_aff_add_constant_num_si(
3005 __isl_take isl_aff *aff, int v);
3006 __isl_give isl_aff *isl_aff_add_coefficient_si(
3007 __isl_take isl_aff *aff,
3008 enum isl_dim_type type, int pos, int v);
3009 __isl_give isl_aff *isl_aff_add_coefficient_val(
3010 __isl_take isl_aff *aff,
3011 enum isl_dim_type type, int pos,
3012 __isl_take isl_val *v);
3014 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3015 set the I<numerator> of the constant or coefficient, while
3016 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3017 the constant or coefficient as a whole.
3018 The C<add_constant> and C<add_coefficient> functions add an integer
3019 or rational value to
3020 the possibly rational constant or coefficient.
3021 The C<add_constant_num> functions add an integer value to
3024 =item * Quasipolynomials
3026 Some simple quasipolynomials can be created using the following functions.
3028 #include <isl/polynomial.h>
3029 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3030 __isl_take isl_space *domain);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3032 __isl_take isl_space *domain);
3033 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3034 __isl_take isl_space *domain);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3036 __isl_take isl_space *domain);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3038 __isl_take isl_space *domain);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3040 __isl_take isl_space *domain,
3041 __isl_take isl_val *val);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3043 __isl_take isl_space *domain,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3046 __isl_take isl_aff *aff);
3048 Recall that the space in which a quasipolynomial lives is a map space
3049 with a one-dimensional range. The C<domain> argument in some of
3050 the functions above corresponds to the domain of this map space.
3052 A quasi-polynomial that can also be represented as a quasi-affine expression
3053 can be converted using the function below.
3055 #include <isl/polynomial.h>
3056 isl_bool isl_qpolynomial_isa_aff(
3057 __isl_keep isl_qpolynomial *qp);
3058 __isl_give isl_aff *isl_qpolynomial_as_aff(
3059 __isl_take isl_qpolynomial *qp);
3061 Quasipolynomials can be copied and freed again using the following
3064 #include <isl/polynomial.h>
3065 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3066 __isl_keep isl_qpolynomial *qp);
3067 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3068 __isl_take isl_qpolynomial *qp);
3070 The constant term of a quasipolynomial can be extracted using
3072 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3073 __isl_keep isl_qpolynomial *qp);
3075 To iterate over all terms in a quasipolynomial,
3078 isl_stat isl_qpolynomial_foreach_term(
3079 __isl_keep isl_qpolynomial *qp,
3080 isl_stat (*fn)(__isl_take isl_term *term,
3081 void *user), void *user);
3083 The terms themselves can be inspected and freed using
3086 isl_size isl_term_dim(__isl_keep isl_term *term,
3087 enum isl_dim_type type);
3088 __isl_give isl_val *isl_term_get_coefficient_val(
3089 __isl_keep isl_term *term);
3090 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3091 enum isl_dim_type type, unsigned pos);
3092 __isl_give isl_aff *isl_term_get_div(
3093 __isl_keep isl_term *term, unsigned pos);
3094 __isl_null isl_term *isl_term_free(
3095 __isl_take isl_term *term);
3097 Each term is a product of parameters, set variables and
3098 integer divisions. The function C<isl_term_get_exp>
3099 returns the exponent of a given dimensions in the given term.
3105 A reduction represents a maximum or a minimum of its
3107 The only reduction type defined by C<isl> is
3108 C<isl_qpolynomial_fold>.
3110 There are currently no functions to directly create such
3111 objects, but they do appear in the piecewise quasipolynomial
3112 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3114 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3116 Reductions can be copied and freed using
3117 the following functions.
3119 #include <isl/polynomial.h>
3120 __isl_give isl_qpolynomial_fold *
3121 isl_qpolynomial_fold_copy(
3122 __isl_keep isl_qpolynomial_fold *fold);
3123 __isl_null isl_qpolynomial_fold *
3124 isl_qpolynomial_fold_free(
3125 __isl_take isl_qpolynomial_fold *fold);
3127 The type of a (union piecewise) reduction
3128 can be obtained using the following functions.
3130 #include <isl/polynomial.h>
3131 enum isl_fold isl_qpolynomial_fold_get_type(
3132 __isl_keep isl_qpolynomial_fold *fold);
3133 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3134 __isl_keep isl_pw_qpolynomial_fold *pwf);
3135 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3136 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3138 The type may be either C<isl_fold_min> or C<isl_fold_max>
3139 (or C<isl_fold_error> in case of error).
3141 To iterate over all quasipolynomials in a reduction, use
3143 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3144 __isl_keep isl_qpolynomial_fold *fold,
3145 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3146 void *user), void *user);
3148 =head3 Multiple Expressions
3150 A multiple expression represents a sequence of zero or
3151 more base expressions, all defined on the same domain space.
3152 The domain space of the multiple expression is the same
3153 as that of the base expressions, but the range space
3154 can be any space. In case the base expressions have
3155 a set space, the corresponding multiple expression
3156 also has a set space.
3157 Objects of the value or identifier type do not have an associated space.
3158 The space of a multiple value or
3159 multiple identifier is therefore always a set space.
3160 Similarly, the space of a multiple union piecewise
3161 affine expression is always a set space.
3162 If the base expressions are not total, then
3163 a corresponding zero-dimensional multiple expression may
3164 have an explicit domain that keeps track of the domain
3165 outside of any base expressions.
3167 The multiple expression types defined by C<isl>
3168 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3169 C<isl_multi_union_pw_aff>.
3171 A multiple expression with the value zero for
3172 each output (or set) dimension can be created
3173 using the following functions.
3175 #include <isl/val.h>
3176 __isl_give isl_multi_val *isl_multi_val_zero(
3177 __isl_take isl_space *space);
3178 __isl_give isl_multi_val *isl_space_zero_multi_val(
3179 __isl_take isl_space *space);
3181 #include <isl/aff.h>
3182 __isl_give isl_multi_aff *isl_multi_aff_zero(
3183 __isl_take isl_space *space);
3184 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3185 __isl_take isl_space *space);
3186 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3187 __isl_take isl_space *space);
3188 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3189 __isl_take isl_space *space);
3190 __isl_give isl_multi_union_pw_aff *
3191 isl_multi_union_pw_aff_zero(
3192 __isl_take isl_space *space);
3193 __isl_give isl_multi_union_pw_aff *
3194 isl_space_zero_multi_union_pw_aff(
3195 __isl_take isl_space *space);
3197 Since there is no canonical way of representing a zero
3198 value of type C<isl_union_pw_aff>, the space passed
3199 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3200 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3201 perform the same operation.
3203 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3204 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3205 for the pair C<isl_multi_union_pw_aff_zero> and
3206 C<isl_space_zero_multi_union_pw_aff>.
3209 An identity function can be created using the following
3211 For the first group of functions, the space needs to be that of a set.
3212 For the second group,
3213 the space needs to be that of a relation
3214 with the same number of input and output dimensions.
3215 For the third group, the input function needs to live in a space
3216 with the same number of input and output dimensions and
3217 the identity function is created in that space.
3219 #include <isl/aff.h>
3220 __isl_give isl_multi_aff *
3221 isl_multi_aff_identity_on_domain_space(
3222 __isl_take isl_space *space);
3223 __isl_give isl_multi_aff *
3224 isl_space_identity_multi_aff_on_domain(
3225 __isl_take isl_space *space);
3226 __isl_give isl_multi_pw_aff *
3227 isl_multi_pw_aff_identity_on_domain_space(
3228 __isl_take isl_space *space);
3229 __isl_give isl_multi_pw_aff *
3230 isl_space_identity_multi_pw_aff_on_domain(
3231 __isl_take isl_space *space);
3232 __isl_give isl_multi_aff *isl_multi_aff_identity(
3233 __isl_take isl_space *space);
3234 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3235 __isl_take isl_space *space);
3236 __isl_give isl_multi_aff *
3237 isl_multi_aff_identity_multi_aff(
3238 __isl_take isl_multi_aff *ma);
3239 __isl_give isl_multi_pw_aff *
3240 isl_multi_pw_aff_identity_multi_pw_aff(
3241 __isl_take isl_multi_pw_aff *mpa);
3243 C<isl_multi_aff_identity_on_domain_space> and
3244 C<isl_space_identity_multi_aff_on_domain>
3245 perform the same operation.
3247 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3248 C<isl_space_identity_multi_pw_aff_on_domain>.
3250 A function that performs a projection on a universe
3251 relation or set can be created using the following functions.
3252 See also the corresponding
3253 projection operations in L</"Unary Operations">.
3255 #include <isl/aff.h>
3256 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3257 __isl_take isl_space *space);
3258 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3259 __isl_take isl_space *space);
3260 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3261 __isl_take isl_space *space);
3262 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3263 __isl_take isl_space *space);
3264 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3265 __isl_take isl_space *space,
3266 enum isl_dim_type type,
3267 unsigned first, unsigned n);
3269 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3272 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3274 A multiple expression can be created from a single
3275 base expression using the following functions.
3276 The space of the created multiple expression is the same
3277 as that of the base expression, except for
3278 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3279 lives in a parameter space and the output lives
3280 in a single-dimensional set space.
3282 #include <isl/aff.h>
3283 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3284 __isl_take isl_aff *aff);
3285 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3286 __isl_take isl_pw_aff *pa);
3287 __isl_give isl_multi_union_pw_aff *
3288 isl_multi_union_pw_aff_from_union_pw_aff(
3289 __isl_take isl_union_pw_aff *upa);
3291 A multiple expression can be created from a list
3292 of base expression in a specified space.
3293 The domain of this space needs to be the same
3294 as the domains of the base expressions in the list.
3295 If the base expressions have a set space (or no associated space),
3296 then this space also needs to be a set space.
3299 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3300 __isl_take isl_space *space,
3301 __isl_take isl_id_list *list);
3302 __isl_give isl_multi_id *isl_space_multi_id(
3303 __isl_take isl_space *space,
3304 __isl_take isl_id_list *list);
3306 #include <isl/val.h>
3307 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3308 __isl_take isl_space *space,
3309 __isl_take isl_val_list *list);
3310 __isl_give isl_multi_val *isl_space_multi_val(
3311 __isl_take isl_space *space,
3312 __isl_take isl_val_list *list);
3314 #include <isl/aff.h>
3315 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3316 __isl_take isl_space *space,
3317 __isl_take isl_aff_list *list);
3318 __isl_give isl_multi_aff *isl_space_multi_aff(
3319 __isl_take isl_space *space,
3320 __isl_take isl_aff_list *list);
3321 __isl_give isl_multi_pw_aff *
3322 isl_multi_pw_aff_from_pw_aff_list(
3323 __isl_take isl_space *space,
3324 __isl_take isl_pw_aff_list *list);
3325 __isl_give isl_multi_pw_aff *
3326 isl_space_multi_pw_aff(
3327 __isl_take isl_space *space,
3328 __isl_take isl_pw_aff_list *list);
3329 __isl_give isl_multi_union_pw_aff *
3330 isl_multi_union_pw_aff_from_union_pw_aff_list(
3331 __isl_take isl_space *space,
3332 __isl_take isl_union_pw_aff_list *list);
3333 __isl_give isl_multi_union_pw_aff *
3334 isl_space_multi_union_pw_aff(
3335 __isl_take isl_space *space,
3336 __isl_take isl_union_pw_aff_list *list);
3338 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3340 Similarly for the pair C<isl_multi_val_from_val_list> and
3341 C<isl_space_multi_val>,
3342 for the pair C<isl_multi_aff_from_aff_list> and
3343 C<isl_space_multi_aff>,
3344 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3345 C<isl_space_multi_pw_aff> and
3346 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3347 C<isl_space_multi_union_pw_aff>.
3349 As a convenience, a multiple piecewise expression can
3350 also be created from a multiple expression,
3351 or even directly from a single base expression.
3352 Each piecewise expression in the result has a single
3355 #include <isl/aff.h>
3356 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3357 __isl_take isl_aff *aff);
3358 __isl_give isl_multi_pw_aff *
3359 isl_multi_aff_to_multi_pw_aff(
3360 __isl_take isl_multi_aff *ma);
3361 __isl_give isl_multi_pw_aff *
3362 isl_multi_pw_aff_from_multi_aff(
3363 __isl_take isl_multi_aff *ma);
3365 C<isl_multi_aff_to_multi_pw_aff> and
3366 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3368 Similarly, a multiple union expression can be
3369 created from a multiple expression.
3371 #include <isl/aff.h>
3372 __isl_give isl_multi_union_pw_aff *
3373 isl_multi_union_pw_aff_from_multi_aff(
3374 __isl_take isl_multi_aff *ma);
3375 __isl_give isl_multi_union_pw_aff *
3376 isl_multi_aff_to_multi_union_pw_aff(
3377 __isl_take isl_multi_aff *ma);
3378 __isl_give isl_multi_union_pw_aff *
3379 isl_multi_union_pw_aff_from_multi_pw_aff(
3380 __isl_take isl_multi_pw_aff *mpa);
3382 C<isl_multi_aff_to_multi_union_pw_aff> and
3383 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3385 A multiple quasi-affine expression can be created from
3386 a multiple value with a given domain space using the following
3389 #include <isl/aff.h>
3390 __isl_give isl_multi_aff *
3391 isl_multi_aff_multi_val_on_domain_space(
3392 __isl_take isl_space *space,
3393 __isl_take isl_multi_val *mv);
3394 __isl_give isl_multi_aff *
3395 isl_space_multi_aff_on_domain_multi_val(
3396 __isl_take isl_space *space,
3397 __isl_take isl_multi_val *mv);
3398 __isl_give isl_multi_aff *
3399 isl_multi_aff_multi_val_on_space(
3400 __isl_take isl_space *space,
3401 __isl_take isl_multi_val *mv);
3403 C<isl_space_multi_aff_on_domain_multi_val> and
3404 C<isl_multi_aff_multi_val_on_space> are alternative names
3405 for C<isl_multi_aff_multi_val_on_domain_space>.
3408 a multiple union piecewise affine expression can be created from
3409 a multiple value with a given domain or
3410 a (piecewise) multiple affine expression with a given domain
3411 using the following functions.
3413 #include <isl/aff.h>
3414 __isl_give isl_multi_union_pw_aff *
3415 isl_multi_union_pw_aff_multi_val_on_domain(
3416 __isl_take isl_union_set *domain,
3417 __isl_take isl_multi_val *mv);
3418 __isl_give isl_multi_union_pw_aff *
3419 isl_multi_union_pw_aff_multi_aff_on_domain(
3420 __isl_take isl_union_set *domain,
3421 __isl_take isl_multi_aff *ma);
3422 __isl_give isl_multi_union_pw_aff *
3423 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3424 __isl_take isl_union_set *domain,
3425 __isl_take isl_pw_multi_aff *pma);
3427 Multiple expressions can be copied and freed using
3428 the following functions.
3431 __isl_give isl_multi_id *isl_multi_id_copy(
3432 __isl_keep isl_multi_id *mi);
3433 __isl_null isl_multi_id *isl_multi_id_free(
3434 __isl_take isl_multi_id *mi);
3436 #include <isl/val.h>
3437 __isl_give isl_multi_val *isl_multi_val_copy(
3438 __isl_keep isl_multi_val *mv);
3439 __isl_null isl_multi_val *isl_multi_val_free(
3440 __isl_take isl_multi_val *mv);
3442 #include <isl/aff.h>
3443 __isl_give isl_multi_aff *isl_multi_aff_copy(
3444 __isl_keep isl_multi_aff *maff);
3445 __isl_null isl_multi_aff *isl_multi_aff_free(
3446 __isl_take isl_multi_aff *maff);
3447 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3448 __isl_keep isl_multi_pw_aff *mpa);
3449 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3450 __isl_take isl_multi_pw_aff *mpa);
3451 __isl_give isl_multi_union_pw_aff *
3452 isl_multi_union_pw_aff_copy(
3453 __isl_keep isl_multi_union_pw_aff *mupa);
3454 __isl_null isl_multi_union_pw_aff *
3455 isl_multi_union_pw_aff_free(
3456 __isl_take isl_multi_union_pw_aff *mupa);
3458 The number of base expressions in a multiple
3459 expression can be obtained using the following functions.
3462 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3464 #include <isl/val.h>
3465 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3467 #include <isl/aff.h>
3468 isl_size isl_multi_aff_size(
3469 __isl_keep isl_multi_aff *multi);
3470 isl_size isl_multi_pw_aff_size(
3471 __isl_keep isl_multi_pw_aff *mpa);
3472 isl_size isl_multi_union_pw_aff_size(
3473 __isl_keep isl_multi_union_pw_aff *mupa);
3475 The base expression at a given position of a multiple
3476 expression can be extracted using the following functions.
3479 __isl_give isl_id *isl_multi_id_get_at(
3480 __isl_keep isl_multi_id *mi, int pos);
3481 __isl_give isl_id *isl_multi_id_get_id(
3482 __isl_keep isl_multi_id *mi, int pos);
3484 #include <isl/val.h>
3485 __isl_give isl_val *isl_multi_val_get_at(
3486 __isl_keep isl_multi_val *mv, int pos);
3487 __isl_give isl_val *isl_multi_val_get_val(
3488 __isl_keep isl_multi_val *mv, int pos);
3490 #include <isl/aff.h>
3491 __isl_give isl_aff *isl_multi_aff_get_at(
3492 __isl_keep isl_multi_aff *ma, int pos);
3493 __isl_give isl_aff *isl_multi_aff_get_aff(
3494 __isl_keep isl_multi_aff *multi, int pos);
3495 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3496 __isl_keep isl_multi_pw_aff *mpa, int pos);
3497 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3498 __isl_keep isl_multi_pw_aff *mpa, int pos);
3499 __isl_give isl_union_pw_aff *
3500 isl_multi_union_pw_aff_get_at(
3501 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3502 __isl_give isl_union_pw_aff *
3503 isl_multi_union_pw_aff_get_union_pw_aff(
3504 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3506 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3507 Similarly for the other pairs of functions.
3509 The base expression can be replaced using the following functions.
3512 __isl_give isl_multi_id *isl_multi_id_set_at(
3513 __isl_take isl_multi_id *mi, int pos,
3514 __isl_take isl_id *id);
3515 __isl_give isl_multi_id *isl_multi_id_set_id(
3516 __isl_take isl_multi_id *mi, int pos,
3517 __isl_take isl_id *id);
3519 #include <isl/val.h>
3520 __isl_give isl_multi_val *isl_multi_val_set_at(
3521 __isl_take isl_multi_val *mv, int pos,
3522 __isl_take isl_val *val);
3523 __isl_give isl_multi_val *isl_multi_val_set_val(
3524 __isl_take isl_multi_val *mv, int pos,
3525 __isl_take isl_val *val);
3527 #include <isl/aff.h>
3528 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3529 __isl_take isl_multi_aff *ma, int pos,
3530 __isl_take isl_aff *aff);
3531 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3532 __isl_take isl_multi_aff *multi, int pos,
3533 __isl_take isl_aff *aff);
3534 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3535 __isl_take isl_multi_pw_aff *mpa, int pos,
3536 __isl_take isl_pw_aff *pa);
3537 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3538 __isl_take isl_multi_pw_aff *mpa, int pos,
3539 __isl_take isl_pw_aff *pa);
3540 __isl_give isl_multi_union_pw_aff *
3541 isl_multi_union_pw_aff_set_at(
3542 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3543 __isl_take isl_union_pw_aff *upa);
3544 __isl_give isl_multi_union_pw_aff *
3545 isl_multi_union_pw_aff_set_union_pw_aff(
3546 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3547 __isl_take isl_union_pw_aff *upa);
3549 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3550 Similarly for the other pairs of functions.
3552 A list of all base expressions of a multiple
3553 expression can be extracted using the following functions.
3556 __isl_give isl_id_list *isl_multi_id_get_list(
3557 __isl_keep isl_multi_id *mi);
3559 #include <isl/val.h>
3560 __isl_give isl_val_list *isl_multi_val_get_list(
3561 __isl_keep isl_multi_val *mv);
3563 #include <isl/aff.h>
3564 __isl_give isl_aff_list *isl_multi_aff_get_list(
3565 __isl_keep isl_multi_aff *multi);
3566 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3567 __isl_keep isl_multi_pw_aff *mpa);
3568 __isl_give isl_union_pw_aff_list *
3569 isl_multi_union_pw_aff_list(
3570 __isl_keep isl_multi_union_pw_aff *mupa);
3572 The constant terms of the base expressions can be obtained using
3573 the following function.
3575 #include <isl/aff.h>
3576 __isl_give isl_multi_val *
3577 isl_multi_aff_get_constant_multi_val(
3578 __isl_keep isl_multi_aff *ma);
3580 As a convenience, a sequence of base expressions that have
3581 their domains in a given space can be extracted from a sequence
3582 of union expressions using the following function.
3584 #include <isl/aff.h>
3585 __isl_give isl_multi_pw_aff *
3586 isl_multi_union_pw_aff_extract_multi_pw_aff(
3587 __isl_keep isl_multi_union_pw_aff *mupa,
3588 __isl_take isl_space *space);
3590 Note that there is a difference between C<isl_multi_union_pw_aff>
3591 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3592 of unions of piecewise expressions, while the second is a union
3593 of piecewise sequences. In particular, multiple affine expressions
3594 in an C<isl_union_pw_multi_aff> may live in different spaces,
3595 while there is only a single multiple expression in
3596 an C<isl_multi_union_pw_aff>, which can therefore only live
3597 in a single space. This means that not every
3598 C<isl_union_pw_multi_aff> can be converted to
3599 an C<isl_multi_union_pw_aff>. Conversely, the elements
3600 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3601 while each multiple expression inside an C<isl_union_pw_multi_aff>
3602 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3603 of dimension greater than one may therefore not be exact.
3604 The following functions can
3605 be used to perform these conversions when they are possible.
3607 #include <isl/aff.h>
3608 __isl_give isl_multi_union_pw_aff *
3609 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3610 __isl_take isl_union_pw_multi_aff *upma);
3611 __isl_give isl_multi_union_pw_aff *
3612 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3613 __isl_take isl_union_pw_multi_aff *upma);
3614 __isl_give isl_union_pw_multi_aff *
3615 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3616 __isl_take isl_multi_union_pw_aff *mupa);
3618 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3619 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3620 perform the same operation.
3622 =head3 Piecewise Expressions
3624 A piecewise expression is an expression that is described
3625 using zero or more base expression defined over the same
3626 number of cells in the domain space of the base expressions.
3627 All base expressions are defined over the same
3628 domain space and the cells are disjoint.
3629 The space of a piecewise expression is the same as
3630 that of the base expressions.
3631 If the union of the cells is a strict subset of the domain
3632 space, then the value of the piecewise expression outside
3633 this union is different for types derived from quasi-affine
3634 expressions and those derived from quasipolynomials.
3635 Piecewise expressions derived from quasi-affine expressions
3636 are considered to be undefined outside the union of their cells.
3637 Piecewise expressions derived from quasipolynomials
3638 are considered to be zero outside the union of their cells.
3640 Piecewise quasipolynomials are mainly used by the C<barvinok>
3641 library for representing the number of elements in a parametric set or map.
3642 For example, the piecewise quasipolynomial
3644 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3646 represents the number of points in the map
3648 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3650 The piecewise expression types defined by C<isl>
3651 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3652 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3654 A piecewise expression with no cells can be created using
3655 the following functions.
3657 #include <isl/aff.h>
3658 __isl_give isl_pw_aff *isl_pw_aff_empty(
3659 __isl_take isl_space *space);
3660 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3661 __isl_take isl_space *space);
3663 A piecewise expression with a single universe cell can be
3664 created using the following functions.
3666 #include <isl/aff.h>
3667 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3668 __isl_take isl_aff *aff);
3669 __isl_give isl_pw_multi_aff *
3670 isl_multi_aff_to_pw_multi_aff(
3671 __isl_take isl_multi_aff *ma);
3672 __isl_give isl_pw_multi_aff *
3673 isl_pw_multi_aff_from_multi_aff(
3674 __isl_take isl_multi_aff *ma);
3676 #include <isl/polynomial.h>
3677 __isl_give isl_pw_qpolynomial *
3678 isl_pw_qpolynomial_from_qpolynomial(
3679 __isl_take isl_qpolynomial *qp);
3680 __isl_give isl_pw_qpolynomial_fold *
3681 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3682 __isl_take isl_qpolynomial_fold *fold);
3684 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3687 The inverse conversions below can only be used if the input
3688 expression is known to be defined over a single universe domain.
3690 #include <isl/aff.h>
3691 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3692 __isl_give isl_aff *isl_pw_aff_as_aff(
3693 __isl_take isl_pw_aff *pa);
3694 isl_bool isl_multi_pw_aff_isa_multi_aff(
3695 __isl_keep isl_multi_pw_aff *mpa);
3696 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3697 __isl_take isl_multi_pw_aff *mpa);
3698 isl_bool isl_pw_multi_aff_isa_multi_aff(
3699 __isl_keep isl_pw_multi_aff *pma);
3700 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3701 __isl_take isl_pw_multi_aff *pma);
3703 #include <isl/polynomial.h>
3704 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3705 __isl_keep isl_pw_qpolynomial *pwqp);
3706 __isl_give isl_qpolynomial *
3707 isl_pw_qpolynomial_as_qpolynomial(
3708 __isl_take isl_pw_qpolynomial *pwqp);
3709 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3710 __isl_keep isl_pw_qpolynomial_fold *pwf);
3711 __isl_give isl_qpolynomial_fold *
3712 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3713 __isl_take isl_pw_qpolynomial_fold *pwf);
3715 A piecewise expression with a single specified cell can be
3716 created using the following functions.
3718 #include <isl/aff.h>
3719 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3720 __isl_take isl_set *set, __isl_take isl_aff *aff);
3721 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3722 __isl_take isl_set *set,
3723 __isl_take isl_multi_aff *maff);
3725 #include <isl/polynomial.h>
3726 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3727 __isl_take isl_set *set,
3728 __isl_take isl_qpolynomial *qp);
3730 The following convenience functions first create a base expression and
3731 then create a piecewise expression over a universe domain.
3733 #include <isl/aff.h>
3734 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3735 __isl_take isl_local_space *ls);
3736 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3737 __isl_take isl_local_space *ls,
3738 enum isl_dim_type type, unsigned pos);
3739 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3740 __isl_take isl_space *space);
3741 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3742 __isl_take isl_local_space *ls);
3743 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3744 __isl_take isl_space *space);
3745 __isl_give isl_pw_multi_aff *
3746 isl_pw_multi_aff_identity_on_domain_space(
3747 __isl_take isl_space *space)
3748 __isl_give isl_pw_multi_aff *
3749 isl_space_identity_pw_multi_aff_on_domain(
3750 __isl_take isl_space *space)
3751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3752 __isl_take isl_space *space);
3753 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3754 __isl_take isl_space *space);
3755 __isl_give isl_pw_multi_aff *
3756 isl_space_domain_map_pw_multi_aff(
3757 __isl_take isl_space *space);
3758 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3759 __isl_take isl_space *space);
3760 __isl_give isl_pw_multi_aff *
3761 isl_space_range_map_pw_multi_aff(
3762 __isl_take isl_space *space);
3763 __isl_give isl_pw_multi_aff *
3764 isl_pw_multi_aff_project_out_map(
3765 __isl_take isl_space *space,
3766 enum isl_dim_type type,
3767 unsigned first, unsigned n);
3769 #include <isl/polynomial.h>
3770 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3771 __isl_take isl_space *space);
3773 C<isl_pw_multi_aff_identity_on_domain_space> and
3774 C<isl_space_identity_pw_multi_aff_on_domain>
3775 perform the same operation.
3777 for the pair C<isl_pw_multi_aff_domain_map> and
3778 C<isl_space_domain_map_pw_multi_aff> and
3779 for the pair C<isl_pw_multi_aff_range_map> and
3780 C<isl_space_range_map_pw_multi_aff>.
3782 The following convenience functions first create a base expression and
3783 then create a piecewise expression over a given domain.
3785 #include <isl/aff.h>
3786 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3787 __isl_take isl_set *domain,
3788 __isl_take isl_val *v);
3789 __isl_give isl_pw_aff *isl_set_pw_aff_on_domain_val(
3790 __isl_take isl_set *domain,
3791 __isl_take isl_val *v);
3792 __isl_give isl_pw_multi_aff *
3793 isl_pw_multi_aff_multi_val_on_domain(
3794 __isl_take isl_set *domain,
3795 __isl_take isl_multi_val *mv);
3796 __isl_give isl_pw_multi_aff *
3797 isl_set_pw_multi_aff_on_domain_multi_val(
3798 __isl_take isl_set *domain,
3799 __isl_take isl_multi_val *mv);
3800 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3801 __isl_take isl_set *domain,
3802 __isl_take isl_id *id);
3803 __isl_give isl_pw_aff *isl_set_param_pw_aff_on_domain_id(
3804 __isl_take isl_set *domain,
3805 __isl_take isl_id *id);
3807 C<isl_set_pw_aff_on_domain_val> is an alternative name
3808 for C<isl_pw_aff_val_on_domain>.
3809 Similarly for the pair
3810 C<isl_set_pw_multi_aff_on_domain_multi_val> and
3811 C<isl_pw_multi_aff_multi_val_on_domain> and
3812 for the pair C<isl_set_param_pw_aff_on_domain_id> and
3813 C<isl_pw_aff_param_on_domain_id>.
3815 As a convenience, a piecewise multiple expression can
3816 also be created from a piecewise expression.
3817 Each multiple expression in the result is derived
3818 from the corresponding base expression.
3820 #include <isl/aff.h>
3821 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3822 __isl_take isl_pw_aff *pa);
3824 Similarly, a piecewise quasipolynomial can be
3825 created from a piecewise quasi-affine expression using
3826 the following function.
3828 #include <isl/polynomial.h>
3829 __isl_give isl_pw_qpolynomial *
3830 isl_pw_qpolynomial_from_pw_aff(
3831 __isl_take isl_pw_aff *pwaff);
3833 Piecewise expressions can be copied and freed using the following functions.
3835 #include <isl/aff.h>
3836 __isl_give isl_pw_aff *isl_pw_aff_copy(
3837 __isl_keep isl_pw_aff *pwaff);
3838 __isl_null isl_pw_aff *isl_pw_aff_free(
3839 __isl_take isl_pw_aff *pwaff);
3840 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3841 __isl_keep isl_pw_multi_aff *pma);
3842 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3843 __isl_take isl_pw_multi_aff *pma);
3845 #include <isl/polynomial.h>
3846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3847 __isl_keep isl_pw_qpolynomial *pwqp);
3848 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3849 __isl_take isl_pw_qpolynomial *pwqp);
3850 __isl_give isl_pw_qpolynomial_fold *
3851 isl_pw_qpolynomial_fold_copy(
3852 __isl_keep isl_pw_qpolynomial_fold *pwf);
3853 __isl_null isl_pw_qpolynomial_fold *
3854 isl_pw_qpolynomial_fold_free(
3855 __isl_take isl_pw_qpolynomial_fold *pwf);
3857 To iterate over the different cells of a piecewise expression,
3858 use the following functions.
3860 #include <isl/aff.h>
3861 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3862 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3863 isl_stat isl_pw_aff_foreach_piece(
3864 __isl_keep isl_pw_aff *pwaff,
3865 isl_stat (*fn)(__isl_take isl_set *set,
3866 __isl_take isl_aff *aff,
3867 void *user), void *user);
3868 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3869 isl_bool (*test)(__isl_keep isl_set *set,
3870 __isl_keep isl_aff *aff, void *user),
3872 isl_size isl_pw_multi_aff_n_piece(
3873 __isl_keep isl_pw_multi_aff *pma);
3874 isl_stat isl_pw_multi_aff_foreach_piece(
3875 __isl_keep isl_pw_multi_aff *pma,
3876 isl_stat (*fn)(__isl_take isl_set *set,
3877 __isl_take isl_multi_aff *maff,
3878 void *user), void *user);
3879 isl_bool isl_pw_multi_aff_every_piece(
3880 __isl_keep isl_pw_multi_aff *pma,
3881 isl_bool (*test)(__isl_keep isl_set *set,
3882 __isl_keep isl_multi_aff *ma, void *user),
3885 #include <isl/polynomial.h>
3886 isl_size isl_pw_qpolynomial_n_piece(
3887 __isl_keep isl_pw_qpolynomial *pwqp);
3888 isl_stat isl_pw_qpolynomial_foreach_piece(
3889 __isl_keep isl_pw_qpolynomial *pwqp,
3890 isl_stat (*fn)(__isl_take isl_set *set,
3891 __isl_take isl_qpolynomial *qp,
3892 void *user), void *user);
3893 isl_bool isl_pw_qpolynomial_every_piece(
3894 __isl_keep isl_pw_qpolynomial *pwqp,
3895 isl_bool (*test)(__isl_keep isl_set *set,
3896 __isl_keep isl_qpolynomial *qp,
3897 void *user), void *user);
3898 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3899 __isl_keep isl_pw_qpolynomial *pwqp,
3900 isl_stat (*fn)(__isl_take isl_set *set,
3901 __isl_take isl_qpolynomial *qp,
3902 void *user), void *user);
3903 isl_size isl_pw_qpolynomial_fold_n_piece(
3904 __isl_keep isl_pw_qpolynomial_fold *pwf);
3905 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3906 __isl_keep isl_pw_qpolynomial_fold *pwf,
3907 isl_stat (*fn)(__isl_take isl_set *set,
3908 __isl_take isl_qpolynomial_fold *fold,
3909 void *user), void *user);
3910 isl_bool isl_pw_qpolynomial_fold_every_piece(
3911 __isl_keep isl_pw_qpolynomial_fold *pwf,
3912 isl_bool (*test)(__isl_keep isl_set *set,
3913 __isl_keep isl_qpolynomial_fold *fold,
3914 void *user), void *user);
3915 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3916 __isl_keep isl_pw_qpolynomial_fold *pwf,
3917 isl_stat (*fn)(__isl_take isl_set *set,
3918 __isl_take isl_qpolynomial_fold *fold,
3919 void *user), void *user);
3921 As usual, the function C<fn> should return C<isl_stat_ok> on success
3922 and C<isl_stat_error> on failure. The difference between
3923 C<isl_pw_qpolynomial_foreach_piece> and
3924 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3925 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3926 compute unique representations for all existentially quantified
3927 variables and then turn these existentially quantified variables
3928 into extra set variables, adapting the associated quasipolynomial
3929 accordingly. This means that the C<set> passed to C<fn>
3930 will not have any existentially quantified variables, but that
3931 the dimensions of the sets may be different for different
3932 invocations of C<fn>.
3933 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3934 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3935 The function C<isl_pw_aff_every_piece> and its variants
3936 check whether each call to the callback returns true and
3937 stop checking as soon as one of these calls returns false (or error).
3939 A piecewise expression consisting of the expressions at a given
3940 position of a piecewise multiple expression can be extracted
3941 using the following function.
3943 #include <isl/aff.h>
3944 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3945 __isl_keep isl_pw_multi_aff *pma, int pos);
3946 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3947 __isl_keep isl_pw_multi_aff *pma, int pos);
3949 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3950 C<isl_pw_multi_aff_get_at>.
3952 These expressions can be replaced using the following function.
3954 #include <isl/aff.h>
3955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3956 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3957 __isl_take isl_pw_aff *pa);
3959 Note that there is a difference between C<isl_multi_pw_aff> and
3960 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3961 affine expressions, while the second is a piecewise sequence
3962 of affine expressions. In particular, each of the piecewise
3963 affine expressions in an C<isl_multi_pw_aff> may have a different
3964 domain, while all multiple expressions associated to a cell
3965 in an C<isl_pw_multi_aff> have the same domain.
3966 It is possible to convert between the two, but when converting
3967 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3968 of the result is the intersection of the domains of the input.
3969 The reverse conversion is exact.
3971 #include <isl/aff.h>
3972 __isl_give isl_pw_multi_aff *
3973 isl_pw_multi_aff_from_multi_pw_aff(
3974 __isl_take isl_multi_pw_aff *mpa);
3975 __isl_give isl_multi_pw_aff *
3976 isl_pw_multi_aff_to_multi_pw_aff(
3977 __isl_take isl_pw_multi_aff *pma);
3978 __isl_give isl_multi_pw_aff *
3979 isl_multi_pw_aff_from_pw_multi_aff(
3980 __isl_take isl_pw_multi_aff *pma);
3982 C<isl_pw_multi_aff_to_multi_pw_aff> and
3983 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3985 =head3 Union Expressions
3987 A union expression collects base expressions defined
3988 over different domains. The space of a union expression
3989 is that of the shared parameter space.
3991 The union expression types defined by C<isl>
3992 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3993 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3995 C<isl_union_pw_aff>,
3996 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3997 there can be at most one base expression for a given domain space.
3999 C<isl_union_pw_multi_aff>,
4000 there can be multiple such expressions for a given domain space,
4001 but the domains of these expressions need to be disjoint.
4003 An empty union expression can be created using the following functions.
4005 #include <isl/aff.h>
4006 __isl_give isl_union_pw_aff *
4007 isl_union_pw_aff_empty_ctx(
4009 __isl_give isl_union_pw_aff *
4010 isl_union_pw_aff_empty_space(
4011 __isl_take isl_space *space);
4012 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
4013 __isl_take isl_space *space);
4014 __isl_give isl_union_pw_multi_aff *
4015 isl_union_pw_multi_aff_empty_ctx(
4017 __isl_give isl_union_pw_multi_aff *
4018 isl_union_pw_multi_aff_empty_space(
4019 __isl_take isl_space *space);
4020 __isl_give isl_union_pw_multi_aff *
4021 isl_union_pw_multi_aff_empty(
4022 __isl_take isl_space *space);
4024 #include <isl/polynomial.h>
4025 __isl_give isl_union_pw_qpolynomial *
4026 isl_union_pw_qpolynomial_zero_ctx(
4028 __isl_give isl_union_pw_qpolynomial *
4029 isl_union_pw_qpolynomial_zero_space(
4030 __isl_take isl_space *space);
4031 __isl_give isl_union_pw_qpolynomial *
4032 isl_union_pw_qpolynomial_zero(
4033 __isl_take isl_space *space);
4035 C<isl_union_pw_aff_empty> is an alternative name for
4036 C<isl_union_pw_aff_empty_space>.
4037 Similarly for the other pairs of functions.
4039 A union expression containing a single base expression
4040 can be created using the following functions.
4042 #include <isl/aff.h>
4043 __isl_give isl_union_pw_aff *
4044 isl_pw_aff_to_union_pw_aff(
4045 __isl_take isl_pw_aff *pa);
4046 __isl_give isl_union_pw_aff *
4047 isl_union_pw_aff_from_pw_aff(
4048 __isl_take isl_pw_aff *pa);
4049 __isl_give isl_union_pw_multi_aff *
4050 isl_union_pw_multi_aff_from_aff(
4051 __isl_take isl_aff *aff);
4052 __isl_give isl_union_pw_multi_aff *
4053 isl_pw_multi_aff_to_union_pw_multi_aff(
4054 __isl_take isl_pw_multi_aff *pma);
4055 __isl_give isl_union_pw_multi_aff *
4056 isl_union_pw_multi_aff_from_pw_multi_aff(
4057 __isl_take isl_pw_multi_aff *pma);
4059 #include <isl/polynomial.h>
4060 __isl_give isl_union_pw_qpolynomial *
4061 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4062 __isl_take isl_pw_qpolynomial *pwqp);
4063 __isl_give isl_union_pw_qpolynomial *
4064 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4065 __isl_take isl_pw_qpolynomial *pwqp);
4066 __isl_give isl_union_pw_qpolynomial_fold *
4067 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4068 __isl_take isl_pw_qpolynomial_fold *pwf);
4069 __isl_give isl_union_pw_qpolynomial_fold *
4070 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4071 __isl_take isl_pw_qpolynomial_fold *pwf);
4073 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4075 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4076 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4078 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4079 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4081 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4082 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4084 The inverse conversions below can only be used if the input
4085 expression is known to live in exactly one space.
4087 #include <isl/aff.h>
4088 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4089 __isl_keep isl_union_pw_multi_aff *upma);
4090 __isl_give isl_pw_multi_aff *
4091 isl_union_pw_multi_aff_as_pw_multi_aff(
4092 __isl_take isl_union_pw_multi_aff *upma);
4094 A union piecewise expression containing a single base expression
4095 on a universe domain can also be created directly from
4096 a base expression using the following functions.
4098 #include <isl/aff.h>
4099 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4100 __isl_take isl_aff *aff);
4101 __isl_give isl_union_pw_multi_aff *
4102 isl_union_pw_multi_aff_from_multi_aff(
4103 __isl_take isl_multi_aff *ma);
4105 The following functions create a base expression on each
4106 of the sets in the union set and collect the results.
4108 #include <isl/aff.h>
4109 __isl_give isl_union_pw_multi_aff *
4110 isl_union_pw_multi_aff_from_union_pw_aff(
4111 __isl_take isl_union_pw_aff *upa);
4112 __isl_give isl_union_pw_aff *
4113 isl_union_pw_multi_aff_get_union_pw_aff(
4114 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4115 __isl_give isl_union_pw_aff *
4116 isl_union_pw_aff_val_on_domain(
4117 __isl_take isl_union_set *domain,
4118 __isl_take isl_val *v);
4119 __isl_give isl_union_pw_multi_aff *
4120 isl_union_pw_multi_aff_multi_val_on_domain(
4121 __isl_take isl_union_set *domain,
4122 __isl_take isl_multi_val *mv);
4123 __isl_give isl_union_pw_aff *
4124 isl_union_pw_aff_param_on_domain_id(
4125 __isl_take isl_union_set *domain,
4126 __isl_take isl_id *id);
4128 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4129 is the identifier of a parameter that may or may not already
4130 be present in C<domain>.
4132 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4134 expression on a given domain can be created using the following
4137 #include <isl/aff.h>
4138 __isl_give isl_union_pw_aff *
4139 isl_union_pw_aff_aff_on_domain(
4140 __isl_take isl_union_set *domain,
4141 __isl_take isl_aff *aff);
4142 __isl_give isl_union_pw_aff *
4143 isl_union_pw_aff_pw_aff_on_domain(
4144 __isl_take isl_union_set *domain,
4145 __isl_take isl_pw_aff *pa);
4147 A base expression can be added to a union expression using
4148 the following functions.
4150 #include <isl/aff.h>
4151 __isl_give isl_union_pw_aff *
4152 isl_union_pw_aff_add_pw_aff(
4153 __isl_take isl_union_pw_aff *upa,
4154 __isl_take isl_pw_aff *pa);
4155 __isl_give isl_union_pw_multi_aff *
4156 isl_union_pw_multi_aff_add_pw_multi_aff(
4157 __isl_take isl_union_pw_multi_aff *upma,
4158 __isl_take isl_pw_multi_aff *pma);
4160 #include <isl/polynomial.h>
4161 __isl_give isl_union_pw_qpolynomial *
4162 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4163 __isl_take isl_union_pw_qpolynomial *upwqp,
4164 __isl_take isl_pw_qpolynomial *pwqp);
4166 Union expressions can be copied and freed using
4167 the following functions.
4169 #include <isl/aff.h>
4170 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4171 __isl_keep isl_union_pw_aff *upa);
4172 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4173 __isl_take isl_union_pw_aff *upa);
4174 __isl_give isl_union_pw_multi_aff *
4175 isl_union_pw_multi_aff_copy(
4176 __isl_keep isl_union_pw_multi_aff *upma);
4177 __isl_null isl_union_pw_multi_aff *
4178 isl_union_pw_multi_aff_free(
4179 __isl_take isl_union_pw_multi_aff *upma);
4181 #include <isl/polynomial.h>
4182 __isl_give isl_union_pw_qpolynomial *
4183 isl_union_pw_qpolynomial_copy(
4184 __isl_keep isl_union_pw_qpolynomial *upwqp);
4185 __isl_null isl_union_pw_qpolynomial *
4186 isl_union_pw_qpolynomial_free(
4187 __isl_take isl_union_pw_qpolynomial *upwqp);
4188 __isl_give isl_union_pw_qpolynomial_fold *
4189 isl_union_pw_qpolynomial_fold_copy(
4190 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4191 __isl_null isl_union_pw_qpolynomial_fold *
4192 isl_union_pw_qpolynomial_fold_free(
4193 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4195 To iterate over the base expressions in a union expression,
4196 use the following functions.
4198 #include <isl/aff.h>
4199 isl_size isl_union_pw_aff_n_pw_aff(
4200 __isl_keep isl_union_pw_aff *upa);
4201 isl_stat isl_union_pw_aff_foreach_pw_aff(
4202 __isl_keep isl_union_pw_aff *upa,
4203 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4204 void *user), void *user);
4205 isl_bool isl_union_pw_aff_every_pw_aff(
4206 __isl_keep isl_union_pw_aff *upa,
4207 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4208 void *user), void *user);
4209 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4210 __isl_keep isl_union_pw_multi_aff *upma);
4211 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4212 __isl_keep isl_union_pw_multi_aff *upma,
4213 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4214 void *user), void *user);
4215 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4216 __isl_keep isl_union_pw_multi_aff *upma,
4218 __isl_keep isl_pw_multi_aff *pma,
4219 void *user), void *user);
4221 #include <isl/polynomial.h>
4222 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4223 __isl_keep isl_union_pw_qpolynomial *upwqp);
4224 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4225 __isl_keep isl_union_pw_qpolynomial *upwqp,
4226 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4227 void *user), void *user);
4228 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4229 __isl_keep isl_union_pw_qpolynomial *upwqp,
4231 __isl_keep isl_pw_qpolynomial *pwqp,
4232 void *user), void *user);
4233 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4234 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4235 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4236 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4237 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4238 void *user), void *user);
4240 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4241 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4243 __isl_keep isl_pw_qpolynomial_fold *pwf,
4244 void *user), void *user);
4246 To extract the base expression in a given space from a union, use
4247 the following functions.
4249 #include <isl/aff.h>
4250 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4251 __isl_keep isl_union_pw_aff *upa,
4252 __isl_take isl_space *space);
4253 __isl_give isl_pw_multi_aff *
4254 isl_union_pw_multi_aff_extract_pw_multi_aff(
4255 __isl_keep isl_union_pw_multi_aff *upma,
4256 __isl_take isl_space *space);
4258 #include <isl/polynomial.h>
4259 __isl_give isl_pw_qpolynomial *
4260 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4261 __isl_keep isl_union_pw_qpolynomial *upwqp,
4262 __isl_take isl_space *space);
4264 It is also possible to obtain a list of the base expressions using
4265 the following functions.
4267 #include <isl/aff.h>
4268 __isl_give isl_pw_aff_list *
4269 isl_union_pw_aff_get_pw_aff_list(
4270 __isl_keep isl_union_pw_aff *upa);
4271 __isl_give isl_pw_multi_aff_list *
4272 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4273 __isl_keep isl_union_pw_multi_aff *upma);
4275 #include <isl/polynomial.h>
4276 __isl_give isl_pw_qpolynomial_list *
4277 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4278 __isl_keep isl_union_pw_qpolynomial *upwqp);
4279 __isl_give isl_pw_qpolynomial_fold_list *
4280 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4281 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4283 The returned list can be manipulated using the functions in L<"Lists">.
4285 =head2 Input and Output
4287 For set and relation,
4288 C<isl> supports its own input/output format, which is similar
4289 to the C<Omega> format, but also supports the C<PolyLib> format
4291 For other object types, typically only an C<isl> format is supported.
4293 =head3 C<isl> format
4295 The C<isl> format is similar to that of C<Omega>, but has a different
4296 syntax for describing the parameters and allows for the definition
4297 of an existentially quantified variable as the integer division
4298 of an affine expression.
4299 For example, the set of integers C<i> between C<0> and C<n>
4300 such that C<i % 10 <= 6> can be described as
4302 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4305 A set or relation can have several disjuncts, separated
4306 by the keyword C<or>. Each disjunct is either a conjunction
4307 of constraints or a projection (C<exists>) of a conjunction
4308 of constraints. The constraints are separated by the keyword
4311 =head3 C<PolyLib> format
4313 If the represented set is a union, then the first line
4314 contains a single number representing the number of disjuncts.
4315 Otherwise, a line containing the number C<1> is optional.
4317 Each disjunct is represented by a matrix of constraints.
4318 The first line contains two numbers representing
4319 the number of rows and columns,
4320 where the number of rows is equal to the number of constraints
4321 and the number of columns is equal to two plus the number of variables.
4322 The following lines contain the actual rows of the constraint matrix.
4323 In each row, the first column indicates whether the constraint
4324 is an equality (C<0>) or inequality (C<1>). The final column
4325 corresponds to the constant term.
4327 If the set is parametric, then the coefficients of the parameters
4328 appear in the last columns before the constant column.
4329 The coefficients of any existentially quantified variables appear
4330 between those of the set variables and those of the parameters.
4332 =head3 Extended C<PolyLib> format
4334 The extended C<PolyLib> format is nearly identical to the
4335 C<PolyLib> format. The only difference is that the line
4336 containing the number of rows and columns of a constraint matrix
4337 also contains four additional numbers:
4338 the number of output dimensions, the number of input dimensions,
4339 the number of local dimensions (i.e., the number of existentially
4340 quantified variables) and the number of parameters.
4341 For sets, the number of ``output'' dimensions is equal
4342 to the number of set dimensions, while the number of ``input''
4347 Objects can be read from input using the following functions.
4350 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4352 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4353 isl_ctx *ctx, const char *str);
4355 #include <isl/val.h>
4356 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4358 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4359 isl_ctx *ctx, const char *str);
4361 #include <isl/space.h>
4362 __isl_give isl_space *isl_space_read_from_str(
4363 isl_ctx *ctx, const char *str);
4365 #include <isl/set.h>
4366 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4367 isl_ctx *ctx, FILE *input);
4368 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4369 isl_ctx *ctx, const char *str);
4370 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4372 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4375 #include <isl/map.h>
4376 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4377 isl_ctx *ctx, FILE *input);
4378 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4379 isl_ctx *ctx, const char *str);
4380 __isl_give isl_map *isl_map_read_from_file(
4381 isl_ctx *ctx, FILE *input);
4382 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4385 #include <isl/union_set.h>
4386 __isl_give isl_union_set *isl_union_set_read_from_file(
4387 isl_ctx *ctx, FILE *input);
4388 __isl_give isl_union_set *isl_union_set_read_from_str(
4389 isl_ctx *ctx, const char *str);
4391 #include <isl/union_map.h>
4392 __isl_give isl_union_map *isl_union_map_read_from_file(
4393 isl_ctx *ctx, FILE *input);
4394 __isl_give isl_union_map *isl_union_map_read_from_str(
4395 isl_ctx *ctx, const char *str);
4397 #include <isl/aff.h>
4398 __isl_give isl_aff *isl_aff_read_from_str(
4399 isl_ctx *ctx, const char *str);
4400 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4401 isl_ctx *ctx, const char *str);
4402 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4403 isl_ctx *ctx, const char *str);
4404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4405 isl_ctx *ctx, const char *str);
4406 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4407 isl_ctx *ctx, const char *str);
4408 __isl_give isl_union_pw_aff *
4409 isl_union_pw_aff_read_from_str(
4410 isl_ctx *ctx, const char *str);
4411 __isl_give isl_union_pw_multi_aff *
4412 isl_union_pw_multi_aff_read_from_str(
4413 isl_ctx *ctx, const char *str);
4414 __isl_give isl_multi_union_pw_aff *
4415 isl_multi_union_pw_aff_read_from_str(
4416 isl_ctx *ctx, const char *str);
4418 #include <isl/polynomial.h>
4419 __isl_give isl_union_pw_qpolynomial *
4420 isl_union_pw_qpolynomial_read_from_str(
4421 isl_ctx *ctx, const char *str);
4423 __isl_give isl_pw_qpolynomial_fold *
4424 isl_pw_qpolynomial_fold_read_from_str(
4425 isl_ctx *ctx, const char *str);
4427 For sets and relations,
4428 the input format is autodetected and may be either the C<PolyLib> format
4429 or the C<isl> format.
4433 Before anything can be printed, an C<isl_printer> needs to
4436 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4438 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4439 __isl_null isl_printer *isl_printer_free(
4440 __isl_take isl_printer *printer);
4442 C<isl_printer_to_file> prints to the given file, while
4443 C<isl_printer_to_str> prints to a string that can be extracted
4444 using the following function.
4446 #include <isl/printer.h>
4447 __isl_give char *isl_printer_get_str(
4448 __isl_keep isl_printer *printer);
4450 The printer can be inspected using the following functions.
4452 FILE *isl_printer_get_file(
4453 __isl_keep isl_printer *printer);
4454 int isl_printer_get_output_format(
4455 __isl_keep isl_printer *p);
4456 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4458 The behavior of the printer can be modified in various ways
4460 __isl_give isl_printer *isl_printer_set_output_format(
4461 __isl_take isl_printer *p, int output_format);
4462 __isl_give isl_printer *isl_printer_set_indent(
4463 __isl_take isl_printer *p, int indent);
4464 __isl_give isl_printer *isl_printer_set_indent_prefix(
4465 __isl_take isl_printer *p, const char *prefix);
4466 __isl_give isl_printer *isl_printer_indent(
4467 __isl_take isl_printer *p, int indent);
4468 __isl_give isl_printer *isl_printer_set_prefix(
4469 __isl_take isl_printer *p, const char *prefix);
4470 __isl_give isl_printer *isl_printer_set_suffix(
4471 __isl_take isl_printer *p, const char *suffix);
4472 __isl_give isl_printer *isl_printer_set_yaml_style(
4473 __isl_take isl_printer *p, int yaml_style);
4475 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4476 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4477 and defaults to C<ISL_FORMAT_ISL>.
4478 Each line in the output is prefixed by C<indent_prefix>,
4479 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4480 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4481 In the C<PolyLib> format output,
4482 the coefficients of the existentially quantified variables
4483 appear between those of the set variables and those
4485 The function C<isl_printer_indent> increases the indentation
4486 by the specified amount (which may be negative).
4487 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4488 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4491 To actually print something, use
4493 #include <isl/printer.h>
4494 __isl_give isl_printer *isl_printer_print_double(
4495 __isl_take isl_printer *p, double d);
4497 #include <isl/val.h>
4498 __isl_give isl_printer *isl_printer_print_val(
4499 __isl_take isl_printer *p, __isl_keep isl_val *v);
4500 __isl_give isl_printer *isl_printer_print_multi_val(
4501 __isl_take isl_printer *p,
4502 __isl_keep isl_multi_val *mv);
4504 #include <isl/set.h>
4505 __isl_give isl_printer *isl_printer_print_basic_set(
4506 __isl_take isl_printer *printer,
4507 __isl_keep isl_basic_set *bset);
4508 __isl_give isl_printer *isl_printer_print_set(
4509 __isl_take isl_printer *printer,
4510 __isl_keep isl_set *set);
4512 #include <isl/map.h>
4513 __isl_give isl_printer *isl_printer_print_basic_map(
4514 __isl_take isl_printer *printer,
4515 __isl_keep isl_basic_map *bmap);
4516 __isl_give isl_printer *isl_printer_print_map(
4517 __isl_take isl_printer *printer,
4518 __isl_keep isl_map *map);
4520 #include <isl/union_set.h>
4521 __isl_give isl_printer *isl_printer_print_union_set(
4522 __isl_take isl_printer *p,
4523 __isl_keep isl_union_set *uset);
4525 #include <isl/union_map.h>
4526 __isl_give isl_printer *isl_printer_print_union_map(
4527 __isl_take isl_printer *p,
4528 __isl_keep isl_union_map *umap);
4531 __isl_give isl_printer *isl_printer_print_multi_id(
4532 __isl_take isl_printer *p,
4533 __isl_keep isl_multi_id *mi);
4535 #include <isl/aff.h>
4536 __isl_give isl_printer *isl_printer_print_aff(
4537 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4538 __isl_give isl_printer *isl_printer_print_multi_aff(
4539 __isl_take isl_printer *p,
4540 __isl_keep isl_multi_aff *maff);
4541 __isl_give isl_printer *isl_printer_print_pw_aff(
4542 __isl_take isl_printer *p,
4543 __isl_keep isl_pw_aff *pwaff);
4544 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4545 __isl_take isl_printer *p,
4546 __isl_keep isl_pw_multi_aff *pma);
4547 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4548 __isl_take isl_printer *p,
4549 __isl_keep isl_multi_pw_aff *mpa);
4550 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4551 __isl_take isl_printer *p,
4552 __isl_keep isl_union_pw_aff *upa);
4553 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4554 __isl_take isl_printer *p,
4555 __isl_keep isl_union_pw_multi_aff *upma);
4556 __isl_give isl_printer *
4557 isl_printer_print_multi_union_pw_aff(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_multi_union_pw_aff *mupa);
4561 #include <isl/polynomial.h>
4562 __isl_give isl_printer *isl_printer_print_qpolynomial(
4563 __isl_take isl_printer *p,
4564 __isl_keep isl_qpolynomial *qp);
4565 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4566 __isl_take isl_printer *p,
4567 __isl_keep isl_pw_qpolynomial *pwqp);
4568 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4569 __isl_take isl_printer *p,
4570 __isl_keep isl_union_pw_qpolynomial *upwqp);
4572 __isl_give isl_printer *
4573 isl_printer_print_pw_qpolynomial_fold(
4574 __isl_take isl_printer *p,
4575 __isl_keep isl_pw_qpolynomial_fold *pwf);
4576 __isl_give isl_printer *
4577 isl_printer_print_union_pw_qpolynomial_fold(
4578 __isl_take isl_printer *p,
4579 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4581 For C<isl_printer_print_qpolynomial>,
4582 C<isl_printer_print_pw_qpolynomial> and
4583 C<isl_printer_print_pw_qpolynomial_fold>,
4584 the output format of the printer
4585 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4586 For C<isl_printer_print_union_pw_qpolynomial> and
4587 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4589 In case of printing in C<ISL_FORMAT_C>, the user may want
4590 to set the names of all dimensions first.
4592 C<isl> also provides limited support for printing YAML documents,
4593 just enough for the internal use for printing such documents.
4595 #include <isl/printer.h>
4596 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4597 __isl_take isl_printer *p);
4598 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4599 __isl_take isl_printer *p);
4600 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4601 __isl_take isl_printer *p);
4602 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4603 __isl_take isl_printer *p);
4604 __isl_give isl_printer *isl_printer_yaml_next(
4605 __isl_take isl_printer *p);
4607 A document is started by a call to either
4608 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4609 Anything printed to the printer after such a call belong to the
4610 first key of the mapping or the first element in the sequence.
4611 The function C<isl_printer_yaml_next> moves to the value if
4612 we are currently printing a mapping key, the next key if we
4613 are printing a value or the next element if we are printing
4614 an element in a sequence.
4615 Nested mappings and sequences are initiated by the same
4616 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4617 Each call to these functions needs to have a corresponding call to
4618 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4620 When called on a file printer, the following function flushes
4621 the file. When called on a string printer, the buffer is cleared.
4623 __isl_give isl_printer *isl_printer_flush(
4624 __isl_take isl_printer *p);
4626 The following functions allow the user to attach
4627 notes to a printer in order to keep track of additional state.
4629 #include <isl/printer.h>
4630 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4631 __isl_keep isl_id *id);
4632 __isl_give isl_id *isl_printer_get_note(
4633 __isl_keep isl_printer *p, __isl_take isl_id *id);
4634 __isl_give isl_printer *isl_printer_set_note(
4635 __isl_take isl_printer *p,
4636 __isl_take isl_id *id, __isl_take isl_id *note);
4638 C<isl_printer_set_note> associates the given note to the given
4639 identifier in the printer.
4640 C<isl_printer_get_note> retrieves a note associated to an
4642 C<isl_printer_has_note> checks if there is such a note.
4643 C<isl_printer_get_note> fails if the requested note does not exist.
4645 Alternatively, a string representation can be obtained
4646 directly using the following functions, which always print
4650 __isl_give char *isl_id_to_str(
4651 __isl_keep isl_id *id);
4652 __isl_give char *isl_multi_id_to_str(
4653 __isl_keep isl_multi_id *mi);
4655 #include <isl/space.h>
4656 __isl_give char *isl_space_to_str(
4657 __isl_keep isl_space *space);
4659 #include <isl/val.h>
4660 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4661 __isl_give char *isl_multi_val_to_str(
4662 __isl_keep isl_multi_val *mv);
4664 #include <isl/set.h>
4665 __isl_give char *isl_basic_set_to_str(
4666 __isl_keep isl_basic_set *bset);
4667 __isl_give char *isl_set_to_str(
4668 __isl_keep isl_set *set);
4670 #include <isl/union_set.h>
4671 __isl_give char *isl_union_set_to_str(
4672 __isl_keep isl_union_set *uset);
4674 #include <isl/map.h>
4675 __isl_give char *isl_basic_map_to_str(
4676 __isl_keep isl_basic_map *bmap);
4677 __isl_give char *isl_map_to_str(
4678 __isl_keep isl_map *map);
4680 #include <isl/union_map.h>
4681 __isl_give char *isl_union_map_to_str(
4682 __isl_keep isl_union_map *umap);
4684 #include <isl/aff.h>
4685 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4686 __isl_give char *isl_pw_aff_to_str(
4687 __isl_keep isl_pw_aff *pa);
4688 __isl_give char *isl_multi_aff_to_str(
4689 __isl_keep isl_multi_aff *ma);
4690 __isl_give char *isl_pw_multi_aff_to_str(
4691 __isl_keep isl_pw_multi_aff *pma);
4692 __isl_give char *isl_multi_pw_aff_to_str(
4693 __isl_keep isl_multi_pw_aff *mpa);
4694 __isl_give char *isl_union_pw_aff_to_str(
4695 __isl_keep isl_union_pw_aff *upa);
4696 __isl_give char *isl_union_pw_multi_aff_to_str(
4697 __isl_keep isl_union_pw_multi_aff *upma);
4698 __isl_give char *isl_multi_union_pw_aff_to_str(
4699 __isl_keep isl_multi_union_pw_aff *mupa);
4701 #include <isl/point.h>
4702 __isl_give char *isl_point_to_str(
4703 __isl_keep isl_point *pnt);
4705 #include <isl/polynomial.h>
4706 __isl_give char *isl_pw_qpolynomial_to_str(
4707 __isl_keep isl_pw_qpolynomial *pwqp);
4708 __isl_give char *isl_union_pw_qpolynomial_to_str(
4709 __isl_keep isl_union_pw_qpolynomial *upwqp);
4713 =head3 Unary Properties
4719 The following functions test whether the given set or relation
4720 contains any integer points. The ``plain'' variants do not perform
4721 any computations, but simply check if the given set or relation
4722 is already known to be empty.
4724 #include <isl/set.h>
4725 isl_bool isl_basic_set_plain_is_empty(
4726 __isl_keep isl_basic_set *bset);
4727 isl_bool isl_basic_set_is_empty(
4728 __isl_keep isl_basic_set *bset);
4729 isl_bool isl_set_plain_is_empty(
4730 __isl_keep isl_set *set);
4731 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4733 #include <isl/union_set.h>
4734 isl_bool isl_union_set_is_empty(
4735 __isl_keep isl_union_set *uset);
4737 #include <isl/map.h>
4738 isl_bool isl_basic_map_plain_is_empty(
4739 __isl_keep isl_basic_map *bmap);
4740 isl_bool isl_basic_map_is_empty(
4741 __isl_keep isl_basic_map *bmap);
4742 isl_bool isl_map_plain_is_empty(
4743 __isl_keep isl_map *map);
4744 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4746 #include <isl/union_map.h>
4747 isl_bool isl_union_map_plain_is_empty(
4748 __isl_keep isl_union_map *umap);
4749 isl_bool isl_union_map_is_empty(
4750 __isl_keep isl_union_map *umap);
4752 #include <isl/aff.h>
4753 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4754 __isl_keep isl_union_pw_multi_aff *upma);
4756 =item * Universality
4758 isl_bool isl_basic_set_plain_is_universe(
4759 __isl_keep isl_basic_set *bset);
4760 isl_bool isl_basic_set_is_universe(
4761 __isl_keep isl_basic_set *bset);
4762 isl_bool isl_basic_map_plain_is_universe(
4763 __isl_keep isl_basic_map *bmap);
4764 isl_bool isl_basic_map_is_universe(
4765 __isl_keep isl_basic_map *bmap);
4766 isl_bool isl_set_plain_is_universe(
4767 __isl_keep isl_set *set);
4768 isl_bool isl_map_plain_is_universe(
4769 __isl_keep isl_map *map);
4771 =item * Single-valuedness
4773 #include <isl/set.h>
4774 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4776 #include <isl/map.h>
4777 isl_bool isl_basic_map_is_single_valued(
4778 __isl_keep isl_basic_map *bmap);
4779 isl_bool isl_map_plain_is_single_valued(
4780 __isl_keep isl_map *map);
4781 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4783 #include <isl/union_map.h>
4784 isl_bool isl_union_map_is_single_valued(
4785 __isl_keep isl_union_map *umap);
4789 isl_bool isl_map_plain_is_injective(
4790 __isl_keep isl_map *map);
4791 isl_bool isl_map_is_injective(
4792 __isl_keep isl_map *map);
4793 isl_bool isl_union_map_plain_is_injective(
4794 __isl_keep isl_union_map *umap);
4795 isl_bool isl_union_map_is_injective(
4796 __isl_keep isl_union_map *umap);
4800 isl_bool isl_map_is_bijective(
4801 __isl_keep isl_map *map);
4802 isl_bool isl_union_map_is_bijective(
4803 __isl_keep isl_union_map *umap);
4807 The following functions test whether the given relation
4808 only maps elements to themselves.
4810 #include <isl/map.h>
4811 isl_bool isl_map_is_identity(
4812 __isl_keep isl_map *map);
4814 #include <isl/union_map.h>
4815 isl_bool isl_union_map_is_identity(
4816 __isl_keep isl_union_map *umap);
4820 __isl_give isl_val *
4821 isl_basic_map_plain_get_val_if_fixed(
4822 __isl_keep isl_basic_map *bmap,
4823 enum isl_dim_type type, unsigned pos);
4824 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4825 __isl_keep isl_set *set,
4826 enum isl_dim_type type, unsigned pos);
4827 __isl_give isl_multi_val *
4828 isl_set_get_plain_multi_val_if_fixed(
4829 __isl_keep isl_set *set);
4830 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4831 __isl_keep isl_map *map,
4832 enum isl_dim_type type, unsigned pos);
4834 If the set or relation obviously lies on a hyperplane where the given dimension
4835 has a fixed value, then return that value.
4836 Otherwise return NaN.
4837 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4842 Stride detection is based on heuristics.
4843 The strides returned by the functions below are always valid,
4844 but there may be larger valid strides that are not detected.
4846 isl_stat isl_set_dim_residue_class_val(
4847 __isl_keep isl_set *set,
4848 int pos, __isl_give isl_val **modulo,
4849 __isl_give isl_val **residue);
4851 Check if the values of the given set dimension are equal to a fixed
4852 value modulo some integer value. If so, assign the modulo to C<*modulo>
4853 and the fixed value to C<*residue>. If the given dimension attains only
4854 a single value, then assign C<0> to C<*modulo> and the fixed value to
4856 If the dimension does not attain only a single value and if no modulo
4857 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4859 #include <isl/set.h>
4860 __isl_give isl_stride_info *isl_set_get_stride_info(
4861 __isl_keep isl_set *set, int pos);
4862 __isl_give isl_val *isl_set_get_stride(
4863 __isl_keep isl_set *set, int pos);
4864 __isl_give isl_fixed_box *isl_set_get_lattice_tile(
4865 __isl_keep isl_set *set);
4867 #include <isl/map.h>
4868 __isl_give isl_stride_info *
4869 isl_map_get_range_stride_info(
4870 __isl_keep isl_map *map, int pos);
4871 __isl_give isl_fixed_box *
4872 isl_map_get_range_lattice_tile(
4873 __isl_keep isl_map *map);
4875 Check if the values of the given set dimension are equal to
4876 some affine expression of the other dimensions (the offset)
4877 modulo some integer stride or
4878 check if the values of the given output dimensions are equal to
4879 some affine expression of the input dimensions (the offset)
4880 modulo some integer stride.
4881 If no more specific information can be found, then the stride
4882 is taken to be one and the offset is taken to be the zero expression.
4883 The function C<isl_set_get_stride> performs the same
4884 computation as C<isl_set_get_stride_info> but only returns the stride.
4885 The function C<isl_map_get_range_lattice_tile> collects the stride
4886 information over all output dimensions.
4887 In particular, it returns a tile of a rectangular lattice
4888 (possibly of size 1 in all directions)
4889 containing the output in terms of the parameters and the input dimensions.
4890 The size and the offset of this tile correspond to
4891 the strides and the offsets of the stride information and
4892 can be extracted from the returned
4893 C<isl_fixed_box> using the functions described under "Box hull" in
4894 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4895 C<isl_map_get_range_lattice_tile> is always valid.
4896 The function C<isl_set_get_lattice_tile> collects the same stride
4897 information over all set dimensions.
4898 For the other functions,
4899 the stride and offset can be extracted from the returned object
4900 using the following functions.
4902 #include <isl/stride_info.h>
4903 __isl_give isl_val *isl_stride_info_get_stride(
4904 __isl_keep isl_stride_info *si);
4905 __isl_give isl_aff *isl_stride_info_get_offset(
4906 __isl_keep isl_stride_info *si);
4908 The stride info object can be copied and released using the following
4911 #include <isl/stride_info.h>
4912 __isl_give isl_stride_info *isl_stride_info_copy(
4913 __isl_keep isl_stride_info *si);
4914 __isl_null isl_stride_info *isl_stride_info_free(
4915 __isl_take isl_stride_info *si);
4919 To check whether a function involves any local variables,
4920 i.e., integer divisions,
4921 the following functions can be used.
4923 #include <isl/set.h>
4924 isl_bool isl_set_involves_locals(
4925 __isl_keep isl_set *set);
4927 #include <isl/aff.h>
4928 isl_bool isl_aff_involves_locals(
4929 __isl_keep isl_aff *aff);
4930 isl_bool isl_multi_aff_involves_locals(
4931 __isl_keep isl_multi_aff *ma);
4932 isl_bool isl_pw_multi_aff_involves_locals(
4933 __isl_keep isl_pw_multi_aff *pma);
4934 isl_bool isl_union_pw_multi_aff_involves_locals(
4935 __isl_keep isl_union_pw_multi_aff *upma);
4937 To check whether the description of a set, relation or function depends
4938 on a parameter or one or more given dimensions,
4939 the following functions can be used.
4941 #include <isl/constraint.h>
4942 isl_bool isl_constraint_involves_dims(
4943 __isl_keep isl_constraint *constraint,
4944 enum isl_dim_type type, unsigned first, unsigned n);
4946 #include <isl/set.h>
4947 isl_bool isl_basic_set_involves_dims(
4948 __isl_keep isl_basic_set *bset,
4949 enum isl_dim_type type, unsigned first, unsigned n);
4950 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4951 enum isl_dim_type type, unsigned first, unsigned n);
4953 #include <isl/map.h>
4954 isl_bool isl_basic_map_involves_dims(
4955 __isl_keep isl_basic_map *bmap,
4956 enum isl_dim_type type, unsigned first, unsigned n);
4957 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4958 enum isl_dim_type type, unsigned first, unsigned n);
4960 #include <isl/union_map.h>
4961 isl_bool isl_union_map_involves_dims(
4962 __isl_keep isl_union_map *umap,
4963 enum isl_dim_type type, unsigned first, unsigned n);
4965 #include <isl/aff.h>
4966 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4967 enum isl_dim_type type, unsigned first, unsigned n);
4968 isl_bool isl_pw_aff_involves_param_id(
4969 __isl_keep isl_pw_aff *pa,
4970 __isl_keep isl_id *id);
4971 isl_bool isl_pw_aff_involves_dims(
4972 __isl_keep isl_pw_aff *pwaff,
4973 enum isl_dim_type type, unsigned first, unsigned n);
4974 isl_bool isl_multi_aff_involves_dims(
4975 __isl_keep isl_multi_aff *ma,
4976 enum isl_dim_type type, unsigned first, unsigned n);
4977 isl_bool isl_pw_multi_aff_involves_param_id(
4978 __isl_keep isl_pw_multi_aff *pma,
4979 __isl_keep isl_id *id);
4980 isl_bool isl_pw_multi_aff_involves_dims(
4981 __isl_keep isl_pw_multi_aff *pma,
4982 enum isl_dim_type type, unsigned first, unsigned n);
4983 isl_bool isl_multi_pw_aff_involves_dims(
4984 __isl_keep isl_multi_pw_aff *mpa,
4985 enum isl_dim_type type, unsigned first, unsigned n);
4986 isl_bool isl_multi_pw_aff_involves_param_id(
4987 __isl_keep isl_multi_pw_aff *mpa,
4988 __isl_keep isl_id *id);
4989 isl_bool isl_multi_pw_aff_involves_param_id_list(
4990 __isl_keep isl_multi_pw_aff *mpa,
4991 __isl_keep isl_id_list *list);
4993 #include <isl/polynomial.h>
4994 isl_bool isl_qpolynomial_involves_dims(
4995 __isl_keep isl_qpolynomial *qp,
4996 enum isl_dim_type type, unsigned first, unsigned n);
4997 isl_bool isl_pw_qpolynomial_involves_param_id(
4998 __isl_keep isl_pw_qpolynomial *pwqp,
4999 __isl_keep isl_id *id);
5000 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
5001 __isl_keep isl_pw_qpolynomial_fold *pwf,
5002 __isl_keep isl_id *id);
5004 Similarly, the following functions can be used to check whether
5005 a given dimension is involved in any lower or upper bound.
5007 #include <isl/set.h>
5008 isl_bool isl_set_dim_has_any_lower_bound(
5009 __isl_keep isl_set *set,
5010 enum isl_dim_type type, unsigned pos);
5011 isl_bool isl_set_dim_has_any_upper_bound(
5012 __isl_keep isl_set *set,
5013 enum isl_dim_type type, unsigned pos);
5015 Note that these functions return true even if there is a bound on
5016 the dimension on only some of the basic sets of C<set>.
5017 To check if they have a bound for all of the basic sets in C<set>,
5018 use the following functions instead.
5020 #include <isl/set.h>
5021 isl_bool isl_set_dim_has_lower_bound(
5022 __isl_keep isl_set *set,
5023 enum isl_dim_type type, unsigned pos);
5024 isl_bool isl_set_dim_has_upper_bound(
5025 __isl_keep isl_set *set,
5026 enum isl_dim_type type, unsigned pos);
5030 To check whether a set is a parameter domain, use this function:
5032 isl_bool isl_set_is_params(__isl_keep isl_set *set);
5033 isl_bool isl_union_set_is_params(
5034 __isl_keep isl_union_set *uset);
5038 The following functions check whether the space of the given
5039 (basic) set or relation domain and/or range is a wrapped relation.
5041 #include <isl/space.h>
5042 isl_bool isl_space_is_wrapping(
5043 __isl_keep isl_space *space);
5044 isl_bool isl_space_domain_is_wrapping(
5045 __isl_keep isl_space *space);
5046 isl_bool isl_space_range_is_wrapping(
5047 __isl_keep isl_space *space);
5048 isl_bool isl_space_is_product(
5049 __isl_keep isl_space *space);
5051 #include <isl/set.h>
5052 isl_bool isl_basic_set_is_wrapping(
5053 __isl_keep isl_basic_set *bset);
5054 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
5056 #include <isl/map.h>
5057 isl_bool isl_map_domain_is_wrapping(
5058 __isl_keep isl_map *map);
5059 isl_bool isl_map_range_is_wrapping(
5060 __isl_keep isl_map *map);
5061 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5064 isl_bool isl_multi_id_range_is_wrapping(
5065 __isl_keep isl_multi_id *mi);
5067 #include <isl/val.h>
5068 isl_bool isl_multi_val_range_is_wrapping(
5069 __isl_keep isl_multi_val *mv);
5071 #include <isl/aff.h>
5072 isl_bool isl_multi_aff_range_is_wrapping(
5073 __isl_keep isl_multi_aff *ma);
5074 isl_bool isl_multi_pw_aff_range_is_wrapping(
5075 __isl_keep isl_multi_pw_aff *mpa);
5076 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5077 __isl_keep isl_multi_union_pw_aff *mupa);
5079 The input to C<isl_space_is_wrapping> should
5080 be the space of a set, while that of
5081 C<isl_space_domain_is_wrapping> and
5082 C<isl_space_range_is_wrapping> should be the space of a relation.
5083 The input to C<isl_space_is_product> can be either the space
5084 of a set or that of a binary relation.
5085 In case the input is the space of a binary relation, it checks
5086 whether both domain and range are wrapping.
5088 =item * Internal Product
5090 isl_bool isl_basic_map_can_zip(
5091 __isl_keep isl_basic_map *bmap);
5092 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5094 Check whether the product of domain and range of the given relation
5096 i.e., whether both domain and range are nested relations.
5100 #include <isl/space.h>
5101 isl_bool isl_space_can_curry(
5102 __isl_keep isl_space *space);
5104 #include <isl/map.h>
5105 isl_bool isl_basic_map_can_curry(
5106 __isl_keep isl_basic_map *bmap);
5107 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5109 Check whether the domain of the (basic) relation is a wrapped relation.
5111 #include <isl/space.h>
5112 isl_bool isl_space_can_uncurry(
5113 __isl_keep isl_space *space);
5115 #include <isl/map.h>
5116 isl_bool isl_basic_map_can_uncurry(
5117 __isl_keep isl_basic_map *bmap);
5118 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5120 Check whether the range of the (basic) relation is a wrapped relation.
5122 #include <isl/space.h>
5123 isl_bool isl_space_can_range_curry(
5124 __isl_keep isl_space *space);
5126 #include <isl/map.h>
5127 isl_bool isl_map_can_range_curry(
5128 __isl_keep isl_map *map);
5130 Check whether the domain of the relation wrapped in the range of
5131 the input is itself a wrapped relation.
5133 =item * Special Values
5135 #include <isl/aff.h>
5136 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5137 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5138 isl_bool isl_multi_pw_aff_is_cst(
5139 __isl_keep isl_multi_pw_aff *mpa);
5141 Check whether the given expression is a constant.
5143 #include <isl/val.h>
5144 isl_bool isl_multi_val_involves_nan(
5145 __isl_keep isl_multi_val *mv);
5147 #include <isl/aff.h>
5148 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5149 isl_bool isl_multi_aff_involves_nan(
5150 __isl_keep isl_multi_aff *ma);
5151 isl_bool isl_pw_aff_involves_nan(
5152 __isl_keep isl_pw_aff *pa);
5153 isl_bool isl_pw_multi_aff_involves_nan(
5154 __isl_keep isl_pw_multi_aff *pma);
5155 isl_bool isl_multi_pw_aff_involves_nan(
5156 __isl_keep isl_multi_pw_aff *mpa);
5157 isl_bool isl_union_pw_aff_involves_nan(
5158 __isl_keep isl_union_pw_aff *upa);
5159 isl_bool isl_union_pw_multi_aff_involves_nan(
5160 __isl_keep isl_union_pw_multi_aff *upma);
5161 isl_bool isl_multi_union_pw_aff_involves_nan(
5162 __isl_keep isl_multi_union_pw_aff *mupa);
5164 #include <isl/polynomial.h>
5165 isl_bool isl_qpolynomial_is_nan(
5166 __isl_keep isl_qpolynomial *qp);
5167 isl_bool isl_qpolynomial_fold_is_nan(
5168 __isl_keep isl_qpolynomial_fold *fold);
5169 isl_bool isl_pw_qpolynomial_involves_nan(
5170 __isl_keep isl_pw_qpolynomial *pwqp);
5171 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5172 __isl_keep isl_pw_qpolynomial_fold *pwf);
5173 isl_bool isl_union_pw_qpolynomial_involves_nan(
5174 __isl_keep isl_union_pw_qpolynomial *upwqp);
5175 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5176 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5178 Check whether the given expression is equal to or involves NaN.
5180 #include <isl/val.h>
5181 isl_bool isl_multi_val_is_zero(
5182 __isl_keep isl_multi_val *mv);
5184 Check whether the multiple value is zero.
5186 #include <isl/aff.h>
5187 isl_bool isl_aff_plain_is_zero(
5188 __isl_keep isl_aff *aff);
5190 Check whether the affine expression is obviously zero.
5194 =head3 Binary Properties
5200 The following functions check whether two objects
5201 represent the same set, relation or function.
5202 The C<plain> variants only return true if the objects
5203 are obviously the same. That is, they may return false
5204 even if the objects are the same, but they will never
5205 return true if the objects are not the same.
5207 #include <isl/set.h>
5208 isl_bool isl_basic_set_plain_is_equal(
5209 __isl_keep isl_basic_set *bset1,
5210 __isl_keep isl_basic_set *bset2);
5211 isl_bool isl_basic_set_is_equal(
5212 __isl_keep isl_basic_set *bset1,
5213 __isl_keep isl_basic_set *bset2);
5214 isl_bool isl_set_plain_is_equal(
5215 __isl_keep isl_set *set1,
5216 __isl_keep isl_set *set2);
5217 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5218 __isl_keep isl_set *set2);
5220 #include <isl/map.h>
5221 isl_bool isl_basic_map_is_equal(
5222 __isl_keep isl_basic_map *bmap1,
5223 __isl_keep isl_basic_map *bmap2);
5224 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5225 __isl_keep isl_map *map2);
5226 isl_bool isl_map_plain_is_equal(
5227 __isl_keep isl_map *map1,
5228 __isl_keep isl_map *map2);
5230 #include <isl/union_set.h>
5231 isl_bool isl_union_set_is_equal(
5232 __isl_keep isl_union_set *uset1,
5233 __isl_keep isl_union_set *uset2);
5235 #include <isl/union_map.h>
5236 isl_bool isl_union_map_is_equal(
5237 __isl_keep isl_union_map *umap1,
5238 __isl_keep isl_union_map *umap2);
5241 isl_bool isl_multi_id_plain_is_equal(
5242 __isl_keep isl_multi_id *mi1,
5243 __isl_keep isl_multi_id *mi2);
5245 #include <isl/val.h>
5246 isl_bool isl_multi_val_plain_is_equal(
5247 __isl_keep isl_multi_val *mv1,
5248 __isl_keep isl_multi_val *mv2);
5250 #include <isl/aff.h>
5251 isl_bool isl_aff_plain_is_equal(
5252 __isl_keep isl_aff *aff1,
5253 __isl_keep isl_aff *aff2);
5254 isl_bool isl_multi_aff_plain_is_equal(
5255 __isl_keep isl_multi_aff *maff1,
5256 __isl_keep isl_multi_aff *maff2);
5257 isl_bool isl_pw_aff_plain_is_equal(
5258 __isl_keep isl_pw_aff *pwaff1,
5259 __isl_keep isl_pw_aff *pwaff2);
5260 isl_bool isl_pw_aff_is_equal(
5261 __isl_keep isl_pw_aff *pa1,
5262 __isl_keep isl_pw_aff *pa2);
5263 isl_bool isl_pw_multi_aff_plain_is_equal(
5264 __isl_keep isl_pw_multi_aff *pma1,
5265 __isl_keep isl_pw_multi_aff *pma2);
5266 isl_bool isl_pw_multi_aff_is_equal(
5267 __isl_keep isl_pw_multi_aff *pma1,
5268 __isl_keep isl_pw_multi_aff *pma2);
5269 isl_bool isl_multi_pw_aff_plain_is_equal(
5270 __isl_keep isl_multi_pw_aff *mpa1,
5271 __isl_keep isl_multi_pw_aff *mpa2);
5272 isl_bool isl_multi_pw_aff_is_equal(
5273 __isl_keep isl_multi_pw_aff *mpa1,
5274 __isl_keep isl_multi_pw_aff *mpa2);
5275 isl_bool isl_union_pw_aff_plain_is_equal(
5276 __isl_keep isl_union_pw_aff *upa1,
5277 __isl_keep isl_union_pw_aff *upa2);
5278 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5279 __isl_keep isl_union_pw_multi_aff *upma1,
5280 __isl_keep isl_union_pw_multi_aff *upma2);
5281 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5282 __isl_keep isl_multi_union_pw_aff *mupa1,
5283 __isl_keep isl_multi_union_pw_aff *mupa2);
5285 #include <isl/polynomial.h>
5286 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5287 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5288 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5289 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5290 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5291 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5293 =item * Disjointness
5295 #include <isl/set.h>
5296 isl_bool isl_basic_set_is_disjoint(
5297 __isl_keep isl_basic_set *bset1,
5298 __isl_keep isl_basic_set *bset2);
5299 isl_bool isl_set_plain_is_disjoint(
5300 __isl_keep isl_set *set1,
5301 __isl_keep isl_set *set2);
5302 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5303 __isl_keep isl_set *set2);
5305 #include <isl/map.h>
5306 isl_bool isl_basic_map_is_disjoint(
5307 __isl_keep isl_basic_map *bmap1,
5308 __isl_keep isl_basic_map *bmap2);
5309 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5310 __isl_keep isl_map *map2);
5312 #include <isl/union_set.h>
5313 isl_bool isl_union_set_is_disjoint(
5314 __isl_keep isl_union_set *uset1,
5315 __isl_keep isl_union_set *uset2);
5317 #include <isl/union_map.h>
5318 isl_bool isl_union_map_is_disjoint(
5319 __isl_keep isl_union_map *umap1,
5320 __isl_keep isl_union_map *umap2);
5324 isl_bool isl_basic_set_is_subset(
5325 __isl_keep isl_basic_set *bset1,
5326 __isl_keep isl_basic_set *bset2);
5327 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5328 __isl_keep isl_set *set2);
5329 isl_bool isl_set_is_strict_subset(
5330 __isl_keep isl_set *set1,
5331 __isl_keep isl_set *set2);
5332 isl_bool isl_union_set_is_subset(
5333 __isl_keep isl_union_set *uset1,
5334 __isl_keep isl_union_set *uset2);
5335 isl_bool isl_union_set_is_strict_subset(
5336 __isl_keep isl_union_set *uset1,
5337 __isl_keep isl_union_set *uset2);
5338 isl_bool isl_basic_map_is_subset(
5339 __isl_keep isl_basic_map *bmap1,
5340 __isl_keep isl_basic_map *bmap2);
5341 isl_bool isl_basic_map_is_strict_subset(
5342 __isl_keep isl_basic_map *bmap1,
5343 __isl_keep isl_basic_map *bmap2);
5344 isl_bool isl_map_is_subset(
5345 __isl_keep isl_map *map1,
5346 __isl_keep isl_map *map2);
5347 isl_bool isl_map_is_strict_subset(
5348 __isl_keep isl_map *map1,
5349 __isl_keep isl_map *map2);
5350 isl_bool isl_union_map_is_subset(
5351 __isl_keep isl_union_map *umap1,
5352 __isl_keep isl_union_map *umap2);
5353 isl_bool isl_union_map_is_strict_subset(
5354 __isl_keep isl_union_map *umap1,
5355 __isl_keep isl_union_map *umap2);
5357 Check whether the first argument is a (strict) subset of the
5362 Every comparison function returns a negative value if the first
5363 argument is considered smaller than the second, a positive value
5364 if the first argument is considered greater and zero if the two
5365 constraints are considered the same by the comparison criterion.
5367 #include <isl/constraint.h>
5368 int isl_constraint_plain_cmp(
5369 __isl_keep isl_constraint *c1,
5370 __isl_keep isl_constraint *c2);
5372 This function is useful for sorting C<isl_constraint>s.
5373 The order depends on the internal representation of the inputs.
5374 The order is fixed over different calls to the function (assuming
5375 the internal representation of the inputs has not changed), but may
5376 change over different versions of C<isl>.
5378 #include <isl/constraint.h>
5379 int isl_constraint_cmp_last_non_zero(
5380 __isl_keep isl_constraint *c1,
5381 __isl_keep isl_constraint *c2);
5383 This function can be used to sort constraints that live in the same
5384 local space. Constraints that involve ``earlier'' dimensions or
5385 that have a smaller coefficient for the shared latest dimension
5386 are considered smaller than other constraints.
5387 This function only defines a B<partial> order.
5389 #include <isl/set.h>
5390 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5391 __isl_keep isl_set *set2);
5393 This function is useful for sorting C<isl_set>s.
5394 The order depends on the internal representation of the inputs.
5395 The order is fixed over different calls to the function (assuming
5396 the internal representation of the inputs has not changed), but may
5397 change over different versions of C<isl>.
5399 #include <isl/aff.h>
5400 int isl_multi_aff_plain_cmp(
5401 __isl_keep isl_multi_aff *ma1,
5402 __isl_keep isl_multi_aff *ma2);
5403 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5404 __isl_keep isl_pw_aff *pa2);
5406 The functions C<isl_multi_aff_plain_cmp> and
5407 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5408 C<isl_pw_aff>s. The order is not strictly defined.
5409 The current order sorts expressions that only involve
5410 earlier dimensions before those that involve later dimensions.
5414 =head2 Unary Operations
5420 __isl_give isl_set *isl_set_complement(
5421 __isl_take isl_set *set);
5422 __isl_give isl_map *isl_map_complement(
5423 __isl_take isl_map *map);
5427 #include <isl/space.h>
5428 __isl_give isl_space *isl_space_reverse(
5429 __isl_take isl_space *space);
5430 __isl_give isl_space *isl_space_wrapped_reverse(
5431 __isl_take isl_space *space);
5432 __isl_give isl_space *isl_space_domain_reverse(
5433 __isl_take isl_space *space);
5434 __isl_give isl_space *isl_space_range_reverse(
5435 __isl_take isl_space *space);
5437 #include <isl/aff.h>
5438 __isl_give isl_aff *isl_aff_domain_reverse(
5439 __isl_take isl_aff *aff);
5440 __isl_give isl_multi_aff *
5441 isl_multi_aff_domain_reverse(
5442 __isl_take isl_multi_aff *ma);
5443 __isl_give isl_pw_aff *isl_pw_aff_domain_reverse(
5444 __isl_take isl_pw_aff *pa);
5445 __isl_give isl_pw_multi_aff *
5446 isl_pw_multi_aff_domain_reverse(
5447 __isl_take isl_pw_multi_aff *pma);
5448 __isl_give isl_multi_pw_aff *
5449 isl_multi_pw_aff_domain_reverse(
5450 __isl_take isl_multi_pw_aff *mpa);
5452 #include <isl/set.h>
5453 __isl_give isl_set *isl_set_wrapped_reverse(
5454 __isl_take isl_set *set);
5456 #include <isl/map.h>
5457 __isl_give isl_basic_map *isl_basic_map_reverse(
5458 __isl_take isl_basic_map *bmap);
5459 __isl_give isl_map *isl_map_reverse(
5460 __isl_take isl_map *map);
5461 __isl_give isl_map *isl_map_domain_reverse(
5462 __isl_take isl_map *map);
5463 __isl_give isl_map *isl_map_range_reverse(
5464 __isl_take isl_map *map);
5466 #include <isl/union_map.h>
5467 __isl_give isl_union_map *isl_union_map_reverse(
5468 __isl_take isl_union_map *umap);
5469 __isl_give isl_union_map *isl_union_map_domain_reverse(
5470 __isl_take isl_union_map *umap);
5471 __isl_give isl_union_map *isl_union_map_range_reverse(
5472 __isl_take isl_union_map *umap);
5474 #include <isl/polynomial.h>
5475 __isl_give isl_qpolynomial *
5476 isl_qpolynomial_domain_reverse(
5477 __isl_take isl_qpolynomial *qp);
5478 __isl_give isl_pw_qpolynomial *
5479 isl_pw_qpolynomial_domain_reverse(
5480 __isl_take isl_pw_qpolynomial *pwqp);
5481 __isl_give isl_union_pw_qpolynomial *
5482 isl_union_pw_qpolynomial_domain_reverse(
5483 __isl_take isl_union_pw_qpolynomial *upwqp);
5485 The function C<isl_space_range_reverse> reverses the relation
5486 that is embedded in the range of the input map space.
5487 The identifier of the range, if any, is only preserved
5488 if this embedded relation has identical input and output tuples.
5489 Similarly for C<isl_space_domain_reverse>.
5490 Along the same lines, C<isl_space_wrapped_reverse> reverses
5491 the relation that is embedded in a set space.
5493 =item * Tuple binding
5495 The following function binds
5496 a tuple to a sequence of parameter identifiers, equating
5497 the tuple dimensions to the parameters with those identifiers and
5498 subsequently projecting out the tuple.
5499 If the original object did not reference any such parameters,
5500 then this means that the tuple dimensions are reinterpreted
5502 The space of C<tuple> needs to match that of the bound tuple.
5504 #include <isl/set.h>
5505 __isl_give isl_set *isl_set_bind(
5506 __isl_take isl_set *set,
5507 __isl_take isl_multi_id *tuple);
5509 #include <isl/map.h>
5510 __isl_give isl_set *isl_map_bind_domain(
5511 __isl_take isl_map *map,
5512 __isl_take isl_multi_id *tuple);
5513 __isl_give isl_set *isl_map_bind_range(
5514 __isl_take isl_map *map,
5515 __isl_take isl_multi_id *tuple);
5517 #include <isl/union_map.h>
5518 __isl_give isl_union_set *isl_union_map_bind_range(
5519 __isl_take isl_union_map *umap,
5520 __isl_take isl_multi_id *tuple);
5522 #include <isl/aff.h>
5523 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5524 __isl_take isl_pw_aff *pa,
5525 __isl_take isl_multi_id *tuple);
5526 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5527 __isl_take isl_multi_aff *ma,
5528 __isl_take isl_multi_id *tuple);
5529 __isl_give isl_pw_multi_aff *
5530 isl_pw_multi_aff_bind_domain(
5531 __isl_take isl_pw_multi_aff *pma,
5532 __isl_take isl_multi_id *tuple);
5533 __isl_give isl_multi_pw_aff *
5534 isl_multi_pw_aff_bind_domain(
5535 __isl_take isl_multi_pw_aff *mpa,
5536 __isl_take isl_multi_id *tuple);
5537 __isl_give isl_pw_aff *
5538 isl_pw_aff_bind_domain_wrapped_domain(
5539 __isl_take isl_pw_aff *pa,
5540 __isl_take isl_multi_id *tuple);
5541 __isl_give isl_multi_aff *
5542 isl_multi_aff_bind_domain_wrapped_domain(
5543 __isl_take isl_multi_aff *ma,
5544 __isl_take isl_multi_id *tuple);
5545 __isl_give isl_pw_multi_aff *
5546 isl_pw_multi_aff_bind_domain_wrapped_domain(
5547 __isl_take isl_pw_multi_aff *pma,
5548 __isl_take isl_multi_id *tuple);
5549 __isl_give isl_multi_pw_aff *
5550 isl_multi_pw_aff_bind_domain_wrapped_domain(
5551 __isl_take isl_multi_pw_aff *mpa,
5552 __isl_take isl_multi_id *tuple);
5553 __isl_give isl_basic_set *isl_aff_bind_id(
5554 __isl_take isl_aff *aff,
5555 __isl_take isl_id *id);
5556 __isl_give isl_set *isl_pw_aff_bind_id(
5557 __isl_take isl_pw_aff *pa,
5558 __isl_take isl_id *id);
5559 __isl_give isl_basic_set *isl_multi_aff_bind(
5560 __isl_take isl_multi_aff *ma,
5561 __isl_take isl_multi_id *tuple);
5562 __isl_give isl_set *isl_multi_pw_aff_bind(
5563 __isl_take isl_multi_pw_aff *mpa,
5564 __isl_take isl_multi_id *tuple);
5565 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5566 __isl_take isl_union_pw_aff *upa,
5567 __isl_take isl_id *id);
5568 __isl_give isl_union_set *
5569 isl_multi_union_pw_aff_bind(
5570 __isl_take isl_multi_union_pw_aff *mupa,
5571 __isl_take isl_multi_id *tuple);
5573 Projecting out the domain of the wrapped relation in the domain
5574 of a function leaves the range of that wrapped relation
5575 in the domain of the resulting function.
5576 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5577 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5578 C<isl_union_pw_aff_bind_id> and
5579 C<isl_multi_union_pw_aff_bind>, the parameters
5580 are bound to the function values and the result lives
5581 in the domain of the input function.
5585 #include <isl/space.h>
5586 __isl_give isl_space *isl_space_domain(
5587 __isl_take isl_space *space);
5588 __isl_give isl_space *isl_space_range(
5589 __isl_take isl_space *space);
5590 __isl_give isl_space *isl_space_params(
5591 __isl_take isl_space *space);
5592 __isl_give isl_space *
5593 isl_space_domain_wrapped_domain(
5594 __isl_take isl_space *space);
5595 __isl_give isl_space *
5596 isl_space_domain_wrapped_range(
5597 __isl_take isl_space *space);
5598 __isl_give isl_space *
5599 isl_space_range_wrapped_domain(
5600 __isl_take isl_space *space);
5601 __isl_give isl_space *
5602 isl_space_range_wrapped_range(
5603 __isl_take isl_space *space);
5605 #include <isl/local_space.h>
5606 __isl_give isl_local_space *isl_local_space_domain(
5607 __isl_take isl_local_space *ls);
5608 __isl_give isl_local_space *isl_local_space_range(
5609 __isl_take isl_local_space *ls);
5611 #include <isl/set.h>
5612 __isl_give isl_basic_set *isl_basic_set_project_out(
5613 __isl_take isl_basic_set *bset,
5614 enum isl_dim_type type, unsigned first, unsigned n);
5615 __isl_give isl_set *isl_set_project_out_param_id(
5616 __isl_take isl_set *set,
5617 __isl_take isl_id *id);
5618 __isl_give isl_set *
5619 isl_set_project_out_param_id_list(
5620 __isl_take isl_set *set,
5621 __isl_take isl_id_list *list);
5622 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5623 enum isl_dim_type type, unsigned first, unsigned n);
5624 __isl_give isl_set *isl_set_project_out_all_params(
5625 __isl_take isl_set *set);
5626 __isl_give isl_map *isl_set_project_onto_map(
5627 __isl_take isl_set *set,
5628 enum isl_dim_type type, unsigned first,
5630 __isl_give isl_basic_set *isl_basic_set_params(
5631 __isl_take isl_basic_set *bset);
5632 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5634 The function C<isl_space_domain_wrapped_domain> returns the domain
5635 of the binary relation wrapped inside the domain of the input.
5636 The function C<isl_set_project_onto_map> returns a relation
5637 that projects the input set onto the given set dimensions.
5639 #include <isl/map.h>
5640 __isl_give isl_basic_map *isl_basic_map_project_out(
5641 __isl_take isl_basic_map *bmap,
5642 enum isl_dim_type type, unsigned first, unsigned n);
5643 __isl_give isl_map *isl_map_project_out_param_id(
5644 __isl_take isl_map *map,
5645 __isl_take isl_id *id);
5646 __isl_give isl_map *isl_map_project_out_param_id_list(
5647 __isl_take isl_map *map,
5648 __isl_take isl_id_list *list);
5649 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5650 enum isl_dim_type type, unsigned first, unsigned n);
5651 __isl_give isl_map *isl_map_project_out_all_params(
5652 __isl_take isl_map *map);
5653 __isl_give isl_basic_set *isl_basic_map_domain(
5654 __isl_take isl_basic_map *bmap);
5655 __isl_give isl_basic_set *isl_basic_map_range(
5656 __isl_take isl_basic_map *bmap);
5657 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5658 __isl_give isl_set *isl_map_domain(
5659 __isl_take isl_map *bmap);
5660 __isl_give isl_set *isl_map_range(
5661 __isl_take isl_map *map);
5663 #include <isl/union_set.h>
5664 __isl_give isl_union_set *isl_union_set_project_out(
5665 __isl_take isl_union_set *uset,
5666 enum isl_dim_type type,
5667 unsigned first, unsigned n);
5668 __isl_give isl_union_set *
5669 isl_union_set_project_out_all_params(
5670 __isl_take isl_union_set *uset);
5671 __isl_give isl_set *isl_union_set_params(
5672 __isl_take isl_union_set *uset);
5674 The function C<isl_union_set_project_out> can only project out
5677 #include <isl/union_map.h>
5678 __isl_give isl_union_map *
5679 isl_union_map_project_out_param_id(
5680 __isl_take isl_union_map *umap,
5681 __isl_take isl_id *id);
5682 __isl_give isl_union_map *
5683 isl_union_map_project_out_param_id_list(
5684 __isl_take isl_union_map *umap,
5685 __isl_take isl_id_list *list);
5686 __isl_give isl_union_map *isl_union_map_project_out(
5687 __isl_take isl_union_map *umap,
5688 enum isl_dim_type type, unsigned first, unsigned n);
5689 __isl_give isl_union_map *
5690 isl_union_map_project_out_all_params(
5691 __isl_take isl_union_map *umap);
5692 __isl_give isl_set *isl_union_map_params(
5693 __isl_take isl_union_map *umap);
5694 __isl_give isl_union_set *isl_union_map_domain(
5695 __isl_take isl_union_map *umap);
5696 __isl_give isl_union_set *isl_union_map_range(
5697 __isl_take isl_union_map *umap);
5699 The function C<isl_union_map_project_out> can only project out
5702 #include <isl/aff.h>
5703 __isl_give isl_aff *isl_aff_project_domain_on_params(
5704 __isl_take isl_aff *aff);
5705 __isl_give isl_multi_aff *
5706 isl_multi_aff_project_domain_on_params(
5707 __isl_take isl_multi_aff *ma);
5708 __isl_give isl_pw_aff *
5709 isl_pw_aff_project_domain_on_params(
5710 __isl_take isl_pw_aff *pa);
5711 __isl_give isl_multi_pw_aff *
5712 isl_multi_pw_aff_project_domain_on_params(
5713 __isl_take isl_multi_pw_aff *mpa);
5714 __isl_give isl_pw_multi_aff *
5715 isl_pw_multi_aff_project_domain_on_params(
5716 __isl_take isl_pw_multi_aff *pma);
5717 __isl_give isl_set *isl_pw_aff_domain(
5718 __isl_take isl_pw_aff *pwaff);
5719 __isl_give isl_set *isl_pw_multi_aff_domain(
5720 __isl_take isl_pw_multi_aff *pma);
5721 __isl_give isl_set *isl_multi_pw_aff_domain(
5722 __isl_take isl_multi_pw_aff *mpa);
5723 __isl_give isl_union_set *isl_union_pw_aff_domain(
5724 __isl_take isl_union_pw_aff *upa);
5725 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5726 __isl_take isl_union_pw_multi_aff *upma);
5727 __isl_give isl_union_set *
5728 isl_multi_union_pw_aff_domain(
5729 __isl_take isl_multi_union_pw_aff *mupa);
5730 __isl_give isl_set *isl_pw_aff_params(
5731 __isl_take isl_pw_aff *pwa);
5733 If no explicit domain was set on a zero-dimensional input to
5734 C<isl_multi_union_pw_aff_domain>, then this function will
5735 return a parameter set.
5737 #include <isl/polynomial.h>
5738 __isl_give isl_qpolynomial *
5739 isl_qpolynomial_project_domain_on_params(
5740 __isl_take isl_qpolynomial *qp);
5741 __isl_give isl_pw_qpolynomial *
5742 isl_pw_qpolynomial_project_domain_on_params(
5743 __isl_take isl_pw_qpolynomial *pwqp);
5744 __isl_give isl_pw_qpolynomial_fold *
5745 isl_pw_qpolynomial_fold_project_domain_on_params(
5746 __isl_take isl_pw_qpolynomial_fold *pwf);
5747 __isl_give isl_set *isl_pw_qpolynomial_domain(
5748 __isl_take isl_pw_qpolynomial *pwqp);
5749 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5750 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5751 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5752 __isl_take isl_union_pw_qpolynomial *upwqp);
5754 #include <isl/space.h>
5755 __isl_give isl_space *isl_space_domain_map(
5756 __isl_take isl_space *space);
5757 __isl_give isl_space *isl_space_range_map(
5758 __isl_take isl_space *space);
5760 #include <isl/map.h>
5761 __isl_give isl_map *isl_set_wrapped_domain_map(
5762 __isl_take isl_set *set);
5763 __isl_give isl_basic_map *isl_basic_map_domain_map(
5764 __isl_take isl_basic_map *bmap);
5765 __isl_give isl_basic_map *isl_basic_map_range_map(
5766 __isl_take isl_basic_map *bmap);
5767 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5768 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5770 #include <isl/union_map.h>
5771 __isl_give isl_union_map *isl_union_map_domain_map(
5772 __isl_take isl_union_map *umap);
5773 __isl_give isl_union_pw_multi_aff *
5774 isl_union_map_domain_map_union_pw_multi_aff(
5775 __isl_take isl_union_map *umap);
5776 __isl_give isl_union_map *isl_union_map_range_map(
5777 __isl_take isl_union_map *umap);
5778 __isl_give isl_union_map *
5779 isl_union_set_wrapped_domain_map(
5780 __isl_take isl_union_set *uset);
5782 The functions above construct a (basic, regular or union) relation
5783 that maps (a wrapped version of) the input relation to its domain or range.
5784 C<isl_set_wrapped_domain_map> maps the input set to the domain
5785 of its wrapped relation.
5789 __isl_give isl_basic_set *isl_basic_set_eliminate(
5790 __isl_take isl_basic_set *bset,
5791 enum isl_dim_type type,
5792 unsigned first, unsigned n);
5793 __isl_give isl_set *isl_set_eliminate(
5794 __isl_take isl_set *set, enum isl_dim_type type,
5795 unsigned first, unsigned n);
5796 __isl_give isl_basic_map *isl_basic_map_eliminate(
5797 __isl_take isl_basic_map *bmap,
5798 enum isl_dim_type type,
5799 unsigned first, unsigned n);
5800 __isl_give isl_map *isl_map_eliminate(
5801 __isl_take isl_map *map, enum isl_dim_type type,
5802 unsigned first, unsigned n);
5804 Eliminate the coefficients for the given dimensions from the constraints,
5805 without removing the dimensions.
5807 =item * Constructing a set from a parameter domain
5809 A set space of a given dimension and with an optional name
5810 can be created from a parameter space using the following functions.
5812 #include <isl/space.h>
5813 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5814 __isl_take isl_space *space, unsigned dim);
5815 __isl_give isl_space *
5816 isl_space_add_named_tuple_id_ui(
5817 __isl_take isl_space *space,
5818 __isl_take isl_id *tuple_id, unsigned dim);
5820 A set with a given tuple can be created from a parameter domain
5821 using the following function.
5823 #include <isl/set.h>
5824 __isl_give isl_set *isl_set_unbind_params(
5825 __isl_take isl_set *set,
5826 __isl_take isl_multi_id *tuple);
5828 Any parameters with identifiers in C<tuple> are reinterpreted
5829 as the corresponding set dimensions.
5831 A zero-dimensional (local) space or (basic) set can be constructed
5832 on a given parameter domain using the following functions.
5834 #include <isl/space.h>
5835 __isl_give isl_space *isl_space_set_from_params(
5836 __isl_take isl_space *space);
5838 #include <isl/local_space.h>
5839 __isl_give isl_local_space *
5840 isl_local_space_set_from_params(
5841 __isl_take isl_local_space *ls);
5843 #include <isl/set.h>
5844 __isl_give isl_basic_set *isl_basic_set_from_params(
5845 __isl_take isl_basic_set *bset);
5846 __isl_give isl_set *isl_set_from_params(
5847 __isl_take isl_set *set);
5849 =item * Constructing a relation from one or two sets
5851 A map space with a range of a given dimension and with an optional name
5852 can be created from a domain space using the functions
5853 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5856 A relation with a given domain tuple can be created from a set
5857 that will become the range of the relation
5858 using the following function.
5860 #include <isl/set.h>
5861 __isl_give isl_map *
5862 isl_set_unbind_params_insert_domain(
5863 __isl_take isl_set *set,
5864 __isl_take isl_multi_id *domain);
5866 Any parameters with identifiers in C<domain> are reinterpreted
5867 as the corresponding input dimensions.
5869 Similarly, a function defined over a parameter domain can
5870 be converted into one defined over a set domain
5871 using the following functions.
5873 #include <isl/aff.h>
5874 __isl_give isl_aff *
5875 isl_aff_unbind_params_insert_domain(
5876 __isl_take isl_aff *aff,
5877 __isl_take isl_multi_id *domain);
5878 __isl_give isl_multi_aff *
5879 isl_multi_aff_unbind_params_insert_domain(
5880 __isl_take isl_multi_aff *ma,
5881 __isl_take isl_multi_id *domain);
5882 __isl_give isl_multi_pw_aff *
5883 isl_multi_pw_aff_unbind_params_insert_domain(
5884 __isl_take isl_multi_pw_aff *mpa,
5885 __isl_take isl_multi_id *domain);
5888 any parameters with identifiers in C<domain> are reinterpreted
5889 as the corresponding input dimensions.
5891 Create a relation with the given set(s) as domain and/or range.
5892 If only the domain or the range is specified, then
5893 the range or domain of the created relation is a zero-dimensional
5894 flat anonymous space.
5895 If the case of C<isl_space_map_from_set>, the input space
5896 specifies both the domain and the range of the result.
5898 #include <isl/space.h>
5899 __isl_give isl_space *isl_space_from_domain(
5900 __isl_take isl_space *space);
5901 __isl_give isl_space *isl_space_from_range(
5902 __isl_take isl_space *space);
5903 __isl_give isl_space *isl_space_map_from_set(
5904 __isl_take isl_space *space);
5905 __isl_give isl_space *isl_space_map_from_domain_and_range(
5906 __isl_take isl_space *domain,
5907 __isl_take isl_space *range);
5909 #include <isl/local_space.h>
5910 __isl_give isl_local_space *isl_local_space_from_domain(
5911 __isl_take isl_local_space *ls);
5913 #include <isl/map.h>
5914 __isl_give isl_map *isl_set_insert_domain(
5915 __isl_take isl_set *set,
5916 __isl_take isl_space *domain);
5917 __isl_give isl_map *isl_map_from_domain(
5918 __isl_take isl_set *set);
5919 __isl_give isl_map *isl_map_from_range(
5920 __isl_take isl_set *set);
5922 #include <isl/union_map.h>
5923 __isl_give isl_union_map *isl_union_map_from_domain(
5924 __isl_take isl_union_set *uset);
5925 __isl_give isl_union_map *isl_union_map_from_range(
5926 __isl_take isl_union_set *uset);
5927 __isl_give isl_union_map *
5928 isl_union_map_from_domain_and_range(
5929 __isl_take isl_union_set *domain,
5930 __isl_take isl_union_set *range);
5933 __isl_give isl_multi_id *isl_multi_id_from_range(
5934 __isl_take isl_multi_id *mi);
5936 #include <isl/val.h>
5937 __isl_give isl_multi_val *isl_multi_val_from_range(
5938 __isl_take isl_multi_val *mv);
5940 #include <isl/aff.h>
5941 __isl_give isl_multi_aff *
5942 isl_multi_aff_insert_domain(
5943 __isl_take isl_multi_aff *ma,
5944 __isl_take isl_space *domain);
5945 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5946 __isl_take isl_pw_aff *pa,
5947 __isl_take isl_space *domain);
5948 __isl_give isl_pw_multi_aff *
5949 isl_pw_multi_aff_insert_domain(
5950 __isl_take isl_pw_multi_aff *pma,
5951 __isl_take isl_space *domain);
5952 __isl_give isl_multi_pw_aff *
5953 isl_multi_pw_aff_insert_domain(
5954 __isl_take isl_multi_pw_aff *mpa,
5955 __isl_take isl_space *domain);
5956 __isl_give isl_aff *isl_aff_from_range(
5957 __isl_take isl_aff *aff);
5958 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5959 __isl_take isl_multi_aff *ma);
5960 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5961 __isl_take isl_pw_aff *pwa);
5962 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5963 __isl_take isl_multi_pw_aff *mpa);
5964 __isl_give isl_multi_union_pw_aff *
5965 isl_multi_union_pw_aff_from_range(
5966 __isl_take isl_multi_union_pw_aff *mupa);
5967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5968 __isl_take isl_set *set);
5969 __isl_give isl_union_pw_multi_aff *
5970 isl_union_pw_multi_aff_from_domain(
5971 __isl_take isl_union_set *uset);
5973 #include <isl/polynomial.h>
5974 __isl_give isl_pw_qpolynomial *
5975 isl_pw_qpolynomial_from_range(
5976 __isl_take isl_pw_qpolynomial *pwqp);
5977 __isl_give isl_pw_qpolynomial_fold *
5978 isl_pw_qpolynomial_fold_from_range(
5979 __isl_take isl_pw_qpolynomial_fold *pwf);
5983 #include <isl/set.h>
5984 __isl_give isl_basic_set *isl_basic_set_fix_si(
5985 __isl_take isl_basic_set *bset,
5986 enum isl_dim_type type, unsigned pos, int value);
5987 __isl_give isl_basic_set *isl_basic_set_fix_val(
5988 __isl_take isl_basic_set *bset,
5989 enum isl_dim_type type, unsigned pos,
5990 __isl_take isl_val *v);
5991 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5992 enum isl_dim_type type, unsigned pos, int value);
5993 __isl_give isl_set *isl_set_fix_val(
5994 __isl_take isl_set *set,
5995 enum isl_dim_type type, unsigned pos,
5996 __isl_take isl_val *v);
5998 #include <isl/map.h>
5999 __isl_give isl_basic_map *isl_basic_map_fix_si(
6000 __isl_take isl_basic_map *bmap,
6001 enum isl_dim_type type, unsigned pos, int value);
6002 __isl_give isl_basic_map *isl_basic_map_fix_val(
6003 __isl_take isl_basic_map *bmap,
6004 enum isl_dim_type type, unsigned pos,
6005 __isl_take isl_val *v);
6006 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
6007 enum isl_dim_type type, unsigned pos, int value);
6008 __isl_give isl_map *isl_map_fix_val(
6009 __isl_take isl_map *map,
6010 enum isl_dim_type type, unsigned pos,
6011 __isl_take isl_val *v);
6013 #include <isl/aff.h>
6014 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
6015 __isl_take isl_pw_multi_aff *pma,
6016 enum isl_dim_type type, unsigned pos, int value);
6018 #include <isl/polynomial.h>
6019 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
6020 __isl_take isl_pw_qpolynomial *pwqp,
6021 enum isl_dim_type type, unsigned n,
6022 __isl_take isl_val *v);
6023 __isl_give isl_pw_qpolynomial_fold *
6024 isl_pw_qpolynomial_fold_fix_val(
6025 __isl_take isl_pw_qpolynomial_fold *pwf,
6026 enum isl_dim_type type, unsigned n,
6027 __isl_take isl_val *v);
6029 Intersect the set, relation or function domain
6030 with the hyperplane where the given
6031 dimension has the fixed given value.
6033 #include <isl/set.h>
6034 __isl_give isl_basic_set *
6035 isl_basic_set_lower_bound_val(
6036 __isl_take isl_basic_set *bset,
6037 enum isl_dim_type type, unsigned pos,
6038 __isl_take isl_val *value);
6039 __isl_give isl_basic_set *
6040 isl_basic_set_upper_bound_val(
6041 __isl_take isl_basic_set *bset,
6042 enum isl_dim_type type, unsigned pos,
6043 __isl_take isl_val *value);
6044 __isl_give isl_set *isl_set_lower_bound_si(
6045 __isl_take isl_set *set,
6046 enum isl_dim_type type, unsigned pos, int value);
6047 __isl_give isl_set *isl_set_lower_bound_val(
6048 __isl_take isl_set *set,
6049 enum isl_dim_type type, unsigned pos,
6050 __isl_take isl_val *value);
6051 __isl_give isl_set *isl_set_upper_bound_si(
6052 __isl_take isl_set *set,
6053 enum isl_dim_type type, unsigned pos, int value);
6054 __isl_give isl_set *isl_set_upper_bound_val(
6055 __isl_take isl_set *set,
6056 enum isl_dim_type type, unsigned pos,
6057 __isl_take isl_val *value);
6058 __isl_give isl_set *isl_set_lower_bound_multi_val(
6059 __isl_take isl_set *set,
6060 __isl_take isl_multi_val *lower);
6061 __isl_give isl_set *isl_set_upper_bound_multi_val(
6062 __isl_take isl_set *set,
6063 __isl_take isl_multi_val *upper);
6064 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6065 __isl_take isl_set *set,
6066 __isl_take isl_multi_pw_aff *lower);
6067 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6068 __isl_take isl_set *set,
6069 __isl_take isl_multi_pw_aff *upper);
6071 #include <isl/map.h>
6072 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6073 __isl_take isl_basic_map *bmap,
6074 enum isl_dim_type type, unsigned pos, int value);
6075 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6076 __isl_take isl_basic_map *bmap,
6077 enum isl_dim_type type, unsigned pos, int value);
6078 __isl_give isl_map *isl_map_lower_bound_si(
6079 __isl_take isl_map *map,
6080 enum isl_dim_type type, unsigned pos, int value);
6081 __isl_give isl_map *isl_map_upper_bound_si(
6082 __isl_take isl_map *map,
6083 enum isl_dim_type type, unsigned pos, int value);
6084 __isl_give isl_map *isl_map_lower_bound_val(
6085 __isl_take isl_map *map,
6086 enum isl_dim_type type, unsigned pos,
6087 __isl_take isl_val *value);
6088 __isl_give isl_map *isl_map_upper_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_lower_bound_multi_pw_aff(
6093 __isl_take isl_map *map,
6094 __isl_take isl_multi_pw_aff *lower);
6095 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6096 __isl_take isl_map *map,
6097 __isl_take isl_multi_pw_aff *upper);
6099 Intersect the set or relation with the half-space where the given
6100 dimension has a value bounded by the given fixed integer value or
6101 symbolic constant expression.
6102 For functions taking a multi expression,
6103 this applies to all set dimensions.
6104 Those that bound a map, bound the range of that map.
6105 If the multi expression is zero-dimensional but has an explicit domain,
6106 then the (parameter) domain of the set or map is intersected
6107 with this explicit domain.
6109 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6110 enum isl_dim_type type1, int pos1,
6111 enum isl_dim_type type2, int pos2);
6112 __isl_give isl_basic_map *isl_basic_map_equate(
6113 __isl_take isl_basic_map *bmap,
6114 enum isl_dim_type type1, int pos1,
6115 enum isl_dim_type type2, int pos2);
6116 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6117 enum isl_dim_type type1, int pos1,
6118 enum isl_dim_type type2, int pos2);
6120 Intersect the set or relation with the hyperplane where the given
6121 dimensions are equal to each other.
6123 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6124 enum isl_dim_type type1, int pos1,
6125 enum isl_dim_type type2, int pos2);
6127 Intersect the relation with the hyperplane where the given
6128 dimensions have opposite values.
6130 __isl_give isl_map *isl_map_order_le(
6131 __isl_take isl_map *map,
6132 enum isl_dim_type type1, int pos1,
6133 enum isl_dim_type type2, int pos2);
6134 __isl_give isl_basic_map *isl_basic_map_order_ge(
6135 __isl_take isl_basic_map *bmap,
6136 enum isl_dim_type type1, int pos1,
6137 enum isl_dim_type type2, int pos2);
6138 __isl_give isl_map *isl_map_order_ge(
6139 __isl_take isl_map *map,
6140 enum isl_dim_type type1, int pos1,
6141 enum isl_dim_type type2, int pos2);
6142 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6143 enum isl_dim_type type1, int pos1,
6144 enum isl_dim_type type2, int pos2);
6145 __isl_give isl_basic_map *isl_basic_map_order_gt(
6146 __isl_take isl_basic_map *bmap,
6147 enum isl_dim_type type1, int pos1,
6148 enum isl_dim_type type2, int pos2);
6149 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6150 enum isl_dim_type type1, int pos1,
6151 enum isl_dim_type type2, int pos2);
6153 Intersect the relation with the half-space where the given
6154 dimensions satisfy the given ordering.
6156 #include <isl/union_set.h>
6157 __isl_give isl_union_map *isl_union_map_remove_map_if(
6158 __isl_take isl_union_map *umap,
6159 isl_bool (*fn)(__isl_keep isl_map *map,
6160 void *user), void *user);
6162 This function calls the callback function once for each
6163 pair of spaces for which there are elements in the input.
6164 If the callback returns C<isl_bool_true>, then all those elements
6165 are removed from the result. The only remaining elements in the output
6166 are then those for which the callback returns C<isl_bool_false>.
6170 #include <isl/aff.h>
6171 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6172 __isl_take isl_aff *aff);
6173 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6174 __isl_take isl_aff *aff);
6175 __isl_give isl_set *isl_pw_aff_pos_set(
6176 __isl_take isl_pw_aff *pa);
6177 __isl_give isl_set *isl_pw_aff_nonneg_set(
6178 __isl_take isl_pw_aff *pwaff);
6179 __isl_give isl_set *isl_pw_aff_zero_set(
6180 __isl_take isl_pw_aff *pwaff);
6181 __isl_give isl_set *isl_pw_aff_non_zero_set(
6182 __isl_take isl_pw_aff *pwaff);
6183 __isl_give isl_union_set *
6184 isl_union_pw_aff_zero_union_set(
6185 __isl_take isl_union_pw_aff *upa);
6186 __isl_give isl_union_set *
6187 isl_multi_union_pw_aff_zero_union_set(
6188 __isl_take isl_multi_union_pw_aff *mupa);
6190 The function C<isl_aff_neg_basic_set> returns a basic set
6191 containing those elements in the domain space
6192 of C<aff> where C<aff> is negative.
6193 The function C<isl_pw_aff_nonneg_set> returns a set
6194 containing those elements in the domain
6195 of C<pwaff> where C<pwaff> is non-negative.
6196 The function C<isl_multi_union_pw_aff_zero_union_set>
6197 returns a union set containing those elements
6198 in the domains of its elements where they are all zero.
6202 __isl_give isl_map *isl_set_identity(
6203 __isl_take isl_set *set);
6204 __isl_give isl_union_map *isl_union_set_identity(
6205 __isl_take isl_union_set *uset);
6206 __isl_give isl_union_pw_multi_aff *
6207 isl_union_set_identity_union_pw_multi_aff(
6208 __isl_take isl_union_set *uset);
6210 Construct an identity relation on the given (union) set.
6212 =item * Function Extraction
6214 A piecewise quasi affine expression that is equal to 1 on a set
6215 and 0 outside the set can be created using the following function.
6217 #include <isl/aff.h>
6218 __isl_give isl_pw_aff *isl_set_indicator_function(
6219 __isl_take isl_set *set);
6221 A piecewise multiple quasi affine expression can be extracted
6222 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6223 and the C<isl_map> is single-valued.
6224 In case of a conversion from an C<isl_union_map>
6225 to an C<isl_union_pw_multi_aff>, these properties need to hold
6226 in each domain space.
6227 A conversion to a C<isl_multi_union_pw_aff> additionally
6228 requires that the input is non-empty and involves only a single
6231 #include <isl/aff.h>
6232 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6233 __isl_take isl_set *set);
6234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6235 __isl_take isl_set *set);
6236 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6237 __isl_take isl_map *map);
6238 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6239 __isl_take isl_map *map);
6241 __isl_give isl_union_pw_multi_aff *
6242 isl_union_pw_multi_aff_from_union_set(
6243 __isl_take isl_union_set *uset);
6244 __isl_give isl_union_pw_multi_aff *
6245 isl_union_map_as_union_pw_multi_aff(
6246 __isl_take isl_union_map *umap);
6247 __isl_give isl_union_pw_multi_aff *
6248 isl_union_pw_multi_aff_from_union_map(
6249 __isl_take isl_union_map *umap);
6251 __isl_give isl_multi_union_pw_aff *
6252 isl_union_map_as_multi_union_pw_aff(
6253 __isl_take isl_union_map *umap);
6254 __isl_give isl_multi_union_pw_aff *
6255 isl_multi_union_pw_aff_from_union_map(
6256 __isl_take isl_union_map *umap);
6258 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6260 Similarly for C<isl_set_as_pw_multi_aff> and
6261 C<isl_pw_multi_aff_from_set>,
6262 for C<isl_union_map_as_union_pw_multi_aff> and
6263 C<isl_union_pw_multi_aff_from_union_map> and
6264 for C<isl_union_map_as_multi_union_pw_aff> and
6265 C<isl_multi_union_pw_aff_from_union_map>.
6269 __isl_give isl_basic_set *isl_basic_map_deltas(
6270 __isl_take isl_basic_map *bmap);
6271 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6272 __isl_give isl_union_set *isl_union_map_deltas(
6273 __isl_take isl_union_map *umap);
6275 These functions return a (basic) set containing the differences
6276 between image elements and corresponding domain elements in the input.
6278 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6279 __isl_take isl_basic_map *bmap);
6280 __isl_give isl_map *isl_map_deltas_map(
6281 __isl_take isl_map *map);
6282 __isl_give isl_union_map *isl_union_map_deltas_map(
6283 __isl_take isl_union_map *umap);
6285 The functions above construct a (basic, regular or union) relation
6286 that maps (a wrapped version of) the input relation to its delta set.
6290 #include <isl/map.h>
6291 __isl_give isl_map *isl_set_translation(
6292 __isl_take isl_set *deltas);
6294 This function performs essentially the opposite operation
6295 of C<isl_map_deltas>. In particular, it returns pairs
6296 of elements in the same space that have a difference in C<deltas>.
6300 Simplify the representation of a set, relation or functions by trying
6301 to combine pairs of basic sets or relations into a single
6302 basic set or relation.
6304 #include <isl/set.h>
6305 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6307 #include <isl/map.h>
6308 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6310 #include <isl/union_set.h>
6311 __isl_give isl_union_set *isl_union_set_coalesce(
6312 __isl_take isl_union_set *uset);
6314 #include <isl/union_map.h>
6315 __isl_give isl_union_map *isl_union_map_coalesce(
6316 __isl_take isl_union_map *umap);
6318 #include <isl/aff.h>
6319 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6320 __isl_take isl_pw_aff *pa);
6321 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6322 __isl_take isl_pw_multi_aff *pma);
6323 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6324 __isl_take isl_multi_pw_aff *mpa);
6325 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6326 __isl_take isl_union_pw_aff *upa);
6327 __isl_give isl_union_pw_multi_aff *
6328 isl_union_pw_multi_aff_coalesce(
6329 __isl_take isl_union_pw_multi_aff *upma);
6330 __isl_give isl_multi_union_pw_aff *
6331 isl_multi_union_pw_aff_coalesce(
6332 __isl_take isl_multi_union_pw_aff *mupa);
6334 #include <isl/polynomial.h>
6335 __isl_give isl_pw_qpolynomial_fold *
6336 isl_pw_qpolynomial_fold_coalesce(
6337 __isl_take isl_pw_qpolynomial_fold *pwf);
6338 __isl_give isl_union_pw_qpolynomial *
6339 isl_union_pw_qpolynomial_coalesce(
6340 __isl_take isl_union_pw_qpolynomial *upwqp);
6341 __isl_give isl_union_pw_qpolynomial_fold *
6342 isl_union_pw_qpolynomial_fold_coalesce(
6343 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6345 One of the methods for combining pairs of basic sets or relations
6346 can result in coefficients that are much larger than those that appear
6347 in the constraints of the input. By default, the coefficients are
6348 not allowed to grow larger, but this can be changed by unsetting
6349 the following option.
6351 isl_stat isl_options_set_coalesce_bounded_wrapping(
6352 isl_ctx *ctx, int val);
6353 int isl_options_get_coalesce_bounded_wrapping(
6356 One of the other methods tries to combine pairs of basic sets
6357 with different local variables, treating them as existentially
6358 quantified variables even if they have known (but different)
6359 integer division expressions. The result may then also have
6360 existentially quantified variables. Turning on the following
6361 option prevents this from happening.
6363 isl_stat isl_options_set_coalesce_preserve_locals(
6364 isl_ctx *ctx, int val);
6365 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6367 =item * Detecting equalities
6369 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6370 __isl_take isl_basic_set *bset);
6371 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6372 __isl_take isl_basic_map *bmap);
6373 __isl_give isl_set *isl_set_detect_equalities(
6374 __isl_take isl_set *set);
6375 __isl_give isl_map *isl_map_detect_equalities(
6376 __isl_take isl_map *map);
6377 __isl_give isl_union_set *isl_union_set_detect_equalities(
6378 __isl_take isl_union_set *uset);
6379 __isl_give isl_union_map *isl_union_map_detect_equalities(
6380 __isl_take isl_union_map *umap);
6382 Simplify the representation of a set or relation by detecting implicit
6385 =item * Removing redundant constraints
6387 #include <isl/set.h>
6388 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6389 __isl_take isl_basic_set *bset);
6390 __isl_give isl_set *isl_set_remove_redundancies(
6391 __isl_take isl_set *set);
6393 #include <isl/union_set.h>
6394 __isl_give isl_union_set *
6395 isl_union_set_remove_redundancies(
6396 __isl_take isl_union_set *uset);
6398 #include <isl/map.h>
6399 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6400 __isl_take isl_basic_map *bmap);
6401 __isl_give isl_map *isl_map_remove_redundancies(
6402 __isl_take isl_map *map);
6404 #include <isl/union_map.h>
6405 __isl_give isl_union_map *
6406 isl_union_map_remove_redundancies(
6407 __isl_take isl_union_map *umap);
6411 __isl_give isl_basic_set *isl_set_convex_hull(
6412 __isl_take isl_set *set);
6413 __isl_give isl_basic_map *isl_map_convex_hull(
6414 __isl_take isl_map *map);
6416 If the input set or relation has any existentially quantified
6417 variables, then the result of these operations is currently undefined.
6421 #include <isl/set.h>
6422 __isl_give isl_basic_set *
6423 isl_set_unshifted_simple_hull(
6424 __isl_take isl_set *set);
6425 __isl_give isl_basic_set *isl_set_simple_hull(
6426 __isl_take isl_set *set);
6427 __isl_give isl_basic_set *
6428 isl_set_plain_unshifted_simple_hull(
6429 __isl_take isl_set *set);
6430 __isl_give isl_basic_set *
6431 isl_set_unshifted_simple_hull_from_set_list(
6432 __isl_take isl_set *set,
6433 __isl_take isl_set_list *list);
6435 #include <isl/map.h>
6436 __isl_give isl_basic_map *
6437 isl_map_unshifted_simple_hull(
6438 __isl_take isl_map *map);
6439 __isl_give isl_basic_map *isl_map_simple_hull(
6440 __isl_take isl_map *map);
6441 __isl_give isl_basic_map *
6442 isl_map_plain_unshifted_simple_hull(
6443 __isl_take isl_map *map);
6444 __isl_give isl_basic_map *
6445 isl_map_unshifted_simple_hull_from_map_list(
6446 __isl_take isl_map *map,
6447 __isl_take isl_map_list *list);
6449 #include <isl/union_map.h>
6450 __isl_give isl_union_map *isl_union_map_simple_hull(
6451 __isl_take isl_union_map *umap);
6453 These functions compute a single basic set or relation
6454 that contains the whole input set or relation.
6455 In particular, the output is described by translates
6456 of the constraints describing the basic sets or relations in the input.
6457 In case of C<isl_set_unshifted_simple_hull>, only the original
6458 constraints are used, without any translation.
6459 In case of C<isl_set_plain_unshifted_simple_hull> and
6460 C<isl_map_plain_unshifted_simple_hull>, the result is described
6461 by original constraints that are obviously satisfied
6462 by the entire input set or relation.
6463 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6464 C<isl_map_unshifted_simple_hull_from_map_list>, the
6465 constraints are taken from the elements of the second argument.
6469 (See \autoref{s:simple hull}.)
6475 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6476 __isl_take isl_basic_set *bset);
6477 __isl_give isl_basic_set *isl_set_affine_hull(
6478 __isl_take isl_set *set);
6479 __isl_give isl_union_set *isl_union_set_affine_hull(
6480 __isl_take isl_union_set *uset);
6481 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6482 __isl_take isl_basic_map *bmap);
6483 __isl_give isl_basic_map *isl_map_affine_hull(
6484 __isl_take isl_map *map);
6485 __isl_give isl_union_map *isl_union_map_affine_hull(
6486 __isl_take isl_union_map *umap);
6488 In case of union sets and relations, the affine hull is computed
6491 =item * Polyhedral hull
6493 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6494 __isl_take isl_set *set);
6495 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6496 __isl_take isl_map *map);
6497 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6498 __isl_take isl_union_set *uset);
6499 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6500 __isl_take isl_union_map *umap);
6502 These functions compute a single basic set or relation
6503 not involving any existentially quantified variables
6504 that contains the whole input set or relation.
6505 In case of union sets and relations, the polyhedral hull is computed
6510 #include <isl/set.h>
6511 __isl_give isl_fixed_box *
6512 isl_set_get_simple_fixed_box_hull(
6513 __isl_keep isl_set *set)
6515 #include <isl/map.h>
6516 __isl_give isl_fixed_box *
6517 isl_map_get_range_simple_fixed_box_hull(
6518 __isl_keep isl_map *map);
6520 These functions try to approximate the set or
6521 the range of the map by a box of fixed size.
6522 The box is described in terms of an offset living in the same space as
6523 the input and a size living in the set or range space. For any element
6524 in the input map, the range value is greater than or equal to
6525 the offset applied to the domain value and the difference with
6526 this offset is strictly smaller than the size.
6527 The same holds for the elements of the input set, where
6528 the offset is a parametric constant value.
6529 If no fixed-size approximation can be found,
6530 an I<invalid> box is returned, i.e., one for which
6531 C<isl_fixed_box_is_valid> below returns false.
6533 The validity, the offset and the size of the box can be obtained using
6534 the following functions.
6536 #include <isl/fixed_box.h>
6537 isl_bool isl_fixed_box_is_valid(
6538 __isl_keep isl_fixed_box *box);
6539 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6540 __isl_keep isl_fixed_box *box);
6541 __isl_give isl_multi_val *isl_fixed_box_get_size(
6542 __isl_keep isl_fixed_box *box);
6544 The box can be copied and freed using the following functions.
6546 #include <isl/fixed_box.h>
6547 __isl_give isl_fixed_box *isl_fixed_box_copy(
6548 __isl_keep isl_fixed_box *box);
6549 __isl_null isl_fixed_box *isl_fixed_box_free(
6550 __isl_take isl_fixed_box *box);
6552 An object of type C<isl_fixed_box> can be read from input
6553 using the following function.
6555 #include <isl/fixed_box.h>
6556 __isl_give isl_fixed_box *
6557 isl_fixed_box_read_from_str(isl_ctx *ctx,
6560 A representation of the information contained in an object
6561 of type C<isl_fixed_box> can be obtained using
6563 #include <isl/fixed_box.h>
6564 __isl_give isl_printer *isl_printer_print_fixed_box(
6565 __isl_take isl_printer *p,
6566 __isl_keep isl_fixed_box *box);
6567 __isl_give char *isl_fixed_box_to_str(
6568 __isl_keep isl_fixed_box *box);
6570 C<isl_fixed_box_to_str> prints the information in flow format.
6572 =item * Other approximations
6574 #include <isl/set.h>
6575 __isl_give isl_basic_set *
6576 isl_basic_set_drop_constraints_involving_dims(
6577 __isl_take isl_basic_set *bset,
6578 enum isl_dim_type type,
6579 unsigned first, unsigned n);
6580 __isl_give isl_basic_set *
6581 isl_basic_set_drop_constraints_not_involving_dims(
6582 __isl_take isl_basic_set *bset,
6583 enum isl_dim_type type,
6584 unsigned first, unsigned n);
6585 __isl_give isl_set *
6586 isl_set_drop_constraints_involving_dims(
6587 __isl_take isl_set *set,
6588 enum isl_dim_type type,
6589 unsigned first, unsigned n);
6590 __isl_give isl_set *
6591 isl_set_drop_constraints_not_involving_dims(
6592 __isl_take isl_set *set,
6593 enum isl_dim_type type,
6594 unsigned first, unsigned n);
6596 #include <isl/map.h>
6597 __isl_give isl_basic_map *
6598 isl_basic_map_drop_constraints_involving_dims(
6599 __isl_take isl_basic_map *bmap,
6600 enum isl_dim_type type,
6601 unsigned first, unsigned n);
6602 __isl_give isl_basic_map *
6603 isl_basic_map_drop_constraints_not_involving_dims(
6604 __isl_take isl_basic_map *bmap,
6605 enum isl_dim_type type,
6606 unsigned first, unsigned n);
6607 __isl_give isl_map *
6608 isl_map_drop_constraints_involving_dims(
6609 __isl_take isl_map *map,
6610 enum isl_dim_type type,
6611 unsigned first, unsigned n);
6612 __isl_give isl_map *
6613 isl_map_drop_constraints_not_involving_dims(
6614 __isl_take isl_map *map,
6615 enum isl_dim_type type,
6616 unsigned first, unsigned n);
6618 These functions drop any constraints (not) involving the specified dimensions.
6619 Note that the result depends on the representation of the input.
6621 #include <isl/polynomial.h>
6622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6623 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6624 __isl_give isl_union_pw_qpolynomial *
6625 isl_union_pw_qpolynomial_to_polynomial(
6626 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6628 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6629 the polynomial will be an overapproximation. If C<sign> is negative,
6630 it will be an underapproximation. If C<sign> is zero, the approximation
6631 will lie somewhere in between.
6635 __isl_give isl_basic_set *isl_basic_set_sample(
6636 __isl_take isl_basic_set *bset);
6637 __isl_give isl_basic_set *isl_set_sample(
6638 __isl_take isl_set *set);
6639 __isl_give isl_basic_map *isl_basic_map_sample(
6640 __isl_take isl_basic_map *bmap);
6641 __isl_give isl_basic_map *isl_map_sample(
6642 __isl_take isl_map *map);
6644 If the input (basic) set or relation is non-empty, then return
6645 a singleton subset of the input. Otherwise, return an empty set.
6647 =item * Optimization
6649 #include <isl/ilp.h>
6650 __isl_give isl_val *isl_basic_set_max_val(
6651 __isl_keep isl_basic_set *bset,
6652 __isl_keep isl_aff *obj);
6653 __isl_give isl_val *isl_set_min_val(
6654 __isl_keep isl_set *set,
6655 __isl_keep isl_aff *obj);
6656 __isl_give isl_val *isl_set_max_val(
6657 __isl_keep isl_set *set,
6658 __isl_keep isl_aff *obj);
6659 __isl_give isl_multi_val *
6660 isl_union_set_min_multi_union_pw_aff(
6661 __isl_keep isl_union_set *uset,
6662 __isl_keep isl_multi_union_pw_aff *obj);
6664 Compute the minimum or maximum of the integer affine expression C<obj>
6665 over the points in C<set>.
6666 The result is C<NULL> in case of an error, the optimal value in case
6667 there is one, negative infinity or infinity if the problem is unbounded and
6668 NaN if the problem is empty.
6670 #include <isl/ilp.h>
6671 __isl_give isl_val *isl_pw_aff_min_val(
6672 __isl_take isl_pw_aff *pa);
6673 __isl_give isl_val *isl_pw_aff_max_val(
6674 __isl_take isl_pw_aff *pa);
6675 __isl_give isl_multi_val *
6676 isl_pw_multi_aff_min_multi_val(
6677 __isl_take isl_pw_multi_aff *pma);
6678 __isl_give isl_multi_val *
6679 isl_pw_multi_aff_max_multi_val(
6680 __isl_take isl_pw_multi_aff *pma);
6681 __isl_give isl_multi_val *
6682 isl_multi_pw_aff_min_multi_val(
6683 __isl_take isl_multi_pw_aff *mpa);
6684 __isl_give isl_multi_val *
6685 isl_multi_pw_aff_max_multi_val(
6686 __isl_take isl_multi_pw_aff *mpa);
6687 __isl_give isl_val *isl_union_pw_aff_min_val(
6688 __isl_take isl_union_pw_aff *upa);
6689 __isl_give isl_val *isl_union_pw_aff_max_val(
6690 __isl_take isl_union_pw_aff *upa);
6691 __isl_give isl_multi_val *
6692 isl_multi_union_pw_aff_min_multi_val(
6693 __isl_take isl_multi_union_pw_aff *mupa);
6694 __isl_give isl_multi_val *
6695 isl_multi_union_pw_aff_max_multi_val(
6696 __isl_take isl_multi_union_pw_aff *mupa);
6698 Compute the minimum or maximum of the integer affine expression
6699 over its definition domain.
6700 The result is C<NULL> in case of an error, the optimal value in case
6701 there is one, negative infinity or infinity if the problem is unbounded and
6702 NaN if the problem is empty.
6704 #include <isl/ilp.h>
6705 __isl_give isl_val *isl_basic_set_dim_max_val(
6706 __isl_take isl_basic_set *bset, int pos);
6707 __isl_give isl_val *isl_set_dim_min_val(
6708 __isl_take isl_set *set, int pos);
6709 __isl_give isl_val *isl_set_dim_max_val(
6710 __isl_take isl_set *set, int pos);
6712 Return the minimal or maximal value attained by the given set dimension,
6713 independently of the parameter values and of any other dimensions.
6714 The result is C<NULL> in case of an error, the optimal value in case
6715 there is one, (negative) infinity if the problem is unbounded and
6716 NaN if the input is empty.
6718 =item * Parametric optimization
6720 __isl_give isl_pw_aff *isl_set_dim_min(
6721 __isl_take isl_set *set, int pos);
6722 __isl_give isl_pw_aff *isl_set_dim_max(
6723 __isl_take isl_set *set, int pos);
6724 __isl_give isl_pw_aff *isl_map_dim_min(
6725 __isl_take isl_map *map, int pos);
6726 __isl_give isl_pw_aff *isl_map_dim_max(
6727 __isl_take isl_map *map, int pos);
6728 __isl_give isl_multi_pw_aff *
6729 isl_set_min_multi_pw_aff(
6730 __isl_take isl_set *set);
6731 __isl_give isl_multi_pw_aff *
6732 isl_set_max_multi_pw_aff(
6733 __isl_take isl_set *set);
6734 __isl_give isl_multi_pw_aff *
6735 isl_map_min_multi_pw_aff(
6736 __isl_take isl_map *map);
6737 __isl_give isl_multi_pw_aff *
6738 isl_map_max_multi_pw_aff(
6739 __isl_take isl_map *map);
6741 Compute the minimum or maximum of the (given) set or output dimension(s)
6742 as a function of the parameters (and input dimensions), but independently
6743 of the other set or output dimensions.
6744 For lexicographic optimization, see L<"Lexicographic Optimization">.
6748 The following functions compute either the set of (rational) coefficient
6749 values of valid constraints for the given set or the set of (rational)
6750 values satisfying the constraints with coefficients from the given set.
6751 Internally, these two sets of functions perform essentially the
6752 same operations, except that the set of coefficients is assumed to
6753 be a cone, while the set of values may be any polyhedron.
6754 The current implementation is based on the Farkas lemma and
6755 Fourier-Motzkin elimination, but this may change or be made optional
6756 in future. In particular, future implementations may use different
6757 dualization algorithms or skip the elimination step.
6759 #include <isl/set.h>
6760 __isl_give isl_basic_set *isl_basic_set_coefficients(
6761 __isl_take isl_basic_set *bset);
6762 __isl_give isl_basic_set_list *
6763 isl_basic_set_list_coefficients(
6764 __isl_take isl_basic_set_list *list);
6765 __isl_give isl_basic_set *isl_set_coefficients(
6766 __isl_take isl_set *set);
6767 __isl_give isl_union_set *isl_union_set_coefficients(
6768 __isl_take isl_union_set *bset);
6769 __isl_give isl_basic_set *isl_basic_set_solutions(
6770 __isl_take isl_basic_set *bset);
6771 __isl_give isl_basic_set *isl_set_solutions(
6772 __isl_take isl_set *set);
6773 __isl_give isl_union_set *isl_union_set_solutions(
6774 __isl_take isl_union_set *bset);
6778 __isl_give isl_map *isl_map_fixed_power_val(
6779 __isl_take isl_map *map,
6780 __isl_take isl_val *exp);
6781 __isl_give isl_union_map *
6782 isl_union_map_fixed_power_val(
6783 __isl_take isl_union_map *umap,
6784 __isl_take isl_val *exp);
6786 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6787 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6788 of C<map> is computed.
6790 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6792 __isl_give isl_union_map *isl_union_map_power(
6793 __isl_take isl_union_map *umap, isl_bool *exact);
6795 Compute a parametric representation for all positive powers I<k> of C<map>.
6796 The result maps I<k> to a nested relation corresponding to the
6797 I<k>th power of C<map>.
6798 The result may be an overapproximation. If the result is known to be exact,
6799 then C<*exact> is set to C<1>.
6801 =item * Transitive closure
6803 __isl_give isl_map *isl_map_transitive_closure(
6804 __isl_take isl_map *map, isl_bool *exact);
6805 __isl_give isl_union_map *isl_union_map_transitive_closure(
6806 __isl_take isl_union_map *umap, isl_bool *exact);
6808 Compute the transitive closure of C<map>.
6809 The result may be an overapproximation. If the result is known to be exact,
6810 then C<*exact> is set to C<1>.
6812 =item * Reaching path lengths
6814 __isl_give isl_map *isl_map_reaching_path_lengths(
6815 __isl_take isl_map *map, isl_bool *exact);
6817 Compute a relation that maps each element in the range of C<map>
6818 to the lengths of all paths composed of edges in C<map> that
6819 end up in the given element.
6820 The result may be an overapproximation. If the result is known to be exact,
6821 then C<*exact> is set to C<1>.
6822 To compute the I<maximal> path length, the resulting relation
6823 should be postprocessed by C<isl_map_lexmax>.
6824 In particular, if the input relation is a dependence relation
6825 (mapping sources to sinks), then the maximal path length corresponds
6826 to the free schedule.
6827 Note, however, that C<isl_map_lexmax> expects the maximum to be
6828 finite, so if the path lengths are unbounded (possibly due to
6829 the overapproximation), then you will get an error message.
6833 #include <isl/space.h>
6834 __isl_give isl_space *isl_space_wrap(
6835 __isl_take isl_space *space);
6836 __isl_give isl_space *isl_space_unwrap(
6837 __isl_take isl_space *space);
6839 #include <isl/local_space.h>
6840 __isl_give isl_local_space *isl_local_space_wrap(
6841 __isl_take isl_local_space *ls);
6843 #include <isl/set.h>
6844 __isl_give isl_basic_map *isl_basic_set_unwrap(
6845 __isl_take isl_basic_set *bset);
6846 __isl_give isl_map *isl_set_unwrap(
6847 __isl_take isl_set *set);
6849 #include <isl/map.h>
6850 __isl_give isl_basic_set *isl_basic_map_wrap(
6851 __isl_take isl_basic_map *bmap);
6852 __isl_give isl_set *isl_map_wrap(
6853 __isl_take isl_map *map);
6855 #include <isl/union_set.h>
6856 __isl_give isl_union_map *isl_union_set_unwrap(
6857 __isl_take isl_union_set *uset);
6859 #include <isl/union_map.h>
6860 __isl_give isl_union_set *isl_union_map_wrap(
6861 __isl_take isl_union_map *umap);
6863 The input to C<isl_space_unwrap> should
6864 be the space of a set, while that of
6865 C<isl_space_wrap> should be the space of a relation.
6866 Conversely, the output of C<isl_space_unwrap> is the space
6867 of a relation, while that of C<isl_space_wrap> is the space of a set.
6871 Remove any internal structure of domain (and range) of the given
6872 set or relation. If there is any such internal structure in the input,
6873 then the name of the space is also removed.
6875 #include <isl/space.h>
6876 __isl_give isl_space *isl_space_flatten_domain(
6877 __isl_take isl_space *space);
6878 __isl_give isl_space *isl_space_flatten_range(
6879 __isl_take isl_space *space);
6881 #include <isl/local_space.h>
6882 __isl_give isl_local_space *
6883 isl_local_space_flatten_domain(
6884 __isl_take isl_local_space *ls);
6885 __isl_give isl_local_space *
6886 isl_local_space_flatten_range(
6887 __isl_take isl_local_space *ls);
6889 #include <isl/set.h>
6890 __isl_give isl_basic_set *isl_basic_set_flatten(
6891 __isl_take isl_basic_set *bset);
6892 __isl_give isl_set *isl_set_flatten(
6893 __isl_take isl_set *set);
6895 #include <isl/map.h>
6896 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6897 __isl_take isl_basic_map *bmap);
6898 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6899 __isl_take isl_basic_map *bmap);
6900 __isl_give isl_map *isl_map_flatten_range(
6901 __isl_take isl_map *map);
6902 __isl_give isl_map *isl_map_flatten_domain(
6903 __isl_take isl_map *map);
6904 __isl_give isl_basic_map *isl_basic_map_flatten(
6905 __isl_take isl_basic_map *bmap);
6906 __isl_give isl_map *isl_map_flatten(
6907 __isl_take isl_map *map);
6910 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6911 __isl_take isl_multi_id *mi);
6913 #include <isl/val.h>
6914 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6915 __isl_take isl_multi_val *mv);
6917 #include <isl/aff.h>
6918 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6919 __isl_take isl_multi_aff *ma);
6920 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6921 __isl_take isl_multi_aff *ma);
6922 __isl_give isl_multi_pw_aff *
6923 isl_multi_pw_aff_flatten_range(
6924 __isl_take isl_multi_pw_aff *mpa);
6925 __isl_give isl_multi_union_pw_aff *
6926 isl_multi_union_pw_aff_flatten_range(
6927 __isl_take isl_multi_union_pw_aff *mupa);
6929 #include <isl/map.h>
6930 __isl_give isl_map *isl_set_flatten_map(
6931 __isl_take isl_set *set);
6933 The function above constructs a relation
6934 that maps the input set to a flattened version of the set.
6938 Lift the input set to a space with extra dimensions corresponding
6939 to the existentially quantified variables in the input.
6940 In particular, the result lives in a wrapped map where the domain
6941 is the original space and the range corresponds to the original
6942 existentially quantified variables.
6944 #include <isl/set.h>
6945 __isl_give isl_basic_set *isl_basic_set_lift(
6946 __isl_take isl_basic_set *bset);
6947 __isl_give isl_set *isl_set_lift(
6948 __isl_take isl_set *set);
6949 __isl_give isl_union_set *isl_union_set_lift(
6950 __isl_take isl_union_set *uset);
6952 Given a local space that contains the existentially quantified
6953 variables of a set, a basic relation that, when applied to
6954 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6955 can be constructed using the following function.
6957 #include <isl/local_space.h>
6958 __isl_give isl_basic_map *isl_local_space_lifting(
6959 __isl_take isl_local_space *ls);
6961 #include <isl/aff.h>
6962 __isl_give isl_multi_aff *isl_multi_aff_lift(
6963 __isl_take isl_multi_aff *maff,
6964 __isl_give isl_local_space **ls);
6966 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6967 then it is assigned the local space that lies at the basis of
6968 the lifting applied.
6970 =item * Internal Product
6972 #include <isl/space.h>
6973 __isl_give isl_space *isl_space_zip(
6974 __isl_take isl_space *space);
6976 #include <isl/map.h>
6977 __isl_give isl_basic_map *isl_basic_map_zip(
6978 __isl_take isl_basic_map *bmap);
6979 __isl_give isl_map *isl_map_zip(
6980 __isl_take isl_map *map);
6982 #include <isl/union_map.h>
6983 __isl_give isl_union_map *isl_union_map_zip(
6984 __isl_take isl_union_map *umap);
6986 Given a relation with nested relations for domain and range,
6987 interchange the range of the domain with the domain of the range.
6991 #include <isl/space.h>
6992 __isl_give isl_space *isl_space_curry(
6993 __isl_take isl_space *space);
6994 __isl_give isl_space *isl_space_uncurry(
6995 __isl_take isl_space *space);
6997 #include <isl/map.h>
6998 __isl_give isl_basic_map *isl_basic_map_curry(
6999 __isl_take isl_basic_map *bmap);
7000 __isl_give isl_basic_map *isl_basic_map_uncurry(
7001 __isl_take isl_basic_map *bmap);
7002 __isl_give isl_map *isl_map_curry(
7003 __isl_take isl_map *map);
7004 __isl_give isl_map *isl_map_uncurry(
7005 __isl_take isl_map *map);
7007 #include <isl/union_map.h>
7008 __isl_give isl_union_map *isl_union_map_curry(
7009 __isl_take isl_union_map *umap);
7010 __isl_give isl_union_map *isl_union_map_uncurry(
7011 __isl_take isl_union_map *umap);
7013 Given a relation with a nested relation for domain,
7014 the C<curry> functions
7015 move the range of the nested relation out of the domain
7016 and use it as the domain of a nested relation in the range,
7017 with the original range as range of this nested relation.
7018 The C<uncurry> functions perform the inverse operation.
7020 #include <isl/space.h>
7021 __isl_give isl_space *isl_space_range_curry(
7022 __isl_take isl_space *space);
7024 #include <isl/map.h>
7025 __isl_give isl_map *isl_map_range_curry(
7026 __isl_take isl_map *map);
7028 #include <isl/union_map.h>
7029 __isl_give isl_union_map *isl_union_map_range_curry(
7030 __isl_take isl_union_map *umap);
7032 These functions apply the currying to the relation that
7033 is nested inside the range of the input.
7035 =item * Aligning parameters
7037 Change the order of the parameters of the given set, relation
7039 such that the first parameters match those of C<model>.
7040 This may involve the introduction of extra parameters.
7041 All parameters need to be named.
7043 #include <isl/space.h>
7044 __isl_give isl_space *isl_space_align_params(
7045 __isl_take isl_space *space1,
7046 __isl_take isl_space *space2)
7048 #include <isl/set.h>
7049 __isl_give isl_basic_set *isl_basic_set_align_params(
7050 __isl_take isl_basic_set *bset,
7051 __isl_take isl_space *model);
7052 __isl_give isl_set *isl_set_align_params(
7053 __isl_take isl_set *set,
7054 __isl_take isl_space *model);
7056 #include <isl/map.h>
7057 __isl_give isl_basic_map *isl_basic_map_align_params(
7058 __isl_take isl_basic_map *bmap,
7059 __isl_take isl_space *model);
7060 __isl_give isl_map *isl_map_align_params(
7061 __isl_take isl_map *map,
7062 __isl_take isl_space *model);
7065 __isl_give isl_multi_id *isl_multi_id_align_params(
7066 __isl_take isl_multi_id *mi,
7067 __isl_take isl_space *model);
7069 #include <isl/val.h>
7070 __isl_give isl_multi_val *isl_multi_val_align_params(
7071 __isl_take isl_multi_val *mv,
7072 __isl_take isl_space *model);
7074 #include <isl/aff.h>
7075 __isl_give isl_aff *isl_aff_align_params(
7076 __isl_take isl_aff *aff,
7077 __isl_take isl_space *model);
7078 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7079 __isl_take isl_multi_aff *multi,
7080 __isl_take isl_space *model);
7081 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7082 __isl_take isl_pw_aff *pwaff,
7083 __isl_take isl_space *model);
7084 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7085 __isl_take isl_pw_multi_aff *pma,
7086 __isl_take isl_space *model);
7087 __isl_give isl_union_pw_aff *
7088 isl_union_pw_aff_align_params(
7089 __isl_take isl_union_pw_aff *upa,
7090 __isl_take isl_space *model);
7091 __isl_give isl_union_pw_multi_aff *
7092 isl_union_pw_multi_aff_align_params(
7093 __isl_take isl_union_pw_multi_aff *upma,
7094 __isl_take isl_space *model);
7095 __isl_give isl_multi_union_pw_aff *
7096 isl_multi_union_pw_aff_align_params(
7097 __isl_take isl_multi_union_pw_aff *mupa,
7098 __isl_take isl_space *model);
7100 #include <isl/polynomial.h>
7101 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7102 __isl_take isl_qpolynomial *qp,
7103 __isl_take isl_space *model);
7105 =item * Drop unused parameters
7107 Drop parameters that are not referenced by the isl object.
7108 All parameters need to be named.
7110 #include <isl/set.h>
7111 __isl_give isl_basic_set *
7112 isl_basic_set_drop_unused_params(
7113 __isl_take isl_basic_set *bset);
7114 __isl_give isl_set *isl_set_drop_unused_params(
7115 __isl_take isl_set *set);
7117 #include <isl/map.h>
7118 __isl_give isl_basic_map *
7119 isl_basic_map_drop_unused_params(
7120 __isl_take isl_basic_map *bmap);
7121 __isl_give isl_map *isl_map_drop_unused_params(
7122 __isl_take isl_map *map);
7124 #include <isl/union_set.h>
7125 __isl_give isl_union_set *
7126 isl_union_set_drop_unused_params(
7127 __isl_take isl_union_set *uset);
7129 #include <isl/union_map.h>
7130 __isl_give isl_union_map *
7131 isl_union_map_drop_unused_params(
7132 __isl_take isl_union_map *umap);
7134 #include <isl/aff.h>
7135 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7136 __isl_take isl_pw_aff *pa);
7137 __isl_give isl_pw_multi_aff *
7138 isl_pw_multi_aff_drop_unused_params(
7139 __isl_take isl_pw_multi_aff *pma);
7140 __isl_give isl_union_pw_aff *
7141 isl_union_pw_aff_drop_unused_params(
7142 __isl_take isl_union_pw_aff *upa);
7143 __isl_give isl_union_pw_multi_aff *
7144 isl_union_pw_multi_aff_drop_unused_params(
7145 __isl_take isl_union_pw_multi_aff *upma);
7147 #include <isl/polynomial.h>
7148 __isl_give isl_pw_qpolynomial *
7149 isl_pw_qpolynomial_drop_unused_params(
7150 __isl_take isl_pw_qpolynomial *pwqp);
7151 __isl_give isl_pw_qpolynomial_fold *
7152 isl_pw_qpolynomial_fold_drop_unused_params(
7153 __isl_take isl_pw_qpolynomial_fold *pwf);
7154 __isl_give isl_union_pw_qpolynomial *
7155 isl_union_pw_qpolynomial_drop_unused_params(
7156 __isl_take isl_union_pw_qpolynomial *upwqp);
7157 __isl_give isl_union_pw_qpolynomial_fold *
7158 isl_union_pw_qpolynomial_fold_drop_unused_params(
7159 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7161 =item * Unary Arithmetic Operations
7163 #include <isl/set.h>
7164 __isl_give isl_set *isl_set_neg(
7165 __isl_take isl_set *set);
7166 #include <isl/map.h>
7167 __isl_give isl_map *isl_map_neg(
7168 __isl_take isl_map *map);
7170 C<isl_set_neg> constructs a set containing the opposites of
7171 the elements in its argument.
7172 The domain of the result of C<isl_map_neg> is the same
7173 as the domain of its argument. The corresponding range
7174 elements are the opposites of the corresponding range
7175 elements in the argument.
7177 #include <isl/val.h>
7178 __isl_give isl_multi_val *isl_multi_val_neg(
7179 __isl_take isl_multi_val *mv);
7181 #include <isl/aff.h>
7182 __isl_give isl_aff *isl_aff_neg(
7183 __isl_take isl_aff *aff);
7184 __isl_give isl_multi_aff *isl_multi_aff_neg(
7185 __isl_take isl_multi_aff *ma);
7186 __isl_give isl_pw_aff *isl_pw_aff_neg(
7187 __isl_take isl_pw_aff *pwaff);
7188 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7189 __isl_take isl_pw_multi_aff *pma);
7190 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7191 __isl_take isl_multi_pw_aff *mpa);
7192 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7193 __isl_take isl_union_pw_aff *upa);
7194 __isl_give isl_union_pw_multi_aff *
7195 isl_union_pw_multi_aff_neg(
7196 __isl_take isl_union_pw_multi_aff *upma);
7197 __isl_give isl_multi_union_pw_aff *
7198 isl_multi_union_pw_aff_neg(
7199 __isl_take isl_multi_union_pw_aff *mupa);
7200 __isl_give isl_aff *isl_aff_ceil(
7201 __isl_take isl_aff *aff);
7202 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7203 __isl_take isl_pw_aff *pwaff);
7204 __isl_give isl_aff *isl_aff_floor(
7205 __isl_take isl_aff *aff);
7206 __isl_give isl_multi_aff *isl_multi_aff_floor(
7207 __isl_take isl_multi_aff *ma);
7208 __isl_give isl_pw_aff *isl_pw_aff_floor(
7209 __isl_take isl_pw_aff *pwaff);
7210 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7211 __isl_take isl_union_pw_aff *upa);
7212 __isl_give isl_multi_union_pw_aff *
7213 isl_multi_union_pw_aff_floor(
7214 __isl_take isl_multi_union_pw_aff *mupa);
7216 #include <isl/aff.h>
7217 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7218 __isl_take isl_pw_aff_list *list);
7219 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7220 __isl_take isl_pw_aff_list *list);
7222 #include <isl/polynomial.h>
7223 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7224 __isl_take isl_qpolynomial *qp);
7225 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7226 __isl_take isl_pw_qpolynomial *pwqp);
7227 __isl_give isl_union_pw_qpolynomial *
7228 isl_union_pw_qpolynomial_neg(
7229 __isl_take isl_union_pw_qpolynomial *upwqp);
7230 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7231 __isl_take isl_qpolynomial *qp,
7233 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7234 __isl_take isl_pw_qpolynomial *pwqp,
7239 The following functions evaluate a function in a point.
7241 #include <isl/aff.h>
7242 __isl_give isl_val *isl_aff_eval(
7243 __isl_take isl_aff *aff,
7244 __isl_take isl_point *pnt);
7245 __isl_give isl_val *isl_pw_aff_eval(
7246 __isl_take isl_pw_aff *pa,
7247 __isl_take isl_point *pnt);
7249 #include <isl/polynomial.h>
7250 __isl_give isl_val *isl_pw_qpolynomial_eval(
7251 __isl_take isl_pw_qpolynomial *pwqp,
7252 __isl_take isl_point *pnt);
7253 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7254 __isl_take isl_pw_qpolynomial_fold *pwf,
7255 __isl_take isl_point *pnt);
7256 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7257 __isl_take isl_union_pw_qpolynomial *upwqp,
7258 __isl_take isl_point *pnt);
7259 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7260 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7261 __isl_take isl_point *pnt);
7263 These functions return NaN when evaluated at a void point.
7264 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7265 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7266 when the function is evaluated outside its explicit domain.
7268 =item * Dimension manipulation
7270 It is usually not advisable to directly change the (input or output)
7271 space of a set or a relation as this removes the name and the internal
7272 structure of the space. However, the functions below can be useful
7273 to add new parameters, assuming
7274 C<isl_set_align_params> and C<isl_map_align_params>
7277 #include <isl/space.h>
7278 __isl_give isl_space *isl_space_add_dims(
7279 __isl_take isl_space *space,
7280 enum isl_dim_type type, unsigned n);
7281 __isl_give isl_space *isl_space_insert_dims(
7282 __isl_take isl_space *space,
7283 enum isl_dim_type type, unsigned pos, unsigned n);
7284 __isl_give isl_space *isl_space_drop_dims(
7285 __isl_take isl_space *space,
7286 enum isl_dim_type type, unsigned first, unsigned n);
7287 __isl_give isl_space *isl_space_move_dims(
7288 __isl_take isl_space *space,
7289 enum isl_dim_type dst_type, unsigned dst_pos,
7290 enum isl_dim_type src_type, unsigned src_pos,
7293 #include <isl/local_space.h>
7294 __isl_give isl_local_space *isl_local_space_add_dims(
7295 __isl_take isl_local_space *ls,
7296 enum isl_dim_type type, unsigned n);
7297 __isl_give isl_local_space *isl_local_space_insert_dims(
7298 __isl_take isl_local_space *ls,
7299 enum isl_dim_type type, unsigned first, unsigned n);
7300 __isl_give isl_local_space *isl_local_space_drop_dims(
7301 __isl_take isl_local_space *ls,
7302 enum isl_dim_type type, unsigned first, unsigned n);
7304 #include <isl/set.h>
7305 __isl_give isl_basic_set *isl_basic_set_add_dims(
7306 __isl_take isl_basic_set *bset,
7307 enum isl_dim_type type, unsigned n);
7308 __isl_give isl_set *isl_set_add_dims(
7309 __isl_take isl_set *set,
7310 enum isl_dim_type type, unsigned n);
7311 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7312 __isl_take isl_basic_set *bset,
7313 enum isl_dim_type type, unsigned pos,
7315 __isl_give isl_set *isl_set_insert_dims(
7316 __isl_take isl_set *set,
7317 enum isl_dim_type type, unsigned pos, unsigned n);
7318 __isl_give isl_basic_set *isl_basic_set_move_dims(
7319 __isl_take isl_basic_set *bset,
7320 enum isl_dim_type dst_type, unsigned dst_pos,
7321 enum isl_dim_type src_type, unsigned src_pos,
7323 __isl_give isl_set *isl_set_move_dims(
7324 __isl_take isl_set *set,
7325 enum isl_dim_type dst_type, unsigned dst_pos,
7326 enum isl_dim_type src_type, unsigned src_pos,
7329 #include <isl/map.h>
7330 __isl_give isl_basic_map *isl_basic_map_add_dims(
7331 __isl_take isl_basic_map *bmap,
7332 enum isl_dim_type type, unsigned n);
7333 __isl_give isl_map *isl_map_add_dims(
7334 __isl_take isl_map *map,
7335 enum isl_dim_type type, unsigned n);
7336 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7337 __isl_take isl_basic_map *bmap,
7338 enum isl_dim_type type, unsigned pos,
7340 __isl_give isl_map *isl_map_insert_dims(
7341 __isl_take isl_map *map,
7342 enum isl_dim_type type, unsigned pos, unsigned n);
7343 __isl_give isl_basic_map *isl_basic_map_move_dims(
7344 __isl_take isl_basic_map *bmap,
7345 enum isl_dim_type dst_type, unsigned dst_pos,
7346 enum isl_dim_type src_type, unsigned src_pos,
7348 __isl_give isl_map *isl_map_move_dims(
7349 __isl_take isl_map *map,
7350 enum isl_dim_type dst_type, unsigned dst_pos,
7351 enum isl_dim_type src_type, unsigned src_pos,
7354 #include <isl/val.h>
7355 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7356 __isl_take isl_multi_val *mv,
7357 enum isl_dim_type type, unsigned first, unsigned n);
7358 __isl_give isl_multi_val *isl_multi_val_add_dims(
7359 __isl_take isl_multi_val *mv,
7360 enum isl_dim_type type, unsigned n);
7361 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7362 __isl_take isl_multi_val *mv,
7363 enum isl_dim_type type, unsigned first, unsigned n);
7365 #include <isl/aff.h>
7366 __isl_give isl_aff *isl_aff_insert_dims(
7367 __isl_take isl_aff *aff,
7368 enum isl_dim_type type, unsigned first, unsigned n);
7369 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7370 __isl_take isl_multi_aff *ma,
7371 enum isl_dim_type type, unsigned first, unsigned n);
7372 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7373 __isl_take isl_pw_aff *pwaff,
7374 enum isl_dim_type type, unsigned first, unsigned n);
7375 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7376 __isl_take isl_multi_pw_aff *mpa,
7377 enum isl_dim_type type, unsigned first, unsigned n);
7378 __isl_give isl_aff *isl_aff_add_dims(
7379 __isl_take isl_aff *aff,
7380 enum isl_dim_type type, unsigned n);
7381 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7382 __isl_take isl_multi_aff *ma,
7383 enum isl_dim_type type, unsigned n);
7384 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7385 __isl_take isl_pw_aff *pwaff,
7386 enum isl_dim_type type, unsigned n);
7387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7388 __isl_take isl_multi_pw_aff *mpa,
7389 enum isl_dim_type type, unsigned n);
7390 __isl_give isl_aff *isl_aff_drop_dims(
7391 __isl_take isl_aff *aff,
7392 enum isl_dim_type type, unsigned first, unsigned n);
7393 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7394 __isl_take isl_multi_aff *maff,
7395 enum isl_dim_type type, unsigned first, unsigned n);
7396 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7397 __isl_take isl_pw_aff *pwaff,
7398 enum isl_dim_type type, unsigned first, unsigned n);
7399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7400 __isl_take isl_pw_multi_aff *pma,
7401 enum isl_dim_type type, unsigned first, unsigned n);
7402 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7403 __isl_take isl_union_pw_aff *upa,
7404 enum isl_dim_type type, unsigned first, unsigned n);
7405 __isl_give isl_union_pw_multi_aff *
7406 isl_union_pw_multi_aff_drop_dims(
7407 __isl_take isl_union_pw_multi_aff *upma,
7408 enum isl_dim_type type,
7409 unsigned first, unsigned n);
7410 __isl_give isl_multi_union_pw_aff *
7411 isl_multi_union_pw_aff_drop_dims(
7412 __isl_take isl_multi_union_pw_aff *mupa,
7413 enum isl_dim_type type, unsigned first,
7415 __isl_give isl_aff *isl_aff_move_dims(
7416 __isl_take isl_aff *aff,
7417 enum isl_dim_type dst_type, unsigned dst_pos,
7418 enum isl_dim_type src_type, unsigned src_pos,
7420 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7421 __isl_take isl_multi_aff *ma,
7422 enum isl_dim_type dst_type, unsigned dst_pos,
7423 enum isl_dim_type src_type, unsigned src_pos,
7425 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7426 __isl_take isl_pw_aff *pa,
7427 enum isl_dim_type dst_type, unsigned dst_pos,
7428 enum isl_dim_type src_type, unsigned src_pos,
7430 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7431 __isl_take isl_multi_pw_aff *pma,
7432 enum isl_dim_type dst_type, unsigned dst_pos,
7433 enum isl_dim_type src_type, unsigned src_pos,
7436 #include <isl/polynomial.h>
7437 __isl_give isl_union_pw_qpolynomial *
7438 isl_union_pw_qpolynomial_drop_dims(
7439 __isl_take isl_union_pw_qpolynomial *upwqp,
7440 enum isl_dim_type type,
7441 unsigned first, unsigned n);
7442 __isl_give isl_union_pw_qpolynomial_fold *
7443 isl_union_pw_qpolynomial_fold_drop_dims(
7444 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7445 enum isl_dim_type type,
7446 unsigned first, unsigned n);
7448 The operations on union expressions can only manipulate parameters.
7452 =head2 Binary Operations
7454 The two arguments of a binary operation not only need to live
7455 in the same C<isl_ctx>, they currently also need to have
7456 the same (number of) parameters.
7458 =head3 Basic Operations
7462 =item * Intersection
7464 #include <isl/local_space.h>
7465 __isl_give isl_local_space *isl_local_space_intersect(
7466 __isl_take isl_local_space *ls1,
7467 __isl_take isl_local_space *ls2);
7469 #include <isl/set.h>
7470 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7471 __isl_take isl_basic_set *bset1,
7472 __isl_take isl_basic_set *bset2);
7473 __isl_give isl_basic_set *isl_basic_set_intersect(
7474 __isl_take isl_basic_set *bset1,
7475 __isl_take isl_basic_set *bset2);
7476 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7477 __isl_take struct isl_basic_set_list *list);
7478 __isl_give isl_set *isl_set_intersect_params(
7479 __isl_take isl_set *set,
7480 __isl_take isl_set *params);
7481 __isl_give isl_set *isl_set_intersect(
7482 __isl_take isl_set *set1,
7483 __isl_take isl_set *set2);
7484 __isl_give isl_set *isl_set_intersect_factor_domain(
7485 __isl_take isl_set *set,
7486 __isl_take isl_set *domain);
7487 __isl_give isl_set *isl_set_intersect_factor_range(
7488 __isl_take isl_set *set,
7489 __isl_take isl_set *range);
7491 #include <isl/map.h>
7492 __isl_give isl_basic_map *isl_basic_map_intersect_params(
7493 __isl_take isl_basic_map *bmap,
7494 __isl_take isl_basic_set *bset);
7495 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7496 __isl_take isl_basic_map *bmap,
7497 __isl_take isl_basic_set *bset);
7498 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7499 __isl_take isl_basic_map *bmap,
7500 __isl_take isl_basic_set *bset);
7501 __isl_give isl_basic_map *isl_basic_map_intersect(
7502 __isl_take isl_basic_map *bmap1,
7503 __isl_take isl_basic_map *bmap2);
7504 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7505 __isl_take isl_basic_map_list *list);
7506 __isl_give isl_map *isl_map_intersect_params(
7507 __isl_take isl_map *map,
7508 __isl_take isl_set *params);
7509 __isl_give isl_map *isl_map_intersect_domain(
7510 __isl_take isl_map *map,
7511 __isl_take isl_set *set);
7512 __isl_give isl_map *isl_map_intersect_range(
7513 __isl_take isl_map *map,
7514 __isl_take isl_set *set);
7515 __isl_give isl_map *isl_map_intersect(
7516 __isl_take isl_map *map1,
7517 __isl_take isl_map *map2);
7518 __isl_give isl_map *
7519 isl_map_intersect_domain_factor_domain(
7520 __isl_take isl_map *map,
7521 __isl_take isl_map *factor);
7522 __isl_give isl_map *
7523 isl_map_intersect_domain_factor_range(
7524 __isl_take isl_map *map,
7525 __isl_take isl_map *factor);
7526 __isl_give isl_map *
7527 isl_map_intersect_range_factor_domain(
7528 __isl_take isl_map *map,
7529 __isl_take isl_map *factor);
7530 __isl_give isl_map *
7531 isl_map_intersect_range_factor_range(
7532 __isl_take isl_map *map,
7533 __isl_take isl_map *factor);
7534 __isl_give isl_map *
7535 isl_map_intersect_domain_wrapped_domain(
7536 __isl_take isl_map *map,
7537 __isl_take isl_set *domain);
7538 __isl_give isl_map *
7539 isl_map_intersect_range_wrapped_domain(
7540 __isl_take isl_map *map,
7541 __isl_take isl_set *domain);
7543 #include <isl/union_set.h>
7544 __isl_give isl_union_set *isl_union_set_intersect_params(
7545 __isl_take isl_union_set *uset,
7546 __isl_take isl_set *set);
7547 __isl_give isl_union_set *isl_union_set_intersect(
7548 __isl_take isl_union_set *uset1,
7549 __isl_take isl_union_set *uset2);
7551 #include <isl/union_map.h>
7552 __isl_give isl_union_map *isl_union_map_intersect_params(
7553 __isl_take isl_union_map *umap,
7554 __isl_take isl_set *set);
7555 __isl_give isl_union_map *
7556 isl_union_map_intersect_domain_union_set(
7557 __isl_take isl_union_map *umap,
7558 __isl_take isl_union_set *uset);
7559 __isl_give isl_union_map *
7560 isl_union_map_intersect_domain_space(
7561 __isl_take isl_union_map *umap,
7562 __isl_take isl_space *space);
7563 __isl_give isl_union_map *isl_union_map_intersect_domain(
7564 __isl_take isl_union_map *umap,
7565 __isl_take isl_union_set *uset);
7566 __isl_give isl_union_map *
7567 isl_union_map_intersect_range_union_set(
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_space(
7572 __isl_take isl_union_map *umap,
7573 __isl_take isl_space *space);
7574 __isl_give isl_union_map *isl_union_map_intersect_range(
7575 __isl_take isl_union_map *umap,
7576 __isl_take isl_union_set *uset);
7577 __isl_give isl_union_map *isl_union_map_intersect(
7578 __isl_take isl_union_map *umap1,
7579 __isl_take isl_union_map *umap2);
7580 __isl_give isl_union_map *
7581 isl_union_map_intersect_domain_factor_domain(
7582 __isl_take isl_union_map *umap,
7583 __isl_take isl_union_map *factor);
7584 __isl_give isl_union_map *
7585 isl_union_map_intersect_domain_factor_range(
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_range_factor_domain(
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_range(
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_domain_wrapped_domain_union_set(
7598 __isl_take isl_union_map *umap,
7599 __isl_take isl_union_set *domain);
7600 __isl_give isl_union_map *
7601 isl_union_map_intersect_range_wrapped_domain_union_set(
7602 __isl_take isl_union_map *umap,
7603 __isl_take isl_union_set *domain);
7605 #include <isl/aff.h>
7606 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7607 __isl_take isl_pw_aff *pa,
7608 __isl_take isl_set *set);
7609 __isl_give isl_multi_pw_aff *
7610 isl_multi_pw_aff_intersect_domain(
7611 __isl_take isl_multi_pw_aff *mpa,
7612 __isl_take isl_set *domain);
7613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7614 __isl_take isl_pw_multi_aff *pma,
7615 __isl_take isl_set *set);
7616 __isl_give isl_union_pw_aff *
7617 isl_union_pw_aff_intersect_domain_space(
7618 __isl_take isl_union_pw_aff *upa,
7619 __isl_take isl_space *space);
7620 __isl_give isl_union_pw_aff *
7621 isl_union_pw_aff_intersect_domain_union_set(
7622 __isl_take isl_union_pw_aff *upa,
7623 __isl_take isl_union_set *uset);
7624 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7625 __isl_take isl_union_pw_aff *upa,
7626 __isl_take isl_union_set *uset);
7627 __isl_give isl_union_pw_multi_aff *
7628 isl_union_pw_multi_aff_intersect_domain_space(
7629 __isl_take isl_union_pw_multi_aff *upma,
7630 __isl_take isl_space *space);
7631 __isl_give isl_union_pw_multi_aff *
7632 isl_union_pw_multi_aff_intersect_domain_union_set(
7633 __isl_take isl_union_pw_multi_aff *upma,
7634 __isl_take isl_union_set *uset);
7635 __isl_give isl_union_pw_multi_aff *
7636 isl_union_pw_multi_aff_intersect_domain(
7637 __isl_take isl_union_pw_multi_aff *upma,
7638 __isl_take isl_union_set *uset);
7639 __isl_give isl_multi_union_pw_aff *
7640 isl_multi_union_pw_aff_intersect_domain(
7641 __isl_take isl_multi_union_pw_aff *mupa,
7642 __isl_take isl_union_set *uset);
7643 __isl_give isl_pw_aff *
7644 isl_pw_aff_intersect_domain_wrapped_domain(
7645 __isl_take isl_pw_aff *pa,
7646 __isl_take isl_set *set);
7647 __isl_give isl_pw_multi_aff *
7648 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7649 __isl_take isl_pw_multi_aff *pma,
7650 __isl_take isl_set *set);
7651 __isl_give isl_union_pw_aff *
7652 isl_union_pw_aff_intersect_domain_wrapped_domain(
7653 __isl_take isl_union_pw_aff *upa,
7654 __isl_take isl_union_set *uset);
7655 __isl_give isl_union_pw_multi_aff *
7656 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7657 __isl_take isl_union_pw_multi_aff *upma,
7658 __isl_take isl_union_set *uset);
7659 __isl_give isl_pw_aff *
7660 isl_pw_aff_intersect_domain_wrapped_range(
7661 __isl_take isl_pw_aff *pa,
7662 __isl_take isl_set *set);
7663 __isl_give isl_pw_multi_aff *
7664 isl_pw_multi_aff_intersect_domain_wrapped_range(
7665 __isl_take isl_pw_multi_aff *pma,
7666 __isl_take isl_set *set);
7667 __isl_give isl_union_pw_multi_aff *
7668 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7669 __isl_take isl_union_pw_multi_aff *upma,
7670 __isl_take isl_union_set *uset);
7671 __isl_give isl_union_pw_aff *
7672 isl_union_pw_aff_intersect_domain_wrapped_range(
7673 __isl_take isl_union_pw_aff *upa,
7674 __isl_take isl_union_set *uset);
7675 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7676 __isl_take isl_pw_aff *pa,
7677 __isl_take isl_set *set);
7678 __isl_give isl_multi_pw_aff *
7679 isl_multi_pw_aff_intersect_params(
7680 __isl_take isl_multi_pw_aff *mpa,
7681 __isl_take isl_set *set);
7682 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7683 __isl_take isl_pw_multi_aff *pma,
7684 __isl_take isl_set *set);
7685 __isl_give isl_union_pw_aff *
7686 isl_union_pw_aff_intersect_params(
7687 __isl_take isl_union_pw_aff *upa,
7688 __isl_take isl_set *set);
7689 __isl_give isl_union_pw_multi_aff *
7690 isl_union_pw_multi_aff_intersect_params(
7691 __isl_take isl_union_pw_multi_aff *upma,
7692 __isl_take isl_set *set);
7693 __isl_give isl_multi_union_pw_aff *
7694 isl_multi_union_pw_aff_intersect_params(
7695 __isl_take isl_multi_union_pw_aff *mupa,
7696 __isl_take isl_set *params);
7697 __isl_give isl_multi_union_pw_aff *
7698 isl_multi_union_pw_aff_intersect_range(
7699 __isl_take isl_multi_union_pw_aff *mupa,
7700 __isl_take isl_set *set);
7702 #include <isl/polynomial.h>
7703 __isl_give isl_pw_qpolynomial *
7704 isl_pw_qpolynomial_intersect_domain(
7705 __isl_take isl_pw_qpolynomial *pwpq,
7706 __isl_take isl_set *set);
7707 __isl_give isl_union_pw_qpolynomial *
7708 isl_union_pw_qpolynomial_intersect_domain_space(
7709 __isl_take isl_union_pw_qpolynomial *upwpq,
7710 __isl_take isl_space *space);
7711 __isl_give isl_union_pw_qpolynomial *
7712 isl_union_pw_qpolynomial_intersect_domain_union_set(
7713 __isl_take isl_union_pw_qpolynomial *upwpq,
7714 __isl_take isl_union_set *uset);
7715 __isl_give isl_union_pw_qpolynomial *
7716 isl_union_pw_qpolynomial_intersect_domain(
7717 __isl_take isl_union_pw_qpolynomial *upwpq,
7718 __isl_take isl_union_set *uset);
7719 __isl_give isl_union_pw_qpolynomial_fold *
7720 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7721 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7722 __isl_take isl_space *space);
7723 __isl_give isl_union_pw_qpolynomial_fold *
7724 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7725 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7726 __isl_take isl_union_set *uset);
7727 __isl_give isl_union_pw_qpolynomial_fold *
7728 isl_union_pw_qpolynomial_fold_intersect_domain(
7729 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7730 __isl_take isl_union_set *uset);
7731 __isl_give isl_pw_qpolynomial *
7732 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7733 __isl_take isl_pw_qpolynomial *pwpq,
7734 __isl_take isl_set *set);
7735 __isl_give isl_pw_qpolynomial_fold *
7736 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7737 __isl_take isl_pw_qpolynomial_fold *pwf,
7738 __isl_take isl_set *set);
7739 __isl_give isl_union_pw_qpolynomial *
7740 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7741 __isl_take isl_union_pw_qpolynomial *upwpq,
7742 __isl_take isl_union_set *uset);
7743 __isl_give isl_union_pw_qpolynomial_fold *
7744 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7745 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7746 __isl_take isl_union_set *uset);
7747 __isl_give isl_pw_qpolynomial *
7748 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7749 __isl_take isl_pw_qpolynomial *pwpq,
7750 __isl_take isl_set *set);
7751 __isl_give isl_pw_qpolynomial_fold *
7752 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7753 __isl_take isl_pw_qpolynomial_fold *pwf,
7754 __isl_take isl_set *set);
7755 __isl_give isl_union_pw_qpolynomial *
7756 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7757 __isl_take isl_union_pw_qpolynomial *upwpq,
7758 __isl_take isl_union_set *uset);
7759 __isl_give isl_union_pw_qpolynomial_fold *
7760 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7761 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7762 __isl_take isl_union_set *uset);
7763 __isl_give isl_pw_qpolynomial *
7764 isl_pw_qpolynomial_intersect_params(
7765 __isl_take isl_pw_qpolynomial *pwpq,
7766 __isl_take isl_set *set);
7767 __isl_give isl_pw_qpolynomial_fold *
7768 isl_pw_qpolynomial_fold_intersect_params(
7769 __isl_take isl_pw_qpolynomial_fold *pwf,
7770 __isl_take isl_set *set);
7771 __isl_give isl_union_pw_qpolynomial *
7772 isl_union_pw_qpolynomial_intersect_params(
7773 __isl_take isl_union_pw_qpolynomial *upwpq,
7774 __isl_take isl_set *set);
7775 __isl_give isl_union_pw_qpolynomial_fold *
7776 isl_union_pw_qpolynomial_fold_intersect_params(
7777 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7778 __isl_take isl_set *set);
7780 The second argument to the C<_params> functions needs to be
7781 a parametric (basic) set. For the other functions, a parametric set
7782 for either argument is only allowed if the other argument is
7783 a parametric set as well.
7784 The list passed to C<isl_basic_set_list_intersect> needs to have
7785 at least one element and all elements need to live in the same space.
7786 The function C<isl_multi_union_pw_aff_intersect_range>
7787 restricts the input function to those shared domain elements
7788 that map to the specified range.
7789 C<isl_union_map_intersect_domain> is an alternative name for
7790 C<isl_union_map_intersect_domain_union_set>.
7791 Similarly for the other pairs of functions.
7795 #include <isl/set.h>
7796 __isl_give isl_set *isl_basic_set_union(
7797 __isl_take isl_basic_set *bset1,
7798 __isl_take isl_basic_set *bset2);
7799 __isl_give isl_set *isl_set_union(
7800 __isl_take isl_set *set1,
7801 __isl_take isl_set *set2);
7802 __isl_give isl_set *isl_set_list_union(
7803 __isl_take isl_set_list *list);
7805 #include <isl/map.h>
7806 __isl_give isl_map *isl_basic_map_union(
7807 __isl_take isl_basic_map *bmap1,
7808 __isl_take isl_basic_map *bmap2);
7809 __isl_give isl_map *isl_map_union(
7810 __isl_take isl_map *map1,
7811 __isl_take isl_map *map2);
7813 #include <isl/union_set.h>
7814 __isl_give isl_union_set *isl_union_set_union(
7815 __isl_take isl_union_set *uset1,
7816 __isl_take isl_union_set *uset2);
7817 __isl_give isl_union_set *isl_union_set_list_union(
7818 __isl_take isl_union_set_list *list);
7820 #include <isl/union_map.h>
7821 __isl_give isl_union_map *isl_union_map_union(
7822 __isl_take isl_union_map *umap1,
7823 __isl_take isl_union_map *umap2);
7825 The list passed to C<isl_set_list_union> needs to have
7826 at least one element and all elements need to live in the same space.
7828 =item * Set difference
7830 #include <isl/set.h>
7831 __isl_give isl_set *isl_set_subtract(
7832 __isl_take isl_set *set1,
7833 __isl_take isl_set *set2);
7835 #include <isl/map.h>
7836 __isl_give isl_map *isl_map_subtract(
7837 __isl_take isl_map *map1,
7838 __isl_take isl_map *map2);
7839 __isl_give isl_map *isl_map_subtract_domain(
7840 __isl_take isl_map *map,
7841 __isl_take isl_set *dom);
7842 __isl_give isl_map *isl_map_subtract_range(
7843 __isl_take isl_map *map,
7844 __isl_take isl_set *dom);
7846 #include <isl/union_set.h>
7847 __isl_give isl_union_set *isl_union_set_subtract(
7848 __isl_take isl_union_set *uset1,
7849 __isl_take isl_union_set *uset2);
7851 #include <isl/union_map.h>
7852 __isl_give isl_union_map *isl_union_map_subtract(
7853 __isl_take isl_union_map *umap1,
7854 __isl_take isl_union_map *umap2);
7855 __isl_give isl_union_map *isl_union_map_subtract_domain(
7856 __isl_take isl_union_map *umap,
7857 __isl_take isl_union_set *dom);
7858 __isl_give isl_union_map *isl_union_map_subtract_range(
7859 __isl_take isl_union_map *umap,
7860 __isl_take isl_union_set *dom);
7862 #include <isl/aff.h>
7863 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7864 __isl_take isl_pw_aff *pa,
7865 __isl_take isl_set *set);
7866 __isl_give isl_pw_multi_aff *
7867 isl_pw_multi_aff_subtract_domain(
7868 __isl_take isl_pw_multi_aff *pma,
7869 __isl_take isl_set *set);
7870 __isl_give isl_union_pw_aff *
7871 isl_union_pw_aff_subtract_domain_union_set(
7872 __isl_take isl_union_pw_aff *upa,
7873 __isl_take isl_union_set *uset);
7874 __isl_give isl_union_pw_aff *
7875 isl_union_pw_aff_subtract_domain_space(
7876 __isl_take isl_union_pw_aff *upa,
7877 __isl_take isl_space *space);
7878 __isl_give isl_union_pw_aff *
7879 isl_union_pw_aff_subtract_domain(
7880 __isl_take isl_union_pw_aff *upa,
7881 __isl_take isl_union_set *uset);
7882 __isl_give isl_union_pw_multi_aff *
7883 isl_union_pw_multi_aff_subtract_domain_union_set(
7884 __isl_take isl_union_pw_multi_aff *upma,
7885 __isl_take isl_set *set);
7886 __isl_give isl_union_pw_multi_aff *
7887 isl_union_pw_multi_aff_subtract_domain_space(
7888 __isl_take isl_union_pw_multi_aff *upma,
7889 __isl_take isl_space *space);
7890 __isl_give isl_union_pw_multi_aff *
7891 isl_union_pw_multi_aff_subtract_domain(
7892 __isl_take isl_union_pw_multi_aff *upma,
7893 __isl_take isl_union_set *uset);
7895 #include <isl/polynomial.h>
7896 __isl_give isl_pw_qpolynomial *
7897 isl_pw_qpolynomial_subtract_domain(
7898 __isl_take isl_pw_qpolynomial *pwpq,
7899 __isl_take isl_set *set);
7900 __isl_give isl_pw_qpolynomial_fold *
7901 isl_pw_qpolynomial_fold_subtract_domain(
7902 __isl_take isl_pw_qpolynomial_fold *pwf,
7903 __isl_take isl_set *set);
7904 __isl_give isl_union_pw_qpolynomial *
7905 isl_union_pw_qpolynomial_subtract_domain_union_set(
7906 __isl_take isl_union_pw_qpolynomial *upwpq,
7907 __isl_take isl_union_set *uset);
7908 __isl_give isl_union_pw_qpolynomial *
7909 isl_union_pw_qpolynomial_subtract_domain_space(
7910 __isl_take isl_union_pw_qpolynomial *upwpq,
7911 __isl_take isl_space *space);
7912 __isl_give isl_union_pw_qpolynomial *
7913 isl_union_pw_qpolynomial_subtract_domain(
7914 __isl_take isl_union_pw_qpolynomial *upwpq,
7915 __isl_take isl_union_set *uset);
7916 __isl_give isl_union_pw_qpolynomial_fold *
7917 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7918 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7919 __isl_take isl_union_set *uset);
7920 __isl_give isl_union_pw_qpolynomial_fold *
7921 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7922 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7923 __isl_take isl_space *space);
7924 __isl_give isl_union_pw_qpolynomial_fold *
7925 isl_union_pw_qpolynomial_fold_subtract_domain(
7926 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7927 __isl_take isl_union_set *uset);
7929 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7930 C<isl_union_pw_aff_subtract_domain_union_set>.
7931 Similarly for the other pairs of functions.
7935 #include <isl/space.h>
7936 __isl_give isl_space *isl_space_join(
7937 __isl_take isl_space *left,
7938 __isl_take isl_space *right);
7940 #include <isl/set.h>
7941 __isl_give isl_basic_set *isl_basic_set_apply(
7942 __isl_take isl_basic_set *bset,
7943 __isl_take isl_basic_map *bmap);
7944 __isl_give isl_set *isl_set_apply(
7945 __isl_take isl_set *set,
7946 __isl_take isl_map *map);
7948 #include <isl/union_set.h>
7949 __isl_give isl_union_set *isl_union_set_apply(
7950 __isl_take isl_union_set *uset,
7951 __isl_take isl_union_map *umap);
7953 #include <isl/map.h>
7954 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7955 __isl_take isl_basic_map *bmap1,
7956 __isl_take isl_basic_map *bmap2);
7957 __isl_give isl_basic_map *isl_basic_map_apply_range(
7958 __isl_take isl_basic_map *bmap1,
7959 __isl_take isl_basic_map *bmap2);
7960 __isl_give isl_map *isl_map_apply_domain(
7961 __isl_take isl_map *map1,
7962 __isl_take isl_map *map2);
7963 __isl_give isl_map *isl_map_apply_range(
7964 __isl_take isl_map *map1,
7965 __isl_take isl_map *map2);
7967 #include <isl/union_map.h>
7968 __isl_give isl_union_map *isl_union_map_apply_domain(
7969 __isl_take isl_union_map *umap1,
7970 __isl_take isl_union_map *umap2);
7971 __isl_give isl_union_map *isl_union_map_apply_range(
7972 __isl_take isl_union_map *umap1,
7973 __isl_take isl_union_map *umap2);
7975 #include <isl/aff.h>
7976 __isl_give isl_union_pw_multi_aff *
7977 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7978 __isl_take isl_union_pw_multi_aff *upma1,
7979 __isl_take isl_union_pw_multi_aff *upma2);
7980 __isl_give isl_union_pw_aff *
7981 isl_multi_union_pw_aff_apply_aff(
7982 __isl_take isl_multi_union_pw_aff *mupa,
7983 __isl_take isl_aff *aff);
7984 __isl_give isl_union_pw_aff *
7985 isl_multi_union_pw_aff_apply_pw_aff(
7986 __isl_take isl_multi_union_pw_aff *mupa,
7987 __isl_take isl_pw_aff *pa);
7988 __isl_give isl_multi_union_pw_aff *
7989 isl_multi_union_pw_aff_apply_multi_aff(
7990 __isl_take isl_multi_union_pw_aff *mupa,
7991 __isl_take isl_multi_aff *ma);
7992 __isl_give isl_multi_union_pw_aff *
7993 isl_multi_union_pw_aff_apply_pw_multi_aff(
7994 __isl_take isl_multi_union_pw_aff *mupa,
7995 __isl_take isl_pw_multi_aff *pma);
7997 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7998 over the shared domain of the elements of the input. The dimension is
7999 required to be greater than zero.
8000 The C<isl_multi_union_pw_aff> argument of
8001 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
8002 but only if the range of the C<isl_multi_aff> argument
8003 is also zero-dimensional.
8004 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
8006 #include <isl/polynomial.h>
8007 __isl_give isl_pw_qpolynomial_fold *
8008 isl_set_apply_pw_qpolynomial_fold(
8009 __isl_take isl_set *set,
8010 __isl_take isl_pw_qpolynomial_fold *pwf,
8012 __isl_give isl_pw_qpolynomial_fold *
8013 isl_map_apply_pw_qpolynomial_fold(
8014 __isl_take isl_map *map,
8015 __isl_take isl_pw_qpolynomial_fold *pwf,
8017 __isl_give isl_union_pw_qpolynomial_fold *
8018 isl_union_set_apply_union_pw_qpolynomial_fold(
8019 __isl_take isl_union_set *uset,
8020 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8022 __isl_give isl_union_pw_qpolynomial_fold *
8023 isl_union_map_apply_union_pw_qpolynomial_fold(
8024 __isl_take isl_union_map *umap,
8025 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8028 The functions taking a map
8029 compose the given map with the given piecewise quasipolynomial reduction.
8030 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
8031 over all elements in the intersection of the range of the map
8032 and the domain of the piecewise quasipolynomial reduction
8033 as a function of an element in the domain of the map.
8034 The functions taking a set compute a bound over all elements in the
8035 intersection of the set and the domain of the
8036 piecewise quasipolynomial reduction.
8040 #include <isl/set.h>
8041 __isl_give isl_basic_set *
8042 isl_basic_set_preimage_multi_aff(
8043 __isl_take isl_basic_set *bset,
8044 __isl_take isl_multi_aff *ma);
8045 __isl_give isl_set *isl_set_preimage_multi_aff(
8046 __isl_take isl_set *set,
8047 __isl_take isl_multi_aff *ma);
8048 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8049 __isl_take isl_set *set,
8050 __isl_take isl_pw_multi_aff *pma);
8051 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8052 __isl_take isl_set *set,
8053 __isl_take isl_multi_pw_aff *mpa);
8055 #include <isl/union_set.h>
8056 __isl_give isl_union_set *
8057 isl_union_set_preimage_multi_aff(
8058 __isl_take isl_union_set *uset,
8059 __isl_take isl_multi_aff *ma);
8060 __isl_give isl_union_set *
8061 isl_union_set_preimage_pw_multi_aff(
8062 __isl_take isl_union_set *uset,
8063 __isl_take isl_pw_multi_aff *pma);
8064 __isl_give isl_union_set *
8065 isl_union_set_preimage_union_pw_multi_aff(
8066 __isl_take isl_union_set *uset,
8067 __isl_take isl_union_pw_multi_aff *upma);
8069 #include <isl/map.h>
8070 __isl_give isl_basic_map *
8071 isl_basic_map_preimage_domain_multi_aff(
8072 __isl_take isl_basic_map *bmap,
8073 __isl_take isl_multi_aff *ma);
8074 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8075 __isl_take isl_map *map,
8076 __isl_take isl_multi_aff *ma);
8077 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8078 __isl_take isl_map *map,
8079 __isl_take isl_multi_aff *ma);
8080 __isl_give isl_map *
8081 isl_map_preimage_domain_pw_multi_aff(
8082 __isl_take isl_map *map,
8083 __isl_take isl_pw_multi_aff *pma);
8084 __isl_give isl_map *
8085 isl_map_preimage_range_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_domain_multi_pw_aff(
8090 __isl_take isl_map *map,
8091 __isl_take isl_multi_pw_aff *mpa);
8092 __isl_give isl_basic_map *
8093 isl_basic_map_preimage_range_multi_aff(
8094 __isl_take isl_basic_map *bmap,
8095 __isl_take isl_multi_aff *ma);
8097 #include <isl/union_map.h>
8098 __isl_give isl_union_map *
8099 isl_union_map_preimage_domain_multi_aff(
8100 __isl_take isl_union_map *umap,
8101 __isl_take isl_multi_aff *ma);
8102 __isl_give isl_union_map *
8103 isl_union_map_preimage_range_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_domain_pw_multi_aff(
8108 __isl_take isl_union_map *umap,
8109 __isl_take isl_pw_multi_aff *pma);
8110 __isl_give isl_union_map *
8111 isl_union_map_preimage_range_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_domain_union_pw_multi_aff(
8116 __isl_take isl_union_map *umap,
8117 __isl_take isl_union_pw_multi_aff *upma);
8118 __isl_give isl_union_map *
8119 isl_union_map_preimage_range_union_pw_multi_aff(
8120 __isl_take isl_union_map *umap,
8121 __isl_take isl_union_pw_multi_aff *upma);
8123 #include <isl/aff.h>
8124 __isl_give isl_pw_multi_aff *
8125 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8126 __isl_take isl_pw_multi_aff *pma1,
8127 __isl_take isl_pw_multi_aff *pma2);
8128 __isl_give isl_union_pw_multi_aff *
8129 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8130 __isl_take isl_union_pw_multi_aff *upma1,
8131 __isl_take isl_union_pw_multi_aff *upma2);
8133 These functions compute the preimage of the given set or map domain/range under
8134 the given function. In other words, the expression is plugged
8135 into the set description or into the domain/range of the map or function.
8139 #include <isl/aff.h>
8140 __isl_give isl_aff *isl_aff_pullback_aff(
8141 __isl_take isl_aff *aff1,
8142 __isl_take isl_aff *aff2);
8143 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8144 __isl_take isl_aff *aff,
8145 __isl_take isl_multi_aff *ma);
8146 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8147 __isl_take isl_pw_aff *pa,
8148 __isl_take isl_multi_aff *ma);
8149 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8150 __isl_take isl_pw_aff *pa,
8151 __isl_take isl_pw_multi_aff *pma);
8152 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8153 __isl_take isl_pw_aff *pa,
8154 __isl_take isl_multi_pw_aff *mpa);
8155 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8156 __isl_take isl_multi_aff *ma1,
8157 __isl_take isl_multi_aff *ma2);
8158 __isl_give isl_pw_multi_aff *
8159 isl_pw_multi_aff_pullback_multi_aff(
8160 __isl_take isl_pw_multi_aff *pma,
8161 __isl_take isl_multi_aff *ma);
8162 __isl_give isl_multi_pw_aff *
8163 isl_multi_pw_aff_pullback_multi_aff(
8164 __isl_take isl_multi_pw_aff *mpa,
8165 __isl_take isl_multi_aff *ma);
8166 __isl_give isl_pw_multi_aff *
8167 isl_pw_multi_aff_pullback_pw_multi_aff(
8168 __isl_take isl_pw_multi_aff *pma1,
8169 __isl_take isl_pw_multi_aff *pma2);
8170 __isl_give isl_multi_pw_aff *
8171 isl_multi_pw_aff_pullback_pw_multi_aff(
8172 __isl_take isl_multi_pw_aff *mpa,
8173 __isl_take isl_pw_multi_aff *pma);
8174 __isl_give isl_multi_pw_aff *
8175 isl_multi_pw_aff_pullback_multi_pw_aff(
8176 __isl_take isl_multi_pw_aff *mpa1,
8177 __isl_take isl_multi_pw_aff *mpa2);
8178 __isl_give isl_union_pw_aff *
8179 isl_union_pw_aff_pullback_union_pw_multi_aff(
8180 __isl_take isl_union_pw_aff *upa,
8181 __isl_take isl_union_pw_multi_aff *upma);
8182 __isl_give isl_union_pw_multi_aff *
8183 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8184 __isl_take isl_union_pw_multi_aff *upma1,
8185 __isl_take isl_union_pw_multi_aff *upma2);
8186 __isl_give isl_multi_union_pw_aff *
8187 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8188 __isl_take isl_multi_union_pw_aff *mupa,
8189 __isl_take isl_union_pw_multi_aff *upma);
8191 These functions precompose the first expression by the second function.
8192 In other words, the second function is plugged
8193 into the first expression.
8197 #include <isl/aff.h>
8198 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8199 __isl_take isl_aff *aff1,
8200 __isl_take isl_aff *aff2);
8201 __isl_give isl_set *isl_aff_eq_set(
8202 __isl_take isl_aff *aff1,
8203 __isl_take isl_aff *aff2);
8204 __isl_give isl_set *isl_aff_ne_set(
8205 __isl_take isl_aff *aff1,
8206 __isl_take isl_aff *aff2);
8207 __isl_give isl_basic_set *isl_aff_le_basic_set(
8208 __isl_take isl_aff *aff1,
8209 __isl_take isl_aff *aff2);
8210 __isl_give isl_set *isl_aff_le_set(
8211 __isl_take isl_aff *aff1,
8212 __isl_take isl_aff *aff2);
8213 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8214 __isl_take isl_aff *aff1,
8215 __isl_take isl_aff *aff2);
8216 __isl_give isl_set *isl_aff_lt_set(
8217 __isl_take isl_aff *aff1,
8218 __isl_take isl_aff *aff2);
8219 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8220 __isl_take isl_aff *aff1,
8221 __isl_take isl_aff *aff2);
8222 __isl_give isl_set *isl_aff_ge_set(
8223 __isl_take isl_aff *aff1,
8224 __isl_take isl_aff *aff2);
8225 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8226 __isl_take isl_aff *aff1,
8227 __isl_take isl_aff *aff2);
8228 __isl_give isl_set *isl_aff_gt_set(
8229 __isl_take isl_aff *aff1,
8230 __isl_take isl_aff *aff2);
8231 __isl_give isl_set *isl_pw_aff_eq_set(
8232 __isl_take isl_pw_aff *pwaff1,
8233 __isl_take isl_pw_aff *pwaff2);
8234 __isl_give isl_set *isl_pw_aff_ne_set(
8235 __isl_take isl_pw_aff *pwaff1,
8236 __isl_take isl_pw_aff *pwaff2);
8237 __isl_give isl_set *isl_pw_aff_le_set(
8238 __isl_take isl_pw_aff *pwaff1,
8239 __isl_take isl_pw_aff *pwaff2);
8240 __isl_give isl_set *isl_pw_aff_lt_set(
8241 __isl_take isl_pw_aff *pwaff1,
8242 __isl_take isl_pw_aff *pwaff2);
8243 __isl_give isl_set *isl_pw_aff_ge_set(
8244 __isl_take isl_pw_aff *pwaff1,
8245 __isl_take isl_pw_aff *pwaff2);
8246 __isl_give isl_set *isl_pw_aff_gt_set(
8247 __isl_take isl_pw_aff *pwaff1,
8248 __isl_take isl_pw_aff *pwaff2);
8250 __isl_give isl_set *isl_multi_aff_lex_le_set(
8251 __isl_take isl_multi_aff *ma1,
8252 __isl_take isl_multi_aff *ma2);
8253 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8254 __isl_take isl_multi_aff *ma1,
8255 __isl_take isl_multi_aff *ma2);
8256 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8257 __isl_take isl_multi_aff *ma1,
8258 __isl_take isl_multi_aff *ma2);
8259 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8260 __isl_take isl_multi_aff *ma1,
8261 __isl_take isl_multi_aff *ma2);
8263 __isl_give isl_set *isl_pw_aff_list_eq_set(
8264 __isl_take isl_pw_aff_list *list1,
8265 __isl_take isl_pw_aff_list *list2);
8266 __isl_give isl_set *isl_pw_aff_list_ne_set(
8267 __isl_take isl_pw_aff_list *list1,
8268 __isl_take isl_pw_aff_list *list2);
8269 __isl_give isl_set *isl_pw_aff_list_le_set(
8270 __isl_take isl_pw_aff_list *list1,
8271 __isl_take isl_pw_aff_list *list2);
8272 __isl_give isl_set *isl_pw_aff_list_lt_set(
8273 __isl_take isl_pw_aff_list *list1,
8274 __isl_take isl_pw_aff_list *list2);
8275 __isl_give isl_set *isl_pw_aff_list_ge_set(
8276 __isl_take isl_pw_aff_list *list1,
8277 __isl_take isl_pw_aff_list *list2);
8278 __isl_give isl_set *isl_pw_aff_list_gt_set(
8279 __isl_take isl_pw_aff_list *list1,
8280 __isl_take isl_pw_aff_list *list2);
8282 The function C<isl_aff_ge_basic_set> returns a basic set
8283 containing those elements in the shared space
8284 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8285 The function C<isl_pw_aff_ge_set> returns a set
8286 containing those elements in the shared domain
8287 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8288 greater than or equal to C<pwaff2>.
8289 The function C<isl_multi_aff_lex_le_set> returns a set
8290 containing those elements in the shared domain space
8291 where C<ma1> is lexicographically smaller than or
8293 The functions operating on C<isl_pw_aff_list> apply the corresponding
8294 C<isl_pw_aff> function to each pair of elements in the two lists.
8296 #include <isl/aff.h>
8297 __isl_give isl_map *isl_pw_aff_eq_map(
8298 __isl_take isl_pw_aff *pa1,
8299 __isl_take isl_pw_aff *pa2);
8300 __isl_give isl_map *isl_pw_aff_le_map(
8301 __isl_take isl_pw_aff *pa1,
8302 __isl_take isl_pw_aff *pa2);
8303 __isl_give isl_map *isl_pw_aff_lt_map(
8304 __isl_take isl_pw_aff *pa1,
8305 __isl_take isl_pw_aff *pa2);
8306 __isl_give isl_map *isl_pw_aff_ge_map(
8307 __isl_take isl_pw_aff *pa1,
8308 __isl_take isl_pw_aff *pa2);
8309 __isl_give isl_map *isl_pw_aff_gt_map(
8310 __isl_take isl_pw_aff *pa1,
8311 __isl_take isl_pw_aff *pa2);
8313 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8314 __isl_take isl_multi_pw_aff *mpa1,
8315 __isl_take isl_multi_pw_aff *mpa2);
8316 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8317 __isl_take isl_multi_pw_aff *mpa1,
8318 __isl_take isl_multi_pw_aff *mpa2);
8319 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8320 __isl_take isl_multi_pw_aff *mpa1,
8321 __isl_take isl_multi_pw_aff *mpa2);
8322 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8323 __isl_take isl_multi_pw_aff *mpa1,
8324 __isl_take isl_multi_pw_aff *mpa2);
8325 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8326 __isl_take isl_multi_pw_aff *mpa1,
8327 __isl_take isl_multi_pw_aff *mpa2);
8329 These functions return a map between domain elements of the arguments
8330 where the function values satisfy the given relation.
8332 #include <isl/map.h>
8333 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8334 __isl_take isl_map *map,
8335 __isl_take isl_multi_pw_aff *mpa);
8336 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8337 __isl_take isl_map *map,
8338 __isl_take isl_multi_pw_aff *mpa);
8339 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8340 __isl_take isl_map *map,
8341 __isl_take isl_multi_pw_aff *mpa);
8342 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8343 __isl_take isl_map *map,
8344 __isl_take isl_multi_pw_aff *mpa);
8345 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8346 __isl_take isl_map *map,
8347 __isl_take isl_multi_pw_aff *mpa);
8349 #include <isl/union_map.h>
8350 __isl_give isl_union_map *
8351 isl_union_map_eq_at_multi_union_pw_aff(
8352 __isl_take isl_union_map *umap,
8353 __isl_take isl_multi_union_pw_aff *mupa);
8354 __isl_give isl_union_map *
8355 isl_union_map_lex_lt_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_le_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_gt_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_ge_at_multi_union_pw_aff(
8368 __isl_take isl_union_map *umap,
8369 __isl_take isl_multi_union_pw_aff *mupa);
8371 These functions select the subset of elements in the union map
8372 that have an equal or lexicographically smaller or greater function value.
8374 =item * Cartesian Product
8376 #include <isl/space.h>
8377 __isl_give isl_space *isl_space_product(
8378 __isl_take isl_space *space1,
8379 __isl_take isl_space *space2);
8380 __isl_give isl_space *isl_space_domain_product(
8381 __isl_take isl_space *space1,
8382 __isl_take isl_space *space2);
8383 __isl_give isl_space *isl_space_range_product(
8384 __isl_take isl_space *space1,
8385 __isl_take isl_space *space2);
8388 C<isl_space_product>, C<isl_space_domain_product>
8389 and C<isl_space_range_product> take pairs or relation spaces and
8390 produce a single relations space, where either the domain, the range
8391 or both domain and range are wrapped spaces of relations between
8392 the domains and/or ranges of the input spaces.
8393 If the product is only constructed over the domain or the range
8394 then the ranges or the domains of the inputs should be the same.
8395 The function C<isl_space_product> also accepts a pair of set spaces,
8396 in which case it returns a wrapped space of a relation between the
8399 #include <isl/set.h>
8400 __isl_give isl_set *isl_set_product(
8401 __isl_take isl_set *set1,
8402 __isl_take isl_set *set2);
8404 #include <isl/map.h>
8405 __isl_give isl_basic_map *isl_basic_map_domain_product(
8406 __isl_take isl_basic_map *bmap1,
8407 __isl_take isl_basic_map *bmap2);
8408 __isl_give isl_basic_map *isl_basic_map_range_product(
8409 __isl_take isl_basic_map *bmap1,
8410 __isl_take isl_basic_map *bmap2);
8411 __isl_give isl_basic_map *isl_basic_map_product(
8412 __isl_take isl_basic_map *bmap1,
8413 __isl_take isl_basic_map *bmap2);
8414 __isl_give isl_map *isl_map_domain_product(
8415 __isl_take isl_map *map1,
8416 __isl_take isl_map *map2);
8417 __isl_give isl_map *isl_map_range_product(
8418 __isl_take isl_map *map1,
8419 __isl_take isl_map *map2);
8420 __isl_give isl_map *isl_map_product(
8421 __isl_take isl_map *map1,
8422 __isl_take isl_map *map2);
8424 #include <isl/union_set.h>
8425 __isl_give isl_union_set *isl_union_set_product(
8426 __isl_take isl_union_set *uset1,
8427 __isl_take isl_union_set *uset2);
8429 #include <isl/union_map.h>
8430 __isl_give isl_union_map *isl_union_map_domain_product(
8431 __isl_take isl_union_map *umap1,
8432 __isl_take isl_union_map *umap2);
8433 __isl_give isl_union_map *isl_union_map_range_product(
8434 __isl_take isl_union_map *umap1,
8435 __isl_take isl_union_map *umap2);
8436 __isl_give isl_union_map *isl_union_map_product(
8437 __isl_take isl_union_map *umap1,
8438 __isl_take isl_union_map *umap2);
8441 __isl_give isl_multi_id *isl_multi_id_range_product(
8442 __isl_take isl_multi_id *mi1,
8443 __isl_take isl_multi_id *mi2);
8445 #include <isl/val.h>
8446 __isl_give isl_multi_val *isl_multi_val_range_product(
8447 __isl_take isl_multi_val *mv1,
8448 __isl_take isl_multi_val *mv2);
8449 __isl_give isl_multi_val *isl_multi_val_product(
8450 __isl_take isl_multi_val *mv1,
8451 __isl_take isl_multi_val *mv2);
8453 #include <isl/aff.h>
8454 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8455 __isl_take isl_multi_aff *ma1,
8456 __isl_take isl_multi_aff *ma2);
8457 __isl_give isl_multi_aff *isl_multi_aff_product(
8458 __isl_take isl_multi_aff *ma1,
8459 __isl_take isl_multi_aff *ma2);
8460 __isl_give isl_multi_pw_aff *
8461 isl_multi_pw_aff_range_product(
8462 __isl_take isl_multi_pw_aff *mpa1,
8463 __isl_take isl_multi_pw_aff *mpa2);
8464 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8465 __isl_take isl_multi_pw_aff *mpa1,
8466 __isl_take isl_multi_pw_aff *mpa2);
8467 __isl_give isl_pw_multi_aff *
8468 isl_pw_multi_aff_range_product(
8469 __isl_take isl_pw_multi_aff *pma1,
8470 __isl_take isl_pw_multi_aff *pma2);
8471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8472 __isl_take isl_pw_multi_aff *pma1,
8473 __isl_take isl_pw_multi_aff *pma2);
8474 __isl_give isl_union_pw_multi_aff *
8475 isl_union_pw_multi_aff_range_product(
8476 __isl_take isl_union_pw_multi_aff *upma1,
8477 __isl_take isl_union_pw_multi_aff *upma2);
8478 __isl_give isl_multi_union_pw_aff *
8479 isl_multi_union_pw_aff_range_product(
8480 __isl_take isl_multi_union_pw_aff *mupa1,
8481 __isl_take isl_multi_union_pw_aff *mupa2);
8483 The above functions compute the cross product of the given
8484 sets, relations or functions. The domains and ranges of the results
8485 are wrapped maps between domains and ranges of the inputs.
8486 To obtain a ``flat'' product, use the following functions
8489 #include <isl/set.h>
8490 __isl_give isl_basic_set *isl_basic_set_flat_product(
8491 __isl_take isl_basic_set *bset1,
8492 __isl_take isl_basic_set *bset2);
8493 __isl_give isl_set *isl_set_flat_product(
8494 __isl_take isl_set *set1,
8495 __isl_take isl_set *set2);
8497 #include <isl/map.h>
8498 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8499 __isl_take isl_basic_map *bmap1,
8500 __isl_take isl_basic_map *bmap2);
8501 __isl_give isl_map *isl_map_flat_domain_product(
8502 __isl_take isl_map *map1,
8503 __isl_take isl_map *map2);
8504 __isl_give isl_map *isl_map_flat_range_product(
8505 __isl_take isl_map *map1,
8506 __isl_take isl_map *map2);
8507 __isl_give isl_basic_map *isl_basic_map_flat_product(
8508 __isl_take isl_basic_map *bmap1,
8509 __isl_take isl_basic_map *bmap2);
8510 __isl_give isl_map *isl_map_flat_product(
8511 __isl_take isl_map *map1,
8512 __isl_take isl_map *map2);
8514 #include <isl/union_map.h>
8515 __isl_give isl_union_map *
8516 isl_union_map_flat_domain_product(
8517 __isl_take isl_union_map *umap1,
8518 __isl_take isl_union_map *umap2);
8519 __isl_give isl_union_map *
8520 isl_union_map_flat_range_product(
8521 __isl_take isl_union_map *umap1,
8522 __isl_take isl_union_map *umap2);
8525 __isl_give isl_multi_id *
8526 isl_multi_id_flat_range_product(
8527 __isl_take isl_multi_id *mi1,
8528 __isl_take isl_multi_id *mi2);
8530 #include <isl/val.h>
8531 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8532 __isl_take isl_multi_val *mv1,
8533 __isl_take isl_multi_val *mv2);
8535 #include <isl/aff.h>
8536 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8537 __isl_take isl_multi_aff *ma1,
8538 __isl_take isl_multi_aff *ma2);
8539 __isl_give isl_pw_multi_aff *
8540 isl_pw_multi_aff_flat_range_product(
8541 __isl_take isl_pw_multi_aff *pma1,
8542 __isl_take isl_pw_multi_aff *pma2);
8543 __isl_give isl_multi_pw_aff *
8544 isl_multi_pw_aff_flat_range_product(
8545 __isl_take isl_multi_pw_aff *mpa1,
8546 __isl_take isl_multi_pw_aff *mpa2);
8547 __isl_give isl_union_pw_multi_aff *
8548 isl_union_pw_multi_aff_flat_range_product(
8549 __isl_take isl_union_pw_multi_aff *upma1,
8550 __isl_take isl_union_pw_multi_aff *upma2);
8551 __isl_give isl_multi_union_pw_aff *
8552 isl_multi_union_pw_aff_flat_range_product(
8553 __isl_take isl_multi_union_pw_aff *mupa1,
8554 __isl_take isl_multi_union_pw_aff *mupa2);
8556 #include <isl/space.h>
8557 __isl_give isl_space *isl_space_factor_domain(
8558 __isl_take isl_space *space);
8559 __isl_give isl_space *isl_space_factor_range(
8560 __isl_take isl_space *space);
8561 __isl_give isl_space *isl_space_domain_factor_domain(
8562 __isl_take isl_space *space);
8563 __isl_give isl_space *isl_space_domain_factor_range(
8564 __isl_take isl_space *space);
8565 __isl_give isl_space *isl_space_range_factor_domain(
8566 __isl_take isl_space *space);
8567 __isl_give isl_space *isl_space_range_factor_range(
8568 __isl_take isl_space *space);
8570 The functions C<isl_space_range_factor_domain> and
8571 C<isl_space_range_factor_range> extract the two arguments from
8572 the result of a call to C<isl_space_range_product>.
8574 The arguments of a call to a product can be extracted
8575 from the result using the following functions.
8577 #include <isl/map.h>
8578 __isl_give isl_map *isl_map_factor_domain(
8579 __isl_take isl_map *map);
8580 __isl_give isl_map *isl_map_factor_range(
8581 __isl_take isl_map *map);
8582 __isl_give isl_map *isl_map_domain_factor_domain(
8583 __isl_take isl_map *map);
8584 __isl_give isl_map *isl_map_domain_factor_range(
8585 __isl_take isl_map *map);
8586 __isl_give isl_map *isl_map_range_factor_domain(
8587 __isl_take isl_map *map);
8588 __isl_give isl_map *isl_map_range_factor_range(
8589 __isl_take isl_map *map);
8591 #include <isl/union_map.h>
8592 __isl_give isl_union_map *isl_union_map_factor_domain(
8593 __isl_take isl_union_map *umap);
8594 __isl_give isl_union_map *isl_union_map_factor_range(
8595 __isl_take isl_union_map *umap);
8596 __isl_give isl_union_map *
8597 isl_union_map_domain_factor_domain(
8598 __isl_take isl_union_map *umap);
8599 __isl_give isl_union_map *
8600 isl_union_map_domain_factor_range(
8601 __isl_take isl_union_map *umap);
8602 __isl_give isl_union_map *
8603 isl_union_map_range_factor_domain(
8604 __isl_take isl_union_map *umap);
8605 __isl_give isl_union_map *
8606 isl_union_map_range_factor_range(
8607 __isl_take isl_union_map *umap);
8610 __isl_give isl_multi_id *isl_multi_id_factor_range(
8611 __isl_take isl_multi_id *mi);
8612 __isl_give isl_multi_id *
8613 isl_multi_id_range_factor_domain(
8614 __isl_take isl_multi_id *mi);
8615 __isl_give isl_multi_id *
8616 isl_multi_id_range_factor_range(
8617 __isl_take isl_multi_id *mi);
8619 #include <isl/val.h>
8620 __isl_give isl_multi_val *isl_multi_val_factor_range(
8621 __isl_take isl_multi_val *mv);
8622 __isl_give isl_multi_val *
8623 isl_multi_val_range_factor_domain(
8624 __isl_take isl_multi_val *mv);
8625 __isl_give isl_multi_val *
8626 isl_multi_val_range_factor_range(
8627 __isl_take isl_multi_val *mv);
8629 #include <isl/aff.h>
8630 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8631 __isl_take isl_multi_aff *ma);
8632 __isl_give isl_multi_aff *
8633 isl_multi_aff_range_factor_domain(
8634 __isl_take isl_multi_aff *ma);
8635 __isl_give isl_multi_aff *
8636 isl_multi_aff_range_factor_range(
8637 __isl_take isl_multi_aff *ma);
8638 __isl_give isl_multi_pw_aff *
8639 isl_multi_pw_aff_factor_range(
8640 __isl_take isl_multi_pw_aff *mpa);
8641 __isl_give isl_multi_pw_aff *
8642 isl_multi_pw_aff_range_factor_domain(
8643 __isl_take isl_multi_pw_aff *mpa);
8644 __isl_give isl_multi_pw_aff *
8645 isl_multi_pw_aff_range_factor_range(
8646 __isl_take isl_multi_pw_aff *mpa);
8647 __isl_give isl_pw_multi_aff *
8648 isl_pw_multi_aff_range_factor_domain(
8649 __isl_take isl_pw_multi_aff *pma);
8650 __isl_give isl_pw_multi_aff *
8651 isl_pw_multi_aff_range_factor_range(
8652 __isl_take isl_pw_multi_aff *pma);
8653 __isl_give isl_union_pw_multi_aff *
8654 isl_union_pw_multi_aff_range_factor_domain(
8655 __isl_take isl_union_pw_multi_aff *upma);
8656 __isl_give isl_union_pw_multi_aff *
8657 isl_union_pw_multi_aff_range_factor_range(
8658 __isl_take isl_union_pw_multi_aff *upma);
8659 __isl_give isl_multi_union_pw_aff *
8660 isl_multi_union_pw_aff_factor_range(
8661 __isl_take isl_multi_union_pw_aff *mupa);
8662 __isl_give isl_multi_union_pw_aff *
8663 isl_multi_union_pw_aff_range_factor_domain(
8664 __isl_take isl_multi_union_pw_aff *mupa);
8665 __isl_give isl_multi_union_pw_aff *
8666 isl_multi_union_pw_aff_range_factor_range(
8667 __isl_take isl_multi_union_pw_aff *mupa);
8669 The splice functions are a generalization of the flat product functions,
8670 where the second argument may be inserted at any position inside
8671 the first argument rather than being placed at the end.
8672 The functions C<isl_multi_val_factor_range>,
8673 C<isl_multi_aff_factor_range>,
8674 C<isl_multi_pw_aff_factor_range> and
8675 C<isl_multi_union_pw_aff_factor_range>
8676 take functions that live in a set space.
8679 __isl_give isl_multi_id *isl_multi_id_range_splice(
8680 __isl_take isl_multi_id *mi1, unsigned pos,
8681 __isl_take isl_multi_id *mi2);
8683 #include <isl/val.h>
8684 __isl_give isl_multi_val *isl_multi_val_range_splice(
8685 __isl_take isl_multi_val *mv1, unsigned pos,
8686 __isl_take isl_multi_val *mv2);
8688 #include <isl/aff.h>
8689 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8690 __isl_take isl_multi_aff *ma1, unsigned pos,
8691 __isl_take isl_multi_aff *ma2);
8692 __isl_give isl_multi_aff *isl_multi_aff_splice(
8693 __isl_take isl_multi_aff *ma1,
8694 unsigned in_pos, unsigned out_pos,
8695 __isl_take isl_multi_aff *ma2);
8696 __isl_give isl_multi_pw_aff *
8697 isl_multi_pw_aff_range_splice(
8698 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8699 __isl_take isl_multi_pw_aff *mpa2);
8700 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8701 __isl_take isl_multi_pw_aff *mpa1,
8702 unsigned in_pos, unsigned out_pos,
8703 __isl_take isl_multi_pw_aff *mpa2);
8704 __isl_give isl_multi_union_pw_aff *
8705 isl_multi_union_pw_aff_range_splice(
8706 __isl_take isl_multi_union_pw_aff *mupa1,
8708 __isl_take isl_multi_union_pw_aff *mupa2);
8710 =item * Simplification
8712 When applied to a set or relation,
8713 the gist operation returns a set or relation that has the
8714 same intersection with the context as the input set or relation.
8715 Any implicit equality in the intersection is made explicit in the result,
8716 while all inequalities that are redundant with respect to the intersection
8718 In case of union sets and relations, the gist operation is performed
8721 When applied to a function,
8722 the gist operation applies the set gist operation to each of
8723 the cells in the domain of the input piecewise expression.
8724 The context is also exploited
8725 to simplify the expression associated to each cell.
8727 #include <isl/set.h>
8728 __isl_give isl_basic_set *isl_basic_set_gist(
8729 __isl_take isl_basic_set *bset,
8730 __isl_take isl_basic_set *context);
8731 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8732 __isl_take isl_set *context);
8733 __isl_give isl_set *isl_set_gist_params(
8734 __isl_take isl_set *set,
8735 __isl_take isl_set *context);
8737 #include <isl/map.h>
8738 __isl_give isl_basic_map *isl_basic_map_gist(
8739 __isl_take isl_basic_map *bmap,
8740 __isl_take isl_basic_map *context);
8741 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8742 __isl_take isl_basic_map *bmap,
8743 __isl_take isl_basic_set *context);
8744 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8745 __isl_take isl_map *context);
8746 __isl_give isl_map *isl_map_gist_params(
8747 __isl_take isl_map *map,
8748 __isl_take isl_set *context);
8749 __isl_give isl_map *isl_map_gist_domain(
8750 __isl_take isl_map *map,
8751 __isl_take isl_set *context);
8752 __isl_give isl_map *isl_map_gist_range(
8753 __isl_take isl_map *map,
8754 __isl_take isl_set *context);
8756 #include <isl/union_set.h>
8757 __isl_give isl_union_set *isl_union_set_gist(
8758 __isl_take isl_union_set *uset,
8759 __isl_take isl_union_set *context);
8760 __isl_give isl_union_set *isl_union_set_gist_params(
8761 __isl_take isl_union_set *uset,
8762 __isl_take isl_set *set);
8764 #include <isl/union_map.h>
8765 __isl_give isl_union_map *isl_union_map_gist(
8766 __isl_take isl_union_map *umap,
8767 __isl_take isl_union_map *context);
8768 __isl_give isl_union_map *isl_union_map_gist_params(
8769 __isl_take isl_union_map *umap,
8770 __isl_take isl_set *set);
8771 __isl_give isl_union_map *isl_union_map_gist_domain(
8772 __isl_take isl_union_map *umap,
8773 __isl_take isl_union_set *uset);
8774 __isl_give isl_union_map *isl_union_map_gist_range(
8775 __isl_take isl_union_map *umap,
8776 __isl_take isl_union_set *uset);
8778 #include <isl/aff.h>
8779 __isl_give isl_aff *isl_aff_gist_params(
8780 __isl_take isl_aff *aff,
8781 __isl_take isl_set *context);
8782 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8783 __isl_take isl_set *context);
8784 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8785 __isl_take isl_multi_aff *maff,
8786 __isl_take isl_set *context);
8787 __isl_give isl_multi_aff *isl_multi_aff_gist(
8788 __isl_take isl_multi_aff *maff,
8789 __isl_take isl_set *context);
8790 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8791 __isl_take isl_pw_aff *pwaff,
8792 __isl_take isl_set *context);
8793 __isl_give isl_pw_aff *isl_pw_aff_gist(
8794 __isl_take isl_pw_aff *pwaff,
8795 __isl_take isl_set *context);
8796 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8797 __isl_take isl_pw_multi_aff *pma,
8798 __isl_take isl_set *set);
8799 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8800 __isl_take isl_pw_multi_aff *pma,
8801 __isl_take isl_set *set);
8802 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8803 __isl_take isl_multi_pw_aff *mpa,
8804 __isl_take isl_set *set);
8805 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8806 __isl_take isl_multi_pw_aff *mpa,
8807 __isl_take isl_set *set);
8808 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8809 __isl_take isl_union_pw_aff *upa,
8810 __isl_take isl_union_set *context);
8811 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8812 __isl_take isl_union_pw_aff *upa,
8813 __isl_take isl_set *context);
8814 __isl_give isl_union_pw_multi_aff *
8815 isl_union_pw_multi_aff_gist_params(
8816 __isl_take isl_union_pw_multi_aff *upma,
8817 __isl_take isl_set *context);
8818 __isl_give isl_union_pw_multi_aff *
8819 isl_union_pw_multi_aff_gist(
8820 __isl_take isl_union_pw_multi_aff *upma,
8821 __isl_take isl_union_set *context);
8822 __isl_give isl_multi_union_pw_aff *
8823 isl_multi_union_pw_aff_gist_params(
8824 __isl_take isl_multi_union_pw_aff *mupa,
8825 __isl_take isl_set *context);
8826 __isl_give isl_multi_union_pw_aff *
8827 isl_multi_union_pw_aff_gist(
8828 __isl_take isl_multi_union_pw_aff *mupa,
8829 __isl_take isl_union_set *context);
8831 #include <isl/polynomial.h>
8832 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8833 __isl_take isl_qpolynomial *qp,
8834 __isl_take isl_set *context);
8835 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8836 __isl_take isl_qpolynomial *qp,
8837 __isl_take isl_set *context);
8838 __isl_give isl_qpolynomial_fold *
8839 isl_qpolynomial_fold_gist_params(
8840 __isl_take isl_qpolynomial_fold *fold,
8841 __isl_take isl_set *context);
8842 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8843 __isl_take isl_qpolynomial_fold *fold,
8844 __isl_take isl_set *context);
8845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8846 __isl_take isl_pw_qpolynomial *pwqp,
8847 __isl_take isl_set *context);
8848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8849 __isl_take isl_pw_qpolynomial *pwqp,
8850 __isl_take isl_set *context);
8851 __isl_give isl_pw_qpolynomial_fold *
8852 isl_pw_qpolynomial_fold_gist(
8853 __isl_take isl_pw_qpolynomial_fold *pwf,
8854 __isl_take isl_set *context);
8855 __isl_give isl_pw_qpolynomial_fold *
8856 isl_pw_qpolynomial_fold_gist_params(
8857 __isl_take isl_pw_qpolynomial_fold *pwf,
8858 __isl_take isl_set *context);
8859 __isl_give isl_union_pw_qpolynomial *
8860 isl_union_pw_qpolynomial_gist_params(
8861 __isl_take isl_union_pw_qpolynomial *upwqp,
8862 __isl_take isl_set *context);
8863 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8864 __isl_take isl_union_pw_qpolynomial *upwqp,
8865 __isl_take isl_union_set *context);
8866 __isl_give isl_union_pw_qpolynomial_fold *
8867 isl_union_pw_qpolynomial_fold_gist(
8868 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8869 __isl_take isl_union_set *context);
8870 __isl_give isl_union_pw_qpolynomial_fold *
8871 isl_union_pw_qpolynomial_fold_gist_params(
8872 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8873 __isl_take isl_set *context);
8875 =item * Binary Arithmetic Operations
8877 #include <isl/set.h>
8878 __isl_give isl_set *isl_set_sum(
8879 __isl_take isl_set *set1,
8880 __isl_take isl_set *set2);
8881 #include <isl/map.h>
8882 __isl_give isl_map *isl_map_sum(
8883 __isl_take isl_map *map1,
8884 __isl_take isl_map *map2);
8886 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8887 i.e., the set containing the sums of pairs of elements from
8888 C<set1> and C<set2>.
8889 The domain of the result of C<isl_map_sum> is the intersection
8890 of the domains of its two arguments. The corresponding range
8891 elements are the sums of the corresponding range elements
8892 in the two arguments.
8894 #include <isl/val.h>
8895 __isl_give isl_multi_val *isl_multi_val_add(
8896 __isl_take isl_multi_val *mv1,
8897 __isl_take isl_multi_val *mv2);
8898 __isl_give isl_multi_val *isl_multi_val_sub(
8899 __isl_take isl_multi_val *mv1,
8900 __isl_take isl_multi_val *mv2);
8901 __isl_give isl_multi_val *isl_multi_val_min(
8902 __isl_take isl_multi_val *mv1,
8903 __isl_take isl_multi_val *mv2);
8904 __isl_give isl_multi_val *isl_multi_val_max(
8905 __isl_take isl_multi_val *mv1,
8906 __isl_take isl_multi_val *mv2);
8908 #include <isl/aff.h>
8909 __isl_give isl_aff *isl_aff_add(
8910 __isl_take isl_aff *aff1,
8911 __isl_take isl_aff *aff2);
8912 __isl_give isl_multi_aff *isl_multi_aff_add(
8913 __isl_take isl_multi_aff *maff1,
8914 __isl_take isl_multi_aff *maff2);
8915 __isl_give isl_pw_aff *isl_pw_aff_add(
8916 __isl_take isl_pw_aff *pwaff1,
8917 __isl_take isl_pw_aff *pwaff2);
8918 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8919 __isl_take isl_multi_pw_aff *mpa1,
8920 __isl_take isl_multi_pw_aff *mpa2);
8921 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8922 __isl_take isl_pw_multi_aff *pma1,
8923 __isl_take isl_pw_multi_aff *pma2);
8924 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8925 __isl_take isl_union_pw_aff *upa1,
8926 __isl_take isl_union_pw_aff *upa2);
8927 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8928 __isl_take isl_union_pw_multi_aff *upma1,
8929 __isl_take isl_union_pw_multi_aff *upma2);
8930 __isl_give isl_multi_union_pw_aff *
8931 isl_multi_union_pw_aff_add(
8932 __isl_take isl_multi_union_pw_aff *mupa1,
8933 __isl_take isl_multi_union_pw_aff *mupa2);
8934 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8935 __isl_take isl_pw_aff *pa,
8936 __isl_take isl_val *v);
8937 __isl_give isl_multi_aff *
8938 isl_multi_aff_add_constant_val(
8939 __isl_take isl_multi_aff *pa,
8940 __isl_take isl_val *v);
8941 __isl_give isl_pw_multi_aff *
8942 isl_pw_multi_aff_add_constant_val(
8943 __isl_take isl_pw_multi_aff *pma,
8944 __isl_take isl_val *v);
8945 __isl_give isl_pw_multi_aff *
8946 isl_pw_multi_aff_add_constant_multi_val(
8947 __isl_take isl_pw_multi_aff *pma,
8948 __isl_take isl_multi_val *mv);
8949 __isl_give isl_multi_pw_aff *
8950 isl_multi_pw_aff_add_constant_val(
8951 __isl_take isl_multi_pw_aff *mpa,
8952 __isl_take isl_val *v);
8953 __isl_give isl_multi_aff *
8954 isl_multi_aff_add_constant_multi_val(
8955 __isl_take isl_multi_aff *pa,
8956 __isl_take isl_multi_val *mv);
8957 __isl_give isl_multi_pw_aff *
8958 isl_multi_pw_aff_add_constant_multi_val(
8959 __isl_take isl_multi_pw_aff *mpa,
8960 __isl_take isl_multi_val *mv);
8961 __isl_give isl_pw_aff *isl_pw_aff_min(
8962 __isl_take isl_pw_aff *pwaff1,
8963 __isl_take isl_pw_aff *pwaff2);
8964 __isl_give isl_pw_aff *isl_pw_aff_max(
8965 __isl_take isl_pw_aff *pwaff1,
8966 __isl_take isl_pw_aff *pwaff2);
8967 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8968 __isl_take isl_multi_pw_aff *mpa1,
8969 __isl_take isl_multi_pw_aff *mpa2);
8970 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8971 __isl_take isl_multi_pw_aff *mpa1,
8972 __isl_take isl_multi_pw_aff *mpa2);
8973 __isl_give isl_aff *isl_aff_sub(
8974 __isl_take isl_aff *aff1,
8975 __isl_take isl_aff *aff2);
8976 __isl_give isl_multi_aff *isl_multi_aff_sub(
8977 __isl_take isl_multi_aff *ma1,
8978 __isl_take isl_multi_aff *ma2);
8979 __isl_give isl_pw_aff *isl_pw_aff_sub(
8980 __isl_take isl_pw_aff *pwaff1,
8981 __isl_take isl_pw_aff *pwaff2);
8982 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8983 __isl_take isl_multi_pw_aff *mpa1,
8984 __isl_take isl_multi_pw_aff *mpa2);
8985 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8986 __isl_take isl_pw_multi_aff *pma1,
8987 __isl_take isl_pw_multi_aff *pma2);
8988 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8989 __isl_take isl_union_pw_aff *upa1,
8990 __isl_take isl_union_pw_aff *upa2);
8991 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8992 __isl_take isl_union_pw_multi_aff *upma1,
8993 __isl_take isl_union_pw_multi_aff *upma2);
8994 __isl_give isl_multi_union_pw_aff *
8995 isl_multi_union_pw_aff_sub(
8996 __isl_take isl_multi_union_pw_aff *mupa1,
8997 __isl_take isl_multi_union_pw_aff *mupa2);
8999 C<isl_aff_sub> subtracts the second argument from the first.
9001 #include <isl/polynomial.h>
9002 __isl_give isl_qpolynomial *isl_qpolynomial_add(
9003 __isl_take isl_qpolynomial *qp1,
9004 __isl_take isl_qpolynomial *qp2);
9005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
9006 __isl_take isl_pw_qpolynomial *pwqp1,
9007 __isl_take isl_pw_qpolynomial *pwqp2);
9008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
9009 __isl_take isl_pw_qpolynomial *pwqp1,
9010 __isl_take isl_pw_qpolynomial *pwqp2);
9011 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
9012 __isl_take isl_pw_qpolynomial_fold *pwf1,
9013 __isl_take isl_pw_qpolynomial_fold *pwf2);
9014 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
9015 __isl_take isl_union_pw_qpolynomial *upwqp1,
9016 __isl_take isl_union_pw_qpolynomial *upwqp2);
9017 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
9018 __isl_take isl_qpolynomial *qp1,
9019 __isl_take isl_qpolynomial *qp2);
9020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
9021 __isl_take isl_pw_qpolynomial *pwqp1,
9022 __isl_take isl_pw_qpolynomial *pwqp2);
9023 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
9024 __isl_take isl_union_pw_qpolynomial *upwqp1,
9025 __isl_take isl_union_pw_qpolynomial *upwqp2);
9026 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
9027 __isl_take isl_pw_qpolynomial_fold *pwf1,
9028 __isl_take isl_pw_qpolynomial_fold *pwf2);
9029 __isl_give isl_union_pw_qpolynomial_fold *
9030 isl_union_pw_qpolynomial_fold_fold(
9031 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
9032 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
9034 #include <isl/aff.h>
9035 __isl_give isl_pw_aff *isl_pw_aff_union_add(
9036 __isl_take isl_pw_aff *pwaff1,
9037 __isl_take isl_pw_aff *pwaff2);
9038 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
9039 __isl_take isl_multi_pw_aff *mpa1,
9040 __isl_take isl_multi_pw_aff *mpa2);
9041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9042 __isl_take isl_pw_multi_aff *pma1,
9043 __isl_take isl_pw_multi_aff *pma2);
9044 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9045 __isl_take isl_union_pw_aff *upa1,
9046 __isl_take isl_union_pw_aff *upa2);
9047 __isl_give isl_union_pw_multi_aff *
9048 isl_union_pw_multi_aff_union_add(
9049 __isl_take isl_union_pw_multi_aff *upma1,
9050 __isl_take isl_union_pw_multi_aff *upma2);
9051 __isl_give isl_multi_union_pw_aff *
9052 isl_multi_union_pw_aff_union_add(
9053 __isl_take isl_multi_union_pw_aff *mupa1,
9054 __isl_take isl_multi_union_pw_aff *mupa2);
9055 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9056 __isl_take isl_pw_aff *pwaff1,
9057 __isl_take isl_pw_aff *pwaff2);
9058 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9059 __isl_take isl_pw_aff *pwaff1,
9060 __isl_take isl_pw_aff *pwaff2);
9062 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9063 expression with a domain that is the union of those of C<pwaff1> and
9064 C<pwaff2> and such that on each cell, the quasi-affine expression is
9065 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9066 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9067 associated expression is the defined one.
9068 This in contrast to the C<isl_pw_aff_max> function, which is
9069 only defined on the shared definition domain of the arguments.
9071 #include <isl/val.h>
9072 __isl_give isl_multi_val *isl_multi_val_add_val(
9073 __isl_take isl_multi_val *mv,
9074 __isl_take isl_val *v);
9075 __isl_give isl_multi_val *isl_multi_val_mod_val(
9076 __isl_take isl_multi_val *mv,
9077 __isl_take isl_val *v);
9078 __isl_give isl_multi_val *isl_multi_val_scale_val(
9079 __isl_take isl_multi_val *mv,
9080 __isl_take isl_val *v);
9081 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9082 __isl_take isl_multi_val *mv,
9083 __isl_take isl_val *v);
9085 #include <isl/aff.h>
9086 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9087 __isl_take isl_val *mod);
9088 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9089 __isl_take isl_pw_aff *pa,
9090 __isl_take isl_val *mod);
9091 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9092 __isl_take isl_union_pw_aff *upa,
9093 __isl_take isl_val *f);
9094 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9095 __isl_take isl_val *v);
9096 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9097 __isl_take isl_multi_aff *ma,
9098 __isl_take isl_val *v);
9099 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9100 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9101 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9102 __isl_take isl_multi_pw_aff *mpa,
9103 __isl_take isl_val *v);
9104 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9105 __isl_take isl_pw_multi_aff *pma,
9106 __isl_take isl_val *v);
9107 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9108 __isl_take isl_union_pw_aff *upa,
9109 __isl_take isl_val *f);
9110 __isl_give isl_union_pw_multi_aff *
9111 isl_union_pw_multi_aff_scale_val(
9112 __isl_take isl_union_pw_multi_aff *upma,
9113 __isl_take isl_val *val);
9114 __isl_give isl_multi_union_pw_aff *
9115 isl_multi_union_pw_aff_scale_val(
9116 __isl_take isl_multi_union_pw_aff *mupa,
9117 __isl_take isl_val *v);
9118 __isl_give isl_aff *isl_aff_scale_down_ui(
9119 __isl_take isl_aff *aff, unsigned f);
9120 __isl_give isl_aff *isl_aff_scale_down_val(
9121 __isl_take isl_aff *aff, __isl_take isl_val *v);
9122 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9123 __isl_take isl_multi_aff *ma,
9124 __isl_take isl_val *v);
9125 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9126 __isl_take isl_pw_aff *pa,
9127 __isl_take isl_val *f);
9128 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9129 __isl_take isl_multi_pw_aff *mpa,
9130 __isl_take isl_val *v);
9131 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9132 __isl_take isl_pw_multi_aff *pma,
9133 __isl_take isl_val *v);
9134 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9135 __isl_take isl_union_pw_aff *upa,
9136 __isl_take isl_val *v);
9137 __isl_give isl_union_pw_multi_aff *
9138 isl_union_pw_multi_aff_scale_down_val(
9139 __isl_take isl_union_pw_multi_aff *upma,
9140 __isl_take isl_val *val);
9141 __isl_give isl_multi_union_pw_aff *
9142 isl_multi_union_pw_aff_scale_down_val(
9143 __isl_take isl_multi_union_pw_aff *mupa,
9144 __isl_take isl_val *v);
9146 #include <isl/polynomial.h>
9147 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9148 __isl_take isl_qpolynomial *qp,
9149 __isl_take isl_val *v);
9150 __isl_give isl_qpolynomial_fold *
9151 isl_qpolynomial_fold_scale_val(
9152 __isl_take isl_qpolynomial_fold *fold,
9153 __isl_take isl_val *v);
9154 __isl_give isl_pw_qpolynomial *
9155 isl_pw_qpolynomial_scale_val(
9156 __isl_take isl_pw_qpolynomial *pwqp,
9157 __isl_take isl_val *v);
9158 __isl_give isl_pw_qpolynomial_fold *
9159 isl_pw_qpolynomial_fold_scale_val(
9160 __isl_take isl_pw_qpolynomial_fold *pwf,
9161 __isl_take isl_val *v);
9162 __isl_give isl_union_pw_qpolynomial *
9163 isl_union_pw_qpolynomial_scale_val(
9164 __isl_take isl_union_pw_qpolynomial *upwqp,
9165 __isl_take isl_val *v);
9166 __isl_give isl_union_pw_qpolynomial_fold *
9167 isl_union_pw_qpolynomial_fold_scale_val(
9168 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9169 __isl_take isl_val *v);
9170 __isl_give isl_qpolynomial *
9171 isl_qpolynomial_scale_down_val(
9172 __isl_take isl_qpolynomial *qp,
9173 __isl_take isl_val *v);
9174 __isl_give isl_qpolynomial_fold *
9175 isl_qpolynomial_fold_scale_down_val(
9176 __isl_take isl_qpolynomial_fold *fold,
9177 __isl_take isl_val *v);
9178 __isl_give isl_pw_qpolynomial *
9179 isl_pw_qpolynomial_scale_down_val(
9180 __isl_take isl_pw_qpolynomial *pwqp,
9181 __isl_take isl_val *v);
9182 __isl_give isl_pw_qpolynomial_fold *
9183 isl_pw_qpolynomial_fold_scale_down_val(
9184 __isl_take isl_pw_qpolynomial_fold *pwf,
9185 __isl_take isl_val *v);
9186 __isl_give isl_union_pw_qpolynomial *
9187 isl_union_pw_qpolynomial_scale_down_val(
9188 __isl_take isl_union_pw_qpolynomial *upwqp,
9189 __isl_take isl_val *v);
9190 __isl_give isl_union_pw_qpolynomial_fold *
9191 isl_union_pw_qpolynomial_fold_scale_down_val(
9192 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9193 __isl_take isl_val *v);
9195 #include <isl/val.h>
9196 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9197 __isl_take isl_multi_val *mv1,
9198 __isl_take isl_multi_val *mv2);
9199 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9200 __isl_take isl_multi_val *mv1,
9201 __isl_take isl_multi_val *mv2);
9202 __isl_give isl_multi_val *
9203 isl_multi_val_scale_down_multi_val(
9204 __isl_take isl_multi_val *mv1,
9205 __isl_take isl_multi_val *mv2);
9207 #include <isl/aff.h>
9208 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9209 __isl_take isl_multi_aff *ma,
9210 __isl_take isl_multi_val *mv);
9211 __isl_give isl_multi_union_pw_aff *
9212 isl_multi_union_pw_aff_mod_multi_val(
9213 __isl_take isl_multi_union_pw_aff *upma,
9214 __isl_take isl_multi_val *mv);
9215 __isl_give isl_multi_pw_aff *
9216 isl_multi_pw_aff_mod_multi_val(
9217 __isl_take isl_multi_pw_aff *mpa,
9218 __isl_take isl_multi_val *mv);
9219 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9220 __isl_take isl_multi_aff *ma,
9221 __isl_take isl_multi_val *mv);
9222 __isl_give isl_pw_multi_aff *
9223 isl_pw_multi_aff_scale_multi_val(
9224 __isl_take isl_pw_multi_aff *pma,
9225 __isl_take isl_multi_val *mv);
9226 __isl_give isl_multi_pw_aff *
9227 isl_multi_pw_aff_scale_multi_val(
9228 __isl_take isl_multi_pw_aff *mpa,
9229 __isl_take isl_multi_val *mv);
9230 __isl_give isl_multi_union_pw_aff *
9231 isl_multi_union_pw_aff_scale_multi_val(
9232 __isl_take isl_multi_union_pw_aff *mupa,
9233 __isl_take isl_multi_val *mv);
9234 __isl_give isl_union_pw_multi_aff *
9235 isl_union_pw_multi_aff_scale_multi_val(
9236 __isl_take isl_union_pw_multi_aff *upma,
9237 __isl_take isl_multi_val *mv);
9238 __isl_give isl_multi_aff *
9239 isl_multi_aff_scale_down_multi_val(
9240 __isl_take isl_multi_aff *ma,
9241 __isl_take isl_multi_val *mv);
9242 __isl_give isl_pw_multi_aff *
9243 isl_pw_multi_aff_scale_down_multi_val(
9244 __isl_take isl_pw_multi_aff *pma,
9245 __isl_take isl_multi_val *mv);
9246 __isl_give isl_multi_pw_aff *
9247 isl_multi_pw_aff_scale_down_multi_val(
9248 __isl_take isl_multi_pw_aff *mpa,
9249 __isl_take isl_multi_val *mv);
9250 __isl_give isl_multi_union_pw_aff *
9251 isl_multi_union_pw_aff_scale_down_multi_val(
9252 __isl_take isl_multi_union_pw_aff *mupa,
9253 __isl_take isl_multi_val *mv);
9255 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9256 by the corresponding elements of C<mv>.
9258 #include <isl/aff.h>
9259 __isl_give isl_aff *isl_aff_mul(
9260 __isl_take isl_aff *aff1,
9261 __isl_take isl_aff *aff2);
9262 __isl_give isl_aff *isl_aff_div(
9263 __isl_take isl_aff *aff1,
9264 __isl_take isl_aff *aff2);
9265 __isl_give isl_pw_aff *isl_pw_aff_mul(
9266 __isl_take isl_pw_aff *pwaff1,
9267 __isl_take isl_pw_aff *pwaff2);
9268 __isl_give isl_pw_aff *isl_pw_aff_div(
9269 __isl_take isl_pw_aff *pa1,
9270 __isl_take isl_pw_aff *pa2);
9271 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9272 __isl_take isl_pw_aff *pa1,
9273 __isl_take isl_pw_aff *pa2);
9274 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9275 __isl_take isl_pw_aff *pa1,
9276 __isl_take isl_pw_aff *pa2);
9278 When multiplying two affine expressions, at least one of the two needs
9279 to be a constant. Similarly, when dividing an affine expression by another,
9280 the second expression needs to be a constant.
9281 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9282 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9285 #include <isl/polynomial.h>
9286 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9287 __isl_take isl_qpolynomial *qp1,
9288 __isl_take isl_qpolynomial *qp2);
9289 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9290 __isl_take isl_pw_qpolynomial *pwqp1,
9291 __isl_take isl_pw_qpolynomial *pwqp2);
9292 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9293 __isl_take isl_union_pw_qpolynomial *upwqp1,
9294 __isl_take isl_union_pw_qpolynomial *upwqp2);
9298 =head3 Lexicographic Optimization
9300 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9301 the following functions
9302 compute a set that contains the lexicographic minimum or maximum
9303 of the elements in C<set> (or C<bset>) for those values of the parameters
9304 that satisfy C<dom>.
9305 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9306 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9308 In other words, the union of the parameter values
9309 for which the result is non-empty and of C<*empty>
9312 #include <isl/set.h>
9313 __isl_give isl_set *isl_basic_set_partial_lexmin(
9314 __isl_take isl_basic_set *bset,
9315 __isl_take isl_basic_set *dom,
9316 __isl_give isl_set **empty);
9317 __isl_give isl_set *isl_basic_set_partial_lexmax(
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_set_partial_lexmin(
9322 __isl_take isl_set *set, __isl_take isl_set *dom,
9323 __isl_give isl_set **empty);
9324 __isl_give isl_set *isl_set_partial_lexmax(
9325 __isl_take isl_set *set, __isl_take isl_set *dom,
9326 __isl_give isl_set **empty);
9328 Given a (basic) set C<set> (or C<bset>), the following functions simply
9329 return a set containing the lexicographic minimum or maximum
9330 of the elements in C<set> (or C<bset>).
9331 In case of union sets, the optimum is computed per space.
9333 #include <isl/set.h>
9334 __isl_give isl_set *isl_basic_set_lexmin(
9335 __isl_take isl_basic_set *bset);
9336 __isl_give isl_set *isl_basic_set_lexmax(
9337 __isl_take isl_basic_set *bset);
9338 __isl_give isl_set *isl_set_lexmin(
9339 __isl_take isl_set *set);
9340 __isl_give isl_set *isl_set_lexmax(
9341 __isl_take isl_set *set);
9342 __isl_give isl_union_set *isl_union_set_lexmin(
9343 __isl_take isl_union_set *uset);
9344 __isl_give isl_union_set *isl_union_set_lexmax(
9345 __isl_take isl_union_set *uset);
9347 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9348 the following functions
9349 compute a relation that maps each element of C<dom>
9350 to the single lexicographic minimum or maximum
9351 of the elements that are associated to that same
9352 element in C<map> (or C<bmap>).
9353 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9354 that contains the elements in C<dom> that do not map
9355 to any elements in C<map> (or C<bmap>).
9356 In other words, the union of the domain of the result and of C<*empty>
9359 #include <isl/map.h>
9360 __isl_give isl_map *isl_basic_map_partial_lexmax(
9361 __isl_take isl_basic_map *bmap,
9362 __isl_take isl_basic_set *dom,
9363 __isl_give isl_set **empty);
9364 __isl_give isl_map *isl_basic_map_partial_lexmin(
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_map_partial_lexmax(
9369 __isl_take isl_map *map, __isl_take isl_set *dom,
9370 __isl_give isl_set **empty);
9371 __isl_give isl_map *isl_map_partial_lexmin(
9372 __isl_take isl_map *map, __isl_take isl_set *dom,
9373 __isl_give isl_set **empty);
9375 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9376 return a map mapping each element in the domain of
9377 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9378 of all elements associated to that element.
9379 In case of union relations, the optimum is computed per space.
9381 #include <isl/map.h>
9382 __isl_give isl_map *isl_basic_map_lexmin(
9383 __isl_take isl_basic_map *bmap);
9384 __isl_give isl_map *isl_basic_map_lexmax(
9385 __isl_take isl_basic_map *bmap);
9386 __isl_give isl_map *isl_map_lexmin(
9387 __isl_take isl_map *map);
9388 __isl_give isl_map *isl_map_lexmax(
9389 __isl_take isl_map *map);
9390 __isl_give isl_union_map *isl_union_map_lexmin(
9391 __isl_take isl_union_map *umap);
9392 __isl_give isl_union_map *isl_union_map_lexmax(
9393 __isl_take isl_union_map *umap);
9395 The following functions return their result in the form of
9396 a piecewise multi-affine expression,
9397 but are otherwise equivalent to the corresponding functions
9398 returning a basic set or relation.
9400 #include <isl/set.h>
9401 __isl_give isl_pw_multi_aff *
9402 isl_basic_set_partial_lexmin_pw_multi_aff(
9403 __isl_take isl_basic_set *bset,
9404 __isl_take isl_basic_set *dom,
9405 __isl_give isl_set **empty);
9406 __isl_give isl_pw_multi_aff *
9407 isl_basic_set_partial_lexmax_pw_multi_aff(
9408 __isl_take isl_basic_set *bset,
9409 __isl_take isl_basic_set *dom,
9410 __isl_give isl_set **empty);
9411 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9412 __isl_take isl_set *set);
9413 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9414 __isl_take isl_set *set);
9416 #include <isl/map.h>
9417 __isl_give isl_pw_multi_aff *
9418 isl_basic_map_lexmin_pw_multi_aff(
9419 __isl_take isl_basic_map *bmap);
9420 __isl_give isl_pw_multi_aff *
9421 isl_basic_map_partial_lexmin_pw_multi_aff(
9422 __isl_take isl_basic_map *bmap,
9423 __isl_take isl_basic_set *dom,
9424 __isl_give isl_set **empty);
9425 __isl_give isl_pw_multi_aff *
9426 isl_basic_map_partial_lexmax_pw_multi_aff(
9427 __isl_take isl_basic_map *bmap,
9428 __isl_take isl_basic_set *dom,
9429 __isl_give isl_set **empty);
9430 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9431 __isl_take isl_map *map);
9432 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9433 __isl_take isl_map *map);
9435 The following functions return the lexicographic minimum or maximum
9436 on the shared domain of the inputs and the single defined function
9437 on those parts of the domain where only a single function is defined.
9439 #include <isl/aff.h>
9440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9441 __isl_take isl_pw_multi_aff *pma1,
9442 __isl_take isl_pw_multi_aff *pma2);
9443 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9444 __isl_take isl_pw_multi_aff *pma1,
9445 __isl_take isl_pw_multi_aff *pma2);
9447 If the input to a lexicographic optimization problem has
9448 multiple constraints with the same coefficients for the optimized
9449 variables, then, by default, this symmetry is exploited by
9450 replacing those constraints by a single constraint with
9451 an abstract bound, which is in turn bounded by the corresponding terms
9452 in the original constraints.
9453 Without this optimization, the solver would typically consider
9454 all possible orderings of those original bounds, resulting in a needless
9455 decomposition of the domain.
9456 However, the optimization can also result in slowdowns since
9457 an extra parameter is introduced that may get used in additional
9459 The following option determines whether symmetry detection is applied
9460 during lexicographic optimization.
9462 #include <isl/options.h>
9463 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9465 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9469 See also \autoref{s:offline}.
9473 =head2 Ternary Operations
9475 #include <isl/aff.h>
9476 __isl_give isl_pw_aff *isl_pw_aff_cond(
9477 __isl_take isl_pw_aff *cond,
9478 __isl_take isl_pw_aff *pwaff_true,
9479 __isl_take isl_pw_aff *pwaff_false);
9481 The function C<isl_pw_aff_cond> performs a conditional operator
9482 and returns an expression that is equal to C<pwaff_true>
9483 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9484 where C<cond> is zero.
9488 Lists are defined over several element types, including
9489 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9490 C<isl_union_pw_aff>,
9491 C<isl_union_pw_multi_aff>,
9492 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9494 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9495 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9496 Here we take lists of C<isl_set>s as an example.
9497 Lists can be created, copied, modified and freed using the following functions.
9499 #include <isl/set.h>
9500 __isl_give isl_set_list *isl_set_to_list(
9501 __isl_take isl_set *el);
9502 __isl_give isl_set_list *isl_set_list_from_set(
9503 __isl_take isl_set *el);
9504 __isl_give isl_set_list *isl_set_list_alloc(
9505 isl_ctx *ctx, int n);
9506 __isl_give isl_set_list *isl_set_list_copy(
9507 __isl_keep isl_set_list *list);
9508 __isl_give isl_set_list *isl_set_list_insert(
9509 __isl_take isl_set_list *list, unsigned pos,
9510 __isl_take isl_set *el);
9511 __isl_give isl_set_list *isl_set_list_add(
9512 __isl_take isl_set_list *list,
9513 __isl_take isl_set *el);
9514 __isl_give isl_set_list *isl_set_list_drop(
9515 __isl_take isl_set_list *list,
9516 unsigned first, unsigned n);
9517 __isl_give isl_set_list *isl_set_list_clear(
9518 __isl_take isl_set_list *list);
9519 __isl_give isl_set_list *isl_set_list_swap(
9520 __isl_take isl_set_list *list,
9521 unsigned pos1, unsigned pos2);
9522 __isl_give isl_set_list *isl_set_list_reverse(
9523 __isl_take isl_set_list *list);
9524 __isl_give isl_set_list *isl_set_list_set_at(
9525 __isl_take isl_set_list *list, int index,
9526 __isl_take isl_set *set);
9527 __isl_give isl_set_list *isl_set_list_set_set(
9528 __isl_take isl_set_list *list, int index,
9529 __isl_take isl_set *set);
9530 __isl_give isl_set_list *isl_set_list_concat(
9531 __isl_take isl_set_list *list1,
9532 __isl_take isl_set_list *list2);
9533 __isl_give isl_set_list *isl_set_list_map(
9534 __isl_take isl_set_list *list,
9535 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9538 __isl_give isl_set_list *isl_set_list_sort(
9539 __isl_take isl_set_list *list,
9540 int (*cmp)(__isl_keep isl_set *a,
9541 __isl_keep isl_set *b, void *user),
9543 __isl_null isl_set_list *isl_set_list_free(
9544 __isl_take isl_set_list *list);
9546 C<isl_set_list_alloc> creates an empty list with an initial capacity
9547 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9548 add elements to a list, increasing its capacity as needed.
9549 C<isl_set_to_list> creates a list with a single element.
9550 C<isl_set_list_from_set> performs the same operation.
9551 C<isl_set_list_clear> removes all elements from a list.
9552 C<isl_set_list_swap> swaps the elements at the specified locations.
9553 C<isl_set_list_reverse> reverses the elements in the list.
9554 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9556 Lists can be inspected using the following functions.
9558 #include <isl/set.h>
9559 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9560 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9561 __isl_give isl_set *isl_set_list_get_at(
9562 __isl_keep isl_set_list *list, int index);
9563 __isl_give isl_set *isl_set_list_get_set(
9564 __isl_keep isl_set_list *list, int index);
9565 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9566 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9568 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9569 isl_bool (*test)(__isl_take isl_set *el,
9572 isl_stat isl_set_list_foreach_scc(
9573 __isl_keep isl_set_list *list,
9574 isl_bool (*follows)(__isl_keep isl_set *a,
9575 __isl_keep isl_set *b, void *user),
9577 isl_stat (*fn)(__isl_take isl_set_list *scc,
9581 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9583 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9584 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9585 strongly connected components of the graph with as vertices the elements
9586 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9587 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9588 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9590 Lists can be printed using
9592 #include <isl/set.h>
9593 __isl_give isl_printer *isl_printer_print_set_list(
9594 __isl_take isl_printer *p,
9595 __isl_keep isl_set_list *list);
9597 Alternatively, a string representation can be obtained
9598 directly using the following function, which always prints
9601 #include <isl/set.h>
9602 __isl_give char *isl_set_list_to_str(
9603 __isl_keep isl_set_list *list);
9605 An C<isl_val_list>, C<isl_id_list>,
9606 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9607 C<isl_union_pw_aff_list>,
9608 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9609 can also be read from input using the following functions.
9611 #include <isl/val.h>
9612 __isl_give isl_val_list *isl_val_list_read_from_str(
9613 isl_ctx *ctx, const char *str);
9616 __isl_give isl_id_list *isl_id_list_read_from_str(
9617 isl_ctx *ctx, const char *str);
9619 #include <isl/aff.h>
9620 __isl_give isl_aff_list *
9621 isl_aff_list_read_from_str(isl_ctx *ctx,
9623 __isl_give isl_pw_aff_list *
9624 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9626 __isl_give isl_pw_multi_aff_list *
9627 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9629 __isl_give isl_union_pw_aff_list *
9630 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9633 #include <isl/set.h>
9634 __isl_give isl_set_list *isl_set_list_read_from_str(
9635 isl_ctx *ctx, const char *str);
9637 #include <isl/map.h>
9638 __isl_give isl_map_list *isl_map_list_read_from_str(
9639 isl_ctx *ctx, const char *str);
9641 #include <isl/union_set.h>
9642 __isl_give isl_union_set_list *
9643 isl_union_set_list_read_from_str(isl_ctx *ctx,
9646 =head2 Associative arrays
9648 Associative arrays map isl objects of a specific type to isl objects
9649 of some (other) specific type. They are defined for several pairs
9650 of types, including (C<isl_map>, C<isl_basic_set>),
9651 (C<isl_id>, C<isl_ast_expr>),
9652 (C<isl_id>, C<isl_id>) and
9653 (C<isl_id>, C<isl_pw_aff>).
9654 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9657 Associative arrays can be created, copied and freed using
9658 the following functions.
9660 #include <isl/id_to_ast_expr.h>
9661 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9662 isl_ctx *ctx, int min_size);
9663 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9664 __isl_keep isl_id_to_ast_expr *id2expr);
9665 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9666 __isl_take isl_id_to_ast_expr *id2expr);
9668 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9669 to specify the expected size of the associative array.
9670 The associative array will be grown automatically as needed.
9672 Associative arrays can be inspected using the following functions.
9674 #include <isl/id_to_ast_expr.h>
9675 __isl_give isl_maybe_isl_ast_expr
9676 isl_id_to_ast_expr_try_get(
9677 __isl_keep isl_id_to_ast_expr *id2expr,
9678 __isl_keep isl_id *key);
9679 isl_bool isl_id_to_ast_expr_has(
9680 __isl_keep isl_id_to_ast_expr *id2expr,
9681 __isl_keep isl_id *key);
9682 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9683 __isl_keep isl_id_to_ast_expr *id2expr,
9684 __isl_take isl_id *key);
9685 isl_stat isl_id_to_ast_expr_foreach(
9686 __isl_keep isl_id_to_ast_expr *id2expr,
9687 isl_stat (*fn)(__isl_take isl_id *key,
9688 __isl_take isl_ast_expr *val, void *user),
9690 isl_bool isl_id_to_ast_expr_every(
9691 __isl_keep isl_id_to_ast_expr *id2expr,
9692 isl_bool (*test)(__isl_keep isl_id *key,
9693 __isl_keep isl_ast_expr *val, void *user),
9696 The function C<isl_id_to_ast_expr_try_get> returns a structure
9697 containing two elements, C<valid> and C<value>.
9698 If there is a value associated to the key, then C<valid>
9699 is set to C<isl_bool_true> and C<value> contains a copy of
9700 the associated value. Otherwise C<value> is C<NULL> and
9701 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9702 on whether some error has occurred or there simply is no associated value.
9703 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9704 in the structure and
9705 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9707 Associative arrays can be modified using the following functions.
9709 #include <isl/id_to_ast_expr.h>
9710 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9711 __isl_take isl_id_to_ast_expr *id2expr,
9712 __isl_take isl_id *key,
9713 __isl_take isl_ast_expr *val);
9714 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9715 __isl_take isl_id_to_ast_expr *id2expr,
9716 __isl_take isl_id *key);
9718 Associative arrays can be checked for (obvious) equality
9719 using the following function.
9721 #include <isl/id_to_ast_expr.h>
9722 isl_bool isl_id_to_ast_expr_is_equal(
9723 __isl_take isl_id_to_ast_expr *id2expr1,
9724 __isl_take isl_id_to_ast_expr *id2expr2);
9726 Note that depending on how the keys and values are being compared,
9727 for other types of keys and/or values, this function may be called
9728 C<plain_is_equal> rather than C<is_equal>.
9730 Associative arrays can be printed using the following functions.
9732 #include <isl/id_to_ast_expr.h>
9733 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9734 __isl_take isl_printer *p,
9735 __isl_keep isl_id_to_ast_expr *id2expr);
9736 __isl_give char *isl_id_to_ast_expr_to_str(
9737 __isl_keep isl_id_to_ast_expr *id2expr);
9739 They can be read from input using the following function.
9741 #include <isl/id_to_ast_expr.h>
9742 __isl_give isl_id_to_ast_expr *
9743 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9748 Vectors can be created, copied and freed using the following functions.
9750 #include <isl/vec.h>
9751 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9753 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9755 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9756 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9758 Note that the elements of a vector created by C<isl_vec_alloc>
9759 may have arbitrary values.
9760 A vector created by C<isl_vec_zero> has elements with value zero.
9761 The elements can be changed and inspected using the following functions.
9763 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9764 __isl_give isl_val *isl_vec_get_element_val(
9765 __isl_keep isl_vec *vec, int pos);
9766 __isl_give isl_vec *isl_vec_set_element_si(
9767 __isl_take isl_vec *vec, int pos, int v);
9768 __isl_give isl_vec *isl_vec_set_element_val(
9769 __isl_take isl_vec *vec, int pos,
9770 __isl_take isl_val *v);
9771 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9773 __isl_give isl_vec *isl_vec_set_val(
9774 __isl_take isl_vec *vec, __isl_take isl_val *v);
9775 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9776 __isl_keep isl_vec *vec2, int pos);
9778 C<isl_vec_get_element> will return a negative value if anything went wrong.
9779 In that case, the value of C<*v> is undefined.
9781 The following function can be used to concatenate two vectors.
9783 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9784 __isl_take isl_vec *vec2);
9788 Matrices can be created, copied and freed using the following functions.
9790 #include <isl/mat.h>
9791 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9792 unsigned n_row, unsigned n_col);
9793 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9794 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9796 Note that the elements of a newly created matrix may have arbitrary values.
9797 The elements can be changed and inspected using the following functions.
9799 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9800 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9801 __isl_give isl_val *isl_mat_get_element_val(
9802 __isl_keep isl_mat *mat, int row, int col);
9803 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9804 int row, int col, int v);
9805 __isl_give isl_mat *isl_mat_set_element_val(
9806 __isl_take isl_mat *mat, int row, int col,
9807 __isl_take isl_val *v);
9809 The following function computes the rank of a matrix.
9810 The return value may be -1 if some error occurred.
9812 #include <isl/mat.h>
9813 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9815 The following function can be used to compute the (right) inverse
9816 of a matrix, i.e., a matrix such that the product of the original
9817 and the inverse (in that order) is a multiple of the identity matrix.
9818 The input matrix is assumed to be of full row-rank.
9820 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9822 The following function can be used to compute the (right) kernel
9823 (or null space) of a matrix, i.e., a matrix such that the product of
9824 the original and the kernel (in that order) is the zero matrix.
9826 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9828 The following function computes a basis for the space spanned
9829 by the rows of a matrix.
9831 __isl_give isl_mat *isl_mat_row_basis(
9832 __isl_take isl_mat *mat);
9834 The following function computes rows that extend a basis of C<mat1>
9835 to a basis that also covers C<mat2>.
9837 __isl_give isl_mat *isl_mat_row_basis_extension(
9838 __isl_take isl_mat *mat1,
9839 __isl_take isl_mat *mat2);
9841 The following function checks whether there is no linear dependence
9842 among the combined rows of "mat1" and "mat2" that is not already present
9843 in "mat1" or "mat2" individually.
9844 If "mat1" and "mat2" have linearly independent rows by themselves,
9845 then this means that there is no linear dependence among all rows together.
9847 isl_bool isl_mat_has_linearly_independent_rows(
9848 __isl_keep isl_mat *mat1,
9849 __isl_keep isl_mat *mat2);
9851 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9853 The following functions determine
9854 an upper or lower bound on a quasipolynomial over its domain.
9856 __isl_give isl_pw_qpolynomial_fold *
9857 isl_pw_qpolynomial_bound(
9858 __isl_take isl_pw_qpolynomial *pwqp,
9859 enum isl_fold type, isl_bool *tight);
9861 __isl_give isl_union_pw_qpolynomial_fold *
9862 isl_union_pw_qpolynomial_bound(
9863 __isl_take isl_union_pw_qpolynomial *upwqp,
9864 enum isl_fold type, isl_bool *tight);
9866 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9867 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9868 is the returned bound is known be tight, i.e., for each value
9869 of the parameters there is at least
9870 one element in the domain that reaches the bound.
9871 If the domain of C<pwqp> is not wrapping, then the bound is computed
9872 over all elements in that domain and the result has a purely parametric
9873 domain. If the domain of C<pwqp> is wrapping, then the bound is
9874 computed over the range of the wrapped relation. The domain of the
9875 wrapped relation becomes the domain of the result.
9877 =head2 Parametric Vertex Enumeration
9879 The parametric vertex enumeration described in this section
9880 is mainly intended to be used internally and by the C<barvinok>
9883 #include <isl/vertices.h>
9884 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9885 __isl_keep isl_basic_set *bset);
9887 The function C<isl_basic_set_compute_vertices> performs the
9888 actual computation of the parametric vertices and the chamber
9889 decomposition and stores the result in an C<isl_vertices> object.
9890 This information can be queried by either iterating over all
9891 the vertices or iterating over all the chambers or cells
9892 and then iterating over all vertices that are active on the chamber.
9894 isl_stat isl_vertices_foreach_vertex(
9895 __isl_keep isl_vertices *vertices,
9896 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9897 void *user), void *user);
9899 isl_stat isl_vertices_foreach_cell(
9900 __isl_keep isl_vertices *vertices,
9901 isl_stat (*fn)(__isl_take isl_cell *cell,
9902 void *user), void *user);
9903 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9904 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9905 void *user), void *user);
9907 Other operations that can be performed on an C<isl_vertices> object are
9910 isl_size isl_vertices_get_n_vertices(
9911 __isl_keep isl_vertices *vertices);
9912 __isl_null isl_vertices *isl_vertices_free(
9913 __isl_take isl_vertices *vertices);
9915 Vertices can be inspected and destroyed using the following functions.
9917 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9918 __isl_give isl_basic_set *isl_vertex_get_domain(
9919 __isl_keep isl_vertex *vertex);
9920 __isl_give isl_multi_aff *isl_vertex_get_expr(
9921 __isl_keep isl_vertex *vertex);
9922 __isl_null isl_vertex *isl_vertex_free(
9923 __isl_take isl_vertex *vertex);
9925 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9926 describing the vertex in terms of the parameters,
9927 while C<isl_vertex_get_domain> returns the activity domain
9930 Chambers can be inspected and destroyed using the following functions.
9932 __isl_give isl_basic_set *isl_cell_get_domain(
9933 __isl_keep isl_cell *cell);
9934 __isl_null isl_cell *isl_cell_free(
9935 __isl_take isl_cell *cell);
9937 =head1 Polyhedral Compilation Library
9939 This section collects functionality in C<isl> that has been specifically
9940 designed for use during polyhedral compilation.
9942 =head2 Schedule Trees
9944 A schedule tree is a structured representation of a schedule,
9945 assigning a relative order to a set of domain elements.
9946 The relative order expressed by the schedule tree is
9947 defined recursively. In particular, the order between
9948 two domain elements is determined by the node that is closest
9949 to the root that refers to both elements and that orders them apart.
9950 Each node in the tree is of one of several types.
9951 The root node is always of type C<isl_schedule_node_domain>
9952 (or C<isl_schedule_node_extension>)
9953 and it describes the (extra) domain elements to which the schedule applies.
9954 The other types of nodes are as follows.
9958 =item C<isl_schedule_node_band>
9960 A band of schedule dimensions. Each schedule dimension is represented
9961 by a union piecewise quasi-affine expression. If this expression
9962 assigns a different value to two domain elements, while all previous
9963 schedule dimensions in the same band assign them the same value,
9964 then the two domain elements are ordered according to these two
9966 Each expression is required to be total in the domain elements
9967 that reach the band node.
9969 =item C<isl_schedule_node_expansion>
9971 An expansion node maps each of the domain elements that reach the node
9972 to one or more domain elements. The image of this mapping forms
9973 the set of domain elements that reach the child of the expansion node.
9974 The function that maps each of the expanded domain elements
9975 to the original domain element from which it was expanded
9976 is called the contraction.
9978 =item C<isl_schedule_node_filter>
9980 A filter node does not impose any ordering, but rather intersects
9981 the set of domain elements that the current subtree refers to
9982 with a given union set. The subtree of the filter node only
9983 refers to domain elements in the intersection.
9984 A filter node is typically only used as a child of a sequence or
9987 =item C<isl_schedule_node_leaf>
9989 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9991 =item C<isl_schedule_node_mark>
9993 A mark node can be used to attach any kind of information to a subtree
9994 of the schedule tree.
9996 =item C<isl_schedule_node_sequence>
9998 A sequence node has one or more children, each of which is a filter node.
9999 The filters on these filter nodes form a partition of
10000 the domain elements that the current subtree refers to.
10001 If two domain elements appear in distinct filters then the sequence
10002 node orders them according to the child positions of the corresponding
10005 =item C<isl_schedule_node_set>
10007 A set node is similar to a sequence node, except that
10008 it expresses that domain elements appearing in distinct filters
10009 may have any order. The order of the children of a set node
10010 is therefore also immaterial.
10014 The following node types are only supported by the AST generator.
10018 =item C<isl_schedule_node_context>
10020 The context describes constraints on the parameters and
10021 the schedule dimensions of outer
10022 bands that the AST generator may assume to hold. It is also the only
10023 kind of node that may introduce additional parameters.
10024 The space of the context is that of the flat product of the outer
10025 band nodes. In particular, if there are no outer band nodes, then
10026 this space is the unnamed zero-dimensional space.
10027 Since a context node references the outer band nodes, any tree
10028 containing a context node is considered to be anchored.
10030 =item C<isl_schedule_node_extension>
10032 An extension node instructs the AST generator to add additional
10033 domain elements that need to be scheduled.
10034 The additional domain elements are described by the range of
10035 the extension map in terms of the outer schedule dimensions,
10036 i.e., the flat product of the outer band nodes.
10037 Note that domain elements are added whenever the AST generator
10038 reaches the extension node, meaning that there are still some
10039 active domain elements for which an AST needs to be generated.
10040 The conditions under which some domain elements are still active
10041 may however not be completely described by the outer AST nodes
10042 generated at that point.
10043 Since an extension node references the outer band nodes, any tree
10044 containing an extension node is considered to be anchored.
10046 An extension node may also appear as the root of a schedule tree,
10047 when it is intended to be inserted into another tree
10048 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10049 In this case, the domain of the extension node should
10050 correspond to the flat product of the outer band nodes
10051 in this other schedule tree at the point where the extension tree
10054 =item C<isl_schedule_node_guard>
10056 The guard describes constraints on the parameters and
10057 the schedule dimensions of outer
10058 bands that need to be enforced by the outer nodes
10059 in the generated AST.
10060 That is, the part of the AST that is generated from descendants
10061 of the guard node can assume that these constraints are satisfied.
10062 The space of the guard is that of the flat product of the outer
10063 band nodes. In particular, if there are no outer band nodes, then
10064 this space is the unnamed zero-dimensional space.
10065 Since a guard node references the outer band nodes, any tree
10066 containing a guard node is considered to be anchored.
10070 Except for the C<isl_schedule_node_context> nodes,
10071 none of the nodes may introduce any parameters that were not
10072 already present in the root domain node.
10074 A schedule tree is encapsulated in an C<isl_schedule> object.
10075 The simplest such objects, those with a tree consisting of single domain node,
10076 can be created using the following functions with either an empty
10077 domain or a given domain.
10079 #include <isl/schedule.h>
10080 __isl_give isl_schedule *isl_schedule_empty(
10081 __isl_take isl_space *space);
10082 __isl_give isl_schedule *isl_schedule_from_domain(
10083 __isl_take isl_union_set *domain);
10085 The function C<isl_schedule_constraints_compute_schedule> described
10086 in L</"Scheduling"> can also be used to construct schedules.
10088 C<isl_schedule> objects may be copied and freed using the following functions.
10090 #include <isl/schedule.h>
10091 __isl_give isl_schedule *isl_schedule_copy(
10092 __isl_keep isl_schedule *sched);
10093 __isl_null isl_schedule *isl_schedule_free(
10094 __isl_take isl_schedule *sched);
10096 The following functions checks whether two C<isl_schedule> objects
10097 are obviously the same.
10099 #include <isl/schedule.h>
10100 isl_bool isl_schedule_plain_is_equal(
10101 __isl_keep isl_schedule *schedule1,
10102 __isl_keep isl_schedule *schedule2);
10104 The domain of the schedule, i.e., the domain described by the root node,
10105 can be obtained using the following function.
10107 #include <isl/schedule.h>
10108 __isl_give isl_union_set *isl_schedule_get_domain(
10109 __isl_keep isl_schedule *schedule);
10111 An extra top-level band node (right underneath the domain node) can
10112 be introduced into the schedule using the following function.
10113 The schedule tree is assumed not to have any anchored nodes.
10115 #include <isl/schedule.h>
10116 __isl_give isl_schedule *
10117 isl_schedule_insert_partial_schedule(
10118 __isl_take isl_schedule *schedule,
10119 __isl_take isl_multi_union_pw_aff *partial);
10121 A top-level context node (right underneath the domain node) can
10122 be introduced into the schedule using the following function.
10124 #include <isl/schedule.h>
10125 __isl_give isl_schedule *isl_schedule_insert_context(
10126 __isl_take isl_schedule *schedule,
10127 __isl_take isl_set *context)
10129 A top-level guard node (right underneath the domain node) can
10130 be introduced into the schedule using the following function.
10132 #include <isl/schedule.h>
10133 __isl_give isl_schedule *isl_schedule_insert_guard(
10134 __isl_take isl_schedule *schedule,
10135 __isl_take isl_set *guard)
10137 A schedule that combines two schedules either in the given
10138 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10139 or an C<isl_schedule_node_set> node,
10140 can be created using the following functions.
10142 #include <isl/schedule.h>
10143 __isl_give isl_schedule *isl_schedule_sequence(
10144 __isl_take isl_schedule *schedule1,
10145 __isl_take isl_schedule *schedule2);
10146 __isl_give isl_schedule *isl_schedule_set(
10147 __isl_take isl_schedule *schedule1,
10148 __isl_take isl_schedule *schedule2);
10150 The domains of the two input schedules need to be disjoint.
10152 The following function can be used to restrict the domain
10153 of a schedule with a domain node as root to be a subset of the given union set.
10154 This operation may remove nodes in the tree that have become
10157 #include <isl/schedule.h>
10158 __isl_give isl_schedule *isl_schedule_intersect_domain(
10159 __isl_take isl_schedule *schedule,
10160 __isl_take isl_union_set *domain);
10162 The following function can be used to simplify the domain
10163 of a schedule with a domain node as root with respect to the given
10166 #include <isl/schedule.h>
10167 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10168 __isl_take isl_schedule *schedule,
10169 __isl_take isl_set *context);
10171 The following function resets the user pointers on all parameter
10172 and tuple identifiers referenced by the nodes of the given schedule.
10174 #include <isl/schedule.h>
10175 __isl_give isl_schedule *isl_schedule_reset_user(
10176 __isl_take isl_schedule *schedule);
10178 The following function aligns the parameters of all nodes
10179 in the given schedule to the given space.
10181 #include <isl/schedule.h>
10182 __isl_give isl_schedule *isl_schedule_align_params(
10183 __isl_take isl_schedule *schedule,
10184 __isl_take isl_space *space);
10186 The following function allows the user to plug in a given function
10187 in the iteration domains. The input schedule is not allowed to contain
10188 any expansion nodes.
10190 #include <isl/schedule.h>
10191 __isl_give isl_schedule *
10192 isl_schedule_pullback_union_pw_multi_aff(
10193 __isl_take isl_schedule *schedule,
10194 __isl_take isl_union_pw_multi_aff *upma);
10196 The following function can be used to plug in the schedule C<expansion>
10197 in the leaves of C<schedule>, where C<contraction> describes how
10198 the domain elements of C<expansion> map to the domain elements
10199 at the original leaves of C<schedule>.
10200 The resulting schedule will contain expansion nodes, unless
10201 C<contraction> is an identity function.
10203 #include <isl/schedule.h>
10204 __isl_give isl_schedule *isl_schedule_expand(
10205 __isl_take isl_schedule *schedule,
10206 __isl_take isl_union_pw_multi_aff *contraction,
10207 __isl_take isl_schedule *expansion);
10209 An C<isl_union_map> representation of the schedule can be obtained
10210 from an C<isl_schedule> using the following function.
10212 #include <isl/schedule.h>
10213 __isl_give isl_union_map *isl_schedule_get_map(
10214 __isl_keep isl_schedule *sched);
10216 The resulting relation encodes the same relative ordering as
10217 the schedule by mapping the domain elements to a common schedule space.
10218 If the schedule_separate_components option is set, then the order
10219 of the children of a set node is explicitly encoded in the result.
10220 If the tree contains any expansion nodes, then the relation
10221 is formulated in terms of the expanded domain elements.
10223 Schedules can be read from input using the following functions.
10225 #include <isl/schedule.h>
10226 __isl_give isl_schedule *isl_schedule_read_from_file(
10227 isl_ctx *ctx, FILE *input);
10228 __isl_give isl_schedule *isl_schedule_read_from_str(
10229 isl_ctx *ctx, const char *str);
10231 A representation of the schedule can be printed using
10233 #include <isl/schedule.h>
10234 __isl_give isl_printer *isl_printer_print_schedule(
10235 __isl_take isl_printer *p,
10236 __isl_keep isl_schedule *schedule);
10237 __isl_give char *isl_schedule_to_str(
10238 __isl_keep isl_schedule *schedule);
10240 C<isl_schedule_to_str> prints the schedule in flow format.
10242 The schedule tree can be traversed through the use of
10243 C<isl_schedule_node> objects that point to a particular
10244 position in the schedule tree. Whenever a C<isl_schedule_node>
10245 is used to modify a node in the schedule tree, the original schedule
10246 tree is left untouched and the modifications are performed to a copy
10247 of the tree. The returned C<isl_schedule_node> then points to
10248 this modified copy of the tree.
10250 The root of the schedule tree can be obtained using the following function.
10252 #include <isl/schedule.h>
10253 __isl_give isl_schedule_node *isl_schedule_get_root(
10254 __isl_keep isl_schedule *schedule);
10256 A pointer to a newly created schedule tree with a single domain
10257 node can be created using the following functions.
10259 #include <isl/schedule_node.h>
10260 __isl_give isl_schedule_node *
10261 isl_schedule_node_from_domain(
10262 __isl_take isl_union_set *domain);
10263 __isl_give isl_schedule_node *
10264 isl_schedule_node_from_extension(
10265 __isl_take isl_union_map *extension);
10267 C<isl_schedule_node_from_extension> creates a tree with an extension
10270 Schedule nodes can be copied and freed using the following functions.
10272 #include <isl/schedule_node.h>
10273 __isl_give isl_schedule_node *isl_schedule_node_copy(
10274 __isl_keep isl_schedule_node *node);
10275 __isl_null isl_schedule_node *isl_schedule_node_free(
10276 __isl_take isl_schedule_node *node);
10278 The following functions can be used to check if two schedule
10279 nodes point to the same position in the same schedule.
10281 #include <isl/schedule_node.h>
10282 isl_bool isl_schedule_node_is_equal(
10283 __isl_keep isl_schedule_node *node1,
10284 __isl_keep isl_schedule_node *node2);
10286 The following properties can be obtained from a schedule node.
10288 #include <isl/schedule_node.h>
10289 enum isl_schedule_node_type isl_schedule_node_get_type(
10290 __isl_keep isl_schedule_node *node);
10291 enum isl_schedule_node_type
10292 isl_schedule_node_get_parent_type(
10293 __isl_keep isl_schedule_node *node);
10294 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10295 __isl_keep isl_schedule_node *node);
10297 The function C<isl_schedule_node_get_type> returns the type of
10298 the node, while C<isl_schedule_node_get_parent_type> returns
10299 type of the parent of the node, which is required to exist.
10300 The function C<isl_schedule_node_get_schedule> returns a copy
10301 to the schedule to which the node belongs.
10303 The following functions can be used to move the schedule node
10304 to a different position in the tree or to check if such a position
10307 #include <isl/schedule_node.h>
10308 isl_bool isl_schedule_node_has_parent(
10309 __isl_keep isl_schedule_node *node);
10310 __isl_give isl_schedule_node *isl_schedule_node_parent(
10311 __isl_take isl_schedule_node *node);
10312 __isl_give isl_schedule_node *
10313 isl_schedule_node_grandparent(
10314 __isl_take isl_schedule_node *node);
10315 __isl_give isl_schedule_node *isl_schedule_node_root(
10316 __isl_take isl_schedule_node *node);
10317 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10318 __isl_take isl_schedule_node *node,
10320 isl_size isl_schedule_node_n_children(
10321 __isl_keep isl_schedule_node *node);
10322 __isl_give isl_schedule_node *isl_schedule_node_child(
10323 __isl_take isl_schedule_node *node, int pos);
10324 isl_bool isl_schedule_node_has_children(
10325 __isl_keep isl_schedule_node *node);
10326 __isl_give isl_schedule_node *
10327 isl_schedule_node_grandchild(
10328 __isl_take isl_schedule_node *node,
10329 int pos1, int pos2);
10330 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10331 __isl_take isl_schedule_node *node);
10332 isl_bool isl_schedule_node_has_previous_sibling(
10333 __isl_keep isl_schedule_node *node);
10334 __isl_give isl_schedule_node *
10335 isl_schedule_node_previous_sibling(
10336 __isl_take isl_schedule_node *node);
10337 isl_bool isl_schedule_node_has_next_sibling(
10338 __isl_keep isl_schedule_node *node);
10339 __isl_give isl_schedule_node *
10340 isl_schedule_node_next_sibling(
10341 __isl_take isl_schedule_node *node);
10343 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10344 is the node itself, the ancestor of generation 1 is its parent and so on.
10346 It is also possible to query the number of ancestors of a node,
10347 the position of the current node
10348 within the children of its parent, the position of the subtree
10349 containing a node within the children of an ancestor
10350 or to obtain a copy of a given
10351 child without destroying the current node.
10352 Given two nodes that point to the same schedule, their closest
10353 shared ancestor can be obtained using
10354 C<isl_schedule_node_get_shared_ancestor>.
10356 #include <isl/schedule_node.h>
10357 isl_size isl_schedule_node_get_tree_depth(
10358 __isl_keep isl_schedule_node *node);
10359 isl_size isl_schedule_node_get_child_position(
10360 __isl_keep isl_schedule_node *node);
10361 isl_size isl_schedule_node_get_ancestor_child_position(
10362 __isl_keep isl_schedule_node *node,
10363 __isl_keep isl_schedule_node *ancestor);
10364 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10365 __isl_keep isl_schedule_node *node, int pos);
10366 __isl_give isl_schedule_node *
10367 isl_schedule_node_get_shared_ancestor(
10368 __isl_keep isl_schedule_node *node1,
10369 __isl_keep isl_schedule_node *node2);
10371 All nodes in a schedule tree or
10372 all descendants of a specific node (including the node) can be visited
10373 in depth-first pre-order using the following functions.
10375 #include <isl/schedule.h>
10376 isl_stat isl_schedule_foreach_schedule_node_top_down(
10377 __isl_keep isl_schedule *sched,
10378 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10379 void *user), void *user);
10381 #include <isl/schedule_node.h>
10382 isl_stat isl_schedule_node_foreach_descendant_top_down(
10383 __isl_keep isl_schedule_node *node,
10384 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10385 void *user), void *user);
10387 The callback function is slightly different from the usual
10388 callbacks in that it not only indicates success (non-negative result)
10389 or failure (negative result), but also indicates whether the children
10390 of the given node should be visited. In particular, if the callback
10391 returns a positive value, then the children are visited, but if
10392 the callback returns zero, then the children are not visited.
10394 The following functions checks whether
10395 all descendants of a specific node (including the node itself)
10396 satisfy a user-specified test.
10398 #include <isl/schedule_node.h>
10399 isl_bool isl_schedule_node_every_descendant(
10400 __isl_keep isl_schedule_node *node,
10401 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10402 void *user), void *user)
10404 The ancestors of a node in a schedule tree can be visited from
10405 the root down to and including the parent of the node using
10406 the following function.
10408 #include <isl/schedule_node.h>
10409 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10410 __isl_keep isl_schedule_node *node,
10411 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10412 void *user), void *user);
10414 The following functions allows for a depth-first post-order
10415 traversal of the nodes in a schedule tree or
10416 of the descendants of a specific node (including the node
10417 itself), where the user callback is allowed to modify the
10420 #include <isl/schedule.h>
10421 __isl_give isl_schedule *
10422 isl_schedule_map_schedule_node_bottom_up(
10423 __isl_take isl_schedule *schedule,
10424 __isl_give isl_schedule_node *(*fn)(
10425 __isl_take isl_schedule_node *node,
10426 void *user), void *user);
10428 #include <isl/schedule_node.h>
10429 __isl_give isl_schedule_node *
10430 isl_schedule_node_map_descendant_bottom_up(
10431 __isl_take isl_schedule_node *node,
10432 __isl_give isl_schedule_node *(*fn)(
10433 __isl_take isl_schedule_node *node,
10434 void *user), void *user);
10436 The traversal continues from the node returned by the callback function.
10437 It is the responsibility of the user to ensure that this does not
10438 lead to an infinite loop. It is safest to always return a pointer
10439 to the same position (same ancestors and child positions) as the input node.
10441 The following function removes a node (along with its descendants)
10442 from a schedule tree and returns a pointer to the leaf at the
10443 same position in the updated tree.
10444 It is not allowed to remove the root of a schedule tree or
10445 a child of a set or sequence node.
10447 #include <isl/schedule_node.h>
10448 __isl_give isl_schedule_node *isl_schedule_node_cut(
10449 __isl_take isl_schedule_node *node);
10451 The following function removes a single node
10452 from a schedule tree and returns a pointer to the child
10453 of the node, now located at the position of the original node
10454 or to a leaf node at that position if there was no child.
10455 It is not allowed to remove the root of a schedule tree,
10456 a set or sequence node, a child of a set or sequence node or
10457 a band node with an anchored subtree.
10459 #include <isl/schedule_node.h>
10460 __isl_give isl_schedule_node *isl_schedule_node_delete(
10461 __isl_take isl_schedule_node *node);
10463 Most nodes in a schedule tree only contain local information.
10464 In some cases, however, a node may also refer to the schedule dimensions
10465 of its outer band nodes.
10466 This means that the position of the node within the tree should
10467 not be changed, or at least that no changes are performed to the
10468 outer band nodes. The following function can be used to test
10469 whether the subtree rooted at a given node contains any such nodes.
10471 #include <isl/schedule_node.h>
10472 isl_bool isl_schedule_node_is_subtree_anchored(
10473 __isl_keep isl_schedule_node *node);
10475 The following function resets the user pointers on all parameter
10476 and tuple identifiers referenced by the given schedule node.
10478 #include <isl/schedule_node.h>
10479 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10480 __isl_take isl_schedule_node *node);
10482 The following function aligns the parameters of the given schedule
10483 node to the given space.
10485 #include <isl/schedule_node.h>
10486 __isl_give isl_schedule_node *
10487 isl_schedule_node_align_params(
10488 __isl_take isl_schedule_node *node,
10489 __isl_take isl_space *space);
10491 Several node types have their own functions for querying
10492 (and in some cases setting) some node type specific properties.
10494 #include <isl/schedule_node.h>
10495 __isl_give isl_space *isl_schedule_node_band_get_space(
10496 __isl_keep isl_schedule_node *node);
10497 __isl_give isl_multi_union_pw_aff *
10498 isl_schedule_node_band_get_partial_schedule(
10499 __isl_keep isl_schedule_node *node);
10500 __isl_give isl_union_map *
10501 isl_schedule_node_band_get_partial_schedule_union_map(
10502 __isl_keep isl_schedule_node *node);
10503 isl_size isl_schedule_node_band_n_member(
10504 __isl_keep isl_schedule_node *node);
10505 isl_bool isl_schedule_node_band_member_get_coincident(
10506 __isl_keep isl_schedule_node *node, int pos);
10507 __isl_give isl_schedule_node *
10508 isl_schedule_node_band_member_set_coincident(
10509 __isl_take isl_schedule_node *node, int pos,
10511 isl_bool isl_schedule_node_band_get_permutable(
10512 __isl_keep isl_schedule_node *node);
10513 __isl_give isl_schedule_node *
10514 isl_schedule_node_band_set_permutable(
10515 __isl_take isl_schedule_node *node, int permutable);
10516 enum isl_ast_loop_type
10517 isl_schedule_node_band_member_get_ast_loop_type(
10518 __isl_keep isl_schedule_node *node, int pos);
10519 __isl_give isl_schedule_node *
10520 isl_schedule_node_band_member_set_ast_loop_type(
10521 __isl_take isl_schedule_node *node, int pos,
10522 enum isl_ast_loop_type type);
10523 enum isl_ast_loop_type
10524 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10525 __isl_keep isl_schedule_node *node, int pos);
10526 __isl_give isl_schedule_node *
10527 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10528 __isl_take isl_schedule_node *node, int pos,
10529 enum isl_ast_loop_type type);
10530 __isl_give isl_union_set *
10531 isl_schedule_node_band_get_ast_build_options(
10532 __isl_keep isl_schedule_node *node);
10533 __isl_give isl_schedule_node *
10534 isl_schedule_node_band_set_ast_build_options(
10535 __isl_take isl_schedule_node *node,
10536 __isl_take isl_union_set *options);
10537 __isl_give isl_set *
10538 isl_schedule_node_band_get_ast_isolate_option(
10539 __isl_keep isl_schedule_node *node);
10541 The function C<isl_schedule_node_band_get_space> returns the space
10542 of the partial schedule of the band.
10543 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10544 returns a representation of the partial schedule of the band node
10545 in the form of an C<isl_union_map>.
10546 The coincident and permutable properties are set by
10547 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10549 A scheduling dimension is considered to be ``coincident''
10550 if it satisfies the coincidence constraints within its band.
10551 That is, if the dependence distances of the coincidence
10552 constraints are all zero in that direction (for fixed
10553 iterations of outer bands).
10554 A band is marked permutable if it was produced using the Pluto-like scheduler.
10555 Note that the scheduler may have to resort to a Feautrier style scheduling
10556 step even if the default scheduler is used.
10557 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10558 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10559 For the meaning of these loop AST generation types and the difference
10560 between the regular loop AST generation type and the isolate
10561 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10562 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10563 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10564 may return C<isl_ast_loop_error> if an error occurs.
10565 The AST build options govern how an AST is generated for
10566 the individual schedule dimensions during AST generation.
10567 See L</"AST Generation Options (Schedule Tree)">.
10568 The isolate option for the given node can be extracted from these
10569 AST build options using the function
10570 C<isl_schedule_node_band_get_ast_isolate_option>.
10572 #include <isl/schedule_node.h>
10573 __isl_give isl_set *
10574 isl_schedule_node_context_get_context(
10575 __isl_keep isl_schedule_node *node);
10577 #include <isl/schedule_node.h>
10578 __isl_give isl_union_set *
10579 isl_schedule_node_domain_get_domain(
10580 __isl_keep isl_schedule_node *node);
10582 #include <isl/schedule_node.h>
10583 __isl_give isl_union_map *
10584 isl_schedule_node_expansion_get_expansion(
10585 __isl_keep isl_schedule_node *node);
10586 __isl_give isl_union_pw_multi_aff *
10587 isl_schedule_node_expansion_get_contraction(
10588 __isl_keep isl_schedule_node *node);
10590 #include <isl/schedule_node.h>
10591 __isl_give isl_union_map *
10592 isl_schedule_node_extension_get_extension(
10593 __isl_keep isl_schedule_node *node);
10595 #include <isl/schedule_node.h>
10596 __isl_give isl_union_set *
10597 isl_schedule_node_filter_get_filter(
10598 __isl_keep isl_schedule_node *node);
10600 #include <isl/schedule_node.h>
10601 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10602 __isl_keep isl_schedule_node *node);
10604 #include <isl/schedule_node.h>
10605 __isl_give isl_id *isl_schedule_node_mark_get_id(
10606 __isl_keep isl_schedule_node *node);
10608 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10609 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10610 partial schedules related to the node.
10612 #include <isl/schedule_node.h>
10613 __isl_give isl_multi_union_pw_aff *
10614 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10615 __isl_keep isl_schedule_node *node);
10616 __isl_give isl_union_pw_multi_aff *
10617 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10618 __isl_keep isl_schedule_node *node);
10619 __isl_give isl_union_map *
10620 isl_schedule_node_get_prefix_schedule_union_map(
10621 __isl_keep isl_schedule_node *node);
10622 __isl_give isl_union_map *
10623 isl_schedule_node_get_prefix_schedule_relation(
10624 __isl_keep isl_schedule_node *node);
10625 __isl_give isl_union_map *
10626 isl_schedule_node_get_subtree_schedule_union_map(
10627 __isl_keep isl_schedule_node *node);
10629 In particular, the functions
10630 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10631 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10632 and C<isl_schedule_node_get_prefix_schedule_union_map>
10633 return a relative ordering on the domain elements that reach the given
10634 node determined by its ancestors.
10635 The function C<isl_schedule_node_get_prefix_schedule_relation>
10636 additionally includes the domain constraints in the result.
10637 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10638 returns a representation of the partial schedule defined by the
10639 subtree rooted at the given node.
10640 If the tree contains any expansion nodes, then the subtree schedule
10641 is formulated in terms of the expanded domain elements.
10642 The tree passed to functions returning a prefix schedule
10643 may only contain extension nodes if these would not affect
10644 the result of these functions. That is, if one of the ancestors
10645 is an extension node, then all of the domain elements that were
10646 added by the extension node need to have been filtered out
10647 by filter nodes between the extension node and the input node.
10648 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10649 may not contain in extension nodes in the selected subtree.
10651 The expansion/contraction defined by an entire subtree, combining
10652 the expansions/contractions
10653 on the expansion nodes in the subtree, can be obtained using
10654 the following functions.
10656 #include <isl/schedule_node.h>
10657 __isl_give isl_union_map *
10658 isl_schedule_node_get_subtree_expansion(
10659 __isl_keep isl_schedule_node *node);
10660 __isl_give isl_union_pw_multi_aff *
10661 isl_schedule_node_get_subtree_contraction(
10662 __isl_keep isl_schedule_node *node);
10664 The total number of outer band members of given node, i.e.,
10665 the shared output dimension of the maps in the result
10666 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10667 using the following function.
10669 #include <isl/schedule_node.h>
10670 isl_size isl_schedule_node_get_schedule_depth(
10671 __isl_keep isl_schedule_node *node);
10673 The following functions return the elements that reach the given node
10674 or the union of universes in the spaces that contain these elements.
10676 #include <isl/schedule_node.h>
10677 __isl_give isl_union_set *
10678 isl_schedule_node_get_domain(
10679 __isl_keep isl_schedule_node *node);
10680 __isl_give isl_union_set *
10681 isl_schedule_node_get_universe_domain(
10682 __isl_keep isl_schedule_node *node);
10684 The input tree of C<isl_schedule_node_get_domain>
10685 may only contain extension nodes if these would not affect
10686 the result of this function. That is, if one of the ancestors
10687 is an extension node, then all of the domain elements that were
10688 added by the extension node need to have been filtered out
10689 by filter nodes between the extension node and the input node.
10691 The following functions can be used to introduce additional nodes
10692 in the schedule tree. The new node is introduced at the point
10693 in the tree where the C<isl_schedule_node> points to and
10694 the results points to the new node.
10696 #include <isl/schedule_node.h>
10697 __isl_give isl_schedule_node *
10698 isl_schedule_node_insert_partial_schedule(
10699 __isl_take isl_schedule_node *node,
10700 __isl_take isl_multi_union_pw_aff *schedule);
10702 This function inserts a new band node with (the greatest integer
10703 part of) the given partial schedule.
10704 The subtree rooted at the given node is assumed not to have
10705 any anchored nodes.
10707 #include <isl/schedule_node.h>
10708 __isl_give isl_schedule_node *
10709 isl_schedule_node_insert_context(
10710 __isl_take isl_schedule_node *node,
10711 __isl_take isl_set *context);
10713 This function inserts a new context node with the given context constraints.
10715 #include <isl/schedule_node.h>
10716 __isl_give isl_schedule_node *
10717 isl_schedule_node_insert_filter(
10718 __isl_take isl_schedule_node *node,
10719 __isl_take isl_union_set *filter);
10721 This function inserts a new filter node with the given filter.
10722 If the original node already pointed to a filter node, then the
10723 two filter nodes are merged into one.
10725 #include <isl/schedule_node.h>
10726 __isl_give isl_schedule_node *
10727 isl_schedule_node_insert_guard(
10728 __isl_take isl_schedule_node *node,
10729 __isl_take isl_set *guard);
10731 This function inserts a new guard node with the given guard constraints.
10733 #include <isl/schedule_node.h>
10734 __isl_give isl_schedule_node *
10735 isl_schedule_node_insert_mark(
10736 __isl_take isl_schedule_node *node,
10737 __isl_take isl_id *mark);
10739 This function inserts a new mark node with the give mark identifier.
10741 #include <isl/schedule_node.h>
10742 __isl_give isl_schedule_node *
10743 isl_schedule_node_insert_sequence(
10744 __isl_take isl_schedule_node *node,
10745 __isl_take isl_union_set_list *filters);
10746 __isl_give isl_schedule_node *
10747 isl_schedule_node_insert_set(
10748 __isl_take isl_schedule_node *node,
10749 __isl_take isl_union_set_list *filters);
10751 These functions insert a new sequence or set node with the given
10752 filters as children.
10754 #include <isl/schedule_node.h>
10755 __isl_give isl_schedule_node *isl_schedule_node_group(
10756 __isl_take isl_schedule_node *node,
10757 __isl_take isl_id *group_id);
10759 This function introduces an expansion node in between the current
10760 node and its parent that expands instances of a space with tuple
10761 identifier C<group_id> to the original domain elements that reach
10762 the node. The group instances are identified by the prefix schedule
10763 of those domain elements. The ancestors of the node are adjusted
10764 to refer to the group instances instead of the original domain
10765 elements. The return value points to the same node in the updated
10766 schedule tree as the input node, i.e., to the child of the newly
10767 introduced expansion node. Grouping instances of different statements
10768 ensures that they will be treated as a single statement by the
10769 AST generator up to the point of the expansion node.
10771 The following functions can be used to flatten a nested
10774 #include <isl/schedule_node.h>
10775 __isl_give isl_schedule_node *
10776 isl_schedule_node_sequence_splice_child(
10777 __isl_take isl_schedule_node *node, int pos);
10778 __isl_give isl_schedule_node *
10779 isl_schedule_node_sequence_splice_children(
10780 __isl_take isl_schedule_node *node);
10782 That is, given a sequence node C<node> that has another sequence node
10783 in its child at position C<pos> (in particular, the child of that filter
10784 node is a sequence node), the function
10785 C<isl_schedule_node_sequence_splice_child>
10786 attaches the children of that other sequence
10787 node as children of C<node>, replacing the original child at position
10789 C<isl_schedule_node_sequence_splice_children> does this for all
10792 The partial schedule of a band node can be scaled (down) or reduced using
10793 the following functions.
10795 #include <isl/schedule_node.h>
10796 __isl_give isl_schedule_node *
10797 isl_schedule_node_band_scale(
10798 __isl_take isl_schedule_node *node,
10799 __isl_take isl_multi_val *mv);
10800 __isl_give isl_schedule_node *
10801 isl_schedule_node_band_scale_down(
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_mod(
10806 __isl_take isl_schedule_node *node,
10807 __isl_take isl_multi_val *mv);
10809 The spaces of the two arguments need to match.
10810 After scaling, the partial schedule is replaced by its greatest
10811 integer part to ensure that the schedule remains integral.
10813 The partial schedule of a band node can be shifted by an
10814 C<isl_multi_union_pw_aff> with a domain that is a superset
10815 of the domain of the partial schedule using
10816 the following function.
10818 #include <isl/schedule_node.h>
10819 __isl_give isl_schedule_node *
10820 isl_schedule_node_band_shift(
10821 __isl_take isl_schedule_node *node,
10822 __isl_take isl_multi_union_pw_aff *shift);
10824 A band node can be tiled using the following function.
10826 #include <isl/schedule_node.h>
10827 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10828 __isl_take isl_schedule_node *node,
10829 __isl_take isl_multi_val *sizes);
10831 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10833 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10834 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10836 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10838 The C<isl_schedule_node_band_tile> function tiles
10839 the band using the given tile sizes inside its schedule.
10840 A new child band node is created to represent the point loops and it is
10841 inserted between the modified band and its children.
10842 The subtree rooted at the given node is assumed not to have
10843 any anchored nodes.
10844 The C<tile_scale_tile_loops> option specifies whether the tile
10845 loops iterators should be scaled by the tile sizes.
10846 If the C<tile_shift_point_loops> option is set, then the point loops
10847 are shifted to start at zero.
10849 A band node can be split into two nested band nodes
10850 using the following function.
10852 #include <isl/schedule_node.h>
10853 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10854 __isl_take isl_schedule_node *node, int pos);
10856 The resulting outer band node contains the first C<pos> dimensions of
10857 the schedule of C<node> while the inner band contains the remaining dimensions.
10858 The schedules of the two band nodes live in anonymous spaces.
10859 The loop AST generation type options and the isolate option
10860 are split over the two band nodes.
10862 A band node can be moved down to the leaves of the subtree rooted
10863 at the band node using the following function.
10865 #include <isl/schedule_node.h>
10866 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10867 __isl_take isl_schedule_node *node);
10869 The subtree rooted at the given node is assumed not to have
10870 any anchored nodes.
10871 The result points to the node in the resulting tree that is in the same
10872 position as the node pointed to by C<node> in the original tree.
10874 #include <isl/schedule_node.h>
10875 __isl_give isl_schedule_node *
10876 isl_schedule_node_order_before(
10877 __isl_take isl_schedule_node *node,
10878 __isl_take isl_union_set *filter);
10879 __isl_give isl_schedule_node *
10880 isl_schedule_node_order_after(
10881 __isl_take isl_schedule_node *node,
10882 __isl_take isl_union_set *filter);
10884 These functions split the domain elements that reach C<node>
10885 into those that satisfy C<filter> and those that do not and
10886 arranges for the elements that do satisfy the filter to be
10887 executed before (in case of C<isl_schedule_node_order_before>)
10888 or after (in case of C<isl_schedule_node_order_after>)
10889 those that do not. The order is imposed by
10890 a sequence node, possibly reusing the grandparent of C<node>
10891 on two copies of the subtree attached to the original C<node>.
10892 Both copies are simplified with respect to their filter.
10894 Return a pointer to the copy of the subtree that does not
10895 satisfy C<filter>. If there is no such copy (because all
10896 reaching domain elements satisfy the filter), then return
10897 the original pointer.
10899 #include <isl/schedule_node.h>
10900 __isl_give isl_schedule_node *
10901 isl_schedule_node_graft_before(
10902 __isl_take isl_schedule_node *node,
10903 __isl_take isl_schedule_node *graft);
10904 __isl_give isl_schedule_node *
10905 isl_schedule_node_graft_after(
10906 __isl_take isl_schedule_node *node,
10907 __isl_take isl_schedule_node *graft);
10909 This function inserts the C<graft> tree into the tree containing C<node>
10910 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10911 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10912 The root node of C<graft>
10913 should be an extension node where the domain of the extension
10914 is the flat product of all outer band nodes of C<node>.
10915 The root node may also be a domain node.
10916 The elements of the domain or the range of the extension may not
10917 intersect with the domain elements that reach "node".
10918 The schedule tree of C<graft> may not be anchored.
10920 The schedule tree of C<node> is modified to include an extension node
10921 corresponding to the root node of C<graft> as a child of the original
10922 parent of C<node>. The original node that C<node> points to and the
10923 child of the root node of C<graft> are attached to this extension node
10924 through a sequence, with appropriate filters and with the child
10925 of C<graft> appearing before or after the original C<node>.
10927 If C<node> already appears inside a sequence that is the child of
10928 an extension node and if the spaces of the new domain elements
10929 do not overlap with those of the original domain elements,
10930 then that extension node is extended with the new extension
10931 rather than introducing a new segment of extension and sequence nodes.
10933 Return a pointer to the same node in the modified tree that
10934 C<node> pointed to in the original tree.
10936 A representation of the schedule node can be printed using
10938 #include <isl/schedule_node.h>
10939 __isl_give isl_printer *isl_printer_print_schedule_node(
10940 __isl_take isl_printer *p,
10941 __isl_keep isl_schedule_node *node);
10942 __isl_give char *isl_schedule_node_to_str(
10943 __isl_keep isl_schedule_node *node);
10945 C<isl_schedule_node_to_str> prints the schedule node in block format.
10947 =head2 Dependence Analysis
10949 C<isl> contains specialized functionality for performing
10950 array dataflow analysis. That is, given a I<sink> access relation,
10951 a collection of possible I<source> accesses and
10952 a collection of I<kill> accesses,
10953 C<isl> can compute relations that describe
10954 for each iteration of the sink access, which iterations
10955 of which of the source access relations may have
10956 accessed the same data element before the given iteration
10957 of the sink access without any intermediate kill of that data element.
10958 The resulting dependence relations map source iterations
10959 to either the corresponding sink iterations or
10960 pairs of corresponding sink iterations and accessed data elements.
10961 To compute standard flow dependences, the sink should be
10962 a read, while the sources should be writes.
10963 If no kills are specified,
10964 then memory based dependence analysis is performed.
10965 If, on the other hand, all sources are also kills,
10966 then value based dependence analysis is performed.
10967 If any of the source accesses are marked as being I<must>
10968 accesses, then they are also treated as kills.
10969 Furthermore, the specification of must-sources results
10970 in the computation of must-dependences.
10971 Only dependences originating in a must access not coscheduled
10972 with any other access to the same element and without
10973 any may accesses between the must access and the sink access
10974 are considered to be must dependences.
10976 =head3 High-level Interface
10978 A high-level interface to dependence analysis is provided
10979 by the following function.
10981 #include <isl/flow.h>
10982 __isl_give isl_union_flow *
10983 isl_union_access_info_compute_flow(
10984 __isl_take isl_union_access_info *access);
10986 The input C<isl_union_access_info> object describes the sink
10987 access relations, the source access relations and a schedule,
10988 while the output C<isl_union_flow> object describes
10989 the resulting dependence relations and the subsets of the
10990 sink relations for which no source was found.
10992 An C<isl_union_access_info> is created, modified, copied and freed using
10993 the following functions.
10995 #include <isl/flow.h>
10996 __isl_give isl_union_access_info *
10997 isl_union_access_info_from_sink(
10998 __isl_take isl_union_map *sink);
10999 __isl_give isl_union_access_info *
11000 isl_union_access_info_set_kill(
11001 __isl_take isl_union_access_info *access,
11002 __isl_take isl_union_map *kill);
11003 __isl_give isl_union_access_info *
11004 isl_union_access_info_set_may_source(
11005 __isl_take isl_union_access_info *access,
11006 __isl_take isl_union_map *may_source);
11007 __isl_give isl_union_access_info *
11008 isl_union_access_info_set_must_source(
11009 __isl_take isl_union_access_info *access,
11010 __isl_take isl_union_map *must_source);
11011 __isl_give isl_union_access_info *
11012 isl_union_access_info_set_schedule(
11013 __isl_take isl_union_access_info *access,
11014 __isl_take isl_schedule *schedule);
11015 __isl_give isl_union_access_info *
11016 isl_union_access_info_set_schedule_map(
11017 __isl_take isl_union_access_info *access,
11018 __isl_take isl_union_map *schedule_map);
11019 __isl_give isl_union_access_info *
11020 isl_union_access_info_copy(
11021 __isl_keep isl_union_access_info *access);
11022 __isl_null isl_union_access_info *
11023 isl_union_access_info_free(
11024 __isl_take isl_union_access_info *access);
11026 The may sources set by C<isl_union_access_info_set_may_source>
11027 do not need to include the must sources set by
11028 C<isl_union_access_info_set_must_source> as a subset.
11029 The kills set by C<isl_union_access_info_set_kill> may overlap
11030 with the may-sources and/or must-sources.
11031 The user is free not to call one (or more) of these functions,
11032 in which case the corresponding set is kept to its empty default.
11033 Similarly, the default schedule initialized by
11034 C<isl_union_access_info_from_sink> is empty.
11035 The current schedule is determined by the last call to either
11036 C<isl_union_access_info_set_schedule> or
11037 C<isl_union_access_info_set_schedule_map>.
11038 The domain of the schedule corresponds to the domains of
11039 the access relations. In particular, the domains of the access
11040 relations are effectively intersected with the domain of the schedule
11041 and only the resulting accesses are considered by the dependence analysis.
11043 An C<isl_union_access_info> object can be read from input
11044 using the following function.
11046 #include <isl/flow.h>
11047 __isl_give isl_union_access_info *
11048 isl_union_access_info_read_from_file(isl_ctx *ctx,
11051 A representation of the information contained in an object
11052 of type C<isl_union_access_info> can be obtained using
11054 #include <isl/flow.h>
11055 __isl_give isl_printer *
11056 isl_printer_print_union_access_info(
11057 __isl_take isl_printer *p,
11058 __isl_keep isl_union_access_info *access);
11059 __isl_give char *isl_union_access_info_to_str(
11060 __isl_keep isl_union_access_info *access);
11062 C<isl_union_access_info_to_str> prints the information in flow format.
11064 The output of C<isl_union_access_info_compute_flow> can be examined,
11065 copied, and freed using the following functions.
11067 #include <isl/flow.h>
11068 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11069 __isl_keep isl_union_flow *flow);
11070 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11071 __isl_keep isl_union_flow *flow);
11072 __isl_give isl_union_map *
11073 isl_union_flow_get_full_must_dependence(
11074 __isl_keep isl_union_flow *flow);
11075 __isl_give isl_union_map *
11076 isl_union_flow_get_full_may_dependence(
11077 __isl_keep isl_union_flow *flow);
11078 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11079 __isl_keep isl_union_flow *flow);
11080 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11081 __isl_keep isl_union_flow *flow);
11082 __isl_give isl_union_flow *isl_union_flow_copy(
11083 __isl_keep isl_union_flow *flow);
11084 __isl_null isl_union_flow *isl_union_flow_free(
11085 __isl_take isl_union_flow *flow);
11087 The relation returned by C<isl_union_flow_get_must_dependence>
11088 relates domain elements of must sources to domain elements of the sink.
11089 The relation returned by C<isl_union_flow_get_may_dependence>
11090 relates domain elements of must or may sources to domain elements of the sink
11091 and includes the previous relation as a subset.
11092 The relation returned by C<isl_union_flow_get_full_must_dependence>
11093 relates domain elements of must sources to pairs of domain elements of the sink
11094 and accessed data elements.
11095 The relation returned by C<isl_union_flow_get_full_may_dependence>
11096 relates domain elements of must or may sources to pairs of
11097 domain elements of the sink and accessed data elements.
11098 This relation includes the previous relation as a subset.
11099 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11100 of the sink relation for which no dependences have been found.
11101 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11102 of the sink relation for which no definite dependences have been found.
11103 That is, it contains those sink access that do not contribute to any
11104 of the elements in the relation returned
11105 by C<isl_union_flow_get_must_dependence>.
11107 A representation of the information contained in an object
11108 of type C<isl_union_flow> can be obtained using
11110 #include <isl/flow.h>
11111 __isl_give isl_printer *isl_printer_print_union_flow(
11112 __isl_take isl_printer *p,
11113 __isl_keep isl_union_flow *flow);
11114 __isl_give char *isl_union_flow_to_str(
11115 __isl_keep isl_union_flow *flow);
11117 C<isl_union_flow_to_str> prints the information in flow format.
11119 =head3 Low-level Interface
11121 A lower-level interface is provided by the following functions.
11123 #include <isl/flow.h>
11125 typedef int (*isl_access_level_before)(void *first, void *second);
11127 __isl_give isl_access_info *isl_access_info_alloc(
11128 __isl_take isl_map *sink,
11129 void *sink_user, isl_access_level_before fn,
11131 __isl_give isl_access_info *isl_access_info_add_source(
11132 __isl_take isl_access_info *acc,
11133 __isl_take isl_map *source, int must,
11134 void *source_user);
11135 __isl_null isl_access_info *isl_access_info_free(
11136 __isl_take isl_access_info *acc);
11138 __isl_give isl_flow *isl_access_info_compute_flow(
11139 __isl_take isl_access_info *acc);
11141 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11142 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11143 void *dep_user, void *user),
11145 __isl_give isl_map *isl_flow_get_no_source(
11146 __isl_keep isl_flow *deps, int must);
11147 __isl_null isl_flow *isl_flow_free(
11148 __isl_take isl_flow *deps);
11150 The function C<isl_access_info_compute_flow> performs the actual
11151 dependence analysis. The other functions are used to construct
11152 the input for this function or to read off the output.
11154 The input is collected in an C<isl_access_info>, which can
11155 be created through a call to C<isl_access_info_alloc>.
11156 The arguments to this functions are the sink access relation
11157 C<sink>, a token C<sink_user> used to identify the sink
11158 access to the user, a callback function for specifying the
11159 relative order of source and sink accesses, and the number
11160 of source access relations that will be added.
11162 The callback function has type C<int (*)(void *first, void *second)>.
11163 The function is called with two user supplied tokens identifying
11164 either a source or the sink and it should return the shared nesting
11165 level and the relative order of the two accesses.
11166 In particular, let I<n> be the number of loops shared by
11167 the two accesses. If C<first> precedes C<second> textually,
11168 then the function should return I<2 * n + 1>; otherwise,
11169 it should return I<2 * n>.
11170 The low-level interface assumes that no sources are coscheduled.
11171 If the information returned by the callback does not allow
11172 the relative order to be determined, then one of the sources
11173 is arbitrarily taken to be executed after the other(s).
11175 The sources can be added to the C<isl_access_info> object by performing
11176 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11177 C<must> indicates whether the source is a I<must> access
11178 or a I<may> access. Note that a multi-valued access relation
11179 should only be marked I<must> if every iteration in the domain
11180 of the relation accesses I<all> elements in its image.
11181 The C<source_user> token is again used to identify
11182 the source access. The range of the source access relation
11183 C<source> should have the same dimension as the range
11184 of the sink access relation.
11185 The C<isl_access_info_free> function should usually not be
11186 called explicitly, because it is already called implicitly by
11187 C<isl_access_info_compute_flow>.
11189 The result of the dependence analysis is collected in an
11190 C<isl_flow>. There may be elements of
11191 the sink access for which no preceding source access could be
11192 found or for which all preceding sources are I<may> accesses.
11193 The relations containing these elements can be obtained through
11194 calls to C<isl_flow_get_no_source>, the first with C<must> set
11195 and the second with C<must> unset.
11196 In the case of standard flow dependence analysis,
11197 with the sink a read and the sources I<must> writes,
11198 the first relation corresponds to the reads from uninitialized
11199 array elements and the second relation is empty.
11200 The actual flow dependences can be extracted using
11201 C<isl_flow_foreach>. This function will call the user-specified
11202 callback function C<fn> for each B<non-empty> dependence between
11203 a source and the sink. The callback function is called
11204 with four arguments, the actual flow dependence relation
11205 mapping source iterations to sink iterations, a boolean that
11206 indicates whether it is a I<must> or I<may> dependence, a token
11207 identifying the source and an additional C<void *> with value
11208 equal to the third argument of the C<isl_flow_foreach> call.
11209 A dependence is marked I<must> if it originates from a I<must>
11210 source and if it is not followed by any I<may> sources.
11212 After finishing with an C<isl_flow>, the user should call
11213 C<isl_flow_free> to free all associated memory.
11215 =head3 Interaction with the Low-level Interface
11217 During the dependence analysis, we frequently need to perform
11218 the following operation. Given a relation between sink iterations
11219 and potential source iterations from a particular source domain,
11220 what is the last potential source iteration corresponding to each
11221 sink iteration. It can sometimes be convenient to adjust
11222 the set of potential source iterations before or after each such operation.
11223 The prototypical example is fuzzy array dataflow analysis,
11224 where we need to analyze if, based on data-dependent constraints,
11225 the sink iteration can ever be executed without one or more of
11226 the corresponding potential source iterations being executed.
11227 If so, we can introduce extra parameters and select an unknown
11228 but fixed source iteration from the potential source iterations.
11229 To be able to perform such manipulations, C<isl> provides the following
11232 #include <isl/flow.h>
11234 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11235 __isl_keep isl_map *source_map,
11236 __isl_keep isl_set *sink, void *source_user,
11238 __isl_give isl_access_info *isl_access_info_set_restrict(
11239 __isl_take isl_access_info *acc,
11240 isl_access_restrict fn, void *user);
11242 The function C<isl_access_info_set_restrict> should be called
11243 before calling C<isl_access_info_compute_flow> and registers a callback function
11244 that will be called any time C<isl> is about to compute the last
11245 potential source. The first argument is the (reverse) proto-dependence,
11246 mapping sink iterations to potential source iterations.
11247 The second argument represents the sink iterations for which
11248 we want to compute the last source iteration.
11249 The third argument is the token corresponding to the source
11250 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11251 The callback is expected to return a restriction on either the input or
11252 the output of the operation computing the last potential source.
11253 If the input needs to be restricted then restrictions are needed
11254 for both the source and the sink iterations. The sink iterations
11255 and the potential source iterations will be intersected with these sets.
11256 If the output needs to be restricted then only a restriction on the source
11257 iterations is required.
11258 If any error occurs, the callback should return C<NULL>.
11259 An C<isl_restriction> object can be created, freed and inspected
11260 using the following functions.
11262 #include <isl/flow.h>
11264 __isl_give isl_restriction *isl_restriction_input(
11265 __isl_take isl_set *source_restr,
11266 __isl_take isl_set *sink_restr);
11267 __isl_give isl_restriction *isl_restriction_output(
11268 __isl_take isl_set *source_restr);
11269 __isl_give isl_restriction *isl_restriction_none(
11270 __isl_take isl_map *source_map);
11271 __isl_give isl_restriction *isl_restriction_empty(
11272 __isl_take isl_map *source_map);
11273 __isl_null isl_restriction *isl_restriction_free(
11274 __isl_take isl_restriction *restr);
11276 C<isl_restriction_none> and C<isl_restriction_empty> are special
11277 cases of C<isl_restriction_input>. C<isl_restriction_none>
11278 is essentially equivalent to
11280 isl_restriction_input(isl_set_universe(
11281 isl_space_range(isl_map_get_space(source_map))),
11283 isl_space_domain(isl_map_get_space(source_map))));
11285 whereas C<isl_restriction_empty> is essentially equivalent to
11287 isl_restriction_input(isl_set_empty(
11288 isl_space_range(isl_map_get_space(source_map))),
11290 isl_space_domain(isl_map_get_space(source_map))));
11294 #include <isl/schedule.h>
11295 __isl_give isl_schedule *
11296 isl_schedule_constraints_compute_schedule(
11297 __isl_take isl_schedule_constraints *sc);
11299 The function C<isl_schedule_constraints_compute_schedule> can be
11300 used to compute a schedule that satisfies the given schedule constraints.
11301 These schedule constraints include the iteration domain for which
11302 a schedule should be computed and dependences between pairs of
11303 iterations. In particular, these dependences include
11304 I<validity> dependences and I<proximity> dependences.
11305 By default, the algorithm used to construct the schedule is similar
11306 to that of C<Pluto>.
11307 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11309 The generated schedule respects all validity dependences.
11310 That is, all dependence distances over these dependences in the
11311 scheduled space are lexicographically positive.
11313 The default algorithm tries to ensure that the dependence distances
11314 over coincidence constraints are zero and to minimize the
11315 dependence distances over proximity dependences.
11316 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11317 for groups of domains where the dependence distances over validity
11318 dependences have only non-negative values.
11319 Note that when minimizing the maximal dependence distance
11320 over proximity dependences, a single affine expression in the parameters
11321 is constructed that bounds all dependence distances. If no such expression
11322 exists, then the algorithm will fail and resort to an alternative
11323 scheduling algorithm. In particular, this means that adding proximity
11324 dependences may eliminate valid solutions. A typical example where this
11325 phenomenon may occur is when some subset of the proximity dependences
11326 has no restriction on some parameter, forcing the coefficient of that
11327 parameter to be zero, while some other subset forces the dependence
11328 distance to depend on that parameter, requiring the same coefficient
11330 When using Feautrier's algorithm, the coincidence and proximity constraints
11331 are only taken into account during the extension to a
11332 full-dimensional schedule.
11334 An C<isl_schedule_constraints> object can be constructed
11335 and manipulated using the following functions.
11337 #include <isl/schedule.h>
11338 __isl_give isl_schedule_constraints *
11339 isl_schedule_constraints_copy(
11340 __isl_keep isl_schedule_constraints *sc);
11341 __isl_give isl_schedule_constraints *
11342 isl_schedule_constraints_on_domain(
11343 __isl_take isl_union_set *domain);
11344 __isl_give isl_schedule_constraints *
11345 isl_schedule_constraints_set_context(
11346 __isl_take isl_schedule_constraints *sc,
11347 __isl_take isl_set *context);
11348 __isl_give isl_schedule_constraints *
11349 isl_schedule_constraints_set_validity(
11350 __isl_take isl_schedule_constraints *sc,
11351 __isl_take isl_union_map *validity);
11352 __isl_give isl_schedule_constraints *
11353 isl_schedule_constraints_set_coincidence(
11354 __isl_take isl_schedule_constraints *sc,
11355 __isl_take isl_union_map *coincidence);
11356 __isl_give isl_schedule_constraints *
11357 isl_schedule_constraints_set_proximity(
11358 __isl_take isl_schedule_constraints *sc,
11359 __isl_take isl_union_map *proximity);
11360 __isl_give isl_schedule_constraints *
11361 isl_schedule_constraints_set_conditional_validity(
11362 __isl_take isl_schedule_constraints *sc,
11363 __isl_take isl_union_map *condition,
11364 __isl_take isl_union_map *validity);
11365 __isl_give isl_schedule_constraints *
11366 isl_schedule_constraints_apply(
11367 __isl_take isl_schedule_constraints *sc,
11368 __isl_take isl_union_map *umap);
11369 __isl_null isl_schedule_constraints *
11370 isl_schedule_constraints_free(
11371 __isl_take isl_schedule_constraints *sc);
11373 The initial C<isl_schedule_constraints> object created by
11374 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11375 That is, it has an empty set of dependences.
11376 The function C<isl_schedule_constraints_set_context> allows the user
11377 to specify additional constraints on the parameters that may
11378 be assumed to hold during the construction of the schedule.
11379 The function C<isl_schedule_constraints_set_validity> replaces the
11380 validity dependences, mapping domain elements I<i> to domain
11381 elements that should be scheduled after I<i>.
11382 The function C<isl_schedule_constraints_set_coincidence> replaces the
11383 coincidence dependences, mapping domain elements I<i> to domain
11384 elements that should be scheduled together with I<I>, if possible.
11385 The function C<isl_schedule_constraints_set_proximity> replaces the
11386 proximity dependences, mapping domain elements I<i> to domain
11387 elements that should be scheduled either before I<I>
11388 or as early as possible after I<i>.
11390 The function C<isl_schedule_constraints_set_conditional_validity>
11391 replaces the conditional validity constraints.
11392 A conditional validity constraint is only imposed when any of the corresponding
11393 conditions is satisfied, i.e., when any of them is non-zero.
11394 That is, the scheduler ensures that within each band if the dependence
11395 distances over the condition constraints are not all zero
11396 then all corresponding conditional validity constraints are respected.
11397 A conditional validity constraint corresponds to a condition
11398 if the two are adjacent, i.e., if the domain of one relation intersect
11399 the range of the other relation.
11400 The typical use case of conditional validity constraints is
11401 to allow order constraints between live ranges to be violated
11402 as long as the live ranges themselves are local to the band.
11403 To allow more fine-grained control over which conditions correspond
11404 to which conditional validity constraints, the domains and ranges
11405 of these relations may include I<tags>. That is, the domains and
11406 ranges of those relation may themselves be wrapped relations
11407 where the iteration domain appears in the domain of those wrapped relations
11408 and the range of the wrapped relations can be arbitrarily chosen
11409 by the user. Conditions and conditional validity constraints are only
11410 considered adjacent to each other if the entire wrapped relation matches.
11411 In particular, a relation with a tag will never be considered adjacent
11412 to a relation without a tag.
11414 The function C<isl_schedule_constraints_apply> takes
11415 schedule constraints that are defined on some set of domain elements
11416 and transforms them to schedule constraints on the elements
11417 to which these domain elements are mapped by the given transformation.
11419 An C<isl_schedule_constraints> object can be inspected
11420 using the following functions.
11422 #include <isl/schedule.h>
11423 __isl_give isl_union_set *
11424 isl_schedule_constraints_get_domain(
11425 __isl_keep isl_schedule_constraints *sc);
11426 __isl_give isl_set *isl_schedule_constraints_get_context(
11427 __isl_keep isl_schedule_constraints *sc);
11428 __isl_give isl_union_map *
11429 isl_schedule_constraints_get_validity(
11430 __isl_keep isl_schedule_constraints *sc);
11431 __isl_give isl_union_map *
11432 isl_schedule_constraints_get_coincidence(
11433 __isl_keep isl_schedule_constraints *sc);
11434 __isl_give isl_union_map *
11435 isl_schedule_constraints_get_proximity(
11436 __isl_keep isl_schedule_constraints *sc);
11437 __isl_give isl_union_map *
11438 isl_schedule_constraints_get_conditional_validity(
11439 __isl_keep isl_schedule_constraints *sc);
11440 __isl_give isl_union_map *
11441 isl_schedule_constraints_get_conditional_validity_condition(
11442 __isl_keep isl_schedule_constraints *sc);
11444 An C<isl_schedule_constraints> object can be read from input
11445 using the following functions.
11447 #include <isl/schedule.h>
11448 __isl_give isl_schedule_constraints *
11449 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11451 __isl_give isl_schedule_constraints *
11452 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11455 The contents of an C<isl_schedule_constraints> object can be printed
11456 using the following functions.
11458 #include <isl/schedule.h>
11459 __isl_give isl_printer *
11460 isl_printer_print_schedule_constraints(
11461 __isl_take isl_printer *p,
11462 __isl_keep isl_schedule_constraints *sc);
11463 __isl_give char *isl_schedule_constraints_to_str(
11464 __isl_keep isl_schedule_constraints *sc);
11466 The following function computes a schedule directly from
11467 an iteration domain and validity and proximity dependences
11468 and is implemented in terms of the functions described above.
11469 The use of C<isl_union_set_compute_schedule> is discouraged.
11471 #include <isl/schedule.h>
11472 __isl_give isl_schedule *isl_union_set_compute_schedule(
11473 __isl_take isl_union_set *domain,
11474 __isl_take isl_union_map *validity,
11475 __isl_take isl_union_map *proximity);
11477 The generated schedule represents a schedule tree.
11478 For more information on schedule trees, see
11479 L</"Schedule Trees">.
11483 #include <isl/schedule.h>
11484 isl_stat isl_options_set_schedule_max_coefficient(
11485 isl_ctx *ctx, int val);
11486 int isl_options_get_schedule_max_coefficient(
11488 isl_stat isl_options_set_schedule_max_constant_term(
11489 isl_ctx *ctx, int val);
11490 int isl_options_get_schedule_max_constant_term(
11492 isl_stat isl_options_set_schedule_serialize_sccs(
11493 isl_ctx *ctx, int val);
11494 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11495 isl_stat isl_options_set_schedule_whole_component(
11496 isl_ctx *ctx, int val);
11497 int isl_options_get_schedule_whole_component(
11499 isl_stat isl_options_set_schedule_maximize_band_depth(
11500 isl_ctx *ctx, int val);
11501 int isl_options_get_schedule_maximize_band_depth(
11503 isl_stat isl_options_set_schedule_maximize_coincidence(
11504 isl_ctx *ctx, int val);
11505 int isl_options_get_schedule_maximize_coincidence(
11507 isl_stat isl_options_set_schedule_outer_coincidence(
11508 isl_ctx *ctx, int val);
11509 int isl_options_get_schedule_outer_coincidence(
11511 isl_stat isl_options_set_schedule_split_scaled(
11512 isl_ctx *ctx, int val);
11513 int isl_options_get_schedule_split_scaled(
11515 isl_stat isl_options_set_schedule_treat_coalescing(
11516 isl_ctx *ctx, int val);
11517 int isl_options_get_schedule_treat_coalescing(
11519 isl_stat isl_options_set_schedule_algorithm(
11520 isl_ctx *ctx, int val);
11521 int isl_options_get_schedule_algorithm(
11523 isl_stat isl_options_set_schedule_carry_self_first(
11524 isl_ctx *ctx, int val);
11525 int isl_options_get_schedule_carry_self_first(
11527 isl_stat isl_options_set_schedule_separate_components(
11528 isl_ctx *ctx, int val);
11529 int isl_options_get_schedule_separate_components(
11534 =item * schedule_max_coefficient
11536 This option enforces that the coefficients for variable and parameter
11537 dimensions in the calculated schedule are not larger than the specified value.
11538 This option can significantly increase the speed of the scheduling calculation
11539 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11540 this option does not introduce bounds on the variable or parameter
11542 This option has no effect on the Feautrier style scheduler.
11544 =item * schedule_max_constant_term
11546 This option enforces that the constant coefficients in the calculated schedule
11547 are not larger than the maximal constant term. This option can significantly
11548 increase the speed of the scheduling calculation and may also prevent fusing of
11549 unrelated dimensions. A value of -1 means that this option does not introduce
11550 bounds on the constant coefficients.
11552 =item * schedule_serialize_sccs
11554 If this option is set, then all strongly connected components
11555 in the dependence graph are serialized as soon as they are detected.
11556 This means in particular that instances of statements will only
11557 appear in the same band node if these statements belong
11558 to the same strongly connected component at the point where
11559 the band node is constructed.
11561 =item * schedule_whole_component
11563 If this option is set, then entire (weakly) connected
11564 components in the dependence graph are scheduled together
11566 Otherwise, each strongly connected component within
11567 such a weakly connected component is first scheduled separately
11568 and then combined with other strongly connected components.
11569 This option has no effect if C<schedule_serialize_sccs> is set.
11571 =item * schedule_maximize_band_depth
11573 If this option is set, then the scheduler tries to maximize
11574 the width of the bands. Wider bands give more possibilities for tiling.
11575 In particular, if the C<schedule_whole_component> option is set,
11576 then bands are split if this might result in wider bands.
11577 Otherwise, the effect of this option is to only allow
11578 strongly connected components to be combined if this does
11579 not reduce the width of the bands.
11580 Note that if the C<schedule_serialize_sccs> options is set, then
11581 the C<schedule_maximize_band_depth> option therefore has no effect.
11583 =item * schedule_maximize_coincidence
11585 This option is only effective if the C<schedule_whole_component>
11586 option is turned off.
11587 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11588 strongly connected components are only combined with each other
11589 if this does not reduce the number of coincident band members.
11591 =item * schedule_outer_coincidence
11593 If this option is set, then we try to construct schedules
11594 where the outermost scheduling dimension in each band
11595 satisfies the coincidence constraints.
11597 =item * schedule_algorithm
11599 Selects the scheduling algorithm to be used.
11600 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11601 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11603 =item * schedule_split_scaled
11605 If this option is set, then we try to construct schedules in which the
11606 constant term is split off from the linear part if the linear parts of
11607 the scheduling rows for all nodes in the graph have a common non-trivial
11609 The constant term is then dropped and the linear
11611 This option is only effective when the Feautrier style scheduler is
11612 being used, either as the main scheduler or as a fallback for the
11613 Pluto-like scheduler.
11615 =item * schedule_treat_coalescing
11617 If this option is set, then the scheduler will try and avoid
11618 producing schedules that perform loop coalescing.
11619 In particular, for the Pluto-like scheduler, this option places
11620 bounds on the schedule coefficients based on the sizes of the instance sets.
11621 For the Feautrier style scheduler, this option detects potentially
11622 coalescing schedules and then tries to adjust the schedule to avoid
11625 =item * schedule_carry_self_first
11627 If this option is set, then the Feautrier style scheduler
11628 (when used as a fallback for the Pluto-like scheduler) will
11629 first try to only carry self-dependences.
11631 =item * schedule_separate_components
11633 If this option is set then the function C<isl_schedule_get_map>
11634 will treat set nodes in the same way as sequence nodes.
11638 =head2 AST Generation
11640 This section describes the C<isl> functionality for generating
11641 ASTs that visit all the elements
11642 in a domain in an order specified by a schedule tree or
11644 In case the schedule given as a C<isl_union_map>, an AST is generated
11645 that visits all the elements in the domain of the C<isl_union_map>
11646 according to the lexicographic order of the corresponding image
11647 element(s). If the range of the C<isl_union_map> consists of
11648 elements in more than one space, then each of these spaces is handled
11649 separately in an arbitrary order.
11650 It should be noted that the schedule tree or the image elements
11651 in a schedule map only specify the I<order>
11652 in which the corresponding domain elements should be visited.
11653 No direct relation between the partial schedule values
11654 or the image elements on the one hand and the loop iterators
11655 in the generated AST on the other hand should be assumed.
11657 Each AST is generated within a build. The initial build
11658 simply specifies the constraints on the parameters (if any)
11659 and can be created, inspected, copied and freed using the following functions.
11661 #include <isl/ast_build.h>
11662 __isl_give isl_ast_build *isl_ast_build_alloc(
11664 __isl_give isl_ast_build *isl_ast_build_from_context(
11665 __isl_take isl_set *set);
11666 __isl_give isl_ast_build *isl_ast_build_copy(
11667 __isl_keep isl_ast_build *build);
11668 __isl_null isl_ast_build *isl_ast_build_free(
11669 __isl_take isl_ast_build *build);
11671 The C<set> argument is usually a parameter set with zero or more parameters.
11672 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11673 this set is required to be a parameter set.
11674 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11675 specify any parameter constraints.
11676 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11677 and L</"Fine-grained Control over AST Generation">.
11678 Finally, the AST itself can be constructed using one of the following
11681 #include <isl/ast_build.h>
11682 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11683 __isl_keep isl_ast_build *build,
11684 __isl_take isl_schedule *schedule);
11685 __isl_give isl_ast_node *
11686 isl_ast_build_node_from_schedule_map(
11687 __isl_keep isl_ast_build *build,
11688 __isl_take isl_union_map *schedule);
11690 =head3 Inspecting the AST
11692 The basic properties of an AST node can be obtained as follows.
11694 #include <isl/ast.h>
11695 enum isl_ast_node_type isl_ast_node_get_type(
11696 __isl_keep isl_ast_node *node);
11698 The type of an AST node is one of
11699 C<isl_ast_node_for>,
11700 C<isl_ast_node_if>,
11701 C<isl_ast_node_block>,
11702 C<isl_ast_node_mark> or
11703 C<isl_ast_node_user>.
11704 An C<isl_ast_node_for> represents a for node.
11705 An C<isl_ast_node_if> represents an if node.
11706 An C<isl_ast_node_block> represents a compound node.
11707 An C<isl_ast_node_mark> introduces a mark in the AST.
11708 An C<isl_ast_node_user> represents an expression statement.
11709 An expression statement typically corresponds to a domain element, i.e.,
11710 one of the elements that is visited by the AST.
11712 Each type of node has its own additional properties.
11714 #include <isl/ast.h>
11715 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11716 __isl_keep isl_ast_node *node);
11717 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11718 __isl_keep isl_ast_node *node);
11719 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11720 __isl_keep isl_ast_node *node);
11721 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11722 __isl_keep isl_ast_node *node);
11723 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11724 __isl_keep isl_ast_node *node);
11725 isl_bool isl_ast_node_for_is_degenerate(
11726 __isl_keep isl_ast_node *node);
11728 An C<isl_ast_for> is considered degenerate if it is known to execute
11731 #include <isl/ast.h>
11732 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11733 __isl_keep isl_ast_node *node);
11734 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11735 __isl_keep isl_ast_node *node);
11736 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11737 __isl_keep isl_ast_node *node);
11738 isl_bool isl_ast_node_if_has_else_node(
11739 __isl_keep isl_ast_node *node);
11740 isl_bool isl_ast_node_if_has_else(
11741 __isl_keep isl_ast_node *node);
11742 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11743 __isl_keep isl_ast_node *node);
11744 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11745 __isl_keep isl_ast_node *node);
11747 C<isl_ast_node_if_get_then>,
11748 C<isl_ast_node_if_has_else> and
11749 C<isl_ast_node_if_get_else>
11750 are alternative names for
11751 C<isl_ast_node_if_get_then_node>,
11752 C<isl_ast_node_if_has_else_node> and
11753 C<isl_ast_node_if_get_else_node>, respectively.
11755 __isl_give isl_ast_node_list *
11756 isl_ast_node_block_get_children(
11757 __isl_keep isl_ast_node *node);
11759 __isl_give isl_id *isl_ast_node_mark_get_id(
11760 __isl_keep isl_ast_node *node);
11761 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11762 __isl_keep isl_ast_node *node);
11764 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11765 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11767 #include <isl/ast.h>
11768 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11769 __isl_keep isl_ast_node *node);
11771 All descendants of a specific node in the AST (including the node itself)
11773 in depth-first pre-order using the following function.
11775 #include <isl/ast.h>
11776 isl_stat isl_ast_node_foreach_descendant_top_down(
11777 __isl_keep isl_ast_node *node,
11778 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11779 void *user), void *user);
11781 The callback function should return C<isl_bool_true> if the children
11782 of the given node should be visited and C<isl_bool_false> if they should not.
11783 It should return C<isl_bool_error> in case of failure, in which case
11784 the entire traversal is aborted.
11786 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11787 the following functions.
11789 #include <isl/ast.h>
11790 enum isl_ast_expr_type isl_ast_expr_get_type(
11791 __isl_keep isl_ast_expr *expr);
11793 The type of an AST expression is one of
11794 C<isl_ast_expr_op>,
11795 C<isl_ast_expr_id> or
11796 C<isl_ast_expr_int>.
11797 An C<isl_ast_expr_op> represents the result of an operation.
11798 An C<isl_ast_expr_id> represents an identifier.
11799 An C<isl_ast_expr_int> represents an integer value.
11801 Each type of expression has its own additional properties.
11803 #include <isl/ast.h>
11804 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11805 __isl_keep isl_ast_expr *expr);
11806 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11807 __isl_keep isl_ast_expr *expr);
11808 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11809 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11810 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11811 __isl_keep isl_ast_expr *expr, int pos);
11812 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11813 __isl_keep isl_ast_expr *expr, int pos);
11814 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11815 __isl_keep isl_ast_expr *expr,
11816 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11817 void *user), void *user);
11818 isl_stat isl_ast_expr_foreach_ast_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_node_foreach_ast_expr_op_type(
11823 __isl_keep isl_ast_node *node,
11824 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11825 void *user), void *user);
11826 isl_stat isl_ast_node_foreach_ast_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);
11831 C<isl_ast_expr_op_get_type> returns the type of the operation
11832 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11833 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11835 C<isl_ast_expr_get_op_type> is an alternative name for
11836 C<isl_ast_expr_op_get_type>.
11838 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11839 C<isl_ast_expr_op_get_n_arg> and
11840 C<isl_ast_expr_get_op_arg> is an alternative name for
11841 C<isl_ast_expr_op_get_arg>.
11843 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11844 C<isl_ast_expr_op_type> that appears in C<expr>.
11845 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11846 C<isl_ast_expr_foreach_ast_expr_op_type>.
11847 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11848 C<isl_ast_expr_op_type> that appears in C<node>.
11849 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11850 C<isl_ast_node_foreach_ast_expr_op_type>.
11851 The operation type is one of the following.
11855 =item C<isl_ast_expr_op_and>
11857 Logical I<and> of two arguments.
11858 Both arguments can be evaluated.
11860 =item C<isl_ast_expr_op_and_then>
11862 Logical I<and> of two arguments.
11863 The second argument can only be evaluated if the first evaluates to true.
11865 =item C<isl_ast_expr_op_or>
11867 Logical I<or> of two arguments.
11868 Both arguments can be evaluated.
11870 =item C<isl_ast_expr_op_or_else>
11872 Logical I<or> of two arguments.
11873 The second argument can only be evaluated if the first evaluates to false.
11875 =item C<isl_ast_expr_op_max>
11877 Maximum of two or more arguments.
11879 =item C<isl_ast_expr_op_min>
11881 Minimum of two or more arguments.
11883 =item C<isl_ast_expr_op_minus>
11887 =item C<isl_ast_expr_op_add>
11889 Sum of two arguments.
11891 =item C<isl_ast_expr_op_sub>
11893 Difference of two arguments.
11895 =item C<isl_ast_expr_op_mul>
11897 Product of two arguments.
11899 =item C<isl_ast_expr_op_div>
11901 Exact division. That is, the result is known to be an integer.
11903 =item C<isl_ast_expr_op_fdiv_q>
11905 Result of integer division, rounded towards negative
11907 The divisor is known to be positive.
11909 =item C<isl_ast_expr_op_pdiv_q>
11911 Result of integer division, where dividend is known to be non-negative.
11912 The divisor is known to be positive.
11914 =item C<isl_ast_expr_op_pdiv_r>
11916 Remainder of integer division, where dividend is known to be non-negative.
11917 The divisor is known to be positive.
11919 =item C<isl_ast_expr_op_zdiv_r>
11921 Equal to zero iff the remainder on integer division is zero.
11922 The divisor is known to be positive.
11924 =item C<isl_ast_expr_op_cond>
11926 Conditional operator defined on three arguments.
11927 If the first argument evaluates to true, then the result
11928 is equal to the second argument. Otherwise, the result
11929 is equal to the third argument.
11930 The second and third argument may only be evaluated if
11931 the first argument evaluates to true and false, respectively.
11932 Corresponds to C<a ? b : c> in C.
11934 =item C<isl_ast_expr_op_select>
11936 Conditional operator defined on three arguments.
11937 If the first argument evaluates to true, then the result
11938 is equal to the second argument. Otherwise, the result
11939 is equal to the third argument.
11940 The second and third argument may be evaluated independently
11941 of the value of the first argument.
11942 Corresponds to C<a * b + (1 - a) * c> in C.
11944 =item C<isl_ast_expr_op_eq>
11948 =item C<isl_ast_expr_op_le>
11950 Less than or equal relation.
11952 =item C<isl_ast_expr_op_lt>
11954 Less than relation.
11956 =item C<isl_ast_expr_op_ge>
11958 Greater than or equal relation.
11960 =item C<isl_ast_expr_op_gt>
11962 Greater than relation.
11964 =item C<isl_ast_expr_op_call>
11967 The number of arguments of the C<isl_ast_expr> is one more than
11968 the number of arguments in the function call, the first argument
11969 representing the function being called.
11971 =item C<isl_ast_expr_op_access>
11974 The number of arguments of the C<isl_ast_expr> is one more than
11975 the number of index expressions in the array access, the first argument
11976 representing the array being accessed.
11978 =item C<isl_ast_expr_op_member>
11981 This operation has two arguments, a structure and the name of
11982 the member of the structure being accessed.
11984 =item C<isl_ast_expr_op_address_of>
11986 The address of its single argument, which is always an array access.
11990 #include <isl/ast.h>
11991 __isl_give isl_id *isl_ast_expr_id_get_id(
11992 __isl_keep isl_ast_expr *expr);
11993 __isl_give isl_id *isl_ast_expr_get_id(
11994 __isl_keep isl_ast_expr *expr);
11996 Return the identifier represented by the AST expression.
11997 C<isl_ast_expr_get_id> is an alternative name for
11998 C<isl_ast_expr_id_get_id>.
12000 #include <isl/ast.h>
12001 __isl_give isl_val *isl_ast_expr_int_get_val(
12002 __isl_keep isl_ast_expr *expr);
12003 __isl_give isl_val *isl_ast_expr_get_val(
12004 __isl_keep isl_ast_expr *expr);
12006 Return the integer represented by the AST expression.
12007 C<isl_ast_expr_get_val> is an alternative name for
12008 C<isl_ast_expr_int_get_val>.
12010 =head3 Properties of ASTs
12012 #include <isl/ast.h>
12013 isl_bool isl_ast_expr_is_equal(
12014 __isl_keep isl_ast_expr *expr1,
12015 __isl_keep isl_ast_expr *expr2);
12017 Check if two C<isl_ast_expr>s are equal to each other.
12019 =head3 Manipulating and printing the AST
12021 AST nodes can be copied and freed using the following functions.
12023 #include <isl/ast.h>
12024 __isl_give isl_ast_node *isl_ast_node_copy(
12025 __isl_keep isl_ast_node *node);
12026 __isl_null isl_ast_node *isl_ast_node_free(
12027 __isl_take isl_ast_node *node);
12029 AST expressions can be copied and freed using the following functions.
12031 #include <isl/ast.h>
12032 __isl_give isl_ast_expr *isl_ast_expr_copy(
12033 __isl_keep isl_ast_expr *expr);
12034 __isl_null isl_ast_expr *isl_ast_expr_free(
12035 __isl_take isl_ast_expr *expr);
12037 New AST expressions can be created either directly or within
12038 the context of an C<isl_ast_build>.
12040 #include <isl/ast.h>
12041 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12042 __isl_take isl_val *v);
12043 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12044 __isl_take isl_id *id);
12045 __isl_give isl_ast_expr *isl_ast_expr_neg(
12046 __isl_take isl_ast_expr *expr);
12047 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12048 __isl_take isl_ast_expr *expr);
12049 __isl_give isl_ast_expr *isl_ast_expr_add(
12050 __isl_take isl_ast_expr *expr1,
12051 __isl_take isl_ast_expr *expr2);
12052 __isl_give isl_ast_expr *isl_ast_expr_sub(
12053 __isl_take isl_ast_expr *expr1,
12054 __isl_take isl_ast_expr *expr2);
12055 __isl_give isl_ast_expr *isl_ast_expr_mul(
12056 __isl_take isl_ast_expr *expr1,
12057 __isl_take isl_ast_expr *expr2);
12058 __isl_give isl_ast_expr *isl_ast_expr_div(
12059 __isl_take isl_ast_expr *expr1,
12060 __isl_take isl_ast_expr *expr2);
12061 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12062 __isl_take isl_ast_expr *expr1,
12063 __isl_take isl_ast_expr *expr2);
12064 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12065 __isl_take isl_ast_expr *expr1,
12066 __isl_take isl_ast_expr *expr2);
12067 __isl_give isl_ast_expr *isl_ast_expr_and(
12068 __isl_take isl_ast_expr *expr1,
12069 __isl_take isl_ast_expr *expr2)
12070 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12071 __isl_take isl_ast_expr *expr1,
12072 __isl_take isl_ast_expr *expr2)
12073 __isl_give isl_ast_expr *isl_ast_expr_or(
12074 __isl_take isl_ast_expr *expr1,
12075 __isl_take isl_ast_expr *expr2)
12076 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12077 __isl_take isl_ast_expr *expr1,
12078 __isl_take isl_ast_expr *expr2)
12079 __isl_give isl_ast_expr *isl_ast_expr_eq(
12080 __isl_take isl_ast_expr *expr1,
12081 __isl_take isl_ast_expr *expr2);
12082 __isl_give isl_ast_expr *isl_ast_expr_le(
12083 __isl_take isl_ast_expr *expr1,
12084 __isl_take isl_ast_expr *expr2);
12085 __isl_give isl_ast_expr *isl_ast_expr_lt(
12086 __isl_take isl_ast_expr *expr1,
12087 __isl_take isl_ast_expr *expr2);
12088 __isl_give isl_ast_expr *isl_ast_expr_ge(
12089 __isl_take isl_ast_expr *expr1,
12090 __isl_take isl_ast_expr *expr2);
12091 __isl_give isl_ast_expr *isl_ast_expr_gt(
12092 __isl_take isl_ast_expr *expr1,
12093 __isl_take isl_ast_expr *expr2);
12094 __isl_give isl_ast_expr *isl_ast_expr_access(
12095 __isl_take isl_ast_expr *array,
12096 __isl_take isl_ast_expr_list *indices);
12097 __isl_give isl_ast_expr *isl_ast_expr_call(
12098 __isl_take isl_ast_expr *function,
12099 __isl_take isl_ast_expr_list *arguments);
12101 The function C<isl_ast_expr_address_of> can be applied to an
12102 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12103 to represent the address of the C<isl_ast_expr_access>.
12104 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12105 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12107 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12108 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12110 #include <isl/ast_build.h>
12111 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12112 __isl_keep isl_ast_build *build,
12113 __isl_take isl_set *set);
12114 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12115 __isl_keep isl_ast_build *build,
12116 __isl_take isl_pw_aff *pa);
12117 __isl_give isl_ast_expr *
12118 isl_ast_build_access_from_pw_multi_aff(
12119 __isl_keep isl_ast_build *build,
12120 __isl_take isl_pw_multi_aff *pma);
12121 __isl_give isl_ast_expr *
12122 isl_ast_build_access_from_multi_pw_aff(
12123 __isl_keep isl_ast_build *build,
12124 __isl_take isl_multi_pw_aff *mpa);
12125 __isl_give isl_ast_expr *
12126 isl_ast_build_call_from_pw_multi_aff(
12127 __isl_keep isl_ast_build *build,
12128 __isl_take isl_pw_multi_aff *pma);
12129 __isl_give isl_ast_expr *
12130 isl_ast_build_call_from_multi_pw_aff(
12131 __isl_keep isl_ast_build *build,
12132 __isl_take isl_multi_pw_aff *mpa);
12135 the domains of C<pa>, C<mpa> and C<pma> should correspond
12136 to the schedule space of C<build>.
12137 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12138 the function being called.
12139 If the accessed space is a nested relation, then it is taken
12140 to represent an access of the member specified by the range
12141 of this nested relation of the structure specified by the domain
12142 of the nested relation.
12144 The following functions can be used to modify an C<isl_ast_expr>.
12146 #include <isl/ast.h>
12147 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12148 __isl_take isl_ast_expr *expr, int pos,
12149 __isl_take isl_ast_expr *arg);
12151 Replace the argument of C<expr> at position C<pos> by C<arg>.
12153 #include <isl/ast.h>
12154 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12155 __isl_take isl_ast_expr *expr,
12156 __isl_take isl_id_to_ast_expr *id2expr);
12158 The function C<isl_ast_expr_substitute_ids> replaces the
12159 subexpressions of C<expr> of type C<isl_ast_expr_id>
12160 by the corresponding expression in C<id2expr>, if there is any.
12163 The following function can be used to modify the descendants
12164 of a specific node in an AST using a depth-first post-order
12165 traversal of those descendants (including the node itself).
12167 #include <isl/ast.h>
12168 __isl_give isl_ast_node *
12169 isl_ast_node_map_descendant_bottom_up(
12170 __isl_take isl_ast_node *node,
12171 __isl_give isl_ast_node *(*fn)(
12172 __isl_take isl_ast_node *node,
12173 void *user), void *user);
12175 User specified data can be attached to an C<isl_ast_node> and obtained
12176 from the same C<isl_ast_node> using the following functions.
12178 #include <isl/ast.h>
12179 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12180 __isl_take isl_ast_node *node,
12181 __isl_take isl_id *annotation);
12182 __isl_give isl_id *isl_ast_node_get_annotation(
12183 __isl_keep isl_ast_node *node);
12185 Basic printing can be performed using the following functions.
12187 #include <isl/ast.h>
12188 __isl_give isl_printer *isl_printer_print_ast_expr(
12189 __isl_take isl_printer *p,
12190 __isl_keep isl_ast_expr *expr);
12191 __isl_give isl_printer *isl_printer_print_ast_node(
12192 __isl_take isl_printer *p,
12193 __isl_keep isl_ast_node *node);
12194 __isl_give char *isl_ast_expr_to_str(
12195 __isl_keep isl_ast_expr *expr);
12196 __isl_give char *isl_ast_node_to_str(
12197 __isl_keep isl_ast_node *node);
12198 __isl_give char *isl_ast_expr_to_C_str(
12199 __isl_keep isl_ast_expr *expr);
12200 __isl_give char *isl_ast_node_to_C_str(
12201 __isl_keep isl_ast_node *node);
12203 The functions C<isl_ast_expr_to_C_str> and
12204 C<isl_ast_node_to_C_str> are convenience functions
12205 that return a string representation of the input in C format.
12207 More advanced printing can be performed using the following functions.
12209 #include <isl/ast.h>
12210 __isl_give isl_printer *
12211 isl_ast_expr_op_type_set_print_name(
12212 __isl_take isl_printer *p,
12213 enum isl_ast_expr_op_type type,
12214 __isl_keep const char *name);
12215 __isl_give isl_printer *isl_ast_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_stat isl_options_set_ast_print_macro_once(
12220 isl_ctx *ctx, int val);
12221 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12222 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12223 enum isl_ast_expr_op_type type,
12224 __isl_take isl_printer *p);
12225 __isl_give isl_printer *isl_ast_op_type_print_macro(
12226 enum isl_ast_expr_op_type type,
12227 __isl_take isl_printer *p);
12228 __isl_give isl_printer *isl_ast_expr_print_macros(
12229 __isl_keep isl_ast_expr *expr,
12230 __isl_take isl_printer *p);
12231 __isl_give isl_printer *isl_ast_node_print_macros(
12232 __isl_keep isl_ast_node *node,
12233 __isl_take isl_printer *p);
12234 __isl_give isl_printer *isl_ast_node_print(
12235 __isl_keep isl_ast_node *node,
12236 __isl_take isl_printer *p,
12237 __isl_take isl_ast_print_options *options);
12238 __isl_give isl_printer *isl_ast_node_for_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_if_print(
12243 __isl_keep isl_ast_node *node,
12244 __isl_take isl_printer *p,
12245 __isl_take isl_ast_print_options *options);
12247 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12248 C<isl> may print out an AST that makes use of macros such
12249 as C<floord>, C<min> and C<max>.
12250 The names of these macros may be modified by a call
12251 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12252 names are associated to the printer object.
12253 C<isl_ast_op_type_set_print_name> is an alternative name for
12254 C<isl_ast_expr_op_type_set_print_name>.
12255 C<isl_ast_expr_op_type_print_macro> prints out the macro
12256 corresponding to a specific C<isl_ast_expr_op_type>.
12257 If the print-macro-once option is set, then a given macro definition
12258 is only printed once to any given printer object.
12259 C<isl_ast_op_type_print_macro> is an alternative name for
12260 C<isl_ast_expr_op_type_print_macro>.
12261 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12262 for subexpressions where these macros would be used and prints
12263 out the required macro definitions.
12264 Essentially, C<isl_ast_expr_print_macros> calls
12265 C<isl_ast_expr_foreach_ast_expr_op_type> with
12266 C<isl_ast_expr_op_type_print_macro>
12267 as function argument.
12268 C<isl_ast_node_print_macros> does the same
12269 for expressions in its C<isl_ast_node> argument.
12270 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12271 C<isl_ast_node_if_print> print an C<isl_ast_node>
12272 in C<ISL_FORMAT_C>, but allow for some extra control
12273 through an C<isl_ast_print_options> object.
12274 This object can be created using the following functions.
12276 #include <isl/ast.h>
12277 __isl_give isl_ast_print_options *
12278 isl_ast_print_options_alloc(isl_ctx *ctx);
12279 __isl_give isl_ast_print_options *
12280 isl_ast_print_options_copy(
12281 __isl_keep isl_ast_print_options *options);
12282 __isl_null isl_ast_print_options *
12283 isl_ast_print_options_free(
12284 __isl_take isl_ast_print_options *options);
12286 __isl_give isl_ast_print_options *
12287 isl_ast_print_options_set_print_user(
12288 __isl_take isl_ast_print_options *options,
12289 __isl_give isl_printer *(*print_user)(
12290 __isl_take isl_printer *p,
12291 __isl_take isl_ast_print_options *options,
12292 __isl_keep isl_ast_node *node, void *user),
12294 __isl_give isl_ast_print_options *
12295 isl_ast_print_options_set_print_for(
12296 __isl_take isl_ast_print_options *options,
12297 __isl_give isl_printer *(*print_for)(
12298 __isl_take isl_printer *p,
12299 __isl_take isl_ast_print_options *options,
12300 __isl_keep isl_ast_node *node, void *user),
12303 The callback set by C<isl_ast_print_options_set_print_user>
12304 is called whenever a node of type C<isl_ast_node_user> needs to
12306 The callback set by C<isl_ast_print_options_set_print_for>
12307 is called whenever a node of type C<isl_ast_node_for> needs to
12309 Note that C<isl_ast_node_for_print> will I<not> call the
12310 callback set by C<isl_ast_print_options_set_print_for> on the node
12311 on which C<isl_ast_node_for_print> is called, but only on nested
12312 nodes of type C<isl_ast_node_for>. It is therefore safe to
12313 call C<isl_ast_node_for_print> from within the callback set by
12314 C<isl_ast_print_options_set_print_for>.
12316 The following option determines the type to be used for iterators
12317 while printing the AST.
12319 isl_stat isl_options_set_ast_iterator_type(
12320 isl_ctx *ctx, const char *val);
12321 const char *isl_options_get_ast_iterator_type(
12324 The AST printer only prints body nodes of C<if> and C<for> nodes
12326 blocks cannot be safely omitted.
12327 For example, a C<for> node with one body node will not be
12328 surrounded with braces in C<ISL_FORMAT_C>.
12329 A block will always be printed by setting the following option.
12331 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12333 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12335 Explicit block nodes that appear inside the AST are always printed as blocks.
12336 If the block node appears as the outermost node,
12337 then it is only printed if the following option is set.
12339 isl_stat isl_options_set_ast_print_outermost_block(
12340 isl_ctx *ctx, int val);
12341 int isl_options_get_ast_print_outermost_block(
12346 #include <isl/ast_build.h>
12347 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12348 isl_ctx *ctx, int val);
12349 int isl_options_get_ast_build_atomic_upper_bound(
12351 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12353 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12354 isl_stat isl_options_set_ast_build_detect_min_max(
12355 isl_ctx *ctx, int val);
12356 int isl_options_get_ast_build_detect_min_max(
12358 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12359 isl_ctx *ctx, int val);
12360 int isl_options_get_ast_build_exploit_nested_bounds(
12362 isl_stat isl_options_set_ast_build_group_coscheduled(
12363 isl_ctx *ctx, int val);
12364 int isl_options_get_ast_build_group_coscheduled(
12366 isl_stat isl_options_set_ast_build_separation_bounds(
12367 isl_ctx *ctx, int val);
12368 int isl_options_get_ast_build_separation_bounds(
12370 isl_stat isl_options_set_ast_build_scale_strides(
12371 isl_ctx *ctx, int val);
12372 int isl_options_get_ast_build_scale_strides(
12374 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12376 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12377 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12379 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12383 =item * ast_build_atomic_upper_bound
12385 Generate loop upper bounds that consist of the current loop iterator,
12386 an operator and an expression not involving the iterator.
12387 If this option is not set, then the current loop iterator may appear
12388 several times in the upper bound.
12389 For example, when this option is turned off, AST generation
12392 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12396 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12399 When the option is turned on, the following AST is generated
12401 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12404 =item * ast_build_prefer_pdiv
12406 If this option is turned off, then the AST generation will
12407 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12408 operators, but no C<isl_ast_expr_op_pdiv_q> or
12409 C<isl_ast_expr_op_pdiv_r> operators.
12410 If this option is turned on, then C<isl> will try to convert
12411 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12412 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12414 =item * ast_build_detect_min_max
12416 If this option is turned on, then C<isl> will try and detect
12417 min or max-expressions when building AST expressions from
12418 piecewise affine expressions.
12420 =item * ast_build_exploit_nested_bounds
12422 Simplify conditions based on bounds of nested for loops.
12423 In particular, remove conditions that are implied by the fact
12424 that one or more nested loops have at least one iteration,
12425 meaning that the upper bound is at least as large as the lower bound.
12426 For example, when this option is turned off, AST generation
12429 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12435 for (int c0 = 0; c0 <= N; c0 += 1)
12436 for (int c1 = 0; c1 <= M; c1 += 1)
12439 When the option is turned on, the following AST is generated
12441 for (int c0 = 0; c0 <= N; c0 += 1)
12442 for (int c1 = 0; c1 <= M; c1 += 1)
12445 =item * ast_build_group_coscheduled
12447 If two domain elements are assigned the same schedule point, then
12448 they may be executed in any order and they may even appear in different
12449 loops. If this options is set, then the AST generator will make
12450 sure that coscheduled domain elements do not appear in separate parts
12451 of the AST. This is useful in case of nested AST generation
12452 if the outer AST generation is given only part of a schedule
12453 and the inner AST generation should handle the domains that are
12454 coscheduled by this initial part of the schedule together.
12455 For example if an AST is generated for a schedule
12457 { A[i] -> [0]; B[i] -> [0] }
12459 then the C<isl_ast_build_set_create_leaf> callback described
12460 below may get called twice, once for each domain.
12461 Setting this option ensures that the callback is only called once
12462 on both domains together.
12464 =item * ast_build_separation_bounds
12466 This option specifies which bounds to use during separation.
12467 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12468 then all (possibly implicit) bounds on the current dimension will
12469 be used during separation.
12470 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12471 then only those bounds that are explicitly available will
12472 be used during separation.
12474 =item * ast_build_scale_strides
12476 This option specifies whether the AST generator is allowed
12477 to scale down iterators of strided loops.
12479 =item * ast_build_allow_else
12481 This option specifies whether the AST generator is allowed
12482 to construct if statements with else branches.
12484 =item * ast_build_allow_or
12486 This option specifies whether the AST generator is allowed
12487 to construct if conditions with disjunctions.
12491 =head3 AST Generation Options (Schedule Tree)
12493 In case of AST construction from a schedule tree, the options
12494 that control how an AST is created from the individual schedule
12495 dimensions are stored in the band nodes of the tree
12496 (see L</"Schedule Trees">).
12498 In particular, a schedule dimension can be handled in four
12499 different ways, atomic, separate, unroll or the default.
12500 This loop AST generation type can be set using
12501 C<isl_schedule_node_band_member_set_ast_loop_type>.
12503 the first three can be selected by including a one-dimensional
12504 element with as value the position of the schedule dimension
12505 within the band and as name one of C<atomic>, C<separate>
12506 or C<unroll> in the options
12507 set by C<isl_schedule_node_band_set_ast_build_options>.
12508 Only one of these three may be specified for
12509 any given schedule dimension within a band node.
12510 If none of these is specified, then the default
12511 is used. The meaning of the options is as follows.
12517 When this option is specified, the AST generator will make
12518 sure that a given domain space only appears in a single
12519 loop at the specified level.
12521 For example, for the schedule tree
12523 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12525 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12526 options: "{ atomic[x] }"
12528 the following AST will be generated
12530 for (int c0 = 0; c0 <= 10; c0 += 1) {
12537 On the other hand, for the schedule tree
12539 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12541 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12542 options: "{ separate[x] }"
12544 the following AST will be generated
12548 for (int c0 = 1; c0 <= 9; c0 += 1) {
12555 If neither C<atomic> nor C<separate> is specified, then the AST generator
12556 may produce either of these two results or some intermediate form.
12560 When this option is specified, the AST generator will
12561 split the domain of the specified schedule dimension
12562 into pieces with a fixed set of statements for which
12563 instances need to be executed by the iterations in
12564 the schedule domain part. This option tends to avoid
12565 the generation of guards inside the corresponding loops.
12566 See also the C<atomic> option.
12570 When this option is specified, the AST generator will
12571 I<completely> unroll the corresponding schedule dimension.
12572 It is the responsibility of the user to ensure that such
12573 unrolling is possible.
12574 To obtain a partial unrolling, the user should apply an additional
12575 strip-mining to the schedule and fully unroll the inner schedule
12580 The C<isolate> option is a bit more involved. It allows the user
12581 to isolate a range of schedule dimension values from smaller and
12582 greater values. Additionally, the user may specify a different
12583 atomic/separate/unroll choice for the isolated part and the remaining
12584 parts. The typical use case of the C<isolate> option is to isolate
12585 full tiles from partial tiles.
12586 The part that needs to be isolated may depend on outer schedule dimensions.
12587 The option therefore needs to be able to reference those outer schedule
12588 dimensions. In particular, the space of the C<isolate> option is that
12589 of a wrapped map with as domain the flat product of all outer band nodes
12590 and as range the space of the current band node.
12591 The atomic/separate/unroll choice for the isolated part is determined
12592 by an option that lives in an unnamed wrapped space with as domain
12593 a zero-dimensional C<isolate> space and as range the regular
12594 C<atomic>, C<separate> or C<unroll> space.
12595 This option may also be set directly using
12596 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12597 The atomic/separate/unroll choice for the remaining part is determined
12598 by the regular C<atomic>, C<separate> or C<unroll> option.
12599 Since the C<isolate> option references outer schedule dimensions,
12600 its use in a band node causes any tree containing the node
12601 to be considered anchored.
12603 As an example, consider the isolation of full tiles from partial tiles
12604 in a tiling of a triangular domain. The original schedule is as follows.
12606 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12608 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12609 { A[i,j] -> [floor(j/10)] }, \
12610 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12614 for (int c0 = 0; c0 <= 10; c0 += 1)
12615 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12616 for (int c2 = 10 * c0;
12617 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12618 for (int c3 = 10 * c1;
12619 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12622 Isolating the full tiles, we have the following input
12624 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12626 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12627 { A[i,j] -> [floor(j/10)] }, \
12628 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12629 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12630 10a+9+10b+9 <= 100 }"
12635 for (int c0 = 0; c0 <= 8; c0 += 1) {
12636 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12637 for (int c2 = 10 * c0;
12638 c2 <= 10 * c0 + 9; c2 += 1)
12639 for (int c3 = 10 * c1;
12640 c3 <= 10 * c1 + 9; c3 += 1)
12642 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12643 for (int c2 = 10 * c0;
12644 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12645 for (int c3 = 10 * c1;
12646 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12649 for (int c0 = 9; c0 <= 10; c0 += 1)
12650 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12651 for (int c2 = 10 * c0;
12652 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12653 for (int c3 = 10 * c1;
12654 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12658 We may then additionally unroll the innermost loop of the isolated part
12660 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12662 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12663 { A[i,j] -> [floor(j/10)] }, \
12664 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12665 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12666 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12671 for (int c0 = 0; c0 <= 8; c0 += 1) {
12672 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12673 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12675 A(c2, 10 * c1 + 1);
12676 A(c2, 10 * c1 + 2);
12677 A(c2, 10 * c1 + 3);
12678 A(c2, 10 * c1 + 4);
12679 A(c2, 10 * c1 + 5);
12680 A(c2, 10 * c1 + 6);
12681 A(c2, 10 * c1 + 7);
12682 A(c2, 10 * c1 + 8);
12683 A(c2, 10 * c1 + 9);
12685 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12686 for (int c2 = 10 * c0;
12687 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12688 for (int c3 = 10 * c1;
12689 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12692 for (int c0 = 9; c0 <= 10; c0 += 1)
12693 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12694 for (int c2 = 10 * c0;
12695 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12696 for (int c3 = 10 * c1;
12697 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12702 =head3 AST Generation Options (Schedule Map)
12704 In case of AST construction using
12705 C<isl_ast_build_node_from_schedule_map>, the options
12706 that control how an AST is created from the individual schedule
12707 dimensions are stored in the C<isl_ast_build>.
12708 They can be set using the following function.
12710 #include <isl/ast_build.h>
12711 __isl_give isl_ast_build *
12712 isl_ast_build_set_options(
12713 __isl_take isl_ast_build *build,
12714 __isl_take isl_union_map *options);
12716 The options are encoded in an C<isl_union_map>.
12717 The domain of this union relation refers to the schedule domain,
12718 i.e., the range of the schedule passed
12719 to C<isl_ast_build_node_from_schedule_map>.
12720 In the case of nested AST generation (see L</"Nested AST Generation">),
12721 the domain of C<options> should refer to the extra piece of the schedule.
12722 That is, it should be equal to the range of the wrapped relation in the
12723 range of the schedule.
12724 The range of the options can consist of elements in one or more spaces,
12725 the names of which determine the effect of the option.
12726 The values of the range typically also refer to the schedule dimension
12727 to which the option applies, with value C<0> representing
12728 the outermost schedule dimension. In case of nested AST generation
12729 (see L</"Nested AST Generation">), these values refer to the position
12730 of the schedule dimension within the innermost AST generation.
12731 The constraints on the domain elements of
12732 the option should only refer to this dimension and earlier dimensions.
12733 We consider the following spaces.
12737 =item C<separation_class>
12739 B<This option has been deprecated. Use the isolate option on
12740 schedule trees instead.>
12742 This space is a wrapped relation between two one dimensional spaces.
12743 The input space represents the schedule dimension to which the option
12744 applies and the output space represents the separation class.
12745 While constructing a loop corresponding to the specified schedule
12746 dimension(s), the AST generator will try to generate separate loops
12747 for domain elements that are assigned different classes.
12748 If only some of the elements are assigned a class, then those elements
12749 that are not assigned any class will be treated as belonging to a class
12750 that is separate from the explicitly assigned classes.
12751 The typical use case for this option is to separate full tiles from
12753 The other options, described below, are applied after the separation
12756 As an example, consider the separation into full and partial tiles
12757 of a tiling of a triangular domain.
12758 Take, for example, the domain
12760 { A[i,j] : 0 <= i,j and i + j <= 100 }
12762 and a tiling into tiles of 10 by 10. The input to the AST generator
12763 is then the schedule
12765 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12768 Without any options, the following AST is generated
12770 for (int c0 = 0; c0 <= 10; c0 += 1)
12771 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12772 for (int c2 = 10 * c0;
12773 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12775 for (int c3 = 10 * c1;
12776 c3 <= min(10 * c1 + 9, -c2 + 100);
12780 Separation into full and partial tiles can be obtained by assigning
12781 a class, say C<0>, to the full tiles. The full tiles are represented by those
12782 values of the first and second schedule dimensions for which there are
12783 values of the third and fourth dimensions to cover an entire tile.
12784 That is, we need to specify the following option
12786 { [a,b,c,d] -> separation_class[[0]->[0]] :
12787 exists b': 0 <= 10a,10b' and
12788 10a+9+10b'+9 <= 100;
12789 [a,b,c,d] -> separation_class[[1]->[0]] :
12790 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12792 which simplifies to
12794 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12795 a >= 0 and b >= 0 and b <= 8 - a;
12796 [a, b, c, d] -> separation_class[[0] -> [0]] :
12797 a >= 0 and a <= 8 }
12799 With this option, the generated AST is as follows
12802 for (int c0 = 0; c0 <= 8; c0 += 1) {
12803 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12804 for (int c2 = 10 * c0;
12805 c2 <= 10 * c0 + 9; c2 += 1)
12806 for (int c3 = 10 * c1;
12807 c3 <= 10 * c1 + 9; c3 += 1)
12809 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12810 for (int c2 = 10 * c0;
12811 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12813 for (int c3 = 10 * c1;
12814 c3 <= min(-c2 + 100, 10 * c1 + 9);
12818 for (int c0 = 9; c0 <= 10; c0 += 1)
12819 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12820 for (int c2 = 10 * c0;
12821 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12823 for (int c3 = 10 * c1;
12824 c3 <= min(10 * c1 + 9, -c2 + 100);
12831 This is a single-dimensional space representing the schedule dimension(s)
12832 to which ``separation'' should be applied. Separation tries to split
12833 a loop into several pieces if this can avoid the generation of guards
12835 See also the C<atomic> option.
12839 This is a single-dimensional space representing the schedule dimension(s)
12840 for which the domains should be considered ``atomic''. That is, the
12841 AST generator will make sure that any given domain space will only appear
12842 in a single loop at the specified level.
12844 Consider the following schedule
12846 { a[i] -> [i] : 0 <= i < 10;
12847 b[i] -> [i+1] : 0 <= i < 10 }
12849 If the following option is specified
12851 { [i] -> separate[x] }
12853 then the following AST will be generated
12857 for (int c0 = 1; c0 <= 9; c0 += 1) {
12864 If, on the other hand, the following option is specified
12866 { [i] -> atomic[x] }
12868 then the following AST will be generated
12870 for (int c0 = 0; c0 <= 10; c0 += 1) {
12877 If neither C<atomic> nor C<separate> is specified, then the AST generator
12878 may produce either of these two results or some intermediate form.
12882 This is a single-dimensional space representing the schedule dimension(s)
12883 that should be I<completely> unrolled.
12884 To obtain a partial unrolling, the user should apply an additional
12885 strip-mining to the schedule and fully unroll the inner loop.
12889 =head3 Fine-grained Control over AST Generation
12891 Besides specifying the constraints on the parameters,
12892 an C<isl_ast_build> object can be used to control
12893 various aspects of the AST generation process.
12894 In case of AST construction using
12895 C<isl_ast_build_node_from_schedule_map>,
12896 the most prominent way of control is through ``options'',
12897 as explained above.
12899 Additional control is available through the following functions.
12901 #include <isl/ast_build.h>
12902 __isl_give isl_ast_build *
12903 isl_ast_build_set_iterators(
12904 __isl_take isl_ast_build *build,
12905 __isl_take isl_id_list *iterators);
12907 The function C<isl_ast_build_set_iterators> allows the user to
12908 specify a list of iterator C<isl_id>s to be used as iterators.
12909 If the input schedule is injective, then
12910 the number of elements in this list should be as large as the dimension
12911 of the schedule space, but no direct correspondence should be assumed
12912 between dimensions and elements.
12913 If the input schedule is not injective, then an additional number
12914 of C<isl_id>s equal to the largest dimension of the input domains
12916 If the number of provided C<isl_id>s is insufficient, then additional
12917 names are automatically generated.
12919 #include <isl/ast_build.h>
12920 __isl_give isl_ast_build *
12921 isl_ast_build_set_create_leaf(
12922 __isl_take isl_ast_build *build,
12923 __isl_give isl_ast_node *(*fn)(
12924 __isl_take isl_ast_build *build,
12925 void *user), void *user);
12928 C<isl_ast_build_set_create_leaf> function allows for the
12929 specification of a callback that should be called whenever the AST
12930 generator arrives at an element of the schedule domain.
12931 The callback should return an AST node that should be inserted
12932 at the corresponding position of the AST. The default action (when
12933 the callback is not set) is to continue generating parts of the AST to scan
12934 all the domain elements associated to the schedule domain element
12935 and to insert user nodes, ``calling'' the domain element, for each of them.
12936 The C<build> argument contains the current state of the C<isl_ast_build>.
12937 To ease nested AST generation (see L</"Nested AST Generation">),
12938 all control information that is
12939 specific to the current AST generation such as the options and
12940 the callbacks has been removed from this C<isl_ast_build>.
12941 The callback would typically return the result of a nested
12942 AST generation or a
12943 user defined node created using the following function.
12945 #include <isl/ast.h>
12946 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12947 __isl_take isl_ast_expr *expr);
12948 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12949 __isl_take isl_ast_expr *expr);
12951 C<isl_ast_node_alloc_user> is an alternative name for
12952 C<isl_ast_node_user_from_expr>.
12954 In some cases, a single user defined node is not enough,
12955 in which case the following function can be used
12956 to create a block node from multiple AST nodes.
12958 #include <isl/ast.h>
12959 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12960 __isl_take isl_ast_node_list *list);
12962 #include <isl/ast_build.h>
12963 __isl_give isl_ast_build *
12964 isl_ast_build_set_at_each_domain(
12965 __isl_take isl_ast_build *build,
12966 __isl_give isl_ast_node *(*fn)(
12967 __isl_take isl_ast_node *node,
12968 __isl_keep isl_ast_build *build,
12969 void *user), void *user);
12970 __isl_give isl_ast_build *
12971 isl_ast_build_set_before_each_for(
12972 __isl_take isl_ast_build *build,
12973 __isl_give isl_id *(*fn)(
12974 __isl_keep isl_ast_build *build,
12975 void *user), void *user);
12976 __isl_give isl_ast_build *
12977 isl_ast_build_set_after_each_for(
12978 __isl_take isl_ast_build *build,
12979 __isl_give isl_ast_node *(*fn)(
12980 __isl_take isl_ast_node *node,
12981 __isl_keep isl_ast_build *build,
12982 void *user), void *user);
12983 __isl_give isl_ast_build *
12984 isl_ast_build_set_before_each_mark(
12985 __isl_take isl_ast_build *build,
12986 isl_stat (*fn)(__isl_keep isl_id *mark,
12987 __isl_keep isl_ast_build *build,
12988 void *user), void *user);
12989 __isl_give isl_ast_build *
12990 isl_ast_build_set_after_each_mark(
12991 __isl_take isl_ast_build *build,
12992 __isl_give isl_ast_node *(*fn)(
12993 __isl_take isl_ast_node *node,
12994 __isl_keep isl_ast_build *build,
12995 void *user), void *user);
12997 The callback set by C<isl_ast_build_set_at_each_domain> will
12998 be called for each domain AST node.
12999 The callbacks set by C<isl_ast_build_set_before_each_for>
13000 and C<isl_ast_build_set_after_each_for> will be called
13001 for each for AST node. The first will be called in depth-first
13002 pre-order, while the second will be called in depth-first post-order.
13003 Since C<isl_ast_build_set_before_each_for> is called before the for
13004 node is actually constructed, it is only passed an C<isl_ast_build>.
13005 The returned C<isl_id> will be added as an annotation (using
13006 C<isl_ast_node_set_annotation>) to the constructed for node.
13007 In particular, if the user has also specified an C<after_each_for>
13008 callback, then the annotation can be retrieved from the node passed to
13009 that callback using C<isl_ast_node_get_annotation>.
13010 The callbacks set by C<isl_ast_build_set_before_each_mark>
13011 and C<isl_ast_build_set_after_each_mark> will be called for each
13012 mark AST node that is created, i.e., for each mark schedule node
13013 in the input schedule tree. The first will be called in depth-first
13014 pre-order, while the second will be called in depth-first post-order.
13015 Since the callback set by C<isl_ast_build_set_before_each_mark>
13016 is called before the mark AST node is actually constructed, it is passed
13017 the identifier of the mark node.
13018 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
13019 The given C<isl_ast_build> can be used to create new
13020 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
13021 or C<isl_ast_build_call_from_pw_multi_aff>.
13023 =head3 Nested AST Generation
13025 C<isl> allows the user to create an AST within the context
13026 of another AST. These nested ASTs are created using the
13027 same C<isl_ast_build_node_from_schedule_map> function that is used to create
13028 the outer AST. The C<build> argument should be an C<isl_ast_build>
13029 passed to a callback set by
13030 C<isl_ast_build_set_create_leaf>.
13031 The space of the range of the C<schedule> argument should refer
13032 to this build. In particular, the space should be a wrapped
13033 relation and the domain of this wrapped relation should be the
13034 same as that of the range of the schedule returned by
13035 C<isl_ast_build_get_schedule> below.
13036 In practice, the new schedule is typically
13037 created by calling C<isl_union_map_range_product> on the old schedule
13038 and some extra piece of the schedule.
13039 The space of the schedule domain is also available from
13040 the C<isl_ast_build>.
13042 #include <isl/ast_build.h>
13043 __isl_give isl_union_map *isl_ast_build_get_schedule(
13044 __isl_keep isl_ast_build *build);
13045 __isl_give isl_space *isl_ast_build_get_schedule_space(
13046 __isl_keep isl_ast_build *build);
13047 __isl_give isl_ast_build *isl_ast_build_restrict(
13048 __isl_take isl_ast_build *build,
13049 __isl_take isl_set *set);
13051 The C<isl_ast_build_get_schedule> function returns a (partial)
13052 schedule for the domains elements for which part of the AST still needs to
13053 be generated in the current build.
13054 In particular, the domain elements are mapped to those iterations of the loops
13055 enclosing the current point of the AST generation inside which
13056 the domain elements are executed.
13057 No direct correspondence between
13058 the input schedule and this schedule should be assumed.
13059 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13060 to create a set for C<isl_ast_build_restrict> to intersect
13061 with the current build. In particular, the set passed to
13062 C<isl_ast_build_restrict> can have additional parameters.
13063 The ids of the set dimensions in the space returned by
13064 C<isl_ast_build_get_schedule_space> correspond to the
13065 iterators of the already generated loops.
13066 The user should not rely on the ids of the output dimensions
13067 of the relations in the union relation returned by
13068 C<isl_ast_build_get_schedule> having any particular value.
13070 =head1 Applications
13072 Although C<isl> is mainly meant to be used as a library,
13073 it also contains some basic applications that use some
13074 of the functionality of C<isl>.
13075 For applications that take one or more polytopes or polyhedra
13076 as input, this input may be specified in either the L<isl format>
13077 or the L<PolyLib format>.
13079 =head2 C<isl_polyhedron_sample>
13081 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13082 an integer element of the polyhedron, if there is any.
13083 The first column in the output is the denominator and is always
13084 equal to 1. If the polyhedron contains no integer points,
13085 then a vector of length zero is printed.
13089 C<isl_pip> takes the same input as the C<example> program
13090 from the C<piplib> distribution, i.e., a set of constraints
13091 on the parameters, a line containing only -1 and finally a set
13092 of constraints on a parametric polyhedron.
13093 The coefficients of the parameters appear in the last columns
13094 (but before the final constant column).
13095 The output is the lexicographic minimum of the parametric polyhedron.
13096 As C<isl> currently does not have its own output format, the output
13097 is just a dump of the internal state.
13099 =head2 C<isl_polyhedron_minimize>
13101 C<isl_polyhedron_minimize> computes the minimum of some linear
13102 or affine objective function over the integer points in a polyhedron.
13103 If an affine objective function
13104 is given, then the constant should appear in the last column.
13106 =head2 C<isl_polytope_scan>
13108 Given a polytope, C<isl_polytope_scan> prints
13109 all integer points in the polytope.
13113 Given an C<isl_union_access_info> object as input,
13114 C<isl_flow> prints out the corresponding dependences,
13115 as computed by C<isl_union_access_info_compute_flow>.
13117 =head2 C<isl_codegen>
13119 Given either a schedule tree or a sequence consisting of
13120 a schedule map, a context set and an options relation,
13121 C<isl_codegen> prints out an AST that scans the domain elements
13122 of the schedule in the order of their image(s) taking into account
13123 the constraints in the context set.
13125 =head2 C<isl_schedule>
13127 Given an C<isl_schedule_constraints> object as input,
13128 C<isl_schedule> prints out a schedule that satisfies the given